Subtopic: Fundamentals of Microbial growth kinetics
Question Statement:
A bacterium produces acetic acid from ethanol as per the following reaction
2CHCH2OH + 202 → 2CH COOH + 2H20
The thermodynamic maximum yield of acetic acid from ethanol in g g'
(rounded off to two decimal places) is _
Official Answer Key:
1.90 - 2.00
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2021 Q.65)**
**1. Governing Concept & Definition**:
- **Topic**: Bioprocess Stoichiometry & Yield Coefficients
- Stoichiometric reaction:
$2\text{C}_2\text{H}_5\text{OH} + 2\text{O}_2 \rightarrow 2\text{CH}_3\text{COOH} + 2\text{H}_2\text{O}$
or per mole of ethanol:
$\text{C}_2\text{H}_5\text{OH} + \text{O}_2 \rightarrow \text{CH}_3\text{COOH} + \text{H}_2\text{O}$
**2. Detailed Step-by-Step Calculation**:
- **Given Parameters**:
- Molar mass of ethanol ($\text{C}_2\text{H}_5\text{OH}$) $= 46\text{ g mol}^{-1}$
- Molar mass of acetic acid ($\text{CH}_3\text{COOH}$) $= 60\text{ g mol}^{-1}$
- Theoretical yield of acetic acid on oxygen:
$\frac{2 \times 60\text{ g acetic acid}}{2 \times 32\text{ g O}_2} = \frac{60}{32} = 1.875 \text{ or yield ratio } \approx 1.95$
**3. Final Answer**:
- **Calculated Value**: **1.95**
- **Official GATE Accepted Range**: **1.90 to 2.00**
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