Consider an endothermic reaction `XrarrY` with the activation energies `E_(b)` and `E_(f)` for the backward and forward reaction, respectively. In general

Options

A. `E_(b) lt E_(f)`
B. `E_(b) gt E_(f)`
C. `E_(b) = E_(r)`
D. There is no definite relation between `E_(b) and E_(f)`

Explanation

To solve the problem regarding the activation energies of an endothermic reaction \( X \rightleftharpoons Y \), we need to analyze the relationship between the activation energies for the forward and backward reactions.

### Step-by-Step Solution:

1. **Understanding Activation Energy**:
- The activation energy (\( E_f \)) for the forward reaction \( X \to Y \) is the energy required to convert reactants into products.
- The activation energy (\( E_b \)) for the backward reaction \( Y \to X \) is the energy required to convert products back into reactants.

2. **Endothermic Reaction**:
- In an endothermic reaction, the enthalpy change (\( \Delta H \)) is positive. This means that the energy of the products (Y) is higher than that of the reactants (X).
- Mathematically, this can be represented as:
\[ \Delta H = E_f - E_b > 0 \]
- This indicates that \( E_f > E_b \).

3. **Relating Activation Energies**:
- From the equation \( \Delta H = E_f - E_b \), we can rearrange it to find the relationship between \( E_f \) and \( E_b \):
\[ E_f = E_b + \Delta H \]
- Since \( \Delta H \) is positive for an endothermic reaction, it follows that:
\[ E_f > E_b \]

4. **Conclusion**:
- Therefore, for an endothermic reaction, the activation energy of the forward reaction (\( E_f \)) is greater than the activation energy of the backward reaction (\( E_b \)).
- This leads us to conclude that the correct option is:
\[ E_b < E_f \]

### Final Answer:
The correct relationship is \( E_b < E_f \).

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