The standard Gibbs free energies for the reaction at `1773K` are given below:
`C(s) +O_(2)(g) rarr CO_(2)(g), DeltaG^(Theta) =- 380 kJ mol^(-1)`
`2C(s) +O_(2)(g) hArr 2CO(g),DeltaG^(Theta) =- 500 kJ mol^(-1)`
Discuss the possibility of reducing `AI_(2)O_(3)` and `PbO` with carbon at this temperature,
`4AI +3O_(2)(g) rarr 2AI_(2)O_(3)(s),DeltaG^(Theta) =- 22500 kJ mol^(-1)`
`2Pb +O_(2)(g) rarr 2PbO(s),DeltaG^(Theta) =- 120 kJ mol^(-1)`

Explanation

Let us consider reduction of `AI_(1)O_(3)` by carbon.
`2AI_(2)O_(3) +3C(s) rarr 4AI(s) +3CO_(2)(g)`,
`DeltaG^(Theta) =- 380 xx3 +(22500) =+21360 kJ mol^(-1)`
`2AI_(2)O_(3) +6C(s) rarr 4AI(s) +6CO(g)`,
`DeltaG^(Theta) =- 500 xx 3+ 22500 = +21000 kJ mol^(-1)`
Positive values of `DeltaG^(Theta)` show that the reduction of `AI_(2)O_(3)` is not possible by any of the above methods.
Now, let us consider the reduction of `PbO`.
`2PbO(s) +C rarr 2Pb +CO_(2)`,
`DeltaG^(Theta) = +120 +(-138) =- 260 k J mol^(-1)`
`2PbO(s) +2C rarr 2Pb +2CO`,
`DeltaG^(Theta) =+120 +(-500) =- 380 k J mol^(-1)`
Negative value of `DeltaG^(Theta)` shows that the process is spontaneous and `Pbo` can be reduced by carbon.