When we introduced you to pKa on p. 167, we said it is the pH at which an acid and its conju-gate base are present in equal concentrations. We can now be more precise about the defi nition of pKa. pKa is the log (to the base ten) of the equilibrium constant for the dissociation of the acid. For an acid HA this is:

The concentration of water is ignored in the definition because it is also constant (at 25 °C). Because of the minus sign in the definition (it’s there too in the defi nition of pH) the lower the pKa the larger the equilibrium constant and the stronger the acid. You may find the way we introduced pKa more helpful as a concept for visualizing pKa: any acid is half dissociated in a solution whose pH matches the acid’s pKa. At a pH above the pKa the acid exists largely as its conjugate base (A−) but at a pH below the pKa the acid largely exists as HA. With pKa we can put fi gures to the relative strengths of hydrochloric and acetic acid we introduced earlier. HCl is a much stronger acid than acetic acid: the pKa of HCl is around –7 compared to 4.76 for acetic acid. This tells us that in solution Ka for hydrogen chloride is 107 mol dm−3. This is an enormous number: only one molecule in 10,000,000 is not dissociated, so it is essentially fully dissociated. But Ka for acetic acid is only 10−4.76 = 1.74 × 10−5 mol dm−3 so it is hardly dissociated at all: only a few molecules in every million of acetic acid are present as the acetate ion.

What about the pKa of water? You know the fi gures already: Ka for water is [H₃O⁺] × [HO⁻ ]/ [H₂O] = 10−14/55.5. So pKa = – log [10−14/55.5] = 15.7. Now you see why water isn’t really quite half dissociated at pH 14—the concentration of water in the equation means that the two ends of the scale on p. 168 are not at 0 and 14, but at –1.7 and 15.7.