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GATE 2025 BT – Question 54

Fundamentals of Biological Engineering · Bioreaction Engineering: Ideal reactors (batch, mixed flow, plug flow), enzyme immobilization, Thiele modulus, effectiveness factor, Damkohler number · 2 marks · Multiple select

An enzyme immobilised in a porous spherical pellet, catalyses a strongly mass-transfer limited first-order reaction. The effectiveness factor for the immobilised enzyme reaction increases with the

  1. decrease in the size of the pellet
  2. increase in the pore diffusivity within the pellet
  3. decrease in the enzyme turnover number
  4. increase in the enzyme concentration within the pellet

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Correct answer: (A) decrease in the size of the pellet; (B) increase in the pore diffusivity within the pellet; (C) decrease in the enzyme turnover number

Explanation

When the reaction is strongly diffusion-limited, $\eta \approx \frac{3}{\phi}$ with the Thiele modulus $\phi = R\sqrt{\frac{k}{D_e}}$. A smaller pellet radius $R$, a larger pore diffusivity $D_e$ and a smaller rate constant $k$ (a lower turnover number) all lower $\phi$ and raise $\eta$. More enzyme raises $k$ and so lowers $\eta$.