For a reaction `A to B , Delta H_R=-10 kJ mol^-1 and E_a=50kJmol^-1` then `E_a` for the backward reaction `B to A` will be :

Options

A. `40 kJ mol^-1`
B. `50 kJ mol^-1`
C. `-50 kJ mol^-1`
D. `60 kJ mol^-1`

Answer

To find the activation energy (E_a) for the backward reaction (B to A) given the activation energy for the forward reaction (A to B) and the enthalpy change (ΔH_R), we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Enthalpy change for the reaction (ΔH_R) = -10 kJ/mol
- Activation energy for the forward reaction (E_a, forward) = 50 kJ/mol

2. **Understand the Relationship**:
- The relationship between the activation energies and the enthalpy change is given by the equation:
\[ \Delta H_R = E_a, \text{forward} - E_a, \text{backward} \]
- Rearranging this equation gives us:
\[ E_a, \text{backward} = E_a, \text{forward} - \Delta H_R \]

3. **Substitute the Known Values**:
- Substitute the values we have into the rearranged equation:
\[ E_a, \text{backward} = 50 \text{ kJ/mol} - (-10 \text{ kJ/mol}) \]

4. **Calculate E_a for the Backward Reaction**:
- Simplifying the equation:
\[ E_a, \text{backward} = 50 \text{ kJ/mol} + 10 \text{ kJ/mol} = 60 \text{ kJ/mol} \]

5. **Conclusion**:
- The activation energy for the backward reaction (B to A) is **60 kJ/mol**.

### Final Answer:
E_a for the backward reaction (B to A) = **60 kJ/mol**.

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