The value of  ${\Delta }_f{G}^0$   for the formation of $C{r}_2{O}_3$  is -540 $kJmo{l}^{-1}$  and that of $A{l}_2{O}_3$    $-827kJ$  $mo{l}^{-1}$  .Is the reduction of $C{r}_2{O}_3$  with Al is feasible reaction?

 $$\begin{gathered} \frac{4}{3}Cr\left(s\right)+O_2\left(g\right)\to \frac{2}{3}C{r}_2{O}_3\left(S\right);{\Delta }_f{G}^0=-540KJmo{l}^{-1}\mathrm{......}\left(i\right) \\ \frac{4}{3}Al\left(s\right)+O_2\left(g\right)\to \frac{2}{3}A{l}_2{O}_3\left(S\right);{\Delta }_f{G}^0=-827KJmo{l}^{-1}\mathrm{......}\left(ii\right) \end{gathered}$$

Subtracting Eq.(ii) from Eq.(i)
$-827-(-540)=-287kj$
Since,  $\Delta G^0$  comes out to be negative the reaction is feasible