An exothermic reaction, `A rarr B`, has an activation energy of `"15 kcal mol"^(-1)` and the energy of reaction is `"5 kcal mol"^(-1)`. The activation energy in `"kcal mol"^(-1)` for the reaction, `BrarrA` is

Answer

To find the activation energy for the reverse reaction \( B \rightarrow A \), we can use the following relationship:

1. **Understanding the Given Data**:
- Activation energy for the forward reaction \( A \rightarrow B \) (denoted as \( E_a \)) = 15 kcal/mol
- Energy of reaction (enthalpy change, \( \Delta H \)) = -5 kcal/mol (since it is exothermic, the energy of products is lower than that of reactants).

2. **Using the Relationship Between Forward and Reverse Activation Energies**:
The activation energy for the reverse reaction can be calculated using the formula:
\[ E_{a, \text{reverse}} = E_{a, \text{forward}} + \Delta H \]
where:
- \( E_{a, \text{reverse}} \) is the activation energy for the reverse reaction.
- \( E_{a, \text{forward}} \) is the activation energy for the forward reaction.
- \( \Delta H \) is the enthalpy change of the reaction.

3. **Substituting the Values**:
Substitute the known values into the equation:
\[ E_{a, \text{reverse}} = 15 \text{ kcal/mol} + (-5 \text{ kcal/mol}) \]
This simplifies to:
\[ E_{a, \text{reverse}} = 15 \text{ kcal/mol} - 5 \text{ kcal/mol} = 10 \text{ kcal/mol} \]

4. **Final Answer**:
Therefore, the activation energy for the reverse reaction \( B \rightarrow A \) is:
\[ \boxed{10 \text{ kcal/mol}} \]