5.08:_Foods_and_Fuels

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<div class="box-objectives">
<span id="Learning_Objectives"></span><span id="Learning_Objectives"></span><h5 class="box-legend"><span class="lt-icon-default"><span style="display:none;"> </span>Learning Objectives</span></h5>

<ul>
    <li class="lt-chem-21727" style="background-color: unset;">To understand the relationship between thermochemistry and nutrition.</li>
</ul>
</div>

<p class="lt-chem-21727" style="background-color: unset;">The thermochemical quantities that you probably encounter most often are the caloric values of food. Food supplies the raw materials that your body needs to replace cells and the energy that keeps those cells functioning. About 80% of this energy is released as heat to maintain your body temperature at a sustainable level to keep you alive. The nutritional Calorie (with a capital C) that you see on food labels is equal to 1 kcal (kilocalorie). The caloric content of food is determined from its enthalpy of combustion (&Delta;<em>H</em><sub>comb</sub>) per gram, as measured in a bomb calorimeter, using the general reaction</p>

<p class="lt-chem-21727" style="background-color: unset;">There are two important differences, however, between the caloric values reported for foods and the &Delta;<em>H</em><sub>comb</sub> of the same foods burned in a calorimeter. First, the &Delta;<em>H</em><sub>comb</sub> described in joules (or kilojoules) are negative for all substances that can be burned. In contrast, the caloric content of a food is always expressed as a <em>positive</em> number because it is <em>stored energy</em>. Therefore,</p>

<p class="lt-chem-21727" style="background-color: unset;">Second, when foods are burned in a calorimeter, any nitrogen they contain (largely from proteins, which are rich in nitrogen) is transformed to N<sub>2</sub>. In the body, however, nitrogen from foods is converted to urea [(H<sub>2</sub>N)<sub>2</sub>C=O], rather than N<sub>2</sub> before it is excreted. The &Delta;<em>H</em><sub>comb</sub> of urea measured by bomb calorimetry is &minus;632.0 kJ/mol. Consequently, the enthalpy change measured by calorimetry for any nitrogen-containing food is greater than the amount of energy the body would obtain from it. The difference in the values is equal to the &Delta;<em>H</em><sub>comb</sub> of urea multiplied by the number of moles of urea formed when the food is broken down. This point is illustrated schematically in the following equations:</p>

