Theory of ion interaction

For higher ionic strength, e g. highly saline waters the PITZER equation can be used (Pitzer 1973). This semi-empirical model is based also on the DEBYE-HUCKEL equation, but additionally integrates virial equations (vires = Latin for forces), that describe ion interactions (intermolecular forces). Compared with the ion dissociation theory the calculation is much more complicated and requires a 

In the following only a simple example of the PITZER equation is briefly described. For the complete calculations and the necessary data of detailed parameters and equations the reader is referred to the original literature (Pitzer 1973, Pitzer 1981, Whitfield 1975, Whitfield 1979, Silvester and Pitzer 1978, Harvie and Weare 1980, Gueddari et al. 1983, Pitzer 1991). 

The calculation of the activity coefficient is separately done for positively (index i) and negatively (index j) charged species applying Eq. 22. In this example the calculation of the activity coefficients for cations is shown, which can be analogously done for anions just exchanging the corresponding indices. 

Bcp = Virial coefficients, modified with regard to the ionic strength k, 1 = indices 

If the ionic strength exceeds 6 mol/L, the PITZER equation is no longer applicable though. 

---

The need to calculate activities coefficients occurred in the 1920 s. The search for methods of their determination was conducted in two major directions from the position of remote electrostatic and close Coulomb interactions between ions. Remote electrostatic interactions in diluted solutions of strong electrolytes were studied by Peter Debye and E. Hiickel. In 1923 they proposed a theory of ion interaction in diluted solutions. According to this theory, electrolytes in a solution are totally dissociated and their ions behave as rigid non-polarizable spheres with charges in the center, which are distributed in a uniform medium with high values of... 

---