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

(a). `2Cr+(3)/(2)O_2toCr_2O_3`
`triangle_(f)G_a^(ɵ)=-540kJmol^-1`
(b). `2Al+(3)/(2)O_2toAl_2O_3`
`triangle_(f)G_(b)^(ɵ)=-827kJmol^-1`
Required:
c. `Cr_2O_3+2AltoAl_2O_3+2Cr`
`triangle_fG_c^(ɵ)=?`
As `(c)=(b)-(a)`
`triangle_fG_c^(ɵ)=triangle_fG_f^(ɵ)-triangle_fG_a^(ɵ)`
`=(-827+540)kJmol^-1`
`=-287kJmol^-1`
Since `triangle_fG_c^(ɵ)` is negative, hence Al can reduce `Cr_2O_3`.