The reaction is:
Fe_2O_3(s)+3CO(g)->2Fe(s)+3CO_2(g)
Since CO is used in excess, therefore, the limiting reactant is Fe_2O_3.
?g Fe(s) = underbrace(1.00xx10^3cancel(gFe_2O_3)xx(1cancel(molFe_2O_3))/(160 cancel(gFe_2O_3)))_(color(blue)("From g to mol"))xxunderbrace((2cancel(molFe))/(1cancel(molFe_2O_3)))_(color(blue)("Molar Ratio"))xxunderbrace((55.9gFe)/(1cancel(molFe)))_(color(blue)("From mol to g"))=color(green)(699gFe)
I used 3 significant figures since 1.00kg is 3 significant figures.
Explaining the dimensional analysis used above:
The first part:
1.00xx10^3cancel(gFe_2O_3)xx(1cancel(molFe_2O_3))/(160 cancel(gFe_2O_3))
is used to convert gFe_2O_3 to molFe_2O_3
The second part:
(2cancel(molFe))/(1cancel(molFe_2O_3))
is the molar ration between Fe and Fe_2O_3. This is taking from the coefficient of the balanced equation.
The third part:
(55.9gFe)/(1cancel(molFe))
is used to convert molFe to gFe.
