Acids, Bases and pH

Measuring How Acidic

Three definitions of increasing generality coexist. Arrhenius: an acid releases $\mathrm{H^+}$ in water, a base releases $\mathrm{OH^-}$. Brønsted-Lowry: an acid donates a proton, a base accepts one, which introduces conjugate pairs, since every acid becomes its conjugate base on donating. Lewis: an acid accepts an electron pair, a base donates one, which covers reactions with no proton at all.

Water is amphoteric, acting as either, and undergoes autoprotolysis:

$$K_w = [\mathrm{H^+}][\mathrm{OH^-}] = 1.0 \times 10^{-14} \text{ at } 25\,^\circ\mathrm{C}$$

This single constant ties the scale together, giving $\mathrm{pH} + \mathrm{pOH} = 14$ and making neutrality pH 7, but only at 25 °C, since $K_w$ is itself temperature-dependent.

$$\mathrm{pH} = -\log[\mathrm{H^+}]$$

Because the scale is logarithmic, one pH unit is a tenfold change in concentration. A strong acid ionises essentially completely, so $[\mathrm{H^+}]$ equals its concentration. A weak acid ionises only partially, described by

$$K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$$

For a weak acid of concentration $C$, assuming ionisation is small, $[\mathrm{H^+}] \approx \sqrt{K_aC}$.

Strength and concentration are independent axes. A 0.1 M solution of hydrochloric acid has pH 1; 0.1 M acetic acid, at the same concentration, has pH about 2.9, because only around 1 % of it ionises. Strength is about the fraction that ionises; concentration is about how much acid is present.

Conjugate strength runs inversely: the stronger the acid, the weaker its conjugate base. The chloride ion, conjugate of a very strong acid, is so weak a base that it has no effect on pH at all.

Common pitfall: treating "weak" as a synonym for "dilute". They are independent. A concentrated weak acid can easily have a lower pH than a dilute strong one, 5 M acetic acid is more acidic than 0.001 M hydrochloric acid.