osmotic coefficient, \(\phi\)

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.
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)