Conformal solution correlation for simple liquids

Abstract

An application of Brown's conformal solution formalism(1, 2 ) to the simple liquids argon, nitrogen, and oxygen was described recently by Calvin and Smith ( 3 ) . The results of that study were promising enough to justify an attempt to develop a broader correlation for mixtures of simple liquids based on the conformal solution formalism. This paper presents the initial version of such a correlation. Despite the limitations inherent in the conformal solution approach, the results are encouraging.Insofar as this paper is concerned, the simple liquids correspond roughly to the Z , = 0. The primary objective of the correlation project was the simultaneous representation of the three primary excessproperties V E , H E , and F E by one set of correlation constants. If this is achieved, then the prediction of F E (and the associated quantities like activity coefficients, x-y diagrams, relative volatilities, and K values) from V E and H E measurements becomes feasible. CORRELATION STRUCTUREThe conformal solution formalism utilized in this correlation project embodies three distinct concepts. The first of these is the universal potential function idea, first stated by Pitzer (7) and utilized by Longuet-Higgins (8) in his development of conformal solution theory. The universal function assumption leads to corresponding states equations which relate the properties of a pure substance a to the properties of a reference substance 0.The second major assumption is that a mixture can be treated as a pure pseudosubstance. The pseudosubstance concept permits the corresponding states equations developed for pure substances to be applied to mixtures.Finally, it is assumed that the properties of a pure substance or a pure pseudosubstance can be accurately represented by a Taylor series expansion around a well-defined reference substance.The working equations based on these three concepts will not be presented in detail here; they are summarized more fully in the previous paper ( 3 ) and are developed in detail by Houng (6) and by Calvin ( 5 ) . Only enough will be included here to make clear the data reduction procedures and to provide a basis for discussion. Corresponding States EquationsThe conformal solution theory provides the followiiig corresponding states relationship between the configura- tional Gibbs free energy of a pure substance a and a reference substance 0.In early applications of the theory, the conformal parameters faa and ha, (the scale-shifting parameters for temperature and pressure, respectively) were always assumed to be constants and usually calculated from the critical properties. Under that assumption, differentiation of Equation ( 1 ) with respect to temperature and with respect to pressure gave the following equations for the configurational enthalpy and volume:The corresponding states principle is not exact and the f a a and ha,, values required to bring the configurational property surfaces together at any point vary with the temperature and pressure. The correct expressions for H,' and V,' obtained by di...

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