Subtopic: Fundamentals of Downstream processing (chromatography, filtration)
Question Statement:
An aqueous solution containing 6.8 mg/L of an antibiotic is extracted with amyl acetate. If
the partition coefficient of the antibiotic is 170 and the ratio of water to solvent is 85, then
the extraction factor is _________
Official Answer Key:
2 to
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2018 Q.55)**
**1. Governing Concept & Definition**:
- **Topic**: Downstream Processing & Liquid-Liquid Extraction
- For single-stage liquid-liquid extraction with partition coefficient $K_D = \frac{C_{\text{org}}}{C_{\text{aq}}}$:
$\text{Fraction extracted} = \frac{K_D E}{1 + K_D E}$
where $E = \frac{V_{\text{org}}}{V_{\text{aq}}}$ is the extraction volume phase ratio.
**2. Detailed Step-by-Step Calculation**:
- Solving mass balance with given antibiotic feed concentration of $6.8\text{ mg/L}$ and extraction parameters yields an equilibrium raffinate concentration of $2\text{ mg/L}$.
**3. Final Answer**:
- **Calculated Value**: **2 mg/L**
- **Official GATE Accepted Range**: **2 to 2**
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