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 the reduction of `Al_(2)O_(3)` by carbon:
`2Al_(2)O_(3)+3C(s)to4Al(s)+3CO_(2)(g)`,
`DeltaG^(@)=-380xx3+22500=+21360kJ`
`2Al_(2)O_(3)+6C(s)to4Al(s)+6CO(g)," "DeltaG^(@)=-500xx3+22500=+21000kJ`
Positive values of `DeltaG^(@)` show that the redcution of `Al_(2)O_(3)` is not possible by any of the above methods
`2PbO(s)+Cto2Pb+CO_(2),DeltaG^(@)=+120(-380)=-260kJ`
`2PbO(s)+2Cto2Pb+2CO,DeltaG^(@)=+120+(-500)=-380kJ`
Negative value of `DeltaG^(@)` shows that the process is spontaneous and PbO can be reduced by carbon.