`Delta_(f)H^(Theta)` of Cyclohexene `(l)` and benzene at `25^(@)C` is `-156` and `+46 kJmol^(-1)`, respectively. `Delta_("hydrogenation")H^(Theta)` of cyclohexene `(l) at 25^(@)C is -119 kJ mol^(-1)`.
Reasonance energy of benzene is found to be `-38x kJ mol^(-1)`. Find the value of `x`.

Explanation

This shows that the generation of one `(C =C)` bond in cyclohexene requires `119kJ mol^(-1)` of enthalpy. To calculate `RE` resonance energy.

`DeltaH_(1)^(Theta) = DeltaH_(2)^(Theta) = DeltaH_(3)^(Theta) = 119 kJ mol^(-1), DeltaH_(4)^(Theta) = RE`
`DeltaH_(5)^(Theta) = Delta_(f)H^(Theta) ("benzene") - Delta_(f)H^(Theta) ("cyclohexene")`
`= 46 -(-156) = 205 kJ mol^(-1)`.
`:.` From Hess' law:
`DeltaH_(4)^(Theta) = DeltaH_(5)^(Theta) - (DeltaH_(1)^(Theta) +DeltaH_(2)^(Theta) +DeltaH_(3)^(Theta))`
`= 205 - 3 xx 119 =- 152 kJ mol^(-1)`
`:. -38x =- 152`
`x = 4`