Under the total pressure conditions of P$\_($CO$)+$P$\_($CO$\_(2))=1$atm $,$ for the reactions: $($i$)$ FeO$\_(($s$))+$CO$\_(($g$))->$Fe$\_(($s$))+$CO$\_(2($g$))($ii$)$ CO$\_(2($g$))+$C$\_(($s$))->2$CO$\_(($g$))$ Utilizing the Van't Hoff equation for reaction $($i$),$ calculate the e$.$quilibrium constants at temperatures of $400,600,800,1000,$ and $1200$K using the graphical method, and determine the reaction quotient at $1$atm $.$ Using the Bouduard reaction $($ii$),$ calculate the percentages of CO and CO$\_(2)$ that maintain the reaction equilibrium at the same temperatures. Finally, plot the percentage of CO against temperature. Gibbs free energy changes for the reactions are given as follows: $($i$)$ Fe$\_(($s$))+(1)/(2)$O$\_(2($g$))->$FeO$\_(($s$)),\backslash$Delta G$\_($T$)=-263700+64\mathrm{.}35$T$(($J$)/($mol$))($ii$)$ C$\_(($s$))+$O$\_(2($g$))->$CO$\_(2($g$)),\backslash$Delta G$\_($T$)=-394100-0\mathrm{.}84$T$(($J$)/($mol$))($iii$)$ C$\_(($s$))+(1)/(2)$O$\_(2($g$))->$CO$\_(($g$)),\backslash$Delta G$\_($T$)=-111700-87\mathrm{.}65$T$(($J$)/($mol$))$