An exothermic reaction `ArarrB` has an activation energy of `17 kJ` per mole of `A`. The heat of the reaction is `40 kJ`. Calculate the activation energy for the reverse reaction `B rarr A`.

Options

A. `60 kJ`
B. `57 kJ`
C. `75 kJ`
D. `90 kJ`

Explanation

To solve the problem, we need to calculate the activation energy for the reverse reaction \( B \rightarrow A \) given the activation energy for the forward reaction \( A \rightarrow B \) and the heat of the reaction.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Activation energy for the forward reaction (\( E_a \) for \( A \rightarrow B \)): \( 17 \, \text{kJ/mol} \)
- Heat of the reaction (\( \Delta H \)): \( -40 \, \text{kJ/mol} \) (since it is exothermic, we take it as negative).

2. **Understand the Relationship**:
The relationship between the activation energies and the heat of the reaction is given by:
\[ \Delta H = E_a (\text{forward}) - E_a (\text{reverse}) \]
Rearranging this gives us the activation energy for the reverse reaction:
\[ E_a (\text{reverse}) = E_a (\text{forward}) - \Delta H \]

3. **Substitute the Values**:
Substitute the known values into the equation:
\[ E_a (\text{reverse}) = 17 \, \text{kJ/mol} - (-40 \, \text{kJ/mol}) \]
This simplifies to:
\[ E_a (\text{reverse}) = 17 \, \text{kJ/mol} + 40 \, \text{kJ/mol} \]

4. **Calculate the Result**:
\[ E_a (\text{reverse}) = 57 \, \text{kJ/mol} \]

5. **Final Answer**:
The activation energy for the reverse reaction \( B \rightarrow A \) is \( 57 \, \text{kJ/mol} \).