Partial surface tension of components of a solution.

First, extending the boundaries of the thermodynamic framework of Gibbs, a definition of the partial surface tension of a component of a solution is provided. Second, a formal thermodynamic relationship is established between the partial surface tensions of different components of a solution and the surface tension of the same solution. Third, the partial surface tension of a component is derived as a function of bulk and surface concentrations of the given component, using general equations for the thermodynamics of solutions. The above equations are derived without an initial knowledge of the Gibbs adsorption equation and without imposing any restrictions on the thickness or structure of the surface region of the solution. Only surface tension and the composition of the surface region are used as independent thermodynamic parameters, similar to Gibbs, who used only the surface tension of the solution and the relative surface excesses of the components. The final result formally coincides with the historical Butler equation (1932), but without its theoretical restrictions. (Butler used too many unnecessary model restrictions during his work: he started from the Gibbs adsorption equation, and he assumed the existence of a surface monolayer.) Thus, the renovated Butler equation has gained general validity in this article. It was applied to derive both the Langmuir equation and the Gibbs adsorption equation, but the latter two equations do not follow from each other. Thus, it is shown that logically (not historically) the renovated Butler equation is a root equation for surface tension and the adsorption of solutions. It can be used to perform calculations for specific systems if the corresponding specific experimental data/models are loaded into it. In this case, both surface tension and surface composition can be calculated from the renovated Butler equation, which cannot be done using the Gibbs adsorption equation alone.