Extrapolation/interpolation of infinite dilution, activity coefficient as well as liquid and solid solubility between solvents: Part 1. Alkane solvents

Abstract

Infinite dilution activity coefficients play a vital role in modeling of phase and chemical equilibrium behavior. From the dependence of the limiting activity coefficient of a solute on the solvent, important properties like liquid and solid solubility in these solvents can be deduced. Although a large amount of experimental information is available in the open literature as well as from thermophysical data banks such as the Dortmund Data Bank (DDB), the behavior of high boiling solutes in low boiling solvents is often not known, partly due to difficulties in experimental determination.A method for the extrapolation of infinite dilution activity coefficients and thus the liquid and solid solubility of any solute in different solvents within one solvent family is under development. Results of a method applicable to any solute in a large variety of different saturated hydrocarbon compounds are presented in this paper.In this method, the activity coefficient is assumed to consist of a combinatorial and residual contribution. In the case of alkane solvents, only this combinatorial contribution changes when going from one solvent to another. Several well known combinatorial expressions were evaluated and were found to produce poor extrapolations in many instances. Quite surprisingly, free-volume combinatorial expressions performed best even for some of the rather low molecular weight compounds used in this test.A new empirically modified free-volume expression is proposed which allows for accurate extrapolation. Additional activity coefficient data have been determined via GLC (gas–liquid chromatography) to validate the method. In most cases extrapolations were within 10% of the experimental findings and safely within or close to the scatter of literature data.The method allows for example the safe estimation of the infinite dilution behavior as well as liquid and solid solubility of high boiling components in hydrocarbons from data for high boiling solvents usually determined easily by gas–liquid chromatography. Additionally, the newly developed combinatorial expression for infinite dilution data should be able to greatly improve other predictive mixture models, e.g. UNIFAC, mod. UNIFAC and COSMO-RS type models in the cases when large molecules in low molecular weight solvents are considered. This was verified for a larger number of experimental limiting activity coefficient data from literature.