Bromley parameters

The binary interaction parameter is obtained by the method of Lindsay and Bromley V... 

Table 3 shows some physicochemical properties used as international GA quality parameters, for example moisture, total ash content, volatile matter and internal energy, with reference to gums taken from Acacia Senegal species in Sudan (FAO, 1990, Larson Bromley, 1991). The physicochemical properties of GA may vary depending on the origin and age of trees, the exudation time, the storage type, and climate. The moisture content facilitates the solubility of GA carbohydrate hydrophilic and hydrophobic proteins. The total ash content is used to determine the critical levels of foreign matter, insoluble matter in... 

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) ... 

The activity of the water is derived from this expression by use of the Gibbs-Duhem equation. To utilize this equation, the interaction parameters fif ) and BH must be estimated for moleculemolecule, molecule-ion and ion-ion interactions. Again the method of Bromley was used for this purpose. Fugacity coefficienls for the vapor phase were determined by the method of Nakamura et al. (JO). 

Recently, the Pitzer equation has been applied to model weak electrolyte systems by Beutier and Renon ( ) and Edwards, et al. (10). Beutier and Renon used a simplified Pitzer equation for the ion-ion interaction contribution, applied Debye-McAulay s electrostatic theory (Harned and Owen, (14)) for the ion-molecule interaction contribution, and adoptee) Margules type terms for molecule-molecule interactions between the same molecular solutes. Edwards, et al. applied the Pitzer equation directly, without defining any new terms, for all interactions (ion-ion, ion-molecule, and molecule-molecule) while neglecting all ternary parameters. Bromley s (1) ideas on additivity of interaction parameters of individual ions and correlation between individual ion and partial molar entropy of ions at infinite dilution were adopted in both studies. In addition, they both neglected contributions from interactions among ions of the same sign. 

In general, data are fit quite well with the model. For example, with only two binary parameters, the average standard deviation of calculated lny versus measured InY of the 50 uni-univalent aqueous single electrolyte systems listed in Table 1 is only 0.009. Although the fit is not as good as the Pitzer equation, which applies only to aqueous electrolyte systems, with two binary parameters and one ternary parameter (Pitzer, (5)), it is quite satisfactory and better than that of Bromley s equation (J). 

The ion-ion electrostatic interaction contribution is kept as proposed by PITZER. BEUTIER estimates the ion - undissociated molecules interactions from BORN - DEBYE - MAC. AULAY electric work contribution, he correlates 8 and 8 parameters in PITZER S treatment with ionic standard entropies following BROMLEY S (9) approach and finally he fits a very limited (one or two) number of ternary parameters on ternary vapor-liquid equilibrium data. 

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. 

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. 

Seby et al. attempted to extrapolate K and K 2 data for the protonation of the selenite ion from Barcza and Sillen [71BAR/S1L] to / = 0 by the modified Bromley methodology , which is shortly presented in the paper and contains interaction parameters reminiscent of the SIT approach. It is not clear to the review if only data at... 

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. 

Bromley s equation - a suggested equation for the Guggenheim parameter... 

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 ... 

Bromley was led to believe that the Interaction parameters are linear in ionic strength, particularly at low molalities, after viewing Figure 22-8 in the Pitzer and Brewer revision of Thermodynamics (B2). Consequently, he presented a method for calculating activity coefficients that takes this dependence into account (B3). He found that the best correlation to experimental data for strong electrolytes was ... 

Bromley determined values for the E constant and resulting new B parameters for some bivalent metal sulfates. These are tabulated in Appendix 4.2. 

The methods for calculating activity coefficients have, up to this point, been presented for solutions at 25 C. This is due to the fact that most experimental data available, used for determining the various parameters of the acitivity coefficient models, was measured at 25°C. Recognizing that activity coefficients can be strongly affected by temperature, Bromley, Meissner, Pitzer and Chen have suggested methods of adapting their models and parameters to any temperature solution. 

In 1973, Bromley (B3) presented two equations that he felt adequately correlated the effect of temperature on the B parameter of his equation (4.44). They are ... 

In order to test Bromley. Meissner, Pitzer and Chen s methods for calculating activity coefficients, the models were coded on the HP-85 and HP-87 desktop computers. The calculated values for various electrolytes were plotted against smoothed experimental data published by the National Bureau of Standards and others. In the first plot for each electrolyte, the maximum molality to which they were plotted is the maximum molality of the published parameters. For some of the electrolytes, when there was experimental data available, the maximum molality was extended on a second plot. These plots illustrate the wide deviation from experimental data that may occur when using the published parameters for solutions with ionic strengths greater than the noted maximum molality. 

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. ... 

As mentioned earlier, most experimental data is measured at 25 C. This limits the applicability of the published parameters for the activity coefficient models discussed. The foDowing pages compare available experimental data and the activity coefficients calculated using Bromley, Meissner, Pitzer and Chen s models at temperatures other that 25"C. 

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). 

Based on Bromley s (S3) assumption that activity coefficient interaction parameters for individual ions could be added to estimate the value for a salt ... 

As mentioned earlier, the "excess enthalpy term is small and difficult to obtain. For purposes of illustration only, we can estimate the Yi(T) for the Na and Cl ions based upon binary correlation parameters published by Rastogi and Tassios (14). The Bromley formulation for calculating activity coefficients, simplified for a 1 1 salt, is ... 

The table of Bromley interaction parameters in Appendix 4.2 gives a value of ... 

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

The similar behavior of the Bromley equation B parameters allows for the estimation of the parameter for untabulated species. VIhen Bromley presented his equations in 1973, along with the B values for many species, he presented tabulated values based upon an expanded estimation equation ... 

A nonlinear regression option to allow users to generate their own Bromley and/or Pitzer and/or NRTL Interaction parameter values In order to develop private databanks. 

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