Physical Chemistry , 1st ed.

c.However, our volume is only 0.02271 m^3. The total number of collisions

occurring in 1.000 mol of Xe is therefore

5.23  1034 m^3 s^1 0.02271 m^3 1.19  1033 s^1

This total number of collisions is roughly equal to NAgas particles (that is,

1 mole) having four billion collisions per second. (Verify this by multiplying

those two quantities together—and don’t forget the factor of 2!)

If two different gases are present in a sample, then the number of collisions

of any particular gas particle can be divided into collisions with like particles

and collisions with different particles. We can therefore define a mean free path

between collisions of unlike particles as well as a collision rate between unlike

particles. For two particles P 1 and P 2 that have diameters d 1 and d 2 (see Figure

19.8) and masses m 1 and m 2 , we give (but do not derive) the mean free path

for a P 1 particle hitting a P 2 particle, labeled (^1) → 2 :
(^1) → 2 
m 1
m

2
m 2 (19.43)
where N 2 is the number of particles of gas P 2. Since N 2 /Vis the density of P 2
gas particles, we can rewrite this expression in terms of the density  2 :
(^1) → 2 
m 1
m

2
m 2 (19.44)
Similarly, we can define a collision rate for a P 1 particle hitting a P 2 particle,
labeled z 1 → 2 :
z 1 → 2  (19.45)
where  12 is the reduced mass of the two particles:
 12 
m
m
1
1

m
m
2
2
 (19.46)
(Because m 1 and m 2 are different, we cannot use m/2 here as we did for equa-
tion 19.41.) Mean free paths and collision rates for P 2 hitting P 1 are found by
simply exchanging the subscripts 1 and 2 where they appear in equations
19.43–19.45. The total number of collisions per second per unit volume can be
determined from equation 19.45 and its counterpart:

Z 1 → 2  (19.47)

Use of these expressions is left for the end-of-chapter exercises.

19.5 Effusion and Diffusion

An understanding of how gas particles travel within the gas sample itself helps

us understand the effusion and diffusion of gases.Effusionis the passage of gas

particles through a barrier (like a small hole) into a different region where no

 1  2 

d 1 

2

d 2



2



8 kT



 12

 2 

d 1 

2

d 2



2



8 kT



 12

1





d 1 

2

d 2



2

 2

V





d 1 

2

d 2



2

N 2

19.5 Effusion and Diffusion 671

d 2

P 2

P 1

d 1

Figure 19.8 If the gas particles involved in the
collision are of different types, then two different
masses and diameters enter into the equation for
collision frequencies.