Chemical reaction rates, collision definitions

Hie chemical reaction rate is usually dependent on the molar concentrations of the reactants and not on their mass fractions, because it depends on the chance of collision of molecules. However, here the definition of in terms of mass fractions is preferred, because it can readily be incorporated into mass balances. A definition in terms of moles or molar concentrations might invite the use of mole balances instead of mass balances. Since, contrary to conservation of mass, there is no such thing as conservation of moles (because one molecule might divide into several molecules, or several might condense into one), the use of mole balances is strongly dissuaded. More information concerning the definition of conversion can be found elsewhere [2]. 

Our approach is very simple, but it has the virtue of providing exact general rate expressions which are closely related to the traditional formulations of both the collision and activated complex theory as given by equations (3A) and (5A), respectively. Thus, it directly yields precise definitions of both the quantum and classical (or semiclassical) corrections to be introduced in these equations, as well as in the properly adiabatic formulations of transition state theory also discussed in this book. We hope, therefore, that the unified treatment presented will contribute to a full elucidation of the relations between the various theories of chemical reaction rates. 

We define the reaction cross-section, ctr, in a way suggested by the definition of the total collision cross-section (Section 2.1.5). For molecules colliding with a well-defined relative velocity v, the reaction cross-section is defined such that the chemical reaction rate constant k v) is given by... 

A theoretical determination of the rate constant for a chemical reaction requires a calculation of the reaction cross-section based on the dynamics of the collision process between the reactant molecules. We shall develop a general relation, based on classical dynamics, between reaction probabilities that can be extracted from the dynamics of the collision process and the phenomenological reaction cross-section introduced in Chapter 2. That is, we give a recipe for how to calculate the reaction cross-section in accord with the general definition in Eq. (2.7). 

Some elementary chemical reactions follow a third order rate expression at all normally accessible experimental conditions, and according to the definitions of molecularity must be classified as termolecular. The most common example is the combination of two atoms in the presence of a third species. The rate expression is r = A ( J)[A] [M] for combination of Hke atoms. A, in the presence of the collider or heat bath species M. These reactions do not occur by the simultaneous collision of all three species, which is a very rare event, but by two bimolecular steps that take place within lpsec of one another. An energy transfer mechanism of the reaction may be written as follows ... 

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