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GATE 2020 CH – Question 17

Chemical Reaction Engineering · Heterogeneous catalysis, diffusion effects and catalyst deactivation · 1 mark · Multiple choice

The squared Thiele modulus is $M_T^2=L^2k/D_{eff}$ for a first-order reaction in a porous catalyst. It measures the ratio of

  1. Pore-diffusion time scale to reaction time scale.
  2. Pore-diffusion rate to reaction rate.
  3. Reaction time scale to pore-diffusion time scale.
  4. Reaction rate to external mass-transfer rate.

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Show answer and explanation

Correct answer: (A) Pore-diffusion time scale to reaction time scale.

Explanation

Characteristic diffusion time over distance L is $t_D=L^2/D_{eff}$ and first-order reaction time is $t_R=1/k$. Their ratio is $t_D/t_R=L^2k/D_{eff}=M_T^2$. Thus A. A large value means reaction is fast relative to internal pore transport, making diffusion limitations important.

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