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pH is formally defined as the negative decimal logarithm of the hydrogen ion activity, [latex]a_{H^+}[/latex]. The formula is [latex]pH = -\log_{10}(a_{H^+})[/latex]. Activity is the effective concentration of hydrogen ions, accounting for intermolecular forces, and is dimensionless. For dilute solutions, activity is approximately equal to the molar concentration of [latex]H^+[/latex] ions, simplifying the calculation.
The modern definition of pH using hydrogen ion activity ([latex]a_{H^+}[/latex]) is a refinement of Sørensen’s original 1909 proposal, which used hydrogen ion concentration. The activity is related to concentration ([latex]c[/latex]) by the activity coefficient ([latex]\gamma_{H^+}[/latex]): [latex]a_{H^+} = \gamma_{H^+} \cdot c/c^0[/latex], where [latex]c^0[/latex] is the standard concentration (1 mol/L). In dilute solutions, [latex]\gamma_{H^+}[/latex] approaches 1, and activity approximates concentration. However, in more concentrated solutions, ionic interactions reduce the effective concentration, making the activity-based definition more accurate.
Because the activity of a single ion cannot be measured independently, the IUPAC has established an operational definition. This definition relies on a primary standard reference cell and a series of certified standard buffer solutions with assigned pH values. A practical pH measurement compares the potential of an electrode in the sample solution to its potential in these standard buffers, effectively calibrating the measurement against the established scale. This ensures consistency and comparability of pH values measured worldwide.
PH
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