Lindemann theory reactions

Rice and Ramsperger and independently Kassel proposed the theories to explain unimolecular reaction, in which both (k2) and (kfk[) have been treated as dependent on the energy of an individual energized molecule E. These theories jointly are referred as RRK theory. According to the theory the expression for the first order rate constant given by Lindemann theory i.e. 

We continue our study of chemical kinetics with a presentation of reaction mechanisms. As time permits, we complete this section of the course with a presentation of one or more of the topics Lindemann theory, free radical chain mechanism, enzyme kinetics, or surface chemistry. The study of chemical kinetics is unlike both thermodynamics and quantum mechanics in that the overarching goal is not to produce a formal mathematical structure. Instead, techniques are developed to help design, analyze, and interpret experiments and then to connect experimental results to the proposed mechanism. We devote the balance of the semester to a traditional treatment of classical thermodynamics. In Appendix 2 the reader will find a general outline of the course in place of further detailed descriptions. 

The theoretical analysis of chemical activation reactions is similar to the Lindemann theory of unimolecular and association reactions. There are a number of competing reaction pathways. Depending on total pressure, concentrations of the participating species, and temperature, the outcome of the competition can change. 

The treatment given in this section is analogous to the Lindemann theory of unimolecu-lar reactions. It provides a general explanation of pressure effects in bimolecular chemical activation reactions. A more sound theoretical treatment of chemical activation kinetics is given in Section 10.5. 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

The Lindemann theory thus has the correct behavior at the high- and low-pressure limits. However, quantitative comparisons between this theory and experiment revealed a number of problems. The remainder of this section discusses more detailed theoretical treatments of unimolecular reaction kinetics. 

The Hinshelwood model thus corrects one of the major deficiencies in the Lindemann theory of unimolecular reactions. The greater excitation rate constant of Eq. 10.132 brings the predicted fall-off concentration [M]j/2 of Eq. 10.109 into much better accord with experiment. However, because of the many simplifying assumptions invoked in the Hinshelwood model, there are still a number of shortcomings. 

The facts that have just been described lend considerable support to the Lindemann theory. If this theory is to be applicable, the rate of activation and deactivation at higher pressures ought to be great compared with the rate of chemical change, in order that there may be little disturbance of the statistical equilibrium and hence an absolute rate of reaction directly proportional to the total concentration. At first some difficulty was felt about this point, but the solution appears to have been found, and indeed the solution itself constitutes a rather strong piece of evidence in favour of the theory. 

Although the Lindemann theory is often satisfactory, it is incomplete since it does not fully recognise the relation between translational and internal energies. In many reactions the rate of activation by collision is not itself explicable unless it is assumed that activation can also occur by the transfer of vibrational energy from one molecule to another. This possibility was recognised by Hinshelwood and by Lewis and may be equivalent, in effect, to multiplying the frequency factor by 10" or more. 

M is Br2 or any other gas that is present. By the principle of microscopic reversibility , the reverse processes are also pressure-dependent. A related pressure effect occurs in unimolecular decompositions which are in their pressure-dependent regions (including unimolecular initiation processes in free radical reactions). According to the simple Lindemann theory the mechanism for the unimolecular decomposition of a species A is given by the following scheme (for more detailed theories see ref. 47b, p.283)... 

Demonstrate the application of the Lindemann theory to an isomerization reaction A <-> B under conditions that might be encountered in practice. 

One can expect the Lindemann theory to predict a linear change in the initial rate of a unimolecular reaction with respect to concentration of M at low pressure. The transition from high-pressure rate constant to low-pressure is called fall off region . 

The initiation step has been written as a nnimolecular reaction. In terms of the Lindemann theory presented in Section 4.3.1.3, this initiation reaction will shift to a bimolecular process at low pressures. 

Taking into account the activation and deactivation processes and using the Lindemann theory, the mechanism of a bimolecular reaction X + Y products can be represented by a simplified scheme [167] involving active species of one kind only... 

Lindemann F A 1922 Discussion on the radiation theory of chemical reactions Trans. Faraday Soo. 17 598-9... 

Collisions play a tremendously important role in stimulating reacting systems to cross the activation barrier. The theory of Lindemann emphasizes this and provides us with a method to describe the influence of the surrounding medium upon a chemical reaction. It gives important insight into the conditions under which the reaction rate theories discussed here are valid. 

In most chemical reactions the rates are dominated by collisions of two species that may have the capability to react. Thus, most simple reactions are second-order. Other reactions are dominated by a loose bond-breaking step and thus are first-order. Most of these latter type reactions fall in the class of decomposition processes. Isomerization reactions are also found to be first-order. According to Lindemann s theory [1, 4] of first-order processes, first-order reactions occur as a result of a two-step process. This point will be discussed in a subsequent section. 

Of course, in a thermal reaction, molecules of the reactant do not all have the same energy, and so application of RRKM theory to the evaluation of the overall unimolecular rate constant, k m, requires that one specify the distribution of energies. This distribution is usually derived from the Lindemann-Hinshelwood model, in which molecules A become activated to vibrationally and rotationally excited states A by collision with some other molecules in the system, M. In this picture, collisions between M and A are assumed to transfer energy in the other direction, that is, returning A to A ... 

The theory of Lindemann explains most of the trends observed in the kinetics of uni-molecular reactions. It has been very useful in understanding the qualitative behavior of this class of reactions. It provides the starting point for all modem theories of unimolecu-lar reactions. The theoretical basis for unimolecular reaction rates is treated in much more detail in Chapter 10. 

The Lindemann treatment for association reactions is analogous to the theory just given for unimolecular reactions. For convenience, rewrite reactions 9.100 and 9.101 in the reverse directions... 

This reaction also involves the elimination of carbon monoxide and the formation of a mixture of hydrocarbons, principally ethane and methane. It is homogeneous and conveniently measurable between 450° and 600° C. The decomposition is kinetically unimolecular over a considerable range of pressure, but at pressures below about 80 mm. Hg the velocity constant falls appreciably, in the manner which would be expected if Lindemann s theory were correct. In the region of pressure where the reaction is unimolecular the velocity constants (sec-1) are given by... 

Perrin s argument that the very nature of a unimolecular reaction demands independence of collisions, and therefore dependence on radiation, is adequately met both by the theory of Lindemann and by that of Christiansen and Kramers. Both these theories have the essential element in common that the distribution of energy among the molecules is not appreciably disturbed by the chemical transformation of the activated molecules thus the rate of reaction is proportional simply to the number of activated molecules and therefore to the total number of molecules, sinc in statistical equilibrium the activated molecules are a constant fraction of the whole. Thus the radiation theory is not necessary to explain the existence of reactions which are unimolecular over a wide range of pressures. 

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