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data-semantic-annotation="clearspeak:simple;depth:10" data-semantic-="" data-semantic-parent="64" 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" data-semantic-role="multiplication" data-semantic-annotation="depth:9" data-semantic-="" data-semantic-parent="99" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="8" data-speech-node="true">&#8290;</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="67" data-semantic-content="66,68" data-semantic-parent="99" data-semantic-owns="66 67 68" 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="91" 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="91" 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="91" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="9" data-speech-node="true">)</mo></mrow></mrow></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="108" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="3" data-speech-node="true">+</mo><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="70,97,95" data-semantic-content="109,110" data-semantic-parent="108" data-semantic-owns="70 109 97 110 95" data-semantic-level-number="3" data-speech-node="true"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-parent="111" data-semantic-attributes="latex:2" data-semantic-level-number="4" 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:5" data-semantic-="" data-semantic-parent="111" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true">&#8290;</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-children="72,75" data-semantic-content="96,72" data-semantic-parent="111" data-semantic-owns="72 96 75" data-semantic-level-number="4" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{H}"><mi mathvariant="normal" data-latex="H" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="97" data-semantic-attributes="latex:\mathrm{H};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">H</mi></mrow><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="97" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">&#8289;</mo><msub data-latex="{\vphantom{A}}_{\smash[t]{2}}" data-semantic-type="subscript" data-semantic-role="unknown" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-children="73,74" data-semantic-parent="97" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="73 74" data-semantic-level-number="5" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}" data-semantic-type="empty" data-semantic-role="unknown" data-semantic-annotation="nemeth:number;depth:7" data-semantic-="" data-semantic-parent="75" data-semantic-attributes="latex:{\vphantom{A}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="75" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub></mrow><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="111" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true">&#8290;</mo><mrow data-semantic-added="true" data-semantic-type="appl" data-semantic-role="simple function" data-semantic-annotation="clearspeak:simple;depth:5" data-semantic-="" data-semantic-children="76,92" data-semantic-content="94,76" data-semantic-parent="111" data-semantic-owns="76 94 92" data-semantic-level-number="4" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{O}"><mi mathvariant="normal" data-latex="O" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:6" data-semantic-="" data-semantic-parent="95" data-semantic-attributes="latex:\mathrm{O};texclass:ORD" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">O</mi></mrow><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-annotation="nemeth:number;depth:6" data-semantic-="" data-semantic-parent="95" data-semantic-added="true" data-semantic-operator="appl" data-semantic-level-number="5" data-speech-node="true">&#8289;</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="79" data-semantic-content="78,80" data-semantic-parent="95" data-semantic-owns="78 79 80" 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="92" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{l}"><mi mathvariant="normal" data-latex="l" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:7" data-semantic-="" data-semantic-parent="92" data-semantic-attributes="latex:\mathrm{l};texclass:ORD" data-semantic-level-number="6" data-speech-node="true">l</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:7" data-semantic-="" data-semantic-parent="92" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="6" data-speech-node="true">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mo data-latex="+" data-semantic-type="operator" data-semantic-role="addition" data-semantic-annotation="depth:4" data-semantic-="" data-semantic-parent="108" data-semantic-attributes="latex:+" data-semantic-operator="infixop,+" data-semantic-level-number="3" data-speech-node="true">+</mo><mrow data-mjx-texclass="ORD" data-latex="{}"></mrow><mrow data-semantic-added="true" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-annotation="clearspeak:unit;depth:4" data-semantic-="" data-semantic-children="85,93" data-semantic-content="112" data-semantic-parent="108" data-semantic-owns="85 112 93" data-semantic-level-number="3" data-speech-node="true"><mrow data-mjx-texclass="ORD" data-latex="\mathrm{N}"><mrow data-semantic-added="true" data-semantic-type="subscript" data-semantic-role="identifier" data-semantic-annotation="collapsed:identifier;depth:5" data-semantic-="" data-semantic-children="82,84" data-semantic-parent="113" data-semantic-attributes="latex:{\vphantom{A}}_{\smash[t]{2}}" data-semantic-owns="82 84" data-semantic-level-number="4" data-speech-node="true"><mi mathvariant="normal" data-latex="N" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="85" data-semantic-attributes="latex:\mathrm{N};texclass:ORD" data-semantic-level-number="5" data-speech-node="true">N</mi></mrow></mrow><msub data-latex="{\vphantom{A}}_{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="{\vphantom{A}}"><mrow data-mjx-texclass="ORD" data-latex="\vphantom{A}"><mpadded width="0"><mphantom><mi data-latex="A">A</mi></mphantom></mpadded></mrow></mrow><mrow data-mjx-texclass="ORD" data-latex="{\smash[t]{2}}"><mrow data-mjx-texclass="ORD" data-latex="\smash[t]{2}"><mpadded height="0"><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="85" data-semantic-attributes="latex:{\smash[t]{2}};texclass:ORD" data-semantic-level-number="5" data-speech-node="true">2</mn></mpadded></mrow></mrow></msub><mspace width="0.111em" data-latex="\mskip2mu"></mspace><mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-annotation="depth:5" data-semantic-="" data-semantic-parent="113" data-semantic-added="true" data-semantic-operator="infixop,&#8290;" data-semantic-level-number="4" data-speech-node="true">&#8290;</mo><mrow data-semantic-added="true" data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-annotation="fences:paren;depth:5" data-semantic-="" data-semantic-children="88" data-semantic-content="87,89" data-semantic-parent="113" data-semantic-owns="87 88 89" data-semantic-level-number="4" data-speech-node="true"><mo data-latex="(" stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:(" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">(</mo><mrow data-mjx-texclass="ORD" data-latex="\mathrm{g}"><mi mathvariant="normal" data-latex="g" data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;depth:6" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:\mathrm{g};texclass:ORD" data-semantic-level-number="5" data-speech-node="true">g</mi></mrow><mo data-latex=")" stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-annotation="depth:6" data-semantic-="" data-semantic-parent="93" data-semantic-attributes="latex:)" data-semantic-operator="fenced" data-semantic-level-number="5" data-speech-node="true">)</mo></mrow></mrow></mrow></mtd></mlabeledtr></mtable></math></mjx-assistive-mml></mjx-container></p>

