Form and Sources of Equilibrium Data

Equilibrium data are required to understand and design the separations in Chapters 1 to 16 and 18. In principle, we can always experimentally determine the VLE data we require. For a simple experiment, we could take a chamber similar to Figure 1-2, fill it with the chemicals of interest, and at different pressures and temperatures, allow the liquid and vapor sufficient time to come to equilibrium and then take samples of liquid and vapor and analyze them. If we are very careful, we can obtain reliable

equilibrium data. In practice, the measurement is fairly difficult and a variety of special equilibrium stills have been developed. Marsh (1978) and Van Ness and Abbott (1982, Section 6-7) briefly review

methods of determining equilibrium. With a static equilibrium cell, concentration measurements are not required for binary systems. Concentrations can be calculated from pressure and temperature data, but the calculation is complex.

If we obtained equilibrium measurements for a binary mixture of ethanol and water at 1 atm, we would generate data similar to those shown in Table 2-1. The mole fractions in each phase must sum to 1.0. Thus for this binary system,

(2-3) Table 2-1. Vapor-liquid equilibrium data for ethanol and water at 1 atm y and x in mole fractions

where x is mole fraction in the liquid and y is mole fraction in the vapor. Very often only the composition of the most volatile component (ethanol in this case) will be given. The mole fraction of the less volatile component can be found from Eqs. (2-3). Equilibrium depends on pressure. (Data in Table 2-1 are

specified for a pressure of 1 atm.) Table 2-1 is only one source of equilibrium data for the ethanol-water system, and over a dozen studies have explored this system (Wankat, 1988), and data are contained in the more general sources listed in Table 2-2. The data in different references do not agree perfectly, and care must be taken in choosing good data. We will refer back to this (and other) data quite often. If you have difficulty finding it, either look in the index under ethanol data or water data, or look in Appendix D under ethanol-water VLE.

Table 2-2. Sources of vapor-liquid equilibrium data

Chu, J. C., R. J. Getty, L. F. Brennecke, and R. Paul, Distillation Equilibrium Data, Reinhold, New York, 1950.

Engineering Data Book, Natural Gasoline Supply Men’s Association, 421 Kennedy Bldg., Tulsa, Oklahoma, 1953.

Hala, E., I. Wichterle, J. Polak, and T. Boublik, Vapor-Liquid Equilibrium Data at Normal Pressures, Pergamon, New York, 1968.

Hala, E., J. Pick, V. Fried, and O. Vilim, Vapor-Liquid Equilibrium, 3rd ed., 2nd Engl. ed., Pergamon, New York, 1967.

Horsely, L. H., Azeotropic Data, ACS Advances in Chemistry, No. 6, American Chemical Society, Washington, DC, 1952.

Horsely, L. H. Azeotropic Data (II), ACS Advances in Chemistry, No. 35, American Chemical Society, Washington, DC, 1952.

Gess, M. A., R. P. Danner, and M. Nagvekar, Thermodynamic Analysis of Vapor-Liquid

Equilibria: Recommended Models and a Standard Data Base, DIPPR, AIChE, New York, 1991.

Gmehling, J., J. Menke, J. Krafczyk, and K. Fischer, Azeotropic Data, VCH Weinheim, Germany, 1994.

Gmehling, J., U. Onken, W. Arlt, P. Grenzheuser, U. Weidlich, B. Kolbe, J. R. Rarey-Nies, DECHEMA Chemistry Data Series, Vol. I, Vapor-Liquid Equilibrium Data Collection, DECHEMA, Frankfurt (Main), Germany, 1977–1984.

Maxwell, J. B., Data Book on Hydrocarbons, Van Nostrand, Princeton, NJ, 1950.

Perry, R. H., and D. Green, (Eds.), Perry’s Chemical Engineer’s Handbook, 7^th ed., McGraw-Hill, New York, 1997.

Prausnitz, J. M., T. F. Anderson, E. A. Grens, C. A. Eckert, R. Hsieh, and J. P. O’Connell, Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria, Prentice-Hall, Upper Saddle River, NJ, 1980.

Stephan, K., and H. Hildwein, DECHEMA Chemistry Data Series, Vol. IV, Recommended Data of Selected Compounds and Binary Mixtures, DECHEMA, Frankfurt (Main), Germany, 1987.

Timmermans, J., The Physico-Chemical Constants of Binary Systems in Concentrated Solutions, 5 vols., Interscience, New York, 1959–1960.

Van Winkle, M., Distillation, McGraw-Hill, New York, 1967.

Wichterle, I., J. Linek, and E. Hala, Vapor-Liquid Equilibrium Data Bibliography, Elsevier, Amsterdam, 1973.

www.cheric.org/research/kdb/ (click on box Korean Physical Properties Data Bank).

We see in Table 2-1 that if pressure and temperature are set, then there is only one possible vapor

composition for ethanol, y_Etoh, and one possible liquid composition, x_Etoh. Thus we cannot arbitrarily set as many variables as we might wish. For example, at 1 atm we cannot arbitrarily decide that we want vapor and liquid to be in equilibrium at 95 ° C and x_Etoh = 0.1.

The number of variables that we can arbitrarily specify, known as the degrees of freedom, is determined by subtracting the number of thermodynamic equilibrium equations from the number of variables. For nonreacting systems the resulting Gibbs’ phase rule is

(2-4) where F = degrees of freedom, C = number of components, and P = number of phases. For the binary system in Table 2-1, C = 2 (ethanol and water) and P = 2 (vapor and liquid). Thus,

F = 2 − 2 + 2 = 2

When pressure and temperature are set, all the degrees of freedom are used, and at equilibrium all compositions are determined from the experiment. Alternatively, we could set pressure and x_Etoh or x_w and determine temperature and the other mole fractions.

The amount of material and its flow rate are not controlled by the Gibbs’ phase rule. The phase rule refers to intensive variables such as pressure, temperature, or mole fraction, which do not depend on the total amount of material present. The extensive variables, such as number of moles, flow rate, and volume, do depend on the amount of material and are not included in the degrees of freedom. Thus a mixture in

equilibrium must follow Table 2-1 whether there are 0.1, 1.0, 10, 100, or 1,000 moles present.

Binary systems with only two degrees of freedom can be conveniently represented in tabular or graphical form by setting one variable (usually pressure) constant. VLE data have been determined for many binary systems. Sources for these data are listed in Table 2-2; you should become familiar with several of these sources. Note that the data are not of equal quality. Methods for testing the thermodynamic consistency of equilibrium data are discussed in detail by Barnicki (2002), Walas (1985), and Van Ness and Abbott (1982, pp. 56–64, 301–348). Errors in the equilibrium data can have a profound effect on the design of the separation method (e.g., see Carlson, 1996, or Nelson et al., 1983).