A first-order liquid phase reaction A → B is carried out in two isothermal plug flow reactors (PFRs) of volume 1 m³ each, connected in series. The feed flow rate and concentration of A to the first reactor are 10 m³/h and 1 kmol/m³, respectively. At steady-state, the concentration of A at the exit of the second reactor is 0.2 kmol/m³. If the two PFRs are replaced by two equal-volume continuously stirred tank reactors (CSTRs) to achieve the same overall steady-state conversion, the volume of each CSTR, in m³, is

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Accepted Answer

The correct answer is A, 1.54. GATE 2024 official key: (A). PFR: 0.2 = exp(−k×0.2) ⇒ k ≈ 8.047/h. For 2 equal CSTRs: 1/0.2 = (1+kτ)² ⇒ 1+kτ = √5 ⇒ τ ≈ 0.1536 h ⇒ V = τ×F = 0.1536×10 ≈ 1.54 m³.