Explain the thermodynamics of the extraction of iron from its oxide.

(A) In the process of extraction of iron,the key step involving reduction is $FeO_{(s)} + C_{(s)} \rightarrow Fe_{(s/l)} + CO_{(g)}$ $(i)$.
The reaction $(i)$ can be seen as the coupling of the following two reactions:
$FeO_{(s)} \rightarrow Fe_{(s)} + \frac{1}{2} O_{2(g)}$ ; $\Delta_{r} G^{\ominus}_{(FeO, Fe)}$ $(ii)$
$C_{(s)} + \frac{1}{2} O_{2(g)} \rightarrow CO_{(g)}$ ; $\Delta_{r} G^{\ominus}_{(C, CO)}$ $(iii)$
When reactions $(ii)$ and $(iii)$ are coupled to yield $(i)$,the net Gibbs free energy change is:
$\Delta_{r} G^{\ominus} = \Delta_{r} G^{\ominus}_{(C, CO)} + \Delta_{r} G^{\ominus}_{(FeO, Fe)}$ $(iv)$
The reaction will occur spontaneously if the value of $\Delta_{r} G^{\ominus}$ in equation $(iv)$ is negative. This is explained by the Ellingham diagram:
$(i)$ In the given figure,the $\Delta_{r} G^{\ominus}$ vs $T$ plot for the oxidation of $Fe$ to $FeO$ goes upward,while the plot for the oxidation of $C$ to $CO$ goes downward. These two plots intersect at approximately $1073 \ K$.
$(ii)$ At temperatures above $1073 \ K$,the $C \rightarrow CO$ line lies below the $Fe \rightarrow FeO$ line,meaning $\Delta_{r} G^{\ominus}_{(C, CO)} < \Delta_{r} G^{\ominus}_{(FeO, Fe)}$.
Thus,above $1073 \ K$,coke acts as a reducing agent for $FeO$ and is itself oxidized to $CO$.