GATE BT 2024 • Q57 NAT • 2 Marks

Section 2: General Biotechnology

Bioenergetics and Metabolism

Subtopic: Thermodynamics & ATP Bioenergetics

Question Statement:

The free energy change of ATP hydrolysis at 25 C is -32.2 kJ mol-1. The free energy change for hydrolysis of α-glycerophosphate to glycerol is -8.2 kJ mol-1 at 25 C. Using the above information, the free energy change for the formation of α-glycerophosphate from glycerol and ATP is ________ kJ mol-1 (Answer in integer).

Official Answer Key:

-24 to -24

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2024 Q.57)** **1. Governing Concept & Definition**: - **Topic**: Bioenergetics & Coupled Phosphorylation Thermodynamics - Standard Gibbs free energy changes ($\Delta G^{\circ\prime}$) are state functions and additive for coupled enzymatic reactions. **2. Detailed Step-by-Step Calculation**: - **Given Reactions**: 1. $ ext{ATP} + ext{H}_2 ext{O} ightarrow ext{ADP} + ext{P}_i \quad (\Delta G_1^{\circ\prime} = -32.2 ext{ kJ/mol})$ 2. $lpha ext{-glycerophosphate} + ext{H}_2 ext{O} ightarrow ext{Glycerol} + ext{P}_i \quad (\Delta G_2^{\circ\prime} = -8.2 ext{ kJ/mol})$ - **Target Reaction**: $ ext{Glycerol} + ext{ATP} ightarrow lpha ext{-glycerophosphate} + ext{ADP}$ - **Coupling Analysis**: - Target = [Reaction 1] - [Reaction 2] $\Delta G^{\circ\prime} = \Delta G_1^{\circ\prime} - \Delta G_2^{\circ\prime}$ $\Delta G^{\circ\prime} = -32.2 - (-8.2) = -32.2 + 8.2 = -24.0 ext{ kJ/mol}$ **3. Final Answer**: - **Calculated Value**: **-24** - **Official GATE Accepted Range**: **-24 to -24**

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