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5.04:_Enthalpy_of_Reaction
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<div class="box-objectives"> <span id="Learning_Objectives"></span><span id="Learning_Objectives"></span><h5 class="box-legend"><span class="lt-icon-default"><span style="display:none;"> </span>Learning Objectives</span></h5> <ul> <li class="lt-chem-21722" style="background-color: unset;">To understand how enthalpy pertains to chemical reactions</li> </ul> </div> <p class="lt-chem-21722" style="background-color: unset;">We have stated that the change in energy (<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="98" style="font-size: 85%; position: relative;"><svg width="3.604ex" height="1.67ex" role="img" focusable="false" viewbox="0 -716 1593 738" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-99-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-99-NCM-N-2062" d=""></path><path id="MJX-99-NCM-I-1D448" d="M642 680C623 680 559 683 540 683C525 683 518 675 518 659C518 650 525 645 539 644C582 644 603 631 603 605C603 599 602 592 600 585L511 232C496 175 467 126 424 84C377 39 325 17 269 17C195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641C292 643 309 644 338 644C364 644 375 644 375 668C375 678 369 683 358 683L231 680L104 683C88 683 81 674 81 659C81 652 84 647 89 646C99 645 107 644 112 644C143 643 161 641 166 640C171 639 173 636 173 631C173 629 172 622 169 611L74 230C69 211 67 192 67 172C67 57 150-22 265-22C330-22 390 3 445 54C498 102 532 158 548 223L636 574C649 625 677 643 739 644C753 645 760 653 760 668L760 672C757 679 752 683 743 683C724 683 661 680 642 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔU" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔU" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-99-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-99-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:U" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D448" href="#MJX-99-NCM-I-1D448"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔU" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔU" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:U" data-semantic-level-number="1" data-speech-node="true">U</mi></math></mjx-assistive-mml></mjx-container>) is equal to the sum of the heat produced and the work performed. Work done by an expanding gas is called <em>pressure-volume work</em>, (or just <em><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="99" style="font-size: 85%; position: relative;"><svg width="3.448ex" height="1.595ex" role="img" focusable="false" viewbox="0 -683 1524 705" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-100-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path><path id="MJX-100-NCM-N-2062" d=""></path><path id="MJX-100-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 564C652 600 674 623 696 632C711 639 730 643 752 644C763 645 768 652 769 667C770 678 764 683 752 683C737 683 686 680 671 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="PV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:PV" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:P" data-semantic-level-number="1" data-speech-node="true"><use data-c="1D443" href="#MJX-100-NCM-I-1D443"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(754,0)"><use data-c="2062" href="#MJX-100-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true" transform="translate(754,0)"><use data-c="1D449" href="#MJX-100-NCM-I-1D449"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="PV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:PV" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:P" data-semantic-level-number="1" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true">V</mi></math></mjx-assistive-mml></mjx-container> work</em><em>)</em>. Consider, for example, a reaction that produces a gas, such as dissolving a piece of copper in concentrated nitric acid. 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data-semantic-structure="(88 (87 (82 (78 (74 (69 1 68 (56 3 4 5)) 6 (73 7 70 (12 9 11) 71 (57 14 15 16) 72 17)) 18 (77 (67 19 66 (58 20 (24 21 23) 25)) 75 (28 26 27) 76 (59 30 31 32))) 33 (81 34 79 (65 36 64 (39 37 38)) 80 (63 40 62 (60 42 43 44))) 45 (85 46 83 (51 48 50) 84 (61 53 54 55))) 0))"><g data-mml-node="mtable" data-latex="{\mathrm{Cu}\mskip2mu (\mathrm{s}) {}+{} 4\,\mathrm{HNO}{\vphantom{A}}_{\smash[t]{3}}\mskip2mu (\mathrm{aq})~\mhchemrightarrow \mathrm{Cu}(\mathrm{NO}{\vphantom{A}}_{\smash[t]{3}}){\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{aq}) {}+{} 2\,\mathrm{H}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}\mskip2mu (\mathrm{l}) {}+{} 2\,\mathrm{NO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-id="88" data-semantic-children="87" data-semantic-attributes="latex: \ce{Cu(s) + 4HNO3(aq) \rightarrow Cu(NO3)2(aq) + 2H_2O(l) + 2NO2(g)} \nonumber " 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transform="translate(889,0)"><use data-c="29" href="#MJX-101-NCM-N-29"></use></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -750 1 1000"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="87" data-semantic-level-number="2" data-speech-node="true"></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" \ce{Cu(s) + 4HNO3(aq) \rightarrow Cu(NO3)2(aq) + 2H_2O(l) + 2NO2(g)} \nonumber " display="block" data-semantic-structure="(88 (87 (82 (78 (74 (69 1 68 (56 3 4 5)) 6 (73 7 70 (12 9 11) 71 (57 14 15 16) 72 17)) 18 (77 (67 19 66 (58 20 (24 21 23) 25)) 75 (28 26 27) 76 (59 30 31 32))) 33 (81 34 79 (65 36 64 (39 37 38)) 80 (63 40 62 (60 42 43 44))) 45 (85 46 83 (51 48 50) 84 (61 53 54 55))) 0))"><mtable displaystyle="true" data-latex="{\mathrm{Cu}\mskip2mu (\mathrm{s}) {}+{} 4\,\mathrm{HNO}{\vphantom{A}}_{\smash[t]{3}}\mskip2mu (\mathrm{aq})~\mhchemrightarrow \mathrm{Cu}(\mathrm{NO}{\vphantom{A}}_{\smash[t]{3}}){\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{aq}) {}+{} 2\,\mathrm{H}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}\mskip2mu (\mathrm{l}) {}+{} 2\,\mathrm{NO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="87" data-semantic-attributes="latex: \ce{Cu(s) + 4HNO3(aq) \rightarrow Cu(NO3)2(aq) + 2H_2O(l) + 2NO2(g)} \nonumber " data-semantic-owns="87" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="82" data-semantic-content="0" data-semantic-parent="88" data-semantic-owns="82 0" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="87" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-mjx-texclass="ORD" data-latex="{\mathrm{Cu}\mskip2mu(\mathrm{s}){}+{}4\,\mathrm{HNO}{\vphantom{A}}_{\smash[t]{3}}\mskip2mu(\mathrm{aq})~\mhchemrightarrow\mathrm{Cu}(\mathrm{NO}{\vphantom{A}}_{\smash[t]{3}}){\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{aq}){}+{}2\,\mathrm{H}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}\mskip2mu(\mathrm{l}){}+{}2\,\mathrm{NO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g})}" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="78,81,85" data-semantic-content="33,45" data-semantic-parent="87" 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data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="60" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{l}"><mi mathvariant="normal" data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="60" data-semantic-attributes="latex:\mathrm{l};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">l</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="60" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="82" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="3" data-speech-node="true">+</mo><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="46,51,61" data-semantic-content="83,84" data-semantic-parent="82" data-semantic-owns="46 83 51 84 61" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="85" data-semantic-attributes="latex:2" data-semantic-level-number="4" data-speech-node="true">2</mn><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="85" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true"></mspace><mrow data-mjx-texclass="ORD" data-latex="\mathrm{NO}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:5" data-semantic-="" data-semantic-children="48,50" data-semantic-parent="85" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="48 50" data-semantic-level-number="4" data-speech-node="true"><mi data-mjx-auto-op="false" data-latex="NO" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:\mathrm{NO};texclass:ORD" data-semantic-level-number="5" data-speech-node="true">NO</mi></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="5" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="85" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="54" data-semantic-content="53,55" data-semantic-parent="85" data-semantic-owns="53 54 55" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="61" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{g}"><mi mathvariant="normal" data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="61" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="5" data-speech-node="true">g</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="61" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">If the reaction is carried out in a closed system that is maintained at constant pressure by a movable piston, the piston will rise as nitrogen dioxide gas is formed (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="101" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2056 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-102-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-102-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 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data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-102-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="34" href="#MJX-102-NCM-N-34"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-102-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-102-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>). The system is performing work by lifting the piston against the downward force exerted by the atmosphere (i.e., <em>atmospheric pressure</em>). We find the amount of <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="102" style="font-size: 85%; position: relative;"><svg width="3.448ex" height="1.595ex" role="img" focusable="false" viewbox="0 -683 1524 705" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-103-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path><path id="MJX-103-NCM-N-2062" d=""></path><path id="MJX-103-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 564C652 600 674 623 696 632C711 639 730 643 752 644C763 645 768 652 769 667C770 678 764 683 752 683C737 683 686 680 671 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="PV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:PV" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:P" data-semantic-level-number="1" data-speech-node="true"><use data-c="1D443" href="#MJX-103-NCM-I-1D443"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(754,0)"><use data-c="2062" href="#MJX-103-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true" transform="translate(754,0)"><use data-c="1D449" href="#MJX-103-NCM-I-1D449"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="PV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:PV" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:P" data-semantic-level-number="1" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true">V</mi></math></mjx-assistive-mml></mjx-container> work done by multiplying the external pressure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="103" style="font-size: 85%; position: relative;"><svg width="1.706ex" height="1.545ex" role="img" focusable="false" viewbox="0 -683 754 683" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-104-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="P" data-semantic-structure="0"><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:P" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D443" href="#MJX-104-NCM-I-1D443"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="P" data-semantic-structure="0"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:P" data-semantic-level-number="0" data-speech-node="true">P</mi></math></mjx-assistive-mml></mjx-container> by the change in volume caused by movement of the piston (<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="104" style="font-size: 85%; position: relative;"><svg width="3.627ex" height="1.67ex" role="img" focusable="false" viewbox="0 -716 1603 738" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-105-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-105-NCM-N-2062" d=""></path><path id="MJX-105-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 564C652 600 674 623 696 632C711 639 730 643 752 644C763 645 768 652 769 667C770 678 764 683 752 683C737 683 686 680 671 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔV" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-105-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-105-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D449" href="#MJX-105-NCM-I-1D449"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔV" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true">V</mi></math></mjx-assistive-mml></mjx-container>). At a constant external pressure (here, atmospheric pressure),</p> <p class="mt-align-center lt-chem-21722" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="105" style="font-size: 85%; min-width: 28.173ex; position: relative;"><svg width="100%" height="2.262ex" role="img" focusable="false" data-mjx-viewbox="0 -750 12452.6 1000" aria-hidden="true" style="vertical-align: -0.566ex; min-width: 28.173ex;"><defs><path id="MJX-106-NCM-I-1D464" d="M590 391C590 382 595 372 606 362C629 340 641 313 641 281C641 264 635 237 623 198C586 78 539 18 482 18C435 18 412 45 412 100C412 119 416 142 423 171C441 243 460 314 477 387C479 394 480 398 480 401C480 421 469 431 447 431C427 431 414 421 407 401L367 245C352 187 341 167 341 115C341 107 341 101 342 98C319 45 290 18 255 18C205 18 180 47 180 104C180 141 197 204 231 293C242 323 248 344 248 357C248 406 212 442 163 442C118 442 84 417 59 367C39 328 29 301 29 287C29 278 34 273 45 273C58 273 60 279 64 293C88 373 120 413 160 413C174 413 181 403 181 384C181 369 175 347 164 317C127 220 108 154 108 117C108 32 165-11 252-11C294-11 328 10 355 53C375 10 416-11 479-11C541-11 590 30 625 112C648 164 691 302 691 369C691 384 690 394 689 399C685 418 666 442 644 442C618 442 590 417 590 391Z"></path><path id="MJX-106-NCM-N-3D" d="M698 367L80 367C64 367 56 359 56 344C56 329 64 321 80 321L698 321C714 321 722 329 722 344C722 356 711 367 698 367M698 179L80 179C64 179 56 171 56 156C56 141 64 133 80 133L698 133C714 133 722 141 722 156C722 169 711 179 698 179Z"></path><path id="MJX-106-NCM-N-2212" d="M698 270L80 270C64 270 56 263 56 250C56 237 64 230 80 230L698 230C714 230 722 237 722 250C722 262 710 270 698 270Z"></path><path id="MJX-106-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path><path id="MJX-106-NCM-N-2062" d=""></path><path id="MJX-106-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-106-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 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d="M78-245C138-199 188-131 229-40C268 47 288 129 288 208L288 292C288 371 268 453 229 540C188 631 138 699 78 745C75 747 72 748 71 748C62 748 57 743 57 734C57 730 59 726 62 723C114 683 156 617 187 526C214 447 228 369 228 292L228 208C228 131 214 53 187-26C156-117 114-183 62-223C59-227 57-231 57-234C57-243 62-248 71-248C72-248 75-247 78-245Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.021719,-0.021719) translate(0, -750)"><g data-mml-node="math" data-latex="w = −PΔV \label{5.4.2} " data-semantic-structure="(18 (17 (15 5 6 (14 7 (13 8 11 9 12 10))) (4 (3 0 1 2))))"><g data-mml-node="mtable" data-latex="w = −PΔV \label{5.4.2}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-id="18" data-semantic-children="17" data-semantic-attributes="latex:w = −PΔV \label{5.4.2} " data-semantic-owns="17" data-semantic-level-number="0" data-speech-node="true" transform="translate(3634,0) translate(-3634,0)"><g transform="translate(0 750) matrix(1 0 0 -1 0 0) scale(46.04)"><svg data-table="true" preserveaspectratio="xMidYMid" viewbox="2592.3 -750 1 1000"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-id="17" data-semantic-children="15" data-semantic-content="4" data-semantic-parent="18" data-semantic-owns="15 4" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mtd"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:3" data-semantic-id="15" data-semantic-children="5,14" data-semantic-content="6" data-semantic-parent="17" data-semantic-owns="5 6 14" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mi" data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:4" data-semantic-id="5" data-semantic-parent="15" data-semantic-attributes="latex:w" data-semantic-level-number="3" data-speech-node="true"><use data-c="1D464" href="#MJX-106-NCM-I-1D464"></use></g><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-id="6" data-semantic-parent="15" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true" transform="translate(993.8,0)"><use data-c="3D" href="#MJX-106-NCM-N-3D"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:4" data-semantic-id="14" data-semantic-children="13" data-semantic-content="7" data-semantic-parent="15" data-semantic-owns="7 13" data-semantic-level-number="3" data-speech-node="true" transform="translate(2049.6,0)"><g data-mml-node="mo" data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:5" data-semantic-id="7" data-semantic-parent="14" data-semantic-attributes="latex:−" data-semantic-operator="prefixop,−" data-semantic-level-number="4" data-speech-node="true"><use data-c="2212" href="#MJX-106-NCM-N-2212"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="13" data-semantic-children="8,9,10" data-semantic-content="11,12" data-semantic-parent="14" data-semantic-owns="8 11 9 12 10" data-semantic-level-number="4" data-speech-node="true" transform="translate(778,0)"><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" 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data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-id="12" data-semantic-parent="13" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true" transform="translate(1587,0)"><use data-c="2062" href="#MJX-106-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="\label{5.4.2}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-id="10" data-semantic-parent="13" data-semantic-attributes="latex:\label{5.4.2}" data-semantic-level-number="5" data-speech-node="true" transform="translate(1587,0)"><use data-c="1D449" href="#MJX-106-NCM-I-1D449"></use></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="2834 -750 1 1000"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:5.4.2" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="17" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-id="3" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mtext" data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true"><use data-c="28" href="#MJX-106-NCM-N-28"></use></g><g data-mml-node="mtext" data-latex="\text{5.4.1}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.4.1}" data-semantic-level-number="4" data-speech-node="true" transform="translate(389,0)"><use data-c="35" href="#MJX-106-NCM-N-35"></use><use data-c="2E" href="#MJX-106-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-106-NCM-N-34" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-106-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-106-NCM-N-31" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2445,0)"><use data-c="29" href="#MJX-106-NCM-N-29"></use></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex="w = −PΔV \label{5.4.2} " display="block" data-semantic-structure="(18 (17 (15 5 6 (14 7 (13 8 11 9 12 10))) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="w = −PΔV \label{5.4.2}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="17" data-semantic-attributes="latex:w = −PΔV \label{5.4.2} " data-semantic-owns="17" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="15" data-semantic-content="4" data-semantic-parent="18" data-semantic-owns="15 4" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="17" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.1}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" 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data-semantic-annotation="clearspeak:simple;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:w" data-semantic-level-number="3" data-speech-node="true">w</mi><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="13" data-semantic-content="7" data-semantic-parent="15" data-semantic-owns="7 13" data-semantic-level-number="3" data-speech-node="true"><mo data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="14" data-semantic-attributes="latex:−" data-semantic-operator="prefixop,−" data-semantic-level-number="4" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="8,9,10" data-semantic-content="11,12" data-semantic-parent="14" data-semantic-owns="8 11 9 12 10" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:P" data-semantic-level-number="5" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:Δ" data-semantic-level-number="5" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi data-latex="\label{5.4.2}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:\label{5.4.2}" data-semantic-level-number="5" data-speech-node="true">V</mi></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">The negative sign associated with <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="106" style="font-size: 85%; position: relative;"><svg width="3.448ex" height="1.595ex" role="img" focusable="false" viewbox="0 -683 1524 705" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-107-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path><path id="MJX-107-NCM-N-2062" d=""></path><path id="MJX-107-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 564C652 600 674 623 696 632C711 639 730 643 752 644C763 645 768 652 769 667C770 678 764 683 752 683C737 683 686 680 671 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="PV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" 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If the volume increases at constant pressure (<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="107" style="font-size: 85%; position: relative;"><svg width="3.627ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1603 1000" aria-hidden="true" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔV > 0" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:1" data-semantic-id="6" data-semantic-children="5,3" data-semantic-content="2" data-semantic-attributes="latex:ΔV > 0" data-semantic-owns="5 2 3" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(6 (5 0 4 1) 2 3)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:2" 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data-semantic-level-number="1" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:Δ" data-semantic-level-number="2" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:V" data-semantic-level-number="2" data-speech-node="true">V</mi></mrow><mo data-latex=">" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:>" data-semantic-operator="relseq,>" data-semantic-level-number="1" data-speech-node="true">></mo><mn data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:0" data-semantic-level-number="1" data-speech-node="true">0</mn></math></mjx-assistive-mml></mjx-container>), the work done by the system is negative, indicating that a system has lost energy by performing work on its surroundings. Conversely, if the volume decreases (<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="108" style="font-size: 85%; position: relative;"><svg width="3.627ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1603 1000" aria-hidden="true" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔV < 0" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:1" data-semantic-id="6" data-semantic-children="5,3" data-semantic-content="2" data-semantic-attributes="latex:ΔV < 0" data-semantic-owns="5 2 3" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(6 (5 0 4 1) 2 3)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:2" 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stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔV < 0" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:1" data-semantic-id="6" data-semantic-children="5,3" data-semantic-content="2" data-semantic-attributes="latex:ΔV < 0" data-semantic-owns="5 2 3" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(6 (5 0 4 1) 2 3)"><g data-mml-node="mo" data-latex="<" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="6" data-semantic-attributes="latex:<" data-semantic-operator="relseq,<" data-semantic-level-number="1" data-speech-node="true"><use data-c="3C" href="#MJX-109-NCM-N-3C"></use></g><g data-mml-node="mn" data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="6" data-semantic-attributes="latex:0" data-semantic-level-number="1" data-speech-node="true" transform="translate(1055.8,0)"><use data-c="30" href="#MJX-109-NCM-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔV < 0" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="5,3" data-semantic-content="2" data-semantic-attributes="latex:ΔV < 0" data-semantic-owns="5 2 3" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(6 (5 0 4 1) 2 3)"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:2" data-semantic-="" data-semantic-children="0,1" data-semantic-content="4" data-semantic-parent="6" data-semantic-owns="0 4 1" data-semantic-level-number="1" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:Δ" data-semantic-level-number="2" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:V" data-semantic-level-number="2" data-speech-node="true">V</mi></mrow><mo data-latex="<" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:<" data-semantic-operator="relseq,<" data-semantic-level-number="1" data-speech-node="true"><</mo><mn data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:0" data-semantic-level-number="1" data-speech-node="true">0</mn></math></mjx-assistive-mml></mjx-container>), the work done by the system is positive, which means that the surroundings have performed work on the system, thereby increasing its energy.