Title: osmotic coefficient
Long Title: IUPAC Gold Book - osmotic coefficient
DOI: 10.1351/goldbook.O04342
Status: current
Index: quantity

Definition
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: \[\phi =\frac{\mu _{\rm{A}}^{*}- \mu _{\rm{A}}}{R\ T\ M_{\rm{A}}\ \sum _{\begin{array}{c}
i
\end{array}}m_{i}}\] and on an amount fraction basis by: \[\phi =\frac{\mu _{\rm{A}}^{*}- \mu _{\rm{A}}}{R\ T\ \ln x_{\rm{A}}}\] where \(\mu _{\rm{A}}^{*}\) and \(\mu _{\rm{A}}\) are the chemical potentials of the solvent as a pure substance and in solution, respectively, \(M_{\rm{A}}\) is its molar mass, \(x_{\rm{A}}\) its amount fraction, \(R\) the gas constant and \(T\) the temperaure. The latter osmotic coefficient is sometimes called the rational osmotic coefficient.

Related Terms
- Raoult's law: https://dev.goldbook.iupac.org/terms/view/H02783
- coefficient: https://dev.goldbook.iupac.org/terms/view/C01124
- deviation: https://dev.goldbook.iupac.org/terms/view/D01650
- gas constant: https://dev.goldbook.iupac.org/terms/view/G02579
- solvent: https://dev.goldbook.iupac.org/terms/view/S05746

Sources
- Green Book, 2nd ed., p. 51 (https://goldbook.iupac.org/files/pdf/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)

Other Outputs
- html: https://dev.goldbook.iupac.org/terms/view/O04342/html
- json: https://dev.goldbook.iupac.org/terms/view/O04342/json
- xml: https://dev.goldbook.iupac.org/terms/view/O04342/xml

Citation: Citation: 'osmotic coefficient' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.O04342
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Accessed: 2026-06-13T04:29:25+00:00