The geometric configuration, vibration frequency and thermodynamic properties of Al2O3X(X=H, D, T) molecular clusters with lower energy were optimized using B3LYP/6-311++G(d,p) method. The changes of entropy, enthalpy and Gibbs free energy of the reactions between Al2O3 and hydrogen (deuterium or tritium) gas have been calculated under the solid electron-vibration approximation method using formulae in thermodynamics under temperatures of 298—1098 K. Then the equilibrium pressures of hydrogen (deuterium or tritium) gas in these reactions are obtained. The results show that, the gaseous Al2O3X may have two possible ground states Al2O3X(X=H,D,T)(2A′)Cs and Al2O3X (2B2) C2v. Tritium can be displaced by deuterium; deuterium can be displaced by hydrogen in the reactions between Al2O3 and X2 with the production of solid Al2O3X which relates to ground Al2O3X with C2v symmetry. This displacement sequence is the same as that in the reactions between titanium and X2. These displacement effects are very weak. But hydrogen can be displaced by deuterium; deuterium can be displaced by tritium in the reactions between Al2O3 and X2 with the production of solid Al2O3X which relates to ground gaseous Al2O3X with Cs symmetry. This displacement sequence is opposite to that in the reactions between titanium and X2. In all, these displacement effects are very weak, and they grow still weaker as the temperature increases.