</p> <figure><img alt="Diagram showing laboratory apparatus: a flask, plunger, and connected transparent containers with liquids." class="internal" loading="lazy" src="https://chem.libretexts.org/@api/deki/files/129611/imageedit_32_6005530934.jpg?revision=1" width="706" height="304" /> <figcaption>Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="109" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2056 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-110-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 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data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-110-NCM-N-35"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-110-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="34" href="#MJX-110-NCM-N-34"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-110-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-110-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>: An Example of Work Performed by a Reaction Carried Out at Constant Pressure. (a) Initially, the system (a copper penny and concentrated nitric acid) is at atmospheric pressure. (b) When the penny is added to the nitric acid, the volume of NO<sub>2</sub> gas that is formed causes the piston to move upward to maintain the system at atmospheric pressure. In doing so, the system is performing work on its surroundings. (CC BY-NC-SA; anonymous)</figcaption> </figure> <p class="lt-chem-21722" style="background-color: unset;">The internal energy <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="110" style="font-size: 85%; position: relative;"><svg width="1.719ex" height="1.595ex" role="img" focusable="false" viewbox="0 -683 760 705" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-111-NCM-I-1D448" d="M642 680C623 680 559 683 540 683C525 683 518 675 518 659C518 650 525 645 539 644C582 644 603 631 603 605C603 599 602 592 600 585L511 232C496 175 467 126 424 84C377 39 325 17 269 17C195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641C292 643 309 644 338 644C364 644 375 644 375 668C375 678 369 683 358 683L231 680L104 683C88 683 81 674 81 659C81 652 84 647 89 646C99 645 107 644 112 644C143 643 161 641 166 640C171 639 173 636 173 631C173 629 172 622 169 611L74 230C69 211 67 192 67 172C67 57 150-22 265-22C330-22 390 3 445 54C498 102 532 158 548 223L636 574C649 625 677 643 739 644C753 645 760 653 760 668L760 672C757 679 752 683 743 683C724 683 661 680 642 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="U" data-semantic-structure="0"><g data-mml-node="mi" data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:U" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D448" href="#MJX-111-NCM-I-1D448"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="U" data-semantic-structure="0"><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:U" data-semantic-level-number="0" data-speech-node="true">U</mi></math></mjx-assistive-mml></mjx-container> of a system is the sum of the kinetic energy and potential energy of all its components. It is the change in internal energy that produces heat plus work. To measure the energy changes that occur in chemical reactions, chemists usually use a related thermodynamic quantity called <strong>enthalpy </strong>(<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="111" style="font-size: 85%; position: relative;"><svg width="1.993ex" height="1.545ex" role="img" focusable="false" viewbox="0 -683 881 683" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-112-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 39 37 39 15C39 5 45 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 323 39 302 39C262 39 242 43 242 52C242 52 243 55 245 68L312 336L605 336L538 68C535 53 523 43 503 40C498 39 481 39 452 39C433 39 424 31 424 15C424 5 430 0 442 0L568 3L631 2C642 2 683 0 696 0C712 0 720 8 720 24C720 34 709 39 688 39C647 39 627 43 627 52C627 52 628 55 630 68L764 602C769 623 778 636 791 641C797 643 814 644 843 644C869 644 881 644 881 668Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="H" data-semantic-structure="0"><g data-mml-node="mi" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:H" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D43B" href="#MJX-112-NCM-I-1D43B"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="H" data-semantic-structure="0"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:H" data-semantic-level-number="0" data-speech-node="true">H</mi></math></mjx-assistive-mml></mjx-container>) (from the Greek <em>enthalpein</em>, meaning “to warm”). The enthalpy of a system is defined as the sum of its internal energy <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="112" style="font-size: 85%; position: relative;"><svg width="1.719ex" height="1.595ex" role="img" focusable="false" viewbox="0 -683 760 705" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-113-NCM-I-1D448" d="M642 680C623 680 559 683 540 683C525 683 518 675 518 659C518 650 525 645 539 644C582 644 603 631 603 605C603 599 602 592 600 585L511 232C496 175 467 126 424 84C377 39 325 17 269 17C195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641C292 643 309 644 338 644C364 644 375 644 375 668C375 678 369 683 358 683L231 680L104 683C88 683 81 674 81 659C81 652 84 647 89 646C99 645 107 644 112 644C143 643 161 641 166 640C171 639 173 636 173 631C173 629 172 622 169 611L74 230C69 211 67 192 67 172C67 57 150-22 265-22C330-22 390 3 445 54C498 102 532 158 548 223L636 574C649 625 677 643 739 644C753 645 760 653 760 668L760 672C757 679 752 683 743 683C724 683 661 680 642 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="U" data-semantic-structure="0"><g data-mml-node="mi" data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:U" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D448" href="#MJX-113-NCM-I-1D448"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="U" data-semantic-structure="0"><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:U" data-semantic-level-number="0" data-speech-node="true">U</mi></math></mjx-assistive-mml></mjx-container> plus the product of its pressure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="113" style="font-size: 85%; position: relative;"><svg width="1.706ex" height="1.545ex" role="img" focusable="false" viewbox="0 -683 754 683" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-114-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="P" data-semantic-structure="0"><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:P" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D443" href="#MJX-114-NCM-I-1D443"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="P" data-semantic-structure="0"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:P" data-semantic-level-number="0" data-speech-node="true">P</mi></math></mjx-assistive-mml></mjx-container> and volume <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="114" style="font-size: 85%; position: relative;"><svg width="1.742ex" height="1.595ex" role="img" focusable="false" viewbox="0 -683 770 705" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-115-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 564C652 600 674 623 696 632C711 639 730 643 752 644C763 645 768 652 769 667C770 678 764 683 752 683C737 683 686 680 671 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="V" data-semantic-structure="0"><g data-mml-node="mi" data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:V" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D449" href="#MJX-115-NCM-I-1D449"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="V" data-semantic-structure="0"><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:V" data-semantic-level-number="0" data-speech-node="true">V</mi></math></mjx-assistive-mml></mjx-container>:</p> <p class="mt-align-center lt-chem-21722" style="background-color: unset;">\[H =U + <span class="acronym-ignore">PV</span> \label{5.4.3} \]</p> <p class="lt-chem-21722" style="background-color: unset;">Because internal energy, pressure, and volume are all state functions, enthalpy is also a <a title="15.7: State Functions" href="https://chem.libretexts.org/Bookshelves/General_Chemistry/ChemPRIME_(Moore_et_al.)/15%3A_Thermodynamics-_Atoms_Molecules_and_Energy/15.08%3A_State_Functions">state function</a>. So we can define a change in enthalpy (<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="115" style="font-size: 85%; position: relative;"><svg width="3.878ex" height="1.62ex" role="img" focusable="false" viewbox="0 -716 1714 716" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-116-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-116-NCM-N-2062" d=""></path><path id="MJX-116-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 39 37 39 15C39 5 45 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 323 39 302 39C262 39 242 43 242 52C242 52 243 55 245 68L312 336L605 336L538 68C535 53 523 43 503 40C498 39 481 39 452 39C433 39 424 31 424 15C424 5 430 0 442 0L568 3L631 2C642 2 683 0 696 0C712 0 720 8 720 24C720 34 709 39 688 39C647 39 627 43 627 52C627 52 628 55 630 68L764 602C769 623 778 636 791 641C797 643 814 644 843 644C869 644 881 644 881 668Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\Delta H" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:\Delta H" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="\Delta" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:\Delta" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-116-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-116-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D43B" href="#MJX-116-NCM-I-1D43B"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\Delta H" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:\Delta H" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="\Delta" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\Delta" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true">H</mi></math></mjx-assistive-mml></mjx-container>) accordingly</p> <p class="mt-align-center lt-chem-21722" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="116" style="font-size: 85%; min-width: 25.65ex; position: relative;"><svg width="100%" height="2.364ex" role="img" focusable="false" data-mjx-viewbox="0 -772.5 11337.5 1045" aria-hidden="true" style="vertical-align: -0.616ex; min-width: 25.65ex;"><defs><path id="MJX-117-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-117-NCM-N-2062" d=""></path><path id="MJX-117-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 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data-semantic-attributes="latex:a" data-semantic-level-number="7" data-speech-node="true">a</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="13" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:l" data-semantic-level-number="7" data-speech-node="true">l</mi></mrow></mrow></msub><mo data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:−" data-semantic-operator="infixop,−" data-semantic-level-number="4" data-speech-node="true">−</mo><msub 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data-speech-node="true">n</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:i" data-semantic-level-number="6" data-speech-node="true">i</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="t" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:t" data-semantic-level-number="6" data-speech-node="true">t</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:i" data-semantic-level-number="6" data-speech-node="true">i</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:a" data-semantic-level-number="6" data-speech-node="true">a</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:l" data-semantic-level-number="6" data-speech-node="true">l</mi></mrow></msub></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">If a chemical change occurs at constant pressure (i.e., for a given <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="117" style="font-size: 85%; position: relative;"><svg width="1.706ex" height="1.545ex" role="img" focusable="false" viewbox="0 -683 754 683" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-118-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="P" data-semantic-structure="0"><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:P" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D443" href="#MJX-118-NCM-I-1D443"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="P" data-semantic-structure="0"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:P" data-semantic-level-number="0" data-speech-node="true">P</mi></math></mjx-assistive-mml></mjx-container>, <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="118" style="font-size: 85%; position: relative;"><svg width="3.59ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1587 1000" aria-hidden="true" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔP = 0" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-id="6" data-semantic-children="5,3" data-semantic-content="2" data-semantic-attributes="latex:ΔP = 0" data-semantic-owns="5 2 3" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(6 (5 0 4 1) 2 3)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" 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href="#MJX-119-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:P" data-semantic-level-number="2" data-speech-node="true" transform="translate(833,0)"><use data-c="1D443" href="#MJX-119-NCM-I-1D443"></use></g></g></g></g><defs><path id="MJX-119-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-119-NCM-N-2062" d=""></path><path id="MJX-119-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path><path id="MJX-119-NCM-N-3D" d="M698 367L80 367C64 367 56 359 56 344C56 329 64 321 80 321L698 321C714 321 722 329 722 344C722 356 711 367 698 367M698 179L80 179C64 179 56 171 56 156C56 141 64 133 80 133L698 133C714 133 722 141 722 156C722 169 711 179 698 179Z"></path><path id="MJX-119-NCM-N-30" d="M249-22C390-22 460 92 460 320C460 473 428 575 365 625C330 652 291 666 250 666C109 666 39 551 39 320C39 136 88-22 249-22M361 524C368 489 371 425 371 332C371 240 367 172 360 128C347 48 310 8 249 8C226 8 203 17 182 34C155 57 139 104 132 176C129 201 128 253 128 332C128 419 131 480 136 513C145 568 163 603 191 618C213 630 232 636 249 636C314 636 350 583 361 524Z"></path></defs></svg><mjx-break size="4"> </mjx-break><svg width="3.52ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1555.8 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔP = 0" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-id="6" data-semantic-children="5,3" data-semantic-content="2" data-semantic-attributes="latex:ΔP = 0" data-semantic-owns="5 2 3" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(6 (5 0 4 1) 2 3)"><g data-mml-node="mo" data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="6" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="1" data-speech-node="true"><use data-c="3D" href="#MJX-119-NCM-N-3D"></use></g><g data-mml-node="mn" data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="6" data-semantic-attributes="latex:0" data-semantic-level-number="1" data-speech-node="true" transform="translate(1055.8,0)"><use data-c="30" href="#MJX-119-NCM-N-30"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔP = 0" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="5,3" data-semantic-content="2" data-semantic-attributes="latex:ΔP = 0" data-semantic-owns="5 2 3" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(6 (5 0 4 1) 2 3)"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:2" data-semantic-="" data-semantic-children="0,1" data-semantic-content="4" data-semantic-parent="6" data-semantic-owns="0 4 1" data-semantic-level-number="1" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:Δ" data-semantic-level-number="2" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true">⁢</mo><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:P" data-semantic-level-number="2" data-speech-node="true">P</mi></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="1" data-speech-node="true">=</mo><mn data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="6" data-semantic-attributes="latex:0" data-semantic-level-number="1" data-speech-node="true">0</mn></math></mjx-assistive-mml></mjx-container>), the change in enthalpy (<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="119" style="font-size: 85%; position: relative;"><svg width="3.878ex" height="1.62ex" role="img" focusable="false" viewbox="0 -716 1714 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display="block"><math data-latex=" \begin{align} ΔH &= Δ(U + PV) \\[4pt] &= ΔU + ΔPV \\[4pt] &= ΔU + PΔV \label{5.4.4} \end{align} " display="block" data-semantic-structure="(77 (28 (9 (8 5 7 6)) (27 (26 23 11 (25 12 24 (22 13 (21 14 15 (20 16 19 17)) 18)))) (4 (3 0 1 2))) (52 34 (51 (50 43 36 (49 (45 37 44 38) 39 (48 40 46 41 47 42)))) (33 (32 29 30 31))) (76 58 (75 (74 67 60 (73 (69 61 68 62) 63 (72 64 70 65 71 66)))) (57 (56 53 54 55))))"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="0.7em 0.7em 0.30000000000000004em" data-break-align="bottom top" data-latex="\begin{align} ΔH &= Δ(U + PV) \\[4pt] &= ΔU + ΔPV \\[4pt] &= ΔU + PΔV \label{5.4.4} \end{align}" data-semantic-type="table" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="28,52,76" data-semantic-attributes="latex: \begin{align} ΔH &= Δ(U + PV) \\[4pt] &= ΔU + ΔPV \\[4pt] &= ΔU + PΔV \label{5.4.4} \end{align} " 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data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.2}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.4.2}" data-semantic-level-number="4" data-speech-node="true">5.4.2</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" 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data-semantic-parent="8" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="4" data-speech-node="true">H</mi></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="26" data-semantic-parent="28" data-semantic-owns="26" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="23,25" data-semantic-content="11" data-semantic-parent="27" data-semantic-owns="23 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data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:Δ" data-semantic-level-number="5" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="25" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="21" data-semantic-content="13,18" data-semantic-parent="25" data-semantic-owns="13 21 18" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="22" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="14,20" data-semantic-content="15" data-semantic-parent="22" data-semantic-owns="14 15 20" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:U" data-semantic-level-number="7" data-speech-node="true">U</mi><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="7" data-speech-node="true">+</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="16,17" data-semantic-content="19" data-semantic-parent="21" data-semantic-owns="16 19 17" data-semantic-level-number="7" data-speech-node="true"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:P" data-semantic-level-number="8" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="20" data-semantic-added="true" data-semantic-operator="infixop,⁢" 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data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="33" data-semantic-children="32" data-semantic-parent="52" data-semantic-operator="row" data-semantic-owns="32" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="30" data-semantic-content="29,31" data-semantic-parent="33" data-semantic-owns="29 30 31" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.3}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:\text{5.4.3}" data-semantic-level-number="4" data-speech-node="true">5.4.3</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="52" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="50" data-semantic-parent="52" data-semantic-owns="50" 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data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="45" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="45" data-semantic-attributes="latex:U" data-semantic-level-number="6" data-speech-node="true">U</mi></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="5" data-speech-node="true">+</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="40,41,42" data-semantic-content="46,47" data-semantic-parent="49" data-semantic-owns="40 46 41 47 42" data-semantic-level-number="5" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:Δ" data-semantic-level-number="6" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:P" data-semantic-level-number="6" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:V" data-semantic-level-number="6" data-speech-node="true">V</mi></mrow></mrow></mrow></mstyle></mtd></mlabeledtr><mlabeledtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="58,75" data-semantic-content="57" data-semantic-parent="77" data-semantic-owns="58 75 57" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="57" data-semantic-children="56" data-semantic-parent="76" data-semantic-operator="row" data-semantic-owns="56" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="54" data-semantic-content="53,55" data-semantic-parent="57" data-semantic-owns="53 54 55" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="56" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.4}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="56" data-semantic-attributes="latex:\text{5.4.4}" data-semantic-level-number="4" data-speech-node="true">5.4.4</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="56" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="76" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" 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data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="clearspeak:simple;depth:1" data-semantic-="" data-semantic-children="1" data-semantic-content="0" data-semantic-attributes="latex:−w" data-semantic-owns="0 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(2 0 1)"><mo data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:−" data-semantic-operator="prefixop,−" data-semantic-level-number="1" data-speech-node="true">−</mo><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:w" data-semantic-level-number="1" data-speech-node="true">w</mi></math></mjx-assistive-mml></mjx-container> for <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="124" style="font-size: 85%; position: relative;"><svg width="5.333ex" height="1.67ex" role="img" focusable="false" viewbox="0 -716 2357 738" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-125-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path><path id="MJX-125-NCM-N-2062" d=""></path><path id="MJX-125-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-125-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 564C652 600 674 623 696 632C711 639 730 643 752 644C763 645 768 652 769 667C770 678 764 683 752 683C737 683 686 680 671 680Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="PΔV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-id="5" data-semantic-children="0,1,2" data-semantic-content="3,4" data-semantic-attributes="latex:PΔV" data-semantic-owns="0 3 1 4 2" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(5 0 3 1 4 2)"><g data-mml-node="mi" data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:P" data-semantic-level-number="1" data-speech-node="true"><use data-c="1D443" href="#MJX-125-NCM-I-1D443"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(754,0)"><use data-c="2062" href="#MJX-125-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true" transform="translate(754,0)"><use data-c="394" href="#MJX-125-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(1587,0)"><use data-c="2062" href="#MJX-125-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true" transform="translate(1587,0)"><use data-c="1D449" href="#MJX-125-NCM-I-1D449"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="PΔV" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1,2" data-semantic-content="3,4" data-semantic-attributes="latex:PΔV" data-semantic-owns="0 3 1 4 2" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(5 0 3 1 4 2)"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:P" data-semantic-level-number="1" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:V" data-semantic-level-number="1" data-speech-node="true">V</mi></math></mjx-assistive-mml></mjx-container> (Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="125" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2056 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-126-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-126-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-126-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path><path id="MJX-126-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.4.2}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.04:_Enthalpy_of_Reaction#mjx-eqn:5.4.2"><g data-mml-node="mrow" data-latex="\ref{5.4.2}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="699" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.4.2};href:#mjx-eqn%3A5.4.2" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-126-NCM-N-35"></use><use data-c="2E" href="#MJX-126-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-126-NCM-N-34" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-126-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-126-NCM-N-31" transform="translate(1556,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.4.2}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.4.2" data-latex="\ref{5.4.2}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.4.2};href:#mjx-eqn%3A5.4.2" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.4.1</mtext></mrow></math></mjx-assistive-mml></mjx-container>) into Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="126" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2056 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-127-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-127-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-127-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.4.4}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.04:_Enthalpy_of_Reaction#mjx-eqn:5.4.4"><g data-mml-node="mrow" data-latex="\ref{5.4.4}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="699" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.4.4};href:#mjx-eqn%3A5.4.4" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-127-NCM-N-35"></use><use data-c="2E" href="#MJX-127-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-127-NCM-N-34" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-127-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="34" href="#MJX-127-NCM-N-34" transform="translate(1556,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.4.4}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.4.4" data-latex="\ref{5.4.4}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.4.4};href:#mjx-eqn%3A5.4.4" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.4.4</mtext></mrow></math></mjx-assistive-mml></mjx-container>, we obtain</p> <p class="mt-align-center lt-chem-21722" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="127" style="font-size: 85%; min-width: 36.527ex; position: relative;"><svg width="100%" height="10.123ex" role="img" focusable="false" data-mjx-viewbox="0 -2487.2 16145.1 4474.4" aria-hidden="true" style="vertical-align: -4.496ex; min-width: 36.527ex;"><defs><path id="MJX-128-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-128-NCM-N-2062" d=""></path><path id="MJX-128-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 39 37 39 15C39 5 45 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 323 39 302 39C262 39 242 43 242 52C242 52 243 55 245 68L312 336L605 336L538 68C535 53 523 43 503 40C498 39 481 39 452 39C433 39 424 31 424 15C424 5 430 0 442 0L568 3L631 2C642 2 683 0 696 0C712 0 720 8 720 24C720 34 709 39 688 39C647 39 627 43 627 52C627 52 628 55 630 68L764 602C769 623 778 636 791 641C797 643 814 644 843 644C869 644 881 644 881 668Z"></path><path id="MJX-128-NCM-N-3D" d="M698 367L80 367C64 367 56 359 56 344C56 329 64 321 80 321L698 321C714 321 722 329 722 344C722 356 711 367 698 367M698 179L80 179C64 179 56 171 56 156C56 141 64 133 80 133L698 133C714 133 722 141 722 156C722 169 711 179 698 179Z"></path><path id="MJX-128-NCM-I-1D448" d="M642 680C623 680 559 683 540 683C525 683 518 675 518 659C518 650 525 645 539 644C582 644 603 631 603 605C603 599 602 592 600 585L511 232C496 175 467 126 424 84C377 39 325 17 269 17C195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641C292 643 309 644 338 644C364 644 375 644 375 668C375 678 369 683 358 683L231 680L104 683C88 683 81 674 81 659C81 652 84 647 89 646C99 645 107 644 112 644C143 643 161 641 166 640C171 639 173 636 173 631C173 629 172 622 169 611L74 230C69 211 67 192 67 172C67 57 150-22 265-22C330-22 390 3 445 54C498 102 532 158 548 223L636 574C649 625 677 643 739 644C753 645 760 653 760 668L760 672C757 679 752 683 743 683C724 683 661 680 642 680Z"></path><path id="MJX-128-NCM-N-2B" d="M698 274L413 274L413 559C413 575 405 583 389 583C373 583 365 575 365 559L365 274L80 274C64 274 56 266 56 250C56 234 64 226 80 226L365 226L365-59C365-75 373-83 389-83C405-83 413-75 413-59L413 226L698 226C714 226 722 234 722 250C722 263 711 274 698 274Z"></path><path id="MJX-128-NCM-I-1D443" d="M555 683L235 683C212 683 201 682 201 660C201 649 212 644 234 644C254 644 294 647 294 631C294 629 293 623 290 613L158 82C152 60 142 47 128 42C121 40 103 39 72 39C50 39 40 37 40 16C40 5 46 0 59 0L184 3L248 2C259 2 299 0 312 0C328 0 336 8 336 24C336 34 325 39 304 39C264 39 244 43 244 52C244 52 245 55 247 68L307 312L472 312C537 312 599 332 657 371C722 414 754 467 754 530C754 629 660 683 555 683M524 644C611 644 654 614 654 554C654 498 626 423 597 397C559 363 509 346 447 346L313 346L379 610C387 644 387 644 429 644Z"></path><path id="MJX-128-NCM-I-1D449" d="M671 680C652 680 592 683 573 683C558 683 550 675 550 660C550 650 557 645 570 644C598 643 612 633 612 616C612 607 607 595 598 580L300 107L234 619C234 636 255 644 298 644C318 644 327 651 327 668C327 678 321 683 309 683C287 683 209 680 187 680C167 680 99 683 79 683C64 683 56 675 56 660C56 649 66 644 85 644C102 644 114 642 122 640C138 635 137 633 140 614L218 4C221-13 229-22 242-22C255-22 265-15 273-2L629 564C652 600 674 623 696 632C711 639 730 643 752 644C763 645 768 652 769 667C770 678 764 683 752 683C737 683 686 680 671 680Z"></path><path id="MJX-128-NCM-N-28" d="M318-248C327-248 332-243 332-234C332-231 330-227 327-223C275-183 233-117 202-26C175 53 161 131 161 208L161 292C161 369 175 447 202 526C233 617 275 683 327 723C330 726 332 730 332 734C332 743 327 748 318 748C317 748 314 747 311 745C251 699 201 631 160 540C121 453 101 371 101 292L101 208C101 129 121 47 160-40C201-131 251-199 311-245C314-247 317-248 318-248Z"></path><path id="MJX-128-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 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data-speech-node="true" transform="translate(0,-952)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-id="54" data-semantic-children="52" data-semantic-content="51,53" data-semantic-parent="55" data-semantic-owns="51 52 53" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="mtext" data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-id="51" data-semantic-parent="54" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true"><use