## osmotic coefficient, $$\phi$$

https://doi.org/10.1351/goldbook.O04342
Quantity characterizing the deviation of the solvent from ideal behaviour referenced to Raoult's law. The osmotic coefficient on a molality basis is defined by: $\phi =\frac{\mu _{\text{A}}^{*}- \mu _{\text{A}}}{R\ T\ M_{\text{A}}\ \sum _{\begin{array}{c} i \end{array}}m_{i}}$ and on an amount fraction basis by: $\phi =\frac{\mu _{\text{A}}^{*}- \mu _{\text{A}}}{R\ T\ \ln x_{\text{A}}}$ where $$\mu _{\text{A}}^{*}$$ and $$\mu _{\text{A}}$$ are the chemical potentials of the solvent as a pure substance and in solution, respectively, $$M_{\text{A}}$$ is its molar mass, $$x_{\text{A}}$$ its amount fraction, $$R$$ the gas constant and $$T$$ the temperaure. The latter osmotic coefficient is sometimes called the rational osmotic coefficient.
Sources:
Green Book,2nd ed., p. 51 (https://www.cintegrado.com.br/site/documentos/green_book_2ed.pdf)
PAC, 1994, 66, 533. 'Standard quantities in chemical thermodynamics. Fugacities, activities and equilibrium constants for pure and mixed phases (IUPAC Recommendations 1994)' on page 546 (https://doi.org/10.1351/pac199466030533)