The enthalpy of combustion of cyclohexane cyclohexene and ${\mathrm{H}}_2$ are respectively $-3920$, $-3800$ and $-241\mathrm{KJ}{\mathrm{mol}}^{-1}$. The heat of hydrogenation of cyclohexene in $\mathrm{KJ}{\mathrm{mol}}^{-1}$ is

The equations formed by the given data:

$\begin{array}{l}{\mathrm{H}}_2+\frac{1}{2}{\mathrm{O}}_2\to {\mathrm{H}}_2\mathrm{O} -241 \mathrm{k}\mathrm{J}{ \mathrm{m}\mathrm{o}\mathrm{l}}^{-1}\dots \dots \dots ..\left(1\right)\\ {\mathrm{C}}_6{\mathrm{H}}_{10}+\frac{15}{2}{\mathrm{O}}_2\to 6{\mathrm{CO}}_2+5{\mathrm{H}}_2\mathrm{O} -3800 \mathrm{k}\mathrm{J}{ \mathrm{m}\mathrm{o}\mathrm{l}}^{-1}\dots \dots \dots \left(2\right)\\ {\mathrm{C}}_6{\mathrm{H}}_{12}+9{\mathrm{O}}_2\to 6{\mathrm{CO}}_2+6{\mathrm{H}}_2\mathrm{O} -3920 \mathrm{k}\mathrm{J}{ \mathrm{m}\mathrm{o}\mathrm{l}}^{-1}\dots \dots ..\left(3\right)\end{array}$

Adding eqⁿ (1) and (2) and subtracting (3):

C₆H₆ +3H₂ $\to$C₆H₁₂ ?

Enthalpy of hydrogenation is thus:

$$\begin{gathered} {\mathrm{\Delta H}}_{\text{Hydrogen. }}= 3\times \left(\mathrm{i}\right)+\left(\mathrm{ii}\right)-\left(\mathrm{iii}\right) \\ 3 \times -241+(-3800)-(-3920)=-121 \mathrm{kJ}{ \mathrm{mol}}^{-1} \end{gathered}$$