Osmotic coefficient


An osmotic coefficient φ is a quantity which characterises the deviation of a solvent from ideal behaviour, referenced to Raoult's law. It can be also applied to solutes. Its definition depends on the ways of expressing chemical composition of mixtures.
The osmotic coefficient based on molality b is defined by:
and on a mole fraction basis by:
where is the chemical potential of the pure solvent and is the chemical potential of the solvent in a solution, MA is its molar mass, xA its mole fraction, R the gas constant and T the temperature in kelvins. The latter osmotic
coefficient is sometimes called the rational osmotic coefficient. The values for the two definitions are different, but since
the two definitions are similar, and in fact both approach 1 as the concentration goes to zero.

Relation to other quantities

In a single solute solution, the osmotic coefficient and the solute activity coefficient are related to the excess Gibbs free energy by the relations:
and there is thus a differential relationship between them :
In ionic solutions, Debye–Hückel theory implies that is asymptotic to, where I is ionic strength and A is the Debye–Hückel constant. This means that, at least at low concentrations, the vapor pressure of the solvent will be greater than that predicted by Raoult's law. For instance, for solutions of magnesium chloride, the vapor pressure is slightly greater than that predicted by Raoult's law up to a concentration of 0.7 mol/kg, after which the vapor pressure is lower than Raoult's law predicts.
For aqueous solutions, the osmotic coefficients can be calculated theoretically by Pitzer equations or TCPC model.