Equilibrium data

The equilibrium condition for the distribution of one solute between two liquid phases is conveniently considered in terms of the distribution law. Thus, at equilibrium, the ratio of the concentrations of the solute in the two phases is given by CE/CR = K, where K1 is the distribution constant. This relation will apply accurately only if both solvents are immiscible, and if there is no association or dissociation of the solute. If the solute forms molecules of different molecular weights, then the distribution law holds for each molecular species. Where the concentrations are small, the distribution law usually holds provided no chemical reaction occurs. 

The addition of a new solvent to a binary mixture of a solute in a solvent may lead to the formation of several types of mixture  

Of these possibilities, types (b), (c), and (d) all give rise to systems that may be used, although those of types (b) and (c) are the most promising. With conditions of type (b), the equilibrium relation is conveniently shown by a plot of the concentration of solute in one 

One of the most useful features of this method of representation is that, if a solution of composition X is mixed with one of composition Y, then the resulting mixture will have a composition shown by Z on a line XY, such that  

Similarly, if an extract Y is removed, from a mixture Z the remaining liquor will have composition X. 

Adsorbed amounts and integral heat evolved will be suitably reported as a function of the increasing equilibrium pressure, i.e. as volumetric and calorimetric isotherms, respectively. Adsorbed amounts riads = X tsuads were obtained by adding the individual doses amounts, Anads, and will be reported either as mol per unit mass (mol g ) or per unit surface area (mol m ), or as molecules per square nanometer. In zeolites, in order to compare from a structural point of view the affinity of different zeolites towards the given adsorptive, the adsorbed amounts will be more suitably 

A selection of adsorption isotherms obtained for a variety of materials and probe molecules will be illustrated. Note that all the adsorption measurements reported in the following were performed at r = 303 K. 

The affinity towards water of the all-silica counterpart was lower than that of the proton exchanged zeolite, as expected, but it was not negligible. The reported isotherms indicated that hydrophilic sites, responsible for weak and reversible water H-bonding adducts, are developed in zeolites even in the absence of framework A1 atoms. Stmctural defects generating polar species consisting of Si—OH nests (which are characterized by a weak Brpnsted acidic strength),[25, 61] are always present in Al-free zeolites, unless especially prepared in order to obtain hydrophobic, inert materials, as claimed by Flanigen et al.[36]. See also Ref. [24]. 

Cu(I)— and Ag(I)—MFI ads. II isotherms (both volumetric and calorimetric) lie below the ads. I correspondent isotherms, indicating the presence of irreversible phenomena. The irreversible adsorption component was quantified by taking the (ads. I - ads. n) difference in the volumetric isotherms at pco = 90 Torr. It was 30 % of total uptake (ads. I) for copper- and % for silver-exchanged zeolites. 

The differences between the two d-block metal cations can be explained on one hand from an electrostatic point of view, since the charge density of Cu(I) is much larger than that of Ag(I) cations (rCu(I) = 0.96 A and rAg(I) = 1.26 A) [47]. On the other hand, the overlap of the metal cations and CO orbitals in the carbonyl bond is expected to be larger for Cu(I) than for Ag(I). The adsorption of CO on Na+ and K+ cations hosted in the same zeolite framework allowed to roughly single out the electrostatic contribution to the two d-block metal cations/CO interaction. Na+ and K+ cations possess indeed a charge/radius ratio very close to that of Cu(I) and Ag(I), respectively (0.97 A for Na+ and 1.33 A for K+) [47]. 

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American Petroleum Institute, Bibliographies on Hydrocarbons, Vols. 1-4, "Vapor-Liquid Equilibrium Data for Hydrocarbon Systems" (1963), "Vapor Pressure Data for Hydrocarbons" (1964), "Volumetric and Thermodynamic Data for Pure Hydrocarbons and Their Mixtures" (1964), "Vapor-Liquid Equilibrium Data for Hydrocarbon-Nonhydrocarbon Gas Systems" (1964), API, Division of Refining, Washington. 

Source for liquid-liquid and vapor-liquid equilibrium data and vapor-pressure data. 

Gmehling, J., and U. Onken "Vapor-Liquid Equilibrium Data Collection," DECHEMA Chemistry Data Ser., Vol. 1 (1-10), Frankfurt, 1977. 

Boublik "Vapor-Liquid Equilibrium Data at Normal Pressures," Pergamon, Oxford, 1968. 

Comprehensive bibliography for liquid-liquid equilibrium data. 

Bibliography of ternary and quarternary liquid-liquid equilibrium data temperatures are indicated. 

Maczynski, A. "Thermodynamic Data for Technology—Verified Vapor-Liquid Equilibrium Data," Panstwowe Wydawnictwo Naukawa, Warsaw, Volume 1, 1976 Volume 2, 1978. 

Extensive compilation of vapor-liquid equilibrium data, particularly from Eastern Europe. 

Vapor-liquid equilibrium data and vapor pressure data, Vol. 2 (2a) and Vol. 4 (4b) and liquid-liquid equilibrium data, Vol. 2 (2b, 2c). 

