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pH of a Solution

At what pH ...

Question

At what $p H$ of $H C l$ solution will hydrogen gas electrode show electrode potential of $- 0.118$ V? $H_{2}$ gas is bubbled at $298$ K and $1$ atm pressure.

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Solution

Writing electrode reaction as reduction reaction,
$H^{+} + e^{-} \to \frac{1}{2} H_{2}$
Applying Nernst equation,
$E_{H^{+}} / H_{2} = E_{H^{+} / H_{2}}^{0} - \frac{0.0591}{1} l o g \frac{1}{[H^{+}]}$
or
$- 0.118 = - 0.0591 p H$
or $p H = 2$

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