A statistical mechanical solution theory is used as the basis for corresponding states formulations. Universal functions relate the compressibility to the reduced density and the partial molar volume to reduced solvent density only. Correlations are in good agreement with data for all types of nonelectrolytes over wide ranges of temperatures including saturated and compressed systems. The correlations provide simple methods for describing the isothermal pressure dependence of liquid volumes and the pressure dependence of the ideal-solution solubility of gases in liquids. S. CONCLUSIONS AND SIGNIFICANCEFor all liquids the product of compressibility times temperature can be expressed to a high degree of accuracy as a simple function of reduced density only, Equation The single reducing volume is the critical volume for nonpolar substances but is empirically fitted for polar substances. The form of this relation allows a simple expression for the change in volume with an isothermal change in pressure and the entire liquid state can be described from the saturation volumes and the present correlation.The partial molal volume of gases at infinite dilution in liquids can be obtained to within a few yo from a simple function of reduced density of the solvent and the reducing volumes of the gas and solvent, Equations (9) to (11). This generalized expression provides the means to correct for the effect of pressure on Henry's constant as used to predict solubilities of gases. However, the present equation does not describe the partial molal volume of liquids in liquids; apparently the liquid volumetric behavior is different when a substance is above its critical temperature. The expressions for both compressibility and partial molal volume arise from use of a statistical mechanical solution theory involving integrals of the molecular direct correlation function. Their universality can be attributed to the lack of importance of nonspherical forces in the integral of the correlation function. However, it is not clear why the integrals are independent of temperature in the liquid region since essentially complete cancellation of the effects of temperature must occur in the (positive) long range and (negative) short range values of the correlation functions and there is no molecular theory which would predict this. THERMODYNAMIC PROPERTIESA knowledge of the compressibility of the liquidFor mixtures the partial molal volume is useful to de-scribe the volumetric behavior v = 8 x i u i (3) can be used to generate the equation of state for the liquid along an isotherm since the change of pressure which ocand to correct for the pressure dependence of liquid fugaccurs with a change in density is ity f

1corresponding states correlation for the isothermal compressibility of pure liquids. Further, we suggested that the integrated form of this correlation could be useful in determining the volumes of isothermally compressed liquids. Such calculations are reported here for several representative liquids and compared with the predictions of the Yen and Woods correlation (1966), which is now widely used in computerized process design.The generalized correlation for the isothermal compressibility is based on a statistical mechanical solution theory. It contains only one adjustable parameter, a characteristic volume, for each liquid. For many substances, this parameter can be approximated by the critical volume. This feature makes the method potentially very attractive for handling substances for which no compression data are available.The correlation iswhere is the reduced density and v" is the characteristic volume parameter tabulated previously for many substances (Brelvi and O'Connell, 1972). Equation ( 1) describes experimental compressibility data for most liquids in the range 1.6 6 7" 3.7. For nonpolar fluids u", as fitted from experimental data, is close to the critical volume. For polar fluids, however, o" is less than the critical volume.From the definition of the isothermal compressibility K, we have Equation (6) relates the isothermal change in density corresponding to a pressure change and holds over the same reduced density range as Equation (1). Table 1 shows numerically integrated values of the right-hand side of Equation ( 6 )

A Corresponding states method has been developed to predict the binary parameter in the unsymmetric-convention one-term Margules relation for binary activity coefficients of H2 and CH4 in solvents. In addition to the solvent density, only characteristic volumes used previously for partial S. WASEEM BRELVI and JOHN P. OCONNELL molar volumes at infinite dilution and pure solvent compressibility are required. Comparisons with experiment for nonpolar solvents indicate that use of the method is usually significantly more accurate than assuming ideal solution (Henry's law). SCOPEThis paper describes liquid membranes capable of branes much more rapidly than others, and under approsimultaneously separating and concentrating specific salts.priate condition:, can be pumped against its concentrationIn other words, one salt can penetrate the liquid mem-gradient from a solution of low concentration to a solution

convenient, and accurate method of determining hindrance factors for nonsorbing species in stream beds. In operation it serves as a close physical analogue for the process it models. ACKNOWLEDGMENTS= mole fraction potassium chloride at saturation = distance in the vertical direction, cm = void fraction in the salt phase = void fraction of settled soil slurry bed = superscript that refers to saturation a t solid salt = subscript referring to cell entrance interface o

