Every water sample carries loose hydrogen ions, and the count is written $[\mathrm{H^+}]$ — square brackets read aloud as the concentration of, in mol/L. The numbers run absurdly small (a millionth of a mole per litre is ordinary), so chemists compress them with a logarithm and call the result pH: $\mathrm{pH} = -\log[\mathrm{H^+}]$ — read aloud: pH equals negative log of H-plus.

What the compression buys is a ruler that runs about 0 to 14: 7 is neutral (pure water, room temperature), below 7 is acidic — the lower, the fiercer — and above 7 is basic. And because a logarithm counts zeros, one pH step is a factor of TEN: lemon juice at pH 2 is not “a bit” stronger than coffee at pH 5 — it is a thousand times stronger. The pH itself travels naked: the log already ate the units.