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5.06:_Hess's_Law
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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">Learning Objectives</span></h5> <ul> <li class="lt-chem-21725" style="background-color: unset;">To use Hess’s law and thermochemical cycles to calculate enthalpy changes of chemical reactions.</li> </ul> </div> <p class="lt-chem-21725" style="background-color: unset;">Because enthalpy is a state function, the enthalpy change for a reaction depends on only two things: (1) the masses of the reacting substances and (2) the physical states of the reactants and products. It does not depend on the path by which reactants are converted to products. If you climbed a mountain, for example, the altitude change would not depend on whether you climbed the entire way without stopping or you stopped many times to take a break. If you stopped often, the overall change in altitude would be the sum of the changes in altitude for each short stretch climbed. Similarly, when we add two or more balanced chemical equations to obtain a net chemical equation, ΔH for the net reaction is the sum of the ΔH values for the individual reactions. This principle is called Hess’s law, after the Swiss-born Russian chemist Germain Hess (1802–1850), a pioneer in the study of thermochemistry. Hess’s law allows us to calculate ΔH values for reactions that are difficult to carry out directly by adding together the known ΔH values for individual steps that give the overall reaction, even though the overall reaction may not actually occur via those steps.</p> <blockquote> <p class="lt-chem-21725" style="background-color: unset;">Hess's Law argues that ΔH for the net reaction is the sum of the ΔH values for the individual reactions. This is nothing more than arguing that ΔH is a state function.</p> </blockquote> <p class="lt-chem-21725" style="background-color: unset;">We can illustrate Hess’s law using the thermite reaction. The overall reaction shown in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="98" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-99-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-99-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-99-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-99-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{5.6.1}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.06:_Hess's_Law#mjx-eqn:5.6.1"><g data-mml-node="mrow" data-latex="\ref{5.6.1}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-99-NCM-N-35"></use><use data-c="2E" href="#MJX-99-NCM-N-2E" transform="translate(500,0)"></use><use data-c="36" href="#MJX-99-NCM-N-36" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-99-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-99-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{5.6.1}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.6.1" data-latex="\ref{5.6.1}" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.6.1</mtext></mrow></math></mjx-assistive-mml></mjx-container> can be viewed as occurring in three distinct steps with known ΔH values. As shown in Figure 5.6.1, the first reaction produces 1 mol of solid aluminum oxide (Al<sub>2</sub>O<sub>3</sub>) and 2 mol of liquid iron at its melting point of 1758°C (part (a) in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="99" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-100-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-100-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-100-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-100-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{5.6.1}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.06:_Hess's_Law#mjx-eqn:5.6.1"><g data-mml-node="mrow" data-latex="\ref{5.6.1}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-100-NCM-N-35"></use><use data-c="2E" href="#MJX-100-NCM-N-2E" transform="translate(500,0)"></use><use data-c="36" href="#MJX-100-NCM-N-36" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-100-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-100-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{5.6.1}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.6.1" data-latex="\ref{5.6.1}" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.6.1</mtext></mrow></math></mjx-assistive-mml></mjx-container>); the enthalpy change for this reaction is −732.5 kJ/mol of Fe<sub>2</sub>O<sub>3</sub>. The second reaction is the conversion of 2 mol of liquid iron at 1758°C to 2 mol of solid iron at 1758°C (part (b) in Equation 5.6.1); the enthalpy change for this reaction is −13.8 kJ/mol of Fe (−27.6 kJ per 2 mol Fe). In the third reaction, 2 mol of solid iron at 1758°C is converted to 2 mol of solid iron at 25°C (part (c) in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="100" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-101-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-101-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-101-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-101-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{5.6.1}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.06:_Hess's_Law#mjx-eqn:5.6.1"><g data-mml-node="mrow" data-latex="\ref{5.6.1}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-101-NCM-N-35"></use><use data-c="2E" href="#MJX-101-NCM-N-2E" transform="translate(500,0)"></use><use data-c="36" href="#MJX-101-NCM-N-36" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-101-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-101-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{5.6.1}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.6.1" data-latex="\ref{5.6.1}" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.6.1</mtext></mrow></math></mjx-assistive-mml></mjx-container>); the enthalpy change for this reaction is −45.5 kJ/mol of Fe (−91.0 kJ per 2 mol Fe). As you can see in Figure 5.6.1, the overall reaction is given by the longest arrow (shown on the left), which is the sum of the three shorter arrows (shown on the right). Adding parts (a), (b), and (c) in Equation 5.6.1 gives the overall reaction, shown in part (d):</p> <p class="lt-chem-21725" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="101" style="font-size: 85%; min-width: 113.629ex; position: relative;"><svg width="100%" height="13.959ex" role="img" focusable="false" data-mjx-viewbox="0 -3335 50224.2 6170" aria-hidden="true" style="vertical-align: -6.414ex; min-width: 113.629ex;"><defs><path id="MJX-102-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 588 357 666 237 666Z"></path><path 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(\mathrm{s}, 25 \, ^{\circ}) {}+{} \mathrm{Fe}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}{\vphantom{A}}_{\smash[t]{3}}\mskip2mu (\mathrm{s}, 25 \, ^{\circ})& {}\mathrel{\mhchemlongrightarrow}{} \mathrm{Al}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}{\vphantom{A}}_{\smash[t]{3}}\mskip2mu (\mathrm{s}, 25 \, ^{\circ}) {}+{} 2\,\mathrm{Fe}\mskip2mu (\mathrm{s}, 25 \, ^{\circ}) & \Delta H = -851.1\,\text{kJ} &&\text{(d)} \end{aligned} \label{5.6.1}" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-id="402" data-semantic-children="401" data-semantic-attributes="latex: \begin{aligned} \ce{2 Al (s, 25 \, ^{\circ}) + Fe2O3 (s, 25 \, ^{\circ}) &-> 2 Fe (l, 1758 \, ^{\circ}) + Al2O3 (s, 1758 \, ^{\circ})} & \Delta H = - 732.5 \,\text{kJ} &&\text{(a)} \\[4pt] \ce{2 Fe (l, 1758 \, ^{\circ}) &-> 2 Fe (s, 1758 \, ^{\circ})} & \Delta H = -\phantom{0}27.6\,\text{kJ} &&\text{(b)} \\[4pt] \ce{2 Fe (s, 1758 \, ^{\circ}) + Al2O3 (s, 1758 \, ^{\circ}) &-> 2 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data-latex=" \begin{aligned} \ce{2 Al (s, 25 \, ^{\circ}) + Fe2O3 (s, 25 \, ^{\circ}) &-> 2 Fe (l, 1758 \, ^{\circ}) + Al2O3 (s, 1758 \, ^{\circ})} & \Delta H = - 732.5 \,\text{kJ} &&\text{(a)} \\[4pt] \ce{2 Fe (l, 1758 \, ^{\circ}) &-> 2 Fe (s, 1758 \, ^{\circ})} & \Delta H = -\phantom{0}27.6\,\text{kJ} &&\text{(b)} \\[4pt] \ce{2 Fe (s, 1758 \, ^{\circ}) + Al2O3 (s, 1758 \, ^{\circ}) &-> 2 Fe (s, 25 \, ^{\circ}) + Al2O3 (s, 25 \, ^{\circ}) } & \Delta H = -\phantom{0}91.0\,\text{kJ} &&\text{(c)} \\[4pt] \hline \ce{2 Al (s, 25 \, ^{\circ}) + Fe2O3 (s, 25 \, ^{\circ}) &-> Al2O3 (s, 25 \, ^{\circ}) + 2 Fe (s, 25 \, ^{\circ}) } & \Delta H = -851.1\,\text{kJ} &&\text{(d)} \end{aligned} \label{5.6.1}" display="block" data-semantic-structure="(402 (401 (399 (115 (49 (48 (47 5 46 (45 7 44 (36 9 (35 10 11 (15 12 14)) 16))) 17 (43 18 42 (41 (21 19 20) 39 (25 22 24) 40 (38 27 (37 28 29 (33 30 32)) 34))))) (97 (96 (95 51 (94 52 93 (92 54 91 (83 56 (82 57 58 (62 59 61)) 63)))) 64 (90 65 89 (88 (68 66 67) 86 (72 69 71) 87 (85 74 (84 75 76 (80 77 79)) 81))))) (111 (110 (106 98 105 99) 100 (109 101 (108 102 107 104)))) 112 (114 113)) (175 (134 (133 116 132 (131 118 130 (129 120 (128 121 122 (126 123 125)) 127)))) (156 (155 136 (154 137 153 (152 139 151 (150 141 (149 142 143 (147 144 146)) 148))))) (171 (170 (166 157 165 158) 159 (169 160 (168 162 167 164)))) 172 (174 173)) (287 (220 (219 (218 176 217 (216 178 215 (207 180 (206 181 182 (186 183 185)) 187))) 188 (214 189 213 (212 (192 190 191) 210 (196 193 195) 211 (209 198 (208 199 200 (204 201 203)) 205))))) (268 (267 (266 222 (265 223 264 (263 225 262 (254 227 (253 228 229 (233 230 232)) 234)))) 235 (261 236 260 (259 (239 237 238) 257 (243 240 242) 258 (256 245 (255 246 247 (251 248 250)) 252))))) (283 (282 (278 269 277 270) 271 (281 272 (280 274 279 276)))) 284 (286 285)) (398 (332 (331 (330 288 329 (328 290 327 (319 292 (318 293 294 (298 295 297)) 299))) 300 (326 301 325 (324 (304 302 303) 322 (308 305 307) 323 (321 310 (320 311 312 (316 313 315)) 317))))) (380 (379 (376 334 (375 335 374 (373 (338 336 337) 371 (342 339 341) 372 (366 344 (365 345 346 (350 347 349)) 351)))) 352 (378 353 377 (370 355 369 (368 357 (367 358 359 (363 360 362)) 364))))) (394 (393 (389 381 388 382) 383 (392 384 (391 385 390 387)))) 395 (397 396))) (4 (3 0 1 2))))"><mtable displaystyle="true" data-latex="2\,\mathrm{Al}\mskip2mu (\mathrm{s}, 25 \, ^{\circ}) {}+{} \mathrm{Fe}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}{\vphantom{A}}_{\smash[t]{3}}\mskip2mu (\mathrm{s}, 25 \, ^{\circ})& {}\mathrel{\mhchemlongrightarrow}{} \mathrm{Al}{\vphantom{A}}_{\smash[t]{2}}\mathrm{O}{\vphantom{A}}_{\smash[t]{3}}\mskip2mu (\mathrm{s}, 25 \, ^{\circ}) {}+{} 2\,\mathrm{Fe}\mskip2mu (\mathrm{s}, 25 \, ^{\circ}) & \Delta H = -851.1\,\text{kJ} &&\text{(d)} \end{aligned} \label{5.6.1}" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="401" data-semantic-attributes="latex: \begin{aligned} \ce{2 Al (s, 25 \, ^{\circ}) + Fe2O3 (s, 25 \, ^{\circ}) &-> 2 Fe (l, 1758 \, ^{\circ}) + Al2O3 (s, 1758 \, ^{\circ})} & \Delta H = - 732.5 \,\text{kJ} &&\text{(a)} \\[4pt] \ce{2 Fe (l, 1758 \, ^{\circ}) &-> 2 Fe (s, 1758 \, ^{\circ})} & \Delta H = -\phantom{0}27.6\,\text{kJ} &&\text{(b)} \\[4pt] \ce{2 Fe (s, 1758 \, ^{\circ}) + Al2O3 (s, 1758 \, ^{\circ}) &-> 2 Fe (s, 25 \, ^{\circ}) + Al2O3 (s, 25 \, ^{\circ}) } & \Delta H = -\phantom{0}91.0\,\text{kJ} &&\text{(c)} \\[4pt] \hline \ce{2 Al (s, 25 \, ^{\circ}) + Fe2O3 (s, 25 \, ^{\circ}) &-> Al2O3 (s, 25 \, ^{\circ}) + 2 Fe (s, 25 \, ^{\circ}) } & \Delta H = -851.1\,\text{kJ} &&\text{(d)} \end{aligned} \label{5.6.1}" data-semantic-owns="401" 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="399" data-semantic-content="4" data-semantic-parent="402" data-semantic-owns="399 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="401" 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{5.6.1}" 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{5.6.1}" data-semantic-level-number="4" data-speech-node="true">5.6.1</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><mtable displaystyle="true" columnalign="right left right left right" columnspacing="0em 2em 0em 2em" rowspacing="0.7em 0.7em 0.7em 0.30000000000000004em" data-break-align="bottom top bottom top bottom" rowlines="none none solid" data-latex="{aligned}" data-semantic-type="table" data-semantic-role="unknown" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="115,175,287,398" 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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="5,45" data-semantic-content="46" data-semantic-parent="48" data-semantic-owns="5 46 45" 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="47" 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="47" 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="depth:8" data-semantic-="" data-semantic-children="7,36" data-semantic-content="44,7" data-semantic-parent="47" data-semantic-owns="7 44 36" 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="45" 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="45" 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="35" data-semantic-content="9,16" data-semantic-parent="45" data-semantic-owns="9 35 16" 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="36" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="10,11,15" data-semantic-content="11" 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data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="10" data-speech-node="true">s</mi></mrow><mo data-latex="," data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-annotation="depth:11" data-semantic-="" data-semantic-parent="84" data-semantic-attributes="latex:," data-semantic-operator="punctuated" data-semantic-level-number="10" data-speech-node="true">,</mo><mrow data-semantic-added="true" data-semantic-type="superscript" data-semantic-role="number" data-semantic-annotation="collapsed:number;depth:11" data-semantic-="" data-semantic-children="77,79" data-semantic-parent="84" data-semantic-attributes="latex:\,^{\circ}" data-semantic-owns="77 79" data-semantic-level-number="10" data-speech-node="true"><mn data-latex="1758" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="80" data-semantic-attributes="latex:1758" data-semantic-level-number="11" data-speech-node="true">1758</mn><msup data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="80" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="85" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mstyle></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="110" data-semantic-parent="115" data-semantic-owns="110" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="106,109" data-semantic-content="100" data-semantic-parent="111" data-semantic-owns="106 100 109" 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:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="98,99" data-semantic-content="105" data-semantic-parent="110" data-semantic-owns="98 105 99" data-semantic-level-number="6" data-speech-node="true"><mi mathvariant="normal" data-latex="\Delta" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" 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data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="6" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="108" data-semantic-content="101" data-semantic-parent="110" data-semantic-owns="101 108" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="109" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="7" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="unit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="102,104" data-semantic-content="107" data-semantic-parent="109" data-semantic-owns="102 107 104" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="732.5" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:9" data-semantic-="" data-semantic-parent="108" data-semantic-attributes="latex:732.5" data-semantic-level-number="8" data-speech-node="true">732.5</mn><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="108" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><mtext data-latex="\text{kJ}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-parent="108" data-semantic-attributes="latex:\text{kJ}" data-semantic-level-number="8" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="115" data-semantic-level-number="4" data-speech-node="true"><mstyle indentshift="2em"></mstyle></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="113" data-semantic-parent="115" data-semantic-owns="113" data-semantic-level-number="4" data-speech-node="true"><mtext data-latex="\text{(a)}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="114" data-semantic-attributes="latex:\text{(a)}" data-semantic-level-number="5" data-speech-node="true">(a)</mtext></mtd></mtr><mtr data-latex=" " data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="134,156,171,172,174" data-semantic-parent="399" data-semantic-attributes="latex: " data-semantic-owns="134 156 171 172 174" data-semantic-level-number="3" data-speech-node="true"><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="133" data-semantic-parent="175" data-semantic-owns="133" 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:unit;depth:6" data-semantic-="" data-semantic-children="116,131" data-semantic-content="132" data-semantic-parent="134" data-semantic-owns="116 132 131" 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;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="133" 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="133" 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="depth:7" data-semantic-="" data-semantic-children="118,129" data-semantic-content="130,118" data-semantic-parent="133" data-semantic-owns="118 130 129" 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" 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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="129" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-children="121,122,126" data-semantic-content="122" data-semantic-parent="129" data-semantic-owns="121 122 126" data-semantic-level-number="8" data-speech-node="true"><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:10" data-semantic-="" data-semantic-parent="128" data-semantic-attributes="latex:\mathrm{l};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">l</mi></mrow><mo data-latex="," data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="128" data-semantic-attributes="latex:," data-semantic-operator="punctuated" data-semantic-level-number="9" data-speech-node="true">,</mo><mrow data-semantic-added="true" data-semantic-type="superscript" data-semantic-role="number" data-semantic-annotation="collapsed:number;depth:10" data-semantic-="" data-semantic-children="123,125" data-semantic-parent="128" data-semantic-attributes="latex:\,^{\circ}" data-semantic-owns="123 125" data-semantic-level-number="9" data-speech-node="true"><mn data-latex="1758" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:11" data-semantic-="" data-semantic-parent="126" data-semantic-attributes="latex:1758" data-semantic-level-number="10" data-speech-node="true">1758</mn><msup data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:11" data-semantic-="" data-semantic-parent="126" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="10" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="129" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">)</mo></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="155" data-semantic-parent="175" data-semantic-owns="155" data-semantic-level-number="4" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="unknown" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="154" data-semantic-content="136" data-semantic-parent="156" data-semantic-owns="136 154" data-semantic-level-number="5" data-speech-node="true"><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:7" data-semantic-="" data-semantic-parent="155" data-semantic-attributes="latex:\mathrel{\mhchemlongrightarrow};texclass:REL" data-semantic-operator="prefixop," data-semantic-level-number="6" 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:7" data-semantic-="" data-semantic-children="137,152" data-semantic-content="153" data-semantic-parent="155" data-semantic-owns="137 153 152" 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;depth:8" data-semantic-="" data-semantic-parent="154" 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="154" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><mrow 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data-semantic-children="144,146" data-semantic-parent="149" data-semantic-attributes="latex:\,^{\circ}" data-semantic-owns="144 146" data-semantic-level-number="10" data-speech-node="true"><mn data-latex="1758" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="147" data-semantic-attributes="latex:1758" data-semantic-level-number="11" data-speech-node="true">1758</mn><msup data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="147" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" 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data-semantic-parent="169" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="7" data-speech-node="true">−</mo><mrow data-mjx-texclass="ORD" data-latex="\phantom{0}"><mphantom><mn data-latex="0">0</mn></mphantom></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="unit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="162,164" data-semantic-content="167" data-semantic-parent="169" data-semantic-owns="162 167 164" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="27.6" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:9" data-semantic-="" data-semantic-parent="168" data-semantic-attributes="latex:27.6" data-semantic-level-number="8" data-speech-node="true">27.6</mn><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="168" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><mtext data-latex="\text{kJ}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-parent="168" data-semantic-attributes="latex:\text{kJ}" data-semantic-level-number="8" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="175" data-semantic-level-number="4" data-speech-node="true"><mstyle indentshift="2em"></mstyle></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="173" data-semantic-parent="175" data-semantic-owns="173" 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data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="218,214" data-semantic-content="188" data-semantic-parent="220" data-semantic-owns="218 188 214" 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="176,216" data-semantic-content="217" data-semantic-parent="219" data-semantic-owns="176 217 216" 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="218" 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="218" 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="depth:8" data-semantic-="" data-semantic-children="178,207" data-semantic-content="215,178" data-semantic-parent="218" data-semantic-owns="178 215 207" data-semantic-level-number="7" 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:9" data-semantic-="" data-semantic-parent="216" data-semantic-attributes="latex:\mathrm{Fe};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="8" 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:9" data-semantic-="" data-semantic-parent="216" 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="206" data-semantic-content="180,187" data-semantic-parent="216" data-semantic-owns="180 206 187" 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="207" data-semantic-attributes="latex:(" 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data-semantic-attributes="latex:," data-semantic-operator="punctuated" data-semantic-level-number="10" data-speech-node="true">,</mo><mrow data-semantic-added="true" data-semantic-type="superscript" data-semantic-role="number" data-semantic-annotation="collapsed:number;depth:11" data-semantic-="" data-semantic-children="183,185" data-semantic-parent="206" data-semantic-attributes="latex:\,^{\circ}" data-semantic-owns="183 185" data-semantic-level-number="10" data-speech-node="true"><mn data-latex="1758" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="186" data-semantic-attributes="latex:1758" data-semantic-level-number="11" data-speech-node="true">1758</mn><msup data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="186" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="207" 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="219" 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="189,212" data-semantic-content="213,189" data-semantic-parent="219" data-semantic-owns="189 213 212" data-semantic-level-number="6" 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:8" data-semantic-="" data-semantic-parent="214" data-semantic-attributes="latex:\mathrm{Al};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">Al</mi></mrow><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="214" 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="192,196,209" data-semantic-content="210,211" data-semantic-parent="214" data-semantic-owns="192 210 196 211 209" 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="190,191" data-semantic-parent="212" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="190 191" 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="192" 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="192" 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="212" 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="193,195" data-semantic-parent="212" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="193 195" 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="196" 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="196" 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="212" 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="208" data-semantic-content="198,205" data-semantic-parent="212" data-semantic-owns="198 208 205" 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="209" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="199,200,204" data-semantic-content="200" data-semantic-parent="209" data-semantic-owns="199 200 204" data-semantic-level-number="9" data-speech-node="true"><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:11" data-semantic-="" data-semantic-parent="208" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="10" data-speech-node="true">s</mi></mrow><mo data-latex="," data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-annotation="depth:11" data-semantic-="" data-semantic-parent="208" data-semantic-attributes="latex:," data-semantic-operator="punctuated" data-semantic-level-number="10" data-speech-node="true">,</mo><mrow data-semantic-added="true" data-semantic-type="superscript" data-semantic-role="number" data-semantic-annotation="collapsed:number;depth:11" data-semantic-="" data-semantic-children="201,203" data-semantic-parent="208" data-semantic-attributes="latex:\,^{\circ}" data-semantic-owns="201 203" data-semantic-level-number="10" data-speech-node="true"><mn data-latex="1758" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="204" data-semantic-attributes="latex:1758" data-semantic-level-number="11" data-speech-node="true">1758</mn><msup data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="204" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="209" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="267" data-semantic-parent="287" data-semantic-owns="267" data-semantic-level-number="4" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="266,261" data-semantic-content="235" data-semantic-parent="268" data-semantic-owns="266 235 261" data-semantic-level-number="5" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="unknown" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="265" data-semantic-content="222" data-semantic-parent="267" data-semantic-owns="222 265" data-semantic-level-number="6" data-speech-node="true"><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:8" data-semantic-="" data-semantic-parent="266" data-semantic-attributes="latex:\mathrel{\mhchemlongrightarrow};texclass:REL" data-semantic-operator="prefixop," data-semantic-level-number="7" 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:8" data-semantic-="" data-semantic-children="223,263" data-semantic-content="264" data-semantic-parent="266" data-semantic-owns="223 264 263" 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data-semantic-operator="punctuated" data-semantic-level-number="10" data-speech-node="true">,</mo><mrow data-semantic-added="true" data-semantic-type="superscript" data-semantic-role="number" data-semantic-annotation="collapsed:number;depth:11" data-semantic-="" data-semantic-children="248,250" data-semantic-parent="255" data-semantic-attributes="latex:\,^{\circ}" data-semantic-owns="248 250" data-semantic-level-number="10" data-speech-node="true"><mn data-latex="25" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="251" data-semantic-attributes="latex:25" data-semantic-level-number="11" data-speech-node="true">25</mn><msup data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="251" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="256" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mstyle></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="282" data-semantic-parent="287" data-semantic-owns="282" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="278,281" 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data-speech-node="true">25</mn><msup data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="298" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="319" 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="331" 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="301,324" data-semantic-content="325,301" data-semantic-parent="331" data-semantic-owns="301 325 324" 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="326" data-semantic-attributes="latex:\mathrm{Fe};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="7" 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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="324" 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="305,307" data-semantic-parent="324" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="305 307" 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="308" 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="308" 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="324" 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="320" data-semantic-content="310,317" data-semantic-parent="324" data-semantic-owns="310 320 317" 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="321" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-children="311,312,316" data-semantic-content="312" data-semantic-parent="321" data-semantic-owns="311 312 316" data-semantic-level-number="9" data-speech-node="true"><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:11" data-semantic-="" data-semantic-parent="320" data-semantic-attributes="latex:\mathrm{s};texclass:ORD" data-semantic-level-number="10" data-speech-node="true">s</mi></mrow><mo