Physical Chemistry , 1st ed.

particles (and usually no gas of any sort) existed previously. It is usually a slow

process, so that the concentration of gas particles in the original system is ap-

proximately constant.Diffusionis the passage of gas particles (or solute species,

if in solution) from one part of a system to another due to unequal concen-

trations of that gas within the system, with the total pressure constant in the

system (that is, the transport isn’t due to pressure gradients). Figure 19.9 illus-

trates the difference.

Effusion can be understood if we consider the velocity of the gas particles

in one dimension. We start by pointing out that the effusion rate must be pro-

portional to the average velocity in that dimension, since we expect that the

faster the gas particles are traveling, the faster they can escape out of a hole in

the system. This idea can be written mathematically as

rate of effusion vavg

We have already determined a probability density function that describes

the distribution of velocities among the gas particles. It was, for the xdi-

mension,

gx 

2

m

kT



1/2

emvx

(^2) /2kT
If we want to know the number of gas particles that are passing through some
small hole with area Aper second (represented as dN/dt), then we need to de-
termine the number of gas particles that are approaching the hole from one di-
rection.This restriction implies that for a chamber filled with gas particles,
these particles are slowly leaking out of the chamber but not back into the
chamber. (See Figure 19.9a.) If we arbitrarily assign the direction toward the
hole in the chamber as the positive direction, the average velocity of the par-
ticles approaching the hole is
average velocity  

vx 0
vx 
2
m
kT

1/2
emvx
(^2) /2kT
dvx (19.48)
672 CHAPTER 19 The Kinetic Theory of Gases
Barrier
closed
(b)
Barrier
open
(a)
Figure 19.9 (a) Effusion is the movement of
gas particles from a system into the surroundings,
usually through a small hole or holes. Typically,
the surroundings are deficient in gas particles,
and effusion is usually so slow that the pressure
of the gas inside the system can be considered
constant. (b) Diffusion is the movement of gas
particles within a system and is caused by con-
centration differences. For example, two gases
may be separated by a partition, but after that
partition is lifted the two gases will diffuse and
ultimately will become thoroughly mixed.