Ideal Ternary System

PSPS of reactive membrane separation with diagonal [/c]-matrix 

For a more generalized analysis of the qualitative influence of membranes on the singular points, the reactive membrane separation process is now considered with a nondiagonal [/c]-matrix. The condition for a kinetic arheotropes is given by 

It is easy to show that Eq. (103) can be cast into the following quadratic form  

In the composition triangle, Eq. (104) describes a second-order surface the shape of which is fixed by the signs of the eigenvalues Ai and Aj of the symmetric matrix [A], The following cases can be distinguished  

For the special case with a diagonal [ c], Eqs. (116a—f) can be reduced to 

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Fig. 4.2. Potential singular point surfaces (dashed-dotted curve) for an ideal ternary system with single reaction A + B C. (a) Ellipse-type system (b) hyperbola-type system. RA = reactive azeotrope solid curve = chemical equilibrium surface.

Figure A.2 (left) shows the construction of a distillation for an ideal ternary system in which A and C are the light (stable node) and the heavy (unstable node) boilers, while B is an intermediate boiler (saddle). The initial point xiA produces the vapor y, that by condensation gives a liquid with the same composition such that the next point is xi 2 = y,, etc. Accordingly, the distillation line describes the evolution of composition on the stages of a distillation column at equilibrium and total reflux from the bottom to the top. The slope of a distillation line is a measure of the relative volatility of components. The analysis in RCM or DCM leads to the same results.

The KB integrals for an ideal ternary system have been obtained in our previous paper [18], They are (vol/mol)... 

Let us consider an ideal ternary system A-B-C. In this case Eq. (3.190) must be valid for all the three components. From the integral form of Eq. (3.190) for the components A and B, the equation of a projection of the monovariant line of the simultaneous crystallization of these components, E-P in Figure (3.50), can be derived... 

Fig. 5.15. Singular points for ideal ternary system A + B C, chemical equilibrium constant K = 5.0, relative volatilities = 5.0, — 3.0 at different...

The Maxwell-Stefan equations can be extended in a straightforward fashion to ternary and multiconponent systems. For an ideal ternary system, the basic equations are... 

Unfortunately, the same condition does not hold for the Fickian diffusivities. In an ideal ternary system, the values for the Fickian diffusivities are not equal to the values of the Fickian binary pairs. 

P8.10 Determine the solid-liquid equilibrium temperature of the ideal ternary system m-xylene (l)-o-xylene (2)-p-xylene (3) for a composition ofxi = 0.1 and X2 =0.1 with the help of the melting temperatures and enthalpies of fusion given in Example 8.4 in the textbook. Which component will crystallize ... 

Figure 11.11 Composition as a function of time for two ternary systems in the case of open distillation at atmospheric pressure. Ideal ternary system with a low, intermediate and high-boiling compound (a). Ternary system acetone-benzene-cyclohexane (b).

For an ideal ternary system where practically only the solute is soluble in both phases, the design of an extraction process is straightforward. As shown by... 

The first three chapters have explored in a fair amount of detail the four-component quaternary system with the reaction A + B C + D. This system has two reactants and two products. In the next two chapters we will study various aspects of two other types of ideal chemical systems. In Chapter 4 we investigated the impact of a number of kinetic and design parameters on the ideal ternary system with the reaction A + B C with and without inerts in the system. In Chapter 5 we study systems with the reaction A4=> B + C in which there is only one reactant but two products. We will illustrate that the chemistry has an important effect on how the many kinetic and design parameters impact the reactive distillation column. 

Structure. The control stmcture is shown in Figure 15.5. This stmcture is similar to that used in the ideal ternary system with inerts, which was studied in Chapter 12. It consists of the following loops ... 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

For a binary mixture under constant pressure conditions the vapour-liquid equilibrium curve for either component is unique so that, if the concentration of either component is known in the liquid phase, the compositions of the liquid and of the vapour are fixed. It is on the basis of this single equilibrium curve that the McCabe-Thiele method was developed for the rapid determination of the number of theoretical plates required for a given separation. With a ternary system the conditions of equilibrium are more complex, for at constant pressure the mole fraction of two of the components in the liquid phase must be given before the composition of the vapour in equilibrium can be determined, even for an ideal system. Thus, the mole fraction yA in the vapour depends not only on X/ in the liquid, but also on the relative proportions of the other two components. 

Figure 7.12 shows the liquidus surface of a ternary system with complete miscibility at solid state between components 1-2 and complete immiscibility at solid state between components 1-3 and 2-3. Note also that components 1 and 2 form a lens-shaped two-phase field, indicating ideality in the various aggregation states (Roozeboom type I). 

The main areas of application for more generalised models have, until recently, been restricted to binary and ternary systems or limited to ideal industrial materials where only major elements were included. The key to general application of CALPHAD methods in multi-component systems is the development of sound, validated thermodynamic databases which can be accessed by the computing software and, until recently, there has been a dearth of such databases. 

The problem of predicting multicomponent adsorption equilibria from single-component isotherm data has attracted considerable attention, and several more sophisticated approaches have been developed, including the ideal adsorbed solution theory and the vacancy solution theory. These theories provide useful quantitative correlations for a number of binary and ternary systems, although available experimental data are somewhat limited. A simpler but purely empirical approach is to use a modified form of isotherm expression based on Langmuir-Freundlich or loading ratio correlation equations ... 

If the liquid mixture is extremely non-ideal, liquid phase splitting will occur. Here, we first consider the hypothetical ternary system. The physical properties are adopted from Ung and Doherty [17] and Qi et al. [10]. The catalyst is assumed to have equal activity in the two liquid phases. The corresponding PSPS is depicted in Fig. 4.5, together with the liquid-liquid envelope and the chemical equilibrium surface. The PSPS passes through the vertices of pure A, B, C, and the stoichiometric pole Jt. The shape of the PSPS is affected significantly by the liquid phase non-idealities. As a result, there are three binary nonreactive azeotropes located on... 

To illustrate the above method for calculating the excess number of molecules near a central one, the ternary system A,A-dimethylformamide-methanol-water and the corresponding binary mixtures will be considered. This mixture was previously examined in the framework of the KB theory of solutions [24,25]. However, in [24,25] the calculations have been carried out without an appropriate reference state. The use of a reference state is important for this particular mixture, because it deviates slightly from ideality [10] and, consequently, Gjf and Gj are not negligible compared to Gji. ... 

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. 

From the results of the physico-chemical analysis, it follows that deviations from the ideal behavior were observed in all the boundary binaries as well as in the ternary system. With regard to the fact that the investigated system has a common cation, the observed deviations from the ideal behavior have to be a consequence of the anionic interaction only. The observed interaction of components could be of different origin. A different character of interaction has to be considered in the boundary binaries KF-KBF4 and KCI-KBF4. 

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. ... 

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