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

5.1 Hardspherecollisiontheory 97
— number density of B
(5.15)
— Number of collisions of a single A in time : ⇒ number of molecules B in
that volume
= 2 × × (5.16)
• Number of all collisions between A and B:
= 2 × × (5.17)
• Modification for collisions between identical molecules (collisions must not be
counted twice):
= 1 2 × 2 × × (5.18)
=
√
2
2 × 2 × × (5.19)
• Comparison with rate expression:
y
−
= −
= × = (5.20)
• Expression for rate constant for collisions A + B:
max = 2 × = × (5.21)
y
µ 12
max = 2 8
×
(5.22)
• Modification for collisions between identical molecules (A + A):
max = 1 2 2 × = √ 1 µ 12
2 8
×
(5.23)
2
Theseexpressionsgivetheupper limits for the rate constants of bimolecular
reactions. The upper limits are reached only if
• there are no energetic restrictions (no energy barriers),
• all collisions lead to reaction (no steric constraints),
• molecules can be approximated as hard spheres (unrealistic, usually one has
),
• all molecules collide with the same relative speed (in reality there is a distribution
of speeds).