<p class="lt-chem-21727" style="background-color: unset;">which adds up to</p>

<p class="lt-chem-21727" style="background-color: unset;"><br />
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99 92 55C135 11 188-11 249-11M250 21C202 21 166 42 141 85C125 113 117 159 117 222C117 283 125 327 140 355C164 398 200 419 249 419C296 419 332 398 357 357C374 329 382 284 382 222C382 106 348 21 250 21Z"></path><path id="MJX-105-NCM-N-64" d="M374-11L527 0L527 38C491 38 470 40 462 46C454 52 450 67 450 90L450 694L301 683L301 645C336 645 358 642 366 636C374 630 377 616 377 593L377 390C345 427 305 445 257 445C195 445 142 423 99 378C56 333 34 279 34 216C34 155 54 102 95 57C136 12 186-11 247-11C298-11 341 8 374 47M261 415C304 415 339 396 364 358C371 347 374 336 374 323L374 121C374 108 371 97 364 86C336 41 298 19 251 19C210 19 177 39 151 80C133 110 124 155 124 215C124 324 161 415 261 415Z"></path><path id="MJX-105-NCM-N-2B" d="M698 274L413 274L413 559C413 575 405 583 389 583C373 583 365 575 365 559L365 274L80 274C64 274 56 266 56 250C56 234 64 226 80 226L365 226L365-59C365-75 373-83 389-83C405-83 413-75 413-59L413 226L698 226C714 226 722 234 722 250C722 263 711 274 698 274Z"></path><path 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<p class="lt-chem-21727" style="background-color: unset;">All three &Delta;<em>H</em> values are negative, and, by Hess&rsquo;s law, &Delta;<em>H</em><sub>3</sub> = &Delta;<em>H</em><sub>1</sub> + &Delta;<em>H</em><sub>2</sub>. The magnitude of &Delta;<em>H</em><sub>1</sub> must be less than &Delta;<em>H</em><sub>3</sub>, the calorimetrically measured &Delta;<em>H</em><sub>comb</sub> for a food. By producing urea rather than N<sub>2</sub>, therefore, humans are excreting some of the energy that was stored in their food.</p>

<p class="lt-chem-21727" style="background-color: unset;">Because of their different chemical compositions, foods vary widely in caloric content. As we saw <span class="mt-bgcolor-ff8c00">previously</span>, for instance, a fatty acid such as palmitic acid produces about 39 kJ/g during combustion, while a sugar such as glucose produces 15.6 kJ/g. Fatty acids and sugars are the building blocks of fats and carbohydrates, respectively, two of the major sources of energy in the diet. Nutritionists typically assign average values of 38 kJ/g (about 9 Cal/g) and 17 kJ/g (about 4 Cal/g) for fats and carbohydrates, respectively, although the actual values for specific foods vary because of differences in composition. Proteins, the third major source of calories in the diet, vary as well. Proteins are composed of amino acids, which have the following general structure:</p>

<figure><img style="width: 209px; height: 118px;" class="internal" alt="A simple black silhouette of a cat sitting with its tail curled around its body." loading="lazy" width="550" height="312" src="https://chem.libretexts.org/@api/deki/files/409862/Amino_acid.png?revision=1&amp;size=bestfit&amp;width=209&amp;height=118" />
<figcaption><strong class="emphasis bold">General structure of an amino acid.</strong> An amino acid contains an amine group (&minus;NH<sub>2</sub>) and a carboxylic acid group (&minus;CO<sub>2</sub>H).</figcaption>
</figure>

<p class="lt-chem-21727" style="background-color: unset;">In addition to their amine and carboxylic acid components, amino acids may contain a wide range of other functional groups: R can be hydrogen (&ndash;H); an alkyl group (e.g., &ndash;CH<sub>3</sub>); an aryl group (e.g., &ndash;CH<sub>2</sub>C<sub>6</sub>H<sub>5</sub>); or a substituted alkyl group that contains an amine, an alcohol, or a carboxylic acid (Figure <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-38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 441 257 408 294C396 307 365 330 316 361C393 402 431 454 431 515C431 606 344 666 250 666M379 515C379 463 348 418 286 381L167 459C136 479 120 505 120 536C120 596 185 633 249 633C318 633 379 584 379 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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>). Of the 20 naturally occurring amino acids, 10 are required in the human diet; these 10 are called <em>essential amino acids</em> because our bodies are unable to synthesize them from other compounds. Because R can be any of several different groups, each amino acid has a different value of &Delta;<em>H</em><sub>comb</sub>. Proteins are usually estimated to have an average &Delta;<em>H</em><sub>comb</sub> of 17 kJ/g (about 4 Cal/g).</p>

