Silicic acid and the hexa-aqua of Al 3+ are fundamental model aqueous species of chemical importance in nature. In order to investigate their hydroxyl dissociation mechanisms, Car-Parrinello molecular dynamics (CPMD) simulations were carried out, which allow treating the solutes and solvents on the same footing. The method of constraint was employed to trigger the reactions by taking coordination number as the reaction coordinate and the thermodynamic integration was used to obtain the free-energy profiles. The approximate transition states were located and the reactant and product states were also characterized. The free-energy changes of dissociation are found about 15.0 kcal/mol and 7.7 kcal/mol for silicic acid and Al-aqua, respectively. From the simulation results, the first pKas were calculated by using two approaches, which are based on the pristine thermodynamic relation and the RDF (radial distribution function)-free energy relation, respectively. Because of more uncertainties involved in the RDF way, it is suggested that the pristine way should be favored, which shows an error margin of 1 pKa unit. This study provides an encouraging basis for applying the present methodology to predict acidity constants of those groups that are difficult to measure experimentally.