First slide

Nernst Equation

Question

In the given reaction,
$\begin{matrix} 2 {Cu}^{+} (aq) ⇌ {Cu}^{2 +} (aq) + Cu (s) \\ E_{{Cu}^{+} / Cu}^{\circ} = 0 .6 V and E_{{Cu}^{2 +} / Cu}^{\circ} = 0 .41 V \end{matrix}$
Find out the equilibrium constant.

Moderate

A

$2.76 \times 10^{2}$
B

$2.76 \times 10^{4}$
C

$2.76 \times 10^{6}$
D

$2.76 \times 10^{8}$

Solution

Right hand cell reaction, ${Cu}^{+} + e^{-} ⟶ Cu$
Left hand cell reaction, ${Cu}^{+} ⟶ {Cu}^{2 +} + e^{-}$
Cell reactions, $2 {Cu}^{+} ⟶ Cu + {Cu}^{2 +}$
Cell potential $E_{cell}^{\circ} = E_{{Cu}^{+} / Cu}^{\circ} - E_{{Cu}^{2 +} / C}^{\circ}$
$\begin{array}{l} = 0 .60 - 0 .41 = 0 .19 V \\ - {nFE}^{\circ} = - RTln K_{eq} \\ \log K_{eq} = \frac{{nE}^{\circ}}{(2 .303 RT / F)} = \frac{2 \times 0 .19 V}{0 .059 V} = 6 .44 \\ K_{eq} = 10^{6 .44} = 2 .76 \times 10^{6} \end{array}$

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