 ## activity coefficient $$f$$, $$\gamma$$

https://doi.org/10.1351/goldbook.A00116
The activity coefficient $$f_{\text{B}}$$ of a substance B in a liquid or solid mixture containing mole fractions $$x_{\text{B}}$$, $$x_{\text{C}}$$, ... of the substances B, C, ... is a dimensionless quantity defined in terms of the chemical potential $$\mu _{\text{B}}$$ of B in the mixture by: $R\ T\ \ln (x_{\text{B}}\ f_{\text{B}})=\mu _{\text{B}}\left(\text{cd},\,T,\,P,\,x\right)- \mu _{\text{B}}^{*}\left(\text{cd},\,T,\,p\right)$ where $$x$$ denotes the set of mole fractions $$x_{\text{B}}$$, $$x_{\text{C}}$$, ... . The activity coefficient $$\gamma _{\text{B}}$$ of a solute B in a solution (especially a dilute liquid solution) containing molalities $$m_{\text{B}}$$, $$m_{\text{C}}$$, ... of solutes B, C, ... in a solvent A is a dimensionless quantity defined in terms of the chemical potential $$\mu _{\text{B}}$$ by: $R\ T\ \ln \left(\frac{m_{\text{B}}\ \gamma _{\text{B}}}{m^{\ominus}}\right)=\mu _{\text{B}}- \left\{\mu _{\text{B}}- R\ T\ \ln \left(\frac{m_{\text{B}}}{m^{\ominus }}\right)\right\}^{\infty }$
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)