The activation energy for the forward reaction `X rarr Y` is `60 kJ mol^(-1)` and `Delta H` is `-20 kJ mol^(-1)`. The activation energy for the reverse reaction is

Options

A. `40 kJ mol^(-1)`
B. `60 kJ mol^(-1)`
C. `80 kJ mol^(-1)`
D. `20 kJ mol^(-1)`

Explanation

To find the activation energy for the reverse reaction given the activation energy for the forward reaction and the enthalpy change (ΔH), we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Activation energy for the forward reaction (Ea_forward) = 60 kJ/mol
- Enthalpy change (ΔH) = -20 kJ/mol

2. **Understand the Relationship**:
- For an exothermic reaction, the relationship between the activation energies of the forward and reverse reactions is given by:
\[ Ea_{reverse} = Ea_{forward} - \Delta H \]
- Since ΔH is negative for exothermic reactions, we can rewrite this as:
\[ Ea_{reverse} = Ea_{forward} + |ΔH| \]
- Here, |ΔH| is the absolute value of ΔH.

3. **Calculate the Absolute Value of ΔH**:
- Since ΔH = -20 kJ/mol, the absolute value is:
\[ |ΔH| = 20 \text{ kJ/mol} \]

4. **Substitute the Values into the Formula**:
- Now, substituting the known values into the equation:
\[ Ea_{reverse} = 60 \text{ kJ/mol} + 20 \text{ kJ/mol} \]

5. **Perform the Calculation**:
- Adding the two values:
\[ Ea_{reverse} = 80 \text{ kJ/mol} \]

6. **Conclusion**:
- The activation energy for the reverse reaction is **80 kJ/mol**.

### Final Answer:
The activation energy for the reverse reaction is **80 kJ/mol**.

---