Calculate the resonance enegry of isoprene `(C_(5)H_(8))` from the data given. Standard Heats of combustion of isoprene, carbon and hydrogen are `-3186, -393.5`, and `-285.83 kJ mol^(-1)`, respectively. Bond energies of `C=C, C-C, C-H` and `H-H` bonds are `615, 348, 413` and `435.8 kJ mol^(-1)` respectively. Standard heat of sulbilmation of graphite is `718.3 kJ mol^(-1)`.

Explanation

Calculate `Delta_(f)H^(ө)` of isoprene from its heat of combustion (This will give the value for the actual isoprene existing in nature).
`5C(s)+4H_(2)(g)rarr C_(5)H_(8)(g) , Delta_(f)H^(ө)=?`
1. `C_(5)H_(8)(g)+7O_(2)(g)rarr 5CO_(2)(g)+4H_(2)O(l) , Delta_(r )H_(1)^(ө)=-3186` kJ/mole
2. `C(s)+O_(2)(g)rarr CO_(2)(g), Delta_(r )H_(2)^(ө)=-393.5` kJ/mole
3. `H_(2)(g)+1//2O_(2)(g)rarr H_(2)O(l), Delta_(r ) H_(3)^(ө)=-285.83` kJ/mole
Now operating `5(2)+4(3)-1` to get equation of heat of formation.
From Hess's Law we have :
`Delta_(f)H^(ө)=5Delta_(r )H_(2)^(ө)+4Delta_(r )H_(3)^(ө)-Delta_(r )H_(1)^(ө)`
`rArr Delta_(f)H^(ө)=5(-393.5)+4(-285.83)-(-3186) rArr (Delta_(f)H^(ө))_("actual")=75.18` kJ/mole
Now calculate heat of formation usin the bond energies and structure of isoprene. `[H_(2)C=underset(CH_(3))underset("|")(C )-HC=CH_(2)]`