Binary mixture experimental data

Figure 9,5 Activity-concentration relationships in binary gaseous H2O-CO2 mixtures. Experimental data from Shmulovich et al. (1982).

To test the NRTL equation for predicting VLE data for ternary mixtures, experimental data for the ternary mixtures and for the binary components of the mixtures are necessary. A literature survey showed that data were not readily available for any of the ternaries or for the two binaries ethanol-3-methyl-l-propanol and 3-methyl-l-butanol-water, and it was therefore necessary to obtain these data experimentally. 

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6. 

They then compared measured and predicted fluxes for diffusion experiments in the mixture He-N. The tests covered a range of pressures and a variety of compositions at the pellet faces but, like the model itself, they were confined to binary mixtures and isobaric conditions. Feng and Stewart [49] compared their models with isobaric flux measurements in binary mixtures and with some non-isobaric measurements in mixtures of helium and nitrogen, using data from a variety of sources. Unfortunately the information on experimental conditions provided in their paper is very sparse, so it is difficult to assess how broadly based are the conclusions they reached about the relative merits oi their different models. 

The vapor-liquid equilibrium of the binary mixture is well fitted by Van Laar s equations (228). It was determined from 100 to 760 mm Hg. and the experimental data was correlated by the Antoine equation (289, 290), with P in mm Hg and t in °C ... 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

Mathematical Consistency. Consistency requirements based on the property of exact differentials can be apphed to smooth and extrapolate experimental data (2,3). An example is the use of the Gibbs-Duhem coexistence equation to estimate vapor mole fractions from total pressure versus Hquid mole fraction data for a binary mixture. 

Most of the assumptions are based on idealized models, indicating the limitations of the mathematical methods employed and the quantity and type of experimental data available. For example, the details of the combinatorial entropy of a binary mixture may be well understood, but modeling requires, in large measure, uniformity so the statistical relationships can be determined. This uniformity is manifested in mixing rules and a minimum number of adjustable parameters so as to avoid problems related to the mathematics, eg, local minima and multiple solutions. 

The diffusivity of solute 1 in the mixture is related to the binary infinite dilution diffiisivities for each of the other components calculated from Eq. (2-155) or the Umesi method. The viscosities are calculated by the methods in the previous section. Errors are not quantifiable, as little experimental data exist, although these errors would be related to those assumed for the binaiy pairs. 

Binary interaction parameters are determined for each pq pair p q) from experimental data. Note that = k and k = k = 0. Since the quantity on the left-hand side of Eq. (4-305) represents the second virial coefficient as predicted by Eq. (4-231), the basis for Eq. (4-305) lies in Eq. (4-183), which expresses the quadratic dependence of the mixture second virial coefficient on mole fraction. 

The possibilities of analyzing binary mixtures of known gases may be judged from Table 3-1. With mixtures of higher order, absorptiometry is of value in supplying an item )f experimental information to be used with other data in arriving at the composition of the gas. It cannot be stressed too strongly that information of the kind in Table 3-1 can be obtained with little more effort than is required to measure the pressure or temperature of a gas near standard conditions. 

By adopting mixing rules similar to those given in Section II, Chueh showed that Eq. (55) can be used for calculating partial molar volumes in saturated liquid mixtures containing any number of components. Some results for binary systems are given in Figs. 7 and 8, which compare calculated partial molar volumes with those obtained from experimental data. 

The parameters A, B,. .., depend on temperature but not on pressure, and must be determined from experimental data for the binary mixture. 

Thermodynamic consistency tests for binary vapor-liquid equilibria at low pressures have been described by many authors a good discussion is given in the monograph by Van Ness (VI). Extension of these methods to isothermal high-pressure equilibria presents two difficulties first, it is necessary to have experimental data for the density of the liquid mixture along the saturation line, and second, since the ideal gas law is not valid, it is necessary to calculate vapor-phase fugacity coefficients either from volumetric data for... 

As an example, the cM data of the binary mixtures dependent on the mixture composition were experimentally determined for the systems alkanesul-fonate/fatty acid isethionate, alkanesulfonate/betaine, and fatty acid isethionate/ betaine. In Fig. 31 the calculated ternary cM area of state is depicted for the mixture alkanesulfonate/fatty acid isethionate/betaine [58]. Interestingly, the... 

