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Gay Lussac's Law, Avagadro's Law

Find the vale...

Question

Find the valency of copper from the following cell at $298 K$ , if the emf of the cell is $0.0295 V$ .
$C u (s) | C u S O_{4} (a q, 0.1 M) | | C u S O_{4} (a q, 1 M) | C u (s)$

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Solution

$C u (s) | C u S O_{4} (a q, 0.1 M) | | C u S O_{4} (a q, 1 M) | C u (s)$

Life side electrode will act as anode and right side electrode will act as cathode.

For the given concentration cell,

$E = E^{0} - \frac{0.0591}{n} l o g \frac{[A n o d e]}{[C a t h o d e]}$

For concentration cell,
$E^{0} = 0$
$∴$
$E = - \frac{0.0591}{n} l o g \frac{[A n o d e]}{[C a t h o d e]}$

$0.0295 = - \frac{0.0591}{n} l o g \frac{0.1}{[1]}$

$0.0295 = \frac{0.0591}{n} l o g \frac{1}{[0.1]}$

$0.0295 = \frac{0.0591}{n}$

$n = \frac{0.0591}{0.029}$

$n \approx 2$

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