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Q. $E^{\circ}_{cell}$ for the reaction, $2H_{2}O \to H_{2}O^{+}+OH^{-}$ at $25\,{}^{\circ}C$ is $- 0.8277\, V$. The equilibrium constant for the reaction is

Electrochemistry

Solution:

$2H_{2}O \to H_{3}O^{+} +OH^{-}$
$E^{\circ}_{cell}=\frac{0.0591}{n} log \,K$
$log\,K=\frac{E^{\circ}_{cell}\times n}{0.0591}$
$=\frac{-0.8277\times1}{0.0591}=-14$
$\Rightarrow K=10^{-14}$