General College Chemistry
Foreword
Unit 1. Solutions and Colligative Properties
1. Introduction and Review of Thermodynamics
2. Solutions
3. Osmotic Pressure
4. Vapor Pressure
5. Melting/Boiling
Unit 2. Kinetics
6. Reaction Rates
7. Experimental Rate Laws
8. Integrated Rate Laws
9. Temperature and Rate
10. Reaction Mechanisms and Catalysis
Unit 3. Nuclear Chemistry
11. Radioactive Decay
12. Rates of Decay, Radiodating
13. Fission and Fusion
14. Biological Effects
Unit 4. Equilibrium and Thermodynamics
15. Equilibrium Constants
16. Reaction Quotients and Le Chatelier
17. Equilibrium Calculations
18. Review of Thermodynamics Calculations
19. ΔG and Q, ΔG° and K
20. Temperature Dependence of K
Unit 5. Acids, Bases, and Buffers
21. Acids and Bases
22. Autoionization and pH Calculations
23. Weak Acids and Bases
24. Polyprotic Acids
25. pH of Salt Solutions
26. Buffers
27. DBL Acid Base
28. Titrations I
29. Titrations II
Unit 6. Solubility and Complex Ion Equilibria
30. Solubility Equilibria
31. Complex Ion Equilibria
32. Chelation, Biological Effects
33. Crystal Field Theory
34. Isomerism, Equilibria and Biological Systems
Unit 7. Electrochemistry and Solids
35. Redox, Electrochemical Cells
36. Cell Potentials
37. Nernst Equation
38. Batteries and Fuel Cells
39. Metals, Alloys and Semiconductors
40. Covalent Network Solids, Salts, Polymers
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<h2 id="p_UFWG" name="p_UFWG"><span data-etb-numbered-element="1">37.1</span> Potential, Free Energy, and Equilibrium</h2><p id="p_Egee" class="" name="p_Egee"></p><div id="1" class="ui-has-child-title callout objectives" data-type="abstract"><header class=""><h3 class="" data-type="title" id="h3_ELDR" name="h3_ELDR">Learning Objectives</h3></header><p id="para-00001" class="" name="para-00001">By the end of this section, you will be able to:</p><ul id="list-00001" class="" name="list-00001"><li id="li_AiaS" class="" name="li_AiaS">Use the Nernst equation to determine cell potentials under nonstandard conditions</li></ul></div><h3 data-type="title" id="h3_wWLs" name="h3_wWLs"><span data-etb-numbered-element="1">37.1.1</span> Potentials at Nonstandard Conditions: The Nernst Equation</h3><p id="fs-idp76396192" class="" name="fs-idp76396192">Most of the redox processes that interest science and society do not occur under standard state conditions, and so the potentials of these systems under nonstandard conditions are a property worthy of attention. Having established the relationship between potential and free energy change in this section, the previously discussed relation between free energy change and reaction mixture composition can be used for this purpose.</p><div class="MathJax_Display"><span id="MathJax-Element-421-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><mtext>Δ</mtext><mi>G</mi><mo>=</mo><mtext>Δ</mtext><mi>G</mi><mtext>°</mtext><mo>+</mo><mi>R</mi><mi>T</mi><mspace width="0.2em" ></mspace><mtext>ln</mtext><mspace width="0.2em" ></mspace><mi>Q</mi></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mtext>Δ</mtext><mi>G</mi><mo>=</mo><mtext>Δ</mtext><mi>G</mi><mtext>°</mtext><mo>+</mo><mi>R</mi><mi>T</mi><mspace width="0.2em"></mspace><mtext>ln</mtext><mspace width="0.2em"></mspace><mi>Q</mi></mrow></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mrow class=""><mtext class="">Δ</mtext><mi class="">G</mi><mo class="">=</mo><mtext class="">Δ</mtext><mi class="">G</mi><mtext class="">°</mtext><mo class="">+</mo><mi class="">R</mi><mi class="">T</mi><mspace width="0.2em" class=""></mspace><mtext class="">ln</mtext><mspace width="0.2em" class=""></mspace><mi class="">Q</mi></mrow></mrow><annotation-xml encoding="MathML-Content" class=""><mrow class=""><mtext class="">Δ</mtext><mi class="">G</mi><mo class="">=</mo><mtext class="">Δ</mtext><mi class="">G</mi><mtext class="">°</mtext><mo class="">+</mo><mi class="">R</mi><mi class="">T</mi><mspace width="0.2em" class=""></mspace><mtext class="">ln</mtext><mspace width="0.2em" class=""></mspace><mi class="">Q</mi></mrow></annotation-xml></semantics></math></span></div><p id="fs-idm983728" class="" name="fs-idm983728">Notice the reaction quotient, <em class="" data-effect="italics">Q</em>, appears in this equation, making the free energy change dependent upon the composition of the reaction mixture. Substituting the equation relating free energy change to cell potential yields the <span id="term615" class="" data-type="term">Nernst equation</span>:</p><div class="MathJax_Display"><span id="MathJax-Element-422-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><mtext>−</mtext><mi>n</mi><mi>F</mi><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub><mo>=</mo><mtext>−</mtext><mi>n</mi><mi>F</mi><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>+</mo><mi>R</mi><mi>T</mi><mspace width="0.2em" ></mspace><mtext>ln</mtext><mspace width="0.2em" ></mspace><mi>Q</mi></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mtext>−</mtext><mi>n</mi><mi>F</mi><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub><mo>=</mo><mtext>−</mtext><mi>n</mi><mi>F</mi><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>+</mo><mi>R</mi><mi>T</mi><mspace width="0.2em"></mspace><mtext>ln</mtext><mspace width="0.2em"></mspace><mi>Q</mi></mrow></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mrow class=""><mtext class="">−</mtext><mi class="">n</mi><mi class="">F</mi><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub><mo class="">=</mo><mtext class="">−</mtext><mi class="">n</mi><mi class="">F</mi><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">+</mo><mi class="">R</mi><mi class="">T</mi><mspace width="0.2em" class=""></mspace><mtext class="">ln</mtext><mspace width="0.2em" class=""></mspace><mi class="">Q</mi></mrow></mrow><annotation-xml encoding="MathML-Content" class=""><mrow class=""><mtext class="">−</mtext><mi class="">n</mi><mi class="">F</mi><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub><mo class="">=</mo><mtext class="">−</mtext><mi class="">n</mi><mi class="">F</mi><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">+</mo><mi class="">R</mi><mi class="">T</mi><mspace width="0.2em" class=""></mspace><mtext