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GATE 2019 CY – Question 58

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 SO₂(g)+½O₂(g)⇌SO₃(g), standard Gibbs formation energies at 298 K are −300 and −371 kJ/mol for SO₂ and SO₃. Express Kp as a number ×10¹⁰ (nearest integer). Use R=8.31 J/(mol K).

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Correct answer: 265 to 295

Explanation

Reaction ΔG°=−371−(−300)=−71 kJ/mol; elemental oxygen has zero standard formation Gibbs energy. Then $K_p=\exp[71000/(8.31\times298)]\simeq2.8288\times10^{12}$. Divide by 10¹⁰ to obtain 282.88, so enter 283.

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