Question

The value of Δ_tG^θ for formation of Cr₂O₃ is −540 kJ mol⁻¹ and that of Al₂O₃ is −827 kJ mol⁻¹. Is the reduction of Cr₂O₃ possible with Al?

Answer 1

The value of Δ_rG^θ for the formation of Cr₂O₃ from Cr (−540 kJ mol⁻¹) is higher than that of Al₂O₃ from Al (−827 kJ mol⁻¹). Therefore, Al can reduce Cr₂O₃ to Cr. Hence, the reduction of Cr₂O₃ with Al is possible.

Alternatively,

\[\ce{2Al + \frac{3}{2}O2 -> Al2O3}\], Δ_rG^θ = −827 kJ mol⁻¹    ...(i)

\[\ce{2Cr + \frac{3}{2} O2 -> Cr2O3}\], Δ_rG^θ = −540 kJ mol⁻¹    ...(ii)

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

\[\ce{2Al + Cr2O3 -> Al2O3 + 2Cr}\]

Δ_rG^θ = −827 − (−540)

= −287 kJ mol⁻¹

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