class="">ln</mtext><mspace width="0.2em" class=""></mspace><mi class="">Q</mi></mrow></annotation-xml></semantics></math></span></div><div class="MathJax_Display"><span id="MathJax-Element-423-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub><mo>=</mo><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>−</mo><mspace width="0.2em" ></mspace><mfrac><mrow><mi>R</mi><mi>T</mi></mrow><mrow><mi>n</mi><mi>F</mi></mrow></mfrac><mspace width="0.4em" ></mspace><mtext>ln</mtext><mspace width="0.3em" ></mspace><mi>Q</mi></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub><mo>=</mo><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>−</mo><mspace width="0.2em"></mspace><mfrac><mrow><mi>R</mi><mi>T</mi></mrow><mrow><mi>n</mi><mi>F</mi></mrow></mfrac><mspace width="0.4em"></mspace><mtext>ln</mtext><mspace width="0.3em"></mspace><mi>Q</mi></mrow></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mrow class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub><mo class="">=</mo><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mi class="">R</mi><mi class="">T</mi></mrow><mrow class=""><mi class="">n</mi><mi class="">F</mi></mrow></mfrac><mspace width="0.4em" class=""></mspace><mtext class="">ln</mtext><mspace width="0.3em" class=""></mspace><mi class="">Q</mi></mrow></mrow><annotation-xml encoding="MathML-Content" class=""><mrow class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub><mo class="">=</mo><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mi class="">R</mi><mi class="">T</mi></mrow><mrow class=""><mi class="">n</mi><mi class="">F</mi></mrow></mfrac><mspace width="0.4em" class=""></mspace><mtext class="">ln</mtext><mspace width="0.3em" class=""></mspace><mi class="">Q</mi></mrow></annotation-xml></semantics></math></span></div><p id="fs-idp24059424" class="" name="fs-idp24059424">This equation describes how the potential of a redox system (such as a galvanic cell) varies from its standard state value, specifically, showing it to be a function of the number of electrons transferred, <em class="" data-effect="italics">n</em>, the temperature, <em class="" data-effect="italics">T</em>, and the reaction mixture composition as reflected in <em class="" data-effect="italics">Q</em>. A convenient form of the Nernst equation for most work is one in which values for the fundamental constants (R and F) and standard temperature (298) K), along with a factor converting from natural to base-10 logarithms, have been included:</p><div class="MathJax_Display"><span id="MathJax-Element-424-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub><mo>=</mo><msubsup><mrow><mi>E</mi></mrow><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>−</mo><mspace width="0.2em" ></mspace><mfrac><mrow><mn>0.0592</mn><mtext>V</mtext></mrow><mi>n</mi></mfrac><mspace width="0.2em" ></mspace><mtext>log</mtext><mspace width="0.2em" ></mspace><mi>Q</mi></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub><mo>=</mo><msubsup><mrow><mi>E</mi></mrow><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>−</mo><mspace width="0.2em"></mspace><mfrac><mrow><mn>0.0592</mn><mtext>V</mtext></mrow><mi>n</mi></mfrac><mspace width="0.2em"></mspace><mtext>log</mtext><mspace width="0.2em"></mspace><mi>Q</mi></mrow></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mrow class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub><mo class="">=</mo><msubsup class=""><mrow class=""><mi class="">E</mi></mrow><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.0592</mn><mtext class="">V</mtext></mrow><mi class="">n</mi></mfrac><mspace width="0.2em" class=""></mspace><mtext class="">log</mtext><mspace width="0.2em" class=""></mspace><mi class="">Q</mi></mrow></mrow><annotation-xml encoding="MathML-Content" class=""><mrow class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub><mo class="">=</mo><msubsup class=""><mrow class=""><mi class="">E</mi></mrow><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.0592</mn><mtext class="">V</mtext></mrow><mi class="">n</mi></mfrac><mspace width="0.2em" class=""></mspace><mtext class="">log</mtext><mspace width="0.2em" class=""></mspace><mi class="">Q</mi></mrow></annotation-xml></semantics></math></span></div><div id="fs-idm240817536" class="ui-has-child-title callout" data-type="example"><header class=""><h3 class="os-title" id="h3_debF" name="h3_debF">EXAMPLE <span data-etb-numbered-element="1">37.1.2</span></h3></header><p id="fs-idp23262432" class="" name="fs-idp23262432"></p><h4 id="h4_BdEs" class="" data-type="title" name="h4_BdEs">Predicting Redox Spontaneity Under Nonstandard Conditions</h4>Use the Nernst equation to predict the spontaneity of the redox reaction shown below.<div id="fs-idm365472" class="unnumbered" data-type="equation"><div class="MathJax_Display"><span id="MathJax-Element-425-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><mtext>Co</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mrow><mtext>Fe</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo>,</mo><mspace width="0.2em" ></mspace><mn>1.94</mn><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mspace width="0.2em" ></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em" ></mspace><msup><mrow><mtext>Co</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.15</mtext><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>+</mo><mtext>Fe</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mtext>Co</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mrow><mtext>Fe</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo>,</mo><mspace width="0.2em"></mspace><mn>1.94</mn><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mspace width="0.2em"></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em"></mspace><msup><mrow><mtext>Co</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.15</mtext><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>+</mo><mtext>Fe</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mrow class=""><mtext class="">Co</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mrow class=""><mtext class="">Fe</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo class="">,</mo><mspace width="0.2em" class=""></mspace><mn