Given:

 $\begin{array}{r}\mathrm{C}\left(\text{ graphite }\right)+2{\mathrm{H}}_2\left(\mathrm{g}\right)\to {\mathrm{CH}}_4\left(\mathrm{g}\right); \mathrm{\Delta }{H}_1\\ \mathrm{C}\left(\mathrm{g}\right)+4\mathrm{H}\left(\mathrm{g}\right)\to {\mathrm{CH}}_4\left(\mathrm{g}\right); \mathrm{\Delta }{H}_2\end{array}$

which one of the following is true?

The equation $\mathrm{C}\text{ (graphite })+2{\mathrm{H}}_2(\mathrm{g})\to {\mathrm{CH}}_4(\mathrm{g})$ may be considered as the sum of the following three equations.

$\begin{array}{l}\mathrm{C}\text{ (graphite) }\to \mathrm{C}\left(\mathrm{g}\right)\mathrm{\Delta }{H}_{\mathrm{a}}\\ 2{\mathrm{H}}_2\left(\mathrm{g}\right)\to 4\mathrm{H}\left(\mathrm{g}\right)\mathrm{\Delta }{H}_{\mathrm{b}}\\ \mathrm{C}\left(\mathrm{g}\right)+4\mathrm{H}\left(\mathrm{g}\right)\to {\mathrm{CH}}_4\left(\mathrm{g}\right)\mathrm{\Delta }{H}_2\end{array}$

Hence $\mathrm{\Delta }{H}_1=\mathrm{\Delta }{H}_{\mathrm{a}}+\mathrm{\Delta }{H}_{\mathrm{b}}+\mathrm{\Delta }{H}_2$

Since $\mathrm{\Delta }{H}_{\mathrm{a}}$ and  $\mathrm{\Delta }{H}_{\mathrm{b}}$ are positive,  $\mathrm{\Delta }{H}_1>\mathrm{\Delta }{H}_2$