data-latex="," data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-annotation="depth:11" data-semantic-="" data-semantic-parent="320" data-semantic-attributes="latex:," data-semantic-operator="punctuated" data-semantic-level-number="10" data-speech-node="true">,</mo><mrow data-semantic-added="true" data-semantic-type="superscript" data-semantic-role="number" data-semantic-annotation="collapsed:number;depth:11" data-semantic-="" data-semantic-children="313,315" data-semantic-parent="320" data-semantic-attributes="latex:\,^{\circ}" data-semantic-owns="313 315" data-semantic-level-number="10" data-speech-node="true"><mn data-latex="25" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:12" data-semantic-="" data-semantic-parent="316" data-semantic-attributes="latex:25" data-semantic-level-number="11" data-speech-node="true">25</mn><msup data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="316" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="321" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="379" data-semantic-parent="398" data-semantic-owns="379" data-semantic-level-number="4" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="376,378" data-semantic-content="352" data-semantic-parent="380" data-semantic-owns="376 352 378" data-semantic-level-number="5" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="unknown" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="375" data-semantic-content="334" data-semantic-parent="379" data-semantic-owns="334 375" data-semantic-level-number="6" data-speech-node="true"><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:8" data-semantic-="" data-semantic-parent="376" data-semantic-attributes="latex:\mathrel{\mhchemlongrightarrow};texclass:REL" data-semantic-operator="prefixop," data-semantic-level-number="7" data-speech-node="true"></mo></mrow><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:8" data-semantic-="" data-semantic-children="335,373" data-semantic-content="374,335" data-semantic-parent="376" data-semantic-owns="335 374 373" 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="375" data-semantic-attributes="latex:\mathrm{Al};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="8" data-speech-node="true">Al</mi></mrow><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:9" data-semantic-="" data-semantic-parent="375" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="8" 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data-semantic-parent="338" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="10" 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:11" data-semantic-="" data-semantic-parent="338" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="10" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="373" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="9" 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:10" data-semantic-="" data-semantic-children="339,341" data-semantic-parent="373" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{3}}" data-semantic-owns="339 341" data-semantic-level-number="9" 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:11" data-semantic-="" data-semantic-parent="342" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-level-number="10" 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 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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:7" data-semantic-="" data-semantic-parent="379" 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="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="353,370" data-semantic-content="377" data-semantic-parent="379" data-semantic-owns="353 377 370" 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;depth:8" data-semantic-="" data-semantic-parent="378" 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="378" 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="depth:8" data-semantic-="" data-semantic-children="355,368" data-semantic-content="369,355" data-semantic-parent="378" data-semantic-owns="355 369 368" data-semantic-level-number="7" 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" 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data-latex="\,^{\circ}"><mspace width="0.167em" data-latex="\,"></mspace><mrow data-mjx-texclass="ORD" data-latex="{\circ}"><mo data-latex="\circ" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:12" data-semantic-="" data-semantic-parent="363" data-semantic-attributes="latex:{\circ};texclass:ORD" data-semantic-level-number="11" data-speech-node="true">∘</mo></mrow></msup></mrow></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:10" data-semantic-="" data-semantic-parent="368" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mstyle></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="393" data-semantic-parent="398" data-semantic-owns="393" data-semantic-level-number="4" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="389,392" data-semantic-content="383" data-semantic-parent="394" data-semantic-owns="389 383 392" 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:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="381,382" data-semantic-content="388" data-semantic-parent="393" data-semantic-owns="381 388 382" data-semantic-level-number="6" 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:8" data-semantic-="" data-semantic-parent="389" data-semantic-attributes="latex:\Delta" data-semantic-level-number="7" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="389" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" 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:8" data-semantic-="" data-semantic-parent="389" data-semantic-attributes="latex:H" data-semantic-level-number="7" data-speech-node="true">H</mi></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="393" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="6" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="391" data-semantic-content="384" data-semantic-parent="393" data-semantic-owns="384 391" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="392" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="7" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="unit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="385,387" data-semantic-content="390" data-semantic-parent="392" data-semantic-owns="385 390 387" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="851.1" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:9" data-semantic-="" data-semantic-parent="391" data-semantic-attributes="latex:851.1" data-semantic-level-number="8" data-speech-node="true">851.1</mn><mspace width="0.167em" data-latex="\," data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="391" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><mtext data-latex="\text{kJ}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-parent="391" data-semantic-attributes="latex:\text{kJ}" data-semantic-level-number="8" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="398" data-semantic-level-number="4" data-speech-node="true"><mstyle indentshift="2em"></mstyle></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="396" data-semantic-parent="398" data-semantic-owns="396" data-semantic-level-number="4" data-speech-node="true"><mtext data-latex="\text{(d)}" data-semantic-type="text" data-semantic-role="annotation" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="397" data-semantic-attributes="latex:\text{(d)}" data-semantic-level-number="5" data-speech-node="true">(d)</mtext></mtd></mtr></mtable></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">The net reaction in part (d) in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="102" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-103-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-103-NCM-N-2E" d="M192 53C192 82 168 106 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666Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\ref{5.6.1}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.06:_Hess's_Law#mjx-eqn:5.6.1"><g data-mml-node="mrow" data-latex="\ref{5.6.1}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-103-NCM-N-35"></use><use data-c="2E" href="#MJX-103-NCM-N-2E" transform="translate(500,0)"></use><use data-c="36" href="#MJX-103-NCM-N-36" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-103-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-103-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{5.6.1}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.6.1" data-latex="\ref{5.6.1}" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.6.1</mtext></mrow></math></mjx-assistive-mml></mjx-container> is identical to the equation for the thermite reaction that we saw in a previous section. By Hess’s law, the enthalpy change for part (d) is the sum of the enthalpy changes for parts (a), (b), and (c). In essence, Hess’s law enables us to calculate the enthalpy change for the sum of a series of reactions without having to draw a diagram like that in Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="103" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-104-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 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href="#MJX-104-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="6" 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:6" data-semantic-level-number="1" data-speech-node="true">6</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> <figure><img alt="A diagram illustrating a mathematical relationship with labeled variables and arrows indicating different values and calculations." style="width: 553px; height: 403px;" class="internal" loading="lazy" width="1218" height="891" src="https://chem.libretexts.org/@api/deki/files/41887/e74491d8e968d0e6920192460d7edd69.jpg?revision=1&size=bestfit&width=553&height=403" /> <figcaption>Figure <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="104" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-105-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-105-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-105-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-105-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-105-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-105-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="6" 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:6" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="36" href="#MJX-105-NCM-N-36"></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-105-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-105-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="6" 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:6" data-semantic-level-number="1" data-speech-node="true">6</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>: Energy Changes accompanying the thermite reaction. Because enthalpy is a state function, the overall enthalpy change for the reaction of 2 mol of Al(s) with 1 mol of Fe<sub>2</sub>O<sub>3</sub>(s) is −851.1 kJ, whether the reaction occurs in a single step (ΔH<sub>4</sub>, shown on the left) or in three hypothetical steps (shown on the right) that involve the successive formation of solid Al<sub>2</sub>O<sub>3</sub> and liquid iron (ΔH<sub>1</sub>), solid iron at 1758°C (ΔH<sub>2</sub>), and solid iron at 25°C (ΔH<sub>3</sub>). Thus ΔH<sub>4</sub> = ΔH<sub>1</sub> + ΔH<sub>2</sub> + ΔH<sub>3</sub>, as stated by Hess’s law.</figcaption> </figure> <p class="lt-chem-21725" style="background-color: unset;">Comparing parts (a) and (d) in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="105" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-106-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-106-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-106-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-106-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{5.6.1}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.06:_Hess's_Law#mjx-eqn:5.6.1"><g data-mml-node="mrow" data-latex="\ref{5.6.1}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><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="36" href="#MJX-106-NCM-N-36" 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></a></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\ref{5.6.1}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.6.1" data-latex="\ref{5.6.1}" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.6.1</mtext></mrow></math></mjx-assistive-mml></mjx-container> also illustrates an important point: The magnitude of ΔH for a reaction depends on the physical states of the reactants and the products (gas, liquid, solid, or solution). When the product is liquid iron at its melting point (part (a) in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="106" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-107-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-107-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-107-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-107-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{5.6.1}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.06:_Hess's_Law#mjx-eqn:5.6.1"><g data-mml-node="mrow" data-latex="\ref{5.6.1}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-107-NCM-N-35"></use><use data-c="2E" href="#MJX-107-NCM-N-2E" transform="translate(500,0)"></use><use data-c="36" href="#MJX-107-NCM-N-36" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-107-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-107-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{5.6.1}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.6.1" data-latex="\ref{5.6.1}" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.6.1</mtext></mrow></math></mjx-assistive-mml></mjx-container>), only 732.5 kJ of heat are released to the surroundings compared with 852 kJ when the product is solid iron at 25°C (part (d) in Equation <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="107" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-108-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-108-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-108-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-108-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{5.6.1}" data-semantic-structure="0"><a href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.06:_Hess's_Law#mjx-eqn:5.6.1"><g data-mml-node="mrow" data-latex="\ref{5.6.1}" class="MathJax_ref"><rect data-hitbox="true" fill="none" stroke="none" pointer-events="all" width="2056" height="688" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true"><use data-c="35" href="#MJX-108-NCM-N-35"></use><use data-c="2E" href="#MJX-108-NCM-N-2E" transform="translate(500,0)"></use><use data-c="36" href="#MJX-108-NCM-N-36" transform="translate(778,0)"></use><use data-c="2E" href="#MJX-108-NCM-N-2E" transform="translate(1278,0)"></use><use data-c="31" href="#MJX-108-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{5.6.1}" data-semantic-structure="0"><mrow href="#mjx-eqn%3A5.6.1" data-latex="\ref{5.6.1}" 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{5.6.1};href:#mjx-eqn%3A5.6.1" data-semantic-postfix="link" data-semantic-level-number="0" data-speech-node="true">5.6.1</mtext></mrow></math></mjx-assistive-mml></mjx-container>). The difference, 120 kJ, is the amount of energy that is released when 2 mol of liquid iron solidifies and cools to 25°C. It is important to specify the physical state of all reactants and products when writing a thermochemical equation.