To be useful, a thermodynamic treatment of high-pressure vapor-liquid equilibria must describe how the fugacity of each component, in each phase, depends on the temperature, pressure, and composition. In the vapor phase, this dependence i s given by the fugacity coefficient which can be found from vapor-phase volumetric properties a s given by an equation of state. In the liquid phase it is more convenient to express the fugacity of a component as the product of the mole fraction, an arbitrary standard state fugacity and an activity coefficient; the effect of temperature, pressure, and composition on the fugacity of a component in the liquid phase i s determined by the effect of these variables on the activity coefficient. In this work we are concerned with the effect of pressure on the activity coefficient.At low or moderate pressures, liquid-phase activity coefficients are very weakly dependent on pressure and, as a result, it has been customary to assume that, for practical purposes, activity coefficients depend only on temperature and composition. In many c a s e s this is a good assumption but for phase equilibria a t high pressures, especially for those near critical conditions, it can lead to serious error.When the standard state fugacity is defined a t a constant pressure, then for any component i the pressure dependence of the activity coefficient y i i s given exactly by On the other hand, when the standard state fugacity is defined a t the total pressure of the system, Equation (1) must be modified to ( l a )By judicious choice, i t is sometimes possible to use a standard state such that V, = z'io, in which case the activity coefficient is very nearly independent of pressure (17).However, since "i is a function of composition, whereasis not, such a happy choice of standard state can make the right-hand side of Equation (2) very small over only a narrow range of composition. At high pressures in the critical region, Ci is usually a strong function of composition, especially for heavy components where Gi frequently changes sign a s well a s magnitude.Experimental activity coefficients obtained a t P, the total pressure of the system, can be corrected to a constant, arbitrary reference pressure P' by integration of Equation (1):

= concentration emerging from batch reactor after literature Cited Asbjgrnsen, 0.

While much attention has been given to second virial coefficients of nonpolar gases, experimental and theoretical studies on third virial coefficients are scarce. This work presents a correlation of third virial coefficients within the framework of the corresponding states principle. The correlation is useful for estimating third virial coefficients of pure and mixed nonpolar gases, including the quantum gases helium, hydrogen, and neon. The importance of third virial cross coefficients in phase equilibrium predictions is illustrated with calculations for the solid-gas, methane-hydrogen system a t 76°K.Brief attention is given to the pressure series form of the virial equation. Because of fortuitous cancellations, it is shown that for reduced temperatures above 1.4, the pressure series, truncated after the second term, is applicable to a wider range of density than the density series truncated after the second term. However, when both series are truncated after the third term, the density series appears to be superior regardless of reduced temperature.To describe the volumetric properties of gases, many For practical work, the advantages and disadvantages of the virial e uation have often been discussed (16, 46, 47, 48) ; briefy, th e advantages follow from the direct relationship between virial coefficients and intermolecular forces and the disadvantages follow from our inadequate quantitative knowled e of virial coefficients higher than at moderate densities, below the critical, but has little practical utility at high densities beyond the critical.The technical literature abounds with studies of the second virial coefficient and, as a result of much theoretical and experimental work, it is now possible to make good estimates of the second virial coefficient of a large number of gases from a minimum of experimental data (29, 30, 58). For typical applied calculations, the correlation of Pitzer and Curl (27, 45) is probably the most useful. However, much less attention has been given to the third virial coefficient, primarily for two reasons: first, because of experimental difficulties, good data for the third virial coefficient are scarce, and second, theoretical calculations with potential energy functions used are tedious and, for accurate results, require corrections to the assumption of pairwise additivity which are at best known only approximately (55 to 57). In this work we have collected and examined the limited amount of experimental third virial coefficients now available and we have correlated them as best as we can. Our correlation is limited to nonpolar gases but holds also for the quantum fluids helium, hydrogen, and neon. Since the purpose of our correlation is application oriented, we have given the second. As a resu 7 t, the virial equation is most useful brief attention to the third virial coefficient of the pressure series virial equation which, while theoretically less significant, is sometimes more convenient. More important, we have considered how our correlation may be used to estimate th...

Effective critical constants for helium and normal hydrogen have been determined by fitting experimental volumetric data for these gases to the generalized tables of Pitzer. The effective critical temperature and pressure are found to depend on the temperature and on the molecular mass in a simple manner permitting good estimates to be made of effective cribical constants for other quantum gases for which experimental data are scarce (neon, isotopes of helium and hydrogen). Pitzer's tables are used with pseudocritical mixing rules to predict thermodynamic properties of mixtures a t high pressures and low temperatures. Calculated compressibility factors and enthalpies are in excellent agreement with experimental results for dense mixtures of hydrogen-methane, hydrogen-argon, and helium-nitrogen.The volumetric properties of nonpolar or slightly polar fluids have been correlated by Pitzer et al. (7,19,20) using an extended form of the theorem of corresponding states. Pitzer's correlation excludes highly polar fluids and also those light (quantum) gases whose configurational properties must be described by quantum rather than classical statistical mechanics. In this work we describe a simple, semiempirical procedure which, in effect, extends Pitzer's correlation to the quantum gases. This extension may be useful for predicting volumetric and derived thermodynamic properties of neon and isotopes of helium and hydrogen for which experimental data are scarce. More important for technical applications, however, this extension provides a good method for predicting thermodynamic properties of dense gaseous mixtures which contain one or more of thg quantum gases. Such mixtures are common in many technical operations in petroleum and related industries; since these mixtures are frequently at low temperatures and high pressures, deviations from ideal behavior are sometimes very large. The configurational property of most interest for rational design of cryogenic processes is the configurational enthalpy which, at high pressures and low temperatures, may make a significant contribution to the refrigeration load. Optimization of cryogenic separation processes requires accurate enthalpy information and, since experimental enthalpy data for dense mixtures are scarce, it is desirable to be able to predict such enthalpies with confidence. EXTENSION OF PITZER'S C O R R E L A T I O N TO QUANTUM GASESPitzer correlated the compressibility factors of pure gases in terms of two generalized functions, d o ) and z(l), such that Equation (1) is a direct consequence of Pitzer's form of the theorem of corresponding states. The acentric factor, which is a constant for any given gas, is a measure of the importance of noncentral intermolecular forces and for small molecules (for example, nitrogen, methane, argon) it is very nearly zero. The functions .do) and dl) have been tabulated (20).Pitzer's tables are not applicable to the quantum gases when the true critical constants and acentric factor are used in Equation ( I ) , because these gases do...