https://doi.org/10.1351/goldbook.15312
For a substance \(\ce{B}\), activity coefficient \(f_{\ce{B}}\) extrapolated to infinite dilution: \[\ln (f_{\ce{B}}^{\infty}) = \lim \limits_{x_{\ce{B}} \to 0} (\frac{\mu_{\ce{B}} - \mu_{\ce{B}}^{\ast}}{RT} - \ln x_{\ce{B}})\]
Notes:
- Useful for dilute mixtures as an alternative to the standard chemical potential on a molality basis.
- The relation between the activity coefficient at infinite dilution and the standard chemical potentials is, for a solute \(\ce{B}\) in a solvent \(\ce{A}\), \[\ln f_{\ce{B}}^{\infty} = \frac{\mu_{m,\ce{B}}^{_{^⦵\!}} - \mu_{\ce{B}}^{\ast}}{RT} - \ln (M_{\ce{A}}m_{\ce{B}}^{_{^⦵\!}})\] where \(M_{\ce{A}}\) is the molar mass of the solvent.