Equilibrium for mixtures

So far, we have described the effect of pressure and temperature on the phase equilibria of a pure substance. We now want to describe phase equilibrium for mixtures. Composition, usually expressed as mole fraction x or j, now becomes a variable, and the effect of composition on phase equilibrium in mixtures becomes of interest and importance. 

For rapid approximations of the phase envelope, the process engineer is wise to keep this chart handy. With some insight, the design engineer can use this chart to obtain estimates of the phase equilibrium for mixtures other than those shown. 

Correlation of Phase Equilibrium for Mixtures that Form Microstructured Micellar Solutions... 

FIGURE 3.17 High-pressure equilibrium for mixtures of poly-(ethylene-co-methyl acrylate) (EMA) and propylene for different repeat-unit compositions of the EMA. Comparison of experimental clond-point measurements to calculation results of the PC-SAFT equation of state. (EMA [0% MA] is equal to LDPE open diamonds and dashed line.) (From Gross, J. et al., Ind. Eng. Chem. Res., 42,1266, 2003. With... 

Liquid-Vapour Equilibrium. For mixtures of Ar + N2 + Oy the method described above yields excellent K-values (28). Similar results were obtained by Mollerup and Fredenslund for Ar + N2, using a method almost identical with that described here (32). The principal error in the work on the ternary system arose in the pure... 

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

Given the estimate of the reactor effluent in Example 4.2 for fraction of methane in the purge of 0.4, calculate the.actual separation in the phase split assuming a temperature in the phase separator of 40°C. Phase equilibrium for this mixture can be represented by the Soave-Redlich-Kwong equation of state. Many computer programs are available commercially to carry out such calculations. 

For mixtures, the calculation is more complex because it is necessary to determine the bubble point pressure by calculating the partial fugacities of the components in the two phases at equilibrium. 

Nearly all experimental eoexistenee eurves, whether from liquid-gas equilibrium, liquid mixtures, order-disorder in alloys, or in ferromagnetie materials, are far from parabolie, and more nearly eubie, even far below the eritieal temperature. This was known for fluid systems, at least to some experimentalists, more than one hundred years ago. Versehaflfelt (1900), from a eareflil analysis of data (pressure-volume and densities) on isopentane, eoneluded that the best fit was with p = 0.34 and 8 = 4.26, far from the elassieal values. Van Laar apparently rejeeted this eonelusion, believing that, at least very elose to the eritieal temperature, the eoexistenee eurve must beeome parabolie. Even earlier, van der Waals, who had derived a elassieal theory of eapillarity with a surfaee-tension exponent of 3/2, found (1893)... 

The object of this part of the project is to determine the energy ("enthalpy) levels in each the three con formers and so to determine the composition of the equilibrium conformational mixture. That having been done for the cis isomer, the procedure is repeated for the trans isomer. 

For mixtures containing more than two species, an additional degree of freedom is available for each additional component. Thus, for a four-component system, the equihbrium vapor and liquid compositions are only fixed if the pressure, temperature, and mole fractious of two components are set. Representation of multicomponent vapor-hquid equihbrium data in tabular or graphical form of the type shown earlier for biuaiy systems is either difficult or impossible. Instead, such data, as well as biuaiy-system data, are commonly represented in terms of ivapor-liquid equilibrium ratios), which are defined by... 

As discussed in Sec. 4, the icomplex function of temperature, pressure, and equilibrium vapor- and hquid-phase compositions. However, for mixtures of compounds of similar molecular structure and size, the K value depends mainly on temperature and pressure. For example, several major graphical ilight-hydrocarbon systems. The easiest to use are the DePriester charts [Chem. Eng. Prog. Symp. Ser 7, 49, 1 (1953)], which cover 12 hydrocarbons (methane, ethylene, ethane, propylene, propane, isobutane, isobutylene, /i-butane, isopentane, /1-pentane, /i-hexane, and /i-heptane). These charts are a simplification of the Kellogg charts [Liquid-Vapor Equilibiia in Mixtures of Light Hydrocarbons, MWK Equilibnum Con.stants, Polyco Data, (1950)] and include additional experimental data. The Kellogg charts, and hence the DePriester charts, are based primarily on the Benedict-Webb-Rubin equation of state [Chem. Eng. Prog., 47,419 (1951) 47, 449 (1951)], which can represent both the liquid and the vapor phases and can predict K values quite accurately when the equation constants are available for the components in question. 

