Heat of hydrogenation of cyclohexene to cyclohexane is -28.6 kcal/mol.The observed heat of hydrogenation of benzene to cyclohexane is -49.8 kcal/mol. Calculate the resonance energy of benzene in kcal/mole.

Explanation

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

### Step 1: Understand the Heat of Hydrogenation
The heat of hydrogenation is the amount of energy released when hydrogen is added to an unsaturated compound. For cyclohexene, the heat of hydrogenation to cyclohexane is given as -28.6 kcal/mol. This means that when cyclohexene is converted to cyclohexane, 28.6 kcal of energy is released.

### Step 2: Calculate the Expected Heat of Hydrogenation for Benzene
Benzene can be thought of as having three double bonds (or pi bonds). If we were to treat benzene as three separate cyclohexene-like structures, the expected heat of hydrogenation for benzene (if it had no resonance stabilization) would be three times the heat of hydrogenation of cyclohexene:

\[ \text{Expected heat of hydrogenation for benzene} = 3 \times (-28.6 \text{ kcal/mol}) = -85.8 \text{ kcal/mol} \]

### Step 3: Compare with the Observed Heat of Hydrogenation
The observed heat of hydrogenation of benzene to cyclohexane is given as -49.8 kcal/mol. This value is less negative than the expected value, indicating that benzene is more stable than expected due to resonance.

### Step 4: Calculate the Resonance Energy
The resonance energy can be calculated as the difference between the expected heat of hydrogenation and the observed heat of hydrogenation:

\[ \text{Resonance Energy} = \text{Expected heat of hydrogenation} - \text{Observed heat of hydrogenation} \]

Substituting the values we have:

\[ \text{Resonance Energy} = (-85.8 \text{ kcal/mol}) - (-49.8 \text{ kcal/mol}) \]

\[ \text{Resonance Energy} = -85.8 + 49.8 = -36.0 \text{ kcal/mol} \]

### Conclusion
The resonance energy of benzene is 36.0 kcal/mol.

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