Activity Coefficient - Thermodynamics

Thermodynamics

The chemical potential, of a substance B in an ideal mixture is given by

where is the chemical potential in the standard state and x_B is the mole fraction of the substance in the mixture.

This is generalised to include non-ideal behavior by writing

when is the activity of the substance in the mixture with

where is the activity coefficient. As approaches 1, the substance behaves as if it were ideal. For instance, if, then Raoult's Law is accurate. For and, substance B shows positive and negative deviation from Raoult's law, respectively. A positive deviation implies that substance B is more volatile.

In many cases, as goes to zero, the activity coefficient of substance B approaches a constant; this relationship is Henry's Law for the solvent. These relationships are related to each other through the Gibbs-Duhem equation. Note that in general activity coefficients are dimensionless.

Modifying mole fractions or concentrations by activity coefficients gives the effective activities of the components, and hence allows expressions such as Raoult's law and equilibrium constants constants to be applied to both ideal and non-ideal mixtures.

Knowledge of activity coefficients is particularly important in the context of electrochemistry since the behaviour of electrolyte solutions is often far from ideal, due to the effects of the ionic atmosphere. Additionally, they are particularly important in the context of soil chemistry due to the low volumes of solvent and, consequently, the high concentration of electrolytes.