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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.
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Related concepts (16)
Enthalpy of mixing
In thermodynamics, the enthalpy of mixing (also heat of mixing and excess enthalpy) is the enthalpy liberated or absorbed from a substance upon mixing. When a substance or compound is combined with any other substance or compound, the enthalpy of mixing is the consequence of the new interactions between the two substances or compounds. This enthalpy, if released exothermically, can in an extreme case cause an explosion. Enthalpy of mixing can often be ignored in calculations for mixtures where other heat terms exist, or in cases where the mixture is ideal.
Determination of equilibrium constants
Equilibrium constants are determined in order to quantify chemical equilibria. When an equilibrium constant K is expressed as a concentration quotient, it is implied that the activity quotient is constant. For this assumption to be valid, equilibrium constants must be determined in a medium of relatively high ionic strength. Where this is not possible, consideration should be given to possible activity variation. The equilibrium expression above is a function of the concentrations [A], [B] etc.
Thermodynamic activity
In chemical thermodynamics, activity (symbol a) is a measure of the "effective concentration" of a species in a mixture, in the sense that the species' chemical potential depends on the activity of a real solution in the same way that it would depend on concentration for an ideal solution. The term "activity" in this sense was coined by the American chemist Gilbert N. Lewis in 1907. By convention, activity is treated as a dimensionless quantity, although its value depends on customary choices of standard state for the species.
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