Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 32

where x i is the mole fraction of component i in the solution. The reference state for
the solution is pure liquid for which the mole fraction is 1.
2.6 THERMODYNAMICS OF SURFACES AND
COLLOIDAL SYSTEMS
The boundary between any two contiguous phases is called a surface or an interface .
The term “surface” is reserved for those that involve air as one of the contiguous
phases. In environmental chemistry, we encounter several interfaces: liquid/gas (e.g.,
air-sea, air bubbles in water, fog droplets in air, foam), liquid/liquid (e.g., oil-water),
liquid/solid (e.g., sediment-water, soil-water, colloid-water), and solid/air (e.g., soil-
air, aerosols in air). Often when one phase is dispersed in another at submicron
dimensions (e.g., air bubbles in sea, fog droplets in air, colloids in groundwater, acti-
vated carbon in wastewater treatment), very large surface areas are involved. Surface
tension accounts for the spherical shape of liquid droplets, for the ability of water
to rise in capillaries as in porous materials (e.g., soils), and for a variety of other
reactions and processes at interfaces. It is therefore important to discuss some basics
of surface and interfacial chemistry.
2.6.1 S URFACE T ENSION
Surfaces and interfaces are different from bulk phases. Consider, for example, water
in contact with air (Figure 2.4a). The number density of water molecules gradually
decreasesasonemovesfrombulkwaterintoair(Figure2.4b).Similargradualchanges
in all other physical properties will be noticed as one moves from water to air across
the interface. At a molecular level there is no distinct dividing surface at which the
liquid phase ceases and the air phase begins. The so-called interface is therefore a
diffuse region where the macroscopic properties change rather gradually across a
certain thickness. The definition of this thickness is compounded when we realize
that it generally depends upon the property considered. The thickness is at least a few
molecular diameters (a few angstroms). The ambiguity with respect to the location
of an exact dividing surface makes it difficult to assign properties to an interface.
However, Gibbs showed how this can be overcome.
The reason for the diffuse nature of the surface becomes clear when we consider
the forces on a water molecule at the surface. Obviously, since there is a larger number
density of molecules on the water-side than on the air-side, the molecule experiences
different forces on either side of the interface. The pressure (force) experienced by
a water molecule in the bulk is the time-averaged force exerted on it per unit area
by the surrounding water molecules and is isotropic (i.e., the same in all directions).
For a molecule on the surface, however, the pressure is anisotropic (Figure 2.4a). It
has two components, one normal to the surface, P n , and the other tangential to the
surface, P t . The net pressure forces in the lateral direction are substantially reduced
in the interfacial region compared with the bulk region. Because fewer liquid phase
molecules than those in the bulk phase act upon the surface molecules, the surface
molecules possess greater energy than the bulk molecules. It requires work to bring
a bulk molecule to the surface since it means increasing the surface area. The net