<figure><img alt="Chemical structures and formulae depicting various molecular compounds, including bonds and functional groups." style="width: 772px; height: 789px;" class="internal" loading="lazy" width="772px" height="789px" src="https://chem.libretexts.org/@api/deki/files/410046/3c3079abf412e9471884f30f7f5fdf86.jpg?revision=1&amp;size=bestfit&amp;width=772&amp;height=789" />
<figcaption><span class="title-prefix">Figure </span><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-38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 441 257 408 294C396 307 365 330 316 361C393 402 431 454 431 515C431 606 344 666 250 666M379 515C379 463 348 418 286 381L167 459C136 479 120 505 120 536C120 596 185 633 249 633C318 633 379 584 379 515M250 14C168 14 99 73 99 153C99 220 136 274 210 315L328 240C376 209 400 174 400 134C400 62 325 14 250 14Z"></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="\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-107-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-107-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="8" 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:8" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="38" href="#MJX-107-NCM-N-38"></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-107-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-107-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="8" 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:8" data-semantic-level-number="1" data-speech-node="true">8</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="1" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:1" data-semantic-level-number="1" data-speech-node="true">1</mn></mrow></math></mjx-assistive-mml></mjx-container>: The Structures of 10 Amino Acids. Essential amino acids in this group are indicated with an asterisk.</figcaption>

<figcaption>Structures of glycine, alanine, valine, serine, threonine, aspartic acid, phenylalanine, tyrosine, lysine, methionine.</figcaption>
</figure>

<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="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-38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 441 257 408 294C396 307 365 330 316 361C393 402 431 454 431 515C431 606 344 666 250 666M379 515C379 463 348 418 286 381L167 459C136 479 120 505 120 536C120 596 185 633 249 633C318 633 379 584 379 515M250 14C168 14 99 73 99 153C99 220 136 274 210 315L328 240C376 209 400 174 400 134C400 62 325 14 250 14Z"></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="\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-108-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-108-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="8" 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:8" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="38" href="#MJX-108-NCM-N-38"></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-108-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-108-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" 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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-21727" style="background-color: unset;">Calculate the amount of available energy obtained from the biological oxidation of 1.000 g of alanine (an amino acid). Remember that the nitrogen-containing product is urea, not N<sub>2</sub>, so biological oxidation of alanine will yield <em>less</em> energy than will combustion. The value of &Delta;<em>H</em><sub>comb</sub> for alanine is &minus;1577 kJ/mol.</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">Given: </strong>amino acid and &Delta;<em>H</em><sub>comb</sub> per mole</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">Asked for: </strong>caloric content per gram</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-21727" style="background-color: unset;">Write balanced chemical equations for the oxidation of alanine to CO<sub>2</sub>, H<sub>2</sub>O, and urea; the combustion of urea; and the combustion of alanine. Multiply both sides of the equations by appropriate factors and then rearrange them to cancel urea from both sides when the equations are added.</li>
    <li class="lt-chem-21727" style="background-color: unset;">Use Hess&rsquo;s law to obtain an expression for &Delta;<em>H</em> for the oxidation of alanine to urea in terms of the &Delta;<em>H</em><sub>comb</sub> of alanine and urea. Substitute the appropriate values of &Delta;<em>H</em><sub>comb</sub> into the equation and solve for &Delta;<em>H</em> for the oxidation of alanine to CO<sub>2</sub>, H<sub>2</sub>O, and urea.</li>
    <li class="lt-chem-21727" style="background-color: unset;">Calculate the amount of energy released per gram by dividing the value of &Delta;<em>H</em> by the molar mass of alanine.</li>
</ol>

<span id="Solution:"></span><span id="Solution:"></span><h6>Solution:</h6>

<p class="lt-chem-21727" style="background-color: unset;">The actual energy available biologically from alanine is less than its &Delta;<em>H</em><sub>comb</sub> because of the production of urea rather than N<sub>2</sub>. We know the &Delta;<em>H</em><sub>comb</sub> values for alanine and urea, so we can use Hess&rsquo;s law to calculate &Delta;<em>H</em> for the oxidation of alanine to CO<sub>2</sub>, H<sub>2</sub>O, and urea.</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">A</strong> We begin by writing balanced chemical equations for (1) the oxidation of alanine to CO<sub>2</sub>, H<sub>2</sub>O, and urea; (2) the combustion of urea; and (3) the combustion of alanine. Because alanine contains only a single nitrogen atom, whereas urea and N<sub>2</sub> each contain two nitrogen atoms, it is easier to balance Equations 1 and 3 if we write them for the oxidation of 2 mol of alanine:</p>

