Methanol is produced by the reversible, gas-phase hydrogenation of carbon monoxide as
$$ \mathrm{CO}+2 \mathrm{H}_{2} \leftrightarrow \mathrm{CH}_{3} \mathrm{OH}$$
$\mathrm{CO}$ and $\mathrm{H}_{2}$ are charged to a reactor and the reaction proceeds to equilibrium at $453 \: \mathrm{K}$ and $2\: \mathrm{ atm}$ . The reaction equilibrium constant, which depends only on the temperature, is $1.68$ at the reaction conditions. The mole fraction of $\mathrm{H}_{2}$ in the product is $0.4$. Assuming ideal gas behaviour, the mole fraction of methanol in the product is $\_\_\_\_\_$ (rounded off to $2$ decimal places).
