The heat of dissociation of ${\mathrm{H}}_2$  is  $435{\mathrm{KJmol}}^{-1}$. If $\mathrm{C}\left(\mathrm{s}\right)\to \mathrm{C}\left(\mathrm{g}\right)$$\mathrm{\Delta H}=720{\mathrm{KJmol}}^{-1}$ , calculate the bond energy per mol C-H of  bond in ${\mathrm{CH}}_4$ molecule.  ${\mathrm{\Delta H}}_{\mathrm{f}}$ for ${\mathrm{CH}}_4\mathrm{is}-75{\mathrm{KJmol}}^{-1}$

$\begin{array}{l}{\mathrm{H}}_2\to 2\mathrm{H};\Delta H_1=435{\mathrm{KJmol}}^{-1}\\ C\left(s\right)\to C\left(g\right);\Delta H_2=720{\mathrm{KJmol}}^{-1}\\ \mathrm{C}+2{\mathrm{H}}_2\to {\mathrm{CH}}_4;\Delta {\mathrm{H}}_3=-75{\mathrm{KJmol}}^{-1}\\ {\mathrm{CH}}_4( \mathrm{g})\to C\left(g\right)+4H\left(g\right);\Delta H=?\\ \Delta \mathrm{H}=2\Delta {\mathrm{H}}_1+\Delta {\mathrm{H}}_2-\Delta {\mathrm{H}}_3\end{array}$

$\begin{array}{l}=2\times \left(435\right)+720-(-75)\\ =1665\mathrm{KJ}/\mathrm{mol}\end{array}$

$\begin{array}{l}\text{ But }\Delta H=4\times {\epsilon }_{C-H}=1665{\mathrm{KJmol}}^{-1}\\ {\epsilon }_{C-H}=\frac{1665}{4}=416.25{\mathrm{KJmol}}^{-1}\end{array}$