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The activation energies for forward and ...

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?

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`

Text Solution

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The correct Answer is:
To solve the question regarding the relationship between the activation energies for forward and backward reactions in an exothermic reaction, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Definitions**: - Activation Energy (E_f): The energy required to initiate the forward reaction. - Activation Energy (E_b): The energy required to initiate the backward reaction. - Exothermic Reaction: A reaction that releases energy, resulting in products that have lower energy than the reactants. 2. **Visualize the Energy Profile**: - Draw a potential energy diagram for an exothermic reaction. The y-axis represents potential energy, and the x-axis represents the reaction coordinate. - Mark the energy levels of reactants and products. The reactants will be at a higher energy level than the products. 3. **Identify the Transition State**: - The peak of the energy profile represents the transition state, which is the highest energy point along the reaction pathway. 4. **Calculate the Activation Energies**: - The activation energy for the forward reaction (E_f) is the energy difference between the reactants and the transition state. - The activation energy for the backward reaction (E_b) is the energy difference between the products and the transition state. 5. **Establish the Relationship**: - Since the reaction is exothermic, the energy difference (ΔH) between the reactants and products is negative (ΔH = E_products - E_reactants). - The relationship can be expressed as: \[ E_b = E_f + |\Delta H| \] - This indicates that the activation energy for the backward reaction (E_b) is greater than that for the forward reaction (E_f). 6. **Conclusion**: - Therefore, for an exothermic reaction, the relationship between the activation energies is: \[ E_b > E_f \] - This means that the activation energy for the backward reaction is greater than that for the forward reaction. ### Final Answer: In an exothermic reaction, the activation energy for the backward reaction (E_b) is greater than the activation energy for the forward reaction (E_f). Thus, the correct relation is: \[ E_b > E_f \]
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