Kinetic Considerations Collision Theory

Elementary reactions occnrring in the gas phase have been fruitfully discussed in terms derived from the Kinetic-Molecular Theory of Gases. The result is Equation 1.9, 

---

The science of reaction kinetics between molecular species in a homogeneous gas phase was one of the earliest fields to be developed, and a quantitative calculation of the rates of chemical reactions was considerably advanced by the development of the collision theory of gases. According to this approach the rate at which the classic reaction... 

Although the transition state theory has advantages over collision theories in its generality, avoiding detailed consideration of kinetic mechanism by appeal to thermodynamic principles, it rests upon eqiially weak experimental foundations. However, its flexibility permits applications to reactions in the liquid phase where the gas kinetic model breaks down. In such applications the entropy factor is all-important and may range roughly from 10" to 10+ . 

Collision theory, which only suffices for simple gas reactions, essentially views reactants as if they were particles with a certain kinetic energy. Matter dynamic considerations play no role here. In the following, we will get to know a more comprehensive theory that can, in principle, be applied to every possible type of reaction. 

The simple collision theory and the activated complex theory have appeared as two alternative treatments of chemical reaction kinetics. It is clear, however, that they represent only two different kinds of approximation to an exact collision theory based either on classical or quantum mechanics. During the past few years considerable progress has been achieved in the colllsional treatment of bimole-cular reactions /7,8/. For more complicated reactions, however, the collision theory yields untractable expressions so that the activated complex theory provides a unique general method for an estimation of the rates of these reactions. Therefore, it is very important to determine well the limits of its validity. 

The condition (75.Ill) for a reactive collision is well known from the simple kinetic collision theory in which it is postulated without any justification. It is evident only in the special case of a completely separable reaction coordinate in which the motion along it does not influence the non-reactive modes. In general, however, the condition (75 111) requires a justification which is given by the above considerations based on the classical mechanics of non-adiabatic processes. 

A treatment of the kinetic isotope effects from the point of view of an accurate collision theory, including its statistical formulation, was recently done by CHRISTOV and PARLAPANSKI /132/. The present and more detailed discussion is an extension of this consideration with particular emphasis on the condJ.tions at which the isotope effects can be related to the quantum effects, such as non-adia-batic changes of the electronic state, quantization of the vibrational-rotational energy, and nuclear tunneling. 

All above conclusions are involved as special cases in the general consequences of the collision theory rate equation (51j III) derived in Sec.7.III. The corresponding consequences from the statistical formulation (67.Ill) of the reaction rate theory were also discussed there. The current interpretations of kinetic isotope effects are based on transition state theory. The correction for proton tunneling is first taken into consideration by BELL et al./155/. More extensive work in this direction has been carried out by CALDIN et al. /I53/. In this treatment estimations of the tunneling correction are made using one-dimensional (parabolic) barrier by neglecting the coupling of the proton motion with other motions of reactants or solvent. 

The concept that a gas comprises a large number of distinct particles between which - aside from the collisions - there are no effective forces, has led to a number of theoretical considerations which we summarize today under the designation kinetic theory of gases". 

Processes in which two atoms combine to give a single molecule demand further consideration. No activation is required, but another condition has to be fulfilled, as Herzfeld j- and Polanyi J have pointed out. When two atoms collide, the nascent molecule which is formed contains all the energy of formation, and this, moreover, must be exactly quantized. Unless therefore its energy can be adjusted by a collision with a third molecule or with the wall of the vessel it will be incapable of continued existence and will fall apart again. This view about the necessity of collision with a third molecule is often referred to as the Dreierstoss theory. Reactions of the type A + BC = AC + B are not affected by these considerations, since the kinetic energy with which the two products of the reaction fly apart adjusts itself in accordance with the quantum demands of the molecule AB. 

As the fundamental concepts of chemical kinetics developed, there was a strong interest in studying chemical reactions in the gas phase. At low pressures the reacting molecules in a gaseous solution are far from one another, and the theoretical description of equilibrium thermodynamic properties was well developed. Thus, the kinetic theory of gases and collision processes was applied first to construct a model for chemical reaction kinetics. This was followed by transition state theory and a more detailed understanding of elementary reactions on the basis of quantum mechanics. Eventually, these concepts were applied to reactions in liquid solutions with consideration of the role of the non-reacting medium, that is, the solvent. 

Process licensors have tried to supplant this overall assessment by a finer analysis of the severity of operation of a pyrolysis furnace operating on a complex feed. Among the values thus determined are the MCP (Molecular Collision Parameter) for the treat ment of naphthas, based on considerations stemming from the kinetic theory of gases and developed by Wall and Witt of the Selas Corporation, and especially the KSF (Kinetic Severity Function) proposed by Zdonik et al of Stone ami Webster Engineering. 

Before closing this section, we should remark that although this analysis of velocity relaxation effects has focused on a simple collision model, we expect that the detailed structure of the rate kernel for short times will depend on the precise form of the chemical interactions in the system under consideration. It is clear, however, that a number of fundamental questions need to be answered before more specific calculations can be undertaken form the kinetic theory point of view. 

---