Phase diagram binary liquid-vapor system

ZAF Zafarani-Moatlar, M.T., Hamzehzadeh, S., and Hosseinzadeh, S., Phase diagrams for liquid-hquid equilibrium of ternary poly(ethylene glycol) + disodium tartrate aqueous system and vapor-liquid equilibrium of constituting binary aqueous systerrrs at r = (298.15, 308.15, and 318.15) K. Experiment and correlation. Fluid Phase Equil, 268, 142, 2008. 

Another common way of representing a binary liquid-vapor equilibrium is through a temperature-composition phase diagram, in which the pressure is held fixed and phase coexistence is examined as a function of temperature and composition. Figure 9.13 shows the temperature-composition phase diagram for the benzene-toluene system at a pressure of 1 atm. In Figure 9.13, the lower curve (the boiling-point curve)... 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

Figure 7.9 P-xB diagram (b) for a binary two-phase system (a), showing the compositions of coexisting vapor Oeap) and liquid (xgq) phases for a particular vapor-pressure value (dotted line), and the connecting tie-line (heavy solid line) that connects vapor and liquid compositions at this pressure. Varying amounts (rcvap, nhq) of the two phases correspond to different positions along the tie-line, as determined by the lever rule (see text).

GIBBS-KONOVALOV THEOREMS. Consider a binary system containing two phases (e.g.. liquid and vapor). Both components can pass from one phase lo another. The Gibbs Konovalov theorems refer to the properties of the phase diagrams of such systems (see also Azeotropic System). The lirst theorem is At constant pressure, the temperature of coexistence passes through tin extreme value (maximum, minimum or inflexion with a horizontal value), if the comfutsirlon of the two phases is the same. Conversely, al a point at winch the temperature passes through an extreme value, the phases have the same composition. The second theorem is similar. It refers lo the coexistence pressure at constant temperature. 

Chapter 14 describes the phase behavior of binary mixtures. It begins with a discussion of (vapor -l- liquid) phase equilibria, followed by a description of (liquid + liquid) phase equilibria. (Fluid + fluid) phase equilibria extends this description into the supercritical region, where the five fundamental types of (fluid + fluid) phase diagrams are described. Examples of (solid + liquid) phase diagrams are presented that demonstrate the wide variety of systems that are observed. Of interest is the combination of (liquid + liquid) and (solid 4- liquid) equilibria into a single phase diagram, where a quadruple point is described. 

Obtain (or plot from data) a phase diagram for the benzene/toluene system. Vapor-liquid equilibrium behavior of binary systems can be represented by a temperature-composition diagram at... 

Liquid-vapor phase diagrams, and boiling-point diagrams in particular, are of importance in connection with distillation, which usually has as its object the partial or complete separation of a liquid solution into its components. Distillation consists basically of boiUng the solution and condensing the vapor into a separate receiver. A simple one-plate distillation of a binary system having no maximum or minimum in its boiling-point curve can be understood by reference to Fig. 3. Let the mole fraction of B in the initial solution be represented by... 

The phase behavior of multicomponent hydrocarbon systems in the liquid-vapor region is very similar to that of binary systems. However, it is obvious that two-dimensional pressure-composition and temperature-composition diagrams no longer suffice to describe the behavior of multicomponent systems. For a multicomponent system with a given overall composition, the characteristics of the P-T and P-V diagrams are very similar to those of a two-component system. For systems involving crude oils which usually contain appreciable amounts of relatively r on-volatile constituents, the dew points may occur at such low pressures that they are practically unattainable. This fact will modify the behavior of these systems to some extent. 

A conventional bubble point calculation involves the specification of the liquid mole fractions and pressure the subsequent computation of the vapor-phase mole fractions and the system temperature. For a binary system (and only for a binary system) we may specify the temperature and pressure and compute the mole fractions of both phases. Thus, our first step is to estimate the interface temperature T. The second step is to solve the equilibrium equations for the mole fractions on either side of the interface. This step is, in fact, equivalent to reading the composition of both phases from a T-x-y equilibrium diagram. 

The phase behavior for the polymer-solvent systems can be described using two classes of binary P-T diagrams, which originate from P—T diagrams for small molecule systems. Figure 3.24A shows the schematic P-T diagram for a type-III system where the vapor-liquid equilibrium curves for two pure components end in their respective critical points, Ci and C2. The steep dashed line in figure 3.24A at the lower temperatures is the P-T trace of the UCST... 

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