The value of `Delta_(f)G^(@)` for the formation of `Cr_(2)O_(3)` is-540 kJ `"mol"(-1)` and that of `Al_(2)O_(3)` is - 827 kJ mol-¹. Is the reduction of `Cr_(2)O_(3)` possible with Al?

Explanation

The two thermochemical equations may be written as:
`(4)/(3)Cr+O_(2) to (2)/(3)Cr_(2)O_(3), DeltaG^(@)= -540kJ` ….(i)
`(4)/(3)Al+O_(2) to (2)/(3)Al_(2)O_(3), DeltaG^(@)= -827 kJ` …….(ii)
On subtracting Eq. (i) from Eq. (ii), we get
`(2)/(3)Cr_(2)O_(3)+(4)/(3)Al to (2)/(3)Al_(2)O_(3)+(4)/(3)Cr,DeltaG=- 287 kj`
As `DeltaG^(@)` comes out to be negative, the reaction is feasible, i.e. Al can be used for the reduction of `Cr_(2)O_(3)`