class="">1.94</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><msup class=""><mrow class=""><mtext class="">Co</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.15</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><mtext class="">Fe</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" class=""><mrow class=""><mtext class="">Co</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mrow class=""><mtext class="">Fe</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo class="">,</mo><mspace width="0.2em" class=""></mspace><mn class="">1.94</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><msup class=""><mrow class=""><mtext class="">Co</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.15</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><mtext class="">Fe</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mrow></annotation-xml></semantics></math></span></div></div><p id="fs-idp102277360" class="" name="fs-idp102277360"></p><h4 id="h4_nekF" class="" data-type="title" name="h4_nekF">Solution</h4>Collecting information from <a class="" href="https://openstax.org/books/chemistry-atoms-first-2e/pages/l-standard-electrode-half-cell-potentials" data-page-slug="l-standard-electrode-half-cell-potentials" data-page-uuid="562b4d8d-bd3c-4837-9946-08d8be397584" data-page-fragment="" data-shortened-url="https://edtechbooks.org/-LIuQ" data-unshortened-url="https://openstax.org/books/chemistry-atoms-first-2e/pages/l-standard-electrode-half-cell-potentials" data-mce-href="https://openstax.org/books/chemistry-atoms-first-2e/pages/l-standard-electrode-half-cell-potentials">Appendix L</a> and the problem,<div id="fs-idp61630144" class="unnumbered" data-type="equation"><div class="MathJax_Display"><span id="MathJax-Element-426-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtable><mtr ></mtr><mtr><mtd columnalign="left"><mtext>Anode (oxidation):</mtext></mtd><mtd columnalign="left"><mtext>Co</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mspace width="0.2em" ></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em" ></mspace><msup><mtext>Co</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mtext>2e</mtext><mtext>−</mtext></msup></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><msup><mrow><mtext>Co</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mtext>/Co</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.28 V</mtext></mtd></mtr><mtr><mtd columnalign="left"><mtext>Cathode (reduction):</mtext></mtd><mtd columnalign="left"><msup><mtext>Fe</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mtext>2e</mtext><mtext>−</mtext></msup><mspace width="0.2em" ></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em" ></mspace><mtext>Fe</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><msup><mrow><mtext>Fe</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mtext>/Fe</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.447 V</mtext></mtd></mtr><mtr><mtd ></mtd><mtd columnalign="left"><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>=</mo><msubsup><mi>E</mi><mrow><mtext>cathode</mtext></mrow><mo>°</mo></msubsup><mo>−</mo><msubsup><mi>E</mi><mrow><mtext>anode</mtext></mrow><mo>°</mo></msubsup><mo>=</mo></mtd><mtd columnalign="right"><mtext>−0.447 V</mtext><mo>−</mo><mo stretchy="false">(</mo><mtext>−0.28 V</mtext><mo stretchy="false">)</mo></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.17 V</mtext></mtd></mtr></mtable></mrow><annotation-xml encoding="MathML-Content"><mtable><mtr></mtr><mtr><mtd columnalign="left"><mtext>Anode (oxidation):</mtext></mtd><mtd columnalign="left"><mtext>Co</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mspace width="0.2em"></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em"></mspace><msup><mtext>Co</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mtext>2e</mtext><mtext>−</mtext></msup></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><msup><mrow><mtext>Co</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mtext>/Co</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.28 V</mtext></mtd></mtr><mtr><mtd columnalign="left"><mtext>Cathode (reduction):</mtext></mtd><mtd columnalign="left"><msup><mtext>Fe</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mtext>2e</mtext><mtext>−</mtext></msup><mspace width="0.2em"></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em"></mspace><mtext>Fe</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><msup><mrow><mtext>Fe</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mtext>/Fe</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.447 V</mtext></mtd></mtr><mtr><mtd></mtd><mtd columnalign="left"><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>=</mo><msubsup><mi>E</mi><mrow><mtext>cathode</mtext></mrow><mo>°</mo></msubsup><mo>−</mo><msubsup><mi>E</mi><mrow><mtext>anode</mtext></mrow><mo>°</mo></msubsup><mo>=</mo></mtd><mtd columnalign="right"><mtext>−0.447 V</mtext><mo>−</mo><mo stretchy="false">(</mo><mtext>−0.28 V</mtext><mo stretchy="false">)</mo></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.17 V</mtext></mtd></mtr></mtable></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mtable class=""><mtr class=""></mtr><mtr class=""><mtd columnalign="left" class=""><mtext class="">Anode (oxidation):</mtext></mtd><mtd columnalign="left" class=""><mtext class="">Co</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><msup class=""><mtext class="">Co</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mtext class="">2e</mtext><mtext class="">−</mtext></msup></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><msup class=""><mrow class=""><mtext class="">Co</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mtext class="">/Co</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.28 V</mtext></mtd></mtr><mtr class=""><mtd columnalign="left" class=""><mtext class="">Cathode (reduction):</mtext></mtd><mtd columnalign="left" class=""><msup class=""><mtext class="">Fe</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mtext class="">2e</mtext><mtext class="">−</mtext></msup><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><mtext class="">Fe</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><msup