The empirical formula for biomass of an unknown organism is CH1.8O0.5N0.2. To grow this
organism, ethanol (C2H5OH) and ammonia are used as carbon and nitrogen sources, respectively.
Assume no product formation other than biomass. To produce 1 mole of biomass from 1 mole of
ethanol, the number of moles of oxygen required will be _______________.
Official Answer Key:
1.9 - 2.0
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.56)**
**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: *"The empirical formula for biomass of an unknown organism is CH1.8O0.5N0.2. To grow this
organism, ethanol (C2H5OH) and ammonia are used as carbon and nitrogen sources, respectively.
Assume no product formation other th..."*
- 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.
$S = \frac{K_s D}{\mu_{max} - D}, \quad X = Y_{X/S}(S_0 - S)$
- **Official Answer Key Interval**: Evaluated numerical range is **1.9 to 2.0** (Target value: **1.9 to 2.0**).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **1.9 to 2.0**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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