Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 89

the fundamental equation of surface thermodynamics that forms the basis for all
of the relationships between surfaces or interfaces and the bulk phases in equilib-
rium. Examples of phase boundaries of relevance in environmental chemistry include
the following: air/water, soil (sediment)/water, soil(sediment)/air, colloids/water, and
atmospheric particulate (aerosols, fog)/air. Typically the relationship between the
bulk-phase and surface-phase concentrations is given by an adsorption isotherm .

3.5.1 G IBBS E QUATION FOR N ONIONIC AND I ONIC S YSTEMS
Let us apply the Gibbs equation to two different systems, that is, compounds that are
neutral (nonionic) and those that are ionic (dissociating).
Let us consider a binary system (solute/ i , solvent (water)/w) for which the Gibbs
adsorption equation was derived in Chapter 2.

d σ wa

d

Γ i =− , (3.70)

w
i

μ

where the surface excess is defined relative to a zero surface excess of solvent (water).
σ wa representsthesurfacetensionofwater.Forasolid-waterinterfacewherethesolute
dissolved in water, the surface tension is replaced by the interfacial tension of the
solid-water boundary. For a solid-air interface, the analogous term is the interfacial
tension (energy) of the solid-air boundary.
If the solute in water is nondissociating (neutral and nonionic), then the equation
for chemical potential is

w
i

w0
i

μ = μ + RT ln a i , (3.71)

where a i is the activity of solute i in water. Using the above expression, we obtain the
following

1
RT ·

σ wa
d ln a i .

d

Γ i =− (3.72)

If the solute dissociates in solution to give two or more species in the aqueous phase,
then the above equation has to be modified

1
nRT

σ wa
d ln a

d

Γ i =− , (3.73)

±

where n is the number of dissociated ionic species in water resulting from the solute.
Note the difference between the expressions for ionic and nonionic systems. In both
cases, the surface excess can be determined by obtaining the solution surface tension
(interfacial energy in the case of solids) as a function of the activity of solute i in
solution. If (d

σ / dln a)> 0, then Γ i is negative and we have net depletion at the

surface. If, on the other hand, (d σ / dlna )< 0, then Γ i is positive and we have a net

surface excess (positive adsorption) on the surface.
Although the Gibbs equation applies theoretically to solid-water interfaces as
well, the direct determination of the interfacial tension at the solid-water boundary is
impractical. However, adsorption of both molecules and ions at this boundary leads