The standard potential of a cell using the reaction $2 N i (s) + O_{2} + 2 H_{2} O ⇌ 2 N i {(O H)}_{2}$ is 1.12.The heat of the reaction is $- 504.2 K j {m o l}^{- 1}$ at $25^{\circ} C$ . Calculate the entropy change.

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Solution

Given, $E_{c e l l}^{o} - 1.12 V, △ H = - 504.2 K J / m o l$
$T = 25^{o} C = 298 K$
$n = 4$
Using the relation, $△ G = △ H - T △ S$
$△ S = \frac{△ H - △ G}{T}$
where $△ G = - n f E_{c e l l}^{o} = - 4 \times 96485 \times 1.12 V$
$△ G = - 432.25 K J / m o l$
$△ S = \frac{- 504.2 K / m o l - (- 432.25 K J / m o l)}{298 K}$
$△ S = \frac{(- 504.2 + 432.25) K J / m o l}{298 K}$
$= - 0.24144 K J K^{- 1}$
$Δ S = - 241.44 J K^{- 1}$

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