The protolytic dissociation process of hydrochloric acid (HCl) and hydrofluoric acid (HF) is studied using the B3LYP and MP2 methods with the 6-311+G(d,p) basis set in the gas phase and in aqueous solution. To study the phenomena in detail, discrete and discrete/continuum models were applied by placing water molecules in various positions around the acid. The dissociation process was studied using the thermodynamic cycle involving the structures optimized both in the gas phase and in aqueous solution and was analyzed with two key energy factors, relaxation free energy (${Delta}G_{Rex(g)}$) and solvation free energy (${Delta}G_s$). Based on the results, we could understand the dissociation mechanism and wish to propose the best way to study acid dissociation process using the CPCM methodology in aqueous solution.