Binary Subsystems

Laves phases occurring in ternary systems, the binary subsystems of which contain no Laves phases, generally pertain to the hexagonal MgZn2-type structure. 

The activity coefficients of a solute in a mixed solvent could be also calculated by employing various well-known phase equilibria models, such as the Wilson, NRTL, Margules, etc., which using information for binary subsystems could predict the activity coefficients in ternary mixtures (Fan and Jafvert, 1997 Domanska, 1990). 

The binary subsystem 11 is water/methanol with mole fractions of components z eOH 1 yMeoif " and molar volume... 

The solubilities of naphthalene in the binary subsystems 1 and 11 can be calculated from Equation 23 for binary mixed solvents, which requires only the solubilities in the individual constituents of the solvent. 

From the experimental solubilities in binary solvents and molar volumes of the individual constituents. The calculation procedure is the same as above, with the exception that the solubilities of naphthalene in the binary subsystems 1 and 11 were obtained from experiment. The calculation of the solubilities in binary aqueous solvents was described in detail in previous sections. It should be noted that the water/ methanol/ 1-butanol mixed solventand the binary subsystem water/1-butanol are not completely miscible. Only the homogeneous regions of mixed solvents were considered in this paper. 

The boundary curves, coming out from the individual binary eutectic points, represent curves of the common crystallization of both components of the respective binary subsystems. All boundary curves meet at the ternary eutectic point, which is the lowest temperature where there is the liquid phase in this ternary system. 

If the excess thermodynamic properties of the three binary subsystems of the A-B-C ternary system are similar to each other, the ternary system is symmetric. If the deviation of the binary system A-B and A-C from the ideal behavior are similar, but differ markedly from that of the binary system B-C, then the A-B-C ternary system is asymmetric. In the asymmetric system the component A in two binary subsystems with thermodynamic similarity should be chosen as the thermodynamic asymmetric component. ... 

Table 3.5. Coefficients Ci of the concentration dependence of the molar excess Gibbs energy of mixing and the standard deviations of the temperature of primary crystallization in the binary subsystems of the quaternary system KF—KCl—KBF4—K2Tip6...

Sassen, C.L., Cassielles, A.G., De Loos, T.W. and De Swaan-Arons, J. (1992) The influence of pressure and temperature on the phase behavior of the system H20 + C12 + C7E5 and relevant binary subsystems. Fluid Phase Equilibria, 72, 173-187. 

The Si-B-N system was calculated in this work by extrapolation from the binary subsystems. The isothermal section at 1273 K is shown in Fig. 15. 

The Si-C-N system was calculated thermodynamically by extrapolations from the datasets for the binary subsystems. The ternary phases Si2CN4 and jS-SiC2N4 [21] are not stable at T > 1273 K and were not taken into account for... 

The ternary system was calculated by extrapolation from the binary subsystems (Kasper, 1996) [33]. The calculations cover phase equilibria at one bar and do not assume any solubilities as no experimental evidence for stable sohd solutions between B4+5C and BN or a-BN and graphite exist. The section between graphite and boron nitride including the invariant reactions Uj, Dj and U2 (Fig. 23) is shown in Fig. 22. A calculated potential phase diagram (logpN2-T) can be found in [244], The complete Scheil reaction scheme (P = 1 bar) is shown in Fig. 23. 

The principle of distillation is the use of differences in volatiHties of the components to be separated. Distillation processes are usually carried out in countercurrent mode in multistage units. The differences that can be obtained in concentrations of the components in the vapor and liquid phases are determined by the vapor-liquid equihbrium (VLE). Until the 1970s reliable data for vapor-liquid equilibria could only be obtained by measurement, which, for a mixture containing more than two components, required a large number of time-consuming measurements. Advances in chemical thermodynamics have resulted in methods activity coefficient models (g models or equations of state) for the calculation of the phase-equihbrium behavior of multicomponent mixtures on the basis of binary subsystems. In the case that no information about the binary subsystems is available, predictive methods (group contribution methods) are available to allow estimation of the required phase equilibria. 

