Chemistry - Thermochemistry Question with Solution | TestHub

Given:

$\text{C}\left(\text{graphite}\right)+{\text{O}}_2\left(\text{g}\right)\to {\text{CO}}_2\left(\text{g}\right);{\text{Δ}}_{\text{r}}{\text{H}}^{\text{o}}=-393.5{\text{ kJ mol}}^{-1}$

${\text{H}}_2\left(\text{g}\right)+\frac{1}{2}{\text{O}}_2\left(\text{g}\right)\to {\text{H}}_2\text{O}\left(\text{l}\right);{\text{Δ}}_{\text{r}}{\text{H}}^{\text{o}}=-285.8\text{k}\text{J}\text{m}\text{o}{\text{l}}^{-1}$

$\text{C}{\text{O}}_2\left(\text{g}\right)+2{\text{H}}_2\text{O}\left(\text{l}\right)\to \text{C}{\text{H}}_4\left(\text{g}\right)+2{\text{O}}_2\left(\text{g}\right);{\text{Δ}}_{\text{r}}{\text{H}}^{\text{o}}=+890.3\text{k}\text{J}\text{m}\text{o}{\text{l}}^{-1}$

Based on the above thermochemical equations, the value of${\text{Δ}}_{\text{r}}{\text{H}}^{\text{o}}$at$\text{298 K}$for the reaction

$\text{C}\left(\text{g}\text{r}\text{a}\text{p}\text{h}\text{i}\text{t}\text{e}\right)+2{\text{H}}_2\left(\text{g}\right)\to \text{C}{\text{H}}_4\left(\text{g}\right)$will be: