Bromley activity coefficient equation

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) ... 

Recently, there have been a number of significant developments in the modeling of electrolyte systems. Bromley (1), Meissner and Tester (2), Meissner and Kusik (2), Pitzer and co-workers (4, ,j5), and" Cruz and Renon (7j, presented models for calculating the mean ionic activity coefficients of many types of aqueous electrolytes. In addition, Edwards, et al. (8) proposed a thermodynamic framework to calculate equilibrium vapor-liquid compositions for aqueous solutions of one or more volatile weak electrolytes which involved activity coefficients of ionic species. Most recently, Beutier and Renon (9) and Edwards, et al.(10) used simplified forms of the Pitzer equation to represent ionic activity coefficients. 

For applications where the ionic strength is as high as 6 M, the ion activity coefficients can be calculated using expressions developed by Bromley (4 ). These expressions retain the first term of equation 9 and additional terms are added, to improve the fit. The expressions are much more complex than equation 9 and require the molalities of the dissolved species to calculate the ion activity coefficients. If all of the molalities of dissolved species are used to calculate the ion activity coefficients, then the expressions are quite unwieldy. However, for the applications discussed in this paper many of the dissolved species are of low concentration and only the major dissolved species need be considered in the calculation of ion activity coefficients. For lime or limestone applications with a high chloride coal and a tight water balance, calcium chloride is the dominant dissolved specie. For this situation Kerr (5) has presented these expressions for the calculation of ion activity coefficients. 

Although there is a large number of experimental data (1, 2.,.3) for ternary aqueous electrolyte systems, few equations are available to correlate the activity coefficients of these systems 1n the concentrated region. The most successful present techniques are those discussed by Meissner and co-workers (4 ) and Bromley ( )... 

The LCM is a semi-theoretical model with a minimum number of adjustable parameters and is based on the Non-Random Two Liquid (NRTL) model for nonelectrolytes (20). The LCM does not have the inherent drawbacks of virial-expansion type equations as the modified Pitzer, and it proved to be more accurate than the Bromley method. Some advantages of the LCM are that the binary parameters are well defined, have weak temperature dependence, and can be regressed from various thermodynamic data sources. Additionally, the LCM does not require ion-pair equilibria to correct for activity coefficient prediction at higher ionic strengths. Thus, the LCM avoids defining, and ultimately solving, ion-pair activity coefficients and equilibrium expressions necessary in the Davies technique. Overall, the LCM appears to be the most suitable activity coefficient technique for aqueous solutions used in FGD hence, a data base and methods to use the LCM were developed. 

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. 

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. 

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] ... 

Bromley notes that equation (4.44) gives good results for strong electrolytes to ionic strengths of 6 molal, but due to the exponential quality of the expression, attempts to extrapolate to higher ionic strengths will show increasing error in the activity coefficient. Values for B can be found in Appendix 4.2. 

The Bromley B parameter for the species at 25°C was used to calculate the activity coefficient for ionic strength I with Bromley s equation (4.44). 

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 ... 

Bromley s (S) method of calculating the activity coefficients of ionic species in multicomponent solutions, detailed in Chapter V. leads to the following equations ... 

The second assumption was also made by relying on the low solubility. Recalling from Chapter V Bromley s <5) equations for the activity coefficient of a single ion in a multicomponent solution ... 

More recently, Brossia et al. [35] introduced an approach based on new correlations for activity coefficients in concentrated solutions. This proach [101] is based on the Helgeson-Kirkham-Flowers equation for standard-state properties with a nonideal solution model based on the activity coefficient expression developed by Bromley and Pitzer. Using specific software, Brossia et al. were able to predict the dominant ionic species and the salt precipitation in Ni, Fe, Cr, and 308 stainless steels crevice solutions. Fair agreement was observed with the in situ analyses of these crevice solutions by Raman spectroscopy. 

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