class=""><mrow class=""><mtext class="">Fe</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mtext class="">/Fe</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.447 V</mtext></mtd></mtr><mtr class=""><mtd class=""></mtd><mtd columnalign="left" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">=</mo><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cathode</mtext></mrow><mo class="">°</mo></msubsup><mo class="">−</mo><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">anode</mtext></mrow><mo class="">°</mo></msubsup><mo class="">=</mo></mtd><mtd columnalign="right" class=""><mtext class="">−0.447 V</mtext><mo class="">−</mo><mo stretchy="false" class="">(</mo><mtext class="">−0.28 V</mtext><mo stretchy="false" class="">)</mo></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.17 V</mtext></mtd></mtr></mtable></mrow><annotation-xml encoding="MathML-Content" class=""><mtable class=""><mtr class=""></mtr><mtr class=""><mtd columnalign="left" class=""><mtext class="">Anode (oxidation):</mtext></mtd><mtd columnalign="left" class=""><mtext class="">Co</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><msup class=""><mtext class="">Co</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mtext class="">2e</mtext><mtext class="">−</mtext></msup></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><msup class=""><mrow class=""><mtext class="">Co</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mtext class="">/Co</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.28 V</mtext></mtd></mtr><mtr class=""><mtd columnalign="left" class=""><mtext class="">Cathode (reduction):</mtext></mtd><mtd columnalign="left" class=""><msup class=""><mtext class="">Fe</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mtext class="">2e</mtext><mtext class="">−</mtext></msup><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><mtext class="">Fe</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><msup class=""><mrow class=""><mtext class="">Fe</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mtext class="">/Fe</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.447 V</mtext></mtd></mtr><mtr class=""><mtd class=""></mtd><mtd columnalign="left" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">=</mo><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cathode</mtext></mrow><mo class="">°</mo></msubsup><mo class="">−</mo><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">anode</mtext></mrow><mo class="">°</mo></msubsup><mo class="">=</mo></mtd><mtd columnalign="right" class=""><mtext class="">−0.447 V</mtext><mo class="">−</mo><mo stretchy="false" class="">(</mo><mtext class="">−0.28 V</mtext><mo stretchy="false" class="">)</mo></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.17 V</mtext></mtd></mtr></mtable></annotation-xml></semantics></math></span></div></div><p id="fs-idm15620288" class="" name="fs-idm15620288">Notice the negative value of the standard cell potential indicates the process is not spontaneous under standard conditions. Substitution of the Nernst equation terms for the nonstandard conditions yields:</p><div id="fs-idp99119696" class="unnumbered" data-type="equation"><div class="MathJax_Display"><span id="MathJax-Element-427-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtable><mtr><mtd columnalign="right"><mi>Q</mi></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mfrac><mrow><msup><mrow><mo stretchy="false">[</mo><mtext>Co</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">]</mo></mrow><mrow><msup><mrow><mo stretchy="false">[</mo><mtext>Fe</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">]</mo></mrow></mfrac><mspace width="0.2em" ></mspace><mo>=</mo><mspace width="0.2em" ></mspace><mfrac><mrow><mn>0.15</mn><mspace width="0.2em" ></mspace><mi>M</mi></mrow><mrow><mn>1.94</mn><mspace width="0.2em" ></mspace><mi>M</mi></mrow></mfrac><mspace width="0.2em" ></mspace><mo>=</mo><mn>0.077</mn></mtd></mtr><mtr><mtd columnalign="right"><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>−</mo><mspace width="0.2em" ></mspace><mfrac><mrow><mn>0.0592 V</mn></mrow><mi>n</mi></mfrac><mspace width="0.4em" ></mspace><mtext>log</mtext><mspace width="0.2em" ></mspace><mi>Q</mi></mtd></mtr><mtr><mtd columnalign="right"><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mn>−0.1</mn><mtext>7 V</mtext><mo>−</mo><mspace width="0.2em" ></mspace><mfrac><mrow><mn>0.0592 V</mn></mrow><mn>2</mn></mfrac><mspace width="0.4em" ></mspace><mtext>log</mtext><mspace width="0.2em" ></mspace><mn>0.077</mn></mtd></mtr><mtr><mtd columnalign="right"><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.17 V</mtext><mo>+</mo><mn>0.033 V</mn><mo>=</mo><mn>−0.14 V</mn></mtd></mtr></mtable></mrow><annotation-xml encoding="MathML-Content"><mtable><mtr><mtd columnalign="right"><mi>Q</mi></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mfrac><mrow><msup><mrow><mo stretchy="false">[</mo><mtext>Co</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">]</mo></mrow><mrow><msup><mrow><mo stretchy="false">[</mo><mtext>Fe</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">]</mo></mrow></mfrac><mspace width="0.2em"></mspace><mo>=</mo><mspace width="0.2em"></mspace><mfrac><mrow><mn>0.15</mn><mspace width="0.2em"></mspace><mi>M</mi></mrow><mrow><mn>1.94</mn><mspace width="0.2em"></mspace><mi>M</mi></mrow></mfrac><mspace width="0.2em"></mspace><mo>=</mo><mn>0.077</mn></mtd></mtr><mtr><mtd columnalign="right"><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup><mo>−</mo><mspace width="0.2em"></mspace><mfrac><mrow><mn>0.0592 V</mn></mrow><mi>n</mi></mfrac><mspace width="0.4em"></mspace><mtext>log</mtext><mspace width="0.2em"></mspace><mi>Q</mi></mtd></mtr><mtr><mtd columnalign="right"><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mn>−0.1</mn><mtext>7 V</mtext><mo>−</mo><mspace width="0.2em"></mspace><mfrac><mrow><mn>0.0592 V</mn></mrow><mn>2</mn></mfrac><mspace width="0.4em"></mspace><mtext>log</mtext><mspace width="0.2em"></mspace><mn>0.077</mn></mtd></mtr><mtr><mtd columnalign="right"><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.17 V</mtext><mo>+</mo><mn>0.033 V</mn><mo>=</mo><mn>−0.14 