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errata 24202 first equation test
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oscryan committed Oct 2, 2024
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<equation id="fs-idm212442528" class="unnumbered"><m:math><m:mrow><m:mi>M</m:mi><m:mo>=</m:mo><m:mfrac><m:mi>n</m:mi><m:mi>V</m:mi></m:mfrac><m:mo>=</m:mo><m:mfrac><m:mi>P</m:mi><m:mrow><m:mi>R</m:mi><m:mi>T</m:mi></m:mrow></m:mfrac></m:mrow></m:math></equation>
<para id="fs-idm191541472">and so changes in the partial pressures of any reactant or product are essentially changes in concentrations and thus yield the same effects on equilibria. Aside from adding or removing reactant or product, the pressures (concentrations) of species in a gas-phase equilibrium can also be changed by <emphasis effect="italics">changing the volume occupied by the system</emphasis>. Since all species of a gas-phase equilibrium occupy the same volume, a given change in volume will cause the same change in concentration for both reactants and products. In order to discern what shift, if any, this type of stress will induce the stoichiometry of the reaction must be considered.</para>
<para id="fs-idm188989264">At equilibrium, the reaction H<sub>2</sub>(<emphasis effect="italics">g</emphasis>) + I<sub>2</sub>(<emphasis effect="italics">g</emphasis>) ⇌ 2HI(<emphasis effect="italics">g</emphasis>) is described by the reaction quotient</para>
<equation id="fs-idm216219232" class="unnumbered"><m:math><m:mrow><m:msub><m:mi>Q</m:mi><m:mi>P</m:mi></m:msub><m:mo>=</m:mo><m:mfrac><m:mrow><m:msub><m:mi>P</m:mi><m:mrow><m:mtext>HI</m:mtext></m:mrow></m:msub><m:msup><m:mrow/><m:mn>2</m:mn></m:msup></m:mrow><m:mrow><m:msub><m:mi>P</m:mi><m:mrow><m:msub><m:mtext>H</m:mtext><m:mn>2</m:mn></m:msub></m:mrow></m:msub><m:mspace width="0.2em"/><m:msub><m:mi>P</m:mi><m:mrow><m:msub><m:mtext>I</m:mtext><m:mn>2</m:mn></m:msub></m:mrow></m:msub></m:mrow></m:mfrac><m:mo>=</m:mo><m:msub><m:mi>K</m:mi><m:mi>p</m:mi></m:msub></m:mrow></m:math></equation>
<equation id="fs-idm216219232" class="unnumbered">
<m:math><m:mrow><m:msub><m:mi>Q</m:mi><m:mi>P</m:mi></m:msub>
<m:mo>=</m:mo>
<m:mfrac>
<m:mrow><m:msub><m:mi>P</m:mi><m:mtext fontstyle="italic">HI</m:mtext></m:msub><m:msup><m:mrow/><m:mn>2</m:mn></m:msup></m:mrow>
<m:mrow><m:msub><m:mi>P</m:mi><m:mrow><m:msub><m:mtext>H</m:mtext><m:mn>2</m:mn></m:msub></m:mrow></m:msub><m:mspace width="0.2em"/><m:msub><m:mi>P</m:mi><m:mrow><m:msub><m:mtext>I</m:mtext><m:mn>2</m:mn></m:msub></m:mrow></m:msub></m:mrow></m:mfrac><m:mo>=</m:mo><m:msub><m:mi>K</m:mi><m:mi>P</m:mi></m:msub></m:mrow></m:math></equation>
<para id="fs-idm224442448">If the volume occupied by an equilibrium mixture of these species is decreased by a factor of 3, the partial pressures of all three species will be increased by a factor of 3:</para>
<equation id="fs-idm214218336" class="unnumbered"><m:math><m:mtable><m:mtr/><m:mtr/><m:mtr/><m:mtr><m:mtd columnalign="left"><m:msub><m:mi>Q</m:mi><m:mi>p</m:mi></m:msub><m:msup><m:mrow/><m:mo>'</m:mo></m:msup><m:mo>=</m:mo>
<m:mfrac><m:mrow><m:msup><m:mrow><m:mo stretchy="false">(</m:mo><m:mn>3</m:mn><m:msub><m:mi>P</m:mi><m:mrow><m:mtext>HI</m:mtext></m:mrow></m:msub><m:mo stretchy="false">)</m:mo></m:mrow><m:mn>2</m:mn></m:msup></m:mrow>
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