Problem $2$

Methanation of $C{O}_2$ is described by $Rx4$ :

$C{O}_2+H_{2}C{H}_4+H_{2}O$

$Rx4$

$($a$)$ Show that you can calculate the standard heat of reaction from $Rx4$ based on the standard heat of reactions from the water gas shift $(Rx5)$ and the $CO-$methanation $(Rx6)$ reactions? Which rule did you apply?

$CO+H_{2}OC{O}_2+H2O,H_R^0=-41\mathrm{.}1kJmo{l}^{-1},Rx5$

$CO+H_{2}C{H}_4+H_{2}O,H_R^0=-206\mathrm{.}2kJmo{l}^{-1},Rx6$

$($b$)$ Calculate the heat of reactions for the $C{O}_2$ methanation at $25,100,200,300,400,$ and $500C.$ How does the heat of reactions behave with increasing temperature? Plot a graph with the results.