By Herbert August Laitinen, Walter E. Harris
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Additional resources for Chemical Analysis: An Advanced Text and Reference
If the protons originate from water, and for an ion A', we have two stages of hydrolysis: HA- + H20 H2A + OH- K,, = K bZ = Kw - Kl (3-54) Equations (3-53) and (3-54) bear a relation to each other similar to that of (3-32) and (3-33) for the successive ionization steps of multibasic acids. Therefore, in general, the second and higher stages of hydrolysis may be ignored except in situations involving extreme dilution and close proximity of the constants Kl and K2. A simple equation [(3-27) or (3-28)] may therefore be used in almost all practical situations involving titration end points.
The acid cannot, however, be an anion HA-, because in general such an anion is also a weak base and so two acid-base systems in addition to water are involved. For a cationic acid BH' the ionization constants of the acid and of the conjugate base are related. Thus the ionization constant of BH' as an acid is For the conjugate base B the ionization constant Kb is Multiplying (3-23) by (3-24), we obtain K,,Kb = [H+][OH-] = Kw (3-25) The ionization constant KOfor the cationic acid is thus Kw/Kb,the classical value for the hydrolysist constant of the cation (conjugate acid) of a weak base.
If the water of hydration is assumed to be associated largely with the cations of the salt, the ion-size parameter can be estimated12 from the crystallographic radii of the unhydrated ions and the hydration number n. If a semiempirical relation between a and n is introduced into (2-23), the hydration number n becomes the only parameter, which is then found by trial and error. The remarkable agreement between experiment and the fitted one-parameter equation 'up to an ionic strength of the order of 4 is evident from Figure 2-4.