The activation energies for forward and backward reactions are `E_f and E_b` respectively. If the reaction is exothermic then which is true regarding relation of activation energies?

Options

A. `E_t gt E_b`
B. `E_f lt E_b`
C. `E_F=E_b`
D. There is no direct relation between `E_t and E_b`

Answer

To determine the relationship between the activation energies for the forward and backward reactions in an exothermic reaction, we can follow these steps:

### Step 1: Understand the Definitions
- **Activation Energy (Ea)**: The minimum energy required for a reaction to occur.
- **Exothermic Reaction**: A reaction that releases energy, usually in the form of heat, to the surroundings.

### Step 2: Identify the Activation Energies
- Let \( E_f \) be the activation energy for the forward reaction.
- Let \( E_b \) be the activation energy for the backward (reverse) reaction.

### Step 3: Analyze the Energy Profile
- In an exothermic reaction, the products have lower energy than the reactants. This means that the energy released during the reaction is greater than the energy required to initiate the reaction.

### Step 4: Relate the Activation Energies
- For an exothermic reaction:
- The activation energy for the forward reaction \( E_f \) is less than the activation energy for the backward reaction \( E_b \).
- This is because the forward reaction requires less energy to proceed (as it is moving towards a more stable state), while the backward reaction requires more energy to overcome the energy barrier to revert to the reactants.

### Conclusion
Thus, the relationship can be summarized as:
\[ E_f < E_b \]

### Final Answer
In an exothermic reaction, the activation energy for the forward reaction is less than that for the backward reaction.