Which of the following expressions represent the EMF of the above cell at 25°C?

Moderate

A

$E = \frac{0 .0592}{2} \log \frac{{[^{a} {Pb}^{2 +}]}_{RHS}}{{[^{a} {Pb}^{2 +}]}_{LHS}}$
B

$E = \frac{0 .0592}{2} \log \frac{{[^{a} {Pb}^{2 +}]}_{LHS}}{{[^{a} {Pb}^{2 +}]}_{RHS}}$
C

$E = \frac{0 .0592}{2} \log {[K_{sp} ({PbI}_{2})]}^{1 / 3}$
D

$E = \frac{0 .0592}{2} \log \frac{K_{sp} [{PbI}_{2}]}{K_{sp} [{PbSO}_{4}]}$

Solution

$\begin{matrix} \underset{(I)}{{Pb}_{(s)}} |\underset{}{Pb {SO}_{4}}| |\underset{(II)}{{PbI}_{2}}| {Pb}_{(s)} \end{matrix}$
$Pb ⟶ {Pb}_{1}^{2 +} + 2 e^{-}$ (oxidation)
${Pb}_{II}^{2 +} + 2 e^{-} ⟶ Pb$ (Reduction)
$Net cell reaction: {Pb}_{𝕀}^{2 +} ⟶ {Pb}_{1}^{2 +}$
$E_{c e 𝕀𝕀} = E_{c e l l}^{'} - \frac{0.0592}{n} \log \frac{{[{Pb}^{2 +}]}_{I}}{{[{Pb}^{2 +}]}_{II}}$ [Nernst's equation]
$E_{cell}^{°} = 0, ∴ E_{cell} = \frac{0 .0592}{n} \log \frac{{[{Pb}^{2 +}]}_{II}}{{[{Pb}^{2 +}]}_{I}}$

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