David Keeports uses the definition that the activity of water is 1(1). I do not take exception to his arguments, but I would like to point out a situation in which it is pedagogically advantageous to use the molar concentration of water instead. It is useful in teaching the effects of structure on acid strength to compare, inter alia, water with primary alcohols. We expect that methanol, ethanol, and water will have closely similar pKa values since substitution of a methyl group for a hydrogen generally affects the acid strength by no more than a factor of 2 or so. (Ballinger and Long (2) give the pKa values for methanol, ethanol, and water as 15.5, 16, and 15.7). The conventional way to write the dissociation constant for methanol (or any other acid) is: Ka=[H+][MeO–]/[MeOH]. (In this and other equations the positively charged species stands for all positively charged species not the non-existent proton.) If the dissociation constant for water is expressed in this form, the corresponding pKa is 15.7 (at 25 °C). If it is expressed with a defined activity for water = 1, then pKa = 14 making it appear (inexplicably) considerably stronger than methanol. That is, if we treat the dissociation of water in the same way that we treat other acids, we can make a useful comparison with other structures. On the same basis, the pKa for the hydronium ion (or rather the sum of the protonated species) is about -1.7. Cox gives a balanced discussion of the theoretical problems (3).
Ballinger, P.; Long, F. A. J. Am. Chem. Soc. 1960, 82, 795. See also, March, J. Advanced Organic Chemistry, 4th ed.; Wiley: New York, 1992; p 251, and references therein.
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