In the reaction `A^(+) + B rarr A+ B^(+)` , there is no entropy change. Enthalpy change, `Delta H ` equals 22 kJ `mol^(-1)` of `A^(+)` . Calculate the `DeltaG` for the reaction . Under what condition free energy change will have negative value ?

Explanation

To solve the problem, we need to calculate the Gibbs free energy change (ΔG) for the reaction given the enthalpy change (ΔH) and the entropy change (ΔS).

### Step-by-Step Solution:

1. **Identify the Given Data:**
- The reaction is: \( A^+ + B \rightarrow A + B^+ \)
- The change in entropy (ΔS) is given as 0 (no entropy change).
- The change in enthalpy (ΔH) is given as 22 kJ/mol.

2. **Use the Gibbs Free Energy Equation:**
The Gibbs free energy change is calculated using the formula:
\[ \Delta G = \Delta H - T \Delta S \]
where:
- \( \Delta G \) is the change in Gibbs free energy,
- \( \Delta H \) is the change in enthalpy,
- \( T \) is the temperature in Kelvin,
- \( \Delta S \) is the change in entropy.

3. **Substitute the Values:**
Since ΔS = 0, the equation simplifies to:
\[ \Delta G = \Delta H - T \cdot 0 \]
\[ \Delta G = \Delta H \]
Now substituting the value of ΔH:
\[ \Delta G = 22 \, \text{kJ/mol} \]

4. **Conclusion:**
Therefore, the Gibbs free energy change (ΔG) for the reaction is:
\[ \Delta G = 22 \, \text{kJ/mol} \]

5. **Condition for Negative ΔG:**
For ΔG to be negative, we need to consider the conditions under which this can happen. Since ΔS = 0, the only way to make ΔG negative is to have ΔH be negative. Thus:
- If ΔH < 0, then ΔG can become negative.

### Summary:
- The calculated ΔG for the reaction is **22 kJ/mol**.
- The free energy change (ΔG) will have a negative value if **ΔH is negative**.