Overview of Activity Coefficient Models for Ions

The algorithms that describe the change in ion activity coefficients (y,) with ionic strength all relate the logarithm of yi to a function of with or without additional terms. In generalizing the applicability of such models it is, therefore, helpful to do so with a schematic plot of log y, versus Such a plot is shown in Fig. 4.5 for hypothetical cation, M.  

The Davies equation (Eq. 4.31) generates the positive change in slope with an add-on term, bl, where b is the same constant for all ions. The denominator of the Davies equation equals I + VT, which is equivalent to assigning a constant a -, value of about 3.0 to all ions in the extended DH equation. These simplifications make the Davies equation less accurate than the extended Debye-Hiickel equation at low ionic strengths, and limit its use to ionic strengths below that of seawater (0.7 mol/kg). 

The TJ equation (Eq. 4.51) improves on shortcomings of the Davies equation by retaining the extended DH equation with its a, parameter and assigning different values to b in the add-on bl term based on the Macinnes convention and on fitting mean salt data for the ions. The TJ equation has been found reliable up to / = 3.5 mol/kg in some cases, but is conservatively limited to / 2 mol/1.  

The denominator of the DH term in the SIT model (Eqs. 4.32 and 4.33) equals 1 + 1.5V/, which is equivalent to assuming a, 4.6 and constant in the extended DH equation. The SIT model accounts for binary interactions of anions and cations with interaction parameters that are specific for individual ions in chloride or other media. Lacking an adjustable ion size parameter, the SIT model is less accurate than the extended DH model at low ionic strengths. It does, however, give accurate results in some solutions up to / = 3.5 mol/kg. 

At ionic strengths between about 2 and 3.5 mol/kg the high salt concentrations lead to further interaction between anion and cation pairs, but also to important interaction between pairs of ions of the same charge and simultaneously between three ions where two have the same charge. The Pitzer model can accurately account for such effects with a complex series of interaction terms added to a 

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