Through an empirical but rational approach to the development of equations to represent the composition dependence of the excess Gibbs function for binary liquid systems, it has been found possible to correlate VLE data precisely, even for highly nonideal systems. This makes possible the application of Barker's method to the reduction of VLE data on a routine basis. The validity of the method is demonstrated through application to several sets of data from the literature, and new experimental data are presented for six diverse binary systems in vapor-liquid equilibrium at 5OOC. M SCOPEIn Part I of this series of papers Van Ness et al. (1973) described the numerical methods by which one may accomplish the reduction of binary VLE data to yield a correlation for the excess Gibbs function of the liquid phase. Byer et al. (1973) in Part I1 demonstrated the effectiveness of the numerical procedure based on P-x data alone for 15 binary systems. There is an additional procedure for the reduction of P-x data, developed by Barker (1953), that was not pursued in these earlier papers. It is based on Equation (15) only one showed such large deviations from ideality that it could not be characterized by the four-suffix Margules equation. In fact, the data for this system, n-pentanol-n-hexane, defied representation within the precision of the data by all known equations. It was the existence of such highly nonideal systems that deterred us from the exploitation of Barker's method as a general procedure for the reduction of P-x data. However, Barker's method is a most attractive one-step fitting procedure, and this fact provides the incentive for development here of the means by which it can be made more generally applicable. CONCLUSIONS AND SIGNIFICANCEWe have found that highly nonideal systems, even those verging on instability, may be very precisely fit by one of two simple equations, the 5-suffix Margules equation or a new equation called the modified Margules equation. Both are basically four-parameter equations that reduce to the three-and four-suffix Margules equations as special cases. Thus they retain all of the advantages associated with the Margules equations, including the capability of predicting limited liquid-liquid miscibility. Applied to data from the literature for the methanol-carbon tetrachloride and chloroform-ethanol systems these equations are shown to yield very precise correlations of the P-x-y data when regression is carried out by Barker's method, which is based on just the P-x data. From this we conclude that reliable P-x data only are required to provide reliable VLE relationships. Moreover, it is shown that use of the reported y values along with the P-x data in the datareduction process distorts the correlation of both the P-x and y-x relationships. Barker's method in conjunction with the two types of Margules equations mentioned earlier are applied in the correlation of new VLE data at 5OoC for the binary systems acetone-chloroform, acetone-methanol, chloroform-methanol, chloroform-ethanol, chlo...

Extensive heat-of-mixing data taken wlth an isothermal tltration calorimeter for the acetone-chloroform-methanol system at 5OoC are reported, and a correlation of the results Is presented. When combined wlth a correlatlon for the excess Gibbs free energy reported earlier, these results allow calculation of excess entropies.The isothermal titration calorimeter described by Winterhalter and Van Ness (9) has been used without modification for measurement of heats of mixing for the system acetonechloroform-methanol over the full composition range of the ternary system. Included are data for the constituent binaries; for ternary mixtures 15 runs were made by addition of a pure component to an initial mixture made up of known amounts of the other two components. The extent of coverage of the ternary composition diagram is indicated by the lines of Figure 1.The chemicals employed were chromatoquality reagents supplied by Matheson Coleman & Bell; they were used as received with a minimum indicated purity of 99.8 mol %. Data for Binary SystemsThe experimental results for the three binary systems, acetone( 1)-chloroform(2), acetone( l)-methanol(3), and chloroform(2)-methanol(3), are given in Table I (deposited with the ACS Microfilm Depository Service). These data are well correlated by equations of the form: ---Ajpj + AI?~ -HE XixglT (Xjixi + XfljIXix, +

A simple glass rectification apparatus proves effective for the rapid degassing of liquids prior to their introduction into a device for vapor/liquid equilibrium measurement by the total-pressure method.Recent years have seen increasing use of the static method for measurement of vapor/liquid equilibrium data; the

