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.

Explanation

Given:
`C_(6)H_(10)(l)+H_(2)(g) rarr C_(6)H_(12)(l), Delta_("Hydrogenation") H^(Theta) =- 119 kJ mol^(-1)`
Find te 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^(Theta) =- 156 kJ mol^(-1)`
2. `6C(s) +3H_(2)(g) rarr C_(6)H_(6) (l),Delta_(f)H^(Theta) =+49 kJ mol^(-1)`
`C_(6)H_(6)(l) (g) rarr C_(6)H_(12)(l),Delta_("Hydrogenation") H^(Theta)`
`rArr (Delta_("Hydrogenation")H^(Theta))_("Actual") =- 156 -49 =- 205 kJ mol^(-1)`
Note: `Delta_("Hydrogenation")H^(Theta)` is always negative.
Now,
`{:(("Hypothetical heat of"),("hydrogenation of benzene")):}-={:(("Heat of hydrogenation"),("of cyclo hexatriene")):} -=3xx{:(("Heat of hydrogenation"),("of cyclohexane")):}`
`=3 xx (-199) =- 357 kJ mol^(-1)`
Here, we have assumed that there are only `3` double bonds in benzene (kekule's structue) and in hydrogenating it, the enegry obtained will be roughly `3` times of hydrogenating cyclohexene.

Clerly, heat of hydrogenation for theoretical benzene is more negative and thus, it is less stable. So, resonance energy should be negative (since actural benzene is more stable).
`rArr` Resonance enegry `= - 357 -(-205)`
`=- 152 kJ mol^(-1)` of benzene