Physical Chemistry Third Edition

9.5 The Pressure of a Dilute Gas 413

x

z

y

vy

Velocity

vector

Prism

volume

Area

v Wall

Figure 9.14 The Prism That Contains Molecules of a Certain Velocity That Will Strike

Area A in Timeτ.

The particles that are no farther from the wall in theydirection than a distance

equal tovyτwill strike the wall during the time intervalτ(from the familiar relation,

distancerate×time). The distance in theydirection, not the distance along the sur-

face of the prism, must be used because we are consideringvy, not the speed. The

volume of the prism is equal to the area of its base times its altitude:

VprismAvyτ (9.5-7)

We assume that our system is uniform. Thenumber density,N, in any part of the

system is equal toN/VwhereNis the number of particles andVis the volume of the

system. The number of particles in the prism is

(number in prism) 

N

V

AvyτNAvyτ (9.5-8)

The number in the prism with velocities in the specified range is

⎛

⎝

number in prism

with velocities ind^3 v

strikingAin timeτ

⎞

⎠NAvyτg(v)dvxdvydvz (9.5-9)