For the formation of Cr₂O₃ and Al₂O₃, values of  ${∆}_{\mathrm{f}}$G are $-$ 540 kJ mol^–1 and –827 kJ mol^–1 respectively. What will be the possibility for reaction of Cr₂O₃ by Al?

2Cr + $\frac{3}{2}$O₂ $\to$Cr₂O₃ ${∆}_{\mathrm{f}}$G= - 540 Kj/mole

2Al + $\frac{3}{2}$O₂$\to$Al₂O₃ ${∆}_{\mathrm{f}}$G= - 827 Kj/mole

substract equation 1 from equation 2 

Cr₂O₃ $\to$2Cr + $\frac{3}{2}$O₂ ; ${∆}_1$G = 540 kJ/mole

2Al + $\frac{3}{2}$O₂$\to$Al₂O₃ ${∆}_{\mathrm{f}}$G= - 827 Kj/mole

2Al  + Cr₂O₃ $\to$2Cr + Al₂O₃ ${∆}_{\mathrm{r}}\mathrm{G}$ = 540 - 827 = -287 kJ/mole

since ${∆}_{\mathrm{r}}\mathrm{G}$ is negative reduction of Cr₂O₃ by Al is spontaneous