Physical Chemistry Third Edition

5.5 Surfaces in One-Component Systems 225

L

Area!

Figure 5.16 A Wire Frame of Adjustable Size to Illustrate Surface Tension.As the

wire frame is raised, a thin film of liquid fills the area within the frame.

so that

γ

Frev

2 L

(5.5-7)

We recognizeγas the force per unit length exerted by the surface. For this reason it

is called thesurface tension. The SI units of surface tension can be given as N m−^1

(newtons per meter) or as J m−^2 ( joules per square meter). Table A.10 in Appendix A

gives values of the surface tension for several pure substances in contact with a vapor

phase of the same substance.

The surface tension for a liquid in contact with its vapor is always positive. The

surface of a liquid in contact with a vapor phase can lower its energy by decreasing its

surface area. The surface acts somewhat like a stretched elastic film. This is the reason

that droplets of a liquid tend to have spherical shapes, since the sphere has the smallest

area per unit volume of any three-dimensional object. Another effect is that a liquid

such as water is drawn into a vertical glass tube as shown in Figure 5.17a. The surface of

liquid water in a glass capillary tube is very nearly tangent to the surface. Figure 5.17b

shows another case, in which the liquid surface meets the solid surface at an angle,

which is called thecontact angleand denoted byθ. In the case of water on glass, the

contact angle is nearly equal to zero, corresponding to strong attraction between the

water and the glass. A nonzero contact angle corresponds to weaker attractions.

The liquid rises into the tube because the surface tension balances the gravitational

force on the column of liquid in the tube. If the radius of a vertical tube isrand if the

contact angle is zero, the vertical surface tension force is equal to 2πrγ. If the density

of the liquid isρ, the gravitational force on the column of liquid is equal toπr^2 hρg,

wheregis the acceleration due to gravity, and wherehis the height of the column.

Equating the magnitudes of these quantities,

2 πrγπr^2 hρg

so that the height of the column is

h

2 γ

ρgr

(zero contact angle) (5.5-8)