Ind. Eng. Chem. Process Des. Dev. 1902, 21 I 367-370 367 Baddov. R. F.; Brain, P. L. T.; Logeah, B. A.; Eymery, J. P. Chem . Eng . Scl. Blrd, R. B.; Stewart, W. E.; Lightfoot, E. N. "Transport Phenomena"; Wiley: Emery, J. P. Sc.D. Thesls, M.I.T. Cambridge, MA, 1964. Fletcher, R.; Reeves, C. M. -ut. This paper has been presented at 2nd World Congress of Chemical Engineering held at Montreal, Canada, Oct 4-9,1981. The authors are thankful to the Plant Management for extending all facilities. Thanks are also due to M. Sriram for his careful reading and helpful remarks.

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An approximate expression for the direct correlation function of a real fluid in terms of its intermolecular potential and hard-sphere distribution functions is examined. Calculations for argon using the Percus-Yevick hard-sphere distribution functions are compared with molecular correlation functions from X-ray scattering data and the macroscopic integral of the correlation function related to the isothermal compressibility. The results are not satisfactory for any pair potential unless the parameters are made state dependent. However, since partial compensation occurs on integration, fairly good correlation of the isothermal compressibility can be obtained up to twice the critical density (except near the critical point itself) using Lennard-Jones (6-12) potential parameters obtained from second virial coefficient data and the Barker-Henderson hardsphere diameter.Nous utilisons une expression approximative dans le but de determiner la fonction de correlation directe d'un fluide reel en termes de potentiel intermoleculaire et de fonctions de distribution de sphere rigide. Nous comparons les calculs pour I'argon, effectuts a partir des fonctions de distribution de Percus-Yevick pour des spheres rigides aux fonctions de correlation moleculaires tirees de resultats de diffraction de rayons-)<; nous etablissons ensuite la relation entre I'integrale macroscopique de la fonction de correlation et la compressibilite isotherme. Les resultats ne sont pas satisfaisants pour toute paire de potentiel, a moins que les parametres dependent de I'etat. Toutefois, puisqu'une compensation partielle se produit durant I'integration, nous pouvons obtenir une assez bonne correlation de la compressibilite isotherme, jusqu'au double de la densite critique (a I'exception des environs du point critique), en utilisant les parametres de potentiel (6-12) de Lennard-Jones, obtenus a partir du second coefficient du viriel et du diametre de la sphere rigide de Barker-Henderson.[Traduit par le journal]Canadian Journal of Chemistry, 50, 3135 (1972) In statistical thermodynamic studies of fluids, the structure of a real fluid state can be approximated as a perturbation about a reference state whose properties are known (1-3, 12). The relation between the properties in the two states is then found in terms of a perturbation parameter. Most work in this area has been directed towards describing the radial distribution function of the real fluid. Barker and Henderson (3,12) have successfully used their perturbation theory to model the real fluid as a perturbation about the rigid sphere fluid. They have calculated the radial distribution function and thermodynamic properties to a high degree of accuracy. However, little attention has been given to determining a satisfactory expression for the direct correlation function which is of shorter range than the radial distribution function and could lead to more accurate thermodynamic properties. In this paper we have analyzed an analytical expression for the direct correlation function which is a n ap...

A first-order expansion of the Percus-Yevick functional is derived for the properties of a real fluid as a perturbation about a hard-sphere reference fluid. The resulting expression is an integral equa ion relating the real fluid distribution functions and intermolecular potential to those of the reference fluid. Use of a realistic approximation in calculating the integral in the Ornstein-Zernike equation leads to real-fluid distribution functions that are in closer agreement with molecular dynamics results than those of the usual first-order Percus-Yevick equation.