Ternary systems activity coefficients

For the ternary system, activity coefficients for each species in each liquid phase are computed from (5-33) for the given phase compositions in the manner of Example 5.5. Results are... 

Since there are no additional constants which are characteristic only of the ternary systems, then knowledge of the three binary systems alone permits calculation of the ternary-mixture activity coefficients. It is most important to note that, for even this most simple of situations, ordinary interpolation of the binary-solution data is not possible. Simple interpolation of the log y s would be valid only if the —Abci and --Aab... 

The stabiHty criteria for ternary and more complex systems may be obtained from a detailed analysis involving chemical potentials (23). The activity of each component is the same in the two Hquid phases at equiHbrium, but in general the equiHbrium mole fractions are greatiy different because of the different activity coefficients. The distribution coefficient m based on mole fractions, of a consolute component C between solvents B and A can thus be expressed... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

A wide variety of data for mean ionic activity coefficients, osmotic coefficients, vapor pressure depression, and vapor-liquid equilibrium of binary and ternary electrolyte systems have been correlated successfully by the local composition model. Some results are shown in Table 1 to Table 10 and Figure 3 to Figure 7. In each case, the chemical equilibrium between the species has been ignored. That is, complete dissociation of strong electrolytes has been assumed. This assumption is not required by the local composition model but has been made here in order to simplify the systems treated. 

There can be many different types of ternary electrolyte systems. The HCI-KCI-H2O system is an example of a two-electrolyte, one-solvent ternary electrolyte systems. Some data correlation results for the activity coefficients of salts in ternary electrolyte systems of this type are shown in Table 7 and Figure 7. Water-electrolyte binary parameters were obtained from Table 1. 

A second type of ternary electrolyte systems is solvent -supercritical molecular solute - salt systems. The concentration of supercritical molecular solutes in these systems is generally very low. Therefore, the salting out effects are essentially effects of the presence of salts on the unsymmetric activity coefficient of molecular solutes at infinite dilution. The interaction parameters for NaCl-C02 binary pair and KCI-CO2 binary pair are shown in Table 8. Water-electrolyte binary parameters were obtained from Table 1. Water-carbon dioxide binary parameters were correlated assuming dissociation of carbon dioxide in water is negligible. It is interesting to note that the Setschenow equation fits only approximately these two systems (Yasunishi and Yoshida, (24)). 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

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 ( )... 

Figure 6 compares experimental and calculated activity coefficients of water in the ternary system at 25°C and a total molality of 3.0. Equation 18 was used to express the experimental activity coefficients. Agreement between experimental and calculated values is surprisingly good considering that Equation 19 contains no ternary parameters. The activity coefficient of water in the HC1-NaCl -H O system is not a strong function of composition, and Equation T9 provides an adequate description of the activity coefficients. 

We have presented a thermodynamic technique which is useful for the correlation of thermodynamic data of aqueous electrolyte systems in the concentrated region. The approach was illustrated using the ternary system of HC1-NaCl-H20. The correlation gives a good description of solid-liquid and vapor-1iquid equilibria the two ternary parameters required to calculate the activity coefficients of the electrolytes are simple functions of the temperature and the total molality. 

Bendova, M., Rehak, K.. Matous, J., and Novak, J.P. Liquid + liquid equilibrium in the ternary systems water + ethanol + dialkyl phthalate (dimethyl, diethyl, and dibutyl phthalate) at 298.15 K, /. Chem. Eng. Data, 46(6) 1605-1609, 2001. Benes M. andDohnal, V. Limiting activity coefficients ofsome aromatic and aliphatic nitrocompounds in water, / Chem. Eng. Data, 44(5) 1097-1102, 1999. 

A common sitnation is that the electrolyte is completely dissociated in the aqueons phase and incompletely, or hardly at all, in the organic phase of a ternary solvent extraction system (cf. Chapter 3), since solvents that are practically immiscible with water tend to have low valnes for their relative permittivities e. At low solnte concentrations, at which nearly ideal mixing is to be expected for the completely dissociated ions in the aqneons phase and the undissociated electrolyte in the organic phase (i.e., the activity coefficients in each phase are approximately nnity), the distribntion constant is given by... 

The activity coefficients can be calculated using any of the existing models if the binary parameters for all combinations of binary pairs are known. These parameters are obtained by fitting to experimental data. For ternary systems, one can either simultaneously fit all six parameters or first determine the parameters using binary data for those binary systems that have a phase separation and the rest of the parameters from ternary data. 

It may be conjectured that collective behavior implies that the surfactants that make up the mixture are not too different, the presence of an intermediate being a way to reduce the discrepancy. When the activity coefficient is calculated from non-ideal models it is often taken to be proportional to the difference in solubihty parameters [42,43], which in case of a binary is the difference (3i - if the system is multicomponent, then the dil -ference is - Sm) y which is often less, because the mean value exhibits an average lower deviation. In other terms, it means that for a ternary in which the third term is close to the average of the two first terms, then the introduction of the third component reduces the nonideahty because (5i - 53) + ( 2 - < (5i - 52) -... 

For the systems with alcohols, the description of SLE given by the UNIQUAC ASM equation (assuming the association of alcohols) did not provide any better results. It can be understood as a picture of a very complicated interaction between the molecules in the solution it means that it exists not only in the association of alcohol molecules but also between alcohol and IL molecules and between IL molecules themselves. Parameters shown in Table 1.7 may be helpful to describe activity coefficients for any concentration, temperature, and to describe ternary mixtures. They are also useful for the complete thermod5mamic description of the solution. 

In the present study, systems composed of two solvents and a salt are treated as ternary systems. Data on the vapor pressure depression of the solvent by the salt for isothermal systems and on the boiling point elevation of the solvent in the presence of salt for isobaric systems are used to develop the parameters for the solvent-salt binaries. For such binaries only the activity coefficients for the solvent are considered. The parameters for all three binary sets are generated from the binary data by a regression subroutine. 

