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Mixtures, ternary

Extending the relationship given in equation (10) to a ternary mixture of solvents (A), (B) and (C) [Pg.115]

Equation (16) was tested against some data obtained for (R) 4-phenyl-2-oxazolidinone using a range of mixtures of ethanol, acetonitrile and -hexane as the mobile phase. The column chosen was similar to that previously used for the separation of the 4-phenyl-2-oxazolidinone which was 25 cm long, 4.6 mm I.D. packed with 5 mm silica particles bonded with the stationary phase Vancomycin. The results obtained are shown in Table 1 and this is the data used in subsequent computer calculations. [Pg.115]

The range of concentrations that could be used was somewhat restricted due to the immiscibility of certain solvent mixtures. The data given in Table 1 was fitted to equation (16) and the various constants determined. Employing the constants derived from the curve fitting process, the theoretical values for the retention volumes, at the [Pg.115]

Marcel Dekker, Inc. 270 Madison Avenue, New York, New York 10016 [Pg.115]

It is seen that there is a good correlation between experimental and calculated values. The scatter that does exist may be due to the dead volume of the column not being precisely independent of the solvent composition. The dead volume will depend, to a small extent, on the relative proportion of the different solvents adsorbed on the stationary phase surface, which will differ as the solvent composition changes. A constant value for the dead volume was assumed in the computer program that derived the equation. [Pg.116]

In this section, we consider the phase behavior of systems with three components. The Gibbs phase rule for a ternary mixture is [Pg.34]

A ternary system can have at most four degrees of freedom, which occurs when there is only one phase present (i.e., tt = 1). At a given temperature and pressure, only the composition of a ternary system needs to specified to fix its state. [Pg.34]

Some typical phase behavior that can be exhibited by ternary mixtures is shown in Fig. 3.11. Let us consider a situation where binary mixtures of component 1 and component 2 are only partially miscible, where two coexisting liquid phases may be formed one rich in 1 and the other rich in 2. This is represented by the base of the ternary phase diagram shown in Fig. 3.11a. In addition, let us assume that components 1 and 3 are completely miscible and components 2 and 3 are also completely miscible. For this case, one might expect that if enough of component 3 is added to the system, then components 1 and 2 can be made to mix with each other, due to their mutual solubility with component 3. This is type I phase behavior. [Pg.34]

A type II phase diagram, shown in Fig. 3.1 lb, corresponds to a situation where components I and 3 are completely miscible, but both components 1 and 2 and components 2 and 3 are only partially miscible. [Pg.35]

Finally, type III phase behavior is shown in Fig. 3.lie. In tliis case, the various binary mixtures of the three components are each only partially miscible. The shaded triangle in the center of the phase diagram is a region where three phases are in coexistence with each other. Systems with a composition which lies within this shaded triangle will split into three separate phases the composition of each of these phases corresponds to one of tlie comers of the triangle. The composition of the individual phases will not vary with the system s location within the triangle (i.e., its overall composition) however, the relative amounts of each of the phases will. [Pg.35]

In this section we briefly describe some of the phase behavior that has been observed in ternary mixtures. When three components are present, mixtures can exhibit a wealth of phase behavior, including equilibria among solid, gas, and multiple liquid phases. We have space here only to show the most common diagrams ( 9.6.1) observed for simple liquid-liquid ( 9.6.2) and vapor-liquid ( 9.6.3) equilibria. More extensive descriptions can be found elsewhere [5,17]. [Pg.405]

Phase equilibria for ternary mixtures are conventionally represented on equilateral triangular diagrams. Such diagrams provide a convenient way to present basic material balance relations these are reviewed in Appendix H. Triangular diagrams are T diagrams, and for C = 3 components, (9.1.12) gives [Pg.405]

To determine the number of properties needed to identify the state, we apply the phase rule (9.1.13) for ternaries at fixed T and P, it becomes [Pg.405]

So a one-phase ternary has T = 2 these states span areas on a triangular diagram. At fixed T and P, a two-phase ternary has T = 1, which defines a line. Two-phase lines appear in pairs, each giving the composition of one phase. Areas between two-phase lines are traversed by tie lines, and, if the overall mole fractions are known, the relative amounts in the two phases can be found by lever rules. [Pg.405]

At fixed T and P, a three-phase ternary has P = 0, which defines a point. On a triangular diagram, a three-phase situation produces three points, each giving the composition of one of the phases. The three points can be connected to form a triangle, and the relative amounts in the three phases can be found by a tie-triangle rule (see Appendix H). [Pg.405]


