Given that the standard potentials $\left(\mathrm{E}^{0}\right)$ of $\mathrm{Cu}^{2+} / \mathrm{Cu}$ and $\mathrm{Cu}^{+} /$ $\mathrm{Cu}$ are $0.34 \mathrm{~V}$ and $0.522 \mathrm{~V}$ respectively, the $\mathrm{E}^{0}$ of $\mathrm{Cu}^{2+} /$ $\mathrm{Cu}^{+}$is:
Correct Option:
$\mathrm{Cu}^{2+}+2 e^{-} \longrightarrow \mathrm{Cu}, \Delta \mathrm{G}_{1}^{0}=-2 \mathrm{~F}(0.34) \ldots$ (i)
$\mathrm{Cu}^{+}+e^{-} \longrightarrow \mathrm{Cu}, \Delta \mathrm{G}_{2}^{\circ}=-\mathrm{F}(0.522) \quad$...(ii)
Subtract (ii) from (i)
$\mathrm{Cu}^{2+}+\mathrm{e}^{-} \longrightarrow \mathrm{Cu}^{+}, \quad \Delta \mathrm{G}_{3}^{\circ}=-\mathrm{F}\left(\mathrm{E}^{0}\right)$
$\therefore \Delta \mathrm{G}_{1}^{\circ}-\Delta \mathrm{G}_{2}^{\circ}=\mathrm{G}_{3}^{\circ}$
$\Rightarrow-\mathrm{FE}^{\circ}=-2 \mathrm{~F}(0.34)+\mathrm{F}(0.522)$
$\Rightarrow \mathrm{E}^{\circ}=0.68-0.522=0.158 \mathrm{~V}$