Methanation of CO$2$ is described by Rx $4$:

CO$2+\_\_$ H$2->\_\_$ CH$4+\_\_$ H$2$O Rx $4$

$($a$)$ Show that you can calculate the standard heat of reaction from Rx $4$ based on the standard heat of reactions from the water gas shift $($Rx $5)$ and the CO$-$methanation $($Rx $6)$ reactions? Which rule did you apply?

CO $+\_\_$ H$2$O $->\_\_$ CO$2+\_\_$ H$2$HR$0=-41\mathrm{.}1$ kJ mol$-1$ Rx $5$

CO $+\_\_$ H$2->\_\_$ CH$4+\_\_$ H$2$O $$HR$0=-206\mathrm{.}2$ kJ mol$-1$ Rx $6$

$($b$)$ Calculate the heat of reactions for the CO$2$ methanation at $25,100,200,300,400,$ and $500\backslash$deg C$.$ How does the heat of reactions behave with increasing temperature? Plot a graph with the results.

$($c$)$ Calculate the change of internal energy at standard conditions and at $300\backslash$deg C$.$ Do not neglect the influence of the mole$-$change. Compare all three reactions. prepare a table with thermodyna,ic properties and stoichiometric coefficients of the reactions. do not forget the units. show steps for heat capacity integration at least once

Please i need help with part c and for the heat capacities, use tables and the geat capacity integration formula.