In more concentrated solutions, interactions between ions cause their “effective” concentrations, known as their activities, to deviate from their “analytical” concentrations.
Thus in a solution prepared by adding 0.5 mole of the very strong acid HClO4 to sufficient water to make the volume 1 liter, freezing-point depression measurements indicate that the concentrations of hydronium and perchlorate ions are only about 0.4 M. This does not mean that the acid is only 80% dissociated; there is no evidence of HClO4 molecules in the solution. What has happened is that about 20% of the H3O+ and ClO4– ions have formed ion-pair complexes in which the oppositely-charged species are loosely bound by electrostatic forces. Similarly, in a 0.10 M solution of hydrochloric acid, the activity of H+ is 0.81, or only 81% of its concentration. (See the green box below for more on this.)
Activities are important because only these work properly in equilibrium calculations. The relation between the concentration of a species and its activity is expressed by the activity coefficient γ (gamma):
The relation between the concentration C of a species and its activity a is expressed by the activity coefficient γ (gamma):