Physical Chemistry , 1st ed.

The units inside the square root term are s^2 /(kg^2 m^2 ), so the square root of

this unit is s/(kgm). Outside of the square root term, only the unit N (new-

ton) remains. Recalling that N kgm/s^2 , our overall units reduce to 1/s,

which is an appropriate unit for a rate. Solving:



d

d

N

t

2.03  1017 s^1 or 2.03  1017 Fe atoms per second

This is equivalent to 0.3 micromoles per second, or about 16.7 micrograms

per second. At this rate, it would take over 16 hours for 1 gram of Fe to ef-

fuse through the hole.

Because the use of tiny-holed chambers to study the effusion of gases was

pioneered by the Dutch scientist Martin Knudsen in the early 1900s, such

chambers are called Knudsen cellsand this type of effusion is termed Knudsen

effusion.Knudsen cells are still used for vaporizing high-melting materials in

vacuum systems; for example, they are used in the semiconductor industry to

manufacture computer chips.

Diffusion is the movement of gas particles through another gas due to con-

centration differences (see Figure 19.9b). It is one example of what is called a

transport property,which describes the net movement of (in this case) matter

or energy through a nonuniform medium. Other transport properties include

viscosity, electrical conductivity, thermal conductivity, and sedimentation of

particles in fluids.

For our purposes, we will assume that two different gases are present in a

system, separated at first. The initial question to consider is similar to that for

effusion: assuming motion in a single dimension (arbitrarily the xdimension),

at what rate are the gas particles approaching a planar surface of area Athat is

perpendicular to their direction of travel? The system in question is illustrated

in Figure 19.10. Experiments have shown that the rate of flow of gas particles

P 1 across a plane of area Aand into a region filled by gas particles P 2 is given

by the expression



d

d

N

t

^1 DAd

d

c

x

^1 (19.52)

where dN 1 /dtis the rate at which gas particles pass through the plane,Ais the

area of the plane,dc 1 /dxis the concentration gradient of gas particles P 1 in the

xdimension, and Dis a proportionality constant called the diffusion coefficient.

Equation 19.52 is known as Fick’s first law of diffusion.(Fick’s second law of

diffusion involves the change in c 1 over time—rather than over distance—and

will not be considered here.) The negative sign in equation 19.52 implies that

the direction of flow of increasing amount of P 1 particles is opposite the di-

rection of increasing concentration of P 1 particles: that is, particles tend to flow

from high concentrations to low concentrations.

If the concentration c 1 has units of amount per volume, the differential

dc 1 /dxhas units (amt/m^3 )/m. Since area has SI units of m^2 , the diffusion coef-

ficient must have units of m^2 /s in order for the diffusion rate dN 1 /dtto have

units of amount per second. For historical reasons, units for Dare typically

given as (non-SI) cm^2 /s. The specific value ofDdepends not only on the iden-

tity of the gas P 1 , but also on the identity of the gas that P 1 is diffusing into.

With respect to Figure 19.10, it should be noted that the gas particles P 2 are

also diffusing into the left side of the system, but for now we are ignoring this

674 CHAPTER 19 The Kinetic Theory of Gases

Plane; area  A

Gas particles

P 1

Gas particles
P 2
Figure 19.10 Diffusion is understood by de-
termining the rate at which gas particles P 1 move
through some area Aand into an area occupied
by gas particles P 2.