The emf of the cell $M | M (N O_{3})_{x} (0.01 M) | | M (N O_{3})_{x} (0.1 M) | M$ is found to be 0.0197 V at standard conditions. The valency of the metal in the metal nitrate is

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Solution

$\begin{matrix} M (s) + M^{x +} \to & M (s) + M^{x +} 0.1 M & 0.01 M \end{matrix}$
At standard conditions, $\frac{2.303 R T}{F} = 0.0591$
$E_{c e l l} = E^{\circ} - \frac{0.0591}{x} l o g \frac{0.01}{0.1} ⟹ 0 - \frac{0.0591}{x} l o g \frac{0.01}{0.1} = 0.0197 V ⟹ x = 3$
$E °$ is 0 because it is a concentration cell.

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