What chemical principle is involved in choosing a reducing agent for getting the metal from its oxide ore? Consider the metle oxides `Al_(2)O_(3) and Fe_(2)O_(3)`, and justify the choice of the reducing agent.

Explanation

The chemical principle involved in the reduction of metal oxides to metals is that at a given temperature, any metal will reduce the oxides of other metals which lie about it is the Ellingham diagram. This is because the standard free energy change `(Delta_(r)G^(@))` of the combined redox reaction will be `-ve` by an amount equal to the difference in `(Delta_(f)G^(@))` of the two metal oxides at that temperature. From the Ellingham diagram it becomes evident that the `(Delta_(f)G^(@))` curve for the formation of `FeO` (or `Fe_(2)O_(3)`) lies above the `(Delta_(f)G^(@))` curve for reduce `FeO`(or `Fe_(2)O_(3)`) to Fe but the reverse is not true, i.e., Fe cannot reduce `Al_(2)O_(3)` to Al.
`2Al+3FeO overset(Delta)rarr Al_(2)O_(3)+2Fe`

Now, above 1073K, the `(C,CO)` curve lies below `(Fe, FeO)` curve, therefore, above 1073K, can reduce `FeO` to `Fe`.
`FeO +C overset(gt1073J)rarr Fe+CO`
In contrast, below 1073K, the `(CO,CO_(2))` curve lies below `(Fe, FeO)` curve therefore, below 1073K, CO can reduce `FeO` to `Fe`.
`FeO+CO overset(gt1073K)rarr Fe+CO_(2)`