Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

5.1 Hardspherecollisiontheory 98
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Mean free pathlength:
• The mean free pathlength is the distance that a molecule flies between two successive
collisions:
y
=
distance
# of collisions = distance/time
# of collisions/time =
(5.24)
=
1
2 ×
∝ 1
• Modification for collisions between identical molecules (A + A):
(5.25)
= 1 √
2
1
2 ×
(5.26)
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Time between two collisions:
1
=
1
2 ×
(5.27)
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Example 5.1: Collision frequency for O 2 -N 2 @ =298K= 1000 mbar:
Molecular parameters:
2 = 2 2 =3467 Å (5.28)
2 = 2 2 =3798 Å (5.29)
y =36 Å =36 × 10 −10 m (5.30)
= 2 =41Å 2 (5.31)
28 × 32
=
28 + 32 × 10−3 kg mol × 1
s
(5.32)
=
8
=650m s (5.33)
(but (O 2 )=444m s) (5.34)
Rate constant:
µ 12
max = 2 8
×
(5.35)
=26 × 10 −10 cm 3 s (5.36)
=16 × 10 14 cm 3 mol s (5.37)
Mean free pathlength:
=1000mbar (5.38)
=40 × 10 −5 mol cm 3 (5.39)
=25 × 10 25 m 3 (5.40)
=36 × 10 −10 m (5.41)
=1× 10 −7 m (5.42)