Physical Chemistry , 1st ed.

tude of the unbalanced force is represented by F, then the infinitesimal amount

of work needed to increase the rectangular area by moving one boundary out

by an infinitesimal amount dxis

dwFdx (22.1)

The sign is written explicitly to emphasize that this is work done onthe

liquid. This equation is the exact analogy of the physical definition of work

(that is, work equals force times distance). If we refer to the illustration in

Figure 22.2, the rectangle has a width labeled . We can define the (unbal-

anced) force per unit distance, or F/, as the variable , so that equation 22.1

becomes

dwdx

The product of the width and the infinitesimal distance dxequals the infin-

itesimal change in area,dA, of the surface. The above equation becomes

dwdA (22.2)

The variable is called the surface tensionof the liquid.

If the system illustrated in Figure 22.2 were collapsed so that it were a film

of material rather than a bulk liquid, then the work would be twice the amount

predicted from equation 22.2: there are now two surfaces, not one. Figure 22.3

shows a picture of a film in which the work would be twice what equation 22.2

calculates. In this case, the surface tension would be defined as



F

2

fi



lm (22.3)

where the factor of 2 in the denominator is there because we want to con-

sider surface tension as a force per length per surface.In this case,Ffilm—the

unbalanced force experienced by the surfaces of the film—is twice the force

for a single surface, so in either case has the same value. Table 22.1 lists sur-

face tensions of some common liquids. Surface tension has units of force per

22.2 Liquids: Surface Tension 767

Figure 22.3 A film has two surfaces and so re-

quires twice the force to increase its size.

Table 22.1 Surface tensions of various liquids

Liquid Temperature (°C) Surface tension,(dyn/cm or erg/cm^2 )a

Acetic acid 20 27.8

Acetone 20 23.7

Bromine 20 41.5

Chloroform 20 27.1

Diethyl ether 20 17.0

Ethanol 20 22.8

Ethyl ether 50 13.5

Glycerine 20 63.4

Helium 270 0.24

Mercury 25 485.5

Water 0 75.6

Water 10 74.22

Water 20 72.75

Water 60 66.18

Water 100 58.9

Source:a D. R. Lide, ed.,CRC Handbook of Chemistry and Physics,82nd ed., CRC Press, Boca Raton, Fla.

To convert to units of J/m^2 , multiply by 1  10 ^3.

© Richard Megna/Fundamental Photographs, NYC