I
D. Irwin Stock
I
University of Surrey London, s.w.11, England
Dissociation of Weak Acids and Bases at Infinite Dilution
In almost all chemistry textbooks, and certainly not only in the most elementary of these,' discussions on the theory of electrolytic dissociation state, as axiomatic, that all electrolytes become completely dissociated at infinite dilution. I n a few instances a passing reference is made to electrolyte/ solvent interaction, but the point is not pursued in detail. Furthermore, in an attempt to make the account as general as possible, the process of ionization of a weak electrolyte is usually given as MAeM++A-
(or with general values for the valences v+ and v-). Subsequent elaboration, with numerical examples where given, is normally confined to aqueous solutions. From the teaching aspect this approach contains several hidden risks of misapprehension. First, the generality of formulation is dangerous, as it must be realized that in aqueous solutions the only important weak electrolytes are weak acids and bases; all salts are either completely dissociated, or very largely so (with certain reservationse), and no exception can be raised to the application of the usual treatment to this class of electrolyte. The second source of error is much more important, however, and it is to this that the author wishes to draw attention. In aqueous solutions the weak acids and the weak bases have an ion in common with the solvent. This is, of course, well recognized, but it is all too easy to forget that in a solution of inhnite dilution the solvent itself is ionized to an extent governed by its ionization constant, and that the concentration of its ions will appear in the expression for the dissociation constant of the solute. At infinite dilution, in aqueous solution, the activities of the hydrogen ion and of the hydroxyl ion are equal, and have the value K,1/2 or lo-' a t 25'C. For any weak acid HA
efficients being unity a t this low ionic strength), and
(and a similar equation will apply to weak bases). It is obvious from this that not only will or never actually reach unity, but also the deviations from unity can be very large. The figure shows the variation, with strength of acid or base, of the limiting values of a and of (1 - or). For example, an acid as strong as acetic acid (K. = 1.75X lo-' a t 25°C) is still as much as 0.57y0 unionized at infinite dilution. In the case of an acid such as phenolS (pK. = lo), however, 99.9% of the total will still be unionized at infinite dilution. Similar conclusions apply, of course, to weak bases (where a / ( l - a) = Kb/aoa-)-for example, ammonia is more than 0.5% nnionized, while aniline is 99.6% unionized. It is realized that this exercise is quite elementary, but so enshrined is the bald statement (paragraph 1) in physical chemistry teaching that the consequent errors are very rarely appreciated, and great care should be taken when thinking and talking about this subject.
and a t infinite dilution the concentration of hydrogen inn, as above, can be taken as lo-' g-ion/l. If the degree of dissociation of the acid HA is a, [A-]/[HA]
= a/(l
- n)
(where [ ] indicates concentration, the activity co1 GLASSTONE, S., ''Textbook of Physical Chemistry," (8nd ed.) Van Nostrand, New Yark, 1946, pp. 888,907. DAVIE~, C. W., "Ion Association," Buttemorths, London, p. 1 ct seq. "BIGGS, A. I., Tram. Faraday Soc., 52,35 (1956).
764
/
Journol of Chemical Education
Variation, with strength of acid or bsse, of tho frmetion of roluto in i a i r s d and unionized form, at infinite dilution. Fraction (I-a)of acid or base in unionized form is represented by a solid line; the fraction la) of acid or base in ionized form by a broken line.
