92168.pdf

82 Liquid-gas and liquid-liquid interfaces

From the first and second laws of thermodynamics,

d£7 = TdS - pdV + 2/M«/

or, for a surface phase,

dUa = YdS" - pdVff + ydA + 2/i,d«f (^4 -!8)

Subtracting equation (4.18) from equation (4.17),

S'dT - V^dp + Ady + S/ifd/t,- = 0

Therefore, at constant temperature and pressure

(4.19)

For a simple two-component solution (i.e. consisting of a solvent and

a single solute) equation (4.19) becomes

As explained above, surface excess concentrations are defined

relative to an arbitrarily chosen dividing surface. A convenient (and

seemingly realistic) choice of location of this surface for a binary

solution is that at which the surface excess concentration of the

solvent (FA) is zero. The above expression then simplifies to

dy = ~FBd/xB

Since chemical potential changes are related to relative activities by

MB == MB ~^~ •**T In #B

then dfjLB = RT d In aB

Therefore TB = — = -^-. —L (4 20)

RT dlnaB RT daB

or, for dilute solutions,

rB=

~*F*!~"

(4

"

which is the form in which the Gibbs equation is usually quoted.