Phase Equilibrium of Binary Mixtures

Equation (1.5) represents the so-called lever rule points xip, Xio, and xib are located on one straight line, and the lengths of the segments [xif, xid and [xib, Xip] are inversely proportional to the flow rates D and B (Fig. 1.1b). Mixture with a component number n 5 cannot be represented clearly. However, we wiU apply the terms simplex of dimensionality (n -1) for a concentration space of n-component mixture C , hyperfaces C i of this simplex for (n - l)-component constituents of this mixture, etc. 

An equilibrium between hquid and vapor is usually described as follows  

To understand the mutual behavior of the components depending on the degree of the mixture s nonideahty caused by the difference in the components molecular properties, it is better to use graphs yi - x, T - xi,T - yi,Ki - xi, and K2 - xi (Fig. 1.2). In Fig. 1.2, the degree of nonideality increases from atoh.a is an ideal mixture, h is a nonideal mixture with an inflection on the curve y - xi (a and b are zeotropic mixtures), c is a mixture with a so-caUed tangential azeotrope (curve yi - xi touches the diagonal in the point xi = 1), d is an azeotropic mixture with minimum temperature, c is a mixture with a so-called inner tangential azeotrope, / is a mixture with two azeotropes, g is a heteroazeotropic mixture, and h is an azeotropic mixture with two liquid phases. Azeotrope is a binary or multicomponent mixture composition for which the values of phase equihbrium coefficients for all components are equal to one  

Heteroazeotrope is an overall composition of a mixture with two liquid phases for which the values of the overall coefficients of phase equihbrium for all components are equal to one  

In this book, we will see that the previously discussed features are of great importance. Even b case results in serious abnormahties of the distillation process. 

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Figure 1.2. Phase equilibrium of binary mixtures (a) ideal mixture (b) nonideal mixture (c) tangential azeotropic mixture (xi. Az = 1) (d) azeotropic mixture (e) mixture with internal tangential azeotrope (0 < xi, Az < 1) (f) urixture with two azeotropes Azi and Az2, (g) heteroazeotropic mixture and (h) azeotropic mixture with two liquid phases (y — x, T — x — y, and K — x diagrams). Az, azeotropic or heteroazeotropic point x i and x 2, compositions of liquid phases.

The data bank can select all the data for any given substance or data just for a given property according to the users inquiries. In the second case, all the data on the indicated property which are stored in the bank are selected, a statistical analysis is made and the data are delivered to the user with a recommendation of the most reliable published value. The bank also can give information on the phase equilibrium of binary mixtures consisting of components of any multicomponent mixture indicated by the user (total number of components is not more than 40) (Bogomol ny et al. 1984). 

The phase behavior of single-component systems has been discussed as part of thepVT relationship presented in Section 4.2.1. Examiifing the phase behavior of mixtures, we observe that, with mixtures, phase behavior remains one facet of the pVT relationship. But a new phenomenon is encountered with mixtures phases at equilibrium are generally of different compositions. These mixtures show a great variety of phase behavior that can often be exploited to make separations. We examine in broad terms the qualitative features of the phase behavior of binary mixtures of various types. Experience has shown a wealth of phenomena displayed by binary mixtures. 

First of all, three special cases of vapor-hquid equilibrium of binary mixtures are presented qualitatively in Fig. 5.1-2. Considered are ideal mixtures (case A ), mixtures with total miscibiUty gap in the hquid phase (case B), and mixtures with irreversible chemical reaction in the liquid phase (case C). By converrtion, the symbols X and y denote the molar fraction of the low-boiling component a in the hq-ttid and the gas phase, respectively. 

Vittal Prasad, T, E. Deshmukh, R. D. Kumari, A. Preiseid, D. H. L. (Vapor -1- liquid) equilibrium of binary mixtures formed by N,N-dimethylformamide with some compoxmds at 95.1 kPa. Fluid Phase Equilib. 2007, 254, 11-17. 

Dejoz, A. Gonzalez-Alfaro, V Llopis, F. J. Miguel, P. J. Vazquez, M. I. Vapor-liquid equilibrium of binary mixtures of trichloroethylene with 1-pentanol, 2-methyl-1-butanol and 3-methyl-1-butanol at 100 kPa. Fluid Phase Equilib. 1999, 155, 229-239. 

