RRKM theory and the rate of unimolecular reactions

In this section we discuss the rate of formation and dissociation of energy-rich molecules. There are two key ingredients. One is transition state theory as discussed in Section 6.1. If there is a single barrier separating reactants and products, transition state theory allows us to compute the rate of the chemical reaction. But as discussed in Section 5.3.3, we are here interested in reactions where there is more than one barrier along the reaction coordinate. Between any two such barriers there must be a hollow in the potential. This may slow the passage. The second ingredient that we need stems from an examination of the nature of the complex dynamics over such potentials. 

Lindemann sought to explain why polyatomic molecules in die bulk gas phase dissociate by a unimolecrdar rate law, that is, seemingly spontaneously. The question was where the energy required for the bond breaking came from. In the simplest form we assume coUisional activation and deactivation of the energy-rich species A by molecules of the bath gas M, and a competing unimolecular dissociation of A  

This is an approximate description because it overlooks the - as we show, quite steep - energy dependence of the dissociation rate constant k. In Problem G it is 

If the molecule lives longer than the time between deactivating collisions, [M] ki, most of the collisionally activated molecules will also be deactivated by collisions. Then the concentration of energy-rich molecules and hence the rate of formation of products is independent of the pressure of the bath gas. 

This is known as the high pressure limit because the pressure is the measure of the concentration, [M], of the bath gas. In this limit the rate of dissociation is unimolecular. At low enough pressures, A [M] Aj, the rate of reaction is determined by the rate of activating collisions with an apparent rate constant, k M], that is proportional to the pressure. 

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