The standard enthalpy of combustion at `25^(@)C` of hydrogen, cyclohexene `(C_(6)H_(10))`, and cyclohexane `(C_(6)H_(12))` are `-241,-3800`, and `-3920 kJ mol^(-1)` repectively. Calculate the heat of hydrogenation of cyclohexene.

Explanation

The required recation is
`underset("Cyclohexene")(C_(6)H_(10)) +H_(2) rarr underset("Clcohexene")(C_(6)H_(12)), DeltaH_(1) = `? ..(i)
Let us write the gives facts
`H_(2) +(1)/(2)O_(2) rarr 7CO_(2) +5H_(2)O, DeltaH_(2) =- 241 kJ mol^(1)` …(ii)
`C_(6)H_(10) +(17)/(2)O_(2) rarr 6CO_(2) +5H_(2)O, DeltaH_(3) =- 3800 kJ mol^(-1)` ...(iii)
`C_(6)H_(12) +9O_(2) rarr 6CO_(2) +6H_(2)O, DeltaH_(4) =- 3920 kJ mol^(-1) ..(iv)`
The required reaction (i) can be obtained by adding reactions (ii) and (iii) and subtracting reaction (iv) from the sum of reactions (ii) and (iii),
`C_(6)H_(10) +H_(2) rarr C_(6)H_(12)`,
`DeltaH_(1) = (DeltaH_(2) + DeltaH_(3)) - DeltaH_(4)`
`=[-241 + (-3800) - (-3920)`
`=(-241 - 3800) - (3920)`
`=- 4041 + 3920 =- 121 kJ mol^(-1)`