The definition
pH = −log10[H+], where [H+] is the hydrogen ion concentration in mol/L. Each step of 1 pH unit is a tenfold change in concentration. At 25 °C, pH + pOH = 14.
Strong acids and bases
Strong acids such as HCl ionise completely, so [H+] equals the acid concentration. 0.01 M HCl has pH −log(0.01) = 2.00. For a strong base, work out pOH from [OH−] and subtract it from 14: 0.01 M NaOH has pOH 2 and pH 12.
Weak acids
A weak acid ionises only partly, set by its acid dissociation constant Ka. When the acid is not too dilute, [H+] ≈ √(Ka × C). For 0.1 M acetic acid, pKa 4.76: √(10−4.76 × 0.1) = 1.3 × 10−3 M, so pH is about 2.9.
Buffers
A buffer is a weak acid with its conjugate base. The Henderson-Hasselbalch equation gives its pH: pH = pKa + log([A−] ÷ [HA]). For an acetate buffer at pH 5.0 the base-to-acid ratio is 105.0 − 4.76 = 1.74. A buffer works best within about 1 unit of its pKa.
Calculators
The pH Calculator handles [H+], pOH, [OH−] and strong or weak acids and bases. The Buffer Calculator gives the ratio and the amounts of acid and base for a buffer of a set concentration and volume.