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

4.10 References 94
5. Collision theory
So far, we have considered more or less complex chemical reactions following more or
less complicated rate laws, but we have only considered the rate coefficients appearing
in the rate laws as empirical quantities, which had to be determined experimentally.
We shall now ask the question, whether we can rationalize and predict those rate coefficients
using theoretical models. Towards these ends, we have to look at the reactions
at a microscopic, molecular level. In particular, we have to
• consider the relation between the microscopic (individual molecule) properties and
the macroscopic (thermally averaged) rate quantities (rate constants, product
branching ratios)
• develop models for the microscopic (molecular level) progress of individual elementary
reactions, including the different molecular degrees of freedom (quantum
states).
• develop sufficiently simplified models averaging over the molecular degrees of
freedom which still allow us to make practically useful, relevant, and sufficiently
accurate predictions.
We shall do so in the next four chapters.
I Collision theory: To begin with, this chapter considers bimolecular reactions in the
gas phase. These obviously require a collision between two molecules as condition for a
reaction to take place.
• We start with the hard sphere collision model of structureless particles as the
simplest model for bimolecular reactions. Although this model has two major
flaws, it leads to the right result because of a compensation of errors.
• We then consider results of kinetic gas theory, which allow us to properly take
into account the molecular speed distributions.
• We apply the hard sphere collision model to understand transport processes in the
gas phase (diffusion, heat conductivity, viscosity).
• We then proceed with a correct derivation of advanced collision theory models
starting from differential cross sections (which can be measured in crossed molecular
beam experiments). Advanced collision theory is the method of choice for fast
gas phase reactions which can be studied in detail by molecular beam experiments
and handled by quantum theory.