Thermodynamic cycles and the calculation of pKa

A theoretical equation for the calculation of pKa based on a proton transfer reaction between the acid and one water molecule is derived using the general chemical equilibrium relationship. The present result is compared with two equations recently used that were based on thermodynamic cycles, but predict different pKa’s. It is shown that one thermodynamic cycle is wrong, and its better performance when compared with the correct cycle is due to an erroneous value used for the solvation free energy of the H3O+ ion. In addition, this analysis indicates that the PCM-UAHF solvation model is inconsistently parametrized.