For a reversible reaction, `A + B ? C + D , Delta H = – A` kcal. If energy of activation for the forward reaction is B kcal, the energy of activation for backward reaction in kcal is :

Options

A. `-A+B`
B. `A+B`
C. `A-B`
D. `-A-B`

Answer

To solve the problem, we need to understand the relationship between the activation energies of the forward and backward reactions in a reversible reaction, along with the enthalpy change (ΔH) of the reaction.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The reaction is \( A + B \rightleftharpoons C + D \).
- The enthalpy change (ΔH) for the reaction is given as \( -A \) kcal, indicating that the reaction is exothermic.
- The activation energy for the forward reaction is \( B \) kcal.

2. **Understand the Concept of Activation Energy:**
- The activation energy (Ea) for the forward reaction is the energy required to convert reactants (A and B) into products (C and D).
- The activation energy for the backward reaction (Ea, backward) is the energy required to convert products (C and D) back into reactants (A and B).

3. **Use the Relationship Between Activation Energies:**
- For a reversible reaction, the relationship between the activation energies and the enthalpy change can be expressed as:
\[ E_a (\text{backward}) = E_a (\text{forward}) + |\Delta H| \]
- Here, \( |\Delta H| \) is the magnitude of the enthalpy change. Since ΔH is given as \( -A \) kcal, we have:
\[ |\Delta H| = A \]

4. **Substitute the Values:**
- Now, substituting the known values into the equation:
\[ E_a (\text{backward}) = B + A \]

5. **Final Answer:**
- Therefore, the energy of activation for the backward reaction is:
\[ \text{Energy of activation for backward reaction} = A + B \text{ kcal} \]

### Summary:
The energy of activation for the backward reaction is \( A + B \) kcal.

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