GATE BT 2025 • Q58 NAT • 2 Marks

Section 4: Bioprocess Engineering and Process Biotechnology

Bioreactor types, scale-up

Subtopic: Fundamentals of Bioreactor types, scale-up

Question Statement:

In a fermentation process, each mole of glucose is converted to biomass (CH1.8O0.5N0.2), with a biomass yield coefficient of 0.4 C-mol/C-mol, according to the unbalanced equation given below. C6H12O6 + NH3 + O2 → CH1.8O0.5N0.2 + CO2 + H2O The moles of oxygen consumption per mole of glucose consumed during fermentation is _________. (Round off to two decimal places)

Official Answer Key:

3.30 to 3.60

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2025 Q.58)** **1. Governing Concept & Definition**: - **Topic**: Bioprocess Stoichiometry & Macroscopic Elemental Balances - **Reaction Equation**: $\text{C}_6\text{H}_{12}\text{O}_6 + a\text{NH}_3 + b\text{O}_2 \rightarrow c\text{CH}_{1.8}\text{O}_{0.5}\text{N}_{0.2} + d\text{CO}_2 + e\text{H}_2\text{O}$ - **Carbon Basis**: 1 mole of glucose contains 6 C-moles. - **Biomass Yield**: $Y_{X/S} = 0.4\text{ C-mol biomass / C-mol glucose}$. **2. Detailed Step-by-Step Calculation**: - **Step 1: Calculate carbon moles of biomass formed per mole of glucose**: $c = 6 \times 0.4 = 2.4\text{ C-moles of biomass}$ - **Step 2: Carbon Balance**: $\text{Input C} = \text{Output C}$ $6 = c + d = 2.4 + d \implies d = 6 - 2.4 = 3.6\text{ moles of CO}_2$ - **Step 3: Nitrogen Balance**: $a = 0.2 \times c = 0.2 \times 2.4 = 0.48\text{ moles of NH}_3$ - **Step 4: Hydrogen Balance**: $\text{Input H} = 12 + 3a = 12 + 3(0.48) = 12 + 1.44 = 13.44$ $\text{Output H} = 1.8c + 2e = 1.8(2.4) + 2e = 4.32 + 2e$ $2e = 13.44 - 4.32 = 9.12 \implies e = 4.56\text{ moles of H}_2\text{O}$ - **Step 5: Oxygen Balance**: $\text{Input O} = 6 + 2b$ $\text{Output O} = 0.5c + 2d + e = 0.5(2.4) + 2(3.6) + 4.56 = 1.2 + 7.2 + 4.56 = 12.96$ $6 + 2b = 12.96 \implies 2b = 12.96 - 6 = 6.96 \implies b = \frac{6.96}{2} = 3.48\text{ moles of O}_2$ **3. Final Answer**: - **Calculated Value**: **3.48 moles of O₂** - **Official GATE Accepted Range**: **3.30 to 3.60**

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