Methanol is produced by reacting carbon monoxide and hydrogen at 644 K over a ZnO–Cr₂O₃ catalyst. A mixture of CO and H₂ in a ratio 2 mol H₂ /mol CO is compressed and fed to the catalyst bed at 644 K and 34.5 MPa absolute. A single-pass conversion of 25% is obtained. The space velocity, or ratio of the volumetric flow rate of the feed gas to the volume of the catalyst bed, is (25,000 m³/h)/(1m³ catalyst bed). The product gases are passed through a condenser, in which the methanol is liquefied. 

(a) You are designing a reactor to produce 54.5 kmol CH₃OH/h. Estimate (i) the volumetric flow rate that the compressor must be capable of delivering if no gases are recycled, and (ii) the required volume of the catalyst bed. (Use Kay’s rule for pressure–volume calculations.) 

(b) If (as is done in practice) the gases from the condenser are recycled to the reactor, the compressor is then required to deliver only the fresh feed. What volumetric flow rate must it deliver assuming that the methanol produced is completely recovered in the condenser? (In practice it is not; moreover, a purge stream must be taken off to prevent the buildup of impurities in the system.)