Infinite dilution activity coefficients comparing predictions

Chen et al. and the High-Danner equations of state are comparable, each having its strengths and weaknesses. The method of Chen et al. performs as well as UNIFAC-FV for the finite data, and almost as well for the infinite data. Also, Chen et al. performs as well as UNIFAC-FV for infinite dilution data where the number of polymer repeat units is under 200. The drawbacks to using Chen et al. are that it has twice as many worst case occurrences as UNIFAC-FV, and it has problems at certain temperatures. The large number of worst point cases implies the model is not as consistent as UNIFAC-FV. At some temperatures the model cannot find a liquid-like root for the solvent and thus cannot predict a value for the activity coefficient. Neither of the other models have this type of temperature problem. 

The High-Danner equation of state performs well for predictions of activity coefficients for ether-ether systems and for aromatic polymers at infinite dilution. The drawbacks of High-Danner model are the small number of subgroups and lower accuracy compared to the UNIFAC-FV model. The High-Danner model is the only model that was derived as an equation of state and that has been used as an equation of state for prediction. The other two models are not capable of representing pressure dependence in the vapor or liquid phases. 

First, a rigorous expression for the activity coefficient of a solid solute at infinite dilution in an ideal multicomponent solvent was derived using the fluctuation theory of solution. Second, the obtained expression was used to express the solubility of a poorly soluble solid in an ideal multicomponent solvent in terms of the solubilities of this solid in two subsystems of the multicomponent solvent and their molar volumes. Finally, the developed procedure was used to predict the drug solubilities in ternary and quaternary aqueous mixed solvents using the drug solubilities in the constituent binary aqueous mixed solvents. The predicted solubilities were compared with the experimental ones and good agreement was found. 

The question remains, however, of whether the solution is in fact infinitely dilute at a solute concentration of xi. Only if this is true is it valid to assume that yi = y - Literature values of solubility data for several compounds in water were used to obtain parameters for the UNIQUAC and NRTL excess Gibbs energy expressions, and y values for these compounds were calculated. The calculated values are compared with inverse solubility data in Table I. The inverse solubility predicts lower values of y in all cases. However, the difference becomes smaller as the solubility decreases, and for compounds with solubility less than 0,5% the difference is less than 10%. It has been shown that these excess Gibbs energy expressions, while very useful, are not the exact representation of the composition dependence of activity coefficient all expressions have difficulty in representing liquid-liquid equilibria (43-44). Thus, extrapolating these expressions to infinite dilution may be in error. It is therefore inconclusive as to the correctness of using the inverse solubility to calculate... 

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