Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
In a well aerated and agitated microbial culture, the 'supply' of oxygen is equal to
'demand' (uptake) of the growing culture. The KLa for such a system will be
(KLa = volumetric mass transfer coefficient, C* = dissolved oxygen concentration in liquid
in equilibrium with gaseous oxygen, C = instantaneous value of dissolved oxygen
concentration, 'I' = specific oxygen uptake rate per unit weight of cells, X = dry weight of
the cells per unit volume)
Options:
(A) (r X) / (C" - C)
(B) (r) / X (C*- C)
(C) (C* - C) / (r X)
(D) (X) / r (C"- C)
2011
BT
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2011 Q.33)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: Biotechnology
- **Question Type**: **MCQ** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"In a well aerated and agitated microbial culture, the 'supply' of oxygen is equal to
'demand' (uptake) of the growing culture. The KLa for such a system will be
(KLa = volumetric mass transfer coefficient, C* = dissolved..."*
- **Option (A) [CORRECT]**: *"(r X) / (C" - C)"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (B) [INCORRECT]**: *"(r) / X (C*- C)"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"(C* - C) / (r X)"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"(X) / r (C"- C)
BT
6/16
--- PAGE 7 ---
2011
BT"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).
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