Physical Chemistry , 1st ed.

this plot should point out is that there is no single useful definition of an

“average speed” of gas particles, and care should be taken to specify exactly

which one is used in any situation.

19.4 Collisions of Gas Particles

One of the statements that define the kinetic theory of gases is that the gas par-

ticles are constantly colliding with each other, and during the course of these

collisions, the overall energy is conserved. The kinetic theory of gases allows us

to understand some of the characteristics of these collisions. In order to un-

derstand these characteristics, we need to define some parameters of the gas

particles themselves.

For a pure gas, we will assume a hard-sphere model.In this model, each gas

particle is treated as a spherical particle having a specific radius within which

no other gas particle can penetrate. (The best analogy might be to think of gas

particles as croquet or billiard balls.) This is illustrated in Figure 19.6. Each gas

particle has a radius labeled r, and because each particle is rigid, the nearest

that the centers of two particles can approach is twice the radius, or the diam-

eter d. (This is labeled in Figure 19.6.) Because the particles are hard spheres,

the presumption is that no two particles can ever get their two centers closer

than 2rdto each other. One way of writing this is by defining a potential

energy Vbetween any two gas particles:

V 0 if distance between centers is greater than 2r(that is, no inter-

action occurs)

V if distance between centers is less than 2r(not physically possible)

In terms of interparticle collisions, we would like to be able to know three

things: the number of collisions any one particle experiences in a given time,

the average distance between such collisions, and the net rate of travel of any

gas particle through space. The first and second quantities are useful to people

studying gas-phase chemical reactions (occurring, for example, in the atmo-

sphere or in space or at high temperatures), and the last quantity is useful for

understanding the concepts of diffusion and effusion of gas particles.

666 CHAPTER 19 The Kinetic Theory of Gases

0.0025

0

0

Velocity, m/s

1500

Relative probability

vmost prob

0.002

0.0015

0.001

0.0005

500 1000

vrms

v–

Figure 19.5 In the Maxwell-Boltzmann distribution for argon gas at 500 K, the marks show

vrms,vmost prob, and v, showing how they are numerically different.

rr

d

Gas

particle

Gas
particle
Figure 19.6 In the hard-sphere model of gas
particles, each particle is defined as having an im-
penetrable radius r. Two times r, or the diameter
d, is a parameter that will be used in understand-
ing the behavior of gas particles.