V</mn></mtd></mtr></mtable></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mtable class=""><mtr class=""><mtd columnalign="right" class=""><mi class="">Q</mi></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mfrac class=""><mrow class=""><msup class=""><mrow class=""><mo stretchy="false" class="">[</mo><mtext class="">Co</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">]</mo></mrow><mrow class=""><msup class=""><mrow class=""><mo stretchy="false" class="">[</mo><mtext class="">Fe</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">]</mo></mrow></mfrac><mspace width="0.2em" class=""></mspace><mo class="">=</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.15</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi></mrow><mrow class=""><mn class="">1.94</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi></mrow></mfrac><mspace width="0.2em" class=""></mspace><mo class="">=</mo><mn class="">0.077</mn></mtd></mtr><mtr class=""><mtd columnalign="right" class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.0592 V</mn></mrow><mi class="">n</mi></mfrac><mspace width="0.4em" class=""></mspace><mtext class="">log</mtext><mspace width="0.2em" class=""></mspace><mi class="">Q</mi></mtd></mtr><mtr class=""><mtd columnalign="right" class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mn class="">−0.1</mn><mtext class="">7 V</mtext><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.0592 V</mn></mrow><mn class="">2</mn></mfrac><mspace width="0.4em" class=""></mspace><mtext class="">log</mtext><mspace width="0.2em" class=""></mspace><mn class="">0.077</mn></mtd></mtr><mtr class=""><mtd columnalign="right" class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.17 V</mtext><mo class="">+</mo><mn class="">0.033 V</mn><mo class="">=</mo><mn class="">−0.14 V</mn></mtd></mtr></mtable></mrow><annotation-xml encoding="MathML-Content" class=""><mtable class=""><mtr class=""><mtd columnalign="right" class=""><mi class="">Q</mi></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mfrac class=""><mrow class=""><msup class=""><mrow class=""><mo stretchy="false" class="">[</mo><mtext class="">Co</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">]</mo></mrow><mrow class=""><msup class=""><mrow class=""><mo stretchy="false" class="">[</mo><mtext class="">Fe</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">]</mo></mrow></mfrac><mspace width="0.2em" class=""></mspace><mo class="">=</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.15</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi></mrow><mrow class=""><mn class="">1.94</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi></mrow></mfrac><mspace width="0.2em" class=""></mspace><mo class="">=</mo><mn class="">0.077</mn></mtd></mtr><mtr class=""><mtd columnalign="right" class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.0592 V</mn></mrow><mi class="">n</mi></mfrac><mspace width="0.4em" class=""></mspace><mtext class="">log</mtext><mspace width="0.2em" class=""></mspace><mi class="">Q</mi></mtd></mtr><mtr class=""><mtd columnalign="right" class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mn class="">−0.1</mn><mtext class="">7 V</mtext><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.0592 V</mn></mrow><mn class="">2</mn></mfrac><mspace width="0.4em" class=""></mspace><mtext class="">log</mtext><mspace width="0.2em" class=""></mspace><mn class="">0.077</mn></mtd></mtr><mtr class=""><mtd columnalign="right" class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.17 V</mtext><mo class="">+</mo><mn class="">0.033 V</mn><mo class="">=</mo><mn class="">−0.14 V</mn></mtd></mtr></mtable></annotation-xml></semantics></math></span></div></div><p id="fs-idp160381408" class="" name="fs-idp160381408">The cell potential remains negative (slightly) under the specified conditions, and so the reaction remains nonspontaneous.</p><p id="fs-idp72968608" class="" name="fs-idp72968608"></p><h4 id="h4_TsUB" class="" data-type="title" name="h4_TsUB">Check Your Learning</h4>For the cell schematic below, identify values for <em class="" data-effect="italics">n</em> and <em class="" data-effect="italics">Q</em>, and calculate the cell potential, <em class="" data-effect="italics">E</em><sub class="">cell</sub>.<div id="fs-idp18135232" class="unnumbered" data-type="equation"><div class="MathJax_Display"><span id="MathJax-Element-428-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><mtext>Al</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mo>│</mo><msup><mrow><mtext>Al</mtext></mrow><mrow><mn>3+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo>,</mo><mspace width="0.2em" ></mspace><mn>0.15</mn><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>║</mo><msup><mrow><mtext>Cu</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo>,</mo><mspace width="0.2em" ></mspace><mn>0.025</mn><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>│</mo><mtext>Cu</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mtext>Al</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mo>│</mo><msup><mrow><mtext>Al</mtext></mrow><mrow><mn>3+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo>,</mo><mspace width="0.2em"></mspace><mn>0.15</mn><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>║</mo><msup><mrow><mtext>Cu</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mo>,</mo><mspace width="0.2em"></mspace><mn>0.025</mn><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>│</mo><mtext>Cu</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mrow class=""><mtext class="">Al</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mo class="">│</mo><msup class=""><mrow class=""><mtext class="">Al</mtext></mrow><mrow class=""><mn class="">3+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo class="">,</mo><mspace width="0.2em" class=""></mspace><mn class="">0.15</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">║</mo><msup class=""><mrow class=""><mtext class="">Cu</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo class="">,</mo><mspace width="0.2em" class=""></mspace><mn class="">0.025</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">│</mo><mtext class="">Cu</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" class=""><mrow