Frequency of collisions of gas molecules formula 1
Answers
Explanation:
the collision theory of reaction rates, concentrating on the key factors that determine whether a particular collision will result in a reaction—in particular, the energy of the collision, and the orientation of the collision. Reactions in which a single species falls apart are simpler because the orientation of the molecule is unimportant. Reactions involving collisions between more than two species are extremely uncommon.
According to Kinetic Molecular Theory, the collision frequency is equal to the root-mean-square velocity of the molecules divided by their mean free path.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
a
a
ν
=
v
rms
λ
a
a
∣
∣
∣
−−−−−−−−−−−−−
Root-mean-square velocity
The formula relating the rms velocity to the temperature and molar mass is:
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
a
a
v
rms
=
√
3
R
T
M
a
a
∣
∣
∣
−−−−−−−−−−−−−−−−−−
where
R
= the Universal Gas Constant
T
= the temperature
M
= the molar mass
For
H
2
at 24 °C,
T
=
(24 + 273.15) K
=
297.15 K
M
=
2.016 g⋅mol
-1
=
2.016
×
10
-3
l
kg⋅mol
-1
v
rms
=
√
3
R
T
M
=
⎷
3
×
8.314
J⋅K
-1
mol
-1
×
297.15
K
2.016
×
10
-3
kg⋅mol
-1
×
1
kg
⋅
m
2
s
-2
1
J
=
=
1917 m⋅s
-1
The mean free path
If the molecules have diameter d, then we can use a circle of diameter
σ
=
2
d
to represent a molecule's effective collision area.
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For a hydrogen molecule,
σ
=
289 pm
.
The formula for the mean free path is
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
a
a
λ
=
R
T
√
2
π
σ
2
N
A
P
a
a
∣
∣
∣
−−−−−−−−−−−−−−−−−−−−
R
=
0
.083 14 bar⋅L⋅K
-1
mol
-1
=
8.314
×
10
-5
l
bar⋅m
3
⋅
K
-1
mol
-1
T
=
297.15 K
σ
=
289 pm
=
289
×
10
-12
l
m
N
A
=
6.022
×
10
23
l
mol
-1
P
=
2.00 bar
λ
=
R
T
√
2
π
σ
2
N
A
P
=
8.314
×
10
-5
bar
⋅
m
m
3
⋅
K
-1
mol
-1
×
297.15
K
√
2
π
×
(
289
×
10
-12
m
)
2
×
6.022
×
10
23
mol
-1
×
2.00
bar
=
5.52
×
10
-8
l
m
=
55.2 nm
Collision frequency
ν
=
v
rms
λ
=
1917
m
⋅
s
-1
5.52
×
10
-8
m
=
3.46
×
10
10
l
s
-1