GATE 2026 CH – Question 54
Methanol is formed by the following gas phase homogeneous reaction:
CO (g) + 2H$_2$ (g) ⇋ CH$_3$OH (g)
The standard Gibbs free energies of formation at 298 K for CO and CH$_3$OH are −137 kJ mol$^{-1}$ and −162 kJ mol$^{-1}$, respectively. The value of universal gas constant is 8.314 J mol$^{-1}$ K$^{-1}$. The equilibrium constant for the given reaction at 298 K is _____ $\times 10^4$ (rounded off to one decimal place).
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Show answer and explanation
Correct answer: 2.39 to 2.41
Explanation
The standard Gibbs energy change is $\Delta G° = -162 - (-137) - 0 = -25$ kJ/mol (H$_2$ is an element). Then $K = \exp\left(-\frac{\Delta G°}{RT}\right) = \exp\left(\frac{25000}{8.314 \times 298}\right) = e^{10.09} = 2.4 \times 10^4$.