Compilation of vapor-liquid equilibrium data data are correlated with Redlich-Kister equation (in Polish). 

Wichterle, I., J. Linek, and E. H la "Vapor-liquid Equilibrium Data Bibliography,"... 

Compilation of data for binary mixtures reports some vapor-liquid equilibrium data as well as other properties such as density and viscosity. 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. 

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

Unfortunately, many commonly used methods for parameter estimation give only estimates for the parameters and no measures of their uncertainty. This is usually accomplished by calculation of the dependent variable at each experimental point, summation of the squared differences between the calculated and measured values, and adjustment of parameters to minimize this sum. Such methods routinely ignore errors in the measured independent variables. For example, in vapor-liquid equilibrium data reduction, errors in the liquid-phase mole fraction and temperature measurements are often assumed to be absent. The total pressure is calculated as a function of the estimated parameters, the measured temperature, and the measured liquid-phase mole fraction. 

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. 

Vapor-Liquid Equilibrium Data Reduction for Acetone(1)-Methanol(2) System (Othmer, 1928)... 

One of the limitations of most phase-equilibrium data is that variances of experimental measurements are seldom known. 

The maximum-likelihood method is not limited to phase equilibrium data. It is applicable to any type of data for which a model can be postulated and for which there are known random measurement errors in the variables. P-V-T data, enthalpy data, solid-liquid adsorption data, etc., can all be reduced by this method. The advantages indicated here for vapor-liquid equilibrium data apply also to other data. 

VL = vapor-liquid equilibrium data MS = mutual solubility data AZ = azeotropic data... 

CHU, J.C./VAPOR-LIQUID EQUILIBRIUM DATA, ANN ARBOR, MICHIGAN (1956) ... 

UNIQUAC Binary Parameters for Noncondensable Components with Condensable Components. Parameters Obtained from Vapor-Liquid Equilibrium Data in the Dilute Region... 

Subroutine VLDTA2. VLDTA2 loads the binary vapor-liquid equilibrium data to be correlated. If the data are in units other than those used internally, the correct conversions are made here. This subroutine also reads the estimated standard deviations for the measured variables and the initial parameter estimates. All input data are printed for verification. 

DOCUMENT THE INPUT VAPOR-LIQUID EQUILIBRIUM DATA... 

BINARY VAPOR-LIQUIC EQUILIBRIUM DATA 1 MATER 2 ACTACO... 

Repeat the calculation from Example 4.2 with actual phase equilibrium data in the phase split instead of assuming a sharp split. 

Figure Bl.7.11. Van t HofF plot for equilibrium data obtained for die reaetion of isobutene with anuuonia in a high pressure ion soiiree (reprodueed from data in [19]).

Unfortunately, the approach of determining empirical potentials from equilibrium data is intrinsically limited, even if we assume complete knowledge of all equilibrium geometries and their energies. It is obvious that statistical potentials cannot define an energy scale, since multiplication of a potential by a positive, constant factor does not alter its global minimizers. But for the purpose of tertiary structure prediction by global optimization, this does not not matter. 

This database provides thermophysical property data (phase equilibrium data, critical data, transport properties, surface tensions, electrolyte data) for about 21 000 pure compounds and 101 000 mixtures. DETHERM, with its 4.2 million data sets, is produced by Dechema, FIZ Chcmic (Berlin, Germany) and DDBST GmhH (Oldenburg. Germany). Definitions of the more than SOO properties available in the database can be found in NUMERIGUIDE (sec Section 5.18). 

Physical properties of A-4-thiazoline-2-one and derivatives have received less attention than those of A-4-thiazoline-2-thiones. For the protomeric equilibrium, data obtained by infrared spectroscopy favors fbrm 51a in chloroform (55, 96, 887) and in the solid state (36. 97. 98) (Scheme 23). The same structural preference is suggested by the ultraviolet spectroscopy studies of Sheinker (98), despite the fact that previous studie.s in methanol (36) suggested the presence of both 51a and... 

Effects of Structure on Rate Electronic and steric effects influence the rate of hydra tion m the same way that they affect equilibrium Indeed the rate and equilibrium data of Table 17 3 parallel each other almost exactly... 

D. P. Valen2uela and A. L. M.yets,Mdsorption Equilibrium Data Handbook, Prentice Hall, Engelwood Cliffs, N.J., 1989. 

In addition to thermodynamically based predictions of Hquid—Hquid equihbria, a great deal of experimental data is to be found in the research hterature (26). A Hquid—Hquid equilibrium data bank is also available (27). 

J. M. Sorenson and W. Adt, Eiquid—Eiquid Equilibrium Data Collection, Dechema Chemistry Data Series, Frankfurt, Germany, Part 1,1980. 

G. Sorensen and J. M. W. Arit, Hquid-lJquid Equilibrium Data Collection, Binay Systems, DECHEMA Chemistry Data Series, Vol. 5, part 1, Schon Wetzel GmbH, Frankfurt/Main, Germany, 1979. 

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