Calculate the $E M F$ of the cell, $Z n - H g (c_{1} M) | Z n^{2 +} (a q) | H g - Z n (c_{2} M)$
at $25^{o} C$ , if the concentration of the zinc amalgam are: $c_{1} = 10 g$ per $100 g$ of mercury and $c_{2} = 1 g$ per $100 g$ of mercury.

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Solution

The cell reaction in this case are:
At cathode: $Z n^{2 +} + 2 e^{-} ⟶ Z n (C_{2})$
At anode: $Z n (C_{1}) ⟶ Z n^{2 +} + 2 e^{-}$
Net Reaction: $Z n (C_{1}) ⟶ Z n (C_{2})$
$E = \frac{0.059}{2} l o g \frac{C_{2}}{C_{1}}$
$E = - 0.0295 l o g (\frac{1}{2})$
$E = 8.8 \times 10^{- 3} V$

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