To determine the activation energy for the reverse reaction of a chemical reaction \( A \rightarrow B \) given that the activation energy for the forward reaction is \( E_a \), we need to analyze the relationship between the forward and reverse reactions.
### Step-by-Step Solution:
1. **Understanding Activation Energy**:
- Activation energy (\( E_a \)) is the minimum energy required for a reaction to occur. For the forward reaction \( A \rightarrow B \), this is given as \( E_a \).
2. **Identifying the Nature of the Reaction**:
- The nature of the reaction (exothermic or endothermic) affects the activation energy of the reverse reaction.
- If the reaction is exothermic, the products (\( B \)) have lower energy than the reactants (\( A \)). Conversely, if the reaction is endothermic, the products have higher energy than the reactants.
3. **Graphical Representation**:
- For an exothermic reaction, the energy diagram shows that the energy of products is lower than that of reactants. The activation energy for the reverse reaction (\( E_{a, \text{reverse}} \)) will be the energy difference between the products and the transition state.
- For an endothermic reaction, the energy of products is higher than that of reactants, and the activation energy for the reverse reaction will be greater than that of the forward reaction.
4. **Mathematical Relationship**:
- The relationship between the activation energies can be expressed as:
\[
E_{a, \text{reverse}} = E_{a, \text{forward}} + \Delta H
\]
- Where \( \Delta H \) is the enthalpy change of the reaction. If the reaction is exothermic, \( \Delta H \) is negative, and if it is endothermic, \( \Delta H \) is positive.
5. **Conclusion**:
- Therefore, the activation energy for the reverse reaction can be less than, equal to, or greater than \( E_a \) depending on whether the reaction is exothermic or endothermic.
- Thus, the activation energy of the reverse reaction can be expressed as:
\[
E_{a, \text{reverse}} = E_a + \Delta H
\]
- This means that the activation energy of the reverse reaction can be less than, equal to, or greater than \( E_a \).
### Final Answer:
The activation energy for the reverse reaction can be less than, equal to, or greater than \( E_a \).
