Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 34

century ago (Stefan, 1886) that, when a molecule is brought to the surface of a liquid
from the interior, the work done in overcoming the attractive force near the surface
should be related to the work expended when it escapes into the scarce vapor phase
(Adamson and Gast, 1997; Birdi, 1997, 2002). It was suggested that the first quan-
tity should be approximately half of the second. According to the Laplace theory
of capillarity force, the attractive force acts only over a small distance equal to the
radius of the sphere (see Chapter 1, Figure 1.1) and, in the interior, the molecule is
attracted equally in all directions and experiences no resultant force. On the surface,
it experiences a force due to the liquid in the hemisphere, and half the total molecular
attraction is overcome in bringing it there from the interior.
Accordingly (Stefan, 1886), the energy needed to bring a molecule from the bulk
phase to the surface of a liquid should be half the energy needed to bring it entirely
into the gas phase. From geometrical considerations, one knows that a sphere can
be surrounded by 12 molecules of the same size, which corresponds with the most
densely packed structure. The distance between gas molecules is approximately 10
times greater than that in liquids or solids. This indicates that intermolecular forces
in liquids would be weaker than that in solids by a few orders of magnitude, as is also
found experimentally.
The ratio of the enthalpy of surface formation to the enthalpy of vaporization,
h s :h vap , for various substances is given in Table 2.2. Substances with nearly spherical-
shaped molecules have ratios near 1/2, while substances with a polar group on one
end have a much smaller ratio. This difference indicates that the latter molecules
are oriented with the nonpolar end toward the gas phase and the polar end toward

table 2.2
enthalpy of Surface Formation, hs
[10 erg/molecule], and ratio to
enthalpies of vaporization, hvap

molecules (liquid) hs/hvap

Hg 0.64

N 2 0.51

O 2 0.5

CCl 4 0.45

C 6 H 6 0.44

Diethyl ether 0.42

Cl-C 6 H 5 0.42

Methyl formate 0.40

Ethyl acetate 0.4

Acetic acid 0.34

H 2 O 0.28

C 2 H 5 OH 0.19

CH 3 OH 0.16

Note: See text for details.