Collision theory reaction rate description

An understanding of the nature of chemical reactions requires the details of the elementary-reaction steps in which, the molecules come together, rearrange, and leave as species that differ from the reactants. There are two descriptions that deal with the rates of chemical reactions. The collision theory considers the concept that the reaction of molecules can occur only as a result of collision of the reactant molecules. The transition-state theory focuses on the species that corresponds to the maximum-energy stage in the reaction process. This species is called the activated complex or transition state. The transition state, denoted by the symbol A for reaction (1), is a short-lived species, which is converted to C. The reader is referred to [1-10] for a thorough discussion of the energetics involved in chemical reactions. 

Consider a reaction between molecules A and B. The rate expression for molecules that are essentially billiard balls, or hard spheres, will be discussed first. Later studied will be features due to the presence of internal degrees of freedom, which are absent in hard spheres. The description of reaction rates in terms of the kinetic theory of collisions was given by Max Trautz in 1916 and William Lewis in 1918. The rate for collisions between hard spheres is... 

The theory of propagation of flames and detonations is based on the hydrod5mamic equations of change. These equations represent the overall conservation of momentum and energy in molecular collisions and the rate of change of molecular species due to chemical reactions and diffusion. In this way, we obtain the most general description of nonequilibrium processes in fluids. 

There are three stages to any detailed dynamical theory of rate processes.First, the potential describing the molecular interaction is calculated or estimated. Secondly, the equations of motion are solved for individual, fully specified, collisions. Finally, the results of calculations on single collisions must be correctly averaged to yield the required result for example, a reaction cross section or a detailed rate constant. Strictly, the dynamics of intermolecular collisions should be treated quantum mechanically, but the difficulties are formidable and accurate calculations have only been completed for the H + H2 reaction However, there is now a good deal of evidence that quasiclassicalj (QCL) trajectories provide a sufficiently accurate description of reactive collision dynamics for many purposes. 

In spite of the difference in the underlying concepts and the forms of equations, Eqs. (3.3) and (3.4), both descriptions reflect the statistical sense of the rate constant. The latter statement is crucially important for better understanding of the problem existing in heterogeneous kinetics. Indeed, the above-mentioned theories are based on gas statistics and the given equations assume an equilibrium Maxwell-Boltzman distribution for gas species, which in the absence of reaction interact only via elastic collisions. If this can be considered as a satisfactory approximation for gas reactions at moderate temperatures and pressures discussed here (with some exceptions—see Section III.D), its applicability to the processes involving surface sites (i.e., elements of solid lattice) or adsorbed species is not so obvious. 

Marcus12 and others13 extended this model to include reactions in which electron transfer occurred during collisions between the donor and acceptor species, that is, between the short-lived Dn—Am complexes. In this context, electron transfer within transient precursor complexes ([Dn — A" in Scheme 1.1) resulted in the formation of short-lived successor complexes ([D(, + — A(m 1)] in Scheme 1.1). The Debye-Smoluchowski description of the diffusion-controlled collision frequency between D" and A " was retained. This has important implications for application of the Marcus model, particularly where—as is common in inorganic electron transfer reactions—charged donors or acceptors are involved. In these cases, use of the Marcus model to evaluate such reactions is only defensible if the collision rates between the reactants vary with ionic strength as required by the Debye-Smoluchowski model. The requirements of that model, and how electrolyte theory can be used to verify whether a reaction is a defensible candidate for evaluation using the Marcus model, are presented at the end of this section. 

Parameter Calculation and Establishment of Relationships. The use of molecular modeling tools not being evident for nonexperts in the field, alternative tools can be applied for the assessment of values for rate coefficients, preexponential factors, and/or activation energies (22). Collision rate theory provides a simple description of a kinetic process. It counts the number of collisions, Zab, between the reacting species A and B in a bimolecular reaction or between the reacting species and the surface in the case of an adsorption step and applies a reaction probability factor, Prxn, to account for the fact that not every collision leads to a chemical reaction. 

Equation 5 represents a good approximation for situations in which momentum relaxation takes place considerably faster than nonthermal reaction. The local equilibrium model becomes increasingly inadequate as these rates approach one another, so that the present form of the steady state theory will be least accurate for systems that involve very rapid reactions. Higher order Chapman-Enskog solutions of the Boltzmann equation, which provide successive degrees of refinement, could be incorporated into the theory. Such modifications would introduce additional mathematical structure in Eq. 5, which is probably not needed except for the description of systems that closely approach true steady state behavior. This does not occur for any of the cases of present Interest (vide infra) or. Indeed, for any known nuclear recoil reaction system. For this fundamental reason and also because of the crude level of approximation Involved in our treatment of nonreactive collisions, the further refinement of Eq, 3 has not yet been considered to be worthwhile. 

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