Ternary systems coefficients

Two further examples of type I ternary systems are shown in Figure 19 which presents calculated and observed selectivities. For successful extraction, selectivity is often a more important index than the distribution coefficient. Calculations are shown for the case where binary data alone are used and where binary data are used together with a single ternary tie line. It is evident that calculated selectivities are substantially improved by including limited ternary tie-line data in data reduction. 

When the relationship between the distribution coefficient of a solute and solvent composition, or the corrected retention volume and solvent composition, was evaluated for aqueous solvent mixtures, it was found that the simple relationship identified by Purnell and Laub and Katz et al. no longer applied. The suspected cause for the failure was the strong association between the solvent and water. As a consequence, the mixture was not binary in nature but, in fact, a ternary system. An aqueous solution of methanol, for example, contained methanol, water and methanol associated with water. It follows that the prediction of the net distribution coefficient or net retention volume for a ternary system would require the use of three distribution coefficients one representing the distribution of the solute between the stationary phase and water, one representing that between the stationary phase and methanol and one between the stationary phase and the methanol/water associate. Unfortunately, as the relative amount of association varies with the initial... 

Park has also obtained osmotic coefficient data for the aqueous solutions of NaOH-NaCl- NaAl(OH)4 at 25°C employing the isopiestic method (Park and Englezos, 1999 Park, 1999). The solutions were prepared by dissolving AlCl r6H20 in aqueous NaOH solutions. The osmotic coefficient data were then used to evaluate the unknown Pitzer s binary and mixing parameters for the NaOH-NaCI-NaAl(OH)4-H20 system. The binary Pitzer s parameters, [3(0), P0). and C9, for NaAI(OH)4 were found to be -0.0083, 0.0710, and 0.00184 respectively. These binary parameters were obtained from the data on the ternary system because it was not possible to prepare a single (NaAl(OH)4) solution. 

Carbon dioxide supply, for the molten carbonate fuel cell, 72 220 Carbon dioxide ternary systems, phase behavior of, 24 4—5 Carbon diselenide, 22 75t Carbon disulfide, 4 822-842 23 567, 568, 621. See also CS2 in cellulose xanthation, 77 254 chemical reactions, 4 824—828 diffusion coefficient in air at 0° C, 7 70t economic aspects, 4 834-835 electrostatic properties of, 7 621t handling, shipment, and storage, 4 833-834... 

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. 

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. 

Values of a diffusion coefficient matrix, in principle, can be determined from multicomponent diffusion experiments. For ternary systems, the diffusivity matrix is 2 by 2, and there are four values to be determined for a matrix at each composition. For quaternary systems, there are nine unknowns to be determined. For natural silicate melts with many components, there are many unknowns to be determined from experimental data by fitting experimental diffusion profiles. When there are so many unknowns, the fitting of experimental concentration... 

Polymer transport in ternary systems including an analysis of the cross diffusion coefficients and component distribution within the systems. 

In comparison with the qualitative description of diffusion in a binary system as embodied by Eqs. (11), (12) or (14), the thermodynamic factors are now represented by the quantities a, b, c, and d and the dynamic factors by the phenomenological coefficients which are complex functions of the binary frictional coefficients. Experimental measurements of Dy in a ternary system, made on the basis of the knowledge of the concentration gradients of each component and by use of Eqs. (21) and (22), have been reviewed 35). Another method, which has been used recently36), requires the evaluation of py from thermodynamic measurements such as osmotic pressure and evaluation of all fy from diffusion measurements and substitution of these terms into Eqs. (23)—(26). 

The rapid transport of the linear, flexible polymer was found to be markedly dependent on the concentration of the second polymer. While no systematic studies were performed on these ternary systems, it was argued that the rapid rates of transport could be understood in terms of the dominance of strong thermodynamic interactions between polymer components overcoming the effect of frictional interactions this would give rise to increasing apparent diffusion coefficients with concentration 28-45i. This is analogous to the resulting interplay of these parameters associated with binary diffusion of polymers. 

As the dextran concentration is further increased in the ternary system, the transport coefficient values often pass through a maximum, a second transitional point, and then... 

Fig. 16. Graphically smoothed data for calculated ternary diffusion coefficients in a system with a uniform concentration of dextran T500 (Hw 500,000) with an imposed 5 kg m-3 concentration gradient of PVP 360 the dextran concentration is varied...

When all ternary diffusion coefficients are known, we can predict the concentration gradients of all components35 > and therefore density gradients in the system at any time. 

In the ternary system, therefore, the diffusional flux of water is determined by two of the ternary diffusional coefficients. For a binary system, it was shown earlier that the mutual diffusion of solvent and solute is identical and essentially independent of the magnitude of the osmotic pressure gradient across the boundary 30). 

Figure 3.3 Illustration of the calculation of the phase diagram of a mixed biopolymer solution from the experimentally determined osmotic second virial coefficients. The phase diagram of the ternary system glycinin + pectinate + water (pH = 8.0, 0.3 mol/dm3 NaCl, 0.01 mol/dm3 mercaptoethanol, 25 °C) —, experimental binodal curve —, calculated spinodal curve O, experimental critical point A, calculated critical point O—O, binodal tielines AD, rectilinear diameter,, the threshold of phase separation (defined as the point on the binodal curve corresponding to minimal total concentration of biopolymer components). Reproduced from Semenova et al. (1990) with permission.

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. 

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. 

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