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GATE 2024 Chemical Engineering, Q46 · Reaction Engineering

The correct answer is A, 0.905.

Question

The residence time distribution, E, for a non-ideal flow reactor is given in the figure. A first-order liquid phase reaction with a rate constant 0.2min−10.2 min⁻¹ is carried out in the reactor. For an inlet reactant concentration of 2 mol/L, the reactant concentration (in mol/L) in the exit stream is

Figure for Q46 (Reaction Engineering, RTD): The residence time distribution, E, for a non-ideal flow reactor is given in the figure. A first-ord…
  • A. 0.905
  • B. 0.452
  • C. 1.902
  • D. 0.502

Official answer: 0.905

Why

GATE 2024 official key: (A). Using the segregation model, Cexit=C0∫E(t)e−ktdt=2×0.5×∫35e−0.2tdt=1×5×(e−0.6−e−1.0)≈0.905C_{exit} = C₀\int E(t)e^{−kt}dt = 2 \times 0.5 \times \int ₃⁵e^{−0.2t}dt = 1 \times 5 \times (e^{−0.6}−e^{−1.0}) \approx 0.905 mol/L.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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