The pKa of Water and the Fundamental Laws Describing Solution Equilibria: An Appeal for a Consistent Thermodynamic Pedagogy

Abstract

A recurring misconception in some textbooks and research papers has led to an abandonment of fundamental physical laws when describing a subset of acid-base equilibria, especially regarding the role of the solvent. In the specific case of the autoprotolysis of water, experiments and theoretical calculations prove that the K_w of water at 25 °C, 1.00×10⁻¹⁴, is identical to its acid ionization constant, K_a. Nevertheless, several articles have been published erroneously purporting to give theoretical proof that the K_a of water is 10^−15.743 (1.81×10⁻¹⁶) and that the K_a of the aqueous proton (hydronium ion) is 55.3 rather than 1.00. Here we argue that using the incorrect numbers has pedagogical implications beyond those of a simple error. Arguments for the incorrect K_a and pK_a values require a misapplication of Henry's law and violate long-standing methods that use Raoult's law and the conservation of matter to describe the behavior of solutions. As a result, chemistry students may be asked to accept one set of physical principles in one course and another set in another course. Here we argue for adherence to fundamental physical laws governing solution equilibria as applied to the autoprotolysis of water and all aqueous acid base equilibria.