The author replies to Behrman.

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 K_a 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 pK_a value of 15.7 for water is simply wrong.

Secondly, K_a’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 K_a 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 K_a.