Calculate the standard heat of the following gaseous reaction at \(773 \mathrm{~K}\) :

\[ \mathrm{CO}_{2}+4 \mathrm{H}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{CH}_{4} \quad \Delta H_{298}=-164.987 \mathrm{~kJ} \]

The specific heat of the components are represented by \(C_{P}=a+b T+C T^{2}\), where \(C_{P}\) is in \(\mathrm{J} / \mathrm{mol}-\mathrm{K}\) and \

(a, b\), and \(c\) are constants.

\begin{tabular}{lccc}

& \(a\) & \(b \times 10^{3}\) & \(c \times 10^{6}\) \\

\(\mathrm{CO}_{2}\) & 26.75 & 42.26 & -14.25 \\

\(\mathrm{H}_{2}\) & 26.88 & 4.35 & -0.33 \\

\(\mathrm{H}_{2} \mathrm{O}\) & 29.16 & 14.49 & -2.02 \\

\(\mathrm{CH}_{4}\) & 13.41 & 77.03 & -18.74

\end{tabular}