data-c="28" href="#MJX-128-NCM-N-28"></use></g><g data-mml-node="mtext" data-latex="\text{5.4.7}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="52" data-semantic-parent="54" data-semantic-attributes="latex:\text{5.4.7}" data-semantic-level-number="4" data-speech-node="true" transform="translate(389,0)"><use data-c="35" href="#MJX-128-NCM-N-35"></use><use data-c="2E" href="#MJX-128-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-128-NCM-N-34" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-128-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="37" href="#MJX-128-NCM-N-37" transform="translate(1556,0)"></use></g><g data-mml-node="mtext" data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="53" data-semantic-parent="54" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2445,0)"><use data-c="29" href="#MJX-128-NCM-N-29"></use></g></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" \begin{align} ΔH &= ΔU + PΔV \\[4pt] &= q_p + \cancel{w} −\cancel{w} \\[4pt] &= q_p \label{5.4.5} \end{align} " display="block" data-semantic-structure="(66 (27 (9 (8 5 7 6)) (26 (25 18 11 (24 (20 12 19 13) 14 (23 15 21 16 22 17)))) (4 (3 0 1 2))) (50 33 (49 (48 45 35 (47 (46 (38 36 37) 39 (41 40)) 42 (44 43)))) (32 (31 28 29 30))) (65 56 (64 (63 62 58 (61 59 60))) (55 (54 51 52 53))))"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="0.7em 0.7em 0.30000000000000004em" data-break-align="bottom top" data-latex="\begin{align} ΔH &= ΔU + PΔV \\[4pt] &= q_p + \cancel{w} −\cancel{w} \\[4pt] &= q_p \label{5.4.5} \end{align}" data-semantic-type="table" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="27,50,65" data-semantic-attributes="latex: \begin{align} ΔH &= ΔU + PΔV \\[4pt] &= q_p + \cancel{w} −\cancel{w} \\[4pt] &= q_p \label{5.4.5} \end{align} " data-semantic-owns="27 50 65" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="9,26" data-semantic-content="4" data-semantic-parent="66" data-semantic-owns="9 26 4" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="27" data-semantic-operator="row" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.5}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.4.5}" data-semantic-level-number="4" data-speech-node="true">5.4.5</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="8" data-semantic-parent="27" data-semantic-owns="8" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="5,6" data-semantic-content="7" data-semantic-parent="9" data-semantic-owns="5 7 6" data-semantic-level-number="3" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:Δ" data-semantic-level-number="4" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="8" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="4" data-speech-node="true">H</mi></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="25" data-semantic-parent="27" data-semantic-owns="25" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="18,24" data-semantic-content="11" data-semantic-parent="26" data-semantic-owns="18 11 24" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="25" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="20,23" data-semantic-content="14" data-semantic-parent="25" data-semantic-owns="20 14 23" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="12,13" data-semantic-content="19" data-semantic-parent="24" data-semantic-owns="12 19 13" data-semantic-level-number="5" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:Δ" data-semantic-level-number="6" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="20" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:U" data-semantic-level-number="6" data-speech-node="true">U</mi></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="5" data-speech-node="true">+</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="15,16,17" data-semantic-content="21,22" data-semantic-parent="24" data-semantic-owns="15 21 16 22 17" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="P" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:P" data-semantic-level-number="6" data-speech-node="true">P</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="23" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:Δ" data-semantic-level-number="6" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="23" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="V" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:V" data-semantic-level-number="6" data-speech-node="true">V</mi></mrow></mrow></mrow></mstyle></mtd></mlabeledtr><mlabeledtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="33,49" data-semantic-content="32" data-semantic-parent="66" data-semantic-owns="33 49 32" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="32" data-semantic-children="31" data-semantic-parent="50" data-semantic-operator="row" data-semantic-owns="31" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="29" data-semantic-content="28,30" data-semantic-parent="32" data-semantic-owns="28 29 30" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.6}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:\text{5.4.6}" data-semantic-level-number="4" data-speech-node="true">5.4.6</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="31" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="50" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="48" data-semantic-parent="50" data-semantic-owns="48" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="45,47" data-semantic-content="35" data-semantic-parent="49" data-semantic-owns="45 35 47" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="48" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="46,44" data-semantic-content="42" data-semantic-parent="48" data-semantic-owns="46 42 44" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="38,41" data-semantic-content="39" data-semantic-parent="47" data-semantic-owns="38 39 41" data-semantic-level-number="5" data-speech-node="true"><msub data-latex="q_p" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="36,37" data-semantic-parent="46" data-semantic-attributes="latex:q_p" data-semantic-owns="36 37" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="38" data-semantic-attributes="latex:q" data-semantic-level-number="7" data-speech-node="true">q</mi><mi data-latex="p" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="38" data-semantic-attributes="latex:p" data-semantic-level-number="7" data-speech-node="true">p</mi></msub><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="46" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="6" data-speech-node="true">+</mo><menclose notation="updiagonalstrike" data-latex="\cancel{w}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="40" data-semantic-parent="46" data-semantic-attributes="latex:\cancel{w}" data-semantic-owns="40" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:w" data-semantic-level-number="7" data-speech-node="true">w</mi></menclose></mrow><mo data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:−" data-semantic-operator="infixop,−" data-semantic-level-number="5" data-speech-node="true">−</mo><menclose notation="updiagonalstrike" data-latex="\cancel{w}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="43" data-semantic-parent="47" data-semantic-attributes="latex:\cancel{w}" data-semantic-owns="43" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="w" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:w" data-semantic-level-number="6" data-speech-node="true">w</mi></menclose></mrow></mrow></mstyle></mtd></mlabeledtr><mlabeledtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="56,64" data-semantic-content="55" data-semantic-parent="66" data-semantic-owns="56 64 55" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="55" data-semantic-children="54" data-semantic-parent="65" data-semantic-operator="row" data-semantic-owns="54" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="52" data-semantic-content="51,53" data-semantic-parent="55" data-semantic-owns="51 52 53" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="54" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.7}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="54" data-semantic-attributes="latex:\text{5.4.7}" data-semantic-level-number="4" data-speech-node="true">5.4.7</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="54" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="65" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="63" data-semantic-parent="65" data-semantic-owns="63" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="62,61" data-semantic-content="58" data-semantic-parent="64" data-semantic-owns="62 58 61" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="63" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="63" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><msub data-latex="q_p" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="59,60" data-semantic-parent="63" data-semantic-attributes="latex:q_p" data-semantic-owns="59 60" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="61" data-semantic-attributes="latex:q" data-semantic-level-number="5" data-speech-node="true">q</mi><mi data-latex="p" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="61" data-semantic-attributes="latex:p" data-semantic-level-number="5" data-speech-node="true">p</mi></msub></mrow></mstyle></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">The subscript <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="128" style="font-size: 85%; position: relative;"><svg width="1.138ex" height="1.439ex" role="img" focusable="false" viewbox="0 -442 503 636" aria-hidden="true" style="vertical-align: -0.439ex;"><defs><path id="MJX-129-NCM-I-1D45D" d="M355 442C311 442 269 419 228 373C217 419 186 442 137 442C96 442 66 409 45 344C35 311 30 292 30 286C30 277 35 272 46 272C51 272 54 273 57 275C62 284 65 291 66 298C84 374 107 412 134 412C152 412 161 398 161 371C161 356 159 339 154 321L44-118C35-151 34-155-5-155C-23-155-32-163-32-178C-32-189-26-194-15-194C0-194 52-191 67-191C86-191 146-194 165-194C180-194 187-186 187-170C187-160 178-155 159-155C141-155 114-156 114-144C114-131 155 26 159 43C179 6 209-13 249-13C314-13 371 20 421 87C467 148 490 213 490 280C490 367 438 442 355 442M352 412C391 412 411 382 411 323C411 296 405 260 394 215C371 128 342 71 307 42C286 25 267 16 248 16C219 16 199 29 188 56C179 77 174 92 174 100L225 309C230 331 248 354 276 377C304 400 329 412 352 412Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="p" data-semantic-structure="0"><g data-mml-node="mi" data-latex="p" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:p" data-semantic-level-number="0" data-speech-node="true"><use data-c="1D45D" href="#MJX-129-NCM-I-1D45D"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="p" data-semantic-structure="0"><mi data-latex="p" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:p" data-semantic-level-number="0" data-speech-node="true">p</mi></math></mjx-assistive-mml></mjx-container> is used here to emphasize that this equation is true only for a process that occurs at constant pressure. From Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="129" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2056 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-130-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-130-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-130-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path><path id="MJX-130-NCM-N-37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657C125 660 122 667 120 676L89 676L55 464L88 464C98 520 106 550 112 555C115 558 146 560 205 560L401 560L295 410C214 295 174 171 174 36C174-3 190-22 223-22C256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.4.5}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.04:_Enthalpy_of_Reaction#mjx-eqn:5.4.5"><g data-mml-node="mrow" data-latex="\ref{5.4.5}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="699" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.4.5};href:#mjx-eqn%3A5.4.5" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-130-NCM-N-35"></use><use data-c="2E" href="#MJX-130-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-130-NCM-N-34" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-130-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="37" href="#MJX-130-NCM-N-37" transform="translate(1556,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.4.5}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.4.5" data-latex="\ref{5.4.5}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.4.5};href:#mjx-eqn%3A5.4.5" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.4.7</mtext></mrow></math></mjx-assistive-mml></mjx-container> we see that at constant pressure the change in enthalpy, <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="130" style="font-size: 85%; position: relative;"><svg width="3.878ex" height="1.62ex" role="img" focusable="false" viewbox="0 -716 1714 716" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-131-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-131-NCM-N-2062" d=""></path><path id="MJX-131-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 39 37 39 15C39 5 45 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 323 39 302 39C262 39 242 43 242 52C242 52 243 55 245 68L312 336L605 336L538 68C535 53 523 43 503 40C498 39 481 39 452 39C433 39 424 31 424 15C424 5 430 0 442 0L568 3L631 2C642 2 683 0 696 0C712 0 720 8 720 24C720 34 709 39 688 39C647 39 627 43 627 52C627 52 628 55 630 68L764 602C769 623 778 636 791 641C797 643 814 644 843 644C869 644 881 644 881 668Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-131-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-131-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D43B" href="#MJX-131-NCM-I-1D43B"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="H" 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display="block"><math data-latex=" \begin{align} ΔH &= H_{final} − H_{initial} \\[4pt] &= q_p \label{5.4.6} \end{align} " display="block" data-semantic-structure="(62 (46 (9 (8 5 7 6)) (45 (44 42 11 (43 (24 12 (23 13 22 (21 14 18 15 19 16 20 17))) 25 (41 26 (40 27 34 28 35 29 36 30 37 31 38 32 39 33))))) (4 (3 0 1 2))) (61 52 (60 (59 58 54 (57 55 56))) (51 (50 47 48 49))))"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="0.7em 0.30000000000000004em" data-break-align="bottom top" data-latex="\begin{align} ΔH &= H_{final} − H_{initial} \\[4pt] &= q_p \label{5.4.6} \end{align}" data-semantic-type="table" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="46,61" data-semantic-attributes="latex: \begin{align} ΔH &= H_{final} − H_{initial} \\[4pt] &= q_p \label{5.4.6} \end{align} " data-semantic-owns="46 61" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="row" 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data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.8}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.4.8}" data-semantic-level-number="4" data-speech-node="true">5.4.8</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="8" data-semantic-parent="46" data-semantic-owns="8" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="5,6" data-semantic-content="7" data-semantic-parent="9" data-semantic-owns="5 7 6" data-semantic-level-number="3" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:Δ" data-semantic-level-number="4" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="8" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="4" data-speech-node="true">H</mi></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="44" data-semantic-parent="46" data-semantic-owns="44" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="42,43" data-semantic-content="11" data-semantic-parent="45" data-semantic-owns="42 11 43" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="44" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="24,41" data-semantic-content="25" data-semantic-parent="44" data-semantic-owns="24 25 41" data-semantic-level-number="4" data-speech-node="true"><msub data-latex="H_{f i n a l}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="12,23" data-semantic-parent="43" data-semantic-attributes="latex:H_{f i n a l}" data-semantic-owns="12 23" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:H" data-semantic-level-number="6" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{f i n a l}" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="13,21" data-semantic-content="22,13" data-semantic-parent="24" data-semantic-attributes="latex:{f i n a l};texclass:ORD" data-semantic-owns="13 22 21" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="f" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:f" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">f</mi><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="23" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="14,15,16,17" data-semantic-content="18,19,20" data-semantic-parent="23" data-semantic-owns="14 18 15 19 16 20 17" data-semantic-level-number="7" data-speech-node="true"><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:i" data-semantic-level-number="8" data-speech-node="true">i</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:n" data-semantic-level-number="8" data-speech-node="true">n</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:a" data-semantic-level-number="8" data-speech-node="true">a</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:l" data-semantic-level-number="8" data-speech-node="true">l</mi></mrow></mrow></msub><mo data-latex="−" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:−" data-semantic-operator="infixop,−" data-semantic-level-number="5" data-speech-node="true">−</mo><msub data-latex="H_{i n i t i a l}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="26,40" data-semantic-parent="43" data-semantic-attributes="latex:H_{i n i t i a l}" data-semantic-owns="26 40" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:H" data-semantic-level-number="6" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{i n i t i a l}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="27,28,29,30,31,32,33" data-semantic-content="34,35,36,37,38,39" data-semantic-parent="41" data-semantic-attributes="latex:{i n i t i a l};texclass:ORD" data-semantic-owns="27 34 28 35 29 36 30 37 31 38 32 39 33" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:i" data-semantic-level-number="7" data-speech-node="true">i</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:n" data-semantic-level-number="7" data-speech-node="true">n</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:i" data-semantic-level-number="7" data-speech-node="true">i</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="t" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:t" data-semantic-level-number="7" data-speech-node="true">t</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="i" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:i" data-semantic-level-number="7" data-speech-node="true">i</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:a" data-semantic-level-number="7" data-speech-node="true">a</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:l" data-semantic-level-number="7" data-speech-node="true">l</mi></mrow></msub></mrow></mrow></mstyle></mtd></mlabeledtr><mlabeledtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="52,60" data-semantic-content="51" data-semantic-parent="62" data-semantic-owns="52 60 51" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="51" data-semantic-children="50" data-semantic-parent="61" data-semantic-operator="row" data-semantic-owns="50" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="48" data-semantic-content="47,49" data-semantic-parent="51" data-semantic-owns="47 48 49" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.9}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:\text{5.4.9}" data-semantic-level-number="4" data-speech-node="true">5.4.9</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="61" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="59" data-semantic-parent="61" data-semantic-owns="59" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="58,57" data-semantic-content="54" data-semantic-parent="60" data-semantic-owns="58 54 57" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="59" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="59" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><msub data-latex="q_p" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="55,56" data-semantic-parent="59" data-semantic-attributes="latex:q_p" data-semantic-owns="55 56" data-semantic-level-number="4" data-speech-node="true"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="57" data-semantic-attributes="latex:q" data-semantic-level-number="5" data-speech-node="true">q</mi><mi data-latex="p" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="57" data-semantic-attributes="latex:p" data-semantic-level-number="5" data-speech-node="true">p</mi></msub></mrow></mstyle></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">Just as with <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="132" style="font-size: 85%; position: relative;"><svg width="3.604ex" height="1.67ex" role="img" focusable="false" viewbox="0 -716 1593 738" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-133-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-133-NCM-N-2062" d=""></path><path id="MJX-133-NCM-I-1D448" d="M642 680C623 680 559 683 540 683C525 683 518 675 518 659C518 650 525 645 539 644C582 644 603 631 603 605C603 599 602 592 600 585L511 232C496 175 467 126 424 84C377 39 325 17 269 17C195 17 152 67 152 141L153 150C153 169 156 191 163 217L259 602C264 623 273 636 286 641C292 643 309 644 338 644C364 644 375 644 375 668C375 678 369 683 358 683L231 680L104 683C88 683 81 674 81 659C81 652 84 647 89 646C99 645 107 644 112 644C143 643 161 641 166 640C171 639 173 636 173 631C173 629 172 622 169 611L74 230C69 211 67 192 67 172C67 57 150-22 265-22C330-22 390 3 445 54C498 102 532 158 548 223L636 574C649 625 677 643 739 644C753 645 760 653 760 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data-semantic-content="2" data-semantic-attributes="latex:ΔU" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="U" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:U" data-semantic-level-number="1" data-speech-node="true">U</mi></math></mjx-assistive-mml></mjx-container>, because enthalpy is a state function, the magnitude of <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="133" style="font-size: 85%; position: relative;"><svg width="3.878ex" height="1.62ex" role="img" focusable="false" viewbox="0 -716 1714 716" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-134-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-134-NCM-N-2062" d=""></path><path id="MJX-134-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 39 37 39 15C39 5 45 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 323 39 302 39C262 39 242 43 242 52C242 52 243 55 245 68L312 336L605 336L538 68C535 53 523 43 503 40C498 39 481 39 452 39C433 39 424 31 424 15C424 5 430 0 442 0L568 3L631 2C642 2 683 0 696 0C712 0 720 8 720 24C720 34 709 39 688 39C647 39 627 43 627 52C627 52 628 55 630 68L764 602C769 623 778 636 791 641C797 643 814 644 843 644C869 644 881 644 881 668Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-134-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-134-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D43B" href="#MJX-134-NCM-I-1D43B"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true">H</mi></math></mjx-assistive-mml></mjx-container> depends on only the initial and final states of the system, not on the path taken. Most important, the enthalpy change is the same even if the process does <em>not</em> occur at constant pressure.</p> <blockquote> <p class="lt-chem-21722" style="background-color: unset;">To find <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="134" style="font-size: 85%; position: relative;"><svg width="3.878ex" height="1.62ex" role="img" focusable="false" viewbox="0 -716 1714 716" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-135-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-135-NCM-N-2062" d=""></path><path id="MJX-135-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 39 37 39 15C39 5 45 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 323 39 302 39C262 39 242 43 242 52C242 52 243 55 245 68L312 336L605 336L538 68C535 53 523 43 503 40C498 39 481 39 452 39C433 39 424 31 424 15C424 5 430 0 442 0L568 3L631 2C642 2 683 0 696 0C712 0 720 8 720 24C720 34 709 39 688 39C647 39 627 43 627 52C627 52 628 55 630 68L764 602C769 623 778 636 791 641C797 643 814 644 843 644C869 644 881 644 881 668Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-135-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-135-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D43B" href="#MJX-135-NCM-I-1D43B"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true">H</mi></math></mjx-assistive-mml></mjx-container> <em>for a reaction</em>, measure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="135" style="font-size: 85%; position: relative;"><svg width="2.002ex" height="1.65ex" role="img" focusable="false" viewbox="0 -442 884.7 729.2" aria-hidden="true" style="vertical-align: -0.65ex;"><defs><path id="MJX-136-NCM-I-1D45E" d="M372 377C352 420 321 442 280 442C215 442 158 409 109 342C63 280 40 216 40 149C40 62 90-13 173-13C209-13 245 4 282 38L241-126C238-141 229-150 215-153C210-154 197-155 174-155C168-156 164-156 162-156C153-157 148-165 148-179L148-183C151-190 157-194 165-194C184-194 244-191 263-191C282-191 345-194 364-194C378-194 385-186 385-170C385-160 375-155 356-155C338-155 313-156 313-144C313-140 314-133 317-123L452 427C452 436 447 441 438 441C420 441 382 391 372 377M340 373C349 352 354 338 354 329C354 328 353 322 351 313L327 216C308 144 299 107 298 105C279 70 224 16 176 16C137 16 117 46 117 105C117 151 148 263 162 300C181 347 225 412 280 412C307 412 327 399 340 373Z"></path><path id="MJX-136-NCM-I-1D45D" d="M355 442C311 442 269 419 228 373C217 419 186 442 137 442C96 442 66 409 45 344C35 311 30 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data-semantic-children="0,1" data-semantic-attributes="latex:q_p" data-semantic-owns="0 1" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mi" data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="2" data-semantic-attributes="latex:q" data-semantic-level-number="1" data-speech-node="true"><use data-c="1D45E" href="#MJX-136-NCM-I-1D45E"></use></g><g data-mml-node="mi" transform="translate(479,-150) scale(0.707)" data-latex="p" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="2" data-semantic-attributes="latex:p" data-semantic-level-number="1" data-speech-node="true"><use data-c="1D45D" href="#MJX-136-NCM-I-1D45D"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="q_p" data-semantic-structure="(2 0 1)"><msub data-latex="q_p" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-attributes="latex:q_p" data-semantic-owns="0 1" data-semantic-level-number="0" data-speech-node="true"><mi data-latex="q" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:q" data-semantic-level-number="1" data-speech-node="true">q</mi><mi data-latex="p" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:p" data-semantic-level-number="1" data-speech-node="true">p</mi></msub></math></mjx-assistive-mml></mjx-container>.