The reaction `X to Y` is an exothermic reaction. Activation energy of the reaction for X into Y is 150 kJ `mol^(-1)`. Enthalpy of reaction is 135 kJ `"mol"^(-1)`. Calculate the activation energy for the reverse reaction, `Y to X` in `kJ mol^(-1)`.

Explanation

To calculate the activation energy for the reverse reaction (Y to X) given the activation energy for the forward reaction (X to Y) and the enthalpy change of the reaction, we can use the following relationship:

1. **Identify the given values:**
- Activation energy for the forward reaction (X to Y), \( E_a (forward) = 150 \, \text{kJ/mol} \)
- Enthalpy change of the reaction, \( \Delta H = -135 \, \text{kJ/mol} \) (negative because it is exothermic).

2. **Understand the relationship:**
The activation energy for the reverse reaction (Y to X) can be calculated using the formula:
\[ E_a (reverse) = E_a (forward) + |\Delta H| \]
Here, \( |\Delta H| \) is the absolute value of the enthalpy change since we are interested in the energy required to go from Y to X.

3. **Substitute the values:**
\[ E_a (reverse) = 150 \, \text{kJ/mol} + 135 \, \text{kJ/mol} \]

4. **Perform the calculation:**
\[ E_a (reverse) = 150 + 135 = 285 \, \text{kJ/mol} \]

5. **Final answer:**
The activation energy for the reverse reaction (Y to X) is \( 285 \, \text{kJ/mol} \).