Consider the process shown in the figure for manufacturing B via the reaction 2A → B. The feed to the process is 90 mol% A and a close-boiling inert component I, mixed with a recycle stream of unreacted A and I from the separator overhead (recycle-to-purge ratio 10), which is also split off as a purge stream (x_B=0 in both). At a particular steady-state: B product rate is 100 kmol/h (pure B), single-pass conversion of A in the reactor is 50%, and the recycle-to-purge stream flow ratio is 10. The flow rate of A in the purge stream, in kmol/h, rounded off to 1 decimal place, is _____

Question

Accepted Answer

The correct answer is 18.1 to 18.3. GATE 2024 official key: 18.1 to 18.3. With B=100=0.25×A_reactor,in ⇒ A_reactor,in=400 kmol/h (from 2A→B, 50% single-pass conversion). Overall balances on A and inert (fresh feed F: x_A=0.9, x_I=0.1) combined with the recycle/purge split (ratio 10, i.e., 11×purge = total light stream leaving separator) give A in purge = (0.5×400)/11 ≈ 18.2 kmol/h.