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GATE 2026 Chemical Engineering, Q54 · Thermodynamics

The correct answer is 2.3 to 2.5.

Question

Methanol is formed by the gas phase reaction CO (g) + 2H2 (g) ⇌\rightleftharpoons CH3OH (g). The standard Gibbs free energies of formation at 298 K for CO and CH3OH are −137 kJ mol−1mol⁻¹ and −162 kJ mol−1,mol⁻¹, respectively (R = 8.314 J mol−1K−1).mol⁻¹ K⁻¹). The equilibrium constant for the reaction at 298 K is _____ ×104 \times 10⁴ (rounded off to one decimal place).

Official answer: 2.3 to 2.5

Why

GATE 2026 official key: 2.3 to 2.5.ΔG°rxn=−162−(−137)−0=−252.5. \Delta G°rxn = −162 − (−137) − 0 = −25 kJ/mol (H2 is an element). K =exp(25000/(8.314×298))≈2.4×104.= exp(25000/(8.314 \times 298)) \approx 2.4 \times 10⁴.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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