The heat of dissociation of benzene in isolated gaseous atoms is 5335 kJ/mol . The bond enthalpies C-C, C = C and C - H bonds are 347.3, 615 and 416.2 kJ respectively. Magnitude of resonance energy of benzene is

Options

A. `1.15 kJ`
B. `15.1 kJ`
C. `49.1kJ`
D. `151 kJ`

Answer

To find the magnitude of the resonance energy of benzene, we can follow these steps:

### Step 1: Understand the Concept
Resonance energy is the difference between the theoretical energy required to dissociate benzene into isolated gaseous atoms and the actual heat of dissociation of benzene.

### Step 2: Calculate the Theoretical Heat of Dissociation
To calculate the theoretical heat of dissociation of benzene, we need to consider the bonds that need to be broken:

- Benzene has 6 C-H bonds.
- Benzene has 3 C-C bonds.
- Benzene has 3 C=C double bonds.

The formula to calculate the theoretical heat of dissociation (HOD) is:
\[ \text{HOD} = 3 \times (\text{C-C bond enthalpy}) + 3 \times (\text{C=C bond enthalpy}) + 6 \times (\text{C-H bond enthalpy}) \]

### Step 3: Substitute the Given Values
Using the bond enthalpies provided:
- C-C bond enthalpy = 347.3 kJ/mol
- C=C bond enthalpy = 615 kJ/mol
- C-H bond enthalpy = 416.2 kJ/mol

Substituting these values into the formula:
\[ \text{HOD} = 3 \times 347.3 + 3 \times 615 + 6 \times 416.2 \]

### Step 4: Perform the Calculations
Calculating each term:
- \(3 \times 347.3 = 1041.9\) kJ/mol
- \(3 \times 615 = 1845\) kJ/mol
- \(6 \times 416.2 = 2497.2\) kJ/mol

Now, summing these values:
\[ \text{HOD} = 1041.9 + 1845 + 2497.2 = 5384.1 \text{ kJ/mol} \]

### Step 5: Calculate the Resonance Energy
The resonance energy (RE) can now be calculated using the formula:
\[ \text{RE} = \text{Theoretical HOD} - \text{Actual HOD} \]
Where the actual heat of dissociation of benzene is given as 5335 kJ/mol.

Substituting the values:
\[ \text{RE} = 5384.1 - 5335 = 49.1 \text{ kJ/mol} \]

### Conclusion
The magnitude of the resonance energy of benzene is **49.1 kJ/mol**.

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