An endothermic reaction `AtoB` has an activatio energy 15 kaca/mole and the heat of reaction is 5kcal/mole. The activation energy of the reaction `BtoA` is

Options

A. 20 kcal/mole
B. 15 kcal/mole
C. 10 kcal/mole
D. zero

Answer

To find the activation energy of the backward reaction \( B \to A \), we can use the relationship between the activation energies of the forward and backward reactions along with the heat of reaction.

### Step-by-Step Solution:

1. **Identify Given Data**:
- Activation energy of the forward reaction \( A \to B \) (denoted as \( E_a^{forward} \)) = 15 kcal/mole
- Heat of reaction (endothermic) \( \Delta H \) = +5 kcal/mole

2. **Understand the Relationship**:
For a reaction, the relationship between the activation energies and the heat of reaction is given by:
\[ \Delta H = E_a^{forward} - E_a^{backward} \]
where \( E_a^{backward} \) is the activation energy for the backward reaction \( B \to A \).

3. **Substitute Known Values**:
Substitute the known values into the equation:
\[ 5 \text{ kcal} = 15 \text{ kcal} - E_a^{backward} \]

4. **Rearrange the Equation**:
Rearranging the equation to solve for \( E_a^{backward} \):
\[ E_a^{backward} = 15 \text{ kcal} - 5 \text{ kcal} \]
\[ E_a^{backward} = 10 \text{ kcal} \]

5. **Conclusion**:
The activation energy for the backward reaction \( B \to A \) is 10 kcal/mole.

### Final Answer:
The activation energy of the reaction \( B \to A \) is **10 kcal/mole**.

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