Page 248 - Physical Chemistry

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either bulk phase. An adiabatic change in the area of the interface between a and b Section 7.7
will therefore change the system’s internal energy U. The Interphase Region
Forexample, consider a liquid in equilibrium with its vapor (Fig. 7.17). Inter-
molecular interactions in a liquid lower the internal energy. Molecules at the surface of
the liquid experience fewer attractions from other liquid-phase molecules compared
with molecules in the bulk liquid phase and so have a higher average energy than mol-
Vapor
ecules in the bulk liquid phase. The concentration of molecules in the vapor phase is so
low that we can ignore interactions between vapor-phase molecules and molecules at
the surface of the liquid. It requires work to increase the area of the liquid–vapor inter-
face in Fig. 7.17, since such an increase means fewer molecules in the bulk liquid phase Liquid
and more in the surface layer. It is generally true that positive work is required to in-
crease the area of an interface between two phases. For this reason, systems tend to as-
sume a configuration of minimum surface area. Thus an isolated drop of liquid is spher- Figure 7.17
ical, since a sphere is the shape with a minimum ratio of surface area to volume. Attractive forces on molecules in a
Let be the area of the interface between phases a and b. The number of mole- liquid.
cules in the interphase region is proportional to . Suppose we reversibly increase the
area of the interface by d . The increase in the number of molecules in the interphase
region is proportional to d , and so the work needed to increase the interfacial area is
ab
proportional to d . Let the proportionality constant be symbolized by g , where the
superscripts indicate that the value of this constant depends on the nature of the phases
in contact. The reversible work needed to increase the interfacial area is then g ab d .
The quantity g ab is called the interfacial tension or the surface tension. When one
phase is a gas, the term “surface tension” is more commonly used. Since it requires
positive work to increase , the quantity g ab is positive. The stronger the intermo-
lecular attractions in a liquid, the greater the work needed to bring molecules from the
ab
bulk liquid to the surface and therefore the greater the value of g .
In addition to the work g ab d required to change the interfacial area, there is the
work PdV associated with a reversible volume change, where P is the pressure in
each bulk phase and V is the system’s total volume. Thus the work done on the closed
system of phases a and b is
ab
dw rev P dV g d plane interface (7.26)*
We shall take (7.26) as the definition of g ab for a closed two-phase system with a pla-
nar interface. The reason for the restriction to a planar interface will become clear in
the next section. From (7.26), if the piston in Fig. 7.19 is slowly moved an infinitesi-
mal distance, work PdV g ab d is done on the system.
The term surface tension of liquid A refers to the interfacial tension g ab for the
system of liquid a in equilibrium with its vapor b. Surface tensions of liquids are often
measured against air. When phase b is an inert gas at low or moderate pressure, the
value of g ab is nearly independent of the composition of b.
Since we shall be considering systems with only one interface, from here on, g ab
will be symbolized simply by g.
The surface tension g has units of work (or energy) divided by area. Traditionally,
2
g was expressed as erg/cm dyn/cm, using the now obsolete cgs units (Prob. 2.6).
2
The SI units of g are J/m N/m. We have (Prob. 7.46)
3
2
3
2
1 erg>cm 1 dyn>cm 10 J>m 10 N>m 1 mN>m 1 mJ>m 2 (7.27)
For most organic and inorganic liquids, g at room temperature ranges from 15 to
50 mN/m. For water, g has the high value of 73 mN/m at 20°C, because of the strong
intermolecular forces associated with hydrogen bonding. Liquid metals have very
high surface tensions; that of Hg at 20°C is 490 mN/m. For a liquid–liquid interface
with each liquid saturated with the other, g is generally less than g of the pure liquid
with the higher g. Measurement of g is discussed in Sec. 7.8.