For a cell, $C u (s) | C u^{2 +} (0.001 M) ∥ A g^{+} (0.01 M) | A g (s)$ the cell potential is found to be $0.43 V$ at $298 K$ . The magnitude of standard electrode potential for $C u^{2 +}$ /Cu is _____ $\times 10^{- 2} V$ .

[Given : $E_{A g^{+} / A g}^{⊖} = 0.80 V and \frac{2.303 R T}{F} = 0.06 V$ ]

34.00

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34.0

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Solution

Anode : $C u (s) ⟶ C u^{2 +} (a q) + 2 e^{-}$

Cathode : $A g^{+} + e^{-} ⟶ A g (s)] 2$

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$C u (s) + 2 A g^{+} (a q) ⟶ C u^{2 +} (a q) + 2 A g (s)$

$E_{C e l l} = E_{c e l l}^{0} - \frac{0.06}{2} log \frac{[C u^{2 +}]}{[A g^{+}]^{2}}$

$0.43 = E_{c e l l}^{0} - \frac{0.06}{2} log (\frac{10^{- 3}}{(10^{- 2})^{2}})$

$0.43 = E_{c e l l}^{0} - 0.03 log 10$

$E_{c e l l}^{0} = 0.46 V$

$E_{c e l l}^{0} = E_{A g^{+} / A g}^{0} - E_{C u^{2 +} / C u}^{0}$

$E_{C u^{2 + / C u}}^{0} = (0.80 - 0.46) = 0.34 V = 34 \times 10^{- 2}$

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