Activity Coefficients

Basic Definitions

At constant temperature and pressure, the chemical potential of a solute component k in a solution can be written as

$$ {\upmu_{{k}}} = {\upmu_{{k}}}^{\infty } + {\mathrm{ R}{T}\mathrm{ ln}}\ {{\mathrm{ a}}_{{k}}} = {\upmu_{{k}}}^{{\infty (\mathrm{ m})}} + {\mathrm{ R}{T}\mathrm{ ln}}\ {{\mathrm{ m}}_{{k}}}{\upgamma_{{k}}} $$

where μ _k ^∞ is its chemical potential at infinite dilution, m is molality (moles of solute per kg of solvent), R is the gas constant, T the absolute temperature, and γ _k the activity coefficient in the molality scale at a given molality. Note that the reference state is not the pure solution (most of the pure electrolytes are solid and hence in a different aggregation state) but the infinitely dilute solution:

$$ \eqalign{{\upmu_{{k}}}^{{\infty (\mathrm{ m})}} = & \;\mathrm{ li}{{\mathrm{ m}}_{{\mathrm{ x}\ (\mathrm{ solvent}) -> 1}}}({\upmu_{{k}}} - {\mathrm{ R}{T}\mathrm{ ln}}\ {{\mathrm{ m}}_{{k}}}{\upgamma_{{k}}}); \cr & \mathrm{...