Fig. $1$ reported the details of methanol synthesis process. The relevant chemical reactions involved are:

Main reformer reaction: $C{H}_4+2H_{2}OC{O}_2+4H_2$

$($a$)$

Reformer side reaction: $C{H}_4+H_{2}OCO+3H_2$

$($b$)$

CO converter reaction: $2CO+O_{2}2C{O}_2$

$($c$)$

Methanol synthesis reaction: $C{O}_2+3H_{2}C{H}_{3}OH+H_{2}O$

$($d$)$

Based on the reaction $($a$),15\%$ excess steam is fed to the reformer, and conversion of methane is $100\%,$ with a yield of $90\%C{O}_2.$ Conversion of the methanol reactor is $50\%$ on one pass through the reactor.

A stoichiometric quantity of $O_2$ is fed to the $CO$ converter, and the $CO$ is completely converted to $C{O}_2.$ Additional makeup $C{O}_2$ is then introduced to establish a $3$ to $1$ ratio of $H_2$ to $C{O}_2$ in the feed stream to the methanol reactor.

The methanol reactor effluent is cooled to condense all of the methanol and water, with the noncondensable gases recycled to the methanol reactor feed. The $\frac{H_2}{C}{O}_2$ ratio in the recycle stream is also $3$ to $1.$

Because the methane feed contains $1\%$ nitrogen as an impurity, a portion of the recycle stream must be purged to prevent the accumulation of nitrogen in the system. The purge stream analyses $5\%$ nitrogen. On the basis of $100$ moles of $C{H}_4$ feed $($including the $N_2)$ determine:

$\backslash$table$[[$Compound$,C{H}_4,H_{2}O,C{O}_2,CO,C{H}_{3}OH,H_2,O_2$