Using UNIQUAC, Table 2 summarizes vapor-liquid equilibrium predictions for several representative ternary mixtures and one quaternary mixture. Agreement is good between calculated and experimental pressures (or temperatures) and vapor-phase compositions. ... [Pg.53]

Figure A2.5.30. Left-hand side Eight hypothetical phase diagrams (A through H) for ternary mixtures of d-and /-enantiomers with an optically inactive third component. Note the syimnetry about a line corresponding to a racemic mixture. Right-hand side Four T, x diagrams ((a) tlirough (d)) for pseudobinary mixtures of a racemic mixture of enantiomers with an optically inactive third component. Reproduced from [37] 1984 Phase Transitions and Critical Phenomena ed C Domb and J Lebowitz, vol 9, eh 2, Knobler C M and Scott R L Multicritical points in fluid mixtures. Experimental studies pp 213-14, (Copyright 1984) by pennission of the publisher Academic Press. Figure A2.5.30. Left-hand side Eight hypothetical phase diagrams (A through H) for ternary mixtures of d-and /-enantiomers with an optically inactive third component. Note the syimnetry about a line corresponding to a racemic mixture. Right-hand side Four T, x diagrams ((a) tlirough (d)) for pseudobinary mixtures of a racemic mixture of enantiomers with an optically inactive third component. Reproduced from [37] 1984 Phase Transitions and Critical Phenomena ed C Domb and J Lebowitz, vol 9, eh 2, Knobler C M and Scott R L Multicritical points in fluid mixtures. Experimental studies pp 213-14, (Copyright 1984) by pennission of the publisher Academic Press.
As early as 1969, Wlieeler and Widom [73] fomuilated a simple lattice model to describe ternary mixtures. The bonds between lattice sites are conceived as particles. A bond between two positive spins corresponds to water, a bond between two negative spins corresponds to oil and a bond coimecting opposite spins is identified with an amphiphile. The contact between hydrophilic and hydrophobic units is made infinitely repulsive hence each lattice site is occupied by eitlier hydrophilic or hydrophobic units. These two states of a site are described by a spin variable s., which can take the values +1 and -1. Obviously, oil/water interfaces are always completely covered by amphiphilic molecules. The Hamiltonian of this Widom model takes the form... [Pg.2379]

An important example is the one-order-parameter model invented by Gompper and Schick [77], which describes a ternary mixture in temis of the density difference between water and oil ... [Pg.2380]

Most characteristics of amphiphilic systems are associated with the alteration of the interfacial stnicture by the amphiphile. Addition of amphiphiles might reduce the free-energy costs by a dramatic factor (up to 10 dyn cm in the oil/water/amphiphile mixture). Adding amphiphiles to a solution or a mixture often leads to the fomiation of a microenuilsion or spatially ordered phases. In many aspects these systems can be conceived as an assembly of internal interfaces. The interfaces might separate oil and water in a ternary mixture or they might be amphiphilic bilayers in... [Pg.2381]

Explicit expressions for the fluxes can also be found in the case of a ternary mixture, though they are appreciably more complicated than those for a binary mixture. The best starting point is equations (5.7) and (5.8). When there are three components in the mixture it is easy to check that equations (5,8) and the condition = 0 are satisfied by... [Pg.45]

All the experimental teats described so far have been confined to binary mixtures, but of course it is also desirable to know whether flux relations adequate in binary mixtures are still successful in mixtures with more than two components. Even in the case of ternary mixtures the form of explicit flux relations is very complex, and a complete investigation of the various matrix elements, in their dependence on both pressure and composition, would be a forbidding undertaking. Nevertheless some progress in this direction has beet made by Hesse and Koder [55] and by Remick and Geankoplis [56]. [Pg.98]

The use of a ternary mixture in the drying of a liquid (ethyl alcohol) has been described in Section 1,5 the following is an example of its application to the drying of a solid. Laevulose (fructose) is dissolved in warm absolute ethyl alcohol, benzene is added, and the mixture is fractionated. A ternary mixture, alcohol-benzene-water, b.p. 64°, distils first, and then the binary mixture, benzene-alcohol, b.p. 68-3°. The residual, dry alcoholic solution is partially distilled and the concentrated solution is allowed to crystallise the anhydrous sugar separates. [Pg.144]

Binary mixtures of Ga + and Mg +, and ternary mixtures of Ga +, Mg +, and Ba + are determined by titrating with EDTA. The progress of the titration is followed thermometrically. Gomplexation of Ga + and Ba + with EDTA is exothermic, whereas complexation of Mg + with EDTA is endothermic. As EDTA is added, the temperature initially rises due to the complexation of Ga +. The temperature then falls as Mg + is titrated, rising again as Ba + is titrated. [Pg.359]

