Medium INTEGER +4 / -1 PYQ · JEE Mains 2022

Cu(s) + Sn2+ (0.001M) $\to$ Cu2+ (0.01M) + Sn(s)

The Gibbs free energy change for the above reaction at 298 K is x $\times$ 10$-$1 kJ mol$-$1. The value of x is __________. [nearest integer]

[Given : $E_{C{u^{2 + }}/Cu}^\Theta = 0.34\,V$ ; $E_{S{n^{2 + }}/Sn}^\Theta = - 0.14\,V$ ; F = 96500 C mol$-$1]

Answer (integer) 983

Solution

$$ \begin{aligned} \mathrm{Cu} &+\mathrm{Sn}^{+2} \longrightarrow \mathrm{Cu}^{+2}+\mathrm{Sn}(\mathrm{s}) \\\\ \mathrm{E}_{\text {cell }}^{\circ} &=\mathrm{E}_{\mathrm{OX}}^{\circ}+\mathrm{E}_{\text {Red }}^{\circ} \\\\ &=-0.34-0.14 \\\\ &=-0.48 \mathrm{~V} \\\\ \mathrm{E}=& ~\mathrm{E}^{\circ}-\frac{0.0591}{2} \log \frac{\left[\mathrm{Cu}^{+2}\right]}{\left[\mathrm{Sn}^{+2}\right]} \\\\ =&-0.48-0.0295 \log 10 \\\\ =&-0.5095 \mathrm{~V} \\\\ \Delta \mathrm{G}=&-\mathrm{nFE} \\\\ &=-2 \times 96500 \times-0.5095 \mathrm{~J} / \mathrm{mol} \\\\ &=98333.5 \times 10^{-3} \mathrm{~kJ} / \mathrm{mol} \\\\ &=983.3 \times 10^{-1} \mathrm{~kJ} / \mathrm{mol} \\\\ &=983 \times 10^{-1} \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$

About this question

Subject: Chemistry · Chapter: Electrochemistry · Topic: Electrochemical Cells

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