Binary Liquid-Vapor Phase Diagram

If an isoteniscope is used a glass thermostat (e.g., large battery jar) with mechanical stirrer, electrical blade heater, and temperature controller (alternatively a commercial water bath circulator/heater) thermometer isoteniscope. 

Liquid, such as water, //-heptane, cyclohexane, or 2-butanone. 

Selected Values of Properties of Hydrocarbons, Natl. Bur. Std. Circ. C461, U.S. Government Printing Office, Washington, DC (1947). 

Lide (ed.), CPC Handbook of Chemistry and Physics, 89th ed., CRC Press, Boca Raton, FL (2008/2009). 

Thomson and D. R. Douslin, Determination of Pressure and Volume, in A. Weissberger and B. W. Rossiter (eds.). Techniques of Chemistry Vol I, Physical Methods of Chemistry, part V, chap. 2, Wiley-Interscience, New York (1971). 

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Raoult s Law Binary Liquid-Vapor Phase Diagrams 215... 

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... 

Figure 1. Liquid-vapor phase diagram for pure liquid (1, 2) and binary mixture (3, 4) the lines of attainable superheat (1, 3), binodals Ts(p c = const) (2, 4) and liquid-gas critical curve (5). Symbols CP indicate the critical point, "w — the way of superheating ofpure liquid.

The plots of the total vapor pressure as functions of the mole fraction of A in both the liquid and vapor phases are shown in Figure 9.12(a) and (b), respectively. The combined plot shown in Eigure 9.12(c) is a liquid-vapor phase diagram for an ideal binary solution at a fixed temperature T—often called a pressure-composition diagram. At any pressure and composition above the upper curve (the liquid line) the mixtnre is a liquid. Below the lower curve (the vapor line), the mixture is entirely vapor. The region between the two curves is a region of phase coexistence, that is, both liquid and vapor phases are present in the system. 

Figure 9.16 Different types of liquid-vapor phase diagrams for a binary liquid mixture of component A and B as functions of the mole fraction of the component with the higher boiling temperature, (a) The phase diagram for a system with a low-boiling azeotrope (minimum boiling point) and (b) the phase diagram for a system with a high-boiling azeotrope (maximum boiling point). The arrows show how the paths for various distillation processes depend upon the position of the initial composition relative to the azeotrope.

Figure 9.29 One of the many isomorphisms that exist between vapor-liquid and liquid-solid phase diagrams for binary mixtures. (1(0) An isobaric Txy diagram with a minimum boiling-point azeotrope and a miscibility gap above an LLE situation (right) an isobaric Txx diagram with a minimum melting-point solutrope and a miscibility gap above an SSE situation.

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. 

Figure 7.2 A three-dimensional phase diagram for a Type I binary mixture (here, CO2 and methanol). The shaded volume is the two-phase liquid-vapor region. This is shown ti uncated at 25 °C for illustration purposes. The volume surrounding the two-phase region is the continuum of fluid behavior.

The liquid line and vapor line together constitute a binary (vapor + liquid) phase diagram, in which the equilibrium (vapor) pressure is expressed as a function of mole fraction at constant temperature. At pressures less than the vapor (lower) curve, the mixture is all vapor. Two degrees of freedom are present in that region so that p and y2 can be varied independently. At pressures above the liquid (upper) curve, the mixture is all liquid. Again, two degrees of freedom are present so that p and. v can be varied independently/... 

E8.8 (a) Construct the binary (vapor + liquid) phase diagram for an ideal... 

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. 

The principal tools have been density functional theory and computer simulation, especially grand canonical Monte Carlo and molecular dynamics [17-19]. Typical phase diagrams for a simple Lennard-Jones fluid and for a binary mixture of Lennard-Jones fluids confined within cylindrical pores of various diameters are shown in Figs. 9 and 10, respectively. Also shown in Fig. 10 is the vapor-liquid phase diagram for the bulk fluid (i.e., a pore of infinite radius). In these examples, the walls are inert and exert only weak forces on the molecules, which themselves interact weakly. Nevertheless,... 

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