Calculate the cell potential of the following cell at $25$ $^{0}$ C.
$P t, H_{2 (1 a t m)} | H {^{+}}_{(0.01 M)} | | C u {^{+ 2}}_{(0.1 M)} | C u$ :

$[E {^{0}}_{C u^{2 +} / C u} = 0.337 V]$

0.248 V

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0.337 V

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0.425 V

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0.427 V

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Solution

The correct option is D $0.425 V$
The overall cell reaction is given by:
$C u^{2 +} + H_{2} \to C u + 2 H^{+}$

$E_{c e l l}^{\circ} = E_{C u^{2 +} / C u}^{\circ} - E_{H^{+} / H_{2}}^{\circ}$

$⟹ E_{c e l l}^{\circ} = 0.337 - 0 = 0.337 V$ [standard hydrogen electrode potential is zero].

Now, $E_{c e l l} = 0.337 - \frac{0.059}{2} l o g [\frac{[H^{+}]^{2}}{[C u^{2 +}]}]$

$E_{c e l l} = 0.337 - \frac{0.059}{2} l o g (\frac{(0.01)^{2}}{(0.1)})$

$E_{c e l l} = 0.425 V$

Option C is correct.

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