Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 36

C i . Thus, the location of the Gibbs dividing surface
becomes important in the definition of surface excess. Gibbs proposed that to obtain
the surface excess of all other components in a solution, a convenient choice of
the dividing plane is such that the surface excess of the solvent is zero . For a pure
component system there is no surface excess. This is called the Gibbs convention .

new
i

old
i

only if C II
i

Thus Γ = Γ =

2.6.4 S URFACE T HERMODYNAMICS AND G IBBS E QUATION
Consider a system where the total external pressure P and the system temperature T
are kept constant. Let us assume that the system undergoes an increase in interfacial
area while maintaining the total number of moles constant. The overall increase in
free energy of the system is the work done in increasing the surface area. This free
energy increase per unit area is the surface tension. Hence,

∂G
∂A σ

σ = . (2.66)

T , P , n i

Analogous to d G for a bulk phase, we can define a surface free energy in the following
form:

i μ i d n i ,

d G σ =− S σ d T + σ d A σ + (2.67)

where we have replaced σ for P and d A σ for d V . At constant T ,

i μ i d n i .

d G σ = σ d A σ + (2.68)

The total free energy at constant temperature for the surface is given by

i μ i n i .

G

σ = σ

A

σ +

(2.69)

Thus the complete differential obtained for G σ is given by

(n i d

μ i + μ i d n i ) . d G σ = σ d A σ + A σ d σ + (2.70)

Comparing the two expressions for d G σ , we obtain the following equation:

n i d

σ + μ i =

A σ d 0. (2.71)

i

The above equation is fundamental to surface thermodynamics and is called the Gibbs
equation .