Phase Equilibrium (PE) Binary mixtures of a polymer in a single solvent phase-separate at various temperatures, Tsep, depending on the volmne fi-action (/12 of the polymer. The maximmn of the 7 sep=/(< 2) fiuiction is called the critical solution temperature Test-The experiment is repeated for a series of dilute solutions of polymers of the same constitution and configmation but of different molar mass. The relation between the eritieal solution temperature and the molar mass of the polymer is based on the Flory-Huggins lattice theory which predicts that... 

The difficulties encountered in the Chao-Seader correlation can, at least in part, be overcome by the somewhat different formulation recently developed by Chueh (C2, C3). In Chueh s equations, the partial molar volumes in the liquid phase are functions of composition and temperature, as indicated in Section IV further, the unsymmetric convention is used for the normalization of activity coefficients, thereby avoiding all arbitrary extrapolations to find the properties of hypothetical states finally, a flexible two-parameter model is used for describing the effect of composition and temperature on liquid-phase activity coefficients. The flexibility of the model necessarily requires some binary data over a range of composition and temperature to obtain the desired accuracy, especially in the critical region, more binary data are required for Chueh s method than for that of Chao and Seader (Cl). Fortunately, reliable data for high-pressure equilibria are now available for a variety of binary mixtures of nonpolar fluids, mostly hydrocarbons. Chueh s method, therefore, is primarily applicable to equilibrium problems encountered in the petroleum, natural-gas, and related industries. 

Experimental data on only 26 quaternary systems were found by Sorensen and Arlt (1979), and none of more complex systems, although a few scattered measurements do appear in the literature. Graphical representation of quaternary systems is possible but awkward, so that their behavior usually is analyzed with equations. To a limited degree of accuracy, the phase behavior of complex mixtures can be predicted from measurements on binary mixtures, and considerably better when some ternary measurements also are available. The data are correlated as activity coefficients by means of the UNIQUAC or NRTL equations. The basic principle of application is that at equilibrium the activity of each component is the same in both phases. In terms of activity coefficients this... 

The potential of supercritical extraction, a separation process in which a gas above its critical temperature is used as a solvent, has been widely recognized in the recent years. The first proposed applications have involved mainly compounds of low volatility, and processes that utilize supercritical fluids for the separation of solids from natural matrices (such as caffeine from coffee beans) are already in industrial operation. The use of supercritical fluids for separation of liquid mixtures, although of wider applicability, has been less well studied as the minimum number of components for any such separation is three (the solvent, and a binary mixture of components to be separated). The experimental study of phase equilibrium in ternary mixtures at high pressures is complicated and theoretical methods to correlate the observed phase behavior are lacking. 

A recirculation apparatus for the determination of high pressure phase equilibrium data for mixtures of water, polar organic liquids and supercritical fluids was constructed and operated for binary and ternary systems with supercritical carbon dioxide. 

The nature of alloys. Homogeneous and heterogeneous alloys. Solid solutions, intermetallic compounds. The phase rule, P - - P = C 2 number of phases, variance, number of components of a system in equilibrium triple point. Phase diagrams of binary systems eutectic mixture eutectic point. The systems As-Pb, Pb-Sn, Ag-Au, Ag-Sr. 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

McHugh, M. A. 1981. An experimental investigation of the high pressure fluid phase equilibrium of highly asymmetric binary mixtures. Ph.D. diss., Univ. of Delaware. 

Solid-fluid phase diagrams of binary hard sphere mixtures have been studied quite extensively using MC simulations. Kranendonk and Frenkel [202-205] and Kofke [206] have studied the solid-fluid equilibrium for binary hard sphere mixtures for the case of substitutionally disordered solid solutions. Several interesting features emerge from these studies. Azeotropy and solid-solid immiscibility appear very quickly in the phase diagram as the size ratio is changed from unity. This is primarily a consequence of the nonideality in the solid phase. Another aspect of these results concerns the empirical Hume-Rothery rule, developed in the context of metal alloy phase equilibrium, that mixtures of spherical molecules with diameter ratios below about 0.85 should exhibit only limited solubility in the solid phase [207]. The simulation results for hard sphere tend to be consistent with this rule. However, it should be noted that the Hume-Rothery rule was formulated in terms of the ratio of nearest neighbor distances in the pure metals rather than hard sphere diameters. Thus, this observation should be interpreted as an indication that molecular size effects are important in metal alloy equilibria rather than as a quantitative confirmation of the Hume-Rothery rule. 

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