</p> </blockquote> <p class="lt-chem-21722" style="background-color: unset;">When we study energy changes in chemical reactions, the most important quantity is usually the enthalpy of reaction (<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="136" style="font-size: 85%; position: relative;"><svg width="6.549ex" height="1.977ex" role="img" focusable="false" viewbox="0 -716 2894.6 873.8" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-137-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-137-NCM-N-2062" d=""></path><path id="MJX-137-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 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data-speech-node="true" transform="translate(451,0)"><use data-c="2062" href="#MJX-137-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="3" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="3" data-speech-node="true" transform="translate(451,0)"><use data-c="1D465" href="#MJX-137-NCM-I-1D465"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="6" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true" transform="translate(1023,0)"><use data-c="2062" href="#MJX-137-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="4" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="3" data-speech-node="true" transform="translate(1023,0)"><use data-c="1D45B" href="#MJX-137-NCM-I-1D45B"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔH_{rxn}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,8" data-semantic-content="9" data-semantic-attributes="latex:ΔH_{rxn}" data-semantic-owns="0 9 8" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(10 0 9 (8 1 (7 2 5 3 6 4)))"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><msub data-latex="H_{r x n}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="1,7" data-semantic-parent="10" data-semantic-attributes="latex:H_{r x n}" data-semantic-owns="1 7" data-semantic-level-number="1" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="2" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{r x n}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-="" data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-parent="8" data-semantic-attributes="latex:{r x n};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:r" data-semantic-level-number="3" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="3" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="3" data-speech-node="true">n</mi></mrow></msub></math></mjx-assistive-mml></mjx-container>), the change in enthalpy that occurs during a reaction (such as the dissolution of a piece of copper in nitric acid). If heat flows from a system to its surroundings, the enthalpy of the system decreases, so <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="137" style="font-size: 85%; position: relative;"><svg width="6.549ex" height="1.977ex" role="img" focusable="false" viewbox="0 -716 2894.6 873.8" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-138-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-138-NCM-N-2062" d=""></path><path id="MJX-138-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 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data-semantic-attributes="latex:ΔH_{rxn}" data-semantic-owns="0 9 8" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(10 0 9 (8 1 (7 2 5 3 6 4)))"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="10" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-138-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="9" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-138-NCM-N-2062"></use></g><g data-mml-node="msub" data-latex="H_{r x n}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:2" data-semantic-id="8" data-semantic-children="1,7" data-semantic-parent="10" data-semantic-attributes="latex:H_{r x n}" data-semantic-owns="1 7" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><g data-mml-node="mi" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="1" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="2" data-speech-node="true"><use data-c="1D43B" href="#MJX-138-NCM-I-1D43B"></use></g><g data-mml-node="TeXAtom" transform="translate(864,-150) scale(0.707)" data-mjx-texclass="ORD" data-latex="{r x n}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-id="7" data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-parent="8" data-semantic-attributes="latex:{r x n};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mi" data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="2" data-semantic-parent="7" data-semantic-attributes="latex:r" data-semantic-level-number="3" data-speech-node="true"><use data-c="1D45F" href="#MJX-138-NCM-I-1D45F"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="5" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true" transform="translate(451,0)"><use data-c="2062" href="#MJX-138-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="3" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="3" data-speech-node="true" transform="translate(451,0)"><use data-c="1D465" href="#MJX-138-NCM-I-1D465"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="6" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true" transform="translate(1023,0)"><use data-c="2062" href="#MJX-138-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="4" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="3" data-speech-node="true" transform="translate(1023,0)"><use data-c="1D45B" href="#MJX-138-NCM-I-1D45B"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔH_{rxn}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,8" data-semantic-content="9" data-semantic-attributes="latex:ΔH_{rxn}" data-semantic-owns="0 9 8" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(10 0 9 (8 1 (7 2 5 3 6 4)))"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><msub data-latex="H_{r x n}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="1,7" data-semantic-parent="10" data-semantic-attributes="latex:H_{r x n}" data-semantic-owns="1 7" data-semantic-level-number="1" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="2" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{r x n}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-="" data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-parent="8" data-semantic-attributes="latex:{r x n};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:r" data-semantic-level-number="3" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="3" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="3" data-speech-node="true">n</mi></mrow></msub></math></mjx-assistive-mml></mjx-container> is negative. Conversely, if heat flows from the surroundings to a system, the enthalpy of the system increases, so <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="138" style="font-size: 85%; position: relative;"><svg width="6.549ex" height="1.977ex" role="img" focusable="false" viewbox="0 -716 2894.6 873.8" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-139-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-139-NCM-N-2062" d=""></path><path id="MJX-139-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 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n};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="3" data-speech-node="true"><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:r" data-semantic-level-number="4" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="4" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="4" data-speech-node="true">n</mi></mrow></msub></mrow><mo data-latex="<" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:<" data-semantic-operator="relseq,<" data-semantic-level-number="1" data-speech-node="true"><</mo><mn data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" 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0" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="12,10" data-semantic-content="9" data-semantic-attributes="latex:ΔH_{rxn} > 0" data-semantic-owns="12 9 10" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(13 (12 0 11 (8 1 (7 2 5 3 6 4))) 9 10)"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:2" data-semantic-="" data-semantic-children="0,8" data-semantic-content="11" data-semantic-parent="13" data-semantic-owns="0 11 8" data-semantic-level-number="1" data-speech-node="true"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:Δ" data-semantic-level-number="2" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="12" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true">⁢</mo><msub data-latex="H_{r x n}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="1,7" data-semantic-parent="12" data-semantic-attributes="latex:H_{r x n}" data-semantic-owns="1 7" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="3" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{r x n}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-parent="8" data-semantic-attributes="latex:{r x n};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="3" data-speech-node="true"><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:r" data-semantic-level-number="4" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="4" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="4" data-speech-node="true">n</mi></mrow></msub></mrow><mo data-latex=">" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:>" data-semantic-operator="relseq,>" data-semantic-level-number="1" data-speech-node="true">></mo><mn data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="13" data-semantic-attributes="latex:0" data-semantic-level-number="1" data-speech-node="true">0</mn></math></mjx-assistive-mml></mjx-container> for an<em> endothermic reaction</em>.</li> </ul> <p class="lt-chem-21722" style="background-color: unset;">In chemical reactions, bond breaking requires an input of energy and is therefore an endothermic process, whereas bond making releases energy, which is an exothermic process. The sign conventions for heat flow and enthalpy changes are summarized in the following table:</p> <table class="mt-responsive-table" align="center" cellpadding="0" cellspacing="0"> <caption>sign conventions for heat flow and enthalpy changes</caption> <thead> <tr> <th style="text-align:center;"><strong>Reaction Type</strong></th> <th style="text-align:center;"><strong>q</strong></th> <th style="text-align:center;"><strong>ΔH<sub>rxn</sub></strong></th> </tr> </thead> <tbody> <tr> <td class="lt-chem-21722" data-th="Reaction Type" style="text-align: center; background-color: unset;">exothermic</td> <td class="lt-chem-21722" data-th="q" style="text-align: center; background-color: unset;">< 0</td> <td class="lt-chem-21722" data-th="ΔHrxn" style="text-align: center; background-color: unset;">< 0 (heat flows from a system to its surroundings)</td> </tr> <tr> <td class="lt-chem-21722" data-th="Reaction Type" style="text-align: center; background-color: unset;">endothermic</td> <td class="lt-chem-21722" data-th="q" style="text-align: center; background-color: unset;">> 0</td> <td class="lt-chem-21722" data-th="ΔHrxn" style="text-align: center; background-color: unset;">> 0 (heat flows from the surroundings to a system)</td> </tr> </tbody> </table> <p class="lt-chem-21722" style="background-color: unset;">If Δ<em>H</em><sub>rxn</sub> is negative, then the enthalpy of the products is less than the enthalpy of the reactants; that is, <em>an exothermic reaction is energetically downhill</em> (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="141" style="font-size: 85%; position: relative;"><svg width="5.848ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2585 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-142-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 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transform="translate(2056,0)"><use data-c="1D44E" href="#MJX-142-NCM-I-1D44E"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2}a" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="5,6" data-semantic-content="7" data-semantic-attributes="latex:\PageIndex{2}a" data-semantic-owns="5 7 6" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(8 (5 0 1 2 3 4) 7 6)"><mrow data-mjx-texclass="ORD" data-latex="{5{.}4{.}2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-parent="8" data-semantic-attributes="latex:{5{.}4{.}2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="1" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="2" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="2" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="2" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="2" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="2" data-speech-node="true">2</mn></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="8" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:a" data-semantic-level-number="1" data-speech-node="true">a</mi></math></mjx-assistive-mml></mjx-container>). Conversely, if Δ<em>H</em><sub>rxn</sub> is positive, then the enthalpy of the products is greater than the enthalpy of the reactants; thus, <em>an endothermic reaction is energetically uphill</em> (Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="142" style="font-size: 85%; position: relative;"><svg width="5.622ex" height="1.62ex" role="img" focusable="false" viewbox="0 -694 2485 716" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-143-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 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data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-143-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="8" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="34" href="#MJX-143-NCM-N-34"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="8" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-143-NCM-N-2E"></use></g></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:2" data-semantic-id="7" data-semantic-children="4,5" data-semantic-content="6" data-semantic-parent="8" data-semantic-owns="4 6 5" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-id="4" data-semantic-parent="7" data-semantic-attributes="latex:2" data-semantic-level-number="2" data-speech-node="true"><use data-c="32" href="#MJX-143-NCM-N-32"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-id="6" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true" transform="translate(500,0)"><use data-c="2062" href="#MJX-143-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="b" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="5" data-semantic-parent="7" data-semantic-attributes="latex:b" data-semantic-level-number="2" data-speech-node="true" transform="translate(500,0)"><use data-c="1D44F" href="#MJX-143-NCM-I-1D44F"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2b}" data-semantic-structure="(8 0 1 2 3 (7 4 6 5))"><mrow data-mjx-texclass="ORD" data-latex="2b}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,7" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2b};texclass:ORD" data-semantic-owns="0 1 2 3 7" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:2" data-semantic-="" data-semantic-children="4,5" data-semantic-content="6" data-semantic-parent="8" data-semantic-owns="4 6 5" data-semantic-level-number="1" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:3" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:2" data-semantic-level-number="2" data-speech-node="true">2</mn><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true">⁢</mo><mi data-latex="b" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:b" data-semantic-level-number="2" data-speech-node="true">b</mi></mrow></mrow></math></mjx-assistive-mml></mjx-container>). Two important characteristics of enthalpy and changes in enthalpy are summarized in the following discussion.</p> <blockquote> <p class="lt-chem-21722" style="background-color: unset;">Bond breaking <strong><span class="acronym-ignore">ALWAYS</span> </strong>requires an input of energy; bond making <strong>ALWAYS</strong> releases energy.y.</p> </blockquote> <figure><img alt="Illustration of three laboratory flasks showing different liquid levels and labels for 'Equilibrium reactor' and 'Hydrogenation reactor'." style="width: 700px; height: 275px;" class="internal" loading="lazy" width="700px" height="275px" src="https://chem.libretexts.org/@api/deki/files/129614/imageedit_38_4976154517.jpg?revision=1&size=bestfit&width=700&height=275" /> <figcaption>Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="143" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" 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data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-144-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="34" href="#MJX-144-NCM-N-34"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-144-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="32" href="#MJX-144-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>: The Enthalpy of Reaction. Energy changes in chemical reactions are usually measured as changes in enthalpy. (a) If heat flows from a system to its surroundings, the enthalpy of the system decreases, Δ<em>H</em><sub>rxn</sub> is negative, and the reaction is exothermic; it is energetically downhill. (b) Conversely, if heat flows from the surroundings to a system, the enthalpy of the system increases, Δ<em>H</em><sub>rxn</sub> is positive, and the reaction is endothermic; it is energetically uphill. (CC BY-NC-SA; anonymous)</figcaption> </figure> <ul class="itemizedlist block"> <li class="lt-chem-21722" style="background-color: unset;"><strong class="emphasis bold">Reversing a reaction or a process changes the sign of </strong><strong class="emphasis bold">Δ</strong><strong><em class="emphasis bolditalic">H</em></strong><strong class="emphasis bold">.</strong> Ice <em>absorbs</em> heat when it melts (electrostatic interactions are broken), so liquid water must <em>release</em> heat when it freezes (electrostatic interactions are formed): <p class="mt-align-center lt-chem-21722" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="144" style="font-size: 85%; position: relative;"><svg width="35.388ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 15641.7 1000" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-145-NCM-I-210E" d="M512 138C489 59 457 19 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data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-id="40" data-semantic-parent="44" data-semantic-attributes="latex:>" data-semantic-operator="relseq,>" data-semantic-level-number="4" data-speech-node="true" transform="translate(1991.8,0)"><use data-c="3E" href="#MJX-145-NCM-N-3E"></use></g><g data-mml-node="mn" data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-id="41" data-semantic-parent="44" data-semantic-attributes="latex:0" data-semantic-level-number="4" data-speech-node="true" transform="translate(3047.6,0)"><use data-c="30" href="#MJX-145-NCM-N-30"></use></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex=" \begin{matrix} heat+ H_{2}O(s) \rightarrow H_{2}O(l) & \Delta H > 0 \end{matrix} \label{5.4.7} " data-semantic-structure="(47 (46 (37 (36 (35 (34 0 33 (32 1 30 2 31 3)) 4 (29 (7 5 6) 28 (27 8 26 (20 9 10 11)))) 12 (25 (15 13 14) 24 (23 16 22 (21 17 18 19))))) (45 (44 (43 38 42 39) 40 41))))"><mtable columnspacing="1em" rowspacing="4pt" data-latex="\begin{matrix} heat+ H_{2}O(s) \rightarrow H_{2}O(l) & \Delta H > 0 \end{matrix} \label{5.4.7}" data-semantic-type="table" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="46" data-semantic-attributes="latex: \begin{matrix} heat+ H_{2}O(s) \rightarrow H_{2}O(l) & \Delta H > 0 \end{matrix} \label{5.4.7} " data-semantic-owns="46" data-semantic-level-number="0" data-speech-node="true"><mtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="37,45" data-semantic-parent="47" data-semantic-owns="37 45" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" 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data-latex=" \begin{matrix} H_{2}O(l) \rightarrow H_{2}O(s) + heat & \Delta H < 0 \end{matrix} \label{5.4.8} " data-semantic-structure="(47 (46 (37 (36 (34 (2 0 1) 33 (32 3 31 (20 4 5 6))) 7 (35 (30 (10 8 9) 29 (28 11 27 (21 12 13 14))) 15 (26 16 25 (24 17 22 18 23 19))))) (45 (44 (43 38 42 39) 40 41))))"><mtable columnspacing="1em" rowspacing="4pt" data-latex="\begin{matrix} H_{2}O(l) \rightarrow H_{2}O(s) + heat & \Delta H < 0 \end{matrix} \label{5.4.8}" data-semantic-type="table" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="46" data-semantic-attributes="latex: \begin{matrix} H_{2}O(l) \rightarrow H_{2}O(s) + heat & \Delta H < 0 \end{matrix} \label{5.4.8} " data-semantic-owns="46" data-semantic-level-number="0" data-speech-node="true"><mtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="37,45" data-semantic-parent="47" data-semantic-owns="37 45" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="36" data-semantic-parent="46" data-semantic-owns="36" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="arrow" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="34,35" data-semantic-content="7" data-semantic-parent="37" data-semantic-owns="34 7 35" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-children="2,32" data-semantic-content="33,0" data-semantic-parent="36" data-semantic-owns="2 33 32" data-semantic-level-number="4" data-speech-node="true"><msub data-latex="H_{2}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="0,1" data-semantic-parent="34" data-semantic-attributes="latex:H_{2}" data-semantic-owns="0 1" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:H" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{2}"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="2" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">2</mn></mrow></msub><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="34" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-children="3,20" data-semantic-content="31,3" data-semantic-parent="34" data-semantic-owns="3 31 20" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:O" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">O</mi><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="32" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="5" data-semantic-content="4,6" data-semantic-parent="32" data-semantic-owns="4 5 6" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:l" data-semantic-level-number="7" data-speech-node="true">l</mi><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow></mrow></mrow><mo stretchy="false" data-latex="\rightarrow" data-semantic-type="relation" data-semantic-role="arrow" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:\rightarrow" data-semantic-operator="relseq,→" data-semantic-level-number="4" data-speech-node="true">→</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="30,26" data-semantic-content="15" data-semantic-parent="36" data-semantic-owns="30 15 26" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-children="10,28" data-semantic-content="29,8" data-semantic-parent="35" data-semantic-owns="10 29 28" data-semantic-level-number="5" data-speech-node="true"><msub data-latex="H_{2}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="8,9" data-semantic-parent="30" data-semantic-attributes="latex:H_{2}" data-semantic-owns="8 9" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:H" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{2}"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">2</mn></mrow></msub><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="30" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-children="11,21" data-semantic-content="27,11" data-semantic-parent="30" data-semantic-owns="11 27 21" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:O" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">O</mi><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="28" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:8" data-semantic-="" data-semantic-children="13" data-semantic-content="12,14" data-semantic-parent="28" data-semantic-owns="12 13 14" data-semantic-level-number="7" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">(</mo><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:s" data-semantic-level-number="8" data-speech-node="true">s</mi><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">)</mo></mrow></mrow></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="35" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="5" data-speech-node="true">+</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="16,24" data-semantic-content="25,16" data-semantic-parent="35" data-semantic-owns="16 25 24" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="h" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:h" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">h</mi><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="17,18,19" data-semantic-content="22,23" data-semantic-parent="26" data-semantic-owns="17 22 18 23 19" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="e" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:e" data-semantic-level-number="7" data-speech-node="true">e</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="24" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="a" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:a" data-semantic-level-number="7" data-speech-node="true">a</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="24" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="t" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="24" data-semantic-attributes="latex:t" data-semantic-level-number="7" data-speech-node="true">t</mi></mrow></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="44" data-semantic-parent="46" data-semantic-owns="44" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="inequality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="43,41" data-semantic-content="40" data-semantic-parent="45" data-semantic-owns="43 40 41" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="38,39" data-semantic-content="42" data-semantic-parent="44" data-semantic-owns="38 42 39" data-semantic-level-number="4" data-speech-node="true"><mi mathvariant="normal" data-latex="\Delta" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:\Delta" data-semantic-level-number="5" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="43" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:H" data-semantic-level-number="5" data-speech-node="true">H</mi></mrow><mo data-latex="<" data-semantic-type="relation" data-semantic-role="inequality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:<" data-semantic-operator="relseq,<" data-semantic-level-number="4" data-speech-node="true"><</mo><mn data-latex="0" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:0" data-semantic-level-number="4" data-speech-node="true">0</mn></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">In both cases, the <em>magnitude</em> of the enthalpy change is the same; only the <em>sign</em> is different.</p> </li> <li class="lt-chem-21722" style="background-color: unset;"><strong class="emphasis bold">Enthalpy is an extensive property (like mass).</strong> The magnitude of <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="146" style="font-size: 85%; position: relative;"><svg width="3.878ex" height="1.62ex" role="img" focusable="false" viewbox="0 -716 1714 716" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-147-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-147-NCM-N-2062" d=""></path><path id="MJX-147-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 39 37 39 15C39 5 45 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 323 39 302 39C262 39 242 43 242 52C242 52 243 55 245 68L312 336L605 336L538 68C535 53 523 43 503 40C498 39 481 39 452 39C433 39 424 31 424 15C424 5 430 0 442 0L568 3L631 2C642 2 683 0 696 0C712 0 720 8 720 24C720 34 709 39 688 39C647 39 627 43 627 52C627 52 628 55 630 68L764 602C769 623 778 636 791 641C797 643 814 644 843 644C869 644 881 644 881 668Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-147-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="2" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-147-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D43B" href="#MJX-147-NCM-I-1D43B"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true">H</mi></math></mjx-assistive-mml></mjx-container> for a reaction is proportional to the amounts of the substances that react. For example, a large fire produces more heat than a single match, even though the chemical reaction—the combustion of wood—is the same in both cases. For this reason, the enthalpy change for a reaction is usually given in kilojoules per mole of a particular reactant or product. Consider Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="147" style="font-size: 85%; position: relative;"><svg width="5.783ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2556 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-148-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-148-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-148-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path><path id="MJX-148-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path><path id="MJX-148-NCM-N-30" d="M249-22C390-22 460 92 460 320C460 473 428 575 365 625C330 652 291 666 250 666C109 666 39 551 39 320C39 136 88-22 249-22M361 524C368 489 371 425 371 332C371 240 367 172 360 128C347 48 310 8 249 8C226 8 203 17 182 34C155 57 139 104 132 176C129 201 128 253 128 332C128 419 131 480 136 513C145 568 163 603 191 618C213 630 232 636 249 636C314 636 350 583 361 524Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.4.9}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.04:_Enthalpy_of_Reaction#mjx-eqn:5.4.9"><g data-mml-node="mrow" data-latex="\ref{5.4.9}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2556" height="699" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.4.9};href:#mjx-eqn%3A5.4.9" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-148-NCM-N-35"></use><use data-c="2E" href="#MJX-148-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-148-NCM-N-34" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-148-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-148-NCM-N-31" transform="translate(1556,0)"></use><use data-c="30" href="#MJX-148-NCM-N-30" transform="translate(2056,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.4.9}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.4.9" data-latex="\ref{5.4.9}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.4.9};href:#mjx-eqn%3A5.4.9" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.4.10</mtext></mrow></math></mjx-assistive-mml></mjx-container>, which describes the reaction of aluminum with iron(III) oxide (Fe<sub>2</sub>O<sub>3</sub>) at constant pressure. 