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Determine the standard equilibrium constant of the following reaction at $298 K$ .
$2 M n O_{4}^{-} + 6 H^{+} + 5 H_{2} C_{2} O_{4} \to 2 M n^{2 +} + 8 H_{2} O + 10 C O_{2} (E_{c e l l}^{\circ} = 2.0 V)$

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Solution

Anode : $5 H_{2} C_{2} O_{4} \to {10 C O}_{2} + 10 e^{-}$
Cathode : $2 M n {O_{4}}^{-} + 10 e^{-} \to {M n}^{2 +}$
$∴ n = 2 e^{-}, Δ G = R T l n K_{f} = n F E^{0}$
$l o g K_{f} = \frac{2}{0.059} \times E^{0}$
$l o g K_{f} = 67.8$
$K_{f} = 10^{67.8}$

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