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Gibb's Energy and Nernst Equation

For the cell ...

Question

For the cell $C u (s) | C u^{2 +} (a q) (0.1 M) | | A g^{+} (a q) (0.01 M) | A g (s)$ the cell potential $E_{1} = 0.3095 V$
For the cell $C u (s) | C u^{2 +} (a q) (0.01 M) | | A g^{+} (a q) (0.001 M) A g (s)$ the cell potential = ____ $\times 10^{- 2} V .$
(Round off to the Nearest Integer).
$[Use : \frac{2.303 R T}{F} = 0.059]$

28.00

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28.0

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Solution

$C u ⟶ C u^{2 +} + 2 e^{-}$
$2 e^{-} + 2 A g^{+} ⟶ 2 A g$

$2 A g^{+} + C u ⟶ C u^{2 +} + 2 A g$

$0.3095 = E^{0} - \frac{R T}{n F} ln (\frac{[C u^{2 +}]}{[A g^{+}]^{2}})$

$0.3095 = E^{0} - \frac{0.059}{2} log (\frac{0.1}{(0.01)^{2}})$

$E^{0} = 0.3095 + \frac{0.059}{2} log (10^{3})$

$E^{0} = 0.3095 + \frac{0.059}{2} \times 3 E^{0} = 0.398 V$
$E^{0}$ value for both the cells is same since they are similar
For second cell,

$E = 0.398 - \frac{0.059}{2} log [\frac{0.01}{(0.001)^{2}}]$

$E = 0.28 V = 28 \times 10^{- 2} V$

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