Multicomponent solutions activity coefficient

JOH/PYT] Johnson, K. S., Pytkowicz, R. M., Ion association and activity coefficients in multicomponent solutions, Activity coefficients in electrolyte solutions, Pytkowicz, R. M., Ed., II, pp.I-62, CRC Press, Boca Raton, Florida, (1979). Cited on page 588. 

A rigorous test of multicomponent solution activity coefficient prediction methods is the calculation of the mutual solubilities of salts and the calculation of salt solubilities in aqueous electrolyte solutions. The salt solubilities are affected by the solution composition. In order to calculate the saturation molalities, the activity coefficients must be adequately predicted. 

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

Theoretical relationships for activity coefficients. The Setschenow equation is used to calculate the activity coefficients of aqueous molecular species in salt solutions. The Pitzer based methods may be used for binary or multicomponent solution activity coefflcient calculations for all species in the solution. 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

Meissner, H. P. and C. L. Kusik, "Activity Coefficients of Strong Electrolytes in Multicomponent Aqueous Solutions," AIChE J., 1972, 18, 294. 

The typical system for which the equilibrium composition is desired however does not contain a single salt in solution but more usually the equivalent of several salts in solution. In addition, the activities required in equilibrium expressions arising from the law of mass action are single ion activities or in general, single ion activity coefficients. And, we are interested in the ionic activity coefficeint of each species in a multicomponent system. 

Sangster, J. Lenzi,F., "On the Choice of Methods for the Predictions of the Water-activity and Activity Coefficients for Multicomponent Aqueous Solutions", Can. J. Chem. Eng.,... 

Our results lead to good predictions of activity coefficients in multicomponent systems from data measured 1n simple solutions. Also, they yield values similar to those of Pitzer and Kim (8 ) as is shown in Table II. 

Recently, Rubingh ll) and Scamehorn et al. (9) have shown that the activity coefficients obtained by fitting the mixture CMC data can be correlated by assuming the mixed micelle to be a regular solution. This model proposed by Rubingh for binary mixtures has been extended to include multicomponent surfactant mixtures by Holland and Rubingh (10). Based on this concept Kamrath and Frances (11) have made extensive calculations for mixed micelle systems. 

These interactions exist in real systems for which the activity has the physical meaning of the effective concentration. Thus, only for dilute real solutions does A = a. In mixtures, the activity coefficient is usually, but not always, less than one and is affected by all the species in the multicomponent mixture. 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

The last two equations offer an important means in calculating the activity coefficient of a dilute solute in multicomponent solutions. 

The goal of this research was to improve activity coefficient prediction, and hence, equilibrium calculations in flue gas desulfurization (FGD) processes of both low and high ionic strength. A data base and methods were developed to use the local composition model by Chen et al. (MIT/Aspen Technology). The model was used to predict solubilities in various multicomponent systems for gypsum, magnesium sulfite, calcium sulfite, calcium carbonate, and magnesium carbonate SCU vapor pressure over sulfite/ bisulfite solutions and, C02 vapor pressure over car-bonate/bicarbonate solutions. 

Grover, J., Chemical mixing in multicomponent solutions An introduction to the use of Margules and other thermodynamic excess functions to represent non-ideal behavior, pp. 67-97 in Thermodynamics in Geology, ed. by D. G. Fraser, D. Reidel, Dordrecht, The Netherlands, 1977. This review article provides a fine introduction to the thermodynamic theory of mixtures underlying the Margules expansion for adsorbate-species activity coefficients. 

The program estimates the liquid phase activity coefficients at specified temperatures and liquid compositions from molecular structure of the molecules. Binary or multicomponent solutions can be considered. 

A second example is provided by a semiempirical correlation for multi-component activity coefficients in aqueous electrolyte solutions shown in Fig. 2. This correlation, developed by Fritz Meissner at MIT [3], presents a method for scale-up activity-coefficient data for single-salt solutions, which are plentiful, are used to predict activity coefficients for multisalt solutions for which experimental data are rare. The scale-up is guided by an extended Debye-Hilckel theory, but essentially it is based on enlightened empiricism. Meissner s method provides useful estimates of thermodynamic properties needed for process design of multieffect evaporators to produce salts from multicomponent brines. It will be many years before sophisticated statistical mechanical techniques can perform a similar scale-up calculation. Until then, correlations such as Meissner s will be required in a conventional industry that produces vast amounts of inexpensive commodity chemicals. 

The results obtained in the solution of a sample problem are summarized here to illustrate the application of the method. An extractive distillation problem from Oliver (6) was used in which methylcyclo-hexane is separated from toluene by adding phenol. The column contains 11 stages (including the reboiler and condenser) and has a feed of 0.4 moles/unit time of methylcyclohexane and 0.6 moles/unit time of toluene to the fourth stage from the reboiler and 4.848 moles/unit time of phenol to the fourth stage from the condenser. We used the same physical property correlations as Oliver. The activity coefficients were obtained from a multicomponent form of the Van Laar Equation (7). 

