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GATE 2022 CY – Question 65

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. · 2 marks · Numerical answer

The surroundings entropy change when 1 mol supercooled water at 263 K freezes at 263 K and 1 bar is ______ J/K (two decimal places). At 273 K, $\Delta_{fus}H^\circ=6.0$ kJ/mol. Water molar heat capacity exceeds that of ice by 37.0 J mol$^{-1}$ K$^{-1}$ between 263 and 273 K.

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Correct answer: 21.20 to 21.60

Explanation

Fusion enthalpy at 263K is 6000+(37)(263−273)=5630J/mol using the heat capacity difference. Freezing releases this heat to the surroundings at 263K. ThereforeΔSsurr=5630/263=**21.41J/K**, positive because the surroundings receive heat. Using 273 K would ignore the stated supercooling.