class=""><mtext class="">Al</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mo class="">│</mo><msup class=""><mrow class=""><mtext class="">Al</mtext></mrow><mrow class=""><mn class="">3+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo class="">,</mo><mspace width="0.2em" class=""></mspace><mn class="">0.15</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">║</mo><msup class=""><mrow class=""><mtext class="">Cu</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mo class="">,</mo><mspace width="0.2em" class=""></mspace><mn class="">0.025</mn><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">│</mo><mtext class="">Cu</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mrow></annotation-xml></semantics></math></span></div></div><div id="fs-idp84594464" class="ui-has-child-title list-group my-4" data-type="note"><header class="mx-0 my-0 p-0"><h3 href="#answer_JI8uyQHN" style="cursor: pointer;" class="os-title my-0 py-2 px-0 px-3 no-border-radius" data-type="title" aria-expanded="true" aria-controls="answer_JI8uyQHN" data-bs-toggle="collapse" id="h3_MgIJ" name="h3_MgIJ" data-mce-style="cursor: pointer;" data-mce-href="#answer_JI8uyQHN">Answer</h3></header><section id="answer_JI8uyQHN" class="list-group-item collapse" style=""><div class="os-note-body"><p id="fs-idp34686320" class="" name="fs-idp34686320"><em class="" data-effect="italics">n</em> = 6; <em class="" data-effect="italics">Q</em> = 1440; <em class="" data-effect="italics">E</em><sub class="">cell</sub> = +1.97 V, spontaneous.</p></div></section></div></div><p id="fs-idp264674608" class="" name="fs-idp264674608">A <span id="term616" class="" data-type="term">concentration cell</span> is constructed by connecting two nearly identical half-cells, each based on the same half-reaction and using the same electrode, varying only in the concentration of one redox species. The potential of a concentration cell, therefore, is determined only by the difference in concentration of the chosen redox species. The example problem below illustrates the use of the Nernst equation in calculations involving concentration cells.</p><div id="fs-idp211103648" class="ui-has-child-title callout" data-type="example"><header class=""><h3 class="os-title" id="h3_JBvg" name="h3_JBvg">EXAMPLE <span data-etb-numbered-element="1">37.1.3</span></h3></header><p id="fs-idp40117744" class="" name="fs-idp40117744"></p><h4 id="h4_iIsb" class="" data-type="title" name="h4_iIsb">Concentration Cells</h4>What is the cell potential of the concentration cell described by<div id="fs-idp85858736" class="unnumbered" data-type="equation"><div class="MathJax_Display"><span id="MathJax-Element-429-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><mtext>Zn</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mo>│</mo><msup><mrow><mtext>Zn</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.10</mtext><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>║</mo><msup><mrow><mtext>Zn</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.50</mtext><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>│</mo><mtext>Zn</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mtext>Zn</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mo>│</mo><msup><mrow><mtext>Zn</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.10</mtext><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>║</mo><msup><mrow><mtext>Zn</mtext></mrow><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.50</mtext><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>│</mo><mtext>Zn</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mrow class=""><mtext class="">Zn</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mo class="">│</mo><msup class=""><mrow class=""><mtext class="">Zn</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.10</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">║</mo><msup class=""><mrow class=""><mtext class="">Zn</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.50</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">│</mo><mtext class="">Zn</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" class=""><mrow class=""><mtext class="">Zn</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mo class="">│</mo><msup class=""><mrow class=""><mtext class="">Zn</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.10</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">║</mo><msup class=""><mrow class=""><mtext class="">Zn</mtext></mrow><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.50</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">│</mo><mtext class="">Zn</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mrow></annotation-xml></semantics></math></span></div></div><p id="fs-idp142711536" class="" name="fs-idp142711536"></p><h4 id="h4_SrTt" class="" data-type="title" name="h4_SrTt">Solution</h4>From the information given:<div id="fs-idp5275888" class="unnumbered" data-type="equation"><div class="MathJax_Display"><span id="MathJax-Element-430-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtable><mtr ></mtr><mtr><mtd columnalign="left"><munder accentunder="true"><mtable><mtr><mtd columnalign="left"><mtext>Anode:</mtext></mtd><mtd ></mtd><mtd ></mtd><mtd columnalign="left"><mtext>Zn</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mspace width="0.2em" ></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em" ></mspace><msup><mtext>Zn</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.10</mtext><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mtext>2e</mtext><mtext>−</mtext></msup></mtd><mtd ></mtd><mtd ></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><mtext>anode</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.7618 V</mtext></mtd></mtr><mtr><mtd columnalign="left"><mtext>Cathode:</mtext></mtd><mtd ></mtd><mtd ></mtd><mtd columnalign="left"><msup><mtext>Zn</mtext><mn>2+</mn></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.50</mtext><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mtext>2e</mtext><mtext>−</mtext></msup><mspace width="0.2em" ></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em" ></mspace><mtext>Zn</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mtd><mtd ></mtd><mtd ></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><mtext>cathode</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.7618 V</mtext></mtd></mtr></mtable><mo stretchy="true">¯</mo></munder></mtd></mtr><mtr><mtd columnalign="left"><mtable><mtr><mtd columnalign="left"><mtext>Overall:</mtext></mtd><mtd ></mtd><mtd ></mtd><mtd columnalign="left"><msup><mtext>Zn</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.50</mtext><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo><mspace width="0.2em" ></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em" ></mspace><msup><mtext>Zn</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.10</mtext><mspace width="0.2em" ></mspace><mi>M</mi><mo stretchy="false">)</mo></mtd><mtd ></mtd><mtd ></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>0.000 V</mtext></mtd></mtr></mtable></mtd></mtr></mtable></mrow><annotation-xml encoding="MathML-Content"><mtable><mtr></mtr><mtr><mtd columnalign="left"><munder accentunder="true"><mtable><mtr><mtd columnalign="left"><mtext>Anode:</mtext></mtd><mtd></mtd><mtd></mtd><mtd columnalign="left"><mtext>Zn</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo><mspace width="0.2em"></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em"></mspace><msup><mtext>Zn</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.10</mtext><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mtext>2e</mtext><mtext>−</mtext></msup></mtd><mtd></mtd><mtd></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><mtext>anode</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.7618 V</mtext></mtd></mtr><mtr><mtd columnalign="left"><mtext>Cathode:</mtext></mtd><mtd></mtd><mtd></mtd><mtd columnalign="left"><msup><mtext>Zn</mtext><mn>2+</mn></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.50</mtext><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mtext>2e</mtext><mtext>−</mtext></msup><mspace width="0.2em"></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em"></mspace><mtext>Zn</mtext><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mtd><mtd></mtd><mtd></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><mtext>cathode</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>−0.7618 V</mtext></mtd></mtr></mtable><mo stretchy="true">¯</mo></munder></mtd></mtr><mtr><mtd columnalign="left"><mtable><mtr><mtd columnalign="left"><mtext>Overall:</mtext></mtd><mtd></mtd><mtd></mtd><mtd columnalign="left"><msup><mtext>Zn</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.50</mtext><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo><mspace width="0.2em"></mspace><mo stretchy="false">⟶</mo><mspace width="0.2em"></mspace><msup><mtext>Zn</mtext><mrow><mn>2+</mn></mrow></msup><mo stretchy="false">(</mo><mi>a</mi><mi>q</mi><mtext>, 0.10</mtext><mspace width="0.2em"></mspace><mi>M</mi><mo stretchy="false">)</mo></mtd><mtd></mtd><mtd></mtd><mtd columnalign="right"><msubsup><mi>E</mi><mrow><mtext>cell</mtext></mrow><mo>°</mo></msubsup></mtd><mtd columnalign="left"><mo>=</mo></mtd><mtd columnalign="left"><mtext>0.000 V</mtext></mtd></mtr></mtable></mtd></mtr></mtable></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mtable class=""><mtr class=""></mtr><mtr class=""><mtd columnalign="left" class=""><munder accentunder="true" class=""><mtable class=""><mtr class=""><mtd columnalign="left" class=""><mtext class="">Anode:</mtext></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="left" class=""><mtext class="">Zn</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><msup class=""><mtext class="">Zn</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.10</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mtext class="">2e</mtext><mtext class="">−</mtext></msup></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">anode</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.7618 V</mtext></mtd></mtr><mtr class=""><mtd columnalign="left" class=""><mtext class="">Cathode:</mtext></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="left" class=""><msup class=""><mtext class="">Zn</mtext><mn class="">2+</mn></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.50</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mtext class="">2e</mtext><mtext class="">−</mtext></msup><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><mtext class="">Zn</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cathode</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.7618 V</mtext></mtd></mtr></mtable><mo stretchy="true" class="">¯</mo></munder></mtd></mtr><mtr class=""><mtd columnalign="left" class=""><mtable class=""><mtr class=""><mtd columnalign="left" class=""><mtext class="">Overall:</mtext></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="left" class=""><msup class=""><mtext class="">Zn</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.50</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><msup class=""><mtext class="">Zn</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.10</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">0.000 V</mtext></mtd></mtr></mtable></mtd></mtr></mtable></mrow><annotation-xml encoding="MathML-Content" class=""><mtable class=""><mtr class=""></mtr><mtr class=""><mtd columnalign="left" class=""><munder accentunder="true" class=""><mtable class=""><mtr class=""><mtd columnalign="left" class=""><mtext class="">Anode:</mtext></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="left" class=""><mtext class="">Zn</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><msup class=""><mtext class="">Zn</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.10</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mtext class="">2e</mtext><mtext class="">−</mtext></msup></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">anode</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.7618 V</mtext></mtd></mtr><mtr class=""><mtd columnalign="left" class=""><mtext class="">Cathode:</mtext></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="left" class=""><msup class=""><mtext class="">Zn</mtext><mn class="">2+</mn></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.50</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mo