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GATE 2024 CH – Question 44

Chemical Reaction Engineering · Heterogeneous catalysis, diffusion effects and catalyst deactivation · 2 marks · Multiple choice

A first-order heterogenous reaction $A \to B$ is carried out using a porous spherical catalyst. Assume isothermal conditions, and that intraphase diffusion controls the reaction rate. At a bulk $A$ concentration of 0.3 mol L$^{-1}$, the observed reaction rate in a 3 mm diameter catalyst particle is 0.2 mol s$^{-1}$ L$^{-1}$ catalyst volume. At a bulk $A$ concentration of 0.1 mol L$^{-1}$, the observed reaction rate, in mol s$^{-1}$L$^{-1}$ catalyst volume, in a 6 mm diameter catalyst particle, is

  1. 0.011
  2. 0.033
  3. 0.022
  4. 0.005

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Correct answer: (B) 0.033

Explanation

When pore diffusion controls (large Thiele modulus), the effectiveness factor is $\eta \approx \frac{3}{\phi}$ with $\phi = R\sqrt{k/D_e}$, so $\eta \propto \frac{1}{R}$. The observed rate per unit volume is $\eta kC \propto \frac{C}{R}$. So $r_2 = 0.2 \times \frac{0.1}{0.3} \times \frac{3}{6} = 0.0333$ mol s⁻¹ L⁻¹.