It is assumed that there are available NCP experimental binary critical point data. These data include values of the pressure, Pc, the temperature, Tc, and the mole fraction, xc, of one of the components at each of the critical points for the binary mixture. The vector k of interaction parameters is determined by fitting the EoS to the critical data. In explicit formulations the interaction parameters are obtained by the minimization of the following least squares objective function ... 

Several activity coefficient models are available for industrial use. They are presented extensively in the thermodynamics literature (Prausnitz et al., 1986). Here we will give the equations for the activity coefficients of each component in a binary mixture. These equations can be used to regress binary parameters from binary experimental vapor-liquid equilibrium data. 

A significant advantage of the Wilson equation is that it can be used to calculate the equilibrium compositions for multicomponent systems using only the Wilson coefficients obtained for the binary pairs that comprise the multicomponent mixture. The Wilson coefficients for several hundred binary systems are given in the DECHEMA vapour-liquid data collection, DECHEMA (1977), and by Hirata (1975). Hirata gives methods for calculating the Wilson coefficients from vapour liquid equilibrium experimental data. 

The UNIQUAC equation developed by Abrams and Prausnitz is usually preferred to the NRTL equation in the computer aided design of separation processes. It is suitable for miscible and immiscible systems, and so can be used for vapour-liquid and liquid-liquid systems. As with the Wilson and NRTL equations, the equilibrium compositions for a multicomponent mixture can be predicted from experimental data for the binary pairs that comprise the mixture. Also, in the absence of experimental data for the binary pairs, the coefficients for use in the UNIQUAC equation can be predicted by a group contribution method UNIFAC, described below. 

Fig. 6 The relative intensity of the 6.78 A line of anhydrous carbamazepine (/3-form) as a function of its weight fraction in binary mixtures of anhydrous carbamazepine (/3-form) and carbamazepine dihydrate. The line is based on theoretical values (Table 5), while the data points are experimental measurements. (Reproduced with permission of the copyright owner, Plenum Press, from Ref. 47.)...

The theory of chain co-oxidation of binary mixtures of organic compounds was described in Chapter 5. The experimental study of co-oxidation of alcohols (HRiOH) and hydrocarbon R H opens the way to measure the rate constants of one chosen peroxyl radical R OO with several alcohols HRiOH and on the reverse, the chosen alcohol HR1 OH with several peroxyl radicals RiOO. The parameters of co-oxidation of alcohols and hydrocarbons are collected in Table 7.6. The absolute values of peroxyl radical reactions with alcohols were calculated from these data using the values of kp from Table 2.8 (see Table 7.7). 

To our knowledge, direct experimental data on amphibole mixtures have been obtained only for the (pseudo)binary system actinolite-cummingtonite (Cameron, 1975) at Ptotai = -Phjo = 2 kbar and for the (pseudo)binary system tremolite-pargasite at Ptotai = PhjO = 1 kbar (Oba, 1980). In both cases, an extended miscibility gap (or solvus field in the second case), is evident at low T(i.e., 600 to 800 °C), which is indicative of strong positive interactions in the solid mixtures. Unmixing of other compositional terms is also evident in microprobe investigations (see Ghose, 1982 for an appropriate discussion). 

Figure 5. Relationship of AG and average hydrocarbon chain length (m). The dashed lines are the theoretical value, the plotted points experimental data, o-single component, o-binary mixture.

In addition to the experimental results of phase equilibria, the correlation with the widely known GE models was assigned to. It was indicated by many authors that SLE, LLE, and VLE data of ILs can be correlated by Wilson, NRTL, or UNIQUAC models [52,54,64,79,91-101,106,112,131,134]. For the LLE experimental data, the NRTL model is very convenient, especially for the SLE/LLE correlation with the same binary parameters of nonrandom two-liquid equation for mixtures of two components. For the binary systems with alcohols the UNIQUAC equation is more adequate [131]. For simplicity, the IL is treated as a single neutral component in these calculations. The results may be used for prediction in ternary systems or for interpolation purposes. In many systems it is difficult to obtain experimentally the equilibrium curve at very low solubilities of the IL in the solvent. Because this solubility is on the level of mole fraction 10 or 10 , sometimes only... 

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