Question

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

• A. decrease in the size of the pellet
• B. increase in the pore diffusivity within the pellet
• C. decrease in the enzyme turnover number
• D. increase in the enzyme concentration within the pellet

Hint:

In mass-transfer limited reactions, increasing pore diffusivity, reducing pellet size, or decreasing enzyme turnover number can improve the effectiveness factor by addressing diffusion limitations.

Answer 1

The Correct Option is A, B, C

Step 1: Understand the effectiveness factor.
The effectiveness factor, η, of an immobilized enzyme is defined as the ratio of the actual rate of the reaction in the immobilized state to the rate of reaction if the enzyme were fully accessible. The effectiveness factor is influenced by both the enzyme concentration and the rate of mass transfer of the substrate to the active sites of the enzyme.

Step 2: Analyze the impact of each option.

• (A) Decrease in the size of the pellet: Reducing the size of the pellet reduces the diffusion distance, which may reduce mass transfer limitations, thus increasing the effectiveness factor.
• (B) Increase in the pore diffusivity within the pellet: Increasing the pore diffusivity enhances the mass transfer of substrates into the enzyme's active sites. This reduces the impact of mass transfer limitations, thereby increasing the effectiveness factor.
• (C) Decrease in the enzyme turnover number: The enzyme turnover number affects the catalytic efficiency of the enzyme. A lower turnover number can decrease the rate of reaction, but this can increase the effectiveness factor as it reduces the mismatch between the enzyme's catalytic rate and the mass transfer limitations.
• (D) Increase in the enzyme concentration within the pellet: Increasing enzyme concentration could increase the reaction rate but would not necessarily reduce the mass transfer limitations and may not directly improve the effectiveness factor.

Step 3: Conclusion.
The correct answers are: A, B, C, as all three factors can increase the effectiveness factor by reducing the mass transfer limitations.

Final Answer:
The correct answer is (A), (B), (C).