GATE BT 2026 • Q34 NAT • 1 Mark

Section 2: General Biotechnology

Bioenergetics and Metabolism

Subtopic: Thermodynamics & ATP Bioenergetics

Question Statement:

Given below is the Gibbs free energy change (ΔG) in kilo Joules per electron equivalent (kJ e-eq-1) at pH 7.0, of organic and inorganic half reactions. Acetate synthesis: 1 8 CO2 + 1 8 HCO3 - + H+ + e- → 1 8 CH3COO- + 3 8 H2O ΔG=27.4 kJ e-eq-1 Reduction reaction: 1 4 O2 + H+ + e- → 1 2 H2O ΔG= -78.72 kJ e-eq-1 The free energy change of acetate oxidation to CO2, H2O and HCO3 - is _______ kJ e-eq-1. (rounded off to two decimal places)

Official Answer Key:

-106.12 to -106.12

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2026 Q.34)** **1. Governing Concept & Definition**: - **Topic**: Bioprocess Thermodynamics & Energetics of Half-Reactions - The overall redox reaction for acetate oxidation coupled to oxygen reduction: $\Delta G_{\text{overall}} = \Delta G_{\text{reduction}} - \Delta G_{\text{synthesis}}$ expressed per electron equivalent ($\text{kJ e-eq}^{-1}$). **2. Detailed Step-by-Step Calculation**: - **Given Half-Reactions**: - Acetate synthesis: $\Delta G = 27.4\text{ kJ e-eq}^{-1}$ (Reversing for acetate oxidation gives $\Delta G_{\text{ox}} = -27.4\text{ kJ e-eq}^{-1}$) - Terminal electron acceptor (oxygen) reduction: $\Delta G_{\text{red}} = -78.72\text{ kJ e-eq}^{-1}$ - **Overall Free Energy Change**: $\Delta G_{\text{net}} = \Delta G_{\text{ox}} + \Delta G_{\text{red}} = -27.4 + (-78.72) = -106.12\text{ kJ e-eq}^{-1}$ **3. Final Answer**: - **Calculated Value**: **-106.12 kJ e-eq⁻¹** - **Official GATE Accepted Range**: **-106.12 to -106.12**

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