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

Explanation

Given : `C_(6)H_(10)(l)+H_(2)(g)rarr C_(6)H_(12)(l) " " , " " Delta_("Hydrogenation")H^(ө)=-119` kJ/mole
Find the actual heat of hydrogenation of benzene from Hess's law as follows :
1. `6C(s)+6H_(2)(g)rarr C_(6)H_(12)(l) " " , " " Delta_(f)H^(ө)=-156` kJ/mole
2. `6C(s)+3H_(2)(g)rarr C_(6)H_(6)(l)" " , " " Delta_(f)H^(ө)=+49` kJ/mole
`C_(6)H_(6)(l)+3H_(2)(g)rarr C_(6)H_(12)(l)" " , " " Delta_("Hydrogenation")H^(ө)`
`rArr (Delta_("Hydrogenation")H^(ө))_("Actual")=-156-49=-205` kJ/mole
Now, (hypothetical heat of hydrogenation of benzene) `-=` (heat of hydrogenation of cyclo hexatriene)
`-= 3xx` (heat of hydrogenation of cyclohexane)
`= 3xx(-119)=-357` kJ/mole
Here, we have assumed that there are only 3 double bonds in benzene (kekule's structure) and in hydrogenating it, the energy obtained will be roughly 3 times of hydrogenating cyclohexene.

Clearly, heat of hydrogenation for theoretical benzene is more negative and thus, it is less stable. So, Resonance energy should be negative (since actual benzene is more stable).
`rArr` Resonance energy `=-357-(-205)=-152` kJ/mole of benzene