Chemical Education Today
Letters Equilibrium Constants and Water Activity Revisited 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). Literature Cited 1. Keeports, D. J. Chem. Educ. 2005, 82, 999. 2. 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. 3. Cox, R. A. Adv. Phys. Org. Chem. 2000, 35, 2–4.
Department of Biochemistry The Ohio State University Columbus, OH 43210
[email protected] Journal of Chemical Education
Equilibrium constants are correctly expressed only in terms of activities. Physical chemistry textbooks demonstrate that there are some situations where numerical values of molar concentrations provide acceptable activities. For example, numerical values of molar concentrations are perfectly valid in the study of chemical reactions in which all reactants and products are ideal gases. Furthermore, subtle arguments based upon the use of chemical potentials show that numerical values of solute molar concentrations can be used as good approximate activities in equilibrium calculations for reactions involving dilute solutions. However, there exists no justification whatsoever for ever using a solvent’s molar concentration as its activity or even as its approximate activity. Using unity as water’s activity for aqueous reactions is not merely a matter of definition. To the contrary, careful arguments from thermodynamics show that the activity of any solvent approaches unity as solute activities approach zero. Behrman’s letter raises two important points. First, there is only one Ka for water. It is 10᎑14, the product of the activities of H3O+ and OH᎑. The numerical value of the molar concentration of water (about 55.5) has no place at all in the equilibrium constant for water’s dissociation or for any other aqueous reaction. Because it incorrectly assumes that water’s activity is 55.5, the commonly reported pKa value of 15.7 for water is simply wrong. Secondly, Ka’s of the form Behrman gives for methanol are acceptable only if the acid is a solute in a relatively dilute solution. The form of the Ka given for methanol does not apply to a pure acid’s auto-protonation. For the auto-protonation of a weak pure acid, unity is the proper denominator for Ka. David Keeports Chemistry and Physics Department Mills College Oakland, CA 94613
[email protected] E. J. Behrman
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Vol. 83 No. 9 September 2006
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