3.12 Methanol is synthesized from carbon monoxide and hydrogen in a catalytic reactor. The fresh feed to the process contains 32.0 mol% CO, 64.0% H, and 11 4.0% N2. This stream is mixed with a recycle stream in a ratio 5 mol recy- cle/1 mol fresh feed to produce the feed to the reactor, which contains 13.0 mol% 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 prod- uct stream containing essentially all the methanol formed in the reactor, and a gas stream containing all the CO, Hy, and N, leaving the reactor. The gas stream is split into two fractions: one is removed from the process as a purge stream, and the other is the recycle stream that combines with the fresh feed to the reactor. (a) For a basis of 100 mol fresh feed/h, calculate the production rate of methanol (mol/h), the molar flow rate and composition of the purge gas, and the overall and single-pass conversions. (b) Briefly explain in your own words the reasons for including (i) the recy- cle stream and (ii) the purge stream