Osmotic coefficient

An osmotic coefficient φ is a quantity which characterises the deviation of a solvent from ideal behaviour, referenced to Raoult's law. The osmotic coefficient on a molality basis is defined by:

$\varphi ={\frac {\mu _{A}^{*}-\mu _{A}}{RTM_{A}\sum _{i}m_{i}}}\,$

and on an amount fraction basis by:

$\varphi ={\frac {\mu _{A}^{*}-\mu _{A}}{RT\ln x_{A}}}\,$

where $\mu _{A}^{*}$ is the chemical potential of the pure solvent and $\mu _{A}$ is the chemical potential of the solvent in a solution, M_A is its molar mass, x_A its amount fraction, R the gas constant and T the temperature in Kelvins. The latter osmotic coefficient is sometimes called the rational osmotic coefficient.