Question

$ Cu^+ \,(aq) $ is unstable in solution and undergoes simultaneous oxidation and reduction, according to the reaction
$ \ce{2Cu+ (aq) <=> Cu^{2+} (aq) +Cu(s)} $
choose correct $ E^{\circ} $ for above reaction if $ E^{\circ}_{Cu^{2+}/Cu}=0.34\,V $ and $ E^{\circ}_{Cu^{2+}/Cu^{+}}=0.15\,V $

• A. $ -0.38\,V $
• B. $ +0.49\,V $
• C. $ +0.38\,V $
• D. $ -0.19\,V $

Answer 1

Answer: (C)

From given data (From $\left.\Delta G^{\circ}=-n E^{\circ} F\right)$

$(i) Cu (s) \longrightarrow Cu ^{2+}(a q)+2 e^{-}$

$\Delta G_{1}^{\circ} =-2 \times(-0.34) \times F$

$(ii) Cu ^{2+}(a q)+e^{-} \longrightarrow Cu ^{+}(a q)$

$\Delta G_{2}^{\circ}=-1 \times(0.15) F$

On addition

$Cu (s) \longrightarrow Cu ^{+}(a q)+e^{-} .\Delta G_{3}^{\circ}=-1 \times E^{\circ} \times E$

$\Delta G_{3}^{\circ} =\Delta G_{1}^{\circ}+\Delta G_{2}^{\circ}$

$=(-2 \times-0.34 \times F)+(-1 \times 0.15 \times F)$

$=+0.68 F -0.15 F =0.53 F$

or $E^{\circ} =-0.53 V$

Reaction,

$2 Cu ^{+}(a q) \rightleftharpoons Cu ^{2+}(a q)+ Cu (s) E^{\circ}=$?

So, $Cu ^{+}(a q)+e^{-} \rightleftharpoons Cu (s), E^{\circ}=+0.53 V$

$Cu ^{+}(a q) \rightleftharpoons Cu ^{2+}(a q)+e^{-} ; E^{\circ}=-0.15 V$

$2 Cu ^{+}(a q) \rightleftharpoons Cu ^{2+}(a q)+ Cu (s) E^{\circ} =+0.38 V$