Vapor‐liquid equilibrium: Part III. Data reduction with precise expressions for G^E

Abstract

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...

Thermodynamic properties of (n-alkoxyethanols + organic solvents). XII. Total vapour pressure measurements for (n-hexane,n-heptane or cyclohexane + 2-methoxyethanol) at different temperatures

“…Because the experimental technique does not provide experimental values for y, the mole fraction in the vapour phase, the ( p, x) measurements were reduced by Barker's method (23) to obtain values of y and f i , the activity coefficient of component i in the liquid state. To this end, it was assumed that the latter are represented by the five-parameter Margules equation: (24) …”

Thermodynamic consistency of vapor‐liquid equilibrium data at high pressure

“…Therefore, there has been a considerable effort to develop excess Gibbs energy ( G E ) models with enough flexibility to yield random scattering about zero of the P-and y-residuals, as well as with a sufficiently small number of adjusting parameters with respect to the experimental points available. The Redlich-Kister and the Margules equations are widely used G expressions; more flexible correlating equations have been proposed, such as the 5-parameter modified Margules equation (Abbott and Van Ness, 1975) and the sum of symmetric functions equation (Rogalsky and Malanowski, 1977). All of these models provide pressure-independent activity coefficients and are inherently thermodynamically consistent (in the Gibbs-Duhem's sense) only at constant temperature and constant pressure.…”

Isothermal v.l.e. and excess molar Gibbs energy of binary and ternary mixtures containing diisopropyl ether,n -heptane and isopropanol at T= 313.15 K

“…(16)(17)(18) The data reduction of the binary and ternary mixtures has been performed using Barker's method (19) according to well established procedures. (20,21) …”