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data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="16" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="59" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:8" data-semantic-="" data-semantic-children="17,19" data-semantic-parent="59" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="17 19" data-semantic-level-number="7" data-speech-node="true"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">O</mi></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{3}"><mpadded height="0"><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:{\smash[t]{3}};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">3</mn></mpadded></mrow></mrow></msub><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="59" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:8" data-semantic-="" data-semantic-children="23" data-semantic-content="22,24" data-semantic-parent="59" data-semantic-owns="22 23 24" data-semantic-level-number="7" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-mjx-texclass="REL" data-latex="\mathrel{\mhchemlongrightarrow}"><mo data-mjx-variant="-mhchem" data-mjx-texclass="REL" stretchy="true" data-latex="\mhchemlongrightarrow" data-semantic-type="operator" data-semantic-role="unknown" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="69" data-semantic-attributes="latex:\mathrel{\mhchemlongrightarrow};texclass:REL" data-semantic-operator="infixop," data-semantic-level-number="4" data-speech-node="true"></mo></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="26,56" data-semantic-content="67" data-semantic-parent="69" data-semantic-owns="26 67 56" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="68" data-semantic-attributes="latex:2" data-semantic-level-number="5" data-speech-node="true">2</mn><mspace width="0.167em" data-latex="\,"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="68" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-children="28,48" data-semantic-content="55,28" data-semantic-parent="68" data-semantic-owns="28 55 48" data-semantic-level-number="5" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Fe}"><mi data-mjx-auto-op="false" data-latex="Fe" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="56" data-semantic-attributes="latex:\mathrm{Fe};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">Fe</mi></mrow><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="56" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="31" data-semantic-content="30,32" data-semantic-parent="56" data-semantic-owns="30 31 32" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="70" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="3" data-speech-node="true">+</mo><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="34,52" data-semantic-content="53,34" data-semantic-parent="70" data-semantic-owns="34 53 52" data-semantic-level-number="3" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Al}"><mi data-mjx-auto-op="false" data-latex="Al" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="54" data-semantic-attributes="latex:\mathrm{Al};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="4" data-speech-node="true">Al</mi></mrow><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="54" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="4" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="37,41,49" data-semantic-content="50,51" data-semantic-parent="54" data-semantic-owns="37 50 41 51 49" data-semantic-level-number="4" data-speech-node="true"><msub data-latex="{\vphantom{A}}_{\smash[t]{2}}" data-semantic-type="subscript" data-semantic-role="unknown" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="35,36" data-semantic-parent="52" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="35 36" data-semantic-level-number="5" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="52" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:6" data-semantic-="" data-semantic-children="38,40" data-semantic-parent="52" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="38 40" data-semantic-level-number="5" data-speech-node="true"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">O</mi></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{3}"><mpadded height="0"><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:{\smash[t]{3}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">3</mn></mpadded></mrow></mrow></msub><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="52" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="44" data-semantic-content="43,45" data-semantic-parent="52" data-semantic-owns="43 44 45" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="70" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="3" data-speech-node="true">+</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="72,74,75" data-semantic-content="76,77" data-semantic-parent="70" data-semantic-owns="72 76 74 77 75" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="815.5" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="78" data-semantic-attributes="latex:815.5" data-semantic-level-number="4" data-speech-node="true">815.5</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="78" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="78" data-semantic-attributes="latex:k" data-semantic-level-number="4" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="78" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="\label{5.4.9}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="78" data-semantic-attributes="latex:\label{5.4.9}" data-semantic-level-number="4" data-speech-node="true">J</mi></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">Thus Δ<em>H</em> = −851.5 kJ/mol of Fe<sub>2</sub>O<sub>3</sub>. We can also describe Δ<em>H</em> for the reaction as −425.8 kJ/mol of Al: because 2 mol of Al are consumed in the balanced chemical equation, we divide −851.5 kJ by 2. When a value for Δ<em>H</em>, in kilojoules rather than kilojoules per mole, is written after the reaction, as in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="149" style="font-size: 85%; position: relative;"><svg width="5.783ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2556 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-150-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 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data-latex="\ref{5.4.10}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.04:_Enthalpy_of_Reaction#mjx-eqn:5.4.10"><g data-mml-node="mrow" data-latex="\ref{5.4.10}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2556" height="699" x="0" y="-22"></rect><g data-mml-node="mtext" data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-id="0" data-semantic-attributes="latex:\ref{5.4.10};href:#mjx-eqn%3A5.4.10" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-150-NCM-N-35"></use><use data-c="2E" href="#MJX-150-NCM-N-2E" transform="translate(500,0)"></use><use data-c="34" href="#MJX-150-NCM-N-34" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-150-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-150-NCM-N-31" transform="translate(1556,0)"></use><use data-c="31" href="#MJX-150-NCM-N-31" transform="translate(2056,0)"></use></g></g></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.4.10}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.4.10" data-latex="\ref{5.4.10}" class="MathJax_ref"><mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:1" data-semantic-="" data-semantic-attributes="latex:\ref{5.4.10};href:#mjx-eqn%3A5.4.10" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.4.11</mtext></mrow></math></mjx-assistive-mml></mjx-container>, it is the value of Δ<em>H</em> corresponding to the reaction of the molar quantities of reactants as given in the balanced chemical equation: </p> <p class="mt-align-center lt-chem-21722" style="background-color: unset;"><mjx-container class="MathJax 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data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="unknown" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="66,68" data-semantic-content="25" data-semantic-parent="70" data-semantic-owns="66 25 68" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="65,61" data-semantic-content="12" data-semantic-parent="69" data-semantic-owns="65 12 61" data-semantic-level-number="5" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="5,63" data-semantic-content="64" data-semantic-parent="66" data-semantic-owns="5 64 63" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="65" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true">2</mn><mspace width="0.167em" data-latex="\,"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="65" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-children="7,46" data-semantic-content="62,7" data-semantic-parent="65" data-semantic-owns="7 62 46" data-semantic-level-number="7" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Al}"><mi data-mjx-auto-op="false" data-latex="Al" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:9" data-semantic-="" data-semantic-parent="63" data-semantic-attributes="latex:\mathrm{Al};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="8" data-speech-node="true">Al</mi></mrow><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:9" data-semantic-="" data-semantic-parent="63" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="8" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:9" data-semantic-="" data-semantic-children="10" data-semantic-content="9,11" data-semantic-parent="63" data-semantic-owns="9 10 11" data-semantic-level-number="8" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="46" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="46" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="46" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="66" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="6" data-speech-node="true">+</mo><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="13,59" data-semantic-content="60,13" data-semantic-parent="66" data-semantic-owns="13 60 59" data-semantic-level-number="6" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Fe}"><mi data-mjx-auto-op="false" data-latex="Fe" data-semantic-type="identifier" data-semantic-role="simple function" 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data-semantic-role="unknown" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-children="14,15" data-semantic-parent="59" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="14 15" data-semantic-level-number="8" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:10" data-semantic-="" data-semantic-parent="16" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="16" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="59" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:9" data-semantic-="" data-semantic-children="17,19" data-semantic-parent="59" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="17 19" data-semantic-level-number="8" data-speech-node="true"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">O</mi></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{3}"><mpadded height="0"><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:{\smash[t]{3}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">3</mn></mpadded></mrow></mrow></msub><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="59" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:9" data-semantic-="" data-semantic-children="23" data-semantic-content="22,24" data-semantic-parent="59" data-semantic-owns="22 23 24" data-semantic-level-number="8" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-mjx-texclass="REL" data-latex="\mathrel{\mhchemlongrightarrow}"><mo data-mjx-variant="-mhchem" data-mjx-texclass="REL" stretchy="true" data-latex="\mhchemlongrightarrow" data-semantic-type="operator" data-semantic-role="unknown" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="69" data-semantic-attributes="latex:\mathrel{\mhchemlongrightarrow};texclass:REL" data-semantic-operator="infixop," data-semantic-level-number="5" data-speech-node="true"></mo></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="26,56" data-semantic-content="67" data-semantic-parent="69" data-semantic-owns="26 67 56" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="68" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true">2</mn><mspace width="0.167em" data-latex="\,"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="68" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-children="28,48" data-semantic-content="55,28" data-semantic-parent="68" data-semantic-owns="28 55 48" data-semantic-level-number="6" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Fe}"><mi data-mjx-auto-op="false" data-latex="Fe" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="56" data-semantic-attributes="latex:\mathrm{Fe};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">Fe</mi></mrow><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="56" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:8" data-semantic-="" data-semantic-children="31" data-semantic-content="30,32" data-semantic-parent="56" data-semantic-owns="30 31 32" data-semantic-level-number="7" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="48" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="70" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="4" data-speech-node="true">+</mo><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="34,52" data-semantic-content="53,34" data-semantic-parent="70" data-semantic-owns="34 53 52" data-semantic-level-number="4" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Al}"><mi data-mjx-auto-op="false" data-latex="Al" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="54" data-semantic-attributes="latex:\mathrm{Al};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">Al</mi></mrow><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="54" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="37,41,49" data-semantic-content="50,51" data-semantic-parent="54" data-semantic-owns="37 50 41 51 49" data-semantic-level-number="5" data-speech-node="true"><msub data-latex="{\vphantom{A}}_{\smash[t]{2}}" data-semantic-type="subscript" data-semantic-role="unknown" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="35,36" data-semantic-parent="52" 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data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="52" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:7" data-semantic-="" data-semantic-children="38,40" data-semantic-parent="52" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="38 40" data-semantic-level-number="6" data-speech-node="true"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">O</mi></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{3}"><mpadded height="0"><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:{\smash[t]{3}};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">3</mn></mpadded></mrow></mrow></msub><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="52" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="44" data-semantic-content="43,45" data-semantic-parent="52" data-semantic-owns="43 44 45" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{s}"><mi mathvariant="normal" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">s</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="49" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow><mspace width="1em" data-latex="\quad" data-semantic-type="text" data-semantic-role="space" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:4" data-semantic-="" data-semantic-parent="96" data-semantic-attributes="latex:\quad" data-semantic-level-number="3" data-speech-node="true"></mspace><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="88,92" data-semantic-content="81" data-semantic-parent="96" data-semantic-owns="88 81 92" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="72,80" data-semantic-content="87" data-semantic-parent="93" data-semantic-owns="72 87 80" data-semantic-level-number="4" data-speech-node="true"><mi mathvariant="normal" data-latex="\Delta" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="88" data-semantic-attributes="latex:\Delta" data-semantic-level-number="5" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="88" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><msub data-latex="H_{r x n}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="73,79" data-semantic-parent="88" data-semantic-attributes="latex:H_{r x n}" data-semantic-owns="73 79" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="80" data-semantic-attributes="latex:H" data-semantic-level-number="6" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{r x n}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="74,75,76" data-semantic-content="77,78" data-semantic-parent="80" data-semantic-attributes="latex:{r x n};texclass:ORD" data-semantic-owns="74 77 75 78 76" data-semantic-level-number="6" data-speech-node="true"><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="79" data-semantic-attributes="latex:r" data-semantic-level-number="7" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="79" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="79" data-semantic-attributes="latex:x" data-semantic-level-number="7" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="79" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="79" data-semantic-attributes="latex:n" data-semantic-level-number="7" data-speech-node="true">n</mi></mrow></msub></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-children="91" data-semantic-content="82" data-semantic-parent="93" data-semantic-owns="82 91" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="92" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="5" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="83,85,86" data-semantic-content="89,90" data-semantic-parent="92" data-semantic-owns="83 89 85 90 86" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="851.5" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="91" data-semantic-attributes="latex:851.5" data-semantic-level-number="6" data-speech-node="true">851.5</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="91" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="91" data-semantic-attributes="latex:k" data-semantic-level-number="6" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="91" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="\label{5.4.10}" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="91" data-semantic-attributes="latex:\label{5.4.10}" data-semantic-level-number="6" data-speech-node="true">J</mi></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">If 4 mol of Al and 2 mol of <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="151" style="font-size: 85%; position: relative;"><svg width="6.217ex" height="1.994ex" role="img" focusable="false" viewbox="0 -716 2748.1 881.6" aria-hidden="true" style="vertical-align: -0.375ex;"><defs><path id="MJX-152-NCM-N-46" d="M275 641L393 641C464 641 510 626 533 597C565 558 569 521 578 450L611 450L582 680L33 680L33 641L61 641C96 641 117 639 124 634C131 629 135 617 135 599L135 81C135 63 131 51 124 46C117 41 96 39 61 39L33 39L33 0C59 2 110 3 187 3C274 3 330 2 357 0L357 39L320 39C267 39 238 44 233 55C231 60 230 69 230 82L230 321L311 321C354 321 382 313 394 298C406 283 412 253 412 206L444 206L444 475L412 475C412 429 406 398 394 383C382 368 354 360 311 360L230 360L230 606C230 642 236 641 275 641Z"></path><path id="MJX-152-NCM-N-65" d="M415 251C415 366 348 448 236 448C176 448 126 425 85 378C47 334 28 281 28 220C28 157 49 104 91 58C133 12 185-11 247-11C304-11 348 9 378 48C403 81 415 105 415 121C415 131 409 136 398 136C390 136 385 131 382 120C360 54 317 21 253 21C208 21 173 42 146 85C127 116 118 163 117 227L387 227C409 227 415 229 415 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data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-id="9" data-semantic-children="3,7" data-semantic-content="8" data-semantic-attributes="latex:\ce{Fe2O3};texclass:ORD" data-semantic-owns="3 8 7" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\mathrm{Fe}"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:2" data-semantic-id="3" data-semantic-children="0,2" data-semantic-parent="9" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="0 2" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mi" data-latex="Fe" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="3" data-semantic-attributes="latex:\mathrm{Fe};texclass:ORD" data-semantic-level-number="2" data-speech-node="true"><use data-c="46" href="#MJX-152-NCM-N-46"></use><use data-c="65" href="#MJX-152-NCM-N-65" transform="translate(653,0)"></use></g></g></g><g data-mml-node="msub" data-latex="{\vphantom{A}}_{\smash[t]{2}}" transform="translate(1097,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\vphantom{A}"><g data-mml-node="mpadded"><g data-mml-node="mphantom"></g></g></g></g><g data-mml-node="TeXAtom" transform="translate(33,-150) scale(0.707)" data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><g data-mml-node="mpadded"><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="2" data-speech-node="true"><use data-c="32" href="#MJX-152-NCM-N-32"></use></g></g></g></g></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="8" data-semantic-parent="9" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(1533.6,0)"><use data-c="2062" href="#MJX-152-NCM-N-2062"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\mathrm{O}" transform="translate(1533.6,0)"><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:2" data-semantic-id="7" data-semantic-children="4,6" data-semantic-parent="9" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="4 6" data-semantic-level-number="1" data-speech-node="true"><g data-mml-node="mi" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="4" data-semantic-parent="7" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="2" data-speech-node="true"><use data-c="4F" href="#MJX-152-NCM-N-4F"></use></g></g></g></g><g data-mml-node="msub" data-latex="{\vphantom{A}}_{\smash[t]{3}}" transform="translate(2311.6,0)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\vphantom{A}"><g data-mml-node="mpadded"><g data-mml-node="mphantom"></g></g></g></g><g data-mml-node="TeXAtom" transform="translate(33,-150) scale(0.707)" data-mjx-texclass="ORD" data-latex="{\smash[t]{3}}"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\smash[t]{3}"><g data-mml-node="mpadded"><g data-mml-node="mn" data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="6" data-semantic-parent="7" data-semantic-attributes="latex:{\smash[t]{3}};texclass:ORD" data-semantic-level-number="2" data-speech-node="true"><use data-c="33" href="#MJX-152-NCM-N-33"></use></g></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ce{Fe2O3}" data-semantic-structure="(9 (3 0 2) 8 (7 4 6))"><mrow data-mjx-texclass="ORD" data-latex="{\mathrm{Fe}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}{\vphantom{A}}_{\smash[t]{3}}}"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="3,7" data-semantic-content="8" data-semantic-attributes="latex:\ce{Fe2O3};texclass:ORD" data-semantic-owns="3 8 7" data-semantic-level-number="0" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Fe}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:2" data-semantic-="" data-semantic-children="0,2" data-semantic-parent="9" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="0 2" data-semantic-level-number="1" data-speech-node="true"><mi data-mjx-auto-op="false" data-latex="Fe" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\mathrm{Fe};texclass:ORD" data-semantic-level-number="2" data-speech-node="true">Fe</mi></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="2" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="9" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:2" data-semantic-="" data-semantic-children="4,6" data-semantic-parent="9" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="4 6" data-semantic-level-number="1" data-speech-node="true"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="2" data-speech-node="true">O</mi></mrow></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{3}"><mpadded height="0"><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:{\smash[t]{3}};texclass:ORD" data-semantic-level-number="2" data-speech-node="true">3</mn></mpadded></mrow></mrow></msub></mrow></math></mjx-assistive-mml></mjx-container> react, the change in enthalpy is 2 × (−851.5 kJ) = −1703 kJ. We can summarize the relationship between the amount of each substance and the enthalpy change for this reaction as follows:</p> <p class="mt-align-center lt-chem-21722" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="152" style="font-size: 85%; min-width: 58.561ex; position: relative;"><svg width="100%" height="4.676ex" role="img" focusable="false" data-mjx-viewbox="0 -1283.5 25884.1 2067" aria-hidden="true" style="vertical-align: -1.773ex; min-width: 58.561ex;"><defs><path id="MJX-153-NCM-N-2212" d="M698 270L80 270C64 270 56 263 56 250C56 237 64 230 80 230L698 230C714 230 722 237 722 250C722 262 710 270 698 270Z"></path><path id="MJX-153-NCM-N-38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 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data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-id="2" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true" transform="translate(2945,0)"><use data-c="29" href="#MJX-153-NCM-N-29"></use></g></g></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" - \dfrac{851.5 \; kJ}{2 \; mol \;Al} = - \dfrac{425.8 \; kJ}{1 \; mol \;Al} = - \dfrac{1703 \; kJ}{4 \; mol \; Al} \label{5.4.6a} " display="block" data-semantic-structure="(82 (81 (79 (76 5 (27 (12 6 10 8 11 9) (26 13 21 15 22 16 23 17 24 19 25 20))) 28 (77 29 (51 (36 30 34 32 35 33) (50 37 45 39 46 40 47 41 48 43 49 44))) 52 (78 53 (75 (60 54 58 56 59 57) (74 61 69 63 70 64 71 65 72 67 73 68)))) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="- \dfrac{851.5 \; kJ}{2 \; mol \;Al} = - \dfrac{425.8 \; kJ}{1 \; mol \;Al} = - \dfrac{1703 \; kJ}{4 \; mol \; Al} \label{5.4.6a}" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="81" data-semantic-attributes="latex: - \dfrac{851.5 \\0003B kJ}{2 \\0003B mol \\0003BAl} = - \dfrac{425.8 \\0003B kJ}{1 \\0003B mol \\0003BAl} = - \dfrac{1703 \\0003B kJ}{4 \\0003B mol \\0003B Al} \label{5.4.6a} " data-semantic-owns="81" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="79" data-semantic-content="4" data-semantic-parent="82" data-semantic-owns="79 4" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="81" data-semantic-owns="3" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:4" data-semantic-="" data-semantic-children="1" data-semantic-content="0,2" data-semantic-parent="4" data-semantic-owns="0 1 2" data-semantic-level-number="3" data-speech-node="true"><mtext data-latex="\text{(}" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{(}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">(</mtext><mtext data-latex="\text{5.4.12}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{5.4.12}" data-semantic-level-number="4" data-speech-node="true">5.4.12</mtext><mtext data-latex="\text{)}" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="general:text;depth:5" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:\text{)}" data-semantic-operator="fenced" data-semantic-level-number="4" data-speech-node="true">)</mtext></mrow></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="76,77,78" data-semantic-content="28,52" data-semantic-parent="81" data-semantic-owns="76 28 77 52 78" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="27" data-semantic-content="5" data-semantic-parent="79" data-semantic-owns="5 27" data-semantic-level-number="3" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="76" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="4" data-speech-node="true">−</mo><mfrac data-latex="\dfrac{851.5 \; kJ}{2 \; mol \;Al}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="12,26" data-semantic-parent="76" data-semantic-attributes="latex:\dfrac{851.5 \\0003B kJ}{2 \\0003B mol \\0003BAl}" data-semantic-owns="12 26" data-semantic-level-number="4" data-speech-node="true"><mrow data-latex="851.5 \; kJ" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="6,8,9" data-semantic-content="10,11" data-semantic-parent="27" data-semantic-attributes="latex:851.5 \\0003B kJ" data-semantic-owns="6 10 8 11 9" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="851.5" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:851.5" data-semantic-level-number="6" data-speech-node="true">851.5</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:k" data-semantic-level-number="6" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="12" data-semantic-attributes="latex:J" data-semantic-level-number="6" data-speech-node="true">J</mi></mrow><mrow