jas gas Kinetic rev3

The Kinetic Theory of Gas III:
 ZI = collision frequency = number of collisions per molecule
 ZII = collision rate = total number of collisions

  = mean free path = distance traveled between collisions

Drs. Jaslin Ikhsan, M.App.Sc., Ph.D.
Chemistry Ed. Department
State University of Yogyakarta

Collision amongst the molecules
 Collision shall occur when the centers of 2 molecules have
distance d (interaction diameter), which is = d
 The Surface Area of Container is  =  d2
 The long of container
(distance to be
passed):  = dt (:
average speed)
 Volume of the
container (interaction
volume) is V = 

 No. of collision:
N
 
V 

d

Collision Frequency ( ZI )
V  2    d 2  a vg

where :  r ela tive  2  a vg

Define: N* = N/V =
molecules per unit volume

Z I  (V )  ( N *)

Z I  2    d 2  va vg  N *

va vg

8  k T
8  R T


 m
 M

vr ela tive 



8 RT

mAmB
wher e  
mA  mB

if mA  mB :
vr ela tive 



8 RT

2mA
x
2
mA

Collision Rate (ZII)
1
Z II  Z I  N *  
2

Double Counting Factor

1
2
2

Z II 
   d  va vg  ( N*)
2

N
N* 
 ???
V
PV  nRT

N
PV 
RT
N Avog

P

 A
N AvogV RT
N

N PN Avog
P
so


 AN Avog
V
RT
kT

Collision Rate (ZII)
1
2
2
Z II 
 ( N*)    d  va vg
2
8  k T
8  R T

va vg 

 m
 M
For A-B collisions:

AB , AB

Reduced M ass   AB

mA  mB

mA  mB

Relative Velocity  vr ela tive( AB )

8  k T

   AB

Collision Diameter
d AB 

d A  dB

2

Number per Unit Volume
NA
N A* 
V

NB
NB* 
V

Collision Rate (ZII) of 2 different molecules
Z II ( AA) 

1

2

 ( N A*)  
2

2
dA

 8kT 

 
   mA 

1/ 2

Z II ( AB )  N A *  N B *   d AB  va vg ( AB )
2

Z II ( AB )  ( N Avog ) .[ A][ B].  d AB  va vg ( AB )
2

2

Z II ( AB )  N A *  N B *   d AB

remember

AN Avog

 8kT 

 
    AB 

1/ 2

2

N PN Avog
P

 

V
RT
kT

Mean Free Path (  )
va vg
distance traveled per unit time


no molecules it collides with in unit time Z I

1
V


2
2
2    d  N A[ A]

2   d  N

The mean free path is independent of temperature

The mean time between collisions is temperature dependent

Kinetic-Molecular-Theory Gas Properties - Collision Parameters
@ 25 oC and 1 atm
Collision diameter

Mean
free path

Collision
Frequency

Collision
Rate

Species
d / 10-10 m d / Å
H2
He
N2
O2
Ar
CO2
HI

2.73
2.18
3.74
3.57
3.62
4.56
5.56

2.73
2.18
3.74
3.57
3.62
4.56
5.56

 / 10-8 m ZI / 109 s-1

ZII / 1034 m-3 s-1

12.4
19.1
6.56
7.16
6.99
4.41
2.96

17.6
8.1
8.9
7.6
7.0
10.6
10.6

14.3
6.6
7.2
6.2
5.7
8.6
7.5