GATE 2021 CY – Question 62

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

For $CO(g)+Cl_2(g)\rightleftharpoons COCl_2(g)$ at 500 °C, initial pressures are 0.7 bar CO and 1.0 bar $Cl_2$. At equilibrium, $COCl_2$ partial pressure is 0.15 bar. The equilibrium constant is ______ (two decimal places).

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Correct answer: 0.30 to 0.34

Explanation

Formation of 0.15 bar COCl2 consumes 0.15 bar each of CO and Cl2. The equilibrium pressures are therefore 0.55, 0.85 and 0.15 bar. With standard pressure 1 bar, Kp=(0.15)/(0.55×0.85)=0.32086.

Thus **0.32** to two decimals; the initial reactant pressures cannot be used directly.