Understanding pH and pOH

pH is just a compact way of writing the hydrogen-ion concentration. Because that concentration spans many orders of magnitude, we take its negative logarithm so the numbers stay manageable.

The definitions

A low pH means a high [H⁺] and an acidic solution; a high pH means a low [H⁺] and a basic solution. Each whole number on the pH scale is a tenfold change in [H⁺].

Why pH + pOH = 14

Water self-ionises slightly, and at 25 °C the product of the ion concentrations is fixed:

Taking the negative log of both sides gives pH + pOH = 14. This relationship only holds at 25 °C, because Kw changes with temperature.

Strong acids and bases

Strong acids (HCl, HBr, HI, HNO₃, HClO₄, and the first proton of H₂SO₄) dissociate completely, so [H⁺] equals the acid concentration. Strong bases (LiOH, NaOH, KOH, Ca(OH)₂, Ba(OH)₂) dissociate completely too — but remember Ca(OH)₂ and Ba(OH)₂ release two hydroxide ions per formula unit, so [OH⁻] is twice the concentration.

Worked example

For 0.00165 M HNO₃: [H⁺] = 0.00165 M, so pH = −log(0.00165) = 2.78, and pOH = 14 − 2.78 = 11.22.

Try it on the pH & pOH Calculator, which converts between [H⁺], [OH⁻], pH and pOH and handles strong acids and bases directly.