Osmotic coefficient

An osmotic coefficient ${\displaystyle \phi }$ 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 m is defined by: $${\displaystyle \phi ={\frac {\mu _{A}^{*}-\mu _{A}}{RTM_{A}\sum _{i}m_{i}}}}$$

and on a mole fraction basis by:

$${\displaystyle \phi =-{\frac {\mu _{A}^{*}-\mu _{A}}{RT\ln x_{A}}}}$$

where ${\displaystyle \mu _{A}^{*}}$ is the chemical potential of the pure solvent and ${\displaystyle \mu _{A}}$ is the chemical potential of the solvent in a solution, M_A is its molar mass, x_A its mole fraction, R the gas constant and T the temperature in Kelvin.^[1] The latter osmotic coefficient is sometimes called the rational osmotic coefficient. The values for the two definitions are different, but since

$${\displaystyle \ln x_{A}=-\ln \left(1+M_{A}\sum _{i}m_{i}\right)\approx -M_{A}\sum _{i}m_{i},}$$

the two definitions are similar, and in fact both approach 1 as the concentration goes to zero.