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Concept
Activity coefficient
Summary
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. 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.
The chemical potential, , of a substance B in an ideal mixture of liquids or an ideal solution is given by
where μ is the chemical potential of a pure substance , and 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,
where is the activity coefficient, which may itself depend on . As approaches 1, the substance behaves as if it were ideal. For instance, if ≈ 1, then Raoult's law is accurate. For > 1 and < 1, 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.
In detail: Raoult's law states that the partial pressure of component B is related to its vapor pressure (saturation pressure) and its mole fraction in the liquid phase,
with the convention
In other words: Pure liquids represent the ideal case.
Official source
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