A + B
→
Product
E
a
Rate = (# of collisions per second) X (fraction collisions having E > E
a
)
exp(E
a
/RT)
Rate Depends on Collision Frequency (Z
11
)
and Boltzmann Factor (e
Ea/RT
)
P
Rate =
{ Z
11
(10
8
M s
1
)
}
X
{ exp(0/RT)
}
=
10
8
M/s
2
2
11
2
2
⎟
⎠
⎞
⎜
⎝
⎛
=
V
N
c
d
Z
π
If every collision produces product, then Rate = 10
8
M/s (upper limit).
Fastest reaction rate in solution is ~10
10
M/s for H
+
+ OH

→
H
2
O
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Kinetic Theory of Gases Summary
3. Molecular Binary Collision Frequency (Z
11
or Z
AB
) :
4. Rate of Gas Phase Reaction:
(
)
1
3
35
3
25
9
1
11
10
10
5
.
2
2
/
10
2
−
−
−
=
×
=
⎟
⎠
⎞
⎜
⎝
⎛
=
s
m
collisions
m
s
collisions
V
N
Z
Z
1
8
11
10
−
≈
s
M
Z
Rate = (# of collisions per second, Z
11
) X (exp(
E
a
/RT)
Fastest rate = Z
11
X exp(0/RT) = 10
8
M s
1
2. Average molecular speed (c) determined by Maxwell Distribution:
M
RT
c
rms
3
=
M
RT
c
mp
2
=
R = 8.314 J mol
1
K
1
T = Temp (K)
M = molar mass (kg/mol)
1 J = 1 kg m
2
s
2
⎟
⎠
⎞
⎜
⎝
⎛
=
V
N
d
c
Z
2
1
2
π
Mean free path (
λ
) = <c>/Z
1
= 640
Ǻ
M
RT
c
π
8
=
475 m/s
515 m/s
421 m/s
1. Molecular velocity and energy vs
Pressure, Volume and Temp:
3
2
v
Nm
PV
=
3
2
trans
E
N
PV
=
T
k
E
B
trans
2
3
=