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Given the following thermochemical equations:
\( \mathrm{C}_{\text {(graphite })}+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g}) ; \Delta_{r} \mathrm{H}^{\ominus}=-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1} \)
\[
\begin{aligned}
\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) ; \Delta_{r} \mathrm{H}^{\ominus} &=-285.8 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
\mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} O(l) \longrightarrow \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) ; \\
\Delta_{r} \mathrm{H}^{\ominus} &=+890.3 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}
\]
Calculate the value of \( \Delta_{r} \mathrm{H}^{\ominus} \) of the following reaction \( \mathrm{C}_{\text {(graphite) }}+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{4}(\mathrm{~g}) \)
(A) \( +74.8 \mathrm{~kJ} \mathrm{~mol}^{-1} \)
(B) \( +144.0 \mathrm{~kJ} \mathrm{~mol}^{-1} \)
(C) \( -74.8 \mathrm{~kJ} \mathrm{~mol}^{-1} \)
(D) - \( 144.8 \mathrm{~kJ} \mathrm{~mol}^{-1} \)
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