GATE 2023 CY – Question 64

Physical Chemistry · Electrochemistry: Standard electrode potential and electrochemical cells. Nernst Equation and its application, relationship between electrode potential and thermodynamic quantities, Potentiometric and conductometric titrations. Ionic mobility and conductivity. Kohlrausch’s law, Debye-Hückel limiting law. Debye-Hückel- Onsager equation. · 2 marks · Numerical answer

For cell $H_2(g)\mid HCl(aq)\mid Cl_2(g)$, $E^\circ=1.73-(1.25\times10^{-3})T+(1.00\times10^{-6})T^2$, with E in V and T in K. The standard cell-reaction enthalpy change at 300 K is ______ kJ/mol (nearest integer). $F=96500$ C/mol.

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Correct answer: -164 to -154

Explanation

Cell reaction H2+Cl2→2HCl transfers n=2 electrons. ΔG°=−nFE° and ΔS°=nF(dE°/dT), so ΔH°=−nF[E°−T(dE°/dT)]. For the given polynomial, the linear T terms cancel and the bracket is 1.73−10⁻⁶T²=1.64V at 300K.

Thus ΔH°=−2(96500)(1.64)/1000=**−316.52 kJ per reaction**. The official interval−164 to−154 instead corresponds to one mole HCl:−158.26 kJ/mol. The stored scoring follows that normalization.