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Oxidation Number Method

The SRP for ...

Question

The SRP for $S^{2 -}$ (aq) in CuS/Cu half-cell is:
Given $: K_{s p} (C u S) = 10^{- 35} a n d E_{c u^{2 +} / C u}^{0} = 0.34 V$

1.634 V

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1.034 V

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-0.694 V

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0.394 V

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Solution

The correct option is D -0.694 V
Cell reaction is
$C u S + 2 e^{-} \to C u + S^{2 -}$
Cathode reaction:
$C u^{2 +} + 2 e^{-} \to C u (s)$ ; $E_{{C u}^{2 +} / C u} = 0.34 V$ ; $G_{1}$
$C u S \to C u^{2 +} + S^{2 -}$ ; $K_{s p} = 10^{- 35}$ ; $G_{2}$
Hence for the reaction:
$S + 2 e^{-} \to S^{2 -}$ ; $G_{3}$
$G_{3} = G_{1} + G_{2}$
$- n F E_{S / S^{2 -}}^{0} = - n F \times E_{{C u}^{2 +} / C u}^{0} - R T l n (K_{s p})$
$- 2 F E_{S / S^{2 -}}^{0} = - 2 F 0.34 - R T l n (K_{s p})$
upon substitution:
$E_{S / S^{2 -}}^{0} = 0.34 + \frac{2.303 \times 8.314 \times 298}{2 \times 96500} log (10^{- 35}) E_{S / S^{2 -}}^{0} = 0.34 + \frac{0.059}{2} log (10^{- 35}) = - 0.6925 V$
Hence option C is correct.

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