A + B
→
Product
E
a
Rate = (# of collisions per second) X (# of collisions having E > E
a
)
Z
AB
∝
c and density
exp(-E
a
/RT)
2
2
mv
Rate Depends on Collision Frequency (Z
AB
)
and Boltzmann Factor (e
-Ea/RT
)
M
RT
c
π
8
=
P
2
2
2
2
z
y
x
v
v
v
v
c
+
+
=
=

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Collision Frequency (Z
1
)
For one molecule:
Volume of cylinder:
(
)
(
)
t
c
d
2
π
Z
1
=
Volume of cylinder
X
density of molecules
time
Number density:
⎟
⎠
⎞
⎜
⎝
⎛
V
N
collisions s
-1
⎟
⎠
⎞
⎜
⎝
⎛
≈
V
N
c
d
Z
2
1
π
~10
9
Collisions by a single molecule in one second.
1
9
1
3
19
4
2
8
1
10
5
)
10
5
.
2
)(
/
10
5
(
)
10
4
(
−
−
−
×
≈
×
×
×
=
s
Z
cm
s
cm
cm
Z
π
area
x
length
at 298 K