Total pressure measurements taken for the ternary systems acetonechloroform-methanol and chloroform-ethanol-n-heptane at 5OoC are reduced by Barker's method and correlated by an equation similar to one proposed by Wohl (1953 SCOPEThe apparatus of Gibbs and Van Ness (1972) has been adapted to P-x measurements for ternary Systems. Extensive data on the acetone-chloroform-methanol and chloroform-ethanol-n-heptane systems at 5OoC are reported. Data reduction by Barker's method yields analytical expressions for the composition dependence of the excess Gibbs function for these systems. Through use of a general expression for GE similar to one proposed by Wohl (1953), the precise expressions for binary systems discussed by Abbott and Van Ness (1974) in Part 111 are introduced into the equation for ternary systems, and all of the advantages of Barker's method are cxkmded directly to ternary systems. CONCLUSIONS AND SIGNIFICANCEParts I, 11, and I11 of this series of papers have dealt with vapor-liquid equilibrium in binary systems and have tions based on just P-x data. The possible methods of data reduction have been detailed, and the focus of attention has ultimately fallen on Barker's method, a one-step procedure that requires an analytical expression for GE that is capable of reproducing the P-x relation within experimental accuracy. The advantages attending Barker's simple and direct.method for binary systems are of greater significance for muhicomponent systems because the alternative methods more complex. The extension of Barker's method to multicomponent systems requires nothing more than an appropriate analytical expression for G~. Having demonstrated in Part 111 the practicality of the method for highly nonideal binary systems, we here show that the extension to ternary systems is not only feasible, but demonstrated the reliability and advantages of conelaOf data reduction techniques becomeThe apparatus for vapor-liquid equilibrium determination from total pressure measurements described by Gibbs and Van Ness (1972) has been modified by the addition of a third degassing chamber and piston injector so that data may be taken for ternary systems. We report here results for the systems acetone-chloroform-methanol and chloroform-ethanol-n-heptane at 50°C. Data for the six constituent binaries, also for 50"C, were given by Abbott and Van Ness (1974) in Part I11 of this series of papers. The acetone, chloroform, and methanol were chromatoquality reagents supplied by Matheson, Coleman, and Bell; the n-heptane was the pure grade of Phillips Petroleum Company; the reagent-quality ethanol came from U. S.Industrial Chemicals. Except for degassing, all reagents were used as received with a minimum indicated purity of 99.8 mole %.For the acetone-chloroform-methanol system the raw data for ternary mixtures consist of 164 sets of P, XI, x2, x3values: 98 such sets are reported for the chloroform-ethanol-n-heptane system. * TREATMENT OF DATAData reduction by Barker's methocl (Barker, 1953) is accomplished through use of an ...

Limitations and capabilities of a generic cubic equation of state are analyzed in light of observed real-fluid behavior, and criteria are presented for dassification of specializations of the generic equation. An example is worked out which illustrates the application of these criteria to the development of new equations of state. MICHAEL M. ABBOTT Division of Fluid, Chemical, and Thermal Processes Rensselaer Polytechnic institute Troy, New York 12181Since the work of van der Waals a century ago, more than 100 new fluid-phase thermal equations of state have been proposed. Because of the stringent demands for representation of modern high-precision data and of the needs of engineers for ever more versatile design tools, complexity is a dominant feature of the newer equations of state. Given the availability of electronic computers, complexity is of course no longer a severe disadvantage, but there nevertheless remain incentives for the study of equations of state of relatively simple algebraic form containing only a few adjustable parameters. Such equations still enjoy wide use for engineering screening studies and as research tools for semiquantitative prediction or rationalization of equilibrium phenomena. Moreover, the simpler expressions are commonly employed as bases for the development of more comprehensive equations of state. Effective use of a simple equation in any of these capacities clearly requires an understanding of its limitations and capabilities.The best known simple equations of state are cubic in volume; most of them are specializations of the generic equation One may, however, develop in a straightforward manner simple and compact specializations of the generic equation suitable for accurate work for limited ranges of the state variables. We illustrate the development of such a specialization for low pressures and obtain as a byproduct a simple correlation for the second virial coefficients of normal fluids. For many applications, this correlation is comparable in accuracy to the correlation of Pitzer and Curl. and e are constants for a given fluid. Equation (1) may be viewed as an extension of the van der Waals equation, to which it reduces as the simplest nontrivial special case CONCLUSIONS AND SIGNIFICANCE GENERIC CUBIC EQUATION OF STATE