<p class="lt-chem-21727" style="background-color: unset;">Adding Equations 1 and 2 and canceling urea from both sides give the overall chemical equation directly:</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">B</strong> By Hess&rsquo;s law, &Delta;<em>H</em><sub>3</sub> = &Delta;<em>H</em><sub>1</sub> + &Delta;<em>H</em><sub>2</sub>. We know that &Delta;<em>H</em><sub>3</sub> = 2&Delta;<em>H</em><sub>comb</sub> (alanine), &Delta;<em>H</em><sub>2</sub> = &Delta;<em>H</em><sub>comb</sub> (urea), and &Delta;<em>H</em><sub>1</sub> = 2&Delta;<em>H</em> (alanine &rarr; urea). Rearranging and substituting the appropriate values gives</p>

<p class="lt-chem-21727" style="background-color: unset;">Thus &Delta;<em>H</em> (alanine &rarr; urea) = &minus;2522 kJ/(2 mol of alanine) = &minus;1261 kJ/mol of alanine. Oxidation of alanine to urea rather than to nitrogen therefore results in about a 20% decrease in the amount of energy released (&minus;1261 kJ/mol versus &minus;1577 kJ/mol).</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">C</strong> The energy released per gram by the biological oxidation of alanine is</p>

<p class="lt-chem-21727" style="background-color: unset;">This is equal to &minus;3.382 Cal/g.</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="117" 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-118-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-118-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-118-NCM-N-38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 441 257 408 294C396 307 365 330 316 361C393 402 431 454 431 515C431 606 344 666 250 666M379 515C379 463 348 418 286 381L167 459C136 479 120 505 120 536C120 596 185 633 249 633C318 633 379 584 379 515M250 14C168 14 99 73 99 153C99 220 136 274 210 315L328 240C376 209 400 174 400 134C400 62 325 14 250 14Z"></path><path id="MJX-118-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 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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="8" 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:8" data-semantic-level-number="1" data-speech-node="true">8</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-21727" style="background-color: unset;">Calculate the energy released per gram from the oxidation of valine (an amino acid) to CO<sub>2</sub>, H<sub>2</sub>O, and urea. Report your answer to three significant figures. The value of &Delta;<em>H</em><sub>comb</sub> for valine is &minus;2922 kJ/mol.</p>

<dl>
    <dt><strong class="emphasis bold">Answer</strong></dt>
    <dd>
    <p class="lt-chem-21727" style="background-color: unset;">&minus;22.2 kJ/g (&minus;5.31 Cal/g)</p>
    </dd>
</dl>
</div>

<p class="lt-chem-21727" style="background-color: unset;">The reported caloric content of foods does not include &Delta;<em>H</em><sub>comb</sub> for those components that are not digested, such as fiber. Moreover, meats and fruits are 50%&minus;70% water, which cannot be oxidized by O<sub>2</sub> to obtain energy. So water contains no calories. Some foods contain large amounts of fiber, which is primarily composed of sugars. Although fiber can be burned in a calorimeter just like glucose to give carbon dioxide, water, and heat, humans lack the enzymes needed to break fiber down into smaller molecules that can be oxidized. Hence fiber also does not contribute to the caloric content of food.</p>