</p> <p class="lt-chem-21725" style="background-color: unset;">When using Hess’s law to calculate the value of ΔH for a reaction, follow this procedure:</p> <ol> <li class="lt-chem-21725" style="background-color: unset;">Identify the equation whose ΔH value is unknown and write individual reactions with known ΔH values that, when added together, will give the desired equation. We illustrate how to use this procedure in Example <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="108" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-109-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-109-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-109-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-109-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-109-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-109-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="6" 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:6" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="36" href="#MJX-109-NCM-N-36"></use></g><g data-mml-node="TeXAtom" 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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="6" 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:6" data-semantic-level-number="1" data-speech-node="true">6</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>.</li> <li class="lt-chem-21725" style="background-color: unset;">Arrange the chemical equations so that the reaction of interest is the sum of the individual reactions.</li> <li class="lt-chem-21725" style="background-color: unset;">If a reaction must be reversed, change the sign of ΔH for that reaction. Additionally, if a reaction must be multiplied by a factor to obtain the correct number of moles of a substance, multiply its ΔH value by that same factor.</li> <li class="lt-chem-21725" style="background-color: unset;">Add together the individual reactions and their corresponding ΔH values to obtain the reaction of interest and the unknown ΔH.</li> </ol> <div class="box-example"> <span id="Example_.5C(.5CPageIndex.7B1.7D.5C)"></span><span id="Example_.5C(.5CPageIndex.7B1.7D.5C)"></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="109" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" 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 661 406 666 396 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-110-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-110-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-110-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-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="6" 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:6" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="36" href="#MJX-110-NCM-N-36"></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="6" 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:6" data-semantic-level-number="1" data-speech-node="true">6</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></span></h5> <p class="lt-chem-21725" style="background-color: unset;">When carbon is burned with limited amounts of oxygen gas (O<sub>2</sub>), carbon monoxide (CO) is the main product:</p> <p class="mt-align-center lt-chem-21725" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" 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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:9" data-semantic-="" data-semantic-parent="32" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">g</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="32" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">)</mo></mrow></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="63" 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="56,59" data-semantic-content="48" data-semantic-parent="63" data-semantic-owns="56 48 59" 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="46,47" data-semantic-content="55" data-semantic-parent="60" data-semantic-owns="46 55 47" 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="56" 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="56" 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="56" 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="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="60" 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="depth:5" data-semantic-="" data-semantic-children="58" data-semantic-content="49" data-semantic-parent="60" data-semantic-owns="49 58" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="59" 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="unit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="50,52" data-semantic-content="57" data-semantic-parent="59" data-semantic-owns="50 57 52" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="221.0" 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="58" data-semantic-attributes="latex:221.0" data-semantic-level-number="6" data-speech-node="true">221.0</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="58" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mtext data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-parent="58" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">When carbon is burned in excess O<sub>2</sub>, carbon dioxide (CO<sub>2</sub>) is produced:</p> <p class="mt-align-center lt-chem-21725" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="111" style="font-size: 85%; min-width: 51.858ex; position: relative;"><svg width="100%" height="2.262ex" role="img" focusable="false" data-mjx-viewbox="0 -750 22921.3 1000" aria-hidden="true" style="vertical-align: -0.566ex; min-width: 51.858ex;"><defs><path id="MJX-112-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 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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="51" 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="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="55" 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="depth:5" data-semantic-="" data-semantic-children="53" data-semantic-content="44" data-semantic-parent="55" data-semantic-owns="44 53" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="54" 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="unit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="45,47" data-semantic-content="52" data-semantic-parent="54" data-semantic-owns="45 52 47" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="393.5" 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="53" data-semantic-attributes="latex:393.5" data-semantic-level-number="6" data-speech-node="true">393.5</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="53" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mtext data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-parent="53" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">Use this information to calculate the enthalpy change per mole of CO for the reaction of CO with O<sub>2</sub> to give CO<sub>2</sub>.</p> <p class="lt-chem-21725" style="background-color: unset;"><strong class="emphasis bold">Given: </strong>two balanced chemical equations and their ΔH values</p> <p class="lt-chem-21725" style="background-color: unset;"><strong class="emphasis bold">Asked for: </strong>enthalpy change for a third reaction</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-21725" style="background-color: unset;">After balancing the chemical equation for the overall reaction, write two equations whose ΔH values are known and that, when added together, give the equation for the overall reaction. (Reverse the direction of one or more of the equations as necessary, making sure to also reverse the sign of ΔH.)</li> <li class="lt-chem-21725" style="background-color: unset;">Multiply the equations by appropriate factors to ensure that they give the desired overall chemical equation when added together. To obtain the enthalpy change per mole of CO, write the resulting equations as a sum, along with the enthalpy change for each.</li> </ol> <span id="Solution:"></span><span id="Solution:"></span><h6>Solution:</h6> <p class="lt-chem-21725" style="background-color: unset;"><strong class="emphasis bold">A</strong> We begin by writing the balanced chemical equation for the reaction of interest:</p> <p class="mt-align-center lt-chem-21725" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="112" style="font-size: 85%; min-width: 49.241ex; position: relative;"><svg width="100%" height="2.737ex" role="img" focusable="false" data-mjx-viewbox="0 -855 21764.7 1209.9" aria-hidden="true" style="vertical-align: -0.803ex; min-width: 49.241ex;"><defs><path id="MJX-113-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 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data-semantic-annotation="nemeth:number;depth:4" data-semantic-id="58" data-semantic-parent="68" data-semantic-attributes="latex:\nonumber" data-semantic-operator="punctuated" data-semantic-level-number="3" data-speech-node="true" transform="translate(19692.7,0)"><use data-c="3F" href="#MJX-113-NCM-N-3F"></use></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -855 1 1209.9"><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="70" data-semantic-level-number="2" data-speech-node="true" transform="translate(0,-10)"><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 ( 3 \right ) \; \ce{CO (g) + 1/2 O2 (g) -> CO2 (g)} \quad \Delta H_{rxn}=? \nonumber " display="block" data-semantic-structure="(71 (70 (68 (67 (60 (4 1 2 3) 59 (46 (45 (41 6 40 (33 8 9 10)) 11 (44 (14 12 13) 42 (19 16 18) 43 (34 21 22 23))) 24 (39 25 38 (37 (28 26 27) 36 (35 30 31 32))))) 47 (64 (62 48 61 (56 49 (55 50 53 51 54 52))) 57 63)) 58) 0))"><mtable displaystyle="true" data-latex="{\mathrm{CO}\mskip2mu (\mathrm{g}) {}+{} \mathchoice{\textstyle\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}\,\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g}) {}\mathrel{\mhchemlongrightarrow}{} \mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})} \quad \Delta H_{rxn}=? \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="70" data-semantic-attributes="latex: \left ( 3 \right ) \\0003B \ce{CO (g) + 1/2 O2 (g) -> CO2 (g)} \quad \Delta H_{rxn}=? \nonumber " data-semantic-owns="70" 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="68" data-semantic-content="0" data-semantic-parent="71" data-semantic-owns="68 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="70" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="endpunct" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="67,58" data-semantic-content="58" data-semantic-parent="70" data-semantic-owns="67 58" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="text" data-semantic-annotation="depth:4" data-semantic-="" 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data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="60" 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{CO}\mskip2mu(\mathrm{g}){}+{}\mathchoice{\textstyle\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}\,\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g}){}\mathrel{\mhchemlongrightarrow}{}\mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g})}" data-semantic-type="infixop" data-semantic-role="unknown" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="45,39" data-semantic-content="24" data-semantic-parent="60" 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data-semantic-="" data-semantic-children="9" data-semantic-content="8,10" data-semantic-parent="41" data-semantic-owns="8 9 10" 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="33" 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{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:10" data-semantic-="" data-semantic-parent="33" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">g</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="33" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></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:8" data-semantic-="" data-semantic-parent="45" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="7" 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:8" data-semantic-="" data-semantic-children="14,19,34" data-semantic-content="42,43" data-semantic-parent="45" data-semantic-owns="14 42 19 43 34" data-semantic-level-number="7" data-speech-node="true"><mstyle displaystyle="false" data-latex="\textstyle\frac{1}{2}"><mfrac data-latex="\frac{1}{2}" data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-children="12,13" data-semantic-parent="44" data-semantic-attributes="latex:\textstyle\frac{1}{2}" data-semantic-owns="12 13" 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="14" data-semantic-attributes="latex:1" data-semantic-level-number="9" data-speech-node="true">1</mn><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="14" data-semantic-attributes="latex:2" data-semantic-level-number="9" 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data-semantic-parent="19" 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]{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:10" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="operator" 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data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="55" data-semantic-attributes="latex:x" data-semantic-level-number="8" data-speech-node="true">x</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="55" 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="55" data-semantic-attributes="latex:n" data-semantic-level-number="8" 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:6" data-semantic-="" data-semantic-parent="64" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="5" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="64" data-semantic-level-number="5" data-speech-node="true"></mrow></mrow></mrow><mo data-latex="\nonumber" data-semantic-type="punctuation" data-semantic-role="question" data-semantic-annotation="nemeth:number;depth:4" data-semantic-="" data-semantic-parent="68" data-semantic-attributes="latex:\nonumber" data-semantic-operator="punctuated" data-semantic-level-number="3" data-speech-node="true">?</mo></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">There are at least two ways to solve this problem using Hess’s law and the data provided. The simplest is to write two equations that can be added together to give the desired equation and for which the enthalpy changes are known. 