Ternary systems experimental data

Binary data can be represented with a T—x diagram that shows the mutual solubility as function of temperature. Most of the binary systems belong to one of the classes in Fig. 10.1. For ternary systems, experimental data are usually obtained at constant temperature and given in ternary diagrams. There are many types of systems, but more than 95% belong to one of the two classes shown in Fig. 10.1. 

The explicit expressions for the chemical potential derivatives, partial molar volumes, and isothermal compressibility become rather cumbersome for ternary systems. Experimental data are also much less common. However, there are many interesting effects that involve ternary systems (see Chapter 4). Also, we shall see that considerable simplification is obtained when one of the components is at infinite dilution (see Chapters 10 and 11). If one requires specific expressions for the various properties, it will prove convenient to define the following set of variables (Smith 2006a),... 

To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good. 

The vapor is thea withdrawa from the stiH as distillate. The changing Hquid composition is most coavenieafly described by foUowiag the trajectory (or residue curve) of the overall composition of all the coexistiag Hquid phases. An exteasive amouat of valuable experimental data for the water—acetoae—chloroform mixture, including biaary and ternary LLE, VLE, and VLLE data, and both simple distillation and batch distillation residue curves are available (93,101). Experimentally determined simple distillation residue curves have also been reported for the heterogeneous system water—formic acid—1,2-dichloroethane (102). 

For the first time through a liqmd-liquid extrac tion problem, the right-triangular graphical method may be preferred because it is completely rigorous for a ternary system and reasonably easy to understand. However, the shortcut methods with the Bancroft coordinates and the Kremser equations become valuable time-savers for repetitive calculations and for data reduction from experimental runs. The calculation of pseudo inlet compositions and the use of the McCabe-Thiele type of stage calculations lend themselves readily to programmable calculator or computer routines with a simple correlation of equilibrium data. 

In order to make any practical use of this equation, a good deal of experimental data are usually required for a ternary system, and it will be found that, at present, such data are seldom available in the literature. The methods of evaluation of such data are fully described in the works of Chipman and Elliott and of Schuhmann . 

A classic example of where definitive experimental data necessitated refinement and extension of a model of drug-receptor interaction involved the discovery of constitutive receptor activity in GPCR systems. The state of the art model before this finding was the ternary complex model for GPCRs, a model that cannot accommodate ligand-independent (constitutive) receptor activity. 

In this work, a comprehensive kinetic model, suitable for simulation of inilticomponent aiulsion polymerization reactors, is presented A well-mixed, isothermal, batch reactor is considered with illustrative purposes. Typical model outputs are PSD, monomer conversion, multivariate distritution of the i lymer particles in terms of numtoer and type of contained active Chains, and pwlymer ccmposition. Model predictions are compared with experimental data for the ternary system acrylonitrile-styrene-methyl methacrylate. 

Model predictions are caipared with experimental data In the case of the ternary system acrylonitrlle-styrene-methyl methacrylate. Ihe experimental runs have been performed with the same recipe, but monomer feed composition. A glass, thermostat ted, well mixed reactor, equipped with an anchor stirrer and four baffles, has been used. The reactor operates under nitrogen atmosphere and a standard degassing procedure is performed Just before each reaction. The same operating conditions have been maintained in all runs tenperature = 50°C, pressure = 1 atm, stirring speed = 500 rpm, initiator (KgSgOg) 0. 395 gr, enulsifier (SLS) r 2.0 gr, deionized water = 600 gr, total amount of monomers = 100 gr. 

Equilibrium data are thus necessary to estimate compositions of both extract and raffinate when the time of extraction is sufficiently long. Phase equilibria have been studied for many ternary systems and the data can be found in the open literature. However, the position of the envelope can be strongly affected by other components of the feed. Furthermore, the envelope line and the tie lines are a function of temperature. Therefore, they should be determined experimentally. The other shapes of the equilibrium line can be found in literature. Equilibria in multi-component mixtures cannot be presented in planar graphs. To deal with such systems lumping of consolutes has been done to describe the system as pseudo-ternary. This can, however, lead to considerable errors in the estimation of the composition of the phases. A more rigorous thermodynamic approach is needed to regress the experimental data on equilibria in these systems. 

