GATE BT 2025 • Q26
MSQ • 1 Mark
Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
Which of the following compounds have the same degree of reduction per
carbon-mole?
Options:
-
(A) Glucose
-
(B) Lactic acid
-
(C) Acetic acid
-
(D) Formic acid
Official Answer Key:
A;B;C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2025 Q.26)**
**1. Governing Concept**:
- **Topic**: Bioprocess Stoichiometry & Degree of Reductance ($\gamma$)
- The degree of reduction per carbon-mole ($\gamma$) of a compound $\text{C}_c\text{H}_h\text{O}_o\text{N}_n$ is:
$\gamma = \frac{4c + h - 2o - 3n}{c}$
- Evaluating common biochemical carbon sources:
- **Glucose** ($\text{C}_6\text{H}_{12}\text{O}_6 \rightarrow \text{CH}_2\text{O}$): $\gamma = \frac{4(1) + 2 - 2(1)}{1} = 4.0$.
- **Lactic acid** ($\text{C}_3\text{H}_6\text{O}_3 \rightarrow \text{CH}_2\text{O}$): $\gamma = \frac{4(3) + 6 - 2(3)}{3} = \frac{12}{3} = 4.0$.
- **Acetic acid** ($\text{C}_2\text{H}_4\text{O}_2 \rightarrow \text{CH}_2\text{O}$): $\gamma = \frac{4(2) + 4 - 2(2)}{2} = \frac{8}{2} = 4.0$.
- **Ethanol** ($\text{C}_2\text{H}_6\text{O}$): $\gamma = \frac{4(2) + 6 - 2(1)}{2} = \frac{12}{2} = 6.0$.
- **Methane** ($\text{CH}_4$): $\gamma = \frac{4(1) + 4}{1} = 8.0$.
**2. Option Analysis**:
- **Option (A) [Glucose] is CORRECT**: $\gamma = 4.0\text{ e}^-/\text{C-mol}$.
- **Option (B) [Lactic acid] is CORRECT**: $\gamma = 4.0\text{ e}^-/\text{C-mol}$.
- **Option (C) [Acetic acid] is CORRECT**: $\gamma = 4.0\text{ e}^-/\text{C-mol}$.
- **Option (D) [Ethanol] is INCORRECT**: $\gamma = 6.0\text{ e}^-/\text{C-mol}$ (different degree of reduction).
**3. Final Answer**:
- **Correct Options**: **A, B, C**
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