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Equilibrium Constant and Standard Free Energy Change

The standard ...

Question

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

A

0.184 V

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B

0.827 V

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C

0.521 V

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D

0.490 V

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Solution

The correct option is C $0.521 V$
The half-cell reactions are:
$C u^{2 +} + 2 e^{-} \to C u, E^{o} = 0.337 V ∴ Δ G = - n F E^{o} \Rightarrow Δ G = - 2 F \times 0.337 V$
$C u^{2 +} + 2 e^{-} \to C u, Δ G = - 2 F \times 0.337 V . . . (i)$

$C u^{+} \to C u^{2 +} + e^{-}, E^{o} = - 0.153 V \Rightarrow Δ G = 1 F \times 0.153 V$
$C u^{+} \to C u^{2 +} + e^{-}, Δ G = 1 F \times 0.153 V . . . (i i)$

By adding $(i)$ and $(i i)$ , we get
$C u^{+} + e^{-} \to C u, Δ G = (- 2 F \times 0.337 V) + (1 F \times 0.153 V) = - 0.521 F V As, Δ G = - n F E^{o} \Rightarrow - 0.521 F V = - F E^{o} ∴ E^{o} = 0.521 V$

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