Q.The value of ΔfG° for formation of Cr2O3 is – 540 kJmol⁻¹ and that of Al2O3 is – 827 kJmol⁻¹. Is the reduction of Cr2O3 possible with Al ?

For $Cr_2O_3 + 2Al \rightarrow Al_2O_3 + 2Cr$: $\Delta_rG^\circ = \Delta_fG^\circ(Al_2O_3) - \Delta_fG^\circ(Cr_2O_3) = -827 - (-540) = -287$ kJ/mol, which is negative, confirming the reaction is thermodynamically feasible. This is the basis of the …

Step 1 – Write the reaction and the relation for $\Delta_rG^\circ$

Since this can be viewed as "Al reduces $Cr_2O_3$ by taking away the oxygen to form $Al_2O_3$ instead", the free energy change of this reaction equals the free energy of formation of the product oxide minus the free energy of formation of the reactant oxide (both per equivalent amount, here already matched: both $\Delta_fG^\circ$ values given correspond to $M_2O_3$ per mole):

Step 2 – Substitute the given values

Step 3 – Interpret the sign

Since $\Delta_rG^\circ = -287$ kJ/mol is negative, the reaction is thermodynamically feasible (spontaneous under standard conditions) — aluminium is indeed capable of reducing chromium(III) oxide to chromium metal.

Step 4 – Physical significance …

Set up $\Delta_rG^\circ = \Delta_fG^\circ(\text{product oxide}) - \Delta_fG^\circ(\text{reactant oxide})$ for the 'Al displaces Cr from its oxi …

• Getting the subtraction order backwards (computing $\Delta_fG^\circ(Cr_2O_3) - \Delta_fG^\circ(Al_2O_3)$), which would incorrectly give a positive value and the wrong conclusion. …