data-latex="2 \; mol \;Al" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="13,15,16,17,19,20" data-semantic-content="21,22,23,24,25" data-semantic-parent="27" data-semantic-attributes="latex:2 \\0003B mol \\0003BAl" data-semantic-owns="13 21 15 22 16 23 17 24 19 25 20" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true">2</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:m" data-semantic-level-number="6" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="o" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:o" data-semantic-level-number="6" data-speech-node="true">o</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:l" data-semantic-level-number="6" data-speech-node="true">l</mi><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="A" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:A" data-semantic-level-number="6" data-speech-node="true">A</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:l" data-semantic-level-number="6" data-speech-node="true">l</mi></mrow></mfrac></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="79" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="51" data-semantic-content="29" data-semantic-parent="79" data-semantic-owns="29 51" data-semantic-level-number="3" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="77" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="4" data-speech-node="true">−</mo><mfrac data-latex="\dfrac{425.8 \; kJ}{1 \; mol \;Al}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="36,50" data-semantic-parent="77" data-semantic-attributes="latex:\dfrac{425.8 \\0003B kJ}{1 \\0003B mol \\0003BAl}" data-semantic-owns="36 50" data-semantic-level-number="4" data-speech-node="true"><mrow data-latex="425.8 \; kJ" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="30,32,33" data-semantic-content="34,35" data-semantic-parent="51" data-semantic-attributes="latex:425.8 \\0003B kJ" data-semantic-owns="30 34 32 35 33" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="425.8" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:425.8" data-semantic-level-number="6" data-speech-node="true">425.8</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="36" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:k" data-semantic-level-number="6" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="36" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="36" data-semantic-attributes="latex:J" data-semantic-level-number="6" data-speech-node="true">J</mi></mrow><mrow data-latex="1 \; mol \;Al" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="37,39,40,41,43,44" data-semantic-content="45,46,47,48,49" data-semantic-parent="51" data-semantic-attributes="latex:1 \\0003B mol \\0003BAl" data-semantic-owns="37 45 39 46 40 47 41 48 43 49 44" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:1" data-semantic-level-number="6" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:m" data-semantic-level-number="6" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="o" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:o" data-semantic-level-number="6" data-speech-node="true">o</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:l" data-semantic-level-number="6" data-speech-node="true">l</mi><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="A" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:A" data-semantic-level-number="6" data-speech-node="true">A</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="50" data-semantic-attributes="latex:l" data-semantic-level-number="6" data-speech-node="true">l</mi></mrow></mfrac></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="79" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="75" data-semantic-content="53" data-semantic-parent="79" data-semantic-owns="53 75" data-semantic-level-number="3" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="78" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="4" data-speech-node="true">−</mo><mfrac data-latex="\label{5.4.6a}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="60,74" data-semantic-parent="78" data-semantic-attributes="latex:\label{5.4.6a}" data-semantic-owns="60 74" data-semantic-level-number="4" data-speech-node="true"><mrow data-latex="1703 \; kJ" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="54,56,57" data-semantic-content="58,59" data-semantic-parent="75" data-semantic-attributes="latex:1703 \\0003B kJ" data-semantic-owns="54 58 56 59 57" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="1703" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="60" data-semantic-attributes="latex:1703" data-semantic-level-number="6" data-speech-node="true">1703</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="60" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="60" data-semantic-attributes="latex:k" data-semantic-level-number="6" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="60" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="60" data-semantic-attributes="latex:J" data-semantic-level-number="6" data-speech-node="true">J</mi></mrow><mrow data-latex="4 \; mol \; Al" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="61,63,64,65,67,68" data-semantic-content="69,70,71,72,73" data-semantic-parent="75" data-semantic-attributes="latex:4 \\0003B mol \\0003B Al" data-semantic-owns="61 69 63 70 64 71 65 72 67 73 68" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-attributes="latex:4" data-semantic-level-number="6" data-speech-node="true">4</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-attributes="latex:m" data-semantic-level-number="6" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="o" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-attributes="latex:o" data-semantic-level-number="6" data-speech-node="true">o</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-attributes="latex:l" data-semantic-level-number="6" data-speech-node="true">l</mi><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mi data-latex="A" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-attributes="latex:A" data-semantic-level-number="6" data-speech-node="true">A</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="74" data-semantic-attributes="latex:l" data-semantic-level-number="6" data-speech-node="true">l</mi></mrow></mfrac></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> </li> </ul> <p class="lt-chem-21722" style="background-color: unset;">The relationship between the magnitude of the enthalpy change and the mass of reactants is illustrated in Example <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="153" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2056 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-154-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-154-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-154-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path><path id="MJX-154-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-154-NCM-N-35"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-154-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="34" href="#MJX-154-NCM-N-34"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-154-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-154-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>.</p> <div class="box-example"> <span id="Example_.5C(.5CPageIndex.7B1.7D.5C):_Melting_Icebergs"></span><span id="Example_.5C(.5CPageIndex.7B1.7D.5C):_Melting_Icebergs"></span><h5 class="box-legend"><span class="lt-icon-default">Example <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="154" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2056 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-155-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-155-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-155-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path><path id="MJX-155-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use data-c="35" href="#MJX-155-NCM-N-35"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(500,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-155-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="2" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="34" href="#MJX-155-NCM-N-34"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{.}" transform="translate(1278,0)"><g data-mml-node="mo" data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-id="3" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true"><use data-c="2E" href="#MJX-155-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-155-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>: Melting Icebergs</span></h5> <p class="lt-chem-21722" style="background-color: unset;">Certain parts of the world, such as southern California and Saudi Arabia, are short of freshwater for drinking. One possible solution to the problem is to tow icebergs from Antarctica and then melt them as needed. If <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="155" style="font-size: 85%; position: relative;"><svg width="3.878ex" height="1.62ex" role="img" focusable="false" viewbox="0 -716 1714 716" aria-hidden="true" style="vertical-align: 0px;"><defs><path id="MJX-156-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-156-NCM-N-2062" d=""></path><path id="MJX-156-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 646C219 645 227 644 232 644C263 643 281 641 286 640C291 639 293 636 293 631C293 629 292 623 289 613L156 82C151 60 141 47 126 42C119 40 101 39 70 39C48 39 39 37 39 15C39 5 45 0 57 0L183 3L246 2C257 2 299 0 310 0C326 0 334 8 334 24C334 34 323 39 302 39C262 39 242 43 242 52C242 52 243 55 245 68L312 336L605 336L538 68C535 53 523 43 503 40C498 39 481 39 452 39C433 39 424 31 424 15C424 5 430 0 442 0L568 3L631 2C642 2 683 0 696 0C712 0 720 8 720 24C720 34 709 39 688 39C647 39 627 43 627 52C627 52 628 55 630 68L764 602C769 623 778 636 791 641C797 643 814 644 843 644C869 644 881 644 881 668Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-id="3" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" 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data-semantic-id="1" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="1D43B" href="#MJX-156-NCM-I-1D43B"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔH" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,1" data-semantic-content="2" data-semantic-attributes="latex:ΔH" data-semantic-owns="0 2 1" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(3 0 2 1)"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:2" data-semantic-="" data-semantic-parent="3" data-semantic-attributes="latex:H" data-semantic-level-number="1" data-speech-node="true">H</mi></math></mjx-assistive-mml></mjx-container> is 6.01 kJ/mol for the reaction at 0°C and constant pressure:</p> <p class="mt-align-center lt-chem-21722" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="156" style="font-size: 85%; min-width: 22.619ex; position: 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href="#MJX-157-NCM-N-28"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\mathrm{s}" transform="translate(389,0)"><g data-mml-node="mi" data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="8" data-semantic-parent="20" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="6" data-speech-node="true"><use data-c="73" href="#MJX-157-NCM-N-73"></use></g></g><g data-mml-node="mo" data-latex=")" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-id="9" data-semantic-parent="20" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true" transform="translate(783,0)"><use data-c="29" href="#MJX-157-NCM-N-29"></use></g></g></g></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="{}" 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data-semantic-parent="33" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-children="15,21" data-semantic-content="22,15" data-semantic-parent="33" data-semantic-owns="15 22 21" data-semantic-level-number="4" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">O</mi></mrow><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="23" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="18" data-semantic-content="17,19" data-semantic-parent="23" data-semantic-owns="17 18 19" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{l}"><mi mathvariant="normal" data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:\mathrm{l};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">l</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="21" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">How much energy would be required to melt a moderately large iceberg with a mass of 1.00 million metric tons (1.00 × 10<sup>6</sup> metric tons)? (A metric ton is 1000 kg.)</p> <p class="lt-chem-21722" style="background-color: unset;"><strong class="emphasis bold">Given: </strong>energy per mole of ice and mass of iceberg</p> <p class="lt-chem-21722" style="background-color: unset;"><strong class="emphasis bold">Asked for: </strong>energy required to melt iceberg</p> <span id="Strategy:"></span><span id="Strategy:"></span><h6>Strategy:</h6> <ol start="1" style="list-style-type: upper-alpha;"> <li class="lt-chem-21722" style="background-color: unset;">Calculate the number of moles of ice contained in 1 million metric tons (1.00 × 10<sup>6</sup> metric tons) of ice.</li> <li class="lt-chem-21722" style="background-color: unset;">Calculate the energy needed to melt the ice by multiplying the number of moles of ice in the iceberg by the amount of energy required to melt 1 mol of ice.</li> </ol> <span id="Solution:"></span><span id="Solution:"></span><h6>Solution:</h6> <p class="lt-chem-21722" style="background-color: unset;"><strong class="emphasis bold">A</strong> Because enthalpy is an extensive property, the amount of energy required to melt ice depends on the amount of ice present. 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\begin{align*} moles \; H_{2}O & = 1.00\times 10^{6} \; \cancel{\text{metric ton }} \ce{H2O} \left ( \dfrac{1000 \; \cancel{kg}}{1 \; \cancel{\text{metric ton}}} \right ) \left ( \dfrac{1000 \; \cancel{g}}{1 \; \cancel{kg}} \right ) \left ( \dfrac{1 \; mol \; H_{2}O}{18.015 \; \cancel{g \; H_{2}O}} \right ) \\[4pt] & = 5.55\times 10^{10} \; mol \,\ce{H2O} \end{align*} \nonumber " data-semantic-structure="(155 (122 (18 (17 0 12 1 13 2 14 3 15 4 16 (11 (8 6 7) 10 9))) (121 (120 112 20 (119 21 22 (118 (25 23 24) 113 (28 27) 114 (37 29 36 (35 (32 30 31) 34 33)) 115 (56 38 (54 (47 39 46 (45 (44 41 43 42))) (53 48 52 (51 50))) 55) 116 (75 57 (73 (63 58 62 (61 60)) (72 64 71 (70 (69 66 68 67)))) 74) 117 (111 76 (109 (93 77 89 79 90 80 91 81 92 (88 (85 83 84) 87 86)) (108 94 107 (106 (105 96 104 (103 (100 98 99) 102 101))))) 110)))))) (154 123 (153 (152 145 125 (151 126 127 (150 (130 128 129) 146 132 147 133 148 134 149 (144 136 143 (142 (139 137 138) 141 140))))))))"><g data-mml-node="mtable" 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data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><g data-mml-node="mpadded"><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-id="138" data-semantic-parent="139" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true"><use data-c="32" href="#MJX-158-NCM-N-32"></use></g></g></g></g></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-id="141" data-semantic-parent="142" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true" transform="translate(436.6,0)"><use data-c="2062" href="#MJX-158-NCM-N-2062"></use></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="\mathrm{O}" transform="translate(436.6,0)"><g data-mml-node="mi" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-id="140" data-semantic-parent="142" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="8" data-speech-node="true"><use data-c="4F" href="#MJX-158-NCM-N-4F"></use></g></g></g></g></g></g></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" \begin{align*} moles \; H_{2}O & = 1.00\times 10^{6} \; \cancel{\text{metric ton }} \ce{H2O} \left ( \dfrac{1000 \; \cancel{kg}}{1 \; \cancel{\text{metric ton}}} \right ) \left ( \dfrac{1000 \; \cancel{g}}{1 \; \cancel{kg}} \right ) \left ( \dfrac{1 \; mol \; H_{2}O}{18.015 \; \cancel{g \; H_{2}O}} \right ) \\[4pt] & = 5.55\times 10^{10} \; mol \,\ce{H2O} \end{align*} \nonumber " display="block" data-semantic-structure="(155 (122 (18 (17 0 12 1 13 2 14 3 15 4 16 (11 (8 6 7) 10 9))) (121 (120 112 20 (119 21 22 (118 (25 23 24) 113 (28 27) 114 (37 29 36 (35 (32 30 31) 34 33)) 115 (56 38 (54 (47 39 46 (45 (44 41 43 42))) (53 48 52 (51 50))) 55) 116 (75 57 (73 (63 58 62 (61 60)) (72 64 71 (70 (69 66 68 67)))) 74) 117 (111 76 (109 (93 77 89 79 90 80 91 81 92 (88 (85 83 84) 87 86)) (108 94 107 (106 (105 96 104 (103 (100 98 99) 102 101))))) 110)))))) (154 123 (153 (152 145 125 (151 126 127 (150 (130 128 129) 146 132 147 133 148 134 149 (144 136 143 (142 (139 137 138) 141 140))))))))"><mtable displaystyle="true" columnalign="right left" columnspacing="0em" rowspacing="0.7em 0.30000000000000004em" data-break-align="bottom top" data-latex="{\mathrm{H}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}} \end{align*} \nonumber" data-semantic-type="table" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="122,154" data-semantic-attributes="latex: \begin{align*} moles \\0003B H_{2}O & = 1.00\times 10^{6} \\0003B \cancel{\text{metric ton }} \ce{H2O} \left ( \dfrac{1000 \\0003B \cancel{kg}}{1 \\0003B \cancel{\text{metric ton}}} \right ) \left ( \dfrac{1000 \\0003B \cancel{g}}{1 \\0003B \cancel{kg}} \right ) \left ( \dfrac{1 \\0003B mol \\0003B H_{2}O}{18.015 \\0003B \cancel{g \\0003B H_{2}O}} \right ) \\[4pt] & = 5.55\times 10^{10} \\0003B mol \,\ce{H2O} \end{align*} \nonumber " data-semantic-owns="122 154" data-semantic-level-number="0" data-speech-node="true"><mtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="18,121" data-semantic-parent="155" data-semantic-owns="18 121" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="17" data-semantic-parent="122" data-semantic-owns="17" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="0,1,2,3,4,11" data-semantic-content="12,13,14,15,16" data-semantic-parent="18" data-semantic-owns="0 12 1 13 2 14 3 15 4 16 11" data-semantic-level-number="3" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-attributes="latex:m" data-semantic-level-number="4" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="o" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-attributes="latex:o" data-semantic-level-number="4" data-speech-node="true">o</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-attributes="latex:l" data-semantic-level-number="4" data-speech-node="true">l</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="e" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-attributes="latex:e" data-semantic-level-number="4" data-speech-node="true">e</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mi data-latex="s" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-attributes="latex:s" data-semantic-level-number="4" data-speech-node="true">s</mi><mspace width="0.278em" data-latex="\;"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="17" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-children="8,9" data-semantic-content="10,6" data-semantic-parent="17" data-semantic-owns="8 10 9" data-semantic-level-number="4" data-speech-node="true"><msub data-latex="H_{2}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="6,7" data-semantic-parent="11" data-semantic-attributes="latex:H_{2}" data-semantic-owns="6 7" data-semantic-level-number="5" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-operator="appl" data-semantic-level-number="6" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{2}"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">2</mn></mrow></msub><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="11" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">⁡</mo><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="11" data-semantic-attributes="latex:O" data-semantic-level-number="5" data-speech-node="true">O</mi></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="120" data-semantic-parent="122" data-semantic-owns="120" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="112,119" data-semantic-content="20" data-semantic-parent="121" data-semantic-owns="112 20 119" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="120" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="120" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="21,118" data-semantic-content="22" data-semantic-parent="120" data-semantic-owns="21 22 118" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="1.00" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="119" data-semantic-attributes="latex:1.00" data-semantic-level-number="5" data-speech-node="true">1.00</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="119" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="5" data-speech-node="true">×</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="25,28,37,56,75,111" data-semantic-content="113,114,115,116,117" data-semantic-parent="119" data-semantic-owns="25 113 28 114 37 115 56 116 75 117 111" data-semantic-level-number="5" data-speech-node="true"><msup data-latex="10^{6}" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="23,24" data-semantic-parent="118" data-semantic-attributes="latex:10^{6}" data-semantic-owns="23 24" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:10" data-semantic-level-number="7" data-speech-node="true">10</mn><mrow data-mjx-texclass="ORD" data-latex="{6}"><mn data-latex="6" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:{6};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">6</mn></mrow></msup><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="118" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{\text{metric ton }}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="27" data-semantic-parent="118" data-semantic-attributes="latex:\cancel{\text{metric ton }}" data-semantic-owns="27" data-semantic-level-number="6" data-speech-node="true"><mtext data-latex="\text{metric ton }" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:\text{metric ton }" data-semantic-level-number="7" data-speech-node="true">metric ton </mtext></menclose><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="118" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="{\mathrm{H}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}}" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="29,35" data-semantic-content="36,29" data-semantic-parent="118" data-semantic-attributes="latex:{\mathrm{H}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}};texclass:ORD" data-semantic-owns="29 36 35" data-semantic-level-number="6" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{H}"><mi mathvariant="normal" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="37" data-semantic-attributes="latex:\mathrm{H};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">H</mi></mrow><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="37" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="32,33" data-semantic-content="34" data-semantic-parent="37" data-semantic-owns="32 34 33" data-semantic-level-number="7" data-speech-node="true"><msub data-latex="{\vphantom{A}}_{\smash[t]{2}}" data-semantic-type="subscript" data-semantic-role="unknown" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-children="30,31" data-semantic-parent="35" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="30 31" data-semantic-level-number="8" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:10" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="35" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="35" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">O</mi></mrow></mrow></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="118" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left( \dfrac{1000 \; \cancel{kg}}{1 \; \cancel{\text{metric ton}}} \right )" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="54" data-semantic-content="38,55" data-semantic-parent="118" data-semantic-attributes="latex:\left( \dfrac{1000 \\0003B \cancel{kg}}{1 \\0003B \cancel{\text{metric ton}}} \right );texclass:INNER" data-semantic-owns="38 54 55" data-semantic-level-number="6" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="56" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1000 \; \cancel{kg}}{1 \; \cancel{\text{metric ton}}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="47,53" data-semantic-parent="56" data-semantic-attributes="latex:\dfrac{1000 \\0003B \cancel{kg}}{1 \\0003B \cancel{\text{metric ton}}}" data-semantic-owns="47 53" data-semantic-level-number="7" data-speech-node="true"><mrow data-latex="1000 \; \cancel{kg}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="39,45" data-semantic-content="46" data-semantic-parent="54" data-semantic-attributes="latex:1000 \\0003B \cancel{kg}" data-semantic-owns="39 46 45" data-semantic-level-number="8" data-speech-node="true"><mn data-latex="1000" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:1000" data-semantic-level-number="9" data-speech-node="true">1000</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{kg}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="44" data-semantic-parent="47" data-semantic-attributes="latex:\cancel{kg}" data-semantic-owns="44" data-semantic-level-number="9" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:11" data-semantic-="" data-semantic-children="41,42" data-semantic-content="43" data-semantic-parent="45" data-semantic-owns="41 43 42" data-semantic-level-number="10" data-speech-node="true"><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:k" data-semantic-level-number="11" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="44" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="11" data-speech-node="true">⁢</mo><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="44" data-semantic-attributes="latex:g" data-semantic-level-number="11" data-speech-node="true">g</mi></mrow></menclose></mrow><mrow data-latex="1 \; \cancel{\text{metric ton}}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="48,51" data-semantic-content="52" data-semantic-parent="54" data-semantic-attributes="latex:1 \\0003B \cancel{\text{metric ton}}" data-semantic-owns="48 52 51" data-semantic-level-number="8" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="53" data-semantic-attributes="latex:1" data-semantic-level-number="9" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="53" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{\text{metric ton}}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="50" data-semantic-parent="53" data-semantic-attributes="latex:\cancel{\text{metric ton}}" data-semantic-owns="50" data-semantic-level-number="9" data-speech-node="true"><mtext data-latex="\text{metric ton}" data-semantic-type="text" data-semantic-role="text" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:11" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:\text{metric ton}" data-semantic-level-number="10" data-speech-node="true">metric ton</mtext></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="56" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="118" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left( \dfrac{1000 \; \cancel{g}}{1 \; \cancel{kg}} \right )" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="73" data-semantic-content="57,74" data-semantic-parent="118" data-semantic-attributes="latex:\left( \dfrac{1000 \\0003B \cancel{g}}{1 \\0003B \cancel{kg}} \right );texclass:INNER" data-semantic-owns="57 73 74" data-semantic-level-number="6" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="75" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1000 \; \cancel{g}}{1 \; \cancel{kg}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="63,72" data-semantic-parent="75" data-semantic-attributes="latex:\dfrac{1000 \\0003B \cancel{g}}{1 \\0003B \cancel{kg}}" data-semantic-owns="63 72" data-semantic-level-number="7" data-speech-node="true"><mrow data-latex="1000 \; \cancel{g}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="58,61" data-semantic-content="62" data-semantic-parent="73" data-semantic-attributes="latex:1000 \\0003B \cancel{g}" data-semantic-owns="58 62 61" data-semantic-level-number="8" data-speech-node="true"><mn data-latex="1000" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="63" data-semantic-attributes="latex:1000" data-semantic-level-number="9" data-speech-node="true">1000</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="63" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{g}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="60" data-semantic-parent="63" data-semantic-attributes="latex:\cancel{g}" data-semantic-owns="60" data-semantic-level-number="9" data-speech-node="true"><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:11" data-semantic-="" data-semantic-parent="61" data-semantic-attributes="latex:g" data-semantic-level-number="10" data-speech-node="true">g</mi></menclose></mrow><mrow