Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
Which of the following statements are CORRECT for an enzyme entrapped in a
spherical particle?
Options:
(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
Official Answer Key:
A;C;D
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2022 Q.48)**
**1. Governing Concept**:
- **Topic**: Enzyme Engineering & Immobilized Enzyme Particle Kinetics
- For an enzyme entrapped in a porous spherical particle:
- Substrate must diffuse from the bulk liquid across the stagnant boundary layer (external diffusion) and through particle pores (internal diffusion) to reach catalytic sites.
- Internal mass transfer resistance is characterized by the Thiele modulus ($\Phi = R \sqrt{\frac{k_v}{D_{\text{eff}}}}$).
- Effectiveness factor $\eta$ is defined as the ratio of actual reaction rate to the rate evaluated at bulk surface concentration without mass transfer limitations.
**2. Option Analysis**:
- **Option (A) is CORRECT**: Smaller particle radius reduces internal diffusion limitation and increases the effectiveness factor $\eta$.
- **Option (B) is INCORRECT**: Mass transfer limitations decrease apparent $V_{\max}$ and alter apparent $K_m$, rather than leaving them unaffected.
- **Option (C) is CORRECT**: At high Thiele modulus ($\Phi \gg 1$), the reaction rate is internal diffusion-controlled.
- **Option (D) is CORRECT**: Higher enzyme loading within the bead increases internal diffusion limitation, lowering the effectiveness factor.
**3. Final Answer**:
- **Correct Options**: **A, C, D**
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