Thermodynamics: Activity Coefficient

Activity is the measure of the effective concentration of the species in solution. It can be expressed as the product of the molar concentration of the species and its activity coefficient. The activity coefficient is a dimensionless quantity and depends on the total ionic strength of the solution.

The activity coefficient is a measure of the deviation from ideal behavior. When the ionic strength of the solution is minimal, the activity coefficient of an ionic species is close to unity, making activity approximately equal to the molar concentration. Such a solution exhibits behaviors very close to those of an ideal solution. The activity coefficient of an uncharged molecule is approximately unity at all ionic strengths less than 0.1 mol/L.

As the ionic strength of the solution increases, the activity coefficient decreases, making the activity less than the molar concentration. This indicates the deviation of the species from ideal behavior. In solutions with ionic strength higher than 0.1 mol/L, the activity coefficient increases and exceeds unity.

A useful equation for calculating the activity coefficient from ionic strength is the extended Debye–Hückel equation, which relates the coefficient to ionic strength, the effective diameter of the ion, and the ionic charges of the solute. The Debye–Hückel equation relies on the ion size - the effective diameter of a hydrate ion - which can vary widely with charge and the geometry of the ion, thereby introducing uncertainty into the equation.

The equation works well in extremely dilute solutions and solutions with ionic strength less than 0.1 mol/L and extremely dilute solutions, where the uncertainties in ion sizes have negligible effects on the activity coefficients. In these cases, the solution behaves mostly ideally, and the Debye–Hückel equation reduces to a simpler form known as the Debye–Hückel Limiting Law.