The hydrolysis of Adenosine triphosphate [ATP] to give adenosine diphosphate [ADP] is represented by ATP harr ADP. This reaction is exothermic zero[K] . The entropy change for the reaction is `982` J/K at `310` K . The free energy for the reaction is:

Options

A. `31.01` KJ
B. `9.188`KJ
C. `-9.188` KJ
D. `31.012`KJ

Answer

To find the Gibbs free energy change (ΔG) for the hydrolysis of ATP to ADP, we can use the Gibbs free energy equation:

\[ \Delta G = \Delta H - T \Delta S \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Enthalpy change (ΔH) = 0 J (since the reaction is exothermic at 0 K)
- Entropy change (ΔS) = 982 J/K
- Temperature (T) = 310 K

2. **Substitute the values into the Gibbs free energy equation**:
\[ \Delta G = 0 - (310 \, \text{K}) \times (982 \, \text{J/K}) \]

3. **Calculate the product of T and ΔS**:
\[ T \Delta S = 310 \times 982 = 304420 \, \text{J} \]

4. **Substitute this value back into the equation for ΔG**:
\[ \Delta G = 0 - 304420 \, \text{J} = -304420 \, \text{J} \]

5. **Convert ΔG from joules to kilojoules**:
\[ \Delta G = -304.42 \, \text{kJ} \]

6. **Round to appropriate significant figures**:
\[ \Delta G \approx -31.02 \, \text{kJ} \]

### Final Answer:
\[ \Delta G \approx -31.02 \, \text{kJ} \]