PHYSICAL CHEMISTRY IN BRIEF

CHAP. 13: PHYSICAL CHEMISTRY OF SURFACES [CONTENTS] 448

Solution

From Szyszkowski’s equation (13.25) we obtain

(

∂γ

∂c 2

)

=−

a b

1 +b c 2

.

For low concentrations (c 2 → 0 ) we then have

Γ 2 , 1 =−

a b

RT

c 2.

For medium concentrations we obtain

Γ 2 , 1 =−

c 2

RT

(

−

a b

1 +b c 2

)

=

( a

RT

) b c

2

1 +b c 2

.

For high concentrations(b c 2 >>1)it applies that

Γ 2 , 1 =

a

RT

.

13.1.11 Surface films

Some surfactants practically do not dissolve in a liquid but stay on the surface. This surface
phase is known as thesurface film. Surfactants cause asurface pressure,psur, on the liquid
surface, which is given by the relation

psur=γ(ci= 0)−γ , (13.30)

whereγ(ci= 0) is the surface tension of a pure liquid andγis the surface tension of a mixture.
When there is a relatively small amount of a surfactant on the liquid surface, i.e. at low
values of the relative adsorption Γi, 1 , the behaviour of the surface film can be expressed by a
two-dimensional analogy of the equation of state of an ideal gas that may be written in the
form
psur= Γi, 1 RT. (13.31)