Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
A microorganism is grown in a batch culture using glucose as a carbon source.
The apparent growth yield is 0.5
ୠ୧୭୫ୟୱୱ
ୱ୳ୠୱ୲୰ୟ୲ୣ. The initial concentrations of biomass
and substrate are 2 g L-1 and 200 g L-1, respectively. Assuming that there is no
endogenous metabolism, the maximum biomass concentration that can be
achieved is _________________ g L-1.
Official Answer Key:
102 to 102
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2022 Q.28)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (1 Mark)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"A microorganism is grown in a batch culture using glucose as a carbon source.
The apparent growth yield is 0.5
ୠ୧୭୫ୟୱୱ
ୱ୳ୠୱ୲୰ୟ୲ୣ. The initial concentrations of biomass
and substrate are 2 g L-1 and 200 g L-1, res..."*
- Identifying governing bioprocess / mathematical relation:
- In a continuous stirred tank bioreactor (chemostat) at steady state:
$\mu = D = \frac{F}{V}$
where $\mu$ is the specific growth rate ($ ext{h}^{-1}$), $D$ is the dilution rate, $F$ is volumetric feed flow rate, and $V$ is working volume.
$S = \frac{K_s D}{\mu_{max} - D}, \quad X = Y_{X/S}(S_0 - S)$
- **Calculated Quantitative Value**: **102 to 102**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **102 to 102**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.0 marks).
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