Bromleys Method

The Fj term is a summation of interaction parameters. For cation i in a multicomponent solution  

For the activity coeffloient of an anion, the subscript i indicates that anion and the subscript j then indicates the cations in the solution. 

The mean molal activity coefficient of electrolyte CA in the multicomponent solution can be calculated by combining the ionic activity coefficients  

The Meissner interaction parameter q for the solution containing cations i and anions ] is  

---

The conductivity of a gas mixture in the ideal gas state can be calculated by the Lindsay and Bromley method (1950) ... 

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. 

The viscosity is obtained by weighting the viscosities of each component. The recommended method is that of Bromley and Wilke (1951) ... 

For prediction of the vapor viscosity of gaseous mixtures of hydi ocai bons and nonhydixjcai bon gases at low pressures below a 7, of 0.6, the method of Bromley and Wilke is recommended. 

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

Studies by Nelson and Stewart,Bromley, - and Gunes " provide experimental data on air velocities and temperature distribution for this method of air supply at different room configurations, locations of air supply outlets, and velocities and temperatures of air supply. 

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). 

For ionic species i and j with charges of different signs 0 9--numbers were estimated from Pitzer s results forJstrong electrolytes using a method proposed by Bromley (2) 0 ) -numbers were determined from an... 

The method uf Bromley itnd Wilke wav used in cstimuu the vapor viscosities, T ... 

Until recently the ability to predict the vapor-liquid equilibrium of electrolyte systems was limited and only empirical or approximate methods using experimental data, such as that by Van Krevelen (7) for the ammonia-hydrogen sulfide-water system, were used to design sour water strippers. Recently several advances in the prediction and correlation of thermodynamic properties of electrolyte systems have been published by Pitzer (5), Meissner (4), and Bromley ). Edwards, Newman, and Prausnitz (2) established a similar framework for weak electrolyte systems. 

Many methods of estinating enthalpies of formation of binary compounds have been proposed (see, e.g., 13). Wilcox and Bromley (14), treating complex compounds analogous to corderoite as double salts, e.g.. 

B.W. Bromley, G.D. Hegeman, W. Meinschein (1982) A method for measuring natural abundance intramolecular stable carbon isotopic distributions in malic acid. Anal. Biochem. 126. 436-446... 

Aromatic bromides. McKillop, Bromley, and Taylor1 have described a new, simple, general procedure for bromination of aromatic hydrocarbons using thallium triacetate and bromine (CC14). The reaction is remarkable in that a single monobromo product is obtained. Note, however, that the combination of thallium triacetate and chlorine or iodine leads to isomeric mixtures. The method is particularly useful in the case of aromatics that are sensitive to bromine. 

The thermal conductivities of the pure components are estimated by Bromley s method. 

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 ... 

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 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. 

In 1973, Bromley (B3) disputed Meissner and Kusik s method for multicomponent solutions as follows ... 

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 ... 

---