Using a combination of ab initio, DFT and continuum solvation methods, the gas phase and aqueous acidities for a set of weak organic acids with high pK(a) values, which cannot be measured experimentally in aqueous solvent, have been calculated. Comparison of the computed and experimental data for different terms used in the thermodynamic cycle for the calculation of pK(a) values allowed us to estimate that the errors in the pK(a) calculations are of order of 2 pK(a) units, i.e., less than 10% of the expected pK(a) values for the studied weak organic acids. It is shown that inclusion of explicit water molecules in the solute cavity of compounds with pK(a) values over 40 could lead to dubious results due to the inappropriate description of the corresponding anion solvation. Acidity trends for compounds in the gas phase and in aqueous solvent were found to be different, due to the effects of aqueous solvation.