Hypothetical Ternary Systems

In the first considered hypothetical ternary systems, the single chemical reaction A + B = C. (12) 

Assuming constant relative volatilities ay of the components, the vapor-liquid equilibrium is given by  

Chemical equilibrium-controlled case (Do — °°) (vi-vryi) = 0 (vi-vjxi) = 0 

Example 1 a r = 0.2, ctec = 3, i.e., the reaction product C is intermediate boiler. Example 2 u r = 5, ctec = 3, i.e., the reaction product is high boiler. 

Consequently, Eq. (13) can be written as quadratic form in terms of the liquid mole fractions xa and xb  

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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... 

Figure 2.3 (a) Isometric projection (solid diagram) for a hypothetical ternary system (b) isotherm (horizontal section) (c) binary-phase subset (d) liquidus surface. 

We consider a hypothetical ternary system with prescribed feed and overhead compositions, but of an otherwise unspecified nature. One of the final bottoms compositions can be fixed as well, while the remainder follow by calculation. No equilibrium data are available, but any existing ternary azeotrope is assmned known and fixes the overhead composition. 

Figure 9.9 Activity of AC in the hypothetical ternary reciprocal system AC-BD for different values of AXGIRT.

Figure 3-22 A diagram for the representation of compositions in a ternary system, with two hypothetical diffusion couples a-b and c-d. The compositional gradient of the two diffusion couples are orthogonal to each other. For a given point inside the triangle, to find the fraction of a component (such as A), first draw a straight line parallel to BC, and then find where the straight line intersects the CA segment (with fraction indicated on the CA segment).

We can now consider the conditions of stability for pure substances, binary systems, and ternary systems based on Equations (5.122), (5.132), and (5.134), respectively. In order to satisfy the conditions, the coefficient of each term (except the last term in each applicable equation, which is zero) must be positive. If any one of the terms is negative for a hypothetical homogenous system, that system is unstable and cannot exist. 

Cases are encountered in ternary systems where the two dissolved solutes combine in fixed proportions to form a definite double compound. Figure 4.24 shows two possible cases for a hypothetical aqueous solution of two salts A and B. Point C on the AB side of each triangle represents the composition of the double salt points L and O show the solubilities of salts A and B in water at the given temperature. Curves LM and NO denote ternary solutions saturated... 

Due to the fact that macro/microemulsions may be required to be prepared and used at different specific temperatures, i.e. at, below or above the ambient, it is often also necessary to know the phase behavior of W-O-S systems at different temperatures. This involves a vertical axis (considering the phase diagram/ diagrams to be on the horizontal plane) for temperature. Thus, W-O-S phase diagrams obtained at different temperatures provide a picture of thermal evolution of the ternary system. Figure 3.6 shows, as an example, a change in the primary phase field of the W/O microemulsion as a function of temperature in a hypothetical system. Structures and other features of microemulsions have attracted intensive study, and details are available in several reviews [118-121]. 

Figure 3 shows a hypothetical phase diagram for a three-component ternary system of water, oil, and surfactant at constant temperature. The structures illustrate those commonly observed in three-component mixtures of water, oil, and surfactant and also in two components of mixtures of water and surfactant (see below). Details regarding reading and usage of phase diagrams are published elsewhere. 

Hypothetical projections of the solidus surfaces of the Sc-M-C (M=Zr, Hf, V, Nb, Ta) phase diagrams are proposed in a paper of Velikanova et al. (1989). A complete miscibility of the binary carbides ScCi- and MCi- (M=Zr, Hf, V, Nb, Ta) crystallizing in the NaCl type structure, and the absence of ternary compounds in each of these ternary systems is predicted. However, these data need to be confirmed experimentally. Recently Ilyenko et al. (1996) reported the existence of continuous solid solutions between ScCi x and MC] x (M=Zr, Hf), and accordingty these solid solutions are in equilibria with all the phases of the solidus surface. The same authors reported that the VCi x binary carbidedissolves at least 15at.% Sc while the V solubility in ScC x is at least 17at.%. These data reject the earlier prediction of a complete miscibility of the NaCl-t5q)e binary carbides in the system Sc-V-C. However, no figures of the phase equilibria are presented in the brief communication of Ilyenko et al. 

Figure 1.8 presents the phase equilibria in a hypothetical binary eutectic system similar to that in Figure 1.7, represented on each of the three types of diagrams. This diagram is similar to those for the Ag-Cu and Ni-Cr systems. The plot of T versus ub is a Type 1 diagram and the three-phase equilibrium a-L-(3 is represented by a point. The plot of T versus Ab is a Type 2 diagram and the a-L-(3 equilibrium is represented by three points on a line, the eutectic isotherm. The plot of S versus Xb is a Type 3 diagram and the a-L-(3 equilibrium is represented by an area. Note that the forms of these diagrams correspond to those for the unary system in Figure 1.4. (Numerous examples of the three types of phase diagrams are given for unary, binary and ternary systems in Chapter 13 of Reference [2], Reference [5] and Chapter 2 of Reference [8].

In Parts I and II we explored the steady-state designs of several ideal hypothetical systems. The following three chapters examine the control of these systems. Chapter 10 considers the four-component quaternary system with the reaction A + B C + D under conditions of neat operation. Chapter 11 looks at control of two-column flowsheets when an excess of one of the reactants is used. Chapter 12 studies the ternary system A + B C, with and without inerts, and the ternary system A B + C. We will illustrate that the chemistry and resulting process structure have important effects on the control structure needed for effective control of reactive distillation columns. 

By contrast. Figure 2a shows a hypothetical isothermal cut through a state diagram for a ternary aqueous mixture in which water and one solute (e.g. glycine) can crystallise under certain conditions, but the other solute (e.g. sucrose) will invariably vitrify.Results from a detailed investigation of the water-glycine-sucrose system, including... 

Figure 9.2 7 A binary A H- BC system treated as ternary (hypothetical isothermal diagram). Component B is the mesomorphic component in the semirigid copolymer BC. The compositions along the axis are measured in molar fractions x. (According to [II] with permission of Elsevier Science Publ.)...

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