GATE 2022 BT – Question 48
Which of the following statements are CORRECT for an enzyme entrapped in a spherical particle?
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Correct answer: (A) Effectiveness factor is ratio of the reaction rate with diffusion-limitation to the reaction rate without diffusion-limitation; (C) Effectiveness factor increases with decrease in Thiele modulus; (D) Internal diffusion-limitation can be reduced by decreasing the size of the particle
Explanation
Check each statement about an enzyme immobilised in a spherical particle with diffusion limitation.
- **A.** The effectiveness factor $\eta$ is the ratio of the actual reaction rate (with diffusion limitation) to the rate that would occur with no diffusion limitation. True. ✓
- **B.** Internal diffusion is rate-limiting at **low** Thiele modulus. False. A low Thiele modulus means reaction is slow compared with diffusion, so the reaction is the limiting step. Diffusion limits at a **high** Thiele modulus.
- **C.** The effectiveness factor increases as the Thiele modulus decreases. True; $\eta\to1$ when $\phi\to0$. ✓
- **D.** Diffusion limitation is reduced by decreasing the particle size. True, since $\phi\propto R\sqrt{k/D_e}$, so a smaller radius lowers $\phi$. ✓
Answer **A, C and D**.