The Definition of pH

The pH of a solution is defined to be

where the activity is expressed on the molal scale. Methods for calculating the activity are covered later. Commonly as an approximation, the concentration (mol/L) is substituted, and the “p” notation stands for the negative of the common logarithm:

We use this common approximation for introductory examples. The primary use of pH is to characterize a solution as acidic or basic.

Relation of H and OH in Water

Recall at room temperature⁹

The “p” notation is extended to other ions and equilibrium constants. When working with dilute solutions, this means that –log(a_H⁺ a_OH^–) = – log(a_H⁺) = –log(a_OH^–) = –logK_a,w, or

At room temperature, pK_a,w = 14. Thus, when the solution is acidic, the concentration of [OH^–] < 10^–7 mol/L, and when the solution is basic, the concentration of [H⁺] < 10^–7 mol/L. Often one of these concentrations can be neglected when taking sums or differences when it is small relative to other terms.

Importance of Solvent

In water, the pH typically varies in the range 0–14. However, because of the definition, strong acids at high concentrations can have negative pH. In ammonia, however, the pH varies from 0 to 32. Therefore, the environment is important in determining the range of pH.