Kinetics of Reactive Processes

In the discussion of macroscopic kinetic equations for chemical reactions in Sections I.l and 1.2 it was not considered to what extent do these reactions perturb equilibrium distributions over states of reacting molecules, i.e. to what extent they are non-equilibrium reactions. The solution to this problem can be found solely from microscopic kinetic equations. 

Microscopic kinetic equations for non-equilibrium reactions are derived in the same way as are the relaxation equations, i.e. in terms of fluxes incoming to and outgoing from a particular quantum state. Transitions in reactive collisions have to be added to those in unreactive collisions. This yields a system of equations describing both the approach to chemical equilibrium and the relaxation over energy states of molecules. For simplification, consider the initial reaction stages neglecting reverse reactions. 

The rate of change in the distribution function for unreactive collisions is given by Eq. (8.28). For reactive collisions let it be (dai/dt)peact Then, the overall rate of change in population 

For iinimolecular reactions it is usually assumed that molecule A with energy E higher than a certain threshold Eq is converted spontaneously to products. The microscopic rate constant of this conversion from internal state i is denoted as k. Then 

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