Mixture thermodynamic excess functions

Renon, H., Prauznits, J.M., 1968, Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures, AIChE Journal, 14, 135. 

Renon, H. and Prausnitz, J.M., Local composition in thermodynamic excess functions for liquid mixtures, AIChE J., 14,135,1968. 

The thermodynamic excess functions for the 2-propanol-water mixture and the effects of lithium chloride, lithium bromide, and calcium chloride on the phase equilibrium for this binary system have been studied in previous papers (2, 3). In this paper, the effects of lithium perchlorate on the vapor-liquid equilibrium at 75°, 50°, and 25°C for the 2-propanol-water system have been obtained by using a dynamic method with a modified Othmer still. This system was selected because lithium perchlorate may be more soluble in alcohol than in water (4). 

Grover, J., Chemical mixing in multicomponent solutions An introduction to the use of Margules and other thermodynamic excess functions to represent non-ideal behavior, pp. 67-97 in Thermodynamics in Geology, ed. by D. G. Fraser, D. Reidel, Dordrecht, The Netherlands, 1977. This review article provides a fine introduction to the thermodynamic theory of mixtures underlying the Margules expansion for adsorbate-species activity coefficients. 

Before surveying aqueous mixtures, it is informative to examine briefly the thermodynamic excess functions for two particular non-aqueous mixtures, (a) acetone + chloroform (Fig. 27) and (b) methyl alcohol + carbon tetrachloride (Fig. 28). 

Figure 27. Thermodynamic excess functions for acetone + chloroform mixtures at 298 K x j = mole fraction of chloroform (Franks and Ives, 1966).

The mixture dimethyl sulphoxide + water has attracted a great deal of interest. The excess function HE is negative for this mixture at 298 K (Clever and Piggott, 1971 Fox and Whittingham, 1975), as also are GE (Lam and Benoit, 1974 Philippe and Jambon, 1974) and FE-quantities (Lau et al., 1970). A set of smoothed thermodynamic excess functions is shown in Fig. 54 (Kenttamaa and Lindberg, 1960). The dependence on x2 of the isothermal compressibilities of DMSO + water mixtures is quite different from that for the TA monohydric alcohols + water mixtures. The curves for the latter systems show... 

We shall now show how the activity coefficients and thermodynamic excess functions can be evaluated explicitly in a particularly simple case, namely that in which the only complexes formed are the double molecules AB. A solution which appears to correspond to this case is the mixture acetone-f chloroform. 

An accurate equation of state of fluids is used to test the combining rules for the interaction energy uy of mixtures derived from the theories of London energy between small or large (chain) molecules. The tests are based mostly on comparisons with the thermodynamic excess functions of binary systems at P = 0. For long chains the parameter r)/k, determining the dependence of u/k on the temperature, depends on the reduced density p = V°/V of the system (where V° is the close-packed volume) and /k—>0 when P > 0.75 (solid state). 

In addition to the above direct tests, the rule given by Equation 6 was tested by calculating the thermodynamic excess functions of mixtures. The relations are given by Kreglewski and Chen (8). The basic one for the residual Helmholtz energy of a mixture Amr is... 

The Measurement of Thermodynamic Excess Functions of Binary Liquid Mixtures... 

This chapter deals with experimental methods for determining the thermodynamic excess functions of binary liquid mixtures of non-electrolytes. Most of it is concerned with techniques suitable for measurements in the temperature range 250 to 400 K and the pressure range 0 to 100 kPa. Techniques suitable for lower temperatures will be briefly reviewed. Techniques for measuring the molar excess Gibbs function G, the molar excess enthalpy and the molar excess volume will be discussed. The molar excess entropy can only be determined indirectly from either measurements of (7 and at a specific temperature = (If — C /T], or from the temperature dependence of G m [ S m = The molar excess functions have been defined by... 

Binary mixtures of non-aromatic fluorocarbons with hydrocarbons are characterized by large positive values of the major thermodynamic excess functions G , the excess Gibbs function, JT , the excess enthalpy, 5 , the excess entropy, and F , the excess volume. In many cases these large positive deviations from ideality result in the mixture forming two liquid phases at temperatures below rSpper. an upper critical solution temperature. Experimental values of the excess functions and of Tapper for a representative sample of such binary mixtures are given in Table 1. 

The dissolution of a gas in a liquid is basically a two-stage process. First a cavity must be formed within the solvent of sufficient size to accommodate the solute molecule, and this step is followed by the insertion of the solute within the solvent cavity with a resultant change in the energy of the system which depends primarily on the magnitude of the solvent-solute interactions. This second stage of the process is now reasonably well understood in terms of the statistical mechanical theories of fluid mixtures discussed briefly in previous sections, although accurate predictions of thermodynamic excess functions are only possible in a limited number of cases when auxiliary measurements enable explicit values of and x to be estimated. It is, as yet, not possible to predict gas solubilities with comparable confidence. 

H. L. Friedman, Lewis-Randall to McMillan-Mayer conversion for the thermodynamic excess functions of solutions. Part III. Q>mmon-ion mixtures of two electrolytes, J. Solution Chem. 1, 419 (1972). 

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