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For the disproportionation of copper: $2Cu^+ \rightarrow Cu^{2+} + Cu$, $E^\circ$ is : - (Given $E^\circ$ for $Cu^{2+}/Cu$ is 0.34 V and $E^\circ$ for $Cu^{2+}/Cu^+$ is 0.15 V)
A
0.49 V
B
–0.19 V
C
0.38 V
D
–0.38 V
Detailed Solution
Potentials cannot be added directly when the number of electrons differs, so use $\Delta G^\circ = -nFE^\circ$.
$Cu^{2+} + 2e^- \rightarrow Cu$: $\Delta G_1 = -2F(0.34)$
$Cu^{2+} + e^- \rightarrow Cu^+$: $\Delta G_2 = -1F(0.15)$
$Cu^+ + e^- \rightarrow Cu$ = (first) $-$ (second): $\Delta G_3 = -0.68F + 0.15F = -0.53F$, so $E^\circ(Cu^+/Cu) = 0.53$ V.
For $2Cu^+ \rightarrow Cu^{2+} + Cu$: cathode $Cu^+/Cu$ (0.53 V), anode $Cu^{2+}/Cu^+$ (0.15 V).
$E^\circ = 0.53 - 0.15 = 0.38$ V
The positive value shows that $Cu^+$ disproportionates in aqueous solution.
$Cu^{2+} + 2e^- \rightarrow Cu$: $\Delta G_1 = -2F(0.34)$
$Cu^{2+} + e^- \rightarrow Cu^+$: $\Delta G_2 = -1F(0.15)$
$Cu^+ + e^- \rightarrow Cu$ = (first) $-$ (second): $\Delta G_3 = -0.68F + 0.15F = -0.53F$, so $E^\circ(Cu^+/Cu) = 0.53$ V.
For $2Cu^+ \rightarrow Cu^{2+} + Cu$: cathode $Cu^+/Cu$ (0.53 V), anode $Cu^{2+}/Cu^+$ (0.15 V).
$E^\circ = 0.53 - 0.15 = 0.38$ V
The positive value shows that $Cu^+$ disproportionates in aqueous solution.