The value of Δ_fG^⊖ for the formation of Cr₂O₃ from Cr (-540 kJmol^-1) is higher than that of Al₂O₃ from Al (-827 kJmol^-1).

Therefore, Al can reduce Cr₂O₃ to Cr. Hence, the reduction of Cr₂O₃ with Al is possible.

Alternatively,

2Al + \(\frac{3}{2}\)O₂ → Al₂O₃    Δ_fG^⊖ = - 827 kJmol^-1

2Cr + \(\frac{3}{2}\)O₂ → Cr₂O₃    Δ_fG^⊖ = - -540 kJmol^-1

Subtracting equation (ii) from (i), we have

2Al + Cr₂O₃ → Al₂O₃ + 2Cr 

Δ_fG^⊖ = -827 - (-540)

= -287 kJmol^-1

As Δ_fG^⊖ for the reduction reaction of Cr₂O₃ by Al is negative, this reaction is possible.