Discover

An 'Activity coefficient' ^[1]
is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. In an ideal mixture the interactions between each pair of chemical species are the same; more formally, the enthalpy of mixing is zero. Ideal behavior is represented, for example, by Raoult's law, Henry's law and the law of mass action. In each of these examples, a property is related to the concentration or partial pressure of the substances in a mixture. Deviations from ideality are accomodated by replacing concentration with activity. Activity is the product of concentration and activity coefficient. For gases partial pressure may be replaced by fugacity, which is the product of partial pressure and a fugacity coefficient.
All of these examples can be understood by considering the chemical potential of each substance in the mixture. The chemical potential, $mu\_B$, of a substance B in an ideal mixture is given by
:$mu\_B\; =\; mu\_\{B\}^\{ominus\}\; +\; RT\; ln\; x\_B\; ,$
where $mu\_\{B\}^\{ominus\}$ is the chemical potential in the standard state and x_B is the mole fraction of the substance in the mixture. The chemical potential in a non-ideal mixture is given by
:$mu\_B\; =\; mu\_\{B\}^\{ominus\}\; +\; RT\; ln\; a\_B\; ,$
when a_B is the activity of the substance in the mixture. This expression can also be written as
:$mu\_B\; =\; mu\_\{B\}^\{ominus\}\; +\; RT\; ln\; x\_B\; gamma\_B\; ,$
where $gamma\_B$ is the activity coefficient. In this expression mole fraction is dimensionless, so the activity coefficient is also dimensionless. If a concentration unit other than mole fraction is used the dimension of the activity coefficient is the inverse of the dimension of concentration. As concentrations tends to zero activity coefficients tend to one, so in very dilute solution activity is equal to concentration.
Raoult's law and Henry's law relate the partial pressure of a substance in the gas phase in equilibrium with a solution of that substance to the concentration of the substance in the liquid phase. At equilibrium the chemical potential of the substance in the two phases must be equal. Thus, these laws can be derived from the expressions for chemical potential. When concentrations are replaced by activities they apply to both ideal and non-ideal mixtures. Other applications for activity coefficients include equilibrium constants and solubility products.
Activity coefficients may be measured experimentally or calculated theoretically, using the Debye-Hückel equation or extensions such as Davies equation^[2] or Pitzer equations^[3]. Specific Ion Theory (SIT) ^[4] may also be used.

Contents

References

References

1. Gold Book definition
2. C.W. Davies, ''Ion Association'',Butterworths, 1962
3. I. Grenthe and H. Wanner, ''Guidelines for the extrapolation to zero ionic strength'', http://www.nea.fr/html/dbtdb/guidelines/tdb2.pdf
4. SIT theory