Hinshelwood Refinement

It is assumed that for all pressure dki/k.i represents the equilibrium probability and that the A has the energy between E and E + dE. This probability may be denoted P(E)dE. Also, k.j [M] is the collision frequency co between A and M, then 

In order to make accurate quantitative predictions of the fall-off behaviour of a unimolecular reaction it is essential to take into account the energy dependence of the rate constant k(E) for the conversion of energized molecules into activated complexes where products results from decomposition or reaction of the energized complex. 

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Note The Lindemann mechanism was also suggested independently by Christiansen. Hence, it is also sometimes referred to as the Lindemann-Christiansen mechanism. The theory of unimolecular reactions was further developed by Hinshelwood and refined by Rice, Rampsberger, Kassel and Marcus. 

Wicke et al. [3] were the first to apply a MC simulation to a catalytic reaction based on the Langmuir-Hinshelwood mechanism. They studied the importance of the formation of clusters of adsorbed molecules on a catalyst surface. Many microscopic mathematical models of heterogeneous catalytic systems have been developed since then. However, the time dependence of the reactions in real time could not be followed. Recently more refined MC methods have been developed, so that with these new dynamic Monte Carlo (DMC) methods, the behavior of catalytic systems in real time can be simulated. 

The results from this chapter on zeolite catalysis provide a good reference point for the discussion presented later Chapter 8 where we compare heterogeneous catalysis and biocatalysis. The similarity between the Michaelis-Menten kinetic expression for enzyme catalysis and the Langmuir-Hinshelwood kinetic models for heterogeneous catalysis are noted. This ultimately derives from the conservation in the number of active reaction centers for both systems. However, the more refined synergy of the activation of molecular bonds by the enzyme will become apparent as a major difference between the two. 

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