The standard free energy change (AG'°) for ATP hydrolysis is -30 kj-mole 1. The in vivo
concentrations of ATP, ADP and Pj in E. coli are 7.90, 1.04 and 7.90 mM, respectively. When E.
coli cells are cultured at 37 °C, the free energy change (AG) for ATP hydrolysis in vivo is
kJ- mole 1.
-48 to -46
Official Answer Key:
-48 to -46
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2015 Q.60)**
**1. Governing Concept & Definition**:
- **Topic**: Bioenergetics & In Vivo Free Energy of ATP Hydrolysis
- Actual cellular $\Delta G$:
$\Delta G = \Delta G^{\circ\prime} + R T \ln\left(\frac{[\text{ADP}][\text{P}_i]}{[\text{ATP}]}\right)$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- $\Delta G^{\circ\prime} = -30.5\text{ kJ/mol}$
- Intracellular mass action ratio $Q = \frac{[\text{ADP}][\text{P}_i]}{[\text{ATP}]} \approx 10^{-3}\text{ M}$
- **In Vivo Free Energy**:
$\Delta G = -30.5 + 8.314 \times 10^{-3} \times 310 \times \ln(10^{-3}) \approx -30.5 - 17.8 \approx -48.3\text{ kJ/mol}$
**3. Final Answer**:
- **Calculated Value**: **-48 kJ/mol**
- **Official GATE Accepted Range**: **-48 to -46**
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