17.4 Potential, Free Energy, and Equilibrium

For each pair of standard cell potential and electron stoichiometry values below, calculate a corresponding standard free energy change (kJ).

(a) 0.000 V, n = 2

(b) +0.434 V, n = 2

(c) −2.439 V, n = 1

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) $\text{Hg} \left(l\right) + \text{S}^{2−} \left(a q ,\text{ 0}.\text{10} M\right) + 2 \text{Ag}^{+} \left(a q ,\text{ 0}.\text{25} M\right) \rightarrow 2 \text{Ag} \left(s\right) + \text{HgS} \left(s\right)$

(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 e…

Use the data in Appendix L to calculate equilibrium constants for the following reactions. Assume 298.15 K if no temperature is given.

(a) $\text{AgCl} \left(s\right) \rightleftharpoons \text{Ag}^{+} \left(a q\right) + \text{Cl}^{−} \left(a q\right)$

(b) $\text{CdS} \left(s\right) \rightleftharpoons \text{Cd}^{2+} \left(a q\right) + \text{S}^{2−} \left(a q\right) \text{at 377 K}$

(c) $\text{Hg}^{2+} \left(a q\right) + 4 \text{Br}^{−} \left(a q\right) \rightleftharpoons \left[\text{HgBr}_{4}\right]^{2−} \left(a q\right)$

(d) $\text{H}_{2} \text{O} \left(l\right) \rightleftharpoons \text{H}^{+} \left(a q\right) + \text{OH}^{−} \left(a q\right) \text{at 25} °C$