Title: activity coefficient
Long Title: IUPAC Gold Book - activity coefficient
DOI: 10.1351/goldbook.A00116
Status: current
Index: quantity

Definition
The activity coefficient \(f_{\rm{B}}\) of a substance B in a liquid or solid mixture containing mole fractions \(x_{\rm{B}}\), \(x_{\rm{C}}\), ... of the substances B, C, ... is a dimensionless quantity defined in terms of the chemical potential \(\mu _{\rm{B}}\) of B in the mixture by: \[R T \ln (x_{\ce{B}} f_{\ce{B}}) = \mu_{\ce{B}}({\ce{cd}},T,P,x) - \mu_{\ce{B}}^{\ast}({\ce{cd}},T,p)\] where \(x\) denotes the set of mole fractions \(x_{\rm{B}}\), \(x_{\rm{C}}\), ... . The activity coefficient \(\gamma _{\rm{B}}\) of a solute B in a solution (especially a dilute liquid solution) containing molalities \(m_{\rm{B}}\), \(m_{\rm{C}}\), ... of solutes B, C, ... in a solvent A is a dimensionless quantity defined in terms of the chemical potential \(\mu _{\rm{B}}\) by: \[R\ T\ \ln \left(\frac{m_{\rm{B}}\ \gamma _{\rm{B}}}{m^{\ominus}}\right)=\mu _{\rm{B}}- \left\{\mu _{\rm{B}}- R\ T\ \ln \left(\frac{m_{\rm{B}}}{m^{\ominus }}\right)\right\}^{\infty }\]

Related Terms
- chemical potential: https://dev.goldbook.iupac.org/terms/view/C01032
- coefficient: https://dev.goldbook.iupac.org/terms/view/C01124
- mole: https://dev.goldbook.iupac.org/terms/view/M03980

Sources
- PAC, 1990, 62, 2167. 'Glossary of atmospheric chemistry terms (Recommendations 1990)' on page 2171 (https://doi.org/10.1351/pac199062112167)
- PAC, 1994, 66, 533. 'Standard quantities in chemical thermodynamics. Fugacities, activities and equilibrium constants for pure and mixed phases (IUPAC Recommendations 1994)' on page 543 (https://doi.org/10.1351/pac199466030533)
- PAC, 1996, 68, 957. 'Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)' on page 960 (https://doi.org/10.1351/pac199668040957)

Other Outputs
- html: https://dev.goldbook.iupac.org/terms/view/A00116/html
- json: https://dev.goldbook.iupac.org/terms/view/A00116/json
- xml: https://dev.goldbook.iupac.org/terms/view/A00116/xml

Citation: Citation: 'activity 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.A00116
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Accessed: 2026-06-13T03:05:47+00:00