The Kinetic Theory of Gas III:
Drs. Jaslin Ikhsan, M.App.Sc., Ph.D.
Chemistry Ed. Department State University of Yogyakarta
ZI = collision frequency = number of collisions per molecule
ZII = collision rate = total number of collisions
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:
d
V N
a vg r ela tive
a vg
wher e
d
V
2
:
2
2Define: N* = N/V =
molecules per unit volume
*
2
*)
(
)
(
2N
v
d
Z
N
V
Z
a vg I I
M T R m T k va vg 8 8 2 2 8 : 8 A A r ela tive
B A B A B A
r ela tive
m m x RT v m m if m m m m wher e RT v
2 1 *
N Z
ZII I
Double Counting Factor
2 2
*)
(
2
1
N
v
d
Z
II
a vg
??? V
N
N*
Avo g Avo gAvo g
Avo g
N A kT
P
RT PN
V N so
A RT
P
V N
N
RT N
N PV
nRT PV
a vg
II
N
d
v
Z
(
*)
2
2
2
1
M
T
R
m
T
k
v
a vg
8
8
For A-B collisions: AB , AB
AB AB
r ela tive
B A
B A
AB
T
k
v
m
m
m
m
8
Velocity
Relative
M ass
Reduced
) (
2
B A
AB
d
d
d
V
N
N
A*
AV
N
N
B*
BCollision Diameter
2 / 1 2 2 ) (
8
*)
(
2
1
A A A AA IIm
kT
d
N
Z
2 / 1 2 ) ( ) ( 2 2 ) ( ) ( 2 ) (8
*
*
].
][
.[
)
(
*
*
AB AB B A AB II AB a vg AB Avo g AB II AB a vg AB B A AB IIkT
d
N
N
Z
v
d
B
A
N
Z
v
d
N
N
Z
kT
P
RT
PN
V
N
N
A
r emember
Avog
Avog
I a vg
Z
v
unit time
in
with
collides
it
molecules
no
unit time
per
traveled
distance
N
d
V
A
N
d
A
2 22
]
[
2
1
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
Species
Collision diameter Mean free path
Collision Frequency
Collision Rate
d / 10-10 m d / Å / 10-8 m ZI / 109 s-1 ZII / 1034 m-3 s-1
H2 2.73 2.73 12.4 14.3 17.6
He 2.18 2.18 19.1 6.6 8.1
N2 3.74 3.74 6.56 7.2 8.9
O2 3.57 3.57 7.16 6.2 7.6
Ar 3.62 3.62 6.99 5.7 7.0
CO2 4.56 4.56 4.41 8.6 10.6
