Aqueous Acid Model, Including Dissociation

In this model, equation (5) of Clegg and Seinfeld (2006a) is used to represent the activity coefficient of each undissociated acid H2X, and its contribution to the osmotic coefficient of the solution. The activity coefficients of the ions H+(aq), HX−(aq) and X2−(aq), and their contribution to the osmotic coefficient, are estimated using the Pitzer activity coefficient model with the parameters given by Clegg et al. (1994) for aqueous H2SO4. The interactions between H+(aq) and HX−(aq)-, and the parameters for this cation - anion pair, are assumed to be the same as for H+(aq) and HSO4−(aq). Similarly for the interactions between H+(aq) and X2−(aq), and the parameters for H+(aq) and SO42−(aq) interactions.

The dissociation constants from Table 1 of Clegg and Seinfeld (2006a) are used to calculate equilibria, and the osmotic coefficient and water activity of each solution are obtained by combining the two sets of model equations as described in Clegg et al. (2001). This approach is equivalent to assuming that the three ions, and the neutral molecule, do not interact in the solution. That is to say, the activity coefficients of the ions are unaffected by the undissociated H2X, and vice versa.

The calculation of both solvent and solute activities by this method yields more accurate results for dilute solutions than the assumption of zero dissociation adopted by Clegg and Seinfeld (2006a). However, the amount of dissociation calculated for concentrated solutions - for which dissociation is least - is unlikely to be accurate due to the assumptions involved. (Note, though, that the calculated stoichiometric or total quantities will be little affected.) Clegg and Seinfeld (2006b) have developed models of aqueous succinic and malonic acids, including dissociation, but their treatments are limited in their concentration range and involve the same assumptions regarding the interactions of H+(aq) with the acid anions as the model presented here.

References

S. L. Clegg, J. A. Rard, and K. S. Pitzer (1994) Thermodynamic properties of 0 - 6 mol kg-1 aqueous sulphuric acid from 273.15 to 328.15 K. J. Chem. Soc., Faraday Trans. 90, 1875-1894.

S. L. Clegg and J. H. Seinfeld (2006a) Thermodynamic models of aqueous solutions containing inorganic electrolytes and dicarboxylic acids at 298.15 K. I. The acids as non-dissociating components. J. Phys. Chem. A, 110, 5692-5717.

S. L. Clegg and J. H. Seinfeld (2006b) Thermodynamic models of aqueous solutions containing inorganic electrolytes and dicarboxylic acids at 298.15 K. II. systems including dissociation equilibria. J. Phys. Chem. A, 110, 5718-5734.

S. L. Clegg, J. H. Seinfeld, and P. Brimblecombe (2001) Thermodynamic modelling of aqueous aerosols containing electrolytes and dissolved organic compounds. J. Aerosol. Sci. 32, 713-738.