Thermodynamic evaluation of molar surface area and thickness of water + ethanol mixtures

Abstract

The molar surface area, Am, has been a neglected property of liquid mixtures. Here its role as a surface probe over different liquid mixture regions is exposed. A thermodynamic approach to Am calculation of planar binary liquid mixtures is developed. The relative adsorption and surface mole fraction of the surface-active component are the required input quantities. The molar surface area of thermodynamically ideal mixtures, Amid, is calculated analytically. The molar surface volume, Vms, is related to the bulk partial molar volumes and to the dependence of surface tensions on pressure. Thereafter the surface thickness is defined as τ = Vms/Am and an approximate expression is obtained for its evaluation. The method is applied to aqueous ethanol mixtures at 298 K, using literature data and, in accordance with theoretical requirements, the variation of ideal molar surface area with surface mole fraction is not strictly linear. In the real mixture, an unexpected sharp drop in Am is observed upon adding ethanol to water. This behaviour persists up to an ethanol-rich domain in the surface, at equilibrium with the approximately equimolar bulk mixture, then pass to larger than ideal values, reach a maximum and finally drop to the pure ethanol value. The difference Am − Amid is related to the differential enrichment of ethanol in the surface phase, defined as the difference between its equilibrium mole fractions in the surface and bulk phases. The profile for surface thickness variation with composition resembles a mirror image of Am changes. This analysis showed that, for the largest composition difference of 0.56, Am − Amid is a minimum, τ − τid shows a shallow maximum and the Gibbs relative adsorption of ethanol is a maximum. These findings are interpreted at a molecular level in terms of an uneven surface phase with changing thickness accompanying ethanol molecules orientation.