Experimental data necessary to describe this behavior are available in large computerized data bases (e.g. Dortmund Data Bank, DDB). A small part of the data is also published in data collections (Gmehhng et al., 1977 Sorensen et al., 1979 Gmehling et al, 1986 Gmehling et al., 1988 Gmehhng et al., 2004 ). Both routes allow the calculation of VLE (see Ghapter 3.2.2.1, Sections 3.2.2.1.1 and 3.2.2.1.2) for multicomponent systems when the behavior of the binary subsystems is known. 

Fig. 4.6 Binary data fit for the six binary subsystems of the system methanol + acetic acid + methyl acetate + water at 1 bar with two variants of the UNIQUAC model. (McCabe Thiele Diagrams for p = 1 bar in mole fractions of the component appearing first in the system title)...

In the phenomenological model of Kahlweit et al. [46], the behavior of a ternary oil-water-surfactant system can be described in terms of the miscibility gaps of the oil-surfactant and water-surfactant binary subsystems. Their locations are indicated by the upper critical solution temperature (UCST), of the oil-surfactant binary systems and the critical solution temperature of the water-surfactant binary systems. Nonionic surfactants in water normally have a lower critical solution temperature (LCST), Tp, for the temperature ranges encountered in surfactant phase studies. Ionic surfactants, on the other hand, have a UCST, T. Kahlweit and coworkers have shown that techniques for altering surfactant phase behavior can be described in terms of their ability to change the miscibility gaps. One may note an analogy between this analysis and the Winsor analysis in that both involve a comparison of oil - surfactant and water-surfactant interactions. 

In addition to the experimental data, the partitioning behavior of MMA between water and CO2 has been modeled. The Peng-Robinson equation of state combined with various mixing rules as described in Section 14.4.1 has been assessed on the ability to correlate phase equilibrium data from literature of the binary subsystems CO2-H2O, MMA-CO2 and MMA-H2O. Subsequently, the model has been used to predict the phase equilibrium behavior of the ternary system CO2-H2O-MMA. Partition coefficients were calculated at four different temperatures at pressures ranging from 5 to 10 MPa. In order to provide a means for comparison, the experimentally determined partition coefficients obtained in the high-pressure extraction unit were used to evaluate the results of the predictive model for phase equilibrium behavior. 

Based on the interaction parameters for the mixing rules obtained from the binary subsystems, the ternary phase behavior has been modeled by inter- and extrapolation of the interaction parameters. Because of lack of suflicient experimental data, extrapolation is considered to be the only option in some cases, although it obviously wiU introduce errors. Table 14.7 shows the interaction parameters of the various mixing rules used for the prediction of the ternary phase behavior, whereas the resulting partition coefficients per isothermal series... 

The binary subsystem II is water/methanol with the mole fractions of components ZMeOH = xiieOH + Xpw)H aud Zhjo = and molar volume. 

A prerequisite for the correct description of the real behavior of multicomponent systems is a reliable description of the binary subsystems with the help of the fitted binary -model parameters. 

In so-called closed systems (case (a)), which are observed for about 75% of the systems, only one binary pair shows a miscibility gap. For these systems, a critical point C arises, where both liquid phases show the same concentration. Case (b) presents a system where two binary pairs show partial miscibility (open system). This behavior occurs in about 20% of all cases. Besides these most important cases, however, there are a large number of other possibilities [47]. For example, there are systems where all binary subsystems are homogeneous, but a miscibility gap (island) is found in the ternary system (see Figure 5.76). Additionally, there is the chance that three liquid phases are formed. 

Horstmann, S. Gardeler, H. Fischer, K. Koester, F. GmehUng, J. Vapor pressure, vapor-hquid equihbrium, and excess enthalpy data for compounds and binary subsystems of the chlorohydrin process for propylene oxide production J. Chem. Eng. 

Bematova, S. Wichterle, I. Isothermal vapour-Uquid equilibria in the ternary system tert-butyl methyl ether -l- tert-butanol + 2,2,4-trimethylpentane and the three binary subsystems Fluid Phase Equilib. 2001,180, 235-245... 

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