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(\mathrm{s}) {}+{} \mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})} \quad \Delta H=+221.0 \; \text{kJ} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="58" data-semantic-attributes="latex: \ce{2 CO (g) -> 2 C (s) + O2 (g)} \quad \Delta H=+221.0 \\0003B \text{kJ} \nonumber " data-semantic-owns="58" 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="56" data-semantic-content="0" data-semantic-parent="59" data-semantic-owns="56 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="58" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="text" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="39,40,53" data-semantic-parent="58" data-semantic-collapsed="(56 (c 54 55) 39 40 53)" data-semantic-owns="39 40 53" data-semantic-level-number="2" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="{2\,\mathrm{CO}\mskip2mu(\mathrm{g}){}\mathrel{\mhchemlongrightarrow}{}2\,\mathrm{C}\mskip2mu(\mathrm{s}){}+{}\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g})}" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="36,38" data-semantic-content="16" data-semantic-parent="56" data-semantic-attributes="latex:{2\,\mathrm{CO}\mskip2mu(\mathrm{g}){}\mathrel{\mhchemlongrightarrow}{}2\,\mathrm{C}\mskip2mu(\mathrm{s}){}+{}\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g})};texclass:ORD" data-semantic-owns="36 16 38" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="unknown" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="33,35" data-semantic-content="8" data-semantic-parent="39" data-semantic-owns="33 8 35" 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:unit;depth:6" data-semantic-="" data-semantic-children="1,31" data-semantic-content="32" data-semantic-parent="36" data-semantic-owns="1 32 31" 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;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="33" 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="33" 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="3,25" data-semantic-content="30,3" data-semantic-parent="33" data-semantic-owns="3 30 25" data-semantic-level-number="6" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{CO}"><mi data-mjx-auto-op="false" data-latex="CO" 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="31" data-semantic-attributes="latex:\mathrm{CO};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">CO</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="31" 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="6" data-semantic-content="5,7" data-semantic-parent="31" data-semantic-owns="5 6 7" 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="25" 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{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:9" data-semantic-="" data-semantic-parent="25" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">g</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="25" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="8" data-speech-node="true">)</mo></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="36" 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="9,29" data-semantic-content="34" data-semantic-parent="36" data-semantic-owns="9 34 29" 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="35" 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="35" 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="11,26" data-semantic-content="28,11" data-semantic-parent="35" data-semantic-owns="11 28 26" data-semantic-level-number="6" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{C}"><mi mathvariant="normal" data-latex="C" 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="29" data-semantic-attributes="latex:\mathrm{C};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">C</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="29" 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="14" data-semantic-content="13,15" data-semantic-parent="29" data-semantic-owns="13 14 15" 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="26" 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="26" 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="26" 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="39" 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="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="20,27" data-semantic-content="37" data-semantic-parent="39" data-semantic-owns="20 37 27" data-semantic-level-number="4" data-speech-node="true"><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="17,19" data-semantic-parent="38" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="17 19" 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="20" 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]{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:7" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="6" 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:6" data-semantic-="" data-semantic-parent="38" 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="23" data-semantic-content="22,24" data-semantic-parent="38" data-semantic-owns="22 23 24" 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="27" 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{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:7" data-semantic-="" data-semantic-parent="27" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">g</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="27" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></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="56" 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="49,52" data-semantic-content="43" data-semantic-parent="56" data-semantic-owns="49 43 52" 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="41,42" data-semantic-content="48" data-semantic-parent="53" data-semantic-owns="41 48 42" 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="49" 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="49" 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="49" 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="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="53" 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="positive" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="51" data-semantic-content="44" data-semantic-parent="53" data-semantic-owns="44 51" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="52" 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="unit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="45,47" data-semantic-content="50" data-semantic-parent="52" data-semantic-owns="45 50 47" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="221.0" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:221.0" data-semantic-level-number="6" data-speech-node="true">221.0</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="51" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mtext data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-parent="51" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">Because we have reversed the direction of the reaction, the sign of ΔH is changed. 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data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-id="40" data-semantic-parent="46" data-semantic-attributes="latex:393.5" data-semantic-level-number="6" data-speech-node="true"><use data-c="33" href="#MJX-115-NCM-N-33"></use><use data-c="39" href="#MJX-115-NCM-N-39" transform="translate(500,0)"></use><use data-c="33" href="#MJX-115-NCM-N-33" transform="translate(1000,0)"></use><use data-c="2E" href="#MJX-115-NCM-N-2E" transform="translate(1500,0)"></use><use data-c="35" href="#MJX-115-NCM-N-35" transform="translate(1778,0)"></use></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-id="45" data-semantic-parent="46" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true" transform="translate(2278,0)"></g><g data-mml-node="mtext" data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-id="42" data-semantic-parent="46" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true" transform="translate(2556,0)"><use data-c="6B" href="#MJX-115-NCM-N-6B"></use><use data-c="4A" href="#MJX-115-NCM-N-4A" transform="translate(528,0)"></use></g></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="53" 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{C (s) + O2 (g) -> CO2 (s)} \quad \Delta H=-393.5 \; \text{kJ} \nonumber " display="block" 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data-speech-node="true">CO</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:7" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="6" 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:6" data-semantic-="" data-semantic-parent="33" 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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="44" 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="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="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="46" data-semantic-content="39" data-semantic-parent="48" data-semantic-owns="39 46" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="47" 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="unit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="40,42" data-semantic-content="45" data-semantic-parent="47" data-semantic-owns="40 45 42" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="393.5" 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="46" data-semantic-attributes="latex:393.5" data-semantic-level-number="6" data-speech-node="true">393.5</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="46" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mtext data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-parent="46" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;"><strong class="emphasis bold">B</strong> Adding these two equations together does not give the desired reaction, however, because the numbers of C(s) on the left and right sides do not cancel. 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data-mml-node="mtext" data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-id="52" data-semantic-parent="56" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true" transform="translate(2556,0)"><use data-c="6B" href="#MJX-116-NCM-N-6B"></use><use data-c="4A" href="#MJX-116-NCM-N-4A" transform="translate(528,0)"></use></g></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="63" 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{2 C (s) + 2 O2 (g) -> 2 CO2 (s)} \quad \Delta H=-787.0 \; \text{kJ} \nonumber " display="block" data-semantic-structure="(64 (63 (61 (44 (40 (36 1 35 (34 3 33 (30 5 6 7))) 8 (39 9 37 (14 11 13) 38 (31 16 17 18))) 19 (43 20 41 (25 22 24) 42 (32 27 28 29))) 45 (58 (54 46 53 47) 48 (57 49 (56 50 55 52)))) 0))"><mtable displaystyle="true" data-latex="{2\,\mathrm{C}\mskip2mu (\mathrm{s}) {}+{} 2\,\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g}) {}\mathrel{\mhchemlongrightarrow}{} 2\,\mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{s})} \quad \Delta H=-787.0 \; \text{kJ} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="63" data-semantic-attributes="latex: \ce{2 C (s) + 2 O2 (g) -> 2 CO2 (s)} \quad \Delta H=-787.0 \\0003B \text{kJ} \nonumber " data-semantic-owns="63" 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="61" data-semantic-content="0" data-semantic-parent="64" data-semantic-owns="61 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="63" data-semantic-level-number="2" data-speech-node="true"></mtd><mtd><mrow data-semantic-added="true" data-semantic-type="punctuated" data-semantic-role="text" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="44,45,58" data-semantic-parent="63" data-semantic-collapsed="(61 (c 59 60) 44 45 58)" data-semantic-owns="44 45 58" data-semantic-level-number="2" data-speech-node="true"><mrow data-mjx-texclass="ORD" 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39" 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:unit;depth:6" data-semantic-="" data-semantic-children="1,34" data-semantic-content="35" data-semantic-parent="40" data-semantic-owns="1 35 34" 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;nemeth:number;depth:7" data-semantic-="" data-semantic-parent="36" 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="36" 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="3,30" data-semantic-content="33,3" data-semantic-parent="36" data-semantic-owns="3 33 30" data-semantic-level-number="6" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{C}"><mi mathvariant="normal" data-latex="C" 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="34" data-semantic-attributes="latex:\mathrm{C};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="7" data-speech-node="true">C</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" 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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:8" data-semantic-="" data-semantic-parent="14" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="7" 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:7" data-semantic-="" data-semantic-parent="39" 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="17" data-semantic-content="16,18" data-semantic-parent="39" data-semantic-owns="16 17 18" 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data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-id="211" data-semantic-parent="212" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true" transform="translate(2278,0)"></g><g data-mml-node="mtext" data-latex="\text{kJ}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-id="209" data-semantic-parent="212" data-semantic-attributes="latex:\text{kJ}" data-semantic-level-number="6" data-speech-node="true" transform="translate(2556,0)"><use data-c="6B" href="#MJX-117-NCM-N-6B"></use><use data-c="4A" href="#MJX-117-NCM-N-4A" transform="translate(528,0)"></use></g></g></g></g></g></g></g><line data-line="h" class="mjx-solid" x1="0" y1="-930" x2="31639.2" y2="-930"></line></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" \begin{align*} \ce{2 CO (g) &-> \cancel{2 C(s)} + \cancel{O_2 (g)} } & \Delta H & = -\Delta H_1 = +221.0 \; \text{kJ} \\ \ce{\cancel{2 C (s)} + \cancel{2} O2 (g) &-> 2 CO2 (g)} & \Delta H & = -2\Delta H_2 =-787.0 \; \text{kJ} \\[2ex] \hline \ce{2 CO (g) + O2 (g) &-> 2 CO2 (g)} & \Delta H &=-566.0 \; \text{kJ} \end{align*} \nonumber " display="block" data-semantic-structure="(217 (66 (12 (11 0 10 (9 2 8 (7 4 5 6)))) (39 (38 (37 14 (25 (24 15 23 (22 16 21 (20 17 18 19))))) 26 (36 (35 (29 27 28) 34 (33 30 31 32))))) (44 (43 40 42 41)) (65 (64 57 46 (60 47 (59 48 58 (51 49 50))) 52 (63 53 (62 54 61 56))))) (149 (99 (98 (91 (77 (76 67 75 (74 68 73 (72 69 70 71)))) 78 (80 79)) 81 (95 82 94 (93 (85 83 84) 92 (90 87 88 89))))) (120 (119 101 (118 102 117 (116 104 115 (114 (107 105 106) 113 (112 109 110 111)))))) (125 (124 121 123 122)) (148 (147 139 127 (143 128 (142 129 140 130 141 (133 131 132))) 134 (146 135 (145 136 144 138))))) (216 (177 (176 (175 150 174 (173 152 172 (166 154 155 156))) 157 (171 158 170 (169 (161 159 160) 168 (167 163 164 165))))) (198 (197 179 (196 180 195 (194 182 193 (192 (185 183 184) 191 (190 187 188 189)))))) (203 (202 199 201 200)) (215 (214 210 205 (213 206 (212 207 211 209))))))"><mtable displaystyle="true" columnalign="right left right left" columnspacing="0em 2em 0em" rowspacing="3pt 1.16em 0.30000000000000004em" data-break-align="bottom top bottom top" rowlines="none solid" data-latex="2\,\mathrm{CO}\mskip2mu (\mathrm{g}) {}+{} \mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})& {}\mathrel{\mhchemlongrightarrow}{} 2\,\mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g}) & \Delta H &=-566.0 \; \text{kJ} \end{align*} \nonumber" data-semantic-type="table" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="66,149,216" data-semantic-attributes="latex: \begin{align*} \ce{2 CO (g) &-> \cancel{2 C(s)} + \cancel{O_2 (g)} } & \Delta H & = -\Delta H_1 = +221.0 \\0003B \text{kJ} \\ \ce{\cancel{2 C (s)} + \cancel{2} O2 (g) &-> 2 CO2 (g)} & \Delta H & = -2\Delta H_2 =-787.0 \\0003B \text{kJ} \\[2ex] \hline \ce{2 CO (g) + O2 (g) &-> 2 CO2 (g)} & \Delta H &=-566.0 \\0003B \text{kJ} \end{align*} \nonumber " data-semantic-owns="66 149 216" 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="12,39,44,65" data-semantic-parent="217" data-semantic-owns="12 39 44 65" 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="11" data-semantic-parent="66" data-semantic-owns="11" 