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GATE 2024 CH – Question 46

Chemical Reaction Engineering · Non-ideal reactors and residence time distribution · 2 marks · Multiple choice

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 0.2 min$^{-1}$ is carried out in the reactor. For an inlet reactant concentration of 2 mol L$^{-1}$, the reactant concentration (in mol L$^{-1}$) in the exit stream is

$E$ (in min⁻¹) against time. $E$ is zero until 3 min, constant between 3 and 5 min, and zero afterwards.
  1. 0.905
  2. 0.452
  3. 1.902
  4. 0.502

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Correct answer: (A) 0.905

Explanation

The area under $E$ must be 1, so the height is $\frac{1}{5 - 3} = 0.5$ min⁻¹. For a segregated first-order reaction, $\frac{C}{C_0} = \int E(t)e^{-kt}dt = 0.5 \times \frac{e^{-0.6} - e^{-1.0}}{0.2} = 2.5 \times (0.5488 - 0.3679) = 0.4523$. So $C = 2 \times 0.4523 = 0.905$ mol L⁻¹.