Methanol is formed by the following gas phase homogeneous reaction:
\[
\mathrm{CO}(\mathrm{~g})+2 \mathrm{H}_{2}(\mathrm{~g}) \leftrightharpoons \mathrm{CH}_{3} \mathrm{OH}(\mathrm{~g})
\]
The standard Gibbs free energies of formation at $298 \text{ K}$ for $\text{CO}$ and $\mathrm{CH}_{3} \mathrm{OH}$ are $-137 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $-162 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. The value of universal gas constant is $8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. The equilibrium constant for the given reaction at $298 ~\text{K}$ is $\_\_\_\_$ $\times 10^{4}$ (rounded off to one decimal place).
