GATE 2026 CY – Question 34

Physical Chemistry · Equilibrium: Laws of thermodynamics. Standard states. Thermochemistry. Thermodynamic functions and their relationships: Gibbs-Helmholtz and Maxwell relations, Gibbs-Duhem equation, Van’t Hoff equation. Criteria of spontaneity and equilibrium. Absolute entropy. Partial molar quantities. Thermodynamics of mixing. Chemical potential. Fugacity, Activity and Activity coefficient. Chemical equilibria. Dependence of equilibrium constant on temperature and pressure. · 1 mark · Numerical answer

The maximum work magnitude in kJ from complete combustion of 1.0 mol methane at constant pressure and 25 °C (one decimal place) is _____. Given $\Delta S=-241.60$ J K−1 mol−1, $\Delta H=-890.01$ kJ/mol, $R=8.314$ J mol−1 K−1.

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Correct answer: 812.8 to 813.2

Explanation

The question asks for maximum total work, including expansion work. At fixed temperature its magnitude is $-\Delta A$, rather than just the useful non-expansion work $-\Delta G$. First $\Delta G=\Delta H-T\Delta S=-817.98$ kJ/mol. For $CH_4(g)+2O_2(g)\to CO_2(g)+2H_2O(l)$, $\Delta n_g=-2$. Thus $\Delta A=\Delta G-\Delta n_gRT=-817.98+4.96=-813.02$ kJ/mol. The magnitude is 813.0 kJ.

Official GATE 2026 answer key: https://gate2026.iitg.ac.in/doc/download/2026/Keys/CY_Keys.pdf