Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 35

the liquid phase. In other words, molecules with dipoles would be expected to be
oriented perpendicularly at the gas/liquid interfaces.
In fact, any deviation from Stefan's law is an indication that the surface molecules
are oriented differently from those in the bulk phase. This observation is useful in
order to understand surface phenomena.
As an example, one may proceed with this theory and estimate the surface ten-
sion of a liquid with data on its heat of evaporation. The number of near neighbors
of a surface molecule will be about half (6 = 12/2) than those in the bulk phase
(12 neighbors). It is now possible to estimate the ratio of the attractive energies in
the bulk and surface phases per molecule. We have the following data for a liquid
such as CCl 4 :

Molar energy of vaporization = ΔU vap (2.48)

= Δh vap − RT

= 34000 Jmol −1 − 8.315 J K −1 mol −1 (298 K)

= 31522 J mol −1 (2.49)

Energy change per molecule = 31522 Jmol −1 /6.023 10 23 mol −1 = 5.23 10 −20 J(2.50)

If we assume that about half of the energy is gained when a molecule is transferred
to the surface, we get

Energy per molecule at surface = 5.23 10 −20 (2) J = 2.6 10 −20 J (2.51)

The molecules at the surface occupy a certain value of area, which can be estimated
only roughly as follows:

Density of CCl 4 = 1.59 g cm −3
Molar mass = 12 + 4 (35.5) = 154 g mol −1
Volume per molecule = 154/1.59 = 97 cm 3 mol −1
Volume per molecule = 97 10 −6 m 3 mol −1 /6.023 10 23 mol −1
= 1.6 10 −28 m 3

The radius of a sphere (volume = 4/3 Π R 3 ) with this magnitude of volume =
[1.6 10 −28 /(4/3 Π)] 1/3
= 3.5 10 −10 m

Area per molecule = Π R 2
= Π (3.5 10 −10 ) 2 = 38 10 −20 m 2

Surface tension (calculated) for CCl 4 = 2.6 10 −20 J/38 10 −20 m 2
= 0.068 J m −2 = 68 mNm −1