Which of the following concentration cells with produce maximum $E_{c e l l}$ at $298$ K?
[Take $P_{H_{2}} = 1.0$ atm in each case.]

P t | H_{2} (g) | H^{+} (0.01 M) | | H^{+} (0.1 M) | H_{2} (g) | P t

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P t | H_{2} (g) | N H_{4} C l (0.01 M) | | H C l (0.1 M) | H_{2} (g) | P t

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P t | H_{2} (g) | H^{+} (0.1 M) | | H^{+} (0.2 M) | H_{2} (g) | P t

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P t | H_{2} (g) | H^{+} (p H = 0.0) | | H^{+} (p H = 0.0) | H_{2} (g) | P t

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Solution

The correct option is A $P t | H_{2} (g) | H^{+} (0.01 M) | | H^{+} (0.1 M) | H_{2} (g) | P t$
Cathode : $H^{+} + e^{-} \to \frac{1}{2} H_{2}$
$A n o d e : \frac{1}{2} H_{2} \to H^{+} + e^{-} - ---------------------------------------------- -$
$c e l l e q u a t i o n : H^{+} \frac{1}{2} H_{2} C a t h o d e \to H^{+} \frac{1}{2} H_{2} - -------------------------------------------------- - a n o d e$
$E_{c e l l} = E_{c e l l}^{0} - \frac{0.0591}{1} l o g \frac{[H^{+}] a n o d e}{[H^{+}] c a t h o d e}$
$= \frac{- 0.0591}{1} l o g \frac{[H^{+}] A}{[H^{+}] C}$ $E_{c e l l}^{0} = 0$ due to identical half cells.
Given : ${[H^{+}]}_{A} = 0.01 M$
${[H^{+}]}_{C} = 0.1 M$
$E_{c e l l} = - 0.0591 l o g \frac{0.01}{0.1} = 0.0591 V$

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