Bromley Interaction Parameters

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

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

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. 

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. 

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 ... 

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

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

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. 

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