Equilibrium between the various enolates of a ketone can be established by the presence of an excess of the ketone, which permits proton transfer. Equilibration is also favored by the presence of dissociating solvents such as HMPA. The composition of the equilibrium enolate mixture is usually more closely balanced than for kinetically... 

I rcdici.s properties and lompuics ihcmical and solid-liquid phase equilibrium for aqueous mixtures. Up to 20 composition data sets may be handled in memory at once. Requires 512K memory. 

When temperature is constant and at equilibrium for a homogeneous mixture (such as azeotrope), the composition of the liquid is identical with the composition of the vapor, thus xj = y, and the relative volatility is equal to 1.0. 

This graphical representation is easier to use for nonideal systems than the calculation method. This is another limiting condition for column operation, i.e., below this ratio the specified separation cannot be made even with infinite plates. This minimum reflux ratio can be determined graphically from Figure 8-23, as the line with smallest slope from xp intersecting the equilibrium line at the same point as the q line for mixture following Raoul t s Law. 

Since the equilibrium reaction mixture contains at least four products, workup can be difficult and therefore, it may be helpful to bring the reaction to completion. For example, in the transketolase-catalyzed reaction of [l-13C]D-ribosc 5-phosphate and [l-l3C]D-i/ /w-2-pen-tulose 5-phosphatc to [l,3-13C]n-a/b,o-2-heptulose 7-phosphate and D-glyceraldehyde 3-phos-... 

The preceeding discussion was confined mostly to the carbon deposition curves as a function of temperature, pressure, and initial composition. Also of interest, especially for methane synthesis, is the composition and heating value of the equilibrium gas mixture. It is desirable to produce a gas with a high heating value which implies a high concentration of CH4 and low concentrations of the other species. Of particular interest are the concentrations of H2 and CO since these are generally the valuable raw materials. Also, by custom it is desirable to maintain a CO concentration of less than 0.1%. The calculated heating values are reported as is customary in the gas industry on the basis of one cubic foot at 30 in. Hg and 15.6°C (60°F) when saturated with water vapor (II). Furthermore, calculations are made and reported for a C02- and H20-free gas since these components may be removed from the mixture after the final chemical reaction. Concentrations of CH4, CO, and H2 are also reported on a C02 and H20-free basis. 

Since Eqs. (5) and (6) are not restricted to the vapor phase, they can, in principle, be used to calculate fugacities of components in the liquid phase as well. Such calculations can be performed provided we assume the validity of an equation of state for a density range starting at zero density and terminating at the liquid density of interest. That is, if we have a pressure-explicit equation of state which holds for mixtures in both vapor and liquid phases, then we can use Eq. (6) to solve completely the equations of equilibrium without explicitly resorting to the auxiliary-functions activity, standard-state fugacity, and partial molar volume. Such a procedure was discussed many years ago by van der Waals and, more recently, it has been reduced to practice by Benedict and co-workers (B4). 

With a suitable equation of state, all the fugacities in each phase can be found from Eq. (6), and the equation of state itself is substituted into the equilibrium relations Eq. (67) and (68). For an A-component system, it is then necessary to solve simultaneously N + 2 equations of equilibrium. While this is a formidable calculation even for small values of N, modern computers have made such calculations a realistic possibility. The major difficulty of this procedure lies not in computational problems, but in our inability to write for mixtures a single equation of state which remains accurate over a density range that includes the liquid phase. As a result, phase-equilibrium calculations based exclusively on equations of state do not appear promising for high-pressure phase equilibria, except perhaps for certain restricted mixtures consisting of chemically similar components. 

In summary, we now have the tools for describing phase equilibrium for both pure materials and for mixtures, and for understanding chemical processes at equilibrium. We will rely upon the foundation developed in this chapter as we... 

When AGr° for a reaction is strongly negative, equilibrium is reached only after a reaction has gone nearly to completion and the equilibrium reaction mixture consists mainly of products. Because the concentrations or partial pressures of products appear in the numerator of K and those of reactants in the denominator the numerator will be large and the denominator small. Therefore, the value of K is large when the equilibrium mixture consists mostly of products. In contrast, when AGr° for a reaction is strongly positive, equilibrium is reached after very little reaction has taken place, the numerator is small and the denominator large therefore, K is small. 

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