Acid Dissociation as a Function of

The conventional acid dissociation constant in light water (Aha) is 

The neglect of activity coefficients y in equations (12) and (13)—which meant that they were strictly valid only in the limit of infinitely dilute solutions—is less serious in equation (14). The interionic mean activity coefficient y for the hydrogen ion and the anion will, at low ionic strengths, be a function of the nature of the solvent only to the extent that the coefficient A in the Debye-Hiickel limiting law for activity coefficients depends on the dielectric constant of the solvent. In view of the similar values of the dielectric constants of H20 and D20 (see p. 261), the resultant difference between activity coefficients in H20 and D20 solutions of the same low ionic strength should be small. (If both Aha and Kn are results extrapolated to zero ionic strength, the problem disappears in its entirety.) (See also Section IVC.) 

The three factors of equation (14) can be expressed in terms of fractionation factors and n on the basis of the assumptions stated. 

The definition of the fractionation factor (equation 3) can be simplified for the case of a solute containing a single hydrogen nucleus only, so that 

Equation (2) leads to an analogous expression involving the fractionation factor l for the hydrogen ion. Rearrangement of (2) gives 

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