Question $1$

Methanol is synthesized from carbon monoxide and hydrogen in a catalytic reactor. The fresh feed to the process contains $32\%(\frac{n}{n})CO$;$64\%(\frac{n}{n})H2$; and $4\%(\frac{n}{n})$ N$2.$ This stream is mixed with a recycle stream in a ratio $5$ mol recycle $/1$mol fresh feed to the reactor, which contains $13\%(\frac{n}{n})N2.$ A low single$-$pass conversion is attained in the reactor. The reactor effluent goes to a condenser, from which two streams emerge: a liquid product stream containing all the methanol formed in the reactor, and a gas stream containing all the Co$,H2,$ and N$2$ leaving the reactor. The gas stream is split into two fractions: one is removed from the process as a purge stream, while the other is the recycle stream that combines with the fresh feed to the reactor.

a$.$ Draw the system, inserting all relevant information.

b$.$ For a basis of $100$mol fresh feed $\frac{?}{hr},$ calculate the production rate of methanol, the molar flow rate and composition of the purge stream, and the overall and single$-$pass conversions of the reactor.