If `E_(f)` and `E_(r)` are the activation energies of forward and backward reactions and the reaction is known to be exothermic, then

Options

A. `E_(f) gt E_(r)`
B. `E_(f) lt E_(r)`
C. `E_(f)=E_(r)`
D. No relation can be given between `E_(f)` and `E_(r)`

Answer

To solve the problem, we need to analyze the relationship between the activation energies of the forward and backward reactions in an exothermic reaction. Here’s a step-by-step breakdown:

### Step 1: Understand the Nature of Exothermic Reactions
In an exothermic reaction, the reactants have higher energy than the products. This means that energy is released when the reaction occurs.

### Step 2: Draw the Energy Profile Diagram
To visualize the energy changes during the reaction, we can draw an energy profile diagram. The x-axis represents the reaction progress, while the y-axis represents the energy.

1. Start with the reactants (A) at a higher energy level.
2. As the reaction proceeds to form products (B), the energy decreases, indicating that energy is released.
3. The peak of the curve represents the transition state, which is the highest energy point during the reaction.

### Step 3: Identify Activation Energies
- **Activation Energy of Forward Reaction (E_f)**: This is the energy required to convert reactants (A) to products (B). It is the energy difference between the reactants and the transition state.
- **Activation Energy of Backward Reaction (E_r)**: This is the energy required to convert products (B) back to reactants (A). It is the energy difference between the products and the transition state.

### Step 4: Compare E_f and E_r
From the energy profile diagram:
- The activation energy for the forward reaction (E_f) is the energy difference from A to the peak.
- The activation energy for the backward reaction (E_r) is the energy difference from B to the peak.

Since the reactants are at a higher energy level than the products in an exothermic reaction, the energy difference (E_r) from the products (B) to the peak (transition state) will be greater than the energy difference (E_f) from the reactants (A) to the peak.

### Conclusion
Thus, we can conclude that for an exothermic reaction:
\[ E_r > E_f \]
This means that the activation energy for the reverse reaction (E_r) is greater than that for the forward reaction (E_f).

### Final Answer
The correct option is: **E_f < E_r**