Unimolecular reactions Hinshelwood theory

We have calculated the addition channel rate constant using the RRKM approach to unimolecular reaction rate theory, as formulated by Troe ( ) to match RRKM results with a simpler computational approach. The pressure dependence of the addition reaction (1) can be simply decribed by a Lindemann-Hinshelwood mechanism, written most conveniently in the direction of decomposition of the stable adduct ... 

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. 

Derive an expression for the decomposition rate constant kd (e ) for the Hinshelwood theory of unimolecular reactions. 

The development of a theory of unimolecular reactions proceeded rapidly in the mid-1920s, initiated by Hinshelwood with an A whose collision-free lifetime for reaction was approximated by an energy-independent one. The analysis was much elaborated by Rice and Ramsperger [60] and Kassel [61], known later as the RRK theory, where now the lifetime was, as it is in modern times, energy-dependent [62]. These theoretical works of the 1920s stimulated many measurements of the unimolecular rates of dissociation of organic compounds as a function of the gas pressure. Within a few years, however, this entire field collapsed or, more precisely, evolved into a new field It was shown experimentally that the unimolecular reactions , assumed originally to consist of only one chemical step, in-... 

Note The Lindemann mechanism was also suggested independently by Christiansen. Hence, it is also sometimes referred to as the Lindemann-Christiansen mechanism. The theory of unimolecular reactions was further developed by Hinshelwood and refined by Rice, Rampsberger, Kassel and Marcus. 

The important questions in the study of unimolecular reactions are (a) what is the initial state produced in the excitation step, (b) how fast does the system evolve toward products, (c) what are the reaction products, and (d) what are the product energy states Up until about 1975, the first and last questions could not be addressed experimentally. Most experiments were carried out with the reacting system specified in terms of a temperature with its attendant distribution of initial states. From the very beginning, it was recognized that a dissociation rate depends on the internal energy of the molecule (Hinshelwood, 1926). Thus, all detailed statistical theories of unimolecular reactions begin with the calculation of k(E), the rate constant as a function of the infernal energy, E. 

The first microscopic theory of unimolecular reactions was developed by Hinshelwood [4], who used a rather simple molecular model. His assumptions were as follows ... 

Several theories have been developed for the unimolecular reactions. The earliest, proposed by KASSEL, HINSHELWOOD, RICE, and RAMSPERGER /136/, as well as the later theory of SLATER /137/, are based on classical models. The most recent and important theory of MARCUS ans RICE /138/ rests on the semiclassical activated complex theory which makes use of potential energy surfaces. 

The LINDEMANN-HINSHELWOOD theory for unimolecular reactions is based on the following mechanism ... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next 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 ... 

If this Lindemann-Hinshelwood hypothesis is correct, unimolecular gas reactions should be first order at high pressures and should become second order at low pressures. This behavior has now been confirmed for a large number of reactions. In its original form the hypothesis had some difficulty in interpreting results quantitatively, but a number of extensions of the original hypothesis have been made, notably by R. A. Marcus whose treatment is consistent with transition-state theory. 

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