Interpolation and extrapolation of thermodynamic data for liquid mixtures are common necessities in chemical engineering. The model of ideal solutions is useful for providing a first approximation and a reference, but deviations from ideality are frequently large. These deviations are expressed by excess functions which depend on the concentrations of the components and on the temperature.As Gibbs energy cou gl d be conveniently expressed by an algeresults calculated r rom several models. We consider both THE WILSON AND H E I L E Q U A T I O N STo take into account nonrandomness in liquid mixtures, Wilson (24) suggested a relation between local mole fraction x i 1 of molecules 1 and local mole fraction x21 of molecules 2 which are in the immediate neighborhood of molecule 1: Both Equations ( 2 ) and (5) are useful, semiempirical relations for thermodynamic excess functions; both equations contain only two adjustable parameters per binary,

P txpression for the Excess Gibbs Energy of Partly or Completely Miscible SystemsTo obtain a semi-theoretical equation for the excess Gibbs energy of a liquid mixture, Guggenheim's quasi-chemical analysis is generalized through introduction of the local area fraction as the primary concentration variable. The resulting universal quasi-chemical (UNIQUAC) equation uses only two adjustable parameters per binary. Extension to multicomponent systems requires no ternary (or higher) parameters.The UNIQUAC equation gives good representation of both vaporliquid and liquid-liquid equilibria for binary and multicomponent mixtures containing a variety of nonelectrolyte components such as hydrocarbons, ketones, esters, amines, alcohols, nitiles, etc., and water. When well-defined simplifying assumptions are introduced into the generalized quasi-chemical treatment, the UNIQUAC equation reduces to any one of several wellknown equations for the excess Gibbs energy, including the Wilson, Margules, van Laar, and NRTL equations.The effects of molecular size and shape are introduced through structural parameters obtained from pure-component data and through use of Staverman's combinatorial entropy as a boundary condition for athermal mixtures. The UNIQUAC equation, therefore, is applicable also to polymer solutions. SCOPEA significant fraction of chemical process design is concerned with separation of fluid mixtures by diffusional operations. All design methods for such separations require quantitative estimates of fluid-phase equilibria; this work provides a contribution toward making such estimates for liquid-phase mixtures of nonelectrolytes, including polymers, and including those mixtures where nonideality is sufficiently strong to produce two liquid phases.Activity coefficients in liquid mixtures can be calculated from a model which expresses the excess Gibbs energy of the mixture as a function of the composition. A new model, called UNIQUAC, is presented here. This model is derived from a statistical-mechanical basis extending that used by Guggenheim in his quasi-chemical theory. Unlike Guggenheim's theory, however, UNIQUAC is applicable to mixtures wh0.e molecules differ appreciably in size and shape and, unlike previous attempts to gener-alize Guggenheim's method, UNIQUAC contains no more than two adjustable parameters per binary.UNIQUAC is applicable to multicomponent mixtures of nonpolar and polar liquids (including those that participate in hydrogen bonding) as encountered in typical chemical and petrochemical processes. No ternary (or higher) constants are required. Attention is given to vapor-liquid and liquid-liquid equilibria.When well-defined simplifying assumptions are made, the UNIQUAC model can yield any one of several wellknown expressions for the excess Gibbs energy, including the van Law, Wilson, and NRTL equations. Relative to these well-known equations, the advantage of UNIQUAC is that, for a large variety of multicomponent systems and using only two adjustable parameters per binary, reliable estimates can b...

A simple technique is described for calculating the adsorption equilibria for components in a gaseous mixture, using only data for the pure-component adsorption equilibria a t the same temperature and on the same adsorbent. The proposed technique is based on the concept of an ideal adsorbed solution and, using classical surface thermodynamics, an expression analogous to Raoult's law is obtained. The essential idea of the calculation lies in the recognition that in an ideal solution the partial pressure of an adsorbed component is given by the product of its mole fraction in the adsorbed phase and the pressure which it would exert as a pure adsorbed Component a t the same temperature and spreading pressure as those of the mixture. Predicted isotherms give excellent agreement with experimental data for methaneethane and ethylene-carbon dioxide on activated carbon and for carbon monoxide-oxygen and propane-propylene on silica gel. The simDlicitv of the calculation, which requires no data for . . the mixture, makes it espec'ially useful for engineering applications.Adsorption equilibria are required in the design of heterogeneous chemical reactors and in certain types of separation equipment. In many cases the desired equilibria are for a mixed rather than for a pure gas, and it is therefore of considerable practical interest to develop a technique for estimating the adsorption equilibria of a gaseous mixture from the known adsorption isotherms of the pure components. Such a technique is described here. The principal idea on which the proposed technique is based is the proper definition of an ideal adsorbed solution in a manner analogous to that used for liquid-phase solutions. As shown towards the end of this work, the equations developed from the ideal-solution concept predict adsorption isotherms which are in excellent agreement with experimental adsorption data for gaseous mixtures.A complete review of the current status of mixed-gas adsorption is given in the excellent monograph by Young and Crowell (12). The usual procedure for the interpretation of experimental adsorption equilibria for a gaseous mixture is to compare the experimental data with the prediction of some theoretical model. Most models for physical adsorption contain two or three parameters, and it is usually assumed that the parameters for mixture adsorption can be written as some simple function of the purecomponent parameters and the composition of the adsorbed phase. Thus, a determination of the pure-component parameters from experimental data permits the prediction of mixture adsorption equilibria. Unfortunately, the above procedure has not been very successful; the predictions have not been in quantitative agreement with the experimental data ( 2 ) and often not even in qualitative agreement ( 1 ) .An alternative procedure for interpreting mixture data is the liquid entropy model of Arnold ( 1 ) . In this model, it was proposed that Raoult's law should be obeyed but only for adsorption sites having the same heat of adsorption, Using two addit...

