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

5.4 Advanced collision theory 115
5.4 Advanced collision theory
The hard sphere model is a very primitive model. In reality, we have to account for the
following:
• The reaction probability depends on exact details of the collision, i.e.,
hard sphere model → ( ) (5.127)
• Molecules are not hard spheres with = 2 but “soft”, i.e., the reactive cross
section depends on the relative speed (or kinetic energy)
→ () → ( ) (5.128)
• The speed distribution follows the Maxwell-Boltzmann distribution, i.e.,
→ () → ( ) (5.129)
• Molecules in different quantum states behave differently, i.e.,
→ ( ; ) (5.130)
I Examples: The complexity of the problem is illustrated in Fig. 5.12 by two examples:
D( )+H 2 ( 2 2 2 ) −→ HD( )+H( ) (5.131)
OH( Ω )+H 2 ( 2 2 2 )
→ H 2 O( 2 1 2 3 )+H( ) (5.132)
As can be seen, the reaction rate is expected to depend on (speed, translational
energy), (vibrational quantum numbers ( 1 = symmetric stretch, 2 = bend, 3 =
antisymmetric stretch)), (rotational quantum numbers), Ω (fine structure
state, electronic state). In addition, the products are scattered into the spatial angles
.
I
Figure 5.12: Quantum state-specific elementary reactions.