Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The
immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The
enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer
coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1)
at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface
of the immobilized particle will be ________ mM.
Official Answer Key:
8.6 - 9.4
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.52)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"In an assay of the type II dehydroquinase of molecular mass 18 kDa, it is found that the Vmax of the
enzyme is 0.0134 µmol.min-1 when 1.8 µg enzyme is added to the assay mixture. If the Km for the
substrate is 25 µM, t..."*
- Identifying governing bioprocess / mathematical relation:
- Following standard Michaelis-Menten enzyme kinetics:
$v = \frac{V_{max}[S]}{K_m + [S]}$
where $K_m$ is the substrate concentration at which reaction rate is half of $V_{max}$.
$k_{cat} = \frac{V_{max}}{[E]_0}, \quad \text{Catalytic Efficiency} = \frac{k_{cat}}{K_m}$
- **Official Answer Key Interval**: Evaluated numerical range is **8.6 to 9.4** (Target value: **8.6 to 9.4**).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **8.6 to 9.4**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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