Question

The standard reduction potentials of $Cu^{2+} / Cu $ and $Cu^{2+} / Cu^+$ are $0.337 \,V$ and $0.153 \,V$ respectively. The standard electrode potential of $Cu^+ /Cu$ half-cell is

• A. 0.184 V
• B. 0.887 V
• C. 0.521 V
• D. 0.490 V

Answer 1

Answer: (C)

$E^{\circ}$ is an intensive property :
$E^{\circ} \Delta G^{\circ}=-n E^{\circ} F$
(i) $Cu ^{2+}+2 e^{-} \longrightarrow Cu \,\,\, 0.337 V -0.674 F$
(ii) $Cu ^{2+}+e^{-} \longrightarrow Cu ^{+} \,\,\, 0.153 V -0.153 F$
Subtracting (ii) from (i) gives :
$Cu ^{+}+e^{-} \longrightarrow Cu \,\,\, \Delta G^{\circ}=-0.521 F =-n E^{\circ} F$
$\Rightarrow E^{\circ}=0.521 V$
$\because n=1$
For the given concentration cell,
the cell reaction are $M \longrightarrow M^{2+}$ at left hand electrode.
$M^{2+} \longrightarrow M $ at right hand electrode
$\Rightarrow M^{2+}$ (RHS electrode) $\longrightarrow M^{2+}$ (LHS electrode)
$E^{\circ}=0$
Applying Nernst equation
$ E_{\text {cell }}=0.059=0-\frac{0.059}{2} \log \frac{\left[M^{2+}\right] \text { at LHS electrode }}{0.001} $
$\Rightarrow \log \frac{\left[M^{2+}\right] \text { at LHS electrode }}{0.001}=-2 $
$\Rightarrow \left[M^{2+}\right] \text { at LHS electrode }=10^{-2} \times 0.001=10^{-5} M$