Lindemann mechanism, pressure constants

Thus, the competition between deactivation of the intermediate A and product formation is given in terms of the ratio a = Id lk, . When the second-order rate constants k, k2, and ki are set for the system, the ratio a is directly proportional to the pressure [M], since a = ( 2/ 3)[M]. Thus, the effect of varying [M], the variable in the Lindemann mechanism that defines the pressure, can... 

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-dependent rate constants for the syn-anti conformational process in larger alkyl nitrites provide a further test of the ability of RRKM theory to successfully model the kinetics of the internal rotation process in these molecules. Solution of the Lindemann mechanism shows that at the pressure where the rate constant is one-half of its limiting high-pressure value, Pm, the frequency of deactivating collisions is comparable to , the average rate that critically... 

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 apparent first-order rate constant decreases at low pressures. Physically the decrease in value of the rate constant at lower pressures is a result of the decrease in number of activating collisions. If the pressure is increased by addition of an inert gas, the rate constant increases again in value, showing that the molecules can be activated by collision with a molecule of an inert gas as well as by collision with one of their own kind. Several first-order reactions have been investigated over a sufficiently wide range of pressure to confirm the general form of Eq. (32.61). The Lindemann mechanism is accepted as the mechanism of activation of the molecule. 

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). 

Depending upon the concentration of A, the predicted rate law varies between first and second order. At very low pressure ka k [A] and the rate law is second order with an apparent rate constant k. However, when the pressure is high and A [A] k the reaction is first order with an apparent rate constant k = k K, where K is the equilibrium constant for the activation process. To test the Lindemann mechanism express the data in first-order form... 

Therefore, the termolecularreaction rate constant has pressure dependence, and it is explained by the following scheme, called the Lindemann mechanism. According to the mechanism. 

The curve (a) in Fig. 2.9 is the schematic graph of the pressure dependence of a termolecular reaction rate constant according to the Lindemann mechanism. From the figure, it can be seen that the reaction rate constant is proportional to [M] (pressure) in the low-pressure limit, and gets nearly constant independent on the pressure in the high-pressure limit. The intermediate region between these two limits is called the fall-off region. 

The correct treatment of the mechanism (equation (A3.4.25), equation (A3.4.26) and equation (A3.4.27), which goes back to Lindemann [18] and Hinshelwood [19], also describes the pressure dependence of the effective rate constant in the low-pressure limit ([M] < [CHoNC], see section A3.4.8.2). 

Lindemann s mechanism further demands that the velocity constant shall begin to fall at some pressure sufficiently low, but does not predict at what pressure the effect should begin to be observable, since this depends upon a specific factor, namely, the average life of an activated molecule. 

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 this complex state of affairs it seemed of interest to examine some reactions at pressures so low that some differentiation between the proposed mechanisms would be possible, or at least some experimental data in a simplified form would be available. It is evident that, at sufficiently low pressures, a profound modification of the velocity constant should take place whether the mechanism be that of Christiansen and Kramers, Lindemann, Perrin or Rodebush. The relation between collision frequency and observed reaction rate at this point would also be of considerable significance.11... 

The detailed kinetics and energetics of the reactions in the rf-ion trap can be understood by considering that the total pressure inside the ion trap is on the order of 1 Pa, which means that the experiment is operating in the kinetic low-pressure regime. Therefore, a Lindemann-t3rpe mechanism has to be considered for each reaction step, and the reaction rates depend on the buffer gas pressure [187, 188]. As a consequence, the obtained pseudo first order rate constant k contains the termolecular rate constant as well as the concentrations of the helium buffer gas and of the reactants in the case of the adsorption reaction of the first CO molecule (1.1) ... 

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 ... 

Rate constants for the chemical exchange processes that occur in alkyl nitrites, cyclohexane, substituted cyclohexanes, sulfur tetrafluoride and formamide are pressure dependent. The mechanism for these thermally initiated, unimolecular gas-phase processes, reported by Lindemann in 1922, involves competition between the reaction and collisional deactivation of the critically energized molecule. A (Fqn [3]). 

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