The standard oxidation potentials of $\mathrm{Cu} / \mathrm{Cu}^{2+}$ and $\mathrm{Cu}^{+} /…

The standard oxidation potentials of $\mathrm{Cu} / \mathrm{Cu}^{2+}$ and $\mathrm{Cu}^{+} / \mathrm{Cu}^{2+}$ are $-0.34 \mathrm{~V}$ and $-0.16 \mathrm{~V}$ respectively. The standard electrode potential of $\mathrm{Cu}^{+} / \mathrm{Cu}$ would be
  1. $0.18 \mathrm{~V}$
  2. $0.52 \mathrm{~V}$
  3. $0.82 \mathrm{~V}$
  4. $0.49 \mathrm{~V}$

Solution

Reactions
$\mathrm{Cu}^{2+}+2 \mathrm{e}^{-} ightarrow \mathrm{Cu} \quad \quad \quad \Delta \mathrm{G}^{0}=-\mathrm{nFE}^{0}$
$\mathrm{Cu}^{+} ightarrow \mathrm{Cu}^{2+}+\mathrm{e}^{-}$
$\Delta \mathrm{G}_{\mathrm{I}}^{0}=-2 \mathrm{~F} \times 0.34=0.68 \mathrm{~F}$
$\Delta \mathrm{G}_\mathrm{II}^{0}=\mathrm{F} \times 0.16=0.16 \mathrm{~F}$
$\Delta \mathrm{G}_{\mathrm{I}}^{0}=-0.68 \mathrm{~F}$
$\Delta \mathrm{G}_{\mathrm{II}}^{0}=0.16 \mathrm{~F}$
Adding, we get
$\mathrm{Cu}^{+}+\mathrm{e}^{-} ightarrow \mathrm{Cu} \quad\Delta \mathrm{G}_{\mathrm{III}}^{0}=\Delta \mathrm{G}_{\mathrm{I}}^{0}+\Delta \mathrm{G}_{\mathrm{II}}^{0}$
$=0.52 \mathrm{~F}$
$=-\mathrm{FE}^{0}$
$\therefore \mathrm{E}^{\circ}=0.52 \mathrm{~V}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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