Unimolecular reactions Lindemann mechanism

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... 

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 ... 

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. 

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... 

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... 

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 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... 

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. 

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. 

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... 

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

The Lindemann mechanism for thermally activated unimolecular reactions is a simple example of a particular class of compound reaction mechanisms They are mechanisms whose constituent reactions individually follow first-order rate laws [JT, 20, 36,48,40, 5f, 52, 53, 54, 55 and 56] ... 

As an example we take again the Lindemann mechanism of unimolecular reactions. The system of differential equations is given by equation (A3.4.127). equation (A3.4.128) and equation (A3 A. 1291. The rate coefficient matrix is... 

When it is necessary for a reaction to proceed through several successive elementary steps before the product is formed, the rate of the reaction is determined by the rates of all these steps. If one of these reactions is much slower than any of the others, then the rate will depend on the rate of this single slowest step. The slow step is the rate-determining step. The situation is analogous to water flowing through a series of pipes of different diameters. The rate of delivery of the water will depend on the rate at which it can pass through the narrowest pipe. An apt illustration of this feature of consecutive reactions is offered by the Lindemann mechanism of activation for unimolecular decompositions. 

Collision theory does not deal directly with unimolecular reactions but touches on the subject through the Lindemann mechanism. Once the molecule has been provided with sufficient energy by collision, the problem is to calculate the rate constant for the unimolecular decomposition,... 

Our basic understanding of unimolecular reactions can be traced to Lindemann (1922), who proposed that reacting molecules in a thermal system are energized by collisions and that the mechanism for the reaction can be expressed as... 

The Lindemann mechanism consists of three reaction steps. Reactions (1.4) and (1.5) are bimolecular reactions so that the true unimolecular step is reaction (1.6). Because the system described by Eqs. (1.4)-(l. 6) is at some equilibrium temperature, the high-pressure unimolecular rate constant is the canonical k T). This can be derived by transition state theory in terms of partition functions. However, in order to illustrate the connection between microcanonical and canonical systems, we consider here the case of k(E) and use Eq.(1.3) to convert to k(T). 

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 ... 

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