Lindemann unimolecular mechanism

The reason for our reservation in the definition of unimolecular reactions is now clear. Lindemann s mechanism would account for the independence over large ranges— and this corresponds to our experimental criterion of unimolecularity. Perrin seeks to extrapolate the experimental observations to infinite dilution, which may not be permissible. 

How thermal activation can take place following the Lindemann and the Lindemann-Hinshelwood mechanisms. An effective rate constant is found that shows the interplay between collision activation and unimolecular reaction. In the high-pressure limit, the effective rate constant approaches the microcanonical rate... 

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. 

Although the theory does need to be improved in a number of details before it can provide a quantitative description of experiment, the observation of fall-off from first order at high pressures to second order at low pressures is correctly explained by the Lindemann-Christiansen mechanism, and modem theories of unimolecular reactions are based on this mechanism. 

All theories of unimolecular readtions are based upon Lindemann s mechanism, according to which energization and activation occur in two distinct stages, viz. 

It has been seen (p. 92) that, on energetic grounds, a radical non-chain process may be excluded except in very special cases, and so no further consideration need be given to this mechanism. This leaves the decision to be made between the radical chain and the unimolecular mechanisms. There is, at the present time, no criterion which is both necessary and sufficient to prove that a given reaction is proceeding by a unimolecular mechanism. Necessary conditions for a unimolecular mechanism are (a) first-order kinetics at high pressures, (b) Lindemann fall-off at low pressures, (c) absence of induction periods, (d) lack of effect of inhibitors, and (e) an Arrhenius A factor of the order of 1013 sec-1. An additional useful test, though neither a necessary nor a sufficient condition, is the absence of stimulation of the reaction in the presence of atoms or radicals. Finally, the effects of structural alterations on the rates of those related reactions that are claimed to be unimolecular should be capable of interpretation within the framework of current chemical theory. 

Bimolecular steps involving identical species yield correspondingly simpler expressions. A3.4.8.2 THE LINDEMANN-HINSHELWOOD MECHANISM FOR UNIMOLECULAR REACTIONS... 

Figure A3.4.9. Pressure dependence of the effective unimolecular rate constant. Schematic fall-off curve for the Lindemann-Hinshelwood mechanism. A is the (constant) high-pressure limit of the effective rate constant...

A more detailed analysis of the radical mechanisms has been presented . Generally, all three processes show first-order kinetics but Ej reactions do not exhibit an induction period and are unaffected by radical inhibitors such as nitric oxide, propene, cyclohexene or toluene. For the non-chain mechanism, the activation energy should be equivalent to the homolytic bond dissociation energy of the C-X bond and within experimental error this requirement is satisfied for the thermolysis of allyl bromide For the chain mechanism, a lower activation energy is postulated, hence its more frequent occurrence, as the observed rate coefficient is now a function of the rate coefficients for the individual steps. Most alkyl halides react by a mixture of chain and E, mechanisms, but the former can be suppressed by increasing the addition of an inhibitor until a constant rate is observed. Under these conditions a mass of reliable reproducible data has been compiled for Ej processes. Necessary conditions for this unimolecular mechanism are (a) first-order kinetics at high pressures, (b) Lindemann fall-off at low pressures, (c) the absence of induction periods and the lack of effect of inhibitors and d) the absence of stimulation of the reaction in the presence of atoms or radicals. 

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 system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... 

This approxunation is generally valid if For the Lindemann mechanism of unimolecular reactions... 

Lindemann Mechanism of unimolecular reactions — activation by collisions... 

If the stoichiometric equation for unimolecular reaction is A -> B + C, and if the energized molecules are denoted by A, the Lindemann mechanism consists of the following sequence of events. 

Thus, according to this (Lindemann) mechanism, a unimolecular reaction is first-order at relatively high concentration (cM) and second-order at low concentration. There is a... 

As carried out above for the Lindemann mechanism, application of the steady-state approximation gives the apparent unimolecular rate constant in Equation (24) where [Av] represents the IR photon density. Again two limits may be considered. 

The isomerization of cyclopropane follows the Lindemann mechanism and is found to be unimolecular. The rate constant at high pressure is 1.5 x 10- s- and that at low pressure is 6 X 10- torr- s-K The pressure of cyclopropane at which the reaction changes its order, found out ... 

