Guggenheim-Scatchard equations

Pitzer (9) recently has developed a system of equations for electrolyte thermodynamics which yields comparable results to the Guggenheim-Scatchard equations for both single and mixed electrolytes. The main feature of the Pitzer equations is that they include an ionic-strength dependence on the short-range forces in binary interactions. 

The Bronsted-Guggenheim-Scatchard approach (abbreviated B-G-S equation in this document), (see section 6.1). 

The dependence of any excess function, XE on mole fraction can be fitted to an algebraic equation such as the Guggenheim-Scatchard eqn (27) (Guggenheim, 1937a Scatchard, 1949). The data are fitted... 

Several modifications of these equations were tried over the next several decades. Contributions by Guggenheim (1935) and Scatchard (1936) and the KTH or Swedish group (Grenthe et al., 1992, 1997) became the Brpnsted-Guggenheim-Scatchard or SIT method ... 

Bronsted-Guggenheim-Scatchard specific ion interaction theory (SIT) (cf. Grenthe and Wanner 1989 Giridhar and Langmuir 1991 Nordstrom and Munoz 1994) is an ion- and electrolyte-specific approach to activity coefficients, which is, therefore, theoretically capable of greater accuracy than the Davies equation. The general SIT equation for a single ion, i, can be written... 

Figure 1.7 Activities coefficients of ions Na+ and Ch vs. concentration of NaCl calculated using various equations. Equation 1 - Debye-Huckel (1.76), 2 - Bronsted-Guggenheim-Scatchard (1.78), 3 - Pitzer (1.79) 4 - experimental values (Geological evolution..., 2005).

Prausnitz (16) discusses this and related equations as well as the contributions of Margules, Hildebrand, Scatchard, Guggenheim, and others to this topic. For the activity of either component, referenced to the pure liquid, one has... 

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