## Debye Hiickel Corrections to Octanol Water Partition Constants

With the ion-pair conditional constant (log Pion) formalism, no opportunity exists to apply the Debye-Hiickel theory to correct constants for changes in the ionic strength. When neutral species partition into octanol, there should be no dependence of log P on ionic strength. Largely, this is borne out by experiment, as shown, for example, for ibuprofen and chlorpromazine in Fig. 11.

In the course of a titration, ionic strength is maintained nearly constant by the background salt; still it does deviate from the average value, /avg, at very low or high pH, or when the amount of sample is relatively large and when highly ionized species form. All ions contribute to the ionic strength. A scheme was described by us to take into account the effect on the equilibrium constants due do slightly changing ionic strength [3]. We can apply a similar scheme to extraction reactions.

The last squares refinement calculation [3] converts all equilibrium constants to the log/3 form; these in turn are used to calculate pcH, the critical step in the regression analysis. For each pcH the log/3 constants are first adjusted for ionic strength deviations from the mean value, according to the expression log (¡¡(I) = log /3//av,) + (a, Q? + b, Qy2 + c,) {F(i)-F(I^)} (26)

F(l) is the Davies [29] activity coefficient expression, n/) = ^-5(rTV/-0-3 7) (27)

Qx and Qy are the charges of the fully deprotonated components in the reactions. (The overall charge of the ion-pair complex extracted into octanol is assumed to be zero.) Let us consider the octanol: water extraction reaction in the binary prostaglandin (Pg)-glucamine (Glu) system.

Pg" + GluH+ ^ (Pg, GluH+)ocx: Kc = [Pg-, GluH+]OCT / [Pgl [GluH+] (28)

In the example, x may designate Pg (Qx = -1) and y may designate Glu (Qy = 0). The coefficients ajt bj, and c, are the stoichiometric indices for the components Pg, Glu and H, respectively, in the /h equilibrium expression. Consider Eq. (28): a= 1, b—1, and c= 1. Thus log /*,</) = log /?//avg) + 2 {F(i)-F(Img)}.

Likewise, if we wished to know the theoretically expected value of the extraction constant associated with Eq. (28) at zero ionic strength, we would predict that the extraction constant changes by -2F (evaluated at 7=0.15 M). The ion-pair constant would thus be expected to increase by 0.23.

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