GATE 2020 CH – Question 54

Chemical Reaction Engineering · Single and multiple reactions in ideal reactors · 2 marks · Numerical answer

An elementary reversible liquid reaction P ⇌ Q occurs in an isothermal steady ideal CSTR with $-r_P=C_P-0.5C_Q$ mol/(L min). Feed contains only P at 1 mol/L. Exit conversion is 75% of equilibrium conversion, with no volume change. Find reactor space time in minutes, to one decimal place.

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Correct answer: 1.9 to 2.1

Explanation

At equilibrium $C_P=0.5C_Q$, with total concentration 1 mol/L, so equilibrium conversion is 2/3. Actual conversion is 0.75(2/3) = 0.5, giving Cₚ = Cq = 0.5 mol/L. The net consumption rate is $0.5-0.5(0.5)=0.25$ mol/(L min). CSTR space time is $\tau=C_{P0}X/(-r_P)=1(0.5)/0.25=2.0$ min.

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