Iron is produced in a blast furnace by the reaction of iron $($III$)$ oxide with carbon as follows:

$F{e}_2{O}_3+3C2Fe+3CO$

Unfortunately, the following side reaction occurs, producing iron $($II$)$ oxide:

$F{e}_2{O}_3+C2$FeO$+CO$

After mixing $600kg$ carbon with $2000kgFe{e}_2{O}_3,$ the process produces $1200kg$ of pure iron, $183kg$ of FeO and

leaves $85kg$ Fe$203.$ Determine:

a$.$ The limiting reactant and percentage of excess reactant, based on the first reaction

b$.$ The percentage conversion of $F{e}_2{O}_3$ to $Fe$

$F{e}_2{O}_3,33\mathrm{.}3\%$

c$.$ The mass of carbon consumed and the mass of $CO$ produced per $kg$ of $F{e}_2{O}_3$ fed to the blast furnace

$[400\mathrm{.}4$ kg$,0\mathrm{.}47kg$

d$.$ The selectivity and the percentage yield of the process.