Methanol is produced by reacting carbon monoxide and hydrogen. A fresh feed containing $CO$ and $H_2$ joins a recycle stream and the combined stream is fed to a reactor. A portion of the methanol leaving the reactor is condensed and the unconverted $CO$ and $H_2$ together with $C{H}_{3}OH$ recycled. The stream going from the reactor to the condenser flow at a rate of $275mo\frac{l}{m}in$ and contains. The stream going from the reactor to the condenser flow at a rate of $275mo\frac{l}{m}in$ and contains $10\mathrm{.}6wt\%H_2,64\mathrm{.}0wt\%CO,$ and $25\mathrm{.}4wt\%C{H}_{3}OH.$ The mole fraction of methanol in the recycle is $0\mathrm{.}004.$

$($a$)$ Calculate the production rate of liquid methanol in $mo\frac{l}{m}in$

$($b$)$ Determine the recycle rate in $mo\frac{l}{m}in$ and its composition

$($c$)$ Calculate the fresh feed rate in $mo\frac{l}{m}in$ and its composition

$($d$)$ What is the percentage conversion per pass of $CO?$

$($e$)$ What is the percentage overall conversion of CO$?$