Physical Chemistry , 1st ed.

distance or energy per area, and can be expressed in N/m, dyn/cm, erg/cm^2 ,

or J/m^2 .*

Surface tension is a characteristic of a liquid that varies with temperature,

as might be expected. At the critical temperature—the temperature at which

the distinction between liquid and gas phases disappear—the surface tension

goes to zero.

Because work is done when changing the area of a surface, we should be

able to correlate this work to one of the thermodynamic state functions. Recall

that we found in an earlier chapter that the Gibbs energy is equal to the max-

imum amount of non-pVwork that a process could do. Since changing the

area of a surface is not pressure-volume work (just like electrical work isn’t

pressure-volume work), then “surface-tension–area” work must be related to

the Gibbs energy. For a reversible change in surface area that occurs at constant

temperature and pressure, we have

dwdGdA (22.4)

This equation implies three things. First, we can integrate equation 22.4 to get

w  G    A (22.5)

Second, we can rearrange equation 22.4 to solve for the surface tension in

terms of a partial derivative at constant temperature and pressure:



G

A



T,p

(22.6)

Third, if we want to consider the natural variable equation for dGfor a liquid

system whose surface area is changing, we must include the change in the

Gibbs energy due to surface area change:

dGS dTV dpdA (22.7)

The surface tension is sometimes also referred to as the Gibbs surface energyof

a condensed phase. It is understood that it is a Gibbs energy per unit area, since

this is consistent with the units used to define .

Example 22.1

How much work is required to increase the surface area of a container of wa-

ter from 200.0 cm^2 to 300.0 cm^2? Such work might have to be performed on

the water if, for example, a plastic container deforms and exposes a larger sur-

face area. The surface tension of water is 72.75 erg/cm^2 at 20°C.

Solution

Using the integrated expression in equation 22.5, we figure that the change

in area, A, is (300.0 200.0) cm^2 or 100.0 cm^2. Using equation 22.5:

w    A72.75 

c

e

m

rg

 (^2) 100.0 cm
2
or, simply,
w7275 erg
768 CHAPTER 22 Surfaces
*A dyne (abbreviation dyn) is the unit of force in the cgs system of units, and is com-
monly used to express surface tensions. 1 N 100,000 dyn.