Activity coefficient
In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour.
[1] 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.
Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.
< 1, substance B shows positive and negative deviation from Raoult's law, respectively.
goes to zero, the activity coefficient of substance B approaches a constant; this relationship is Henry's law for the solvent.
Comparison with Henry's law, immediately gives In other words: The compound shows nonideal behavior in the dilute case.
The above definition of the activity coefficient is impractical if the compound does not exist as a pure liquid.
In such cases, a different definition is used that considers infinite dilution as the ideal state: with
But there are cases where both kinds of activity coefficients are needed and may even appear in the same equation, e.g., for solutions of salts in (water + alcohol) mixtures.
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 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.
The prevailing view that single ion activity coefficients are unmeasurable independently, or perhaps even physically meaningless, has its roots in the work of Guggenheim in the late 1920s.
For example, pH is defined as the negative logarithm of the hydrogen ion activity.
If the prevailing view on the physical meaning and measurability of single ion activities is correct then defining pH as the negative logarithm of the hydrogen ion activity places the quantity squarely in the unmeasurable category.
[9] The activity coefficient of the electrolyte is split into electric and statistical components by E. Glueckauf who modifies the Robinson–Stokes model.
The statistical part includes hydration index number h, the number of ions from the dissociation and the ratio r between the apparent molar volume of the electrolyte and the molar volume of water and molality b.
Concentrated solution statistical part of the activity coefficient is: The Stokes–Robinson model has been analyzed and improved by other investigators.
[13][14] The problem with this widely accepted idea that electrolyte activity coefficients are driven at higher concentrations by changes in hydration is that water activities are completely dependent on the concentration of the ions themselves, as imposed by a thermodynamic relationship called the Gibbs-Duhem equation.
The rise in activity coefficients found with most aqueous strong electrolyte systems can be explained more plausibly by increasing electrostatic repulsions between ions of the same charge which are forced together as the available space between them decreases.
In this way, the initial attractions between cations and anions at the low concentrations described by Debye and Hueckel are progressively overcome.
This model accurately reproduces the experimental patterns of activity and osmotic coefficients exhibited by numerous 3-ion aqueous electrolyte mixtures.
Activity coefficients may be determined experimentally by making measurements on non-ideal mixtures.
[16] Activity coefficients for binary mixtures are often reported at the infinite dilution of each component.
Because activity coefficient models simplify at infinite dilution, such empirical values can be used to estimate interaction energies.
For non-electrolyte solutions correlative methods such as UNIQUAC, NRTL, MOSCED or UNIFAC may be employed, provided fitted component-specific or model parameters are available.
COSMO-RS is a theoretical method which is less dependent on model parameters as required information is obtained from quantum mechanics calculations specific to each molecule (sigma profiles) combined with a statistical thermodynamics treatment of surface segments.
[25] For uncharged species, the activity coefficient γ0 mostly follows a salting-out model:[26] This simple model predicts activities of many species (dissolved undissociated gases such as CO2, H2S, NH3, undissociated acids and bases) to high ionic strengths (up to 5 mol/kg).
The derivative of an activity coefficient with respect to temperature is related to excess molar enthalpy by Similarly, the derivative of an activity coefficient with respect to pressure can be related to excess molar volume.
It shows the relationship between standard free energy change and equilibrium constant.