<p class="lt-chem-21727" style="background-color: unset;">We can determine the caloric content of foods in two ways. The most precise method is to dry a carefully weighed sample and carry out a combustion reaction in a bomb calorimeter. The more typical approach, however, is to analyze the food for protein, carbohydrate, fat, water, and &ldquo;minerals&rdquo; (everything that doesn&rsquo;t burn) and then calculate the caloric content using the average values for each component that produces energy (9 Cal/g for fats, 4 Cal/g for carbohydrates and proteins, and 0 Cal/g for water and minerals). An example of this approach is shown in Table <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="119" 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-120-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-120-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-120-NCM-N-38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 441 257 408 294C396 307 365 330 316 361C393 402 431 454 431 515C431 606 344 666 250 666M379 515C379 463 348 418 286 381L167 459C136 479 120 505 120 536C120 596 185 633 249 633C318 633 379 584 379 515M250 14C168 14 99 73 99 153C99 220 136 274 210 315L328 240C376 209 400 174 400 134C400 62 325 14 250 14Z"></path><path id="MJX-120-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-120-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-120-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="8" 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:8" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="38" href="#MJX-120-NCM-N-38"></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-120-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-120-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="8" 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:8" data-semantic-level-number="1" data-speech-node="true">8</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> for a slice of roast beef. The compositions and caloric contents of some common foods are given in Table <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-38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 441 257 408 294C396 307 365 330 316 361C393 402 431 454 431 515C431 606 344 666 250 666M379 515C379 463 348 418 286 381L167 459C136 479 120 505 120 536C120 596 185 633 249 633C318 633 379 584 379 515M250 14C168 14 99 73 99 153C99 220 136 274 210 315L328 240C376 209 400 174 400 134C400 62 325 14 250 14Z"></path><path id="MJX-121-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></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="2}" 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{2};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" 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transform="translate(778,0)"><use data-c="38" href="#MJX-121-NCM-N-38"></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="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="32" href="#MJX-121-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="8" 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:8" data-semantic-level-number="1" data-speech-node="true">8</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>.</p>

<table class="mt-responsive-table" align="center" cellpadding="0" cellspacing="0">
    <caption>Table <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="121" 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-122-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-122-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-122-NCM-N-38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 441 257 408 294C396 307 365 330 316 361C393 402 431 454 431 515C431 606 344 666 250 666M379 515C379 463 348 418 286 381L167 459C136 479 120 505 120 536C120 596 185 633 249 633C318 633 379 584 379 515M250 14C168 14 99 73 99 153C99 220 136 274 210 315L328 240C376 209 400 174 400 134C400 62 325 14 250 14Z"></path><path id="MJX-122-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></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="2}" 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{2};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-122-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-122-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="8" 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:8" data-semantic-level-number="1" data-speech-node="true" transform="translate(778,0)"><use data-c="38" href="#MJX-122-NCM-N-38"></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-122-NCM-N-2E"></use></g></g><g data-mml-node="mn" data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-id="4" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true" transform="translate(1556,0)"><use data-c="32" href="#MJX-122-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="8" 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:8" data-semantic-level-number="1" data-speech-node="true">8</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>: Approximate Compositions and Fuel Values of Some Common Foods</caption>
    <thead>
        <tr>
            <th class="mt-align-center" style="vertical-align:middle;">Food (quantity)</th>
            <th class="mt-align-center" colspan="4" style="vertical-align:middle;">Approximate Composition (%)</th>
            <th class="mt-align-center" style="vertical-align:middle;">Food Value (Cal/g)</th>
            <th class="mt-align-center" style="vertical-align:middle;">Calories</th>
        </tr>
    </thead>
    <tbody>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">&nbsp;</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;"><strong class="emphasis bold">Water</strong></td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;"><strong class="emphasis bold">Carbohydrate</strong></td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;"><strong class="emphasis bold">Protein</strong></td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;"><strong class="emphasis bold">Fat</strong></td>
            <td class="mt-align-center lt-chem-21727" colspan="2" data-th="Calories" style="vertical-align: middle; background-color: unset;">&nbsp;</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">beer (12 oz)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">92</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">3.6</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">0.3</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">0</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">0.4</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">150</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">coffee (6 oz)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">100</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">~0</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">~0</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">~0</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">~0</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">~0</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">milk (1 cup)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">88</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">4.5</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">3.3</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">3.3</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">0.6</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">150</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">egg (1 large)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">75</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">2</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">12</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">12</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">1.6</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">80</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">butter (1 tbsp)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">16</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">~0</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">~0</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">79</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">7.1</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">100</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">apple (8 oz)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">84</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">15</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">~0</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">0.5</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">0.6</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">125</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">bread, white (2 slices)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">37</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">48</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">8</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">4</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">2.6</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">130</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">brownie (40 g)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">10</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">55</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">5</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">30</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">4.8</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">190</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">hamburger (4 oz)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">54</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">0</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">24</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">21</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">2.9</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">326</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">fried chicken (1 drumstick)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">53</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">8.3</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">22</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">15</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">2.7</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">195</td>
        </tr>
        <tr>
            <td class="mt-align-center lt-chem-21727" data-th="Food (quantity)" style="vertical-align: middle; background-color: unset;">carrots (1 cup)</td>
            <td class="mt-align-center lt-chem-21727" data-th="Approximate Composition (%)" style="vertical-align: middle; background-color: unset;">87</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">10</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">1.3</td>
            <td class="mt-align-center mt-colspan lt-chem-21727" style="vertical-align: middle; background-color: unset;">~0</td>
            <td class="mt-align-center lt-chem-21727" data-th="Food Value (Cal/g)" style="vertical-align: middle; background-color: unset;">0.4</td>
            <td class="mt-align-center lt-chem-21727" data-th="Calories" style="vertical-align: middle; background-color: unset;">70</td>
        </tr>
    </tbody>
</table>

