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 backward reaction \( B \rightarrow A \), we can use the relationship between the activation energies of the forward and backward reactions and the enthalpy change (\( \Delta H \)) of the reaction.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Activation energy for the forward reaction \( (E_a) \) from \( A \) to \( B \): \( E_a = 15 \, \text{kcal mol}^{-1} \)
- Enthalpy change \( (\Delta H) \) for the exothermic reaction \( A \rightarrow B \): \( \Delta H = -5 \, \text{kcal mol}^{-1} \) (negative because the reaction is exothermic)

2. **Use the Relationship Between Activation Energies:**
The relationship between the activation energies for the forward and backward reactions is given by:
\[ E_a (\text{forward}) = E_a (\text{backward}) + \Delta H \]

3. **Substitute the Known Values:**
Rearranging the equation to solve for the activation energy of the backward reaction:
\[ E_a (\text{backward}) = E_a (\text{forward}) - \Delta H \]
Substituting the values:
\[ E_a (\text{backward}) = 15 \, \text{kcal mol}^{-1} - (-5 \, \text{kcal mol}^{-1}) \]

4. **Calculate the Activation Energy for the Backward Reaction:**
\[ E_a (\text{backward}) = 15 \, \text{kcal mol}^{-1} + 5 \, \text{kcal mol}^{-1} = 20 \, \text{kcal mol}^{-1} \]

5. **Final Answer:**
The activation energy for the reaction \( B \rightarrow A \) is \( 20 \, \text{kcal mol}^{-1} \).