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 reduction of `Cr_2 O_3` possible with `Al` ?

Explanation

The two equations are :
`(i) 4/3 Al (s) + O_2 (g) to 2/3 Al_2 O_3 (s) Delta_f G^@ (Al, Al_2 O_3) = -827 KJ mol^(-1)`
(ii) `4/3 Cr (s) + O_2 (g) to 2/3 Cr_2 O_3 (s) " " Delta_f G^@ (Cr, Cr_2 O_3) =-540 KJ mol^(-1)`
Subtracting eqn. (ii) from eqn (i), we get
`4/3 Al (s) + 2/3 Cr_2 O_3 (s) to 2/3 Al_2 O_3 (s) + 4/3 Cr(s) " " Delta_r G^@ =-287 KJ mol^(-1)`
Since `Delta_r G^@` for the combined reaction is -ve. therefore , the above reaction, i.e. reduction of `Cr_2 O_3` by `Al` is possible.