<p class="lt-chem-21727" style="background-color: unset;">Because the Calorie represents such a large amount of energy, a few of them go a long way. An average 73 kg (160 lb) person needs about 67 Cal/h (1600 Cal/day) to fuel the basic biochemical processes that keep that person alive. This energy is required to maintain body temperature, keep the heart beating, power the muscles used for breathing, carry out chemical reactions in cells, and send the nerve impulses that control those automatic functions. Physical activity increases the amount of energy required but not by as much as many of us hope (Table <mjx-container class="MathJax CtxtMenu_Attached_0" jax="SVG" overflow="linebreak" tabindex="0" ctxtmenu_counter="122" 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-123-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 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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></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" data-latex="2}" 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{2};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" 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href="#MJX-123-NCM-N-32"></use></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math data-latex="\PageIndex{2}" data-semantic-structure="(5 0 1 2 3 4)"><mrow data-mjx-texclass="ORD" data-latex="2}" data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-annotation="depth:1" data-semantic-="" data-semantic-children="0,1,2,3,4" data-semantic-content="1,3" data-semantic-attributes="latex:\PageIndex{2};texclass:ORD" data-semantic-owns="0 1 2 3 4" data-semantic-level-number="0" data-speech-node="true"><mn data-latex="5" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:5" data-semantic-level-number="1" data-speech-node="true">5</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="8" 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:8" data-semantic-level-number="1" data-speech-node="true">8</mn><mrow data-mjx-texclass="ORD" data-latex="{.}"><mo data-latex="." data-semantic-type="punctuation" data-semantic-role="fullstop" data-semantic-annotation="nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:{.};texclass:ORD" data-semantic-operator="punctuated" data-semantic-level-number="1" data-speech-node="true">.</mo></mrow><mn data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container>). A moderately active individual requires about 2500&minus;3000 Cal/day; athletes or others engaged in strenuous activity can burn 4000 Cal/day. Any excess caloric intake is stored by the body for future use, usually in the form of fat, which is the most compact way to store energy. When more energy is needed than the diet supplies, stored fuels are mobilized and oxidized. We usually exhaust the supply of stored carbohydrates before turning to fats, which accounts in part for the popularity of low-carbohydrate diets.</p>

<div class="box-example">
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data-latex="2" data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-annotation="clearspeak:simple;nemeth:number;depth:2" data-semantic-="" data-semantic-parent="5" data-semantic-attributes="latex:2" data-semantic-level-number="1" data-speech-node="true">2</mn></mrow></math></mjx-assistive-mml></mjx-container></span></h5>

<p class="lt-chem-21727" style="background-color: unset;">What is the minimum number of Calories expended by a 72.6 kg person who climbs a 30-story building? (Assume each flight of stairs is 14 ft high.) How many grams of glucose are required to supply this amount of energy? (The energy released during the combustion of glucose was calculated in Example 5.5.4).</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">Given: </strong>mass, height, and energy released by combustion of glucose</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">Asked for: </strong>calories expended and mass of glucose needed</p>

<span id="Strategy:_2"></span><span id="Strategy:_2"></span><h6>Strategy:</h6>

<ol start="1" style="list-style-type: upper-alpha;">
    <li class="lt-chem-21727" style="background-color: unset;">Convert mass and height to <abbr title="International System of Units">SI</abbr> units and then substitute these values into Equation 5.6 to calculate the change in potential energy (in kilojoules). Divide the calculated energy by 4.184 Cal/kJ to convert the potential energy change to Calories.</li>
    <li class="lt-chem-21727" style="background-color: unset;">Use the value obtained in Example 5.5.4 for the combustion of glucose to calculate the mass of glucose needed to supply this amount of energy.</li>
</ol>

