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{{Short description|Value accounting for thermodynamic non-ideality of mixtures}}In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour.{{GoldBookRef|title=Activity coefficient|file=A00116}} In an ideal mixture, the microscopic interactions between each pair of chemical species are the same (or macroscopically equivalent, the enthalpy change of solution and volume variation in mixing is zero) and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult’s law. Deviations from ideality are accommodated by modifying the concentration by an activity coefficient. Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.The concept of activity coefficient is closely linked to that of activity in chemistry.

Thermodynamic definition

The chemical potential, mu_mathrm{B}, of a substance B in an ideal mixture of liquids or an ideal solution is given by where μ{{su|b=B|p=o}} is the chemical potential of a pure substance mathrm{B}, and x_mathrm{B} is the mole fraction of the substance in the mixture.This is generalised to include non-ideal behavior by writing when a_mathrm{B} is the activity of the substance in the mixture, where gamma_mathrm{B} is the activity coefficient, which may itself depend on x_mathrm{B}. As gamma_mathrm{B} approaches 1, the substance behaves as if it were ideal. For instance, if gamma_mathrm{B} â‰ˆ 1, then Raoult’s law is accurate. For gamma_mathrm{B} > 1 and gamma_mathrm{B}