GATE 2025 MT – Question 55
For $\mathrm{Mg}+\mathrm{Cd}^{2+}\rightleftharpoons\mathrm{Mg}^{2+}+\mathrm{Cd}$, the standard Gibbs free energy change is ______ kJ (rounded to an integer). Standard oxidation potentials relative to the standard hydrogen electrode are:
$\mathrm{Mg}\rightleftharpoons\mathrm{Mg}^{2+}+2e^-$: $E^\circ=2.37$ V.
$\mathrm{Cd}\rightleftharpoons\mathrm{Cd}^{2+}+2e^-$: $E^\circ=0.403$ V.
Given: $F=96500\ \mathrm{C\,mol^{-1}}$.
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Correct answer: -381 to -379
Explanation
Reverse the cadmium oxidation to obtain its reduction. The cell potential is $E^\circ_{cell}=2.37-0.403=1.967$ V.
Two electrons transfer per reaction, so $\Delta G^\circ=-nFE=-2\times96500\times1.967=-379631$ J.
This is −379.631 kJ, giving **−380 kJ** after rounding.