The value of `Delta_fG^@` for formation of `Cr_2O_3` is `-540 kJ mol^(-1)` and that of `Al_2O_3` is `-827 kJ mol^(-1)`. Is reduction of `Cr_2O_3` possible with Al ?

Explanation

The two equations are :
(i) `4//3Al(s) + O_2(g) to 2//3Al_2O_3(s),Delta_fG^@ = - 827 kJ mol^(-1)`
(ii) `4//3Cr(s) + O_2(g) to 2//3Cr_2O(s) : Delta_fG^@ = - 540 kJ mol^(-1)`
Subtracting Eq. (ii) from Eq. (i), we get
`4//3 Al(s) + 2//3 Cr_2O_3(s) to 2//3 Al_2O_3 (s) + 4//3 Cr(s): Delta_rG^@ = - 287 kJ mol^(-1)`
Since `Delta_rG^@` of the combined redox reaction is negative, therefore, reduction of `Cr_2O_3` by Al is possible.