Measuring the Acidity of a Solution

It is often useful and necessary to measure the acidity or basicity of a solution. There are a number of ways this could be described or reported, but in the context of the Bronsted-Lowry definitions of acids and bases, it is probably most convenient to monitor the concentration of H⁺(aq). The [H⁺] in a solution can be a very small number. Although modern pocket calculators can readily handle very small numbers, it's a little easier to describe these small concentrations using pH. pH expresses very small concentrations without having to use scientific notation and will be useful for a number of quantities.

pH = -log[H₃O⁺]

Reversing and re-solving that expression:

[H₃O⁺] = 10^-pH

Why do we follow [H⁺] or [H₃O⁺]? We know from the K_w expression that [H₃O⁺] and [OH^-] are related. Depending upon the type of problem, sometimes it's easier to think in terms of [OH^-], but [OH^-] is also usually a very small number, so it's useful to define an analogous quantity, pOH:

pOH = -log[OH^-]

Reversing and re-solving that expression:

[OH^-] = 10^-pOH

pH and pOH are related by K_w and we can derive that expression from K_w:

K_w = [H₃O⁺][OH^-]

-log(K_w) = -log([H₃O⁺][OH^-])

If we generalize that “-log” can be replaced by “p”, and remember that log AB = log A + log B, then:

pK_w = -log [H₃O⁺] + (-log[OH^-]) = pH + pOH

At 25°C, K_w = 10^-14, so pK_w = 14.