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GATE 2021 CY – Question 21

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 · Multiple choice

For $3NO(g)\rightleftharpoons N_2O(g)+NO_2(g)$ at 25 °C, $\Delta G^\circ=-104.18$ kJ. With $R=8.314$ J mol$^{-1}$ K$^{-1}$, the equilibrium constant is closest to ______.

  1. 1.043
  2. $1.8\times10^{18}$
  3. 1.651
  4. $5.7\times10^{-19}$

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Correct answer: (B) $1.8\times10^{18}$

Explanation

Use ΔG°=−RT ln K. With T=298.15 K and ΔG°=−104180 J/mol, ln K=104180/(8.314×298.15)≈42.03. Exponentiation gives K≈1.8×10¹⁸. The large positive logarithm is consistent with the strongly negative standard Gibbs energy. **B**.