Solvent triangle for optimizing reverse-phase HPLC separations. Binary and ternary mixtures contain equal volumes of each of the aqueous mobile phases making up the vertices of the triangle. [Pg.582]

Ternary Blends. Discussion of polymer blends is typically limited to those containing only two different components. Of course, inclusion of additional components may be useful in formulating commercial products. The recent Hterature describes the theoretical treatment and experimental studies of the phase behavior of ternary blends (10,21). The most commonly studied ternary mixtures are those where two of the binary pairs are miscible, but the third pair is not. There are limited regions where such ternary mixtures exhibit one phase. A few cases have been examined where all three binary pairs are miscible however, theoretically this does not always ensure homogeneous ternary mixtures (10,21). [Pg.409]

Fig. 3. Residue curve map for a ternary mixture with a distillation boundary mnning from pure component D to the binary azeotrope C. Fig. 3. Residue curve map for a ternary mixture with a distillation boundary mnning from pure component D to the binary azeotrope C.
The overwhelming majority of all ternary mixtures that can potentially exist are represented by only 113 different residue curve maps (35). Reference 24 contains sketches of 87 of these maps. For each type of separation objective, these 113 maps can be subdivided into those that can potentially meet the objective, ie, residue curve maps where the desired pure component and/or azeotropic products He in the same distillation region, and those that carmot. Thus knowing the residue curve for the mixture to be separated is sufficient to determine if a given separation objective is feasible, but not whether the objective can be achieved economically. [Pg.184]

The simplest form of ternary RCM, as exemplified for the ideal normal-paraffin system of pentane-hexane-heptane, is illustrated in Fig. 13-58 7, using a right-triangle diagram. Maps for all other non-azeotropic ternary mixtures are qiiahtatively similar. Each of the infinite number of possible residue curves originates at the pentane vertex, travels toward and then away from the hexane vertex, and terminates at the heptane vertex. [Pg.1295]

FIG 13-59 (Continued) Distillation region diagrams for ternary mixtures. [Pg.1299]

Where there are multi-layers of solvent, the most polar is the solvent that interacts directly with the silica surface and, consequently, constitutes part of the first layer the second solvent covering the remainder of the surface. Depending on the concentration of the polar solvent, the next layer may be a second layer of the same polar solvent as in the case of ethyl acetate. If, however, the quantity of polar solvent is limited, then the second layer might consist of the less polar component of the solvent mixture. If the mobile phase consists of a ternary mixture of solvents, then the nature of the surface and the solute interactions with the surface can become very complex indeed. In general, the stronger the forces between the solute and the stationary phase itself, the more likely it is to interact by displacement even to the extent of displacing both layers of solvent (one of the alternative processes that is not depicted in Figure 11). Solutes that exhibit weaker forces with the stationary phase are more likely to interact with the surface by sorption. [Pg.101]

Katz et al. tested the theory further and measured the distribution coefficient of n-pentanol between mixtures of carbon tetrachloride and toluene and pure water and mixtures of n-heptane and n-chloroheptane and pure water. The results they obtained are shown in Figure 17. The linear relationship between the distribution coefficient and the volume fraction of the respective solvent was again confirmed. It is seen that the distribution coefficient of -pentanol between water and pure carbon tetrachloride is about 2.2 and that an equivalent value for the distribution coefficient of n-pentanol was obtained between water and a mixture containing 82%v/v chloroheptane and 18%v/v of n-heptane. The experiment with toluene was repeated using a mixture of 82 %v/v chloroheptane and 18% n-heptane mixture in place of carbon tetrachloride which was, in fact, a ternary mixture comprising of toluene, chloroheptane and n-heptane. The chloroheptane and n-heptane was always in the ratio of 82/18 by volume to simulate the interactive character of carbon tetrachloride. [Pg.110]

Considering the hexadecane/water-methanol system the same arguments and treatment can be afforded to the methanol/water mixture on the assumption that it is a ternary mixture containing methanol, water and methanol associated with water. Thus, the equation used for the system of Katz et al. reduces to... [Pg.136]

Schematic phase diagrams for binary mixtures of water with a strong amphiphile, and for ternary mixtures containing oil, water, and amphiphile, are shown in Fig. 3 (adapted from Refs. 7,8). Among the many interesting... Schematic phase diagrams for binary mixtures of water with a strong amphiphile, and for ternary mixtures containing oil, water, and amphiphile, are shown in Fig. 3 (adapted from Refs. 7,8). Among the many interesting...
The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. [Pg.639]


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