In 1909 S.P.L. Sorensen published a paper in Biochem Z in which he discussed the effect of H1+ ions on the activity of enzymes. In the paper he invented the term pH to describe this effect and defined it as the -log[H1+ ]. In 1924 Sorensen realized that the pH of a solution is a function of the "activity" of the H1+ ion not the concentration and published a second paper on the subject. A better definition would be pH=-log[aH1+ ], where aH1+ denotes the activity of the H1+ ion. The activity of an ion is a function of many variables of which concentration is one. It is unfortunate that chemistry texts use a definition for pH that has been obsolete for over 50 years.
Because of the difficulty in accurately measuring the activity of the H1+ ion for most solutions the International Union of Pure and Applied Chemistry (IUPAC) and the National Bureau of Standards (NBS) has defined pH as the reading on a pH meter that has been standardized against standard buffers. The following equation is used to calculate the pH of all solutions:
The activity of the H1+ ion is determined as accurately as possible for the standard solutions used. The identity of these solutions vary from one authority to another, but all give the same values of pH to ± 0.005 pH unit.
The historical definition of pH is correct for those solutions that are so dilute and so pure the H1+ ions are not influenced by anything but the solvent molecules (usually water). In most solutions the pH differs from the -log[H1+ ] in the first decimal point.