The value of`Delta _(f) G^(Ө)` for formation of `Cr_(2) O_(3)` is `– 540 kJmol^(−1) ` and that of `Al_(2) O_(3)` is `– 827 kJmol^(−1)`. Is the reduction of `Cr_(2) O_(3)` possible with `Al` ?

Explanation

The two thermochemical equations may be written as follows :
`{:(4//3 Cr(s)+O_(2)(g)to 2//3Cr_(2)O_(3)(s), Delta_(f)G^(@)=-540 kJ),(4//3Al(s)+O_(2)(g)to 2//3Al_(2)O_(3)(s), Delta_(f)G^(@)=-827 kJ):}/(2//3Cr_(2)O_(3)(s)+4//3Al(s)to 2//3Al_(2)O_(3)(s)+4//3Cr(s), Delta_(f)G^(@)=-287 kJ)`