Question
When metallic copper is shaken with a solution of a copper salt, the reaction Cu + Cu2+ $\rightleftharpoons$2Cu+ proceeds. When equilibrium is established at 298 K, [Cu2+]/ [Cu+]2 = 1.667 × 106 M−1. If the standard potential of the Cu2+|Cu half-cell is +0.3376 V, what is the standard potential of Cu+|Cu half-cell?
(Given: 2.303 RT/F = 0.06, log 2 = 0.3, log 3 = 0.48)
Options
Solution
$E_{cell}^{o} = \frac{0.06}{1}.\log K_{eq} = 0.06\log\frac{1}{1.667 \times 10^{6}} = - 0.3732\text{ V}$
$\text{Now, }E_{Cu^{2 +}|Cu^{+}}^{o} - E_{Cu^{+}|Cu}^{o} = - 0.3732\text{ V}(1) $$${\text{and }E_{Cu^{2 +}|Cu}^{o} = \frac{1 \times E_{Cu^{2 +}|Cu^{+}}^{o} + 1 \times E_{Cu^{+}|Cu}^{o}}{1 + 1} = 0.3376\text{ V} }{\text{Or, }E_{Cu^{2 +}|Cu^{+}}^{o} + E_{Cu^{+}|Cu}^{o} = 0.6752\text{ V}(2) }{\text{From }(1)\text{ and }(2),E_{Cu^{+}|Cu}^{o} = 0.5242\text{ V}}$$
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