What is the activation energy for the reverse of this reaction?
`N_2O_(4(g)) to 2NO_(2(g))`
Data for the given reaction is `Delta`H = 54 KJ/mol and `epsilon_a`=57.2 KJ.

Options

A. `-54` KJ
B. 3.2 KJ
C. 60.2 KJ
D. 111.2 KJ

Answer

To find the activation energy for the reverse reaction \( N_2O_4(g) \rightarrow 2NO_2(g) \), we can use the relationship between the activation energies of the forward and reverse reactions and the enthalpy change of the reaction.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Activation energy for the forward reaction (\( E_f \)) = 57.2 kJ/mol
- Enthalpy change (\( \Delta H \)) = 54 kJ/mol

2. **Understand the Relationship:**
The relationship between the activation energies of the forward and reverse reactions and the enthalpy change is given by:
\[ E_f - E_b = \Delta H \]
where:
- \( E_f \) = activation energy of the forward reaction
- \( E_b \) = activation energy of the reverse reaction
- \( \Delta H \) = enthalpy change of the reaction

3. **Rearranging the Equation:**
We need to find the activation energy for the reverse reaction (\( E_b \)). Rearranging the equation gives:
\[ E_b = E_f - \Delta H \]

4. **Substituting the Values:**
Now, substitute the known values into the equation:
\[ E_b = 57.2 \, \text{kJ/mol} - 54 \, \text{kJ/mol} \]

5. **Calculating \( E_b \):**
Perform the calculation:
\[ E_b = 57.2 - 54 = 3.2 \, \text{kJ/mol} \]

6. **Final Answer:**
Therefore, the activation energy for the reverse reaction \( N_2O_4(g) \rightarrow 2NO_2(g) \) is:
\[ \boxed{3.2 \, \text{kJ/mol}} \]