The standard Gibbs energy of adsorption from the bulk at the surface of liquid mixtures: reinterpretation of Traube's rule: Analysis of the Δ adsG0 contributions under the Extended Langmuir model

Abstract

In this paper, it is shown that the symmetrically normalized activity coefficient of the solute in the bulk solution, γ B b , makes a non-negligible contribution to the standard Gibbs energy of adsorption of solute from the bulk at the surface of binary liquid mixtures, Δ ads G 0. With a view to defining this change with practical purposes, we selected the pure solute and a surface pressure π of 1 mN m −1 as standard states for the bulk and surface phases, respectively. Besides, we assumed availability of data in the highly dilute region, where the two-dimensional ideal equation of state holds. In this way, Δ ads G 0 = − RT ln ( π / γ B b x B ) . When γ B b is taken into account, Traube's rule (that ln ( π / x B ) x B → 0 increases linearly with chain length in the water + 1-alkanol series) does not imply that Δ ads G 0 increases linearly with chain length. On the contrary, together with the fact that in this series ln( γ B b , ∞ ) increases with chain length at the same rate as ln ( π / x B ) x B → 0 , Traube's rule implies that Δ ads G 0 is constant in this series. This can be interpreted in molecular terms as indicating that in highly dilute solutions the hydrocarbon chain of alkanol molecules at the surface does not lie in or on the surface (as is implied by a linear increase in Δ ads G 0 with chain length), but resides completely in the gas phase, as is now known to be true. The constancy of Δ ads G 0 also explains why water + 1-alkanol systems share the same π versus γ B b x B curve except at high surface concentrations, where the degree of discrepancy is in any case limited by the small differences in surface tension among the pure alkanols. We conclude by using the “Extended Langmuir” model of surface behaviour to split Δ ads G 0 into five distinct physically meaningful contributions.