Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
Solvents A and B are completely immiscible. Solute S is soluble in both these solvents. 100 g of S was added to a container which has 2 kg each of A and B. The solute is 1.5 times more soluble in solvent A than in solvent B. The mixture was agitated thoroughly and allowed to reach equilibrium. Assuming that the solute has completely dissolved, the amount of solute in solvent A phase is ________ g.
Official Answer Key:
60 to 60
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2020 Q.30)**
**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: *"Solvents A and B are completely immiscible. Solute S is soluble in both these solvents. 100 g of S was added to a container which has 2 kg each of A and B. The solute is 1.5 times more soluble in solvent A than in solven..."*
- Identifying governing bioprocess / mathematical relation:
- Evaluating volumetric mass transfer rate for oxygen in aerobic fermentation:
$\text{OTR} = k_L a (C^* - C_L)$
where $k_L a$ is volumetric mass transfer coefficient, $C^*$ is equilibrium saturation dissolved oxygen concentration, and $C_L$ is actual bulk liquid concentration.
- **Calculated Quantitative Value**: **60 to 60**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **60 to 60**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.0 marks).
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