In a chemostat, the feed flow rate and culture volume are 100 ml/h and 1.0 L, respectively.
With glucose as substrate, the values of µmax and Ks are 0.2 h-1 and 1 g/L, respectively. For a
glucose concentration of 10 g/L in the feed, the effluent substrate concentration (in g/L)
is _________
Official Answer Key:
1 to
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.57)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (12 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"In a chemostat, the feed flow rate and culture volume are 100 ml/h and 1.0 L, respectively.
With glucose as substrate, the values of µmax and Ks are 0.2 h-1 and 1 g/L, respectively. For a
glucose concentration of 10 g/L..."*
- 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**: **1 to**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **1 to**
- **Scoring Criteria**: 12 Marks (Negative marking: -0.0 marks).
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