Bromleys Extended Equation

As shown earlier, Bromley (B3) presented an extended form of his equation, designed to help compensate for some of the strong ion associations that may occur, and published corresponding parameters for some bivalent metal sulfates. The following pages compare the results of using the two equations for MgSO.  

The extended equation for symmetrical salts, such as the 2-2 MgSO, is  

The experimental points are once again taken from Robinson and Stokes. 

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As explained in section 3.6.1, many modifications have been proposed for the Debye-Hiickel relationship for estimating the mean ionic activity coefficient 7 of an electrolyte in solution and the Davies equation (equation 3.35) was identified as one of the most reliable for concentrations up to about 0.2 molar. More complex modifications of the Debye-Huckel equation (Robinson and Stokes, 1970) can greatly extend the range of 7 estimation, and the Bromley (1973) equation appears to be effective up to about 6 molar. The difficulty with all these extended equations, however, is the need for a large number of interacting parameters to be taken into account for which reliable data are not always available. 

Meissner and Kusik (M7) revised their method for calculating the activity coefficients of electrolytes in multicomponent solutions in 1978. They extended equation (5.16) in order to avert the problem pointed out by Bromley. For an electrolyte of cation i and anion j, the reduced activity coefficient is ... 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

Figure 2. The Henry constant of oxygen in aqueous solutions of sodium sulfate at 25 °C (O) experimental data (a) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the Debye-Hiickel equation (b) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the extended Debye-Hiickel equation (c) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the Bromley equation (d) the Henry constant calculated with eq 15.

For the mean activity coefficient of the salt, several expressions have been used, such as the Debye-Hiickel equation, the extended Debye-Hiickel equation, and the Bromley equation. The Bromley equation was selected because of its simplicity and its accuracy of course, other accurate equations are also available. The values of the parameter B for all cases examined are listed in Table 3. 

With increasing electrolyte concentration, the short-range interactions become more and more dominating. Therefore, in activity coefficient models the Debye-Hiickel term, which describes the long-range interactions, has to be extended by a term describing the short-range interactions. A well-known empirical extension of the Debye-Hiickel theory is the Bromley equation [5] ... 

In 1972, L.A. Bromley had published a paper in which he demonstrated that the 3 or B interaction parameter of Guggenheim s extended Debye-Hiickel equation may be approximated by summing S values for the individual ions for uni-univalent solutions ... 

In 1972, Bromley (4) suggested that the ion interaction parameter B jx extended Oebye-Huckel equation ... 

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