How is the solvent activity related to its chemical potential?

The relationship between the solvent activity and its chemical potential is described by the equation μ_A = μ_A* + RT ln a_A. This equation effectively connects the chemical potential of a solvent (μ_A) with its activity (a_A), using the standard chemical potential (μ_A*) and the temperature (T) as well as the universal gas constant (R).

In this context, the chemical potential (μ_A) represents the change in Gibbs free energy of the solvent when an infinitesimal amount is added to the system, reflecting the solvent's tendency to escape or to mix. The standard chemical potential (μ_A*) pertains to the chemical potential of the solvent in a standard state at a fixed temperature and pressure, where the composition is ideally defined.

The activity of a solvent (a_A) accounts for deviations from ideal behavior in a solution. The expression RT ln a_A thus captures these deviations, with the natural logarithm transformation effectively allowing the representation of activity in terms of concentration or partial pressure, while also controlling for non-ideal effects.

This equation is fundamental in thermodynamics and physical chemistry, particularly in the study of solutions and phase equilibria, as it succinctly relates the thermodynamic driving force of mixing to the activity of the components