data-latex="1 \; \cancel{kg}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="64,70" data-semantic-content="71" data-semantic-parent="73" data-semantic-attributes="latex:1 \\0003B \cancel{kg}" data-semantic-owns="64 71 70" data-semantic-level-number="8" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="72" data-semantic-attributes="latex:1" data-semantic-level-number="9" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="72" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{kg}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="69" data-semantic-parent="72" data-semantic-attributes="latex:\cancel{kg}" data-semantic-owns="69" data-semantic-level-number="9" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:11" data-semantic-="" data-semantic-children="66,67" data-semantic-content="68" data-semantic-parent="70" data-semantic-owns="66 68 67" data-semantic-level-number="10" data-speech-node="true"><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="69" data-semantic-attributes="latex:k" data-semantic-level-number="11" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="69" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="11" data-speech-node="true">⁢</mo><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="69" data-semantic-attributes="latex:g" data-semantic-level-number="11" data-speech-node="true">g</mi></mrow></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="75" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="118" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left( \dfrac{1 \; mol \; H_{2}O}{18.015 \; \cancel{g \; H_{2}O}} \right )" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:7" data-semantic-="" data-semantic-children="109" data-semantic-content="76,110" data-semantic-parent="118" data-semantic-attributes="latex:\left( \dfrac{1 \\0003B mol \\0003B H_{2}O}{18.015 \\0003B \cancel{g \\0003B H_{2}O}} \right );texclass:INNER" data-semantic-owns="76 109 110" data-semantic-level-number="6" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="111" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{1 \; mol \; H_{2}O}{18.015 \; \cancel{g \; H_{2}O}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="93,108" data-semantic-parent="111" data-semantic-attributes="latex:\dfrac{1 \\0003B mol \\0003B H_{2}O}{18.015 \\0003B \cancel{g \\0003B H_{2}O}}" data-semantic-owns="93 108" data-semantic-level-number="7" data-speech-node="true"><mrow data-latex="1 \; mol \; H_{2}O" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="77,79,80,81,88" data-semantic-content="89,90,91,92" data-semantic-parent="109" data-semantic-attributes="latex:1 \\0003B mol \\0003B H_{2}O" data-semantic-owns="77 89 79 90 80 91 81 92 88" data-semantic-level-number="8" data-speech-node="true"><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:1" data-semantic-level-number="9" data-speech-node="true">1</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="93" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true"></mspace><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:m" data-semantic-level-number="9" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="93" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="o" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:o" data-semantic-level-number="9" data-speech-node="true">o</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="93" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:l" data-semantic-level-number="9" data-speech-node="true">l</mi><mspace width="0.278em" data-latex="\;"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="93" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-children="85,86" data-semantic-content="87,83" data-semantic-parent="93" data-semantic-owns="85 87 86" data-semantic-level-number="9" data-speech-node="true"><msub data-latex="H_{2}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:11" data-semantic-="" data-semantic-children="83,84" data-semantic-parent="88" data-semantic-attributes="latex:H_{2}" data-semantic-owns="83 84" data-semantic-level-number="10" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:12" data-semantic-="" data-semantic-parent="85" data-semantic-attributes="latex:H" data-semantic-operator="appl" data-semantic-level-number="11" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{2}"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="85" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">2</mn></mrow></msub><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:11" data-semantic-="" data-semantic-parent="88" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="10" data-speech-node="true">⁡</mo><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:11" data-semantic-="" data-semantic-parent="88" data-semantic-attributes="latex:O" data-semantic-level-number="10" data-speech-node="true">O</mi></mrow></mrow><mrow data-latex="18.015 \; \cancel{g \; H_{2}O}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="94,106" data-semantic-content="107" data-semantic-parent="109" data-semantic-attributes="latex:18.015 \\0003B \cancel{g \\0003B H_{2}O}" data-semantic-owns="94 107 106" data-semantic-level-number="8" data-speech-node="true"><mn data-latex="18.015" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="108" data-semantic-attributes="latex:18.015" data-semantic-level-number="9" data-speech-node="true">18.015</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="108" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{g \; H_{2}O}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="105" data-semantic-parent="108" data-semantic-attributes="latex:\cancel{g \\0003B H_{2}O}" data-semantic-owns="105" data-semantic-level-number="9" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:11" data-semantic-="" data-semantic-children="96,103" data-semantic-content="104,96" data-semantic-parent="106" data-semantic-owns="96 104 103" data-semantic-level-number="10" data-speech-node="true"><mi data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:12" data-semantic-="" data-semantic-parent="105" data-semantic-attributes="latex:g" data-semantic-operator="appl" data-semantic-level-number="11" data-speech-node="true">g</mi><mspace width="0.278em" data-latex="\;"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:12" data-semantic-="" data-semantic-parent="105" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="11" data-speech-node="true">⁡</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-children="100,101" data-semantic-content="102,98" data-semantic-parent="105" data-semantic-owns="100 102 101" data-semantic-level-number="11" data-speech-node="true"><msub data-latex="H_{2}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:13" data-semantic-="" data-semantic-children="98,99" data-semantic-parent="103" data-semantic-attributes="latex:H_{2}" data-semantic-owns="98 99" data-semantic-level-number="12" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:14" data-semantic-="" data-semantic-parent="100" data-semantic-attributes="latex:H" data-semantic-operator="appl" data-semantic-level-number="13" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{2}"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:14" data-semantic-="" data-semantic-parent="100" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="13" data-speech-node="true">2</mn></mrow></msub><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:13" data-semantic-="" data-semantic-parent="103" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="12" data-speech-node="true">⁡</mo><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:13" data-semantic-="" data-semantic-parent="103" data-semantic-attributes="latex:O" data-semantic-level-number="12" data-speech-node="true">O</mi></mrow></mrow></menclose></mrow></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="111" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mstyle></mtd></mtr><mtr data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="123,153" data-semantic-parent="155" data-semantic-owns="123 153" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:3" data-semantic-="" data-semantic-parent="154" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="152" data-semantic-parent="154" data-semantic-owns="152" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="145,151" data-semantic-content="125" data-semantic-parent="153" data-semantic-owns="145 125 151" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="152" data-semantic-level-number="4" data-speech-node="true"></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="152" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="4" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="126,150" data-semantic-content="127" data-semantic-parent="152" data-semantic-owns="126 127 150" data-semantic-level-number="4" data-speech-node="true"><mn data-latex="5.55" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" 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data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:10" data-semantic-="" data-semantic-parent="139" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="139" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="142" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="142" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">O</mi></mrow></mrow></mrow></mrow></mrow></mrow></mstyle></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;"><strong class="emphasis bold">B</strong> The energy needed to melt the iceberg is thus</p> <p class="mt-align-center lt-chem-21722" style="background-color: unset;"><mjx-container 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data-semantic-children="26,53" data-semantic-content="63" data-semantic-parent="69" data-semantic-owns="26 63 53" data-semantic-level-number="3" data-speech-node="true"><g data-mml-node="TeXAtom" data-mjx-texclass="INNER" data-latex="\left( \dfrac{6.01 \; kJ}{\cancel{mol \; H_{2}O}} \right )" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-id="26" data-semantic-children="24" data-semantic-content="1,25" data-semantic-parent="64" data-semantic-attributes="latex:\left( \dfrac{6.01 \\0003B kJ}{\cancel{mol \\0003B H_{2}O}} \right );texclass:INNER" data-semantic-owns="1 24 25" data-semantic-level-number="4" data-speech-node="true"><g data-mml-node="mo" data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-id="1" data-semantic-parent="26" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true"><use data-c="28" href="#MJX-159-NCM-S7-28"></use></g><g data-mml-node="mfrac" data-latex="\dfrac{6.01 \; kJ}{\cancel{mol \; H_{2}O}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-id="24" data-semantic-children="8,23" data-semantic-parent="26" data-semantic-attributes="latex:\dfrac{6.01 \\0003B kJ}{\cancel{mol \\0003B H_{2}O}}" data-semantic-owns="8 23" data-semantic-level-number="5" data-speech-node="true" transform="translate(875,0)"><g data-mml-node="mrow" data-latex="6.01 \; kJ" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-id="8" data-semantic-children="2,4,5" data-semantic-content="6,7" data-semantic-parent="24" data-semantic-attributes="latex:6.01 \\0003B kJ" data-semantic-owns="2 6 4 7 5" data-semantic-level-number="6" data-speech-node="true" 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href="#MJX-159-NCM-N-33"></use><use data-c="2E" href="#MJX-159-NCM-N-2E" transform="translate(500,0)"></use><use data-c="33" href="#MJX-159-NCM-N-33" transform="translate(778,0)"></use><use data-c="34" href="#MJX-159-NCM-N-34" transform="translate(1278,0)"></use></g><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-id="56" data-semantic-parent="68" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="4" data-speech-node="true" transform="translate(2000.2,0)"><use data-c="D7" href="#MJX-159-NCM-N-D7"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-id="67" data-semantic-children="59,61,62" data-semantic-content="65,66" data-semantic-parent="68" data-semantic-owns="59 65 61 66 62" data-semantic-level-number="4" data-speech-node="true" transform="translate(3000.4,0)"><g data-mml-node="msup" data-latex="10^{11}" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:6" data-semantic-id="59" data-semantic-children="57,58" data-semantic-parent="67" data-semantic-attributes="latex:10^{11}" data-semantic-owns="57 58" data-semantic-level-number="5" data-speech-node="true"><g data-mml-node="mn" data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="57" data-semantic-parent="59" data-semantic-attributes="latex:10" data-semantic-level-number="6" data-speech-node="true"><use data-c="31" href="#MJX-159-NCM-N-31"></use><use data-c="30" href="#MJX-159-NCM-N-30" transform="translate(500,0)"></use></g><g data-mml-node="TeXAtom" transform="translate(1033,413) scale(0.707)" data-mjx-texclass="ORD" data-latex="{11}"><g data-mml-node="mn" data-latex="11" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-id="58" data-semantic-parent="59" data-semantic-attributes="latex:{11};texclass:ORD" data-semantic-level-number="6" data-speech-node="true"><use data-c="31" href="#MJX-159-NCM-N-31"></use><use data-c="31" href="#MJX-159-NCM-N-31" transform="translate(500,0)"></use></g></g></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:6" data-semantic-id="65" data-semantic-parent="67" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true" transform="translate(1790.1,0)"></g><g data-mml-node="mi" data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-id="61" data-semantic-parent="67" data-semantic-attributes="latex:k" data-semantic-level-number="5" data-speech-node="true" transform="translate(2068.1,0)"><use data-c="1D458" href="#MJX-159-NCM-I-1D458"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-id="66" data-semantic-parent="67" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true" transform="translate(2589.1,0)"><use data-c="2062" href="#MJX-159-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-id="62" data-semantic-parent="67" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="5" data-speech-node="true" transform="translate(2589.1,0)"><use data-c="1D43D" href="#MJX-159-NCM-I-1D43D"></use></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -1797 1 3094"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:" data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="71" data-semantic-level-number="2" data-speech-node="true" transform="translate(0,52)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,0)"></g></g></g></svg></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" \left ( \dfrac{6.01 \; kJ}{\cancel{mol \; H_{2}O}} \right )\left ( 5.55 \times 10^{10} \; \cancel{mol \; H_{2}O} \right )= 3.34 \times 10^{11} \; kJ \nonumber " display="block" data-semantic-structure="(72 (71 (69 (64 (26 1 (24 (8 2 6 4 7 5) (23 (22 9 19 10 20 11 21 (18 (15 13 14) 17 16)))) 25) 63 (53 27 (52 28 29 (51 (32 30 31) 50 (48 (47 34 44 35 45 36 46 (43 (40 38 39) 42 41))))) 49)) 54 (68 55 56 (67 (59 57 58) 65 61 66 62))) 0))"><mtable displaystyle="true" data-latex="\left ( \dfrac{6.01 \; kJ}{\cancel{mol \; H_{2}O}} \right )\left ( 5.55 \times 10^{10} \; \cancel{mol \; H_{2}O} \right )= 3.34 \times 10^{11} \; kJ \nonumber" data-semantic-type="multiline" data-semantic-role="equality" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="71" data-semantic-attributes="latex: \left ( \dfrac{6.01 \\0003B kJ}{\cancel{mol \\0003B H_{2}O}} \right )\left ( 5.55 \times 10^{10} \\0003B \cancel{mol \\0003B H_{2}O} \right )= 3.34 \times 10^{11} \\0003B kJ \nonumber " data-semantic-owns="71" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="69" data-semantic-content="0" data-semantic-parent="72" data-semantic-owns="69 0" data-semantic-level-number="1" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="label" data-semantic-annotation="nemeth:number;depth:3" data-semantic-id="0" data-semantic-parent="71" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="64,68" data-semantic-content="54" data-semantic-parent="71" data-semantic-owns="64 54 68" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="26,53" data-semantic-content="63" data-semantic-parent="69" data-semantic-owns="26 63 53" data-semantic-level-number="3" data-speech-node="true"><mrow data-mjx-texclass="INNER" data-latex="\left( \dfrac{6.01 \; kJ}{\cancel{mol \; H_{2}O}} \right )" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="24" data-semantic-content="1,25" data-semantic-parent="64" data-semantic-attributes="latex:\left( \dfrac{6.01 \\0003B kJ}{\cancel{mol \\0003B H_{2}O}} \right );texclass:INNER" data-semantic-owns="1 24 25" data-semantic-level-number="4" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mfrac data-latex="\dfrac{6.01 \; kJ}{\cancel{mol \; H_{2}O}}" data-semantic-type="fraction" data-semantic-role="division" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="8,23" data-semantic-parent="26" data-semantic-attributes="latex:\dfrac{6.01 \\0003B kJ}{\cancel{mol \\0003B H_{2}O}}" data-semantic-owns="8 23" data-semantic-level-number="5" data-speech-node="true"><mrow data-latex="6.01 \; kJ" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="2,4,5" data-semantic-content="6,7" data-semantic-parent="24" data-semantic-attributes="latex:6.01 \\0003B kJ" data-semantic-owns="2 6 4 7 5" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="6.01" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:6.01" data-semantic-level-number="7" data-speech-node="true">6.01</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="8" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:k" data-semantic-level-number="7" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="8" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:J" data-semantic-level-number="7" data-speech-node="true">J</mi></mrow><menclose notation="updiagonalstrike" data-latex="\cancel{mol \; H_{2}O}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="22" data-semantic-parent="24" data-semantic-attributes="latex:\cancel{mol \\0003B H_{2}O}" data-semantic-owns="22" data-semantic-level-number="6" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="9,10,11,18" data-semantic-content="19,20,21" data-semantic-parent="23" data-semantic-owns="9 19 10 20 11 21 18" data-semantic-level-number="7" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="22" data-semantic-attributes="latex:m" data-semantic-level-number="8" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="22" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="o" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="22" data-semantic-attributes="latex:o" data-semantic-level-number="8" data-speech-node="true">o</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="22" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="22" data-semantic-attributes="latex:l" data-semantic-level-number="8" data-speech-node="true">l</mi><mspace width="0.278em" data-latex="\;"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="22" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-children="15,16" data-semantic-content="17,13" data-semantic-parent="22" data-semantic-owns="15 17 16" data-semantic-level-number="8" data-speech-node="true"><msub data-latex="H_{2}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="13,14" data-semantic-parent="18" data-semantic-attributes="latex:H_{2}" data-semantic-owns="13 14" data-semantic-level-number="9" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:11" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:H" data-semantic-operator="appl" data-semantic-level-number="10" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{2}"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:11" data-semantic-="" data-semantic-parent="15" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="10" data-speech-node="true">2</mn></mrow></msub><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:10" data-semantic-="" data-semantic-parent="18" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="9" data-speech-node="true">⁡</mo><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:10" data-semantic-="" data-semantic-parent="18" data-semantic-attributes="latex:O" data-semantic-level-number="9" data-speech-node="true">O</mi></mrow></mrow></menclose></mfrac><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="64" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="4" data-speech-node="true">⁢</mo><mrow data-mjx-texclass="INNER" data-latex="\left( 5.55 \times 10^{10} \; \cancel{mol \; H_{2}O} \right )" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="52" data-semantic-content="27,49" data-semantic-parent="64" data-semantic-attributes="latex:\left( 5.55 \times 10^{10} \\0003B \cancel{mol \\0003B H_{2}O} \right );texclass:INNER" data-semantic-owns="27 52 49" data-semantic-level-number="4" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="53" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="28,51" data-semantic-content="29" data-semantic-parent="53" data-semantic-owns="28 29 51" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="5.55" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="52" data-semantic-attributes="latex:5.55" data-semantic-level-number="6" data-speech-node="true">5.55</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="52" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="6" data-speech-node="true">×</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="32,48" data-semantic-content="50" data-semantic-parent="52" data-semantic-owns="32 50 48" data-semantic-level-number="6" data-speech-node="true"><msup data-latex="10^{10}" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="30,31" data-semantic-parent="51" data-semantic-attributes="latex:10^{10}" data-semantic-owns="30 31" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:10" data-semantic-level-number="8" data-speech-node="true">10</mn><mrow data-mjx-texclass="ORD" data-latex="{10}"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:{10};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">10</mn></mrow></msup><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="51" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true"></mspace><menclose notation="updiagonalstrike" data-latex="\cancel{mol \; H_{2}O}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="47" data-semantic-parent="51" data-semantic-attributes="latex:\cancel{mol \\0003B H_{2}O}" data-semantic-owns="47" data-semantic-level-number="7" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-children="34,35,36,43" data-semantic-content="44,45,46" data-semantic-parent="48" data-semantic-owns="34 44 35 45 36 46 43" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="m" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:m" data-semantic-level-number="9" data-speech-node="true">m</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="o" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:o" data-semantic-level-number="9" data-speech-node="true">o</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mi data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-attributes="latex:l" data-semantic-level-number="9" data-speech-node="true">l</mi><mspace width="0.278em" data-latex="\;"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="47" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" data-speech-node="true">⁢</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-children="40,41" data-semantic-content="42,38" data-semantic-parent="47" data-semantic-owns="40 42 41" data-semantic-level-number="9" data-speech-node="true"><msub data-latex="H_{2}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:11" data-semantic-="" data-semantic-children="38,39" data-semantic-parent="43" data-semantic-attributes="latex:H_{2}" data-semantic-owns="38 39" data-semantic-level-number="10" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:12" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:H" data-semantic-operator="appl" data-semantic-level-number="11" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{2}"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">2</mn></mrow></msub><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:11" data-semantic-="" data-semantic-parent="43" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="10" data-speech-node="true">⁡</mo><mi data-latex="O" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:11" data-semantic-="" data-semantic-parent="43" data-semantic-attributes="latex:O" data-semantic-level-number="10" data-speech-node="true">O</mi></mrow></mrow></menclose></mrow></mrow><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="53" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="69" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="3" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="55,67" data-semantic-content="56" data-semantic-parent="69" data-semantic-owns="55 56 67" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="3.34" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:5" data-semantic-="" data-semantic-parent="68" data-semantic-attributes="latex:3.34" data-semantic-level-number="4" data-speech-node="true">3.34</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="68" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="4" data-speech-node="true">×</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="59,61,62" data-semantic-content="65,66" data-semantic-parent="68" data-semantic-owns="59 65 61 66 62" data-semantic-level-number="4" data-speech-node="true"><msup data-latex="10^{11}" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="57,58" data-semantic-parent="67" data-semantic-attributes="latex:10^{11}" data-semantic-owns="57 58" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="59" data-semantic-attributes="latex:10" data-semantic-level-number="6" data-speech-node="true">10</mn><mrow data-mjx-texclass="ORD" data-latex="{11}"><mn data-latex="11" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="59" data-semantic-attributes="latex:{11};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">11</mn></mrow></msup><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="67" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="67" data-semantic-attributes="latex:k" data-semantic-level-number="5" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="67" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="67" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="5" data-speech-node="true">J</mi></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21722" style="background-color: unset;">Because so much energy is needed to melt the iceberg, this plan would require a relatively inexpensive source of energy to be practical. To give you some idea of the scale of such an operation, the amounts of different energy sources equivalent to the amount of energy needed to melt the iceberg are shown below.