The `E_a` for forward reaction is 50 kcal. The `E_a` for its backward reaction is:

Options

A. equal 50 keal
B. greater than 50 keal
C. less than 50
D. less than 50

Answer

To determine the activation energy (\(E_a\)) for the backward reaction given the activation energy for the forward reaction, we can use the relationship between the activation energies and the enthalpy change (\(\Delta H\)) of the reaction.

### Step-by-Step Solution:

1. **Identify Given Information**:
- Activation energy for the forward reaction (\(E_a^{forward}\)) = 50 kcal.

2. **Understand the Relationship**:
- The activation energy for the backward reaction (\(E_a^{backward}\)) can be related to the activation energy for the forward reaction and the enthalpy change of the reaction (\(\Delta H\)).
- The relationship is given by the equation:
\[ E_a^{backward} = E_a^{forward} - \Delta H \]

3. **Determine \(\Delta H\)**:
- The enthalpy change (\(\Delta H\)) for a reaction is defined as:
\[ \Delta H = E_a^{forward} - E_a^{backward} \]
- Rearranging gives us:
\[ E_a^{backward} = E_a^{forward} - \Delta H \]

4. **Assume \(\Delta H\)**:
- Since we do not have a specific value for \(\Delta H\), we can assume that the reaction is exothermic (which is common). In this case, \(\Delta H\) would be a positive value.
- For example, if we assume \(\Delta H\) is 20 kcal, we can substitute this value into the equation.

5. **Calculate \(E_a^{backward}\)**:
- Using the assumed value of \(\Delta H\):
\[ E_a^{backward} = 50 \text{ kcal} - 20 \text{ kcal} = 30 \text{ kcal} \]

6. **Conclusion**:
- The activation energy for the backward reaction is dependent on the value of \(\Delta H\). If \(\Delta H\) is known, you can calculate \(E_a^{backward}\) accordingly. In this example, if \(\Delta H\) is 20 kcal, then \(E_a^{backward} = 30 \text{ kcal}\).

### Final Answer:
- The activation energy for the backward reaction is \(E_a^{backward} = 30 \text{ kcal}\) (assuming \(\Delta H = 20 \text{ kcal}\)).