The standard molar enthalpies of formation of cyclohexane (l) and benzene (l) at `25^@C` are - 156 and +49 KJ `mol^(-1)` respectively. The standard enthalpy of hydrogenation of cyclo hexene (l) at `25^@C " is" -116 "KJ mol" ^(-1)` . Use these data to estimate the magnitude of the resonance energy of benzene.

Options

A. `-143"KJ mol"^(-1)`
B. `1.52"kJ mol"^(-1)`
C. `15.2 "kJ mol"^(-1)`
D. None of these

Answer

To estimate the magnitude of the resonance energy of benzene using the provided data, we can follow these steps:

### Step 1: Write the formation reactions and their enthalpy changes

1. **Formation of Cyclohexane**:
\[ 6C + 3H_2 \rightarrow C_6H_{12} \quad \Delta H_f = -156 \, \text{kJ/mol} \]

2. **Formation of Benzene**:
\[ 6C + 3H_2 \rightarrow C_6H_6 \quad \Delta H_f = +49 \, \text{kJ/mol} \]

3. **Hydrogenation of Cyclohexene**:
\[ C_6H_{10} + H_2 \rightarrow C_6H_{12} \quad \Delta H = -116 \, \text{kJ/mol} \]

### Step 2: Calculate the enthalpy change for the hydrogenation of benzene

To find the enthalpy change for the hydrogenation of benzene, we need to consider that benzene has three double bonds. The enthalpy change for the hydrogenation of benzene can be calculated as follows:

\[ \Delta H_{\text{hydrogenation of benzene}} = 3 \times \Delta H_{\text{hydrogenation of cyclohexene}} \]

Substituting the value:
\[ \Delta H_{\text{hydrogenation of benzene}} = 3 \times (-116 \, \text{kJ/mol}) = -348 \, \text{kJ/mol} \]

### Step 3: Calculate the resonance energy of benzene

The resonance energy can be calculated using the difference between the calculated enthalpy of hydrogenation and the observed enthalpy of hydrogenation for benzene:

\[ \text{Resonance Energy} = \Delta H_{\text{calculated}} - \Delta H_{\text{observed}} \]

Where:
- \(\Delta H_{\text{observed}} = -205 \, \text{kJ/mol}\) (given)
- \(\Delta H_{\text{calculated}} = -348 \, \text{kJ/mol}\)

Substituting the values:
\[ \text{Resonance Energy} = (-205) - (-348) = -205 + 348 = 143 \, \text{kJ/mol} \]

### Step 4: Conclusion

Thus, the magnitude of the resonance energy of benzene is:
\[ \text{Resonance Energy} = 143 \, \text{kJ/mol} \]