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-="" 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data-semantic-content="8,2" data-semantic-parent="11" data-semantic-owns="2 8 7" data-semantic-level-number="4" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{CO}"><mi data-mjx-auto-op="false" data-latex="CO" 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="9" data-semantic-attributes="latex:\mathrm{CO};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">CO</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="9" 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="5" data-semantic-content="4,6" data-semantic-parent="9" data-semantic-owns="4 5 6" 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="7" 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{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:7" data-semantic-="" data-semantic-parent="7" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">g</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="7" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="38" data-semantic-parent="66" data-semantic-owns="38" data-semantic-level-number="2" data-speech-node="true"><mstyle indentshift="2em"><mi></mi><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="37,36" data-semantic-content="26" data-semantic-parent="39" data-semantic-owns="37 26 36" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="unknown" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="25" data-semantic-content="14" data-semantic-parent="38" data-semantic-owns="14 25" data-semantic-level-number="4" data-speech-node="true"><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="37" data-semantic-attributes="latex:\mathrel{\mhchemlongrightarrow};texclass:REL" data-semantic-operator="prefixop," data-semantic-level-number="5" data-speech-node="true"></mo></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><menclose notation="updiagonalstrike" data-latex="\cancel{2 C(s)}" data-semantic-type="enclose" data-semantic-role="updiagonalstrike" data-semantic-annotation="depth:6" 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data-semantic-="" data-semantic-children="212" data-semantic-content="206" data-semantic-parent="214" data-semantic-owns="206 212" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="213" 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="unit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="207,209" data-semantic-content="211" data-semantic-parent="213" data-semantic-owns="207 211 209" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="566.0" 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="212" data-semantic-attributes="latex:566.0" data-semantic-level-number="6" data-speech-node="true">566.0</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="212" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mtext data-latex="\text{kJ}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-parent="212" data-semantic-attributes="latex:\text{kJ}" data-semantic-level-number="6" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mstyle></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">Note that the overall chemical equation and the enthalpy change for the reaction are both for the reaction of 2 mol of CO with O<sub>2</sub>, and the problem asks for the amount per mole of CO. 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data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true" transform="translate(2556,0)"><use data-c="6B" href="#MJX-118-NCM-N-6B"></use><use data-c="4A" href="#MJX-118-NCM-N-4A" transform="translate(528,0)"></use></g></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -855 1 1209.9"><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="60" data-semantic-level-number="2" data-speech-node="true" transform="translate(0,-10)"><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=" \ce{ CO (g) + 1/2 O2 (g) -> CO2 (g)} \quad \Delta H = -283.0 \; \text{kJ} \nonumber " display="block" data-semantic-structure="(61 (60 (58 (41 (40 (36 1 35 (28 3 4 5)) 6 (39 (9 7 8) 37 (14 11 13) 38 (29 16 17 18))) 19 (34 20 33 (32 (23 21 22) 31 (30 25 26 27)))) 42 (55 (51 43 50 44) 45 (54 46 (53 47 52 49)))) 0))"><mtable displaystyle="true" data-latex="{\mathrm{CO}\mskip2mu (\mathrm{g}) {}+{} \mathchoice{\textstyle\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}\,\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g}) {}\mathrel{\mhchemlongrightarrow}{} \mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})} \quad \Delta H = -283.0 \; \text{kJ} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="60" data-semantic-attributes="latex: \ce{ CO (g) + 1/2 O2 (g) -> CO2 (g)} \quad \Delta H = -283.0 \\0003B \text{kJ} \nonumber " data-semantic-owns="60" data-semantic-level-number="0" data-speech-node="true"><mlabeledtr data-semantic-type="line" data-semantic-role="multiline" 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data-latex="{\mathrm{CO}\mskip2mu(\mathrm{g}){}+{}\mathchoice{\textstyle\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}\,\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g}){}\mathrel{\mhchemlongrightarrow}{}\mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g})}" data-semantic-type="infixop" data-semantic-role="unknown" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="40,34" data-semantic-content="19" data-semantic-parent="58" data-semantic-attributes="latex:{\mathrm{CO}\mskip2mu(\mathrm{g}){}+{}\mathchoice{\textstyle\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}{\frac{1}{2}}\,\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g}){}\mathrel{\mhchemlongrightarrow}{}\mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu(\mathrm{g})};texclass:ORD" data-semantic-owns="40 19 34" data-semantic-level-number="3" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="addition" 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data-speech-node="true">CO</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="36" 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="4" data-semantic-content="3,5" data-semantic-parent="36" data-semantic-owns="3 4 5" 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="28" 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{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:8" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">g</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="28" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></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:6" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="5" 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:6" data-semantic-="" data-semantic-children="9,14,29" data-semantic-content="37,38" data-semantic-parent="40" data-semantic-owns="9 37 14 38 29" data-semantic-level-number="5" data-speech-node="true"><mstyle displaystyle="false" data-latex="\textstyle\frac{1}{2}"><mfrac data-latex="\frac{1}{2}" data-semantic-type="fraction" data-semantic-role="vulgar" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-children="7,8" data-semantic-parent="39" data-semantic-attributes="latex:\textstyle\frac{1}{2}" data-semantic-owns="7 8" data-semantic-level-number="6" 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:8" data-semantic-="" data-semantic-parent="9" data-semantic-attributes="latex:1" data-semantic-level-number="7" data-speech-node="true">1</mn><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="9" data-semantic-attributes="latex:2" data-semantic-level-number="7" data-speech-node="true">2</mn></mfrac></mstyle><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="39" 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="11,13" data-semantic-parent="39" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="11 13" 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="14" 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]{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:8" data-semantic-="" data-semantic-parent="14" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="7" 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:7" data-semantic-="" data-semantic-parent="39" 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="17" data-semantic-content="16,18" data-semantic-parent="39" data-semantic-owns="16 17 18" 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="29" 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{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:8" data-semantic-="" data-semantic-parent="29" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">g</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="29" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="7" data-speech-node="true">)</mo></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="41" 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="appl" data-semantic-role="simple function" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="20,32" data-semantic-content="33,20" data-semantic-parent="41" data-semantic-owns="20 33 32" data-semantic-level-number="4" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{CO}"><mi data-mjx-auto-op="false" data-latex="CO" 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="34" data-semantic-attributes="latex:\mathrm{CO};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">CO</mi></mrow><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="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="23,30" data-semantic-content="31" data-semantic-parent="34" data-semantic-owns="23 31 30" 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="21,22" data-semantic-parent="32" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="21 22" data-semantic-level-number="6" 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:8" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="7" 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:8" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="7" 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: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><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="26" data-semantic-content="25,27" data-semantic-parent="32" data-semantic-owns="25 26 27" 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="30" 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{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:8" data-semantic-="" data-semantic-parent="30" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">g</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="30" 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="58" 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="51,54" data-semantic-content="45" data-semantic-parent="58" data-semantic-owns="51 45 54" 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="43,44" data-semantic-content="50" data-semantic-parent="55" data-semantic-owns="43 50 44" 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="51" 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="51" 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="51" 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="equality" data-semantic-annotation="nemeth:number;depth:5" data-semantic-="" data-semantic-parent="55" 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="depth:5" data-semantic-="" data-semantic-children="53" data-semantic-content="46" data-semantic-parent="55" data-semantic-owns="46 53" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="54" 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="unit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="47,49" data-semantic-content="52" data-semantic-parent="54" data-semantic-owns="47 52 49" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="283.0" 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="53" data-semantic-attributes="latex:283.0" data-semantic-level-number="6" data-speech-node="true">283.0</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="53" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mtext data-latex="\nonumber" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-parent="53" data-semantic-attributes="latex:\nonumber" data-semantic-level-number="6" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">An alternative and equally valid way to solve this problem is to write the two given equations as occurring in steps. Note that we have multiplied the equations by the appropriate factors to allow us to cancel terms:</p> <p class="mt-align-center lt-chem-21725" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" tabindex="0" ctxtmenu_counter="118" style="font-size: 85%; position: relative;"><svg width="86.056ex" height="10.543ex" role="img" focusable="false" viewbox="0 -2580 38036.7 4660" aria-hidden="true" style="vertical-align: -4.706ex;"><defs><path id="MJX-119-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-119-NCM-N-41" d="M583 3L717 0L717 39L695 39C670 39 653 40 646 42C631 47 621 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transform="scale(1,-1)"><g data-mml-node="math" data-latex=" \begin{alignat*}{3} \text{(A)} \quad && \ce{ 2 C (s) + O2 (g) &-> \cancel{2 CO (g)}} \qquad & \Delta H_A &= \Delta H_1 &&= + 221.0 \; \text{kJ} \\ \text{(B)} \quad && \ce{ \cancel{2 CO (g)} + O2 (g) &-> 2 CO2 (g)} \qquad & \Delta H_B && &= ? \\ \text{(C)} \quad && \ce{2 C (s) + 2 O2 (g) &-> 2 CO2 (g)} \qquad & \Delta H &= 2 \Delta H_2 &= 2 \times \left ( -393.5 \; \text{kJ} \right ) &= -787.0 \; \text{kJ} \end{alignat*} " data-semantic-structure="(266 (86 (4 (3 0 1)) 5 (33 (32 (31 6 30 (29 8 28 (22 10 11 12))) 13 (27 14 26 (25 (17 15 16) 24 (23 19 20 21))))) (54 (53 (51 35 (49 (48 36 47 (46 37 45 (44 38 43 (42 39 40 41)))))) 50)) (61 (60 55 59 (58 56 57))) (72 (71 68 63 (70 64 69 (67 65 66)))) 73 (85 (84 80 75 (83 76 (82 77 81 79))))) (158 (91 (90 87 88)) 92 (122 (121 (106 (105 93 104 (103 94 102 (101 95 100 (99 96 97 98))))) 107 (120 108 119 (118 (111 109 110) 117 (116 113 114 115))))) (143 (142 (140 124 (139 125 137 (130 127 129) 138 (136 132 133 134))) 135)) (150 (149 144 148 (147 145 146))) 151 152 (157 (156 154 155))) (265 (163 (162 159 160)) 164 (196 (195 (192 165 191 (190 167 189 (183 169 170 171))) 172 (194 173 193 (188 175 187 (186 (178 176 177) 185 (184 180 181 182)))))) (217 (216 (214 198 (213 199 211 (204 201 203) 212 (210 206 207 208))) 209)) (222 (221 218 220 219)) (235 (234 230 224 (233 225 231 226 232 (229 227 228)))) (252 (251 249 236 (250 237 238 (248 239 (247 240 (246 241 245 243)) 244)))) (264 (263 259 254 (262 255 (261 256 260 258))))))"><g data-mml-node="mtable" data-latex="2\,\mathrm{C}\mskip2mu (\mathrm{s}) {}+{} 2\,\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})& {}\mathrel{\mhchemlongrightarrow}{} 2\,\mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g}) \qquad & \Delta H &= 2 \Delta H_2 &= 2 \times \left ( -393.5 \; \text{kJ} \right ) &= -787.0 \; \text{kJ} \end{alignat*}" data-semantic-type="table" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-id="266" data-semantic-children="86,158,265" data-semantic-attributes="latex: \begin{alignat*}{3} \text{(A)} \quad && \ce{ 2 C (s) + O2 (g) &-> \cancel{2 CO (g)}} \qquad & \Delta H_A &= \Delta H_1 &&= + 221.0 \\0003B \text{kJ} \\ \text{(B)} \quad && \ce{ \cancel{2 CO (g)} + O2 (g) &-> 2 CO2 (g)} \qquad & \Delta H_B && &= ? \\ \text{(C)} \quad && \ce{2 C (s) + 2 O2 (g) &-> 2 CO2 (g)} \qquad & \Delta H &= 2 \Delta H_2 &= 2 \times \left ( -393.5 \\0003B \text{kJ} \right ) &= -787.0 \\0003B \text{kJ} \end{alignat*} " data-semantic-owns="86 158 265" data-semantic-level-number="0" data-speech-node="true"><g data-mml-node="mtr" data-latex="{3}" data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-id="86" data-semantic-children="4,5,33,54,61,72,73,85" data-semantic-parent="266" data-semantic-attributes="latex:{3}" data-semantic-owns="4 5 33 54 61 72 73 85" data-semantic-level-number="1" 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transform="translate(1500,0)"></use><use data-c="30" href="#MJX-119-NCM-N-30" transform="translate(1778,0)"></use></g><g data-mml-node="mspace" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:7" data-semantic-id="260" data-semantic-parent="261" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true" transform="translate(2278,0)"></g><g data-mml-node="mtext" data-latex="\text{kJ}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-id="258" data-semantic-parent="261" data-semantic-attributes="latex:\text{kJ}" data-semantic-level-number="6" data-speech-node="true" transform="translate(2556,0)"><use data-c="6B" href="#MJX-119-NCM-N-6B"></use><use data-c="4A" href="#MJX-119-NCM-N-4A" transform="translate(528,0)"></use></g></g></g></g></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math data-latex=" \begin{alignat*}{3} \text{(A)} \quad && \ce{ 2 C (s) + O2 (g) &-> \cancel{2 CO (g)}} \qquad & \Delta H_A &= \Delta H_1 &&= + 221.0 \; \text{kJ} \\ \text{(B)} \quad && \ce{ \cancel{2 CO (g)} + O2 (g) &-> 2 CO2 (g)} \qquad & \Delta H_B && &= ? \\ \text{(C)} \quad && \ce{2 C (s) + 2 O2 (g) &-> 2 CO2 (g)} \qquad & \Delta H &= 2 \Delta H_2 &= 2 \times \left ( -393.5 \; \text{kJ} \right ) &= -787.0 \; \text{kJ} \end{alignat*} " display="block" data-semantic-structure="(266 (86 (4 (3 0 1)) 5 (33 (32 (31 6 30 (29 8 28 (22 10 11 12))) 13 (27 14 26 (25 (17 15 16) 24 (23 19 20 21))))) (54 (53 (51 35 (49 (48 36 47 (46 37 45 (44 38 43 (42 39 40 41)))))) 50)) (61 (60 55 59 (58 56 57))) (72 (71 68 63 (70 64 69 (67 65 66)))) 73 (85 (84 80 75 (83 76 (82 77 81 79))))) (158 (91 (90 87 88)) 92 (122 (121 (106 (105 93 104 (103 94 102 (101 95 100 (99 96 97 98))))) 107 (120 108 119 (118 (111 109 110) 117 (116 113 114 115))))) (143 (142 (140 124 (139 125 137 (130 127 129) 138 (136 132 133 134))) 135)) (150 (149 144 148 (147 145 146))) 151 152 (157 (156 154 155))) (265 (163 (162 159 160)) 164 (196 (195 (192 165 191 (190 167 189 (183 169 170 171))) 172 (194 173 193 (188 175 187 (186 (178 176 177) 185 (184 180 181 182)))))) (217 (216 (214 198 (213 199 211 (204 201 203) 212 (210 206 207 208))) 209)) (222 (221 218 220 219)) (235 (234 230 224 (233 225 231 226 232 (229 227 228)))) (252 (251 249 236 (250 237 238 (248 239 (247 240 (246 241 245 243)) 244)))) (264 (263 259 254 (262 255 (261 256 260 258))))))"><mtable displaystyle="true" columnalign="right left right left right left right left" columnspacing="0em 0em 0em 0em 0em 0em 0em" rowspacing="3pt" data-break-align="bottom top bottom top bottom top bottom top" data-latex="2\,\mathrm{C}\mskip2mu (\mathrm{s}) {}+{} 2\,\mathrm{O}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g})& {}\mathrel{\mhchemlongrightarrow}{} 2\,\mathrm{CO}{\vphantom{A}}_{\smash[t]{2}}\mskip2mu (\mathrm{g}) \qquad & \Delta H &= 2 \Delta H_2 &= 2 \times \left ( -393.5 \; \text{kJ} \right ) &= -787.0 \; \text{kJ} \end{alignat*}" data-semantic-type="table" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="86,158,265" data-semantic-attributes="latex: \begin{alignat*}{3} \text{(A)} \quad && \ce{ 2 C (s) + O2 (g) &-> \cancel{2 CO (g)}} \qquad & \Delta H_A &= \Delta H_1 &&= + 221.0 \\0003B \text{kJ} \\ \text{(B)} \quad && \ce{ \cancel{2 CO (g)} + O2 (g) &-> 2 CO2 (g)} \qquad & \Delta H_B && &= ? \\ \text{(C)} \quad && \ce{2 C (s) + 2 O2 (g) &-> 2 CO2 (g)} \qquad & \Delta H &= 2 \Delta H_2 &= 2 \times \left ( -393.5 \\0003B \text{kJ} \right ) &= -787.0 \\0003B \text{kJ} \end{alignat*} " data-semantic-owns="86 158 265" data-semantic-level-number="0" data-speech-node="true"><mtr data-latex="{3}" data-semantic-type="row" data-semantic-role="table" data-semantic-annotation="depth:2" data-semantic-="" data-semantic-children="4,5,33,54,61,72,73,85" data-semantic-parent="266" 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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="234" data-semantic-parent="265" data-semantic-owns="234" 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="230,233" data-semantic-content="224" data-semantic-parent="235" data-semantic-owns="230 224 233" 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="234" 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="234" 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="implicit" data-semantic-annotation="clearspeak:unit;depth:5" data-semantic-="" data-semantic-children="225,226,229" data-semantic-content="231,232" data-semantic-parent="234" data-semantic-owns="225 231 226 232 229" 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;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="233" data-semantic-attributes="latex:2" data-semantic-level-number="5" data-speech-node="true">2</mn><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="233" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><mi mathvariant="normal" data-latex="\Delta" data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="233" 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="233" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="5" data-speech-node="true">⁢</mo><msub data-latex="H_2" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="227,228" data-semantic-parent="233" data-semantic-attributes="latex:H_2" data-semantic-owns="227 228" 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="229" data-semantic-attributes="latex:H" data-semantic-level-number="6" data-speech-node="true">H</mi><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="229" data-semantic-attributes="latex:2" data-semantic-level-number="6" data-speech-node="true">2</mn></msub></mrow></mrow></mstyle></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="251" data-semantic-parent="265" data-semantic-owns="251" data-semantic-level-number="2" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="249,250" data-semantic-content="236" data-semantic-parent="252" data-semantic-owns="249 236 250" 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="251" 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="251" 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="237,248" data-semantic-content="238" data-semantic-parent="251" data-semantic-owns="237 238 248" 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;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="250" data-semantic-attributes="latex:2" data-semantic-level-number="5" data-speech-node="true">2</mn><mo data-latex="\times" data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="250" data-semantic-attributes="latex:\times" data-semantic-operator="infixop,×" data-semantic-level-number="5" data-speech-node="true">×</mo><mrow data-mjx-texclass="INNER" data-latex="\left( -393.5 \; \text{kJ} \right )" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:6" data-semantic-="" data-semantic-children="247" data-semantic-content="239,244" data-semantic-parent="250" data-semantic-attributes="latex:\left( -393.5 \\0003B \text{kJ} \right );texclass:INNER" data-semantic-owns="239 247 244" data-semantic-level-number="5" data-speech-node="true"><mo data-mjx-texclass="OPEN" data-latex="\left(" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="248" data-semantic-attributes="latex:\left(;texclass:OPEN" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="246" data-semantic-content="240" data-semantic-parent="248" data-semantic-owns="240 246" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="247" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="7" data-speech-node="true">−</mo><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="unit" data-semantic-annotation="clearspeak:unit;depth:8" data-semantic-="" data-semantic-children="241,243" data-semantic-content="245" data-semantic-parent="247" data-semantic-owns="241 245 243" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="393.5" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="246" data-semantic-attributes="latex:393.5" data-semantic-level-number="8" data-speech-node="true">393.5</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="246" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><mtext data-latex="\text{kJ}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:9" data-semantic-="" data-semantic-parent="246" data-semantic-attributes="latex:\text{kJ}" data-semantic-level-number="8" data-speech-node="true">kJ</mtext></mrow></mrow><mo data-mjx-texclass="CLOSE" data-latex="\right)" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="248" data-semantic-attributes="latex:\right);texclass:CLOSE" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow></mrow></mtd><mtd data-semantic-type="cell" data-semantic-role="table" data-semantic-annotation="depth:3" data-semantic-="" data-semantic-children="263" data-semantic-parent="265" data-semantic-owns="263" 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="259,262" data-semantic-content="254" data-semantic-parent="264" data-semantic-owns="259 254 262" 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="263" 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="263" 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="depth:5" data-semantic-="" data-semantic-children="261" data-semantic-content="255" data-semantic-parent="263" data-semantic-owns="255 261" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="262" 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="unit" data-semantic-annotation="clearspeak:unit;depth:6" data-semantic-="" data-semantic-children="256,258" data-semantic-content="260" data-semantic-parent="262" data-semantic-owns="256 260 258" data-semantic-level-number="5" data-speech-node="true"><mn data-latex="787.0" 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="261" data-semantic-attributes="latex:787.0" data-semantic-level-number="6" data-speech-node="true">787.0</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="261" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true"></mspace><mtext data-latex="\text{kJ}" data-semantic-type="identifier" data-semantic-role="unit" data-semantic-font="normal" data-semantic-annotation="clearspeak:unit;depth:7" data-semantic-="" data-semantic-parent="261" data-semantic-attributes="latex:\text{kJ}" data-semantic-level-number="6" data-speech-node="true">kJ</mtext></mrow></mrow></mrow></mstyle></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">The sum of reactions A and B is reaction C, which corresponds to the combustion of 2 mol of carbon to give CO<sub>2</sub>. From Hess’s law, ΔH<sub>A</sub> + ΔH<sub>B</sub> = ΔH<sub>C</sub>, and we are given ΔH for reactions A and C. 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\Delta H_{B} = -787.0 \; kJ \\ \Delta H_{B} = -566.0 \end{matrix} \nonumber " data-semantic-structure="(47 (46 (44 (30 (28 (23 (20 1 (19 2 17 4 18 5)) 6 (22 7 21 (10 8 9))) 11 (27 12 (26 13 24 15 25 16)))) (43 (41 (39 31 38 (34 32 33)) 35 (40 36 37)))) 0))"><g data-mml-node="mtable" data-latex="\begin{matrix} -221.0 \; kJ + \Delta H_{B} = -787.0 \; kJ \\ \Delta H_{B} = -566.0 \end{matrix} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-id="47" data-semantic-children="46" data-semantic-attributes="latex: \begin{matrix} -221.0 \\0003B kJ + \Delta H_{B} = -787.0 \\0003B kJ \\ \Delta H_{B} = -566.0 \end{matrix} \nonumber " data-semantic-owns="46" data-semantic-level-number="0" data-speech-node="true" transform="translate(800,0) translate(-800,0)"><g transform="translate(0 1450) matrix(1 0 0 -1 0 0) scale(46.04)"><svg data-table="true" preserveaspectratio="xMidYMid" viewbox="6907.8 -1450 1 2400"><g transform="matrix(1 0 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data-mml-node="mn" data-latex="566.0" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:7" data-semantic-id="37" data-semantic-parent="40" data-semantic-attributes="latex:566.0" data-semantic-level-number="6" data-speech-node="true" transform="translate(778,0)"><use data-c="35" href="#MJX-120-NCM-N-35"></use><use data-c="36" href="#MJX-120-NCM-N-36" transform="translate(500,0)"></use><use data-c="36" href="#MJX-120-NCM-N-36" transform="translate(1000,0)"></use><use data-c="2E" href="#MJX-120-NCM-N-2E" transform="translate(1500,0)"></use><use data-c="30" href="#MJX-120-NCM-N-30" transform="translate(1778,0)"></use></g></g></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -1450 1 2400"><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="46" 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=" \begin{matrix} -221.0 \; kJ + \Delta H_{B} = -787.0 \; kJ \\ \Delta H_{B} = -566.0 \end{matrix} \nonumber " display="block" data-semantic-structure="(47 (46 (44 (30 (28 (23 (20 1 (19 2 17 4 18 5)) 6 (22 7 21 (10 8 9))) 11 (27 12 (26 13 24 15 25 16)))) (43 (41 (39 31 38 (34 32 33)) 35 (40 36 37)))) 0))"><mtable displaystyle="true" data-latex="\begin{matrix} -221.0 \; kJ + \Delta H_{B} = -787.0 \; kJ \\ \Delta H_{B} = -566.0 \end{matrix} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="46" data-semantic-attributes="latex: \begin{matrix} -221.0 \\0003B kJ + \Delta H_{B} = -787.0 \\0003B kJ \\ \Delta H_{B} = -566.0 \end{matrix} \nonumber 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data-semantic-role="binomial" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="28" data-semantic-parent="44" data-semantic-owns="28" data-semantic-level-number="3" data-speech-node="true"><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="23,27" data-semantic-content="11" data-semantic-parent="30" data-semantic-owns="23 11 27" 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="20,22" data-semantic-content="6" data-semantic-parent="28" data-semantic-owns="20 6 22" data-semantic-level-number="5" data-speech-node="true"><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-children="19" data-semantic-content="1" data-semantic-parent="23" data-semantic-owns="1 19" data-semantic-level-number="6" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="nemeth:number;depth:8" data-semantic-="" data-semantic-parent="20" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" 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="2,4,5" data-semantic-content="17,18" data-semantic-parent="20" data-semantic-owns="2 17 4 18 5" data-semantic-level-number="7" data-speech-node="true"><mn data-latex="221.0" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:9" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:221.0" data-semantic-level-number="8" data-speech-node="true">221.0</mn><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="19" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" 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:9" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:k" data-semantic-level-number="8" data-speech-node="true">k</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="19" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" 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:9" data-semantic-="" data-semantic-parent="19" data-semantic-attributes="latex:J" data-semantic-level-number="8" data-speech-node="true">J</mi></mrow></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="23" data-semantic-attributes="latex:+" 