Consider an electrochemical cell:
$A (s) | A^{n +} (a q, 2 M) ‖ B^{2 n +} (a q, 1 M) | B (s), E_{c e l l} = 0.00 V$ . (at 298K) Calculate the magnitude of standard Gibbs energy change $(Δ G^{o})$ for formation of 1 mole of B, in the units kJ/mole.
Take $R = 8.3 J K^{- 1} m o l^{- 1}, \ln 2 = 0.7$

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answer is 3.46.

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Detailed Solution

Cell reaction : $2 A + B^{2 n +} \to_{}^{} 2 A^{n +} + B$
$Q_{R} = \frac{{[A^{n +}]}^{2}}{[B^{2 n +}]} = 4$

$E_{c e l l} = E_{c e l l}^{o} - \frac{R T}{n F} \ln Q_{R}$
$E_{c e l l}^{o} = \frac{8.3 \times 298}{2 n F} \times \ln 4 = \frac{1731.38}{n F} v o l t s$
$Δ G^{o} = - n F E^{o} = - 1.73 K j / m o l e$

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