Key Concepts and Summary
Potential is a thermodynamic quantity reflecting the intrinsic driving force of a redox process, and it is directly related to the free energy change and equilibrium constant for the process. For redox processes taking place in electrochemical cells, the maximum (electrical) work done by the system is easily computed from the cell potential and the reaction stoichiometry and is equal to the free energy change for the process. The equilibrium constant for a redox reaction is logarithmically related to the reaction’s cell potential, with larger (more positive) potentials indicating reactions with greater driving force that equilibrate when the reaction has proceeded far towards completion (large value of K). Finally, the potential of a redox process varies with the composition of the reaction mixture, being related to the reactions standard potential and the value of its reaction quotient, Q, as described by the Nernst equation.
Practice Questions
Determine the standard cell potential and the cell potential under the stated conditions for the electrochemical reactions described here. State whether each is spontaneous or nonspontaneous under each set of conditions at 298.15 K.
(a) $Hg(l)+S^{2-}(aq,\;0.10\;M)+2Ag^+(aq,\;0.25\;M)⟶2Ag(s)+HgS(s)$
(b) The cell made from an anode half-cell consisting of an aluminum electrode in 0.015 M aluminum nitrate solution and a cathode half-cell consisting of a nickel electrode in 0.25 M nickel(II) nitrate solution.
(c) The cell made of a half-cell in which 1.0 M aqueous bromide is oxidized to 0.11 M bromine ion and a half-cell in which aluminum ion at 0.023 M is reduced to aluminum metal.
Solution
(a) standard cell potential: 1.50 V, spontaneous; cell potential under stated conditions: 1.43 V, spontaneous; (b) standard cell potential: 1.405 V, spontaneous; cell potential under stated conditions: 1.423 V, spontaneous; (c) standard cell potential: −2.749 V, nonspontaneous; cell potential under stated conditions: −2.757 V, nonspontaneous
Determine ΔG and ΔG° for each of the reactions in the previous problem.
Use the data in the Appendix on standard potentials to calculate equilibrium constants for the following reactions. Assume 298.15 K if no temperature is given.
(a) $AgCl(s)⇌Ag^+(aq)+Cl^-(aq)$
(b) $CdS(s)⇌Cd^{2+}(aq)+S^{2-}(aq)\qquad \text{at 377 K}$
(c) $Hg^{2+}(aq)+4Br^-(aq)⇌[HgBr_4]^{2-}(aq)$
(d) $H_2O(l)⇌H^+(aq)+OH^-(aq)\qquad \text{at 25°C}$
Solution
(a) $1.7×10^{-10}$;
(b) $2.6×10^{-21}$;
(c) $4.693×10^{21}$;
(d) $1.0×10^{-14}$;