and Pratt (1933) contained lower values of holdup (most values were < 10 % ) , and V, was shown to be more nearly constant. At low values of holdup, there is little difference between V, and V,. Generally, V, is believed to be a more useful correlating parameter over a wide range of holdup values. However, neither of the parameters is as accurate as one may desire, and improved correlations, especially those with a theoretical basis, are needed. ACKNOWLEDGMENT This work was sponsored by the U.S. Atomic Energy Commission under contract with Union Carbide Corporation. The authors would like to express their appreciation to John S. Taylor, R. 0. Payne, and several students and Directors of the Massachusetts Institute of Technology Chemical Engineering Practice School who made most of the measurements and otherwise assisted in the study.NOTATION a = d p = vc = Vc.f -v d = --Vd,f v, = cm2 of packing surface/cm3 of packing volume diameter of packing, cm superficial velocity of the continuous phase, cm/s superficial velocity of the dispersed phase, cm/s superficial continuous phase velocity at flooding, cm/s superficial dispersed phase velocity at flooding, cm/s characteristic velocity defined by Equation (6), cm/s V, Greek Letters Ap phases, g/cm3 E p = viscosity, poise AVc,01/2 = defined by Equation (5) AV,,01/2 = defined by Equation ( 5 ) Subscripts c, d = continuous and dispersed phases, respectively o = intercept value; flow rate of other phase ap-= superficial slip velocity, cm/s = difference in densities of dispersed and continuous = void fraction of the packing, dimensionless proaching zero A group-contribution method is presented for the prediction of activity coefficients in nonelectrolyte liquid mixtures. The method combines the solution-of-functional-groups concept with a model for activity coefficients based on an extension of the quasi chemical theory of liquid mixtures (UNIQUAC). The resulting UNIFAC model (UNIQUAC Functional-group Activity Coefficients) contains two adjustable parameters per pair of functional groups. AAGE FREDENSLUND, RUSSELL L. JONES, and JOHN M. PRAUSNITZ V IBy using group-interaction parameters obtained from data reduction, activity coefficients in a large number of binary and multicomponent mixtures may be predicted, often with good accuracy. This is demonstrated for mixtures containing water, hydrocarbons, alcohols, chlorides, nitriles, ketones, amines, and other organic fluids in the temperature range 275O to 400OK.

In contrast to the large body of work published on nonelectrolyte and strong electrolyte solutions, theoretical or correlational work is sparse for aqueous, volatile weak electrolytes. Van Krevelen's (1949) studies apply only to ammonia rich systems; further, they are limited to restricted ranges of ammonia/acid ratios and, for some cases, require experimental information which is not available. The more recent work of Edwards et al. (1975) is limited to low concentrations of weak electrolytes and to temperatures below (about) 80°C. The present work extends Edwards' earlier efforts to higher concentrations and higher temperatures.The purpose of this work is to extend a previously presented thermodynamic framework for calculating vaporliquid equilibria for solutions containing volatile weak electrolytes as commonly encountered in the chemical and related industries. The electrolytes examined are ammonia, carbon dioxide, hydrogen sulfide, and sulfur dioxide for the temperature range 0' to 17OOC; the composition range, depending on extent of ionization, may be as high as 10 to 20 moial. Limited information is also given for hydrogen cyanide.Parameters Al, Az, Aa, and A4 are given in Table 1. Parameters for the first and second dissociation constants of carbon dioxide are based on data reported by Clark ( 1966) ; for hydrogen sulfide, ammonia, hydrogen cyanide, and water, the parameters are those given by Tsonopoulos t In some cases it is preferable to write instead of Equation (2) -UNH&P -P w~) RT ~NH.@NE~$ = ~N H , Y O N + J~N H , exp ooo,(P -Pw') yco,@co,P = mco,y*co,Hco, exp RT yielding seventeen simultaneous, independent equations containing tho known partial pressures.