THE TERNARY SYSTEM

Ternary systems contain three components. The composition of such a system cannot be represented on a line. For that reason an equilateral triangle is used. When the temperature is a variable, the composition triangle (figure 6.10) in a T,x diagram is the base on which three T axes are placed perpendicularly on the vertices of the triangle. In a system with the components A, B and C there are three mole fractions for which holds x(A) + x(B) + x(C) = 1. 

Three kinds of systems can be represented in the composition triangle 1. The vertices on the triangle represent the unary system with the pure components. 

Points on the sides of the triangle represent binary systems. For example system P is a binary system with the components A and B and x(B) = 0.30. 

How can we derive the composition in system Q from this triangle In order to to so, two construction lines need to be drawn which are parallel to the sides of the triangle. In figure 6.10 the line AC is thus divided into three sections. Then  

So why is x(A) proportional to line (A) and x(B) to the middle part on line AC This can be made clear by moving from system Q to system Qr We now approach vertex B and the system will consequently contain more B. This is confirmed by drawing two lines parallel to the the two sides of the triangle as we can see x(B) has indeed increased in size. By moving point Q in the direction of vertex C you can increase the line (C) and consequently x(C). 

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Unfortunately, good binary data are often not available, and no model, including the modified UNIQUAC equation, is entirely adequate. Therefore, we require a calculation method which allows utilization of some ternary data in the parameter estimation such that the ternary system is well represented. A method toward that end is described in the next section. 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

Using the ternary tie-line data and the binary VLE data for the miscible binary pairs, the optimum binary parameters are obtained for each ternary of the type 1-2-i for i = 3. .. m. This results in multiple sets of the parameters for the 1-2 binary, since this binary occurs in each of the ternaries containing two liquid phases. To determine a single set of parameters to represent the 1-2 binary system, the values obtained from initial data reduction of each of the ternary systems are plotted with their approximate confidence ellipses. We choose a single optimum set from the intersection of the confidence ellipses. Finally, with the parameters for the 1-2 binary set at their optimum value, the parameters are adjusted for the remaining miscible binary in each ternary, i.e. the parameters for the 2-i binary system in each ternary of the type 1-2-i for i = 3. .. m. This adjustment is made, again, using the ternary tie-line data and binary VLE data. 

Zulauf M and Eicke FI 1979 Inverted micelles and microemulsions in the ternary system Fl20/aerosol-OT-isoctane as studied by photon correlation spectroscopy J. Phys. Chem. 83 480... 

Thermo dynamic data for nitric acid are given ia Table 2. Properties for the ternary systems sulfuric acid—nitric acid—water (5,14) and magnesium nitrate—nitric acid—water (11,15—17) used ia processes for concentrating nitric acid are available. 

Interactions in the ternary system sample components eluent/SEC matrix. 

Most feldspars can be cla.ssified chemically as members of the ternary system NaAlSi30s-KAlSi30s-CaAl2Si20 . This is illustrated in Fig. 9.14, which also indicates the names of the mineral phases. Particularly notable... 

Iuchi and Matsuchima [305] and Zui Bin-Sin, Lushnaya and Konstantinov [306] investigated the melting diagram of the ternary system K2TaF7 - KF -KC1 and observed the compound K3TaF7Cl along with its initial components. 

Kovalev, Kartsev, Ioffe and Leonov [310] investigated melting in the ternary system K2TaF7 - KF - NaF, which is also characterized by the formation of K3TaF8. 

Fig. 57. Projections of the crystallization surfaces of the ternary systems K.2TaF7 - KF - KCl (top). Reproduced from [306], Z. Bin-Sin, N. P. Lushnaya, V. I. Konstantinov, Zh. Neorg. Khim. 8 (1963) 389, Copyright 1963, with permission of Nauka (Russian Academy of Sciences) publishing.

Barrer s discussion4 of his analog of Eq. 28 merits some comment. Equation 28 expresses the equilibrium condition between ice and hydrate. As such it is valid for all equilibria in which the two phases coexist and not only for univariant equilibria corresponding with a P—7" line in the phase diagram. (It holds, for instance, in the entire ice-hydratell-gas region of the ternary system water-methane-propane considered in Section III.C.(2).) In addition to Eq. 28 one has Clapeyron s equation... 

Fig. 8. The system CHCla-HaS-HaO. The univariant equilibria of the single-component systems have been indicated by dotted lines, those of the binary systems by thin lines, and those of the ternary system by heavy lines. The latter are approximate only, except for the lower half of the four-phase line HnLxL%G measured by von Stackelberg and Friihbuss.4 ...

Figure 9 represents the system CC14-H2S-H20, where no hydrates occur in the binary system CC14-H20. In the ternary system von Stackelberg and Fruhbuss again determined the lower half of the four-phase line As the binary quadruple point... 

In contrast to the ternary systems just discussed, the four-phase line HUL1L2G investigated by Carson and Katz in the system... 

Fig. 11. Tentative isothermal cross section of the system HaO-HaS-CH,CHF2 on a water-free basis below 0°C. In the two binary systems H2G-H2S and H20-CHsCHF2 only hydrates of Structure I occur, but in the ternary system mixed hydrates of Structure II have been reported.44...

Therefore, if we have information on the partial molar volumes and the excess Gibbs energy of the ternary system, we can use Eqs. (119)—(122) to find the ends of the tie lines which comprise the coexistence curve. 

To illustrate such a calculation, Balder (Bl) considered a simple case wherein he assumed that the (symmetric) excess Gibbs energy of the ternary system is given by a two-suffix Margules expansion ... 

If the property evaluated, for instance, the critical micelle concentration, can be approximated by a suitable plot, it is depicted in the ternary system as a concave area (e.g., cM area) located in the space above the Gibbs triangle as the basis for the distinct concentrations. The property axis describing the cM data stands vertically on the base triangle. 

Dimethylformamide is also a suitable solvent [50], it has, however, the disadvantage of being oxidized at fairly low potentials to A-acyloxy-iV-methyl formamide [51]. The influence of the composition of the ternary system water/methanol/dimethyl-formamide on the material and current yield has been systematically studied in the electrolysis of co-acetoxy or -acetamido substituted carboxylates [32]. Acetonitrile can also be used, when some water is.added [52]. The influence of various solvents on the ratio of Kolbe to non-Kolbe products is shown in Table 1 [53]. 

A high-T modification of Nb5Si3 crystallizes with the Cf5B3 type. Si—B substitution stabilizes the high-T form to lower T reaching far into the ternary system. The stabilization of the homologous Ta5(Si, 8)3, however, is far less pronounced. 

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. 

Consider the ternary system having some range of mutual solid solu-... 

Krishnan V, Ham D, Mishra KK, Rajeshwar K J (1992) Electrosynthesis of thin films of CdZnSe Composition modulation and bandgap engineering in the ternary system. J Electrochem Soc 139 23-27... 

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