Methanol is produced by the reaction of carbon dioxide and hydrogen:

$C{O}_2+3H_{2}C{H}_{3}OH+H_{2}O$

The fresh feed to the process contains hydrogen, carbon dioxide, and $0\mathrm{.}40$mol$\%$ inert $(1).$ The reactor effluent passes to a separator that removes essentially all of the methanol and water formed, but none of the reactants or inert. The latter substances are recycled to the reactor. To avoid buildup of the inert in the system, a purge stream is withdrawn from the recycle. The feed to the reactor $($not the fresh feed to the process$)$ contains $28\mathrm{.}0$mol$\%CO2,70\mathrm{.}0$mol$\%H2,$ and $2\mathrm{.}00$ mol$\%$ inert. The single$-$pass conversion of hydrogen is $60\mathrm{.}0\%.$ Calculate the molar flow rates and molar compositions of the fresh feed, the total feed to the reactor, the recycle stream, and the purge stream for a production rate of $155$molCH$3O\frac{H}{h}.$