The feed gas to a methanol synthesis reactor is composed of $75$mol$\%H_2,15$ mol$\%CO,5$mol$\%C{O}_2$ and $5$mol$\%N_2.$ The system comes to equilibrium at $550K$ and $100$ bar with respect to the reactions:

$2H_2+CO=C{H}_{3}OH$

$H_2+C{O}_2=CO+H_{2}O$

Standard free energy changes for these reactions at $550K$ are $g{?}_{(1)}=33\mathrm{.}385k\frac{J}{m}ol,$ and $g{?}_{(2)}=18\mathrm{.}562k\frac{J}{m}ol,$ resp. Assuming ideal gases, determine the composition of the equilibrium mixture.