Wikipedia / Osmotic coefficient
Wikipedia / Osmotic coefficient
An osmotic coefficient 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
and on a mole fraction basis by:
is the chemical potential 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 Kelvin. 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.
Applications
For liquid solutions, the osmotic coefficient is often used to calculate the salt activity coefficient from the solvent activity, or vice versa. For example, freezing point depression measurements, or measurements of deviations from ideality for other colligative properties, allows calculation of the salt activity coefficient through the osmotic coefficient.
Relation to other quantities
are related to the excess Gibbs free energy by the relations:
and there is thus a differential relationship between them (temperature and pressure held constant):
Liquid electrolyte solutions
can be calculated from the salt activity coefficient via:
can be calculated from:
According to Debye–Hückel theory is asymptotic, where I is ionic strength and A is the Debye–Hückel constant (equal to about 1.17 for water at 25°C).
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 0.7mol/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.