Question

Which of the following statements are CORRECT for an enzyme entrapped in a spherical particle?

• A. Effectiveness factor is ratio of the reaction rate with diffusion-limitation to the reaction rate without diffusion-limitation
• B. Internal diffusion is rate-limiting at low values of Thiele modulus
• C. Effectiveness factor increases with decrease in Thiele modulus
• D. Internal diffusion-limitation can be reduced by decreasing the size of the particle

Hint:

Lower Thiele modulus always means higher effectiveness factor and lower diffusion resistance.

Answer 1

The Correct Option is A, C, D

For immobilized enzymes, substrate must diffuse into the particle before reaching the enzyme. This creates internal diffusion resistance, quantified using the effectiveness factor \( \eta \).
1. Effectiveness factor definition:
\[ \eta = \frac{\text{Rate with diffusion limitation}}{\text{Rate without diffusion limitation}} \] Thus statement (A) is correct.
2. Role of Thiele modulus:
The Thiele modulus \( \phi \) measures reaction rate vs. internal diffusion rate.
Low \( \phi \Rightarrow \) fast diffusion → reaction-controlled → diffusion not limiting.
Thus statement (B) is incorrect.
As \( \phi \) decreases, diffusion limitation decreases, increasing the effectiveness factor \( \eta \). So statement (C) is correct.
3. Effect of particle size:
\[ \phi \propto R \] Smaller particle radius \( R \Rightarrow \) smaller \( \phi \Rightarrow \) reduced diffusion limitation. Hence statement (D) is correct.