The extension of the CNT to homogeneous nucleation in atmospheric, essentially multicomponent, systems have faced significant problems due to difficulties in determining the activity coefficients, surface tension and density of binary and ternary solutions. The BHN and THN theories have been experiences a number of modifications and updates. At the present time, the updated quasi-steady state BHN model [16] and kinetic quasi-imary nucleation theory [24,66], and classical THN theory [25,33] and kinetic THN model constrained by the experimental data... 

Nucleation in the atmosphere is essentially multicomponent process. However, a commonly used classical approach incapable of the quantitative treatment of multicomponent systems due to (a) excessive sensitivity to poorly defined activity coefficients, density and surface tension of multicomponent solutions (b) strong dependence of nucleation rates on thermochemistry of initial growth steps where... 

In this section, we derive PDT expressions for activity coefficients and standard state chemical potentials that are conventional in physical chemistry and chemical engineering thermodynamics. We assume here a single homogeneous solution phase composed of several components, and write the following conventional expression for the chemical potential of component a in this multicomponent solution ... 

In saline soils and soils contaminated with geothermal brines, the ionic strengths of the soil solution may exceed 0.5 M. This fact poses the necessity of using equations which have been developed to describe the activity coefficients of ions in concentrated, multicomponent electrolyte solutions. As part of a study on the chemistry of ore-forming fluids, Helgeson (50) has proposed that the true individual ion activity coefficients for ions present in small concentrations in multicomponent electrolyte solution having sodium chloride as the dominant component be approximated by a modified form of the Stokes-Robinson equation. The equation proposed is ... 

Therefore, it is important to have a theoretical tool which allows one to examine (or even predict) the thickness of the LC region and the value of the LC on the basis of more easily available experimental information regarding liquid mixtures. A powerful and most promising method for this purpose is the fluctuation theory of Kirkwood and Buff (KB). " The KB theory of solutions allows one to extract information about the excess (or deficit) number of molecules, of the same or different kind, around a given molecule, from macroscopic thermodynamic properties, such as the composition dependence of the activity coefficients, molar volume, partial molar volumes and isothermal compressibilities. This theory was developed for both binary and multicomponent solutions and is applicable to any conditions including the critical and supercritical mixtures. 

The solubilities of gases in binary, ternary or more complex multicomponent solvents are good examples in which the Kirkwood-Buff theory of solutions provides exceUent results that cannot be obtained using the methods of traditional thermodynamics. Thermodynamics cannot provide explicit pressure, temperature, and composition dependence of the thermodynamic functions, such as the activity coefficients of the components. Therefore, various assumptions regarding the activity coefficients must be made. In contrast, the Kirkwood-Buff theory of solution allows one to establish, in some cases, relations between multicomponent... 

The present paper is concerned with mixtures composed of a highly nonideal solute and a multicomponent ideal solvent. A model-free methodology, based on the Kirkwood—Buff (KB) theory of solutions, was employed. The quaternary mixture was considered as an example, and the full set of expressions for the derivatives of the chemical potentials with respect to the number of particles, the partial molar volumes, and the isothermal compressibility were derived on the basis of the KB theory of solutions. Further, the expressions for the derivatives of the activity coefficients were applied to quaternary mixtures composed of a solute and an ideal ternary solvent. It was shown that the activity coefBcient of a solute at infinite dilution in an ideal ternary solvent can be predicted in terms of the activity coefBcients of the solute at infinite dilution in subsystems (solute + the individual three solvents, or solute + two binaries among the solvent species). The methodology could be extended to a system formed of a solute + a multicomponent ideal mixed solvent. The obtained equations were used to predict the gas solubilities and the solubilities of crystalline nonelectrolytes in multicomponent ideal mixed solvents. Good agreement between the predicted and experimental solubilities was obtained. 

Therefore, it is important to have a reliable and accurate method for predicting the solubility in mrdti-component solutions from those in its pure or binary constituents. The main difficulty in predicting the solubility in multicomponent solutions consists of the calculation of the activity coefficient of the solute. Thermodynamics cannot provide the explicit pressure, temperature, and composition dependence of thermodynamic functions, such as the activity coefficients of the components in multicomponent mixtures. For this reason, empirical expressions such as the Wohl expan-sion have often been used to represent thermod5mamic data regarding multicomponent mixtures. 

The aim of the present paper is (a) to derive relations for the activity coefficients in multicomponent mixtures in terms of the KB integrals, (b) to obtain on their basis an expression for the solubility of a solute in an ideal multicomponent solvent, (c) to use the obtained equations to predict the solubilities in real systems, and (d) to compare the predicted solubilities with the experimental ones. 

Solubility of a Solid. For the solubilities of poorly soluble crystalline nonelectrolytes in a multicomponent mixed solvent, one can use the infinite-dilution approximation and consider that the activity coefficient of a solute in a mixed solvent is equal to the activity coefficient at infinite dilution. Therefore, one can write the following relations for the solubility of a poorly soluble crystalline nonelectrolyte in a ternary mixed solvent and in two of its binaries i2,i3... 

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