20080201 Electrochem 3 - Intro Chemistry II 030.102 Chapter...

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Intro Chemistry II – 030.102 - Chapter 12 Spring, 2008 1 12.3. Concentration Effects and the Nernst Equation Apply thermodynamic principles to understand how concentration and pressure affect cell voltage. First, relate free energy change to reaction quotient Q (chapter 9): Δ G ° = Δ G ° + RT ln Q Refresher: For general gas-phase reaction aA ( g ) + bB ( g ) cC ( g ) + dD ( g ) Reaction coefficient is Q = ( P C ) c ( P D ) d ( P A ) a ( P B ) b Pressures in atm (standard state) Combine free energy equation above with Δ G = – n F Δ E and Δ G ° = – n F Δ E ° gives n F Δ E = – n F Δ E ° + RT ln Q Nernst Equation From n F Δ E = – n F Δ E ° + RT ln Q we obtain the Nernst equation Δ E = Δ E ° ln Q Rewrite in terms of common (base-10) logarithms: ln Q = 2.303 log 10 Q At 25 ° C (298.15 K), we have RT n F 2.303 RT F = (2.303) (8.315 J K –1 mol –1 )(298.15 K) 96485 C mol –1 = 0.0592 J C –1 = 0.0592 V Nernst equation becomes ! E = ! E ° 0.0592 V n log 10 Q (at 25 ° C) Exercise: Compute cell voltage with Nernst equation
Intro Chemistry II – 030.102 - Chapter 12 Spring, 2008 2 Problem 12.27 A galvanic cell is constructed that carries out the reaction Pb 2+ ( aq ) + 2 Cr 2+ ( aq ) Pb( s ) + 2 Cr 3+ ( aq ) If the initial concentration of Pb 2+ ( aq ) is 0.15 M, that of Cr 2+ ( aq ) is 0.20 M, and that of Cr 3+ ( aq ) is 0.0030 M, calculate the initial voltage generated by the cell at 25 ° C. From Appendix E: Pb 2+ ( aq ) + 2 e Pb( s ) E ° = –0.1263 V Cr 3+ ( aq ) + e Cr 2+ ( aq ) E ° = –0.424 V Note: Standard voltage for (Cr 3+ ,Cr 2+ ) is slightly different in the student solutions manual. Measuring Equilibrium Constants For overall cell reaction, Δ G ° = – n F Δ E ° Standard free energy change related to equilibrium constant: Δ G ° = – RT ln K Hence, ln K = Δ E ° or log 10 K = Δ E ° (at 25 ° C) Exercises: (1) Calculate equilibrium constant from standard cell voltage.

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