<span id="Solution:_2"></span><span id="Solution:_2"></span><h6>Solution:</h6>

<p class="lt-chem-21727" style="background-color: unset;">The energy needed to climb the stairs equals the difference between the person&rsquo;s potential energy (<em><abbr title="potential energy">PE</abbr></em>) at the top of the building and at ground level.</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">A</strong> Recall that <em>PE</em> = <em>mgh</em>. Because <em>m</em> and <em>h</em> are given in non-SI units, we must convert them to kilograms and meters, respectively</p>

<p class="lt-chem-21727" style="background-color: unset;">To convert to Calories, we divide by 4.184 kJ/kcal:</p>

<p class="lt-chem-21727" style="background-color: unset;"><strong class="emphasis bold">B</strong> Because the combustion of glucose produces 15.6 kJ/g (Example 5), the mass of glucose needed to supply 85.5 kJ of energy is</p>

<p class="lt-chem-21727" style="background-color: unset;">This mass corresponds to only about a teaspoonful of sugar! Because the body is only about 30% efficient in using the energy in glucose, the actual amount of glucose required would be higher: (100%/30%) &times; 5.85 g = 19.5 g. Nonetheless, this calculation illustrates the difficulty many people have in trying to lose weight by exercise alone.</p>
</div>

<div class="box-exercise">
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<p class="lt-chem-21727" style="background-color: unset;">Calculate how many times a 160 lb person would have to climb the tallest building in the United States, the 110-story Willis Tower in Chicago, to burn off 1.0 lb of stored fat. Assume that each story of the building is 14 ft high and use a calorie content of 9.0 kcal/g of fat.</p>

<dl>
    <dt><strong class="emphasis bold">Answer</strong></dt>
    <dd>
    <p class="lt-chem-21727" style="background-color: unset;">About 55 times</p>
    </dd>
</dl>
</div>

<p class="lt-chem-21727" style="background-color: unset;">The calculations in Example 5.8.2 ignore various factors, such as how fast the person is climbing. Although the rate is irrelevant in calculating the change in potential energy, it is very relevant to the amount of energy actually required to ascend the stairs. The calculations also ignore the fact that the body&rsquo;s conversion of chemical energy to mechanical work is significantly less than 100% efficient. According to the average energy expended for various activities listed in Table 5.8.3, a person must run more than 4.5 h at 10 mph or bicycle for 6 h at 13 mph to burn off 1 lb of fat (1.0 lb &times; 454 g/lb &times; 9.0 Cal/g = 4100 Cal). But if a person rides a bicycle at 13 mph for only 1 h per day 6 days a week, that person will burn off 50 lb of fat in the course of a year (assuming, of course, the cyclist doesn&rsquo;t increase his or her intake of calories to compensate for the exercise).</p>

<span id="Summary"></span><span id="Summary"></span><h2 style="background-color: unset;" class="lt-chem-21727">Summary</h2>

<p class="lt-chem-21727" style="background-color: unset;">Thermochemical concepts can be applied to determine the actual energy available in food. The nutritional <strong class="emphasis bold">Calorie</strong> is equivalent to 1 kcal (4.184 kJ). The caloric content of a food is its &Delta;<em>H</em><sub>comb</sub> per gram. The combustion of nitrogen-containing substances produces N<sub>2</sub>(g), but the biological oxidation of such substances produces urea. Hence the actual energy available from nitrogen-containing substances, such as proteins, is less than the &Delta;<em>H</em><sub>comb</sub> of urea multiplied by the number of moles of urea produced. The typical caloric contents for food are 9 Cal/g for fats, 4 Cal/g for carbohydrates and proteins, and 0 Cal/g for water and minerals. </p>

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<hr class="autoattribution-divider" /><div class="autoattribution"><p><a target="_blank" class="internal mt-self-link" href="/Sandboxes/johnnyphung/chemistry_central/05:_Thermochemistry/5.08:_Foods_and_Fuels">5.8: Foods and Fuels</a> is shared under a <a rel="nofollow" href="https://creativecommons.org/licenses/by-nc-sa/3.0" target="_blank">CC BY-NC-SA  3.0</a>  license and was authored, remixed, and/or curated by LibreTexts.</p></div>

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