Chemistry Reference
In-Depth Information
The surface tension of water (72 mN/m, at 25°C) decreases to 63 mN/m in a solu-
tion of SDS of concentration 1.7 mmol/L. The large decrease in surface tension sug-
gests that SDS molecules are concentrated at the surface, as otherwise there should
be very little change in the surface tension. This means that the concentration of SDS
at the surface is much higher than in the bulk. The molar ratio of SDS:water in the
bulk is 0.002:55.5. At the surface, the ratio will be expected to be of a completely
different value, as found from the value of Γ (the ratio is 1000:1). This is also obvious
when considering that foam bubbles form on solutions with very low surface-active
agent concentrations. The foam bubble consists of a bilayer of surface-active agent
with water inside. In fact, it is easy to consider the state of surfactant solutions in
terms of molecular ratios. If we use SDS, for example, since it is a strong electrolyte,
it can be considered to dissociate completely:
C
12
H
25
SO
4
Na → C
12
H
25
SO
4
− + Na
+
SDS → DS
−
+ S
+
′
(3.32)
The appropriate form of the Gibbs equation will be
−d γ = Γ
DS
− dμ
DS
− + Γ
S+
dμ
s+
(3.33)
where the surface excess, Γ
i
, terms for each species in the solution (e.g., DS− and
S+) are included. This equation relates the observed change in surface tension to the
changes in the chemical potential of the respective solutes (here DS− and S+). The
chemical potential terms can be expanded in an analogous way to Equation 3.17, and
then we obtain
−d γ = RT [Γ
DS
− d(ln C
DS−
) + Γ
S
+ d(ln C
s+
)]
(3.34)
= RT (Γ
DS
− dC
DS-
/C
DS−
+ Γ
S
+ dCs+/dCs+)
(3.34a)
In order to simplify this equation, we must assume that electrical neutrality is main-
tained in the interface; then we may write
Γ
SDS
= Γ
DS
− = Γ
S
+
(3.35)
and
C
SDS
= C
DS−
= C
S+
(3.36)
which, on substitution in Equation 3.34, gives
−d γ = 2 RT Γ
SDS
d(ln C
SDS
)
(3.37)
= (2RT/C
SDS
) Γ
SDS
dC
SDS
(3.38)
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