FIGURE 3.14 Ternary phase diagram of (Zr,Y)02-La203-Mn304 system at 1400°C in air. (Zr,Y)02 denotes 3 mol% Y203-Zr02. Symbols + are the experimental data. (From Jiang, S.P. et al., J. Euro. Ceram. Soc., 23 1865-1873, 2003. With permission.)... 

Chapter 18 - The determination region of solubility of methanol with gasoline of high aromatic content was investigated experimentally at temperature of 288.2 K. A type 1 liquid-liquid phase diagram was obtained for this ternary system. These results were correlated simultaneously by the UNIQUAC model. By application of this model and the experimental data the values of the interaction parameters between each pair of components in the system were determined. This revealed that the root mean square deviation (RMSD) between the observed and calculated mole percents was 3.57% for methylcyclohexane + methanol + ethylbenzene. The mutual solubility of methylcyclohexane and ethylbenzene was also demostrated by the addition of methanol at 288.2 K. 

The long-range term has been satisfactorily described by the Debye-Huckel formula and is retained. The short-range contribution is modeled by utilizing the concept of local compositions in a manner similar to Renon and Prausnitz (20) but with additional assumptions appropriate for electrolyte systems. Preliminary results suggest the validity of the model since good fits to experimental data have been obtained for a wide range of binary and ternary systems with only binary parameters. 

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 ( )... 

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... 

In addition to the experimental results of phase equilibria, the correlation with the widely known GE models was assigned to. It was indicated by many authors that SLE, LLE, and VLE data of ILs can be correlated by Wilson, NRTL, or UNIQUAC models [52,54,64,79,91-101,106,112,131,134]. For the LLE experimental data, the NRTL model is very convenient, especially for the SLE/LLE correlation with the same binary parameters of nonrandom two-liquid equation for mixtures of two components. For the binary systems with alcohols the UNIQUAC equation is more adequate [131]. For simplicity, the IL is treated as a single neutral component in these calculations. The results may be used for prediction in ternary systems or for interpolation purposes. In many systems it is difficult to obtain experimentally the equilibrium curve at very low solubilities of the IL in the solvent. Because this solubility is on the level of mole fraction 10 or 10 , sometimes only... 

In the notation used here, congruently melting, narrow-homogeneity-range compounds form in the A-C and B-C binaries of the A-B-C system. These are, of course, the Ga-Sb and In-Sb binaries for the Ga-In-Sb system and the Hg-Te and Cd-Te binaries for the Hg-Cd-Te system. For these binaries it is desired to apply the auxiliary conditions of Eqs. (16) and (17) as well as fit other experimental data before fitting the liquidus lines and then the ternary data. For this purpose it is necessary to carry the development of the model somewhat further. At the same time some insight into the behavior of the model can be attained. We show this development specifically for the A-C or... 

Lecat (32) is responsible for most of the azeotropic data on binary and ternary systems. Recently, however, Horsley (25) has compiled extensive tables of azeotropic data, thus making the information more available. These experimental data may be supplemented by estimations of the azeotropic composition and behavior of unknown systems by several reasonably reliable methods. Graphical methods, based on curves developed from experimental data, have been proposed by Lecat (82), Mair et al. (.ffi), Horsley (26), Skol-... 

Because of the limitations of the Margules equation—especially in predicting multicomponent VLE data—the Wilson, NRTL, and LEMF (16) equations are employed in this study. The experimental data on the systems presented in Table I were used in this work. These are the only systems for which both binary and ternary data could be found in the literature. As a matter of fact, uncertainties do exist about the accuracy of the two HgC systems. The maximum boiling... 

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... 

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