Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
An enzyme catalyzes the conversion of substrate A into product B. The rate
equation for this reaction is
5
A
A
A
C
r
C
mol L-1 min-1
Substrate A at an initial concentration of 10 mol L-1 enters an ideal mixed flow
reactor (MFR) at a flow rate of 10 L min-1. The volume of the MFR required for
50% conversion of substrate to product is ___________ L.
Official Answer Key:
100 to 100
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2022 Q.59)**
**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: *"An enzyme catalyzes the conversion of substrate A into product B. The rate
equation for this reaction is
5
A
A
A
C
r
C
mol L-1 min-1
Substrate A at an initial concentration of 10 mol L-1 enters an ideal mixed f..."*
- 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 $V_{max}$.
$k_{cat} = \frac{V_{max}}{[E]_0}, \quad \text{Catalytic Efficiency} = \frac{k_{cat}}{K_m}$
- **Calculated Quantitative Value**: **100 to 100**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **100 to 100**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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