Pseudo-solubility

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

Fig. 33. Comparisons of the pseudo-solubility data of Figs. 31 and 29 with model calculations assuming various values of parameter A DH, the binding energy of a positive donor D + and H into DH, AE2, the binding energy of 2H° into H2, and eA, the position of the hydrogen acceptor level relative to midgap. Plots (a) and (b) correspond respectively to the values 1.8 and 1.4 eV for A E2- In each of these, curves are shown for four combinations of the other parameters full curves, AEDH = 0.435 eV, eA = 0 dashed curves, AEDH = 0.835 eV, ea = 0 dotted curves AEDH = 0.435 eV, eA = 0.4eV dot-dash curves, A DH = 0.835 eV, eA = 0.4 eV. The chemical potential fi is constant on each curve and has been chosen to make the model curve pass through one of the experimental points of donor doping near 1017 cm-3, as shown. The solid circles are experimental points for arsenic obtained from Fig. 29 as described in the text. The other points are extrapolations of the phosphorus curves of Fig. 31 to zero depth, as described for Fig. 32, with open circles for the newer data and crosses for the older.

This implies that the pseudo solubility of these substances in octanol is 6.31 mol/L. This equation is ideal for screening purposes or when a fast check of the consistency of reported values of SL and Kow is needed. 

Kubota, N., Fugisawa, Y., Yokota, M. and Mullin, J.W. (1999) Pseudo-solubilities of potassium sulphate in water in the presence of Fe(III) impurities. Journal of Crystal Growth, 197, 388-392. 

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