Page 34 - Instant notes

Physical Chemistry 20

other molecules from the liquid. More familiarly, this implies that a liquid will tend to
adopt the minimum surface area possible. Surfaces are higher energy states than the bulk
liquid and G surface, the free energy of a surface of area A, is defined by
G surface=γA

−2
−1
where γ is the surface tension of the liquid. Typically, γ ranges between 47×10 N m
−2
−1
for mercury down to 1.8×10 N m for a liquid with relatively small intermolecular
interactions such as pentane. It follows that small changes of surface area dA result in an
amount of work dG given by dG=γ dA.
In a gas cavity (a volume which is wholly contained by the liquid), the effect of the
surface tension is to minimize the liquid surface area, and hence the volume of the cavity.
The outward pressure of the gas opposes this minimization. For a cavity of radius r, the
pressure difference between the inside and the outside of the cavity, ∆p, is given by:
∆p=p gas−p liquid=2γ/r

The inverse relationship in r means that gas within a small cavity must be at a higher
pressure than the gas in a large cavity for any given liquid. At very small radii, the
pressure difference becomes impractically large, and is the reason why cavities cannot
form in liquids without the presence of nucleation sites, small cavities of gas in the
surface of particles within the liquid.
For bubbles—a volume of gas contained in a thin skin of liquid—two surfaces now
exist, and the pressure differential between the inside and outside of the bubble becomes:
∆p=p inside−p outside=4γ/r

Surfactants
Surfactants are chemical species which have a tendency to accumulate at surfaces, and
tend to lower the surface tension of the liquid. A familiar example is a cleaning detergent,
−
−
which is comprised of a hydrophilic head, such as -SO 3 or -CO 2 , and a hydrophobic
tail, which is usually comprised of a long-chain hydrocarbon. In water or other polar
solvents, the head group has a tendency to solvation, whilst the tail adopts its lowest free
energy state outside the solvent. The compromise between these conflicting requirements
is met at the surface, with the head remaining in the solvent and the tail pointing out of
the solvent. Above a critical surfactant concentration and above the Krafft
temperature, surfactant molecules may not only accumulate at the surface, but may also
form micelles. Micelles are clusters of between some tens and some thousands of
surfactant molecules within a solvent whose tails cluster within the micelle so as to
maximize the interactions of the tails, leaving a surface of solvated hydrophilic heads.
Where surfactants are added to water in the presence of greases or fats, the tails may
solvate in the fatty material, leaving a surface of hydrophilic heads. The effect is to
dissolve the grease in the water, and is the reason for the cleaning properties of detergents
and soaps.