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="7,10" data-semantic-content="21" data-semantic-parent="23" data-semantic-owns="7 21 10" data-semantic-level-number="6" 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;depth:8" data-semantic-="" data-semantic-parent="22" data-semantic-attributes="latex:\Delta" data-semantic-level-number="7" data-speech-node="true">Δ</mi><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-parent="22" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="7" data-speech-node="true">⁢</mo><msub data-latex="H_{B}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:8" data-semantic-="" data-semantic-children="8,9" data-semantic-parent="22" data-semantic-attributes="latex:H_{B}" data-semantic-owns="8 9" data-semantic-level-number="7" 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:9" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:H" data-semantic-level-number="8" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{B}"><mi data-latex="B" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:9" data-semantic-="" data-semantic-parent="10" data-semantic-attributes="latex:{B};texclass:ORD" data-semantic-level-number="8" data-speech-node="true">B</mi></mrow></msub></mrow></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="28" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="5" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-children="26" data-semantic-content="12" data-semantic-parent="28" data-semantic-owns="12 26" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="27" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" 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:simple;clearspeak:unit;depth:7" data-semantic-="" data-semantic-children="13,15,16" data-semantic-content="24,25" data-semantic-parent="27" data-semantic-owns="13 24 15 25 16" data-semantic-level-number="6" data-speech-node="true"><mn data-latex="787.0" data-semantic-type="number" data-semantic-role="float" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:8" data-semantic-="" data-semantic-parent="26" data-semantic-attributes="latex:787.0" data-semantic-level-number="7" data-speech-node="true">787.0</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="26" 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="26" 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="26" 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="26" data-semantic-attributes="latex:J" data-semantic-level-number="7" data-speech-node="true">J</mi></mrow></mrow></mrow></mtd></mtr><mtr data-semantic-type="line" data-semantic-role="binomial" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-children="41" data-semantic-parent="44" data-semantic-owns="41" data-semantic-level-number="3" data-speech-node="true"><mtd><mrow data-semantic-added="true" data-semantic-type="relseq" data-semantic-role="equality" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="39,40" data-semantic-content="35" data-semantic-parent="43" data-semantic-owns="39 35 40" 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:unit;depth:6" data-semantic-="" data-semantic-children="31,34" data-semantic-content="38" data-semantic-parent="41" data-semantic-owns="31 38 34" data-semantic-level-number="5" 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:7" data-semantic-="" data-semantic-parent="39" data-semantic-attributes="latex:\Delta" 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="39" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="6" data-speech-node="true">⁢</mo><msub data-latex="H_{B}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-children="32,33" data-semantic-parent="39" data-semantic-attributes="latex:H_{B}" data-semantic-owns="32 33" 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;depth:8" data-semantic-="" data-semantic-parent="34" data-semantic-attributes="latex:H" data-semantic-level-number="7" data-speech-node="true">H</mi><mrow data-mjx-texclass="ORD" data-latex="{B}"><mi data-latex="B" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:8" data-semantic-="" data-semantic-parent="34" data-semantic-attributes="latex:{B};texclass:ORD" data-semantic-level-number="7" data-speech-node="true">B</mi></mrow></msub></mrow><mo data-latex="=" data-semantic-type="relation" data-semantic-role="equality" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="41" data-semantic-attributes="latex:=" data-semantic-operator="relseq,=" data-semantic-level-number="5" data-speech-node="true">=</mo><mrow data-semantic-added="true" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-children="37" data-semantic-content="36" data-semantic-parent="41" data-semantic-owns="36 37" data-semantic-level-number="5" data-speech-node="true"><mo data-latex="-" data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="40" data-semantic-attributes="latex:-" data-semantic-operator="prefixop,−" data-semantic-level-number="6" data-speech-node="true">−</mo><mn data-latex="566.0" 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="40" data-semantic-attributes="latex:566.0" data-semantic-level-number="6" data-speech-node="true">566.0</mn></mrow></mrow></mtd></mtr></mtable></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">This is again the enthalpy change for the conversion of 2 mol of CO to CO<sub>2</sub>. The enthalpy change for the conversion of 1 mol of CO to CO<sub>2</sub> is therefore −566.0 ÷ 2 = −283.0 kJ/mol of CO, which is the same result we obtained earlier. As you can see, there may be more than one correct way to solve a problem.</p> </div> <div class="box-exercise"> <span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C)"></span><span id="Exercise_.5C(.5CPageIndex.7B1.7D.5C)"></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="120" style="font-size: 85%; position: relative;"><svg width="4.652ex" height="1.557ex" role="img" focusable="false" viewbox="0 -666 2056 688" aria-hidden="true" style="vertical-align: -0.05ex;"><defs><path id="MJX-121-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-121-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-121-NCM-N-36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"></path><path id="MJX-121-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-121-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-121-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="6" 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:6" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="36" href="#MJX-121-NCM-N-36"></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-121-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-121-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="6" 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:6" data-semantic-level-number="1" data-speech-node="true">6</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></span></h5> <p class="lt-chem-21725" style="background-color: unset;">The reaction of acetylene (C<sub>2</sub>H<sub>2</sub>) with hydrogen (H<sub>2</sub>) can produce either ethylene (C<sub>2</sub>H<sub>4</sub>) or ethane (C<sub>2</sub>H<sub>6</sub>):</p> <p class="mt-align-center lt-chem-21725" style="background-color: unset;"><mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" display="true" width="full" tabindex="0" ctxtmenu_counter="121" style="font-size: 85%; min-width: 64.802ex; position: relative;"><svg width="100%" height="5.43ex" role="img" 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data-semantic-level-number="8" data-speech-node="true" transform="translate(3090.6,0)"><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:10" data-semantic-id="138" data-semantic-parent="140" data-semantic-attributes="latex:H" data-semantic-level-number="9" data-speech-node="true"><use data-c="1D43B" href="#MJX-122-NCM-I-1D43B"></use></g><g data-mml-node="TeXAtom" transform="translate(864,-150) scale(0.707)" data-mjx-texclass="ORD" data-latex="{2}"><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="139" data-semantic-parent="140" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="9" data-speech-node="true"><use data-c="32" href="#MJX-122-NCM-N-32"></use></g></g></g></g></g></g></g></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="0 -1450 1 2400"><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="158" 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=" \begin{matrix} C_{2}H_{2}\left ( g \right ) + H_{2}\left ( g \right ) \rightarrow C_{2}H_{4}\left ( g \right ) & \Delta H = -175.7 \; kJ/mol \; C_{2}H_{2} \\ C_{2}H_{2}\left ( g \right ) + 2H_{2}\left ( g \right ) \rightarrow C_{2}H_{6}\left ( g \right ) & \Delta H = -312.0 \; kJ/mol \; C_{2}H_{2} \end{matrix} \nonumber " display="block" data-semantic-structure="(159 (158 (156 (76 (42 (41 (38 (37 (3 1 2) 36 (35 (6 4 5) 34 (10 7 8 9))) 11 (33 (14 12 13) 32 (18 15 16 17))) 19 (40 (22 20 21) 39 (31 (25 23 24) 30 (29 26 27 28))))) (75 (74 (63 43 62 44) 45 (73 (67 46 (66 47 64 49 65 50)) 51 (72 52 68 53 69 54 70 (58 56 57) 71 (61 59 60)))))) (155 (121 (120 (117 (114 (79 77 78) 113 (112 (82 80 81) 111 (86 83 84 85))) 87 (116 88 115 (110 (91 89 90) 109 (95 92 93 94)))) 96 (119 (99 97 98) 118 (108 (102 100 101) 107 (106 103 104 105))))) (154 (153 (142 122 141 123) 124 (152 (146 125 (145 126 143 128 144 129)) 130 (151 131 147 132 148 133 149 (137 135 136) 150 (140 138 139))))))) 0))"><mtable displaystyle="true" data-latex="\begin{matrix} C_{2}H_{2}\left ( g \right ) + H_{2}\left ( g \right ) \rightarrow C_{2}H_{4}\left ( g \right ) & \Delta H = -175.7 \; kJ/mol \; C_{2}H_{2} \\ C_{2}H_{2}\left ( g \right ) + 2H_{2}\left ( g \right ) \rightarrow C_{2}H_{6}\left ( g \right ) & \Delta H = -312.0 \; kJ/mol \; C_{2}H_{2} \end{matrix} \nonumber" data-semantic-type="multiline" data-semantic-role="unknown" 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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="151" data-semantic-attributes="latex:l" data-semantic-level-number="8" data-speech-node="true">l</mi><mspace width="0.278em" data-latex="\;" data-semantic-type="operator" data-semantic-role="space" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="151" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true"></mspace><msub data-latex="C_{2}" data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-children="135,136" data-semantic-parent="151" data-semantic-attributes="latex:C_{2}" data-semantic-owns="135 136" data-semantic-level-number="8" data-speech-node="true"><mi data-latex="C" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="137" data-semantic-attributes="latex:C" data-semantic-level-number="9" data-speech-node="true">C</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:10" data-semantic-="" data-semantic-parent="137" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">2</mn></mrow></msub><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="151" data-semantic-added="true" data-semantic-operator="infixop,⁢" data-semantic-level-number="8" data-speech-node="true">⁢</mo><msub data-latex="H_{2}" data-semantic-type="subscript" data-semantic-role="simple function" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-children="138,139" data-semantic-parent="151" data-semantic-attributes="latex:H_{2}" data-semantic-owns="138 139" data-semantic-level-number="8" 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:10" data-semantic-="" data-semantic-parent="140" data-semantic-attributes="latex:H" data-semantic-level-number="9" 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:10" data-semantic-="" data-semantic-parent="140" data-semantic-attributes="latex:{2};texclass:ORD" data-semantic-level-number="9" data-speech-node="true">2</mn></mrow></msub></mrow></mrow></mrow></mtd></mtr></mtable></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p> <p class="lt-chem-21725" style="background-color: unset;">What is ΔH for the reaction of C<sub>2</sub>H<sub>4</sub> with H<sub>2</sub> to form C<sub>2</sub>H<sub>6</sub>?</p> <dl> <dt><strong class="emphasis bold">Answer</strong></dt> <dd> <p class="lt-chem-21725" style="background-color: unset;">−136.3 kJ/mol of C<sub>2</sub>H<sub>4</sub></p> </dd> </dl> </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/hisUr1fikFU?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=hisUr1fikFU" class="youtubeImageContainer"><img class="youtubeImage" src="https://img.youtube.com/vi/hisUr1fikFU/0.jpg" /><canvas class="thisqrcode" id="this_qrcode0" height="100" width="100" style="height: 100px; width: 100px;"></canvas></a></div></div> <p class="lt-chem-21725 mt-align-center" style="background-color: unset;">Hess’s Law: <a target="_blank" href="https://youtu.be/hisUr1fikFU" rel="external noopener nofollow" class="link-https">Hess's Law, 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-21725">Summary</h2> <p class="lt-chem-21725" style="background-color: unset;">Hess's law is arguing t<span>he overall enthalpy change for a series of reactions is the sum of the enthalpy changes for the individual reactions. </span>For a chemical reaction, the <strong class="emphasis bold">enthalpy of reaction (</strong><strong class="emphasis bold">Δ</strong>H<sub><strong class="emphasis bold">rxn</strong></sub><strong class="emphasis bold">)</strong> is the difference in enthalpy between products and reactants; the units of ΔH<sub>rxn</sub> are kilojoules per mole. Reversing a chemical reaction reverses the sign of ΔH<sub>rxn</sub>. The magnitude of ΔH<sub>rxn</sub> also depends on the physical state of the reactants and the products because processes such as melting solids or vaporizing liquids are also accompanied by enthalpy changes: the <strong class="emphasis bold">enthalpy of fusion (</strong><strong class="emphasis bold">Δ</strong>H<sub><strong class="emphasis bold">fus</strong></sub><strong class="emphasis bold">)</strong> and the <strong class="emphasis bold">enthalpy of vaporization (</strong><strong class="emphasis bold">Δ</strong>H<sub><strong class="emphasis bold">vap</strong></sub><strong class="emphasis bold">)</strong>, respectively. The overall enthalpy change for a series of reactions is the sum of the enthalpy changes for the individual reactions, which is <strong class="emphasis bold">Hess’s law</strong>. The <strong class="emphasis bold">enthalpy of combustion (</strong><strong class="emphasis bold">Δ</strong>H<sub><strong class="emphasis bold">comb</strong></sub><strong class="emphasis bold">)</strong> is the enthalpy change that occurs when a substance is burned in excess oxygen.</p> <span id="Contributors_and_Attributions"></span><span id="Contributors_and_Attributions"></span><h2 style="background-color: unset;" class="lt-chem-21725">Contributors and Attributions</h2> <div class="Attributions"> <ul> <li class="lt-chem-21725" style="background-color: unset;"><p class="contrib">Modified by <a title="http://www.coas.howard.edu/chem/jhalpern/" href="http://www.coas.howard.edu/chem/jhalpern/" target="_blank" rel="external noopener nofollow" class="external">Joshua Halpern</a> (<a title="http://www.howard.edu/" href="http://www.howard.edu/" target="_blank" rel="external noopener nofollow" class="external">Howard University</a>)</p> </li> </ul> </div> <footer class="mt-content-footer"> <style>/*<![CDATA[*/#mt-toc-container {display: none !important;}/*]]>*/</style><script type="text/javascript">/*<![CDATA[*/ $(function() { if(!window['autoDefinitionList']){ window['autoDefinitionList'] = true; 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