The following Lindemann mechanism for the unimolecular decomposition of a molecule A in the presence of a species Y (which may be any molecule such as inert gas like Helium or even A itself)y considered ... 

Pressure effects are also seen in a class of bimolecular reactions known as chemical activation reactions, which were introduced in Section 9.5. The treatment in that chapter was analogous to the Lindemann treatment of unimolecular reactions. The formulas derived in Section 9.5 provide a qualitative explanation of chemical activation reactions, and give the proper high- and low-pressure limits. However, that simple treatment neglected many quantum mechanical effects, namely the energy dependence of various excitation/de-excitation steps. 

Use the following data for a unimolecular decomposition to determine k and k2 which appear in the simple Lindemann mechanism assume that k has a value of 5.0 x 1010 mol 1 dm3 s From this determine the mean lifetime of the activated molecule. Comment on the results. 

In his pioneering work, Lindemann realized that an unimolecular reaction is not a single elementary step but must involve a mechanism in which molecules are energized at a sufficiently high level to undergo reaction. A simple Lindemann scheme leads to the relationship... 

Rabinovitch and co-workers found that the Lindemann mechanism is adequate for modeling the pressure dependence of bimolecular region unimolecular rate constants for extracting collision efficiencies for the methyl isocyanide isomerization [122]. For the conformer conversion of molecule A at constant temperature, it can be written as,... 

The simplest type of system that obeys equation (17) is the unimolecular process 95li products. Since a stable molecule should not spontaneously break up into reaction products, the mechanism by which the unimolecular process occurs must be explained. Many unimolecular reactions are believed to follow the mechanism proposed by Lindemann, namely. 

Conditions necessary for neglecting dc i/dt in the manner employed above may be investigated through formal approximations in reaction-rate theory. This will be considered further, with application to the Lindemann mechanism, in Section B.2.5. The mechanism itself generally contains fundamental inaccuracies and is best viewed as a simplified approximation to more-complex mechanisms. In particular, molecules capable of experiencing unimolecular decomposition or isomerization may exist in many different vibrationally excited states, and the rate constant for the reaction may differ in each state. Approximate means for summing over states to obtain average rate constants have been developed an introduction to these considerations maybe found in [3]. 

The Lindemann mechanism for unimolecular reactions, discussed in Section B.2.2, provides a convenient vehicle for illustrating partial-equilibrium approximations and for comparing them with steady-state approximations, even though this mechanism is not a chain reaction. To use the partial-equilibrium approximation for the two-body production of SRJ, select for example, as the species whose concentration is to be determined by partial equilibrium and use... 

Radical decompositions are unimolecular reactions and show complex temperature and pressure dependence. Section 2.4.l(i) introduces the framework (the Lindemann mechanism) with which unimolecular reactions can be understood. Models of unimolecular reactions are vital to provide rate data under conditions where no experimental data exist and also to interpret and compare experimental results. We briefly examine one empirical method of modelling unimolecular reactions which is based on the Lindemann mechanism. We shall return to more detailed models which provide more physically realistic parameters (but may be unrealistically large for incorporation into combustion models) in Section 2.4.3. 

Figure 2.13 is a sketch of the pressure dependence of a unimolecular reaction showing the two limiting conditions. The region joining the two extremes is known as the fall off region. Theories of unimolecular reactions have advanced considerably since Lindemann s initial proposal but they are still based on the same physical ideas so clearly highlighted in the Lindemann mechanism. 

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)... 

Summary.—The mechanism of the activation process in gaseous systems has been investigated from the point of view of (1) activation by radiation (2) activation by collision. An increase in the radiation density of possible activating frequencies has resulted in no increased reaction velocity. The study of the bimolecular decomposition of nitrous oxide at low pressures has led to the conclusion that the reaction is entirely heterogeneous at these pressures. A study of the unimolecular decomposition of nitrogen pentoxide between pressures of 7io mm. Hg and 2 X 10 3 mm. Hg shows no alteration in the rate of reaction such as was found by Hirst and Rideal but follows exactly the rate determined by Daniels and Johnson at high pressures. No diminution of the reaction velocity as might be ex-expected from Lindemann s theory was observed. 

If we further take fe = 0 this becomes the Lindemann mechanism that is used to explain the observation that many gas-phase reactions of the type A product that appear unimolecular at high pressure change their character to bimolecular at low pressure. Lindemann has postulated that such unimolecular reactions proceed... 

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