The thermodynamic dissociation constant of benzoic acid in water and the solubility of benzoic acid in methanol-water mixtures

The ionization of an acid in water may be represented by the following equilibrium; HA + H₂O ⇌ H₃O⁺ + A’ and by applying the law of mass action the activity of the water being assumed constant it can be shown that [equation here] where Kₐ is the thermodynamic equilibrium constant of the process and α is the activity if the entity denoted by the subscript. Since Kₐ expresses the tendency of the acid to ionize or dissociate, it is called the thermodynamic dissociation constant of the acid and is constant by definition. Historically, the law of mass action was first applied to dissociation processes by Ostwald who, however, used concentrations instead of activities, writing: [equation here] By introducing an expression α to represent the degree of dissociation of the unionized molecules of the substance whose concentration is expressed by c, the following expression was obtained. [equation here] Since the law of mass action is not strictly obeyed in the above firm, the “constant” k varies with concentrations