As seen from Equation 3 only binary parameters are needed for the determination of the ternary activity coefficients, and two parameters per binary system are needed. 

Turning now to the solvent-solvent binary, the effect of the value of a 2 on the quality of the obtained fit is well established (12,16). Since this binary had the largest number of experimental activity coefficients—for the solvent-salt binaries only the y of the solvent is used—it was decided to let a vary between +1.0 and —3.0 with the best fit of the ternary data as criterion for its optimum value. The possibilities of varying the other two as (ai3 and 23) to obtain the best ternary fit was rejected although it would probably lead to better correlation of the ternary results, it could not lead to any predictive scheme. The number of available systems is simply too limited for the establishment of optimum a values for all three binaries. 

For systems of the type under consideration, that is, consisting of two volatile components and a salt, there has been controversy over whether binary or ternary forms of correlating equations should be used, and over whether the presence of the salt should be included in the liquid mole fraction data used to calculate liquid activity coefficient values for the two volatile components. One point, however, is absolutely clear. It would be thermodynamically incorrect not to acknowledge the presence of the salt in calculating liquid-phase activity coefficients. 

Jaques and Furter (37,38,39,40) devised a technique for treating systems consisting of two volatile components and a salt as special binaries rather than as ternary systems. In this pseudo binary technique the presence of the salt is recognized in adjustments made to the pure-component vapor pressures from which the liquid-phase activity coefficients of the two volatile components are calculated, rather than by inclusion of the salt presence in liquid composition data. In other words, alteration is made in the standard states on which the activity coefficients are based. In the special binary approach as applied to salt-saturated systems, for instance, each of the two components of the binary is considered to be one of the volatile components individually saturated with the... 

With the use of thermodynamic relations and numerical procedure, the activity coefficients of the solutes in a ternary system are expressed as a function of binary data and the water activity of the ternary system. The isopiestic method was used to obtain water activity data. The systems KCl-H20-PEG-200 and KBr-H20-PEG-200 were measured. The activity coefficient of potassium chloride is higher in the mixed solvent than in pure water. The activity coefficient of potassium bromide is smaller and changes very little with the increasing nonelectrolyte concentration. PEG-200 is salted out from the system with KCl, but it is salted in in the system with KBr within a certain concentration range. 

His procedure was used for the calculation of the activity coefficients in the aqueous solution of two electrolytes with a common ion from isopiestic data (3). Kelly, Robinson, and Stokes (4) proposed a treatment of isopiestic data of ternary systems with two electrolytes by a procedure based on the assumption that at all values of molal concentrations, mi,m2, the partial derivatives may be expressed by a sum of two functions in their differential form as follows ... 

The Calculation of Activity Coefficients in the Ternary System. The polynomial with 10 constants was used to describe the experimental quantity A(m 1,7712) in the whole concentration range... 

Table VIII. Activity Coefficient of PEG-200 in the Ternary System...

The trend of activity coefficients of potassium chloride and potassium bromide is different in measured mixed solvent. The activity coefficient of potassium chloride is higher in the mixed solvent than in the pure water and rises smoothly with the nonelectrolyte content. The minimum value, about 2.0-3.0m in pure water, can be observed in the mixed solvent also. Because of the activity coefficient of the nonelectrolyte in the ternary system (also higher than that in pure water), both components are mutually salted out. 

Experimental data on only 26 quaternary systems were found by Sorensen and Arlt (1979), and none of more complex systems, although a few scattered measurements do appear in the literature. Graphical representation of quaternary systems is possible but awkward, so that their behavior usually is analyzed with equations. To a limited degree of accuracy, the phase behavior of complex mixtures can be predicted from measurements on binary mixtures, and considerably better when some ternary measurements also are available. The data are correlated as activity coefficients by means of the UNIQUAC or NRTL equations. The basic principle of application is that at equilibrium the activity of each component is the same in both phases. In terms of activity coefficients this... 

To illustrate the system behavior, the ternary mixture 1 = iso-propanol, 2 = water, and 3 = air is considered here. In order to obtain an algebraic solution, both the dif-fusivities of iso-propanol in air and iso-propanol in water vapor were assumed to be approximately the same, which is not far from reality. The liquid phase mass transfer resistance was negligibly small, as will be shown below. The phase equilibrium constants K/,c and Kjrs were calculated with activity coefficients from van Laar s equation. Water vapor diffuses 2.7-fold faster in the inert gas air than iso-propanol. The ratio of the respective mass transfer coefficients kj3 equals the ratio of the respective diffusivities to the power of 2/3rd according to standard convective mass transfer equations Sh =J Re, Sc). 

In fact, there is an apparent excess of constraint equations for a ternary system four equations in the three unknown activity coefficients. The excess is removed, however, by noting that the closure relation in Eq. 5.31 can be applied to the three replicates of Eq. 5.34 ... 

It is important to emphasize that N-ary ion exchange relationships which do not enjoy thermodynamic status must be examined case by case to determine whether they can be built up from binary exchange data. For example, there is no reason to expect any conditional equilibrium constant Kijc to remain invariant under changes in the composition of an ion exchange system from binary to ternary. As another example, one can pose (he question as to whether binary exchange data for adsorbed species activity coefficients can be used, in... 

These equations can be solved for the coefficients c, d 0, c, and d 0 in terms of the infinite-dilution activity coefficients (which are binary-system properties), but the solution will not be unique. Equation 5.48d, connecting the ternary second-order Margules expansion coefficients to the binary infinite-dilution activity coefficients, shows that a constant (say, c0) can be added to any c and c[Pg.202]

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