PHYSICAL CHEMISTRY IN BRIEF

CHAP. 13: PHYSICAL CHEMISTRY OF SURFACES [CONTENTS] 445

wherekis the number of components in the mixture, andρ(l)andρ(l)i are the densities of the

mixture and its components.

For solutions with a low concentration of the dissolved component we may apply the relation

γ=γ(c= 0) +k c , (13.24)

wherecis the concentration of the dissolved substance, γ(c= 0) is the surface tension of

the solvent, andkis a temperature-dependent constant. kusually has a negative value, and

consequently the surface tension decreases with the concentrationc. Substances with a high

absolute value ofkare calledsurfactantsorsurface-active agents.

For aqueous solutions of alcohols, acids, aldehydes or other organic substances with a polar

group at the end of a non-polar hydrocarbon skeleton, another empirical equation, found by

Szyszkowski, applies in a broad concentration interval

γ=γ(c= 0)−aln(1 +b c), (13.25)

whereaandbare constants which are little temperature-dependent.

13.1.10 Gibbs adsorption isotherm

A detailed microscopic description of an interface in mixtures is very complicated. It is therefore

expedient to model the overall system as a set of volume phases of a constant composition, and

the surface phase (Figure13.3). Thesurface phase,σ, is defined here as an infinitesimally

thin layer of a negligible volume separating the volume phases. This layer, however, contains

certain amounts of all system components. The amount of substanceiin the surface phase is

characterized byadsorption

Γi=

n(iσ)

A

, (13.26)

wheren(iσ)is the amount of substanceiandAis the area of the interface.
U Main unit:mol m−^2
The surface phase can be placed in the region of the volume phases transition arbitrarily.
Its position is usually chosen for the adsorption of the solvent or the main unit of the mixture
to equal zero (Γ 1 = 0). The adsorption of other mixture components is then referred to as the
relative adsorptionwith respect to component 1, Γi, 1.