</p> <p class="lt-chem-21722" style="background-color: unset;">Possible sources of the approximately <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="159" style="font-size: 85%; position: relative;"><svg width="4.023ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1778 1000" aria-hidden="true" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3.34 \times 10^{11}\, kJ" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-id="11" data-semantic-children="0,10" data-semantic-content="1" data-semantic-attributes="latex:3.34 \times 10^{11}\, kJ" data-semantic-owns="0 1 10" 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90C71 20 132-22 205-22C255-22 301-6 344 26C387 58 415 97 427 144L542 606C551 642 555 644 602 644C623 644 633 646 633 667Z"></path></defs></svg><mjx-break size="3"> </mjx-break><svg width="6.313ex" height="2.52ex" role="img" focusable="false" viewbox="0 -864 2790.3 1114" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3.34 \times 10^{11}\, kJ" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-id="11" data-semantic-children="0,10" data-semantic-content="1" data-semantic-attributes="latex:3.34 \times 10^{11}\, kJ" data-semantic-owns="0 1 10" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(11 0 1 (10 (4 2 3) 8 6 9 7))"><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="1" data-semantic-parent="11" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="1" data-speech-node="true"><use data-c="D7" href="#MJX-160-NCM-N-D7"></use></g><g data-mml-node="mrow" data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:2" data-semantic-id="10" data-semantic-children="4,6,7" data-semantic-content="8,9" data-semantic-parent="11" data-semantic-owns="4 8 6 9 7" data-semantic-level-number="1" data-speech-node="true" transform="translate(1000.2,0)"><g data-mml-node="msup" data-latex="10^{11}" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:3" data-semantic-id="4" data-semantic-children="2,3" data-semantic-parent="10" data-semantic-attributes="latex:10^{11}" data-semantic-owns="2 3" data-semantic-level-number="2" data-speech-node="true"><g data-mml-node="mn" data-latex="10" data-semantic-type="number" 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data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:3" data-semantic-id="8" data-semantic-parent="10" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true" transform="translate(1790.1,0)"></g></g></g></g></svg><mjx-break size="0"> </mjx-break><svg width="2.989ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1321 1000" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3.34 \times 10^{11}\, kJ" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-id="11" data-semantic-children="0,10" data-semantic-content="1" data-semantic-attributes="latex:3.34 \times 10^{11}\, kJ" data-semantic-owns="0 1 10" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(11 0 1 (10 (4 2 3) 8 6 9 7))"><g data-mml-node="mrow" 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href="#MJX-160-NCM-I-1D458"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-id="9" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true" transform="translate(688,0)"><use data-c="2062" href="#MJX-160-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="7" data-semantic-parent="10" data-semantic-attributes="latex:J" data-semantic-level-number="2" data-speech-node="true" transform="translate(688,0)"><use data-c="1D43D" href="#MJX-160-NCM-I-1D43D"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="3.34 \times 10^{11}\, kJ" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,10" data-semantic-content="1" data-semantic-attributes="latex:3.34 \times 10^{11}\, kJ" data-semantic-owns="0 1 10" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(11 0 1 (10 (4 2 3) 8 6 9 7))"><mn data-latex="3.34" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="11" data-semantic-attributes="latex:3.34" data-semantic-level-number="1" data-speech-node="true">3.34</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="11" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="1" data-speech-node="true">×</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:2" data-semantic-="" data-semantic-children="4,6,7" data-semantic-content="8,9" data-semantic-parent="11" data-semantic-owns="4 8 6 9 7" data-semantic-level-number="1" data-speech-node="true"><msup data-latex="10^{11}" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="2,3" data-semantic-parent="10" data-semantic-attributes="latex:10^{11}" data-semantic-owns="2 3" data-semantic-level-number="2" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="4" data-semantic-attributes="latex:10" data-semantic-level-number="3" data-speech-node="true">10</mn><mrow data-mjx-texclass="ORD" data-latex="{11}"><mn data-latex="11" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="4" data-semantic-attributes="latex:{11};texclass:ORD" data-semantic-level-number="3" data-speech-node="true">11</mn></mrow></msup><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="10" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true"></mspace><mi data-latex="k" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:k" data-semantic-level-number="2" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="2" data-speech-node="true">⁢</mo><mi data-latex="J" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:J" data-semantic-level-number="2" data-speech-node="true">J</mi></mrow></math></mjx-assistive-mml></mjx-container> needed to melt a <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="160" style="font-size: 85%; position: relative;"><svg width="4.023ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1778 1000" aria-hidden="true" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="1.00 \times 10^6" data-semantic-type="infixop" 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stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="1.00 \times 10^6" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,4" data-semantic-content="1" data-semantic-attributes="latex:1.00 \times 10^6" data-semantic-owns="0 1 4" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(5 0 1 (4 2 3))"><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="1" data-speech-node="true"><use data-c="D7" href="#MJX-161-NCM-N-D7"></use></g><g data-mml-node="msup" data-latex="10^6" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:2" data-semantic-id="4" data-semantic-children="2,3" data-semantic-parent="5" data-semantic-attributes="latex:10^6" data-semantic-owns="2 3" data-semantic-level-number="1" data-speech-node="true" transform="translate(1000.2,0)"><g data-mml-node="mn" data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="2" data-semantic-parent="4" data-semantic-attributes="latex:10" data-semantic-level-number="2" data-speech-node="true"><use data-c="31" href="#MJX-161-NCM-N-31"></use><use data-c="30" href="#MJX-161-NCM-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mn" transform="translate(1033,393.1) scale(0.707)" data-latex="6" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="3" data-semantic-parent="4" data-semantic-attributes="latex:6" data-semantic-level-number="2" data-speech-node="true"><use data-c="36" href="#MJX-161-NCM-N-36"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="1.00 \times 10^6" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,4" data-semantic-content="1" data-semantic-attributes="latex:1.00 \times 10^6" data-semantic-owns="0 1 4" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(5 0 1 (4 2 3))"><mn data-latex="1.00" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1.00" data-semantic-level-number="1" data-speech-node="true">1.00</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="1" data-speech-node="true">×</mo><msup data-latex="10^6" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="2,3" data-semantic-parent="5" data-semantic-attributes="latex:10^6" data-semantic-owns="2 3" data-semantic-level-number="1" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="4" data-semantic-attributes="latex:10" data-semantic-level-number="2" data-speech-node="true">10</mn><mn data-latex="6" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="4" data-semantic-attributes="latex:6" data-semantic-level-number="2" data-speech-node="true">6</mn></msup></math></mjx-assistive-mml></mjx-container> metric ton iceberg</p> <ul> <li class="lt-chem-21722" style="background-color: unset;">Combustion of 3.8 × 10<sup>3</sup> ft<sup>3</sup> of natural gas</li> <li class="lt-chem-21722" style="background-color: unset;">Combustion of 68,000 barrels of oil</li> <li class="lt-chem-21722" style="background-color: unset;">Combustion of 15,000 tons of coal</li> <li class="lt-chem-21722" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="161" style="font-size: 85%; position: relative;"><svg width="2.891ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1278 1000" aria-hidden="true" style="vertical-align: -0.566ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="1.1 \times 10^8" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,4" data-semantic-content="1" data-semantic-attributes="latex:1.1 \times 10^8" data-semantic-owns="0 1 4" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(5 0 1 (4 2 3))"><g data-mml-node="mn" data-latex="1.1" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:1.1" data-semantic-level-number="1" data-speech-node="true"><use data-c="31" href="#MJX-162-NCM-N-31"></use><use data-c="2E" href="#MJX-162-NCM-N-2E" transform="translate(500,0)"></use><use data-c="31" href="#MJX-162-NCM-N-31" transform="translate(778,0)"></use></g></g></g><defs><path id="MJX-162-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 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data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,4" data-semantic-content="1" data-semantic-attributes="latex:1.1 \times 10^8" data-semantic-owns="0 1 4" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(5 0 1 (4 2 3))"><g data-mml-node="mo" data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="1" data-semantic-parent="5" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="1" data-speech-node="true"><use data-c="D7" href="#MJX-162-NCM-N-D7"></use></g><g data-mml-node="msup" data-latex="10^8" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:2" data-semantic-id="4" data-semantic-children="2,3" data-semantic-parent="5" data-semantic-attributes="latex:10^8" data-semantic-owns="2 3" data-semantic-level-number="1" data-speech-node="true" transform="translate(1000.2,0)"><g data-mml-node="mn" data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="2" data-semantic-parent="4" data-semantic-attributes="latex:10" data-semantic-level-number="2" data-speech-node="true"><use data-c="31" href="#MJX-162-NCM-N-31"></use><use data-c="30" href="#MJX-162-NCM-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mn" transform="translate(1033,393.1) scale(0.707)" data-latex="8" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-id="3" data-semantic-parent="4" data-semantic-attributes="latex:8" data-semantic-level-number="2" data-speech-node="true"><use data-c="38" href="#MJX-162-NCM-N-38"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="1.1 \times 10^8" data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,4" data-semantic-content="1" data-semantic-attributes="latex:1.1 \times 10^8" data-semantic-owns="0 1 4" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(5 0 1 (4 2 3))"><mn data-latex="1.1" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1.1" data-semantic-level-number="1" data-speech-node="true">1.1</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="1" data-speech-node="true">×</mo><msup data-latex="10^8" data-semantic-type="superscript" data-semantic-role="integer" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="2,3" data-semantic-parent="5" data-semantic-attributes="latex:10^8" data-semantic-owns="2 3" data-semantic-level-number="1" data-speech-node="true"><mn data-latex="10" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="4" data-semantic-attributes="latex:10" data-semantic-level-number="2" data-speech-node="true">10</mn><mn data-latex="8" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="4" data-semantic-attributes="latex:8" data-semantic-level-number="2" data-speech-node="true">8</mn></msup></math></mjx-assistive-mml></mjx-container> kilowatt-hours of electricity</li> </ul> <p class="lt-chem-21722" style="background-color: unset;">Alternatively, we can rely on ambient temperatures to slowly melt the iceberg. The main issue with this idea is the cost of dragging the iceberg to the desired place.</p> </div> <div class="box-exercise"> <span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C):_Thermite_Reaction"></span><span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C):_Thermite_Reaction"></span><h5 class="box-legend"><span class="lt-icon-default">Exercise <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="162" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.581ex" role="img" focusable="false" viewbox="0 -677 2056 699" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-163-NCM-N-35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path><path id="MJX-163-NCM-N-2E" d="M192 53C192 82 168 106 139 106C110 106 86 82 86 53C86 24 110 0 139 0C168 0 192 24 192 53Z"></path><path id="MJX-163-NCM-N-34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"></path><path id="MJX-163-NCM-N-31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-id="5" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mn" data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true"><use 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data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>: Thermite Reaction</span></h5> <p class="lt-chem-21722" style="background-color: unset;">If 17.3 g of powdered aluminum are allowed to react with excess <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="163" style="font-size: 85%; position: relative;"><svg width="6.217ex" height="1.994ex" role="img" focusable="false" viewbox="0 -716 2748.1 881.6" aria-hidden="true" style="vertical-align: -0.375ex;"><defs><path id="MJX-164-NCM-N-46" d="M275 641L393 641C464 641 510 626 533 597C565 558 569 521 578 450L611 450L582 680L33 680L33 641L61 641C96 641 117 639 124 634C131 629 135 617 135 599L135 81C135 63 131 51 124 46C117 41 96 39 61 39L33 39L33 0C59 2 110 3 187 3C274 3 330 2 357 0L357 39L320 39C267 39 238 44 233 55C231 60 230 69 230 82L230 321L311 321C354 321 382 313 394 298C406 283 412 253 412 206L444 206L444 475L412 475C412 429 406 398 394 383C382 368 354 360 311 360L230 360L230 606C230 642 236 641 275 641Z"></path><path id="MJX-164-NCM-N-65" d="M415 251C415 366 348 448 236 448C176 448 126 425 85 378C47 334 28 281 28 220C28 157 49 104 91 58C133 12 185-11 247-11C304-11 348 9 378 48C403 81 415 105 415 121C415 131 409 136 398 136C390 136 385 131 382 120C360 54 317 21 253 21C208 21 173 42 146 85C127 116 118 163 117 227L387 227C409 227 415 229 415 251M326 349C337 316 342 284 342 255L118 255C121 321 138 366 168 389C193 409 215 419 236 419C281 419 311 396 326 349Z"></path><path id="MJX-164-NCM-N-32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 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href="#MJX-164-NCM-N-33"></use></g></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ce{Fe2O3}" data-semantic-structure="(9 (3 0 2) 8 (7 4 6))"><mrow data-mjx-texclass="ORD" data-latex="{\mathrm{Fe}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}{\vphantom{A}}_{\smash[t]{3}}}"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="3,7" data-semantic-content="8" data-semantic-attributes="latex:\ce{Fe2O3};texclass:ORD" data-semantic-owns="3 8 7" data-semantic-level-number="0" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{Fe}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:2" data-semantic-="" data-semantic-children="0,2" data-semantic-parent="9" 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data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="2" data-speech-node="true">O</mi></mrow></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{3}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{3}"><mpadded height="0"><mn data-latex="3" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:{\smash[t]{3}};texclass:ORD" data-semantic-level-number="2" data-speech-node="true">3</mn></mpadded></mrow></mrow></msub></mrow></math></mjx-assistive-mml></mjx-container>, how much heat is produced?</p> <dl> <dt><strong class="emphasis bold">Answer</strong></dt> <dd> <p class="lt-chem-21722" style="background-color: unset;">273 kJ</p> </dd> </dl> </div> <span id="Enthalpies_of_Reaction"></span><span id="Enthalpies_of_Reaction"></span><h2 style="background-color: unset;" class="lt-chem-21722">Enthalpies of Reaction</h2> <p class="lt-chem-21722" style="background-color: unset;">One way to report the heat absorbed or released would be to compile a massive set of reference tables that list the enthalpy changes for all possible chemical reactions, which would require an incredible amount of effort. Fortunately, since enthalpy is a state function, all we have to know is the initial and final states of the reaction. This allows us to calculate the enthalpy change for virtually any conceivable chemical reaction using a relatively small set of tabulated data, such as the following:</p> <ul> <li class="lt-chem-21722" style="background-color: unset;">Enthalpy of combustion (ΔH<sub>comb</sub>)<span class="glossdef"> The change in enthalpy that occurs during a combustion reaction.</span> Enthalpy changes have been measured for the combustion of virtually any substance that will burn in oxygen; these values are usually reported as the enthalpy of combustion per mole of substance.</li> <li class="lt-chem-21722" style="background-color: unset;">Enthalpy of fusion (ΔH<sub>fus</sub>)<span class="glossdef"> The enthalpy change that acompanies the melting (fusion) of 1 mol of a substance.</span> The enthalpy change that accompanies the melting, or fusion, of 1 mol of a substance; these values have been measured for almost all the elements and for most simple compounds.</li> <li class="lt-chem-21722" style="background-color: unset;">Enthalpy of vaporization (ΔH<sub>vap</sub>) <span class="glossdef">The enthalpy change that accompanies the vaporization of 1 mol of a substance.</span> The enthalpy change that accompanies the vaporization of 1 mol of a substance; these values have also been measured for nearly all the elements and for most volatile compounds.</li> <li class="lt-chem-21722" style="background-color: unset;">Enthalpy of solution (ΔH<sub>soln</sub>)<span class="glossdef"> The change in enthalpy that occurs when a specified amount of solute dissolves in a given quantity of solvent.</span> The enthalpy change when a specified amount of solute dissolves in a given quantity of solvent.</li> </ul> <table class="mt-responsive-table" align="center" cellpadding="0" cellspacing="0"> <caption>Table <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="164" style="font-size: 85%; position: relative;"><svg width="4.652ex" 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data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="31" href="#MJX-165-NCM-N-31"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{1}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="1}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{1};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="4" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:4" data-semantic-level-number="1" data-speech-node="true">4</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>: Enthalpies of Vaporization and Fusion for Selected Substances at Their Boiling Points and Melting Points</caption> <thead> <tr> <th style="text-align:center;"><strong>Substance</strong></th> <th style="text-align:center;"><strong>ΔH<sub>vap</sub> (kJ/mol)</strong></th> <th style="text-align:center;"><strong>ΔH<sub>fus</sub> (kJ/mol)</strong></th> </tr> </thead> <tbody> <tr> <td class="lt-chem-21722" data-th="Substance" style="text-align: center; background-color: unset;">argon (Ar)</td> <td class="lt-chem-21722" data-th="ΔHvap (kJ/mol)" style="text-align: center; background-color: unset;">6.3</td> <td class="lt-chem-21722" data-th="ΔHfus (kJ/mol)" style="text-align: center; background-color: unset;">1.3</td> </tr> <tr> <td class="lt-chem-21722" data-th="Substance" style="text-align: center; background-color: unset;">methane (CH<sub>4</sub>)</td> <td class="lt-chem-21722" data-th="ΔHvap (kJ/mol)" style="text-align: center; background-color: unset;">9.2</td> <td class="lt-chem-21722" data-th="ΔHfus (kJ/mol)" style="text-align: center; background-color: unset;">0.84</td> </tr> <tr> <td class="lt-chem-21722" data-th="Substance" style="text-align: center; background-color: unset;">ethanol (CH<sub>3</sub>CH<sub>2</sub>OH)</td> <td class="lt-chem-21722" data-th="ΔHvap (kJ/mol)" style="text-align: center; background-color: unset;">39.3</td> <td class="lt-chem-21722" data-th="ΔHfus (kJ/mol)" style="text-align: center; background-color: unset;">7.6</td> </tr> <tr> <td class="lt-chem-21722" data-th="Substance" style="text-align: center; background-color: unset;">benzene (C<sub>6</sub>H<sub>6</sub>)</td> <td class="lt-chem-21722" data-th="ΔHvap (kJ/mol)" style="text-align: center; background-color: unset;">31.0</td> <td class="lt-chem-21722" data-th="ΔHfus (kJ/mol)" style="text-align: center; background-color: unset;">10.9</td> </tr> <tr> <td class="lt-chem-21722" data-th="Substance" style="text-align: center; background-color: unset;">water (H<sub>2</sub>O)</td> <td class="lt-chem-21722" data-th="ΔHvap (kJ/mol)" style="text-align: center; background-color: unset;">40.7</td> <td class="lt-chem-21722" data-th="ΔHfus (kJ/mol)" style="text-align: center; background-color: unset;">6.0</td> </tr> <tr> <td class="lt-chem-21722" data-th="Substance" style="text-align: center; background-color: unset;">mercury (Hg)</td> <td class="lt-chem-21722" data-th="ΔHvap (kJ/mol)" style="text-align: center; background-color: unset;">59.0</td> <td class="lt-chem-21722" data-th="ΔHfus (kJ/mol)" style="text-align: center; background-color: unset;">2.29</td> </tr> <tr> <td class="lt-chem-21722" data-th="Substance" style="text-align: center; background-color: unset;">iron (Fe)</td> <td class="lt-chem-21722" data-th="ΔHvap (kJ/mol)" style="text-align: center; background-color: unset;">340</td> <td class="lt-chem-21722" data-th="ΔHfus (kJ/mol)" style="text-align: center; background-color: unset;">14</td> </tr> </tbody> </table> <div class="box-note"> <p class="lt-chem-21722" style="background-color: unset;">The sign convention is the same for all enthalpy changes: negative if heat is released by the system and positive if heat is absorbed by the system.</p> </div> <div class="mt-video-widget mt-video-width-55"><div style="width: 100%; height: 0px; position: relative; padding-bottom: 56.25%;"><iframe src="https://www.youtube-nocookie.com/embed/z2KUaIEF9qI?vq=hd1080" frameborder="0" allowfullscreen="true" style="width: 100%; height: 100%; position: absolute; overflow: auto;" id="qrcode0" class="youtubeIFrame"></iframe><a href="https://www.youtube.com/watch?v=z2KUaIEF9qI" class="youtubeImageContainer"><img class="youtubeImage" src="https://img.youtube.com/vi/z2KUaIEF9qI/0.jpg" /><canvas class="thisqrcode" id="this_qrcode0" height="100" width="100" style="height: 100px; width: 100px;"></canvas></a></div></div> <p><b><span style="font-size:12.0pt;line-height:107%;mso-ascii-font-family:Calibri;mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;">Enthalpy of Reaction: </span></b><a target="_blank" href="https://youtu.be/z2KUaIEF9qI" rel="external noopener nofollow" class="link-https">Enthalpy of Reaction, YouTube(opens in new window)</a><span> [youtu.be]</span></p> <span id="Summary"></span><span id="Summary"></span><h2 style="background-color: unset;" class="lt-chem-21722">Summary</h2> <p class="lt-chem-21722" style="background-color: unset;">For a chemical reaction, the <strong class="emphasis bold">enthalpy of reaction </strong>(<mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="165" style="font-size: 85%; position: relative;"><svg width="6.549ex" height="1.977ex" role="img" focusable="false" viewbox="0 -716 2894.6 873.8" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-166-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-166-NCM-N-2062" d=""></path><path id="MJX-166-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 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data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><msub data-latex="H_{r x n}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="1,7" data-semantic-parent="10" data-semantic-attributes="latex:H_{r x n}" data-semantic-owns="1 7" data-semantic-level-number="1" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="2" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{r x n}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-="" data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-parent="8" data-semantic-attributes="latex:{r x n};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:r" data-semantic-level-number="3" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="3" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="3" data-speech-node="true">n</mi></mrow></msub></math></mjx-assistive-mml></mjx-container>) is the difference in enthalpy between products and reactants; the units of <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="166" style="font-size: 85%; position: relative;"><svg width="6.549ex" height="1.977ex" role="img" focusable="false" viewbox="0 -716 2894.6 873.8" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-167-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-167-NCM-N-2062" d=""></path><path id="MJX-167-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 209 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data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(10 0 9 (8 1 (7 2 5 3 6 4)))"><g data-mml-node="mi" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="0" data-semantic-parent="10" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true"><use data-c="394" href="#MJX-167-NCM-N-394"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-id="9" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true" transform="translate(833,0)"><use data-c="2062" href="#MJX-167-NCM-N-2062"></use></g><g data-mml-node="msub" data-latex="H_{r x n}" data-semantic-type="subscript" data-semantic-role="simple function" 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data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="3" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="3" data-speech-node="true" transform="translate(451,0)"><use data-c="1D465" href="#MJX-167-NCM-I-1D465"></use></g><g data-mml-node="mo" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-id="6" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true" transform="translate(1023,0)"><use data-c="2062" href="#MJX-167-NCM-N-2062"></use></g><g data-mml-node="mi" data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-id="4" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="3" data-speech-node="true" transform="translate(1023,0)"><use data-c="1D45B" href="#MJX-167-NCM-I-1D45B"></use></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="ΔH_{rxn}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:1" data-semantic-="" data-semantic-children="0,8" data-semantic-content="9" data-semantic-attributes="latex:ΔH_{rxn}" data-semantic-owns="0 9 8" data-semantic-level-number="0" data-speech-node="true" data-semantic-structure="(10 0 9 (8 1 (7 2 5 3 6 4)))"><mi mathvariant="normal" data-latex="Δ" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:Δ" data-semantic-level-number="1" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-parent="10" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="1" data-speech-node="true">⁢</mo><msub data-latex="H_{r x n}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="1,7" data-semantic-parent="10" data-semantic-attributes="latex:H_{r x n}" data-semantic-owns="1 7" data-semantic-level-number="1" data-speech-node="true"><mi data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:3" data-semantic-="" data-semantic-parent="8" data-semantic-attributes="latex:H" data-semantic-level-number="2" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{r x n}" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:3" data-semantic-="" data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-parent="8" data-semantic-attributes="latex:{r x n};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:r" data-semantic-level-number="3" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="3" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="3" data-speech-node="true">n</mi></mrow></msub></math></mjx-assistive-mml></mjx-container> are kilojoules per mole. Reversing a chemical reaction reverses the sign of <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="167" style="font-size: 85%; position: relative;"><svg width="6.549ex" height="1.977ex" role="img" focusable="false" viewbox="0 -716 2894.6 873.8" aria-hidden="true" style="vertical-align: -0.357ex;"><defs><path id="MJX-168-NCM-N-394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716C403 716 394 709 387 696L52 25C49 18 47 14 47 12C47 4 56 0 73 0M384 604L644 83L124 83Z"></path><path id="MJX-168-NCM-N-2062" d=""></path><path id="MJX-168-NCM-I-1D43B" d="M881 668C881 678 875 683 863 683L736 680L609 683C593 683 586 674 586 659C586 652 589 647 594 646C604 645 612 644 617 644C648 643 665 641 670 640C675 639 678 636 678 631C677 628 676 622 674 613L615 375L321 375L379 602C384 623 393 636 406 641C413 643 430 644 458 644C485 644 496 644 496 668C496 678 490 683 478 683L351 680L223 683C207 683 200 674 200 659C200 652 203 647 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data-semantic-children="2,3,4" data-semantic-content="5,6" data-semantic-parent="8" data-semantic-attributes="latex:{r x n};texclass:ORD" data-semantic-owns="2 5 3 6 4" data-semantic-level-number="2" data-speech-node="true"><mi data-latex="r" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:r" data-semantic-level-number="3" data-speech-node="true">r</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="x" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:x" data-semantic-level-number="3" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="3" data-speech-node="true">⁢</mo><mi data-latex="n" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:4" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:n" data-semantic-level-number="3" data-speech-node="true">n</mi></mrow></msub></math></mjx-assistive-mml></mjx-container>.</p> <span id="Contributors_and_Attributions"></span><span id="Contributors_and_Attributions"></span><h2 style="background-color: unset;" class="lt-chem-21722">Contributors and Attributions</h2> <div class="Attributions"> <ul> <li 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