What is the correct Nernst equation for reaction taking place in the following cell
$M g_{(s)} |M {g^{2 +}}_{(aq)}| |C {l^{-}}_{((aq))}| C l_{2 (g)} (1 atm) / Pt$

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$E_{cell} = E_{cell}^{\circ} - \frac{0 .0592}{n} \times \log [{Mg}^{2 +}] {[{Cl}^{-}]}^{2}$

$E_{cell} = E_{cell}^{\circ} - \frac{0.0592}{n} \times \log \frac{[M^{2 +}]}{[{Cl}^{-}]}$

$E_{cell} = E_{cell}^{\circ} - \frac{0.0592}{n} \times \log \frac{[{Mg}^{2 +}]}{{[{Cl}^{-}]}^{2}}$

$E_{cell} = E_{cell}^{\circ} - \frac{0 .0592}{n} \times \log \frac{{[{Cl}^{-}]}^{2}}{[{Mg}^{2 +}]}$

answer is C.

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Detailed Solution

$M g_{(s)} |M {g^{2 +}}_{(a q)}| |C {l^{-}}_{(a q)}| C l_{2 (g)} (1 atm) / Pt$

Oxidation half reaction, $M g \to M g^{2 +} + 2 e^{-}$

Reduction half reaction $\frac{{Cl}_{2} + 2 e^{-} \to 2 {Cl}^{-}}{Mg + {Cl}_{2} \to {Mg}^{2 +} + 2 {Cl}^{-}}$

Net cell reaction,

Nernst equation, $E_{cell} = E_{cell}^{\circ} - \frac{0.0591}{n} \log {[{Cl}^{-}]}^{2} [{Mg}^{2 +}]$

Here $n = 2$

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