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This paper contains further applications on symmetrical liquid mixtures of the molecular thermodynamic theory which has been developped in part I of this series. The essential feature of this theory is the superposition of "chemical" and “random” exchange equilibria between “complexes” formed by a given molecule and its z nearest neighbours, thus allowing a unified treatment of the thermodynamic phenomena in binary liquid mixtures using the equilibrium constant K of the ideal law of mass action and the energy w of pair interactions as parameters.
The temperature and pressure dependences of K and the evaluation of experimental excess enthalpy and excess volume data are treated. Formulas and examples for the calculation of K and w from isothermal and non-isothermal vapour-liquid equilibrium data are given. The conditions for azeotropy with minimum or maximum vapour pressure, resp., are derived. Melting curves for a symmetric eutectic system with superposed miscibility gap are discussed. Further models for partially miscible liquids with competing self-association and complex-formation are treated showing the phenomenon of two separated miscibility gaps.
A thermodynamic theory of liquid mixtures based on a simple molecular model is developed which describes the equilibrium state as the result of a coupling between a "chemical" and a "statistical" equilibrium. The intermolecular interactions are taken into account by considering "complexes" formed between a given molecule and its z nearest neighbours. The equilibrium mole fractions of these complexes are calculated by application of the ideal law of mass action to an appropriate set of "exchange equilibria". Formulae for the excess functions GE and HE and for the activities of the components are derived for the cases z=1 and z=4. GE depends on an equilibrium constant K describing the deviation from random distribution of the equilibrium mole fractions of the complexes. HE depends on K and on an energy parameter w which is related to differences of pair interactions. K and w are independent parameters, and there is no limitation in respect to amount and sign of the excess functions. The conditions for the existence of a critical solution point are formulated; at this point GE has a value of about 0.56 R T. If a model with two equilibrium constants is used allowing for instance competition between "self-association" and "complex-formation", the existence of closed miscibility gaps becomes possible. Closed miscibility curves are calculated and the conditions for their appearance are discussed. The relations between this theory and Guggenheim's statistical lattice theory of symmetrical mixtures are pointed out.
In this paper equilibrium models for the calculation of the excess Gibbs free energy of binary liquid mixtures are developed, the component A of which undergoes chain-forming self-association whilst the component B acts as an 'inert' solvent. It is shown that the extension of the well-known chain-association model of Mecke and Kempter, in which the probability of chain prolongation is assumed to be independent of chain length, is unable to establish satisfactory results because it does not exhibit sufficient unsymmetry. Reduction of the probability of chain growth with in-creasing chain length leads to an improved model with the geometric series replaced by the exponential series. This model, in which only two parameters are used, i. e. the equilibrium constants K for mutual solvation of A and B, and ρ for self-association of A, allows fitting of isothermal experimental GE /R T literature data on cycloalkanol-cycloalkane, alkanol-alkane, and NMF -CCl4 systems within the limits of experimental error. Compared with the two-parameter Wilson equation which gives equally small standard deviations, our equilibrium model has the advantage of allowing passage from GE to HE data and of being applicable to liquid-liquid equilibria.
Phasentrennung als Folge der Konkurrenz zwischen "statistischer" und "chemischer" Vermischung
(1977)
The fact that common thermodynamic conditions are valid for all known types of critical phases (liquid-liquid, liquid-gas, and "gas-gas") suggests that a common principle for the interpretation of material phase instability from a molecular point of view must exist. In this paper we show that the principle of competition between "statistical mixing" (i. e. random mixing) and "chemical mixing" (i. e. mixing effected under the influence of chemical interactions) can give this common inter pretation. If the equilibrium states resulting from both types of mixing are sufficiently different, phase separation occurs. We refer to our earlier papers (since 1972) in which we have applied this principle to describe liquid-liquid phase equilibria by "chemical" models, using the equilibrium constants of exchange equilibria between nearest-neighbour complexes as a measure of "chemical" mixing. In this paper we show that the well-known reduced gas-liquid coexistence curve, T/Tc =f(q/qc), can accurately be fitted by a very simple "mixture" model of molecules A with "vacan cies", provided that the contributions of both statistical and chemical mixing are incorporated into the formula for GE. From a discussion of the application to "gas-gas" phase equilibria in the hyper critical region it results that the weight factor r, by which the contribution of statistical mixing enters into GE, must depend on the density of the gas mixture. Phase separation can only occur if, by increasing pressure, the contributions to GE of statistical and chemical mixing have reached the same order of magnitude. From an attempt to apply the same principle to solid-liquid equilibria it is shown under which external conditions a critical point for this type of phase transition can be expected.