### 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 X^{2−}(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 X^{2−}(aq),
and the parameters for H^{+}(aq) and
SO4^{2−}(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.

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.