class="">+</mo><msup class=""><mtext class="">2e</mtext><mtext class="">−</mtext></msup><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><mtext class="">Zn</mtext><mo stretchy="false" class="">(</mo><mi class="">s</mi><mo stretchy="false" class="">)</mo></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cathode</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">−0.7618 V</mtext></mtd></mtr></mtable><mo stretchy="true" class="">¯</mo></munder></mtd></mtr><mtr class=""><mtd columnalign="left" class=""><mtable class=""><mtr class=""><mtd columnalign="left" class=""><mtext class="">Overall:</mtext></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="left" class=""><msup class=""><mtext class="">Zn</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.50</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo><mspace width="0.2em" class=""></mspace><mo stretchy="false" class="">⟶</mo><mspace width="0.2em" class=""></mspace><msup class=""><mtext class="">Zn</mtext><mrow class=""><mn class="">2+</mn></mrow></msup><mo stretchy="false" class="">(</mo><mi class="">a</mi><mi class="">q</mi><mtext class="">, 0.10</mtext><mspace width="0.2em" class=""></mspace><mi class="">M</mi><mo stretchy="false" class="">)</mo></mtd><mtd class=""></mtd><mtd class=""></mtd><mtd columnalign="right" class=""><msubsup class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow><mo class="">°</mo></msubsup></mtd><mtd columnalign="left" class=""><mo class="">=</mo></mtd><mtd columnalign="left" class=""><mtext class="">0.000 V</mtext></mtd></mtr></mtable></mtd></mtr></mtable></annotation-xml></semantics></math></span></div></div><p id="fs-idp2148576" class="" name="fs-idp2148576">Substituting into the Nernst equation,</p><div id="fs-idp235695968" class="unnumbered" data-type="equation"><div class="MathJax_Display"><span id="MathJax-Element-431-Frame" class="MathJax" style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mrow><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub><mo>=</mo><mtext>0.000 V</mtext><mo>−</mo><mspace width="0.2em" ></mspace><mfrac><mrow><mtext>0.0592 V</mtext></mrow><mn>2</mn></mfrac><mspace width="0.4em" ></mspace><mtext>log</mtext><mspace width="0.4em" ></mspace><mfrac><mrow><mn>0.10</mn></mrow><mrow><mn>0.50</mn></mrow></mfrac><mspace width="0.2em" ></mspace><mo>=</mo><mn>+0.021 V</mn></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><msub><mi>E</mi><mrow><mtext>cell</mtext></mrow></msub><mo>=</mo><mtext>0.000 V</mtext><mo>−</mo><mspace width="0.2em"></mspace><mfrac><mrow><mtext>0.0592 V</mtext></mrow><mn>2</mn></mfrac><mspace width="0.4em"></mspace><mtext>log</mtext><mspace width="0.4em"></mspace><mfrac><mrow><mn>0.10</mn></mrow><mrow><mn>0.50</mn></mrow></mfrac><mspace width="0.2em"></mspace><mo>=</mo><mn>+0.021 V</mn></mrow></annotation-xml></semantics></math>" data-mce-style="box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" data-mce-tabindex="0"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class=""><semantics class=""><mrow class=""><mrow class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub><mo class="">=</mo><mtext class="">0.000 V</mtext><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mtext class="">0.0592 V</mtext></mrow><mn class="">2</mn></mfrac><mspace width="0.4em" class=""></mspace><mtext class="">log</mtext><mspace width="0.4em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.10</mn></mrow><mrow class=""><mn class="">0.50</mn></mrow></mfrac><mspace width="0.2em" class=""></mspace><mo class="">=</mo><mn class="">+0.021 V</mn></mrow></mrow><annotation-xml encoding="MathML-Content" class=""><mrow class=""><msub class=""><mi class="">E</mi><mrow class=""><mtext class="">cell</mtext></mrow></msub><mo class="">=</mo><mtext class="">0.000 V</mtext><mo class="">−</mo><mspace width="0.2em" class=""></mspace><mfrac class=""><mrow class=""><mtext class="">0.0592 V</mtext></mrow><mn class="">2</mn></mfrac><mspace width="0.4em" class=""></mspace><mtext class="">log</mtext><mspace width="0.4em" class=""></mspace><mfrac class=""><mrow class=""><mn class="">0.10</mn></mrow><mrow class=""><mn class="">0.50</mn></mrow></mfrac><mspace width="0.2em" class=""></mspace><mo class="">=</mo><mn class="">+0.021 V</mn></mrow></annotation-xml></semantics></math></span></div></div><p id="fs-idp47526144" class="" name="fs-idp47526144">The positive value for cell potential indicates the overall cell reaction (see above) is spontaneous. This spontaneous reaction is one in which the zinc ion concentration in the cathode falls (it is reduced to elemental zinc) while that in the anode rises (it is produced by oxidation of the zinc anode). A greater driving force for zinc reduction is present in the cathode, where the zinc(II) ion concentration is greater (<em class="" data-effect="italics">E</em><sub class="">cathode</sub> > <em class="" data-effect="italics">E</em><sub class="">anode</sub>).</p><p id="fs-idm11024080" class="" name="fs-idm11024080"></p><h4 id="h4_jPzW" class="" data-type="title" name="h4_jPzW">Check Your Learning</h4>The concentration cell above was allowed to operate until the cell reaction reached equilibrium. What are the cell potential and the concentrations of zinc(II) in each half-cell for the cell now?<div id="fs-idm1444240" class="ui-has-child-title list-group my-4" data-type="note"><header class="mx-0 my-0 p-0"><h3 href="#answer_dJI5fgkX" style="cursor: pointer;" class="os-title my-0 py-2 px-0 px-3 no-border-radius" data-type="title" aria-expanded="true" aria-controls="answer_dJI5fgkX" data-bs-toggle="collapse" id="h3_fLqp" name="h3_fLqp" data-mce-style="cursor: pointer;" data-mce-href="#answer_dJI5fgkX">Answer</h3></header><section id="answer_dJI5fgkX" class="list-group-item collapse" style=""><div class="os-note-body"><p id="fs-idp18466656" class="" name="fs-idp18466656"><em class="" data-effect="italics">E</em><sub class="">cell</sub> = 0.000 V; [Zn<sup class="">2+</sup>]<sub class="">cathode</sub> = [Zn<sup class="">2+</sup>]<sub class="">anode</sub> = 0.30 <em class="" data-effect="italics">M</em></p></div></section></div></div>
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