Lindemann mechanism high pressure limit

How thermal activation can take place following the Lindemann and the Lindemann-Hinshelwood mechanisms. An effective rate constant is found that shows the interplay between collision activation and unimolecular reaction. In the high-pressure limit, the effective rate constant approaches the microcanonical rate... 

The same result is traditionally derived from the high-pressure limit of the Hinshelwood-Lindemann mechanism see Section 7.4.1. 

Figure A3.4.9. Pressure dependence of the effective unimolecular rate constant. Schematic fall-off curve for the Lindemann-Hinshelwood mechanism. A is the (constant) high-pressure limit of the effective rate constant...

Although it is rarely possible to study any particular unimolecular reaction all the way from the first order (high pressure) limit to the second order (low pressure) limit, many genuine unimolecular reactions have now been characterised over at least part of the fall-off region [72.R]. Thus, we can easily compare the observed shape of the fall-off curve, and its position on the pressure axis with the behaviour suggested by the Lindemann mechanism. 

The curve (a) in Fig. 2.9 is the schematic graph of the pressure dependence of a termolecular reaction rate constant according to the Lindemann mechanism. From the figure, it can be seen that the reaction rate constant is proportional to [M] (pressure) in the low-pressure limit, and gets nearly constant independent on the pressure in the high-pressure limit. The intermediate region between these two limits is called the fall-off region. 

Pressure effects are also seen in a class of bimolecular reactions known as chemical activation reactions, which were introduced in Section 9.5. The treatment in that chapter was analogous to the Lindemann treatment of unimolecular reactions. The formulas derived in Section 9.5 provide a qualitative explanation of chemical activation reactions, and give the proper high- and low-pressure limits. However, that simple treatment neglected many quantum mechanical effects, namely the energy dependence of various excitation/de-excitation steps. 

Pressure-dependent rate constants for the syn-anti conformational process in larger alkyl nitrites provide a further test of the ability of RRKM theory to successfully model the kinetics of the internal rotation process in these molecules. Solution of the Lindemann mechanism shows that at the pressure where the rate constant is one-half of its limiting high-pressure value, Pm, the frequency of deactivating collisions is comparable to , the average rate that critically... 

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