$(20$ points$)$ The Gibbs free energy $\frac{}{b}ar(G)$ of the isothermal compression for $1$ mole vdW $C{O}_2$ with energy transition shown like Figure $2-(1)$ and obtain the saturation vapor pressures, Psat. Please $($a$)$ calculate $\frac{}{b}ar(G)(P_{\text{s}\text{a}\text{t}})$ at $270,280,290,300,$ and $304K,$ referenced to $1$atm. $(5$ points$)($b$)$ Put all the calculated $\frac{}{b}ar(G)\frac{P_{\text{s}\text{a}\text{t}}}{R}T$ in $($a$)$ onto Figure $2-(2).(5$ points$)($c$)$ Calculate the slope in $($b$),$ convert the slope to energy, and tell its physical meaning. $(5$ points$)($d$)$ If providing $32kJ$ can evaporate $1$ moles of liquid $C{O}_2,$ can you explain why this energy differ from that in $($c$)?(5$ points$)$ Given $\frac{d}{b}ar(G)=RTd(lnP),$ the standard pressure mole $*K,$ and the GibbsHelmholtz equation $\frac{d(\frac{?}{\text{b}\text{a}\text{r}}\frac{G}{T})}{dT}=\frac{-H}{T^2}.$ Note: Be careful about units!