Unimolecular Decomposition Reactions

The relative probabilities of Reactions 24, 25, and 26 were, respectively, 1.00, 0.25, and 0.12 at a hydrogen pressure of about 1 atmosphere (9). These numbers could be derived either by analyzing the stable alkanes formed in the unimolecular decompositions (Reactions 24-26) or from the products of the hydride transfer reactions between C5Hi2 and the alkyl ions. Elimination of H2 from protonated pentane may also occur, but it is difficult (although not impossible) to establish this reaction through neutral product analysis. 

This particular mechanism assumes that Rx and Ri are different radicals and that the latter do not participate in the propagation reactions. In the more general case the radical R can participate in propagation reactions analogous to reactions (2) and (3). These propagation steps consist of a bimolecular hydrogen abstraction reaction followed by a unimolecular decomposition reaction. 

For a temperature of 1000 K, calculate the pre-exponential factor in the specific reaction rate constant for (a) any simple bimolecular reaction and (b) any simple unimolecular decomposition reaction following transition state theory. 

Association reactions can be further classified as simple and complex, similarly to the unimolecular decomposition reactions treated earlier. Simple association reactions involve the formation of a single bond, such as those observed in atom and radical recombinations, for example ... 

Since the ionic states formed by high-energy radiation seem to be the chemically important ones, let us consider their reactions. The reactions between ions and neutral molecules in the gas phase can be studied directly in a mass spectrometer. Under ordinary operating conditions the pressure in the ionizing chamber of the mass spectrometer is about 10 6 mm. and the ions formed have little chance to collide with a molecule during their brief lifetime (10-5 sec.) before collection. Therefore, mainly unimolecular decomposition reactions occur and it is the products of these that are detected. The intensity of these primary ions increases with the first power of the pressure in the ionization chamber. However, when the pressure becomes great enough so that ion molecule collisions can occur readily, additional secondary ions which are the products of these ion molecule Collisions appear. The intensity of these secondary product ions depends on the concentrations of both the molecules and the primary ions, and thus on the square of the pressure. 

Statistical theories treat the decomposition of the reaction complex of ion-molecule interactions in an analogous manner to that employed for unimolecular decomposition reactions.466 One approach is that taken by the quasiequilibrium theory (QET).467 Its basic assumptions are (1) the rate of dissociation of the ion is slow relative to the rate of redistribution of energy among the internal degrees of freedom, both electronic and vibrational, of the ion and (2) each dissociation process may be described as a motion along a reaction coordinate separable from all other internal... 

As an example of a unimolecular decomposition reaction, we study the monomolecular catalytic cracking reaction of //-paraffins in high-silica acid zeolites or other crystalline or ordered acid porous materials, in this section [97-102],... 

The inhibited decomposition was studied again by Forst and Rice using ethylene, propene and nitric oxide. The addition of any of these scavengers was found to reduce the rate of decomposition as monitored by nitrogen evolution and also the ratio of CH4/N2 in the product, but each inhibitor affected both quantities to a different extent. Nitric oxide appears to be the most efficient inhibitor. As is the usual case, nitre oxide functions not only as an inhibitor but at higher pressures as an accelerator as well. The fully NO inhibited reaction was thought to correspond to the initial homogeneous unimolecular decomposition reaction... 

The most common initiation or homolysis reaction is the breaking of a covalent C-C bond with the formation of two radicals. This initiation process is highly sensitive to the stability of the formed radicals. Its activation energy is equal to the bond dissociation enthalpy because the reverse, radical-radical recombination reaction is so exothermic that it does not require activation energy. C-C bonds are usually weaker than the C-H bonds. Thus, the initial formation of H radicals can be ignored. The total radical concentration in the reacting system is controlled both by these radical initiation reactions and by the termination or radical recombination reactions. In accordance with Benson (1960), the rate constant expressions of these unimolecular decompositions are calculated from the reverse reaction, the recombination of two radical species to form the stable parent compound, and microscopic reversibility (Curran et al., 1998). The reference kinetic parameters for the unimolecular decomposition reactions of K-alkanes for each single fission of a C-C bond between secondary... 

This is, of course, the reverse of Reaction 19.3 The overall atmospheric lifetime of PAN depends on the ratio of NO to NO2 and the abundance of peroxyacetyl radical, because the reverse reaction to form PAN is also important. The forward rate for the unimolecular decomposition reaction (Reaction 19.4) is 3.3 X 10 " sec at 298 The temperature dependence of the thermal equilibrium is quite strong, with an activation energy of approximately 25 kcal. At the cold temperatures found at higher altitudes and in winter time, PAN is quite stable in the atmosphere, while at lower altitudes in the summer PAN has a fairly short lifetime (< 1 h). These observations have implications for sampling and chromatographic analysis of PAN in warm temperatures. 

Consider first a unimolecular decomposition reaction where the products are not adsorbed or are very weakly adsorbed. 

In one sense this mechanism is akin to Lindemann s picture of unimolecular decomposition reactions (see Section 4.3.1.3). An initial reaction produces a reactive intermediate that subsequently decomposes irreversibly to yield products or is reversibly decomposed into enzyme and substrate. 

Besides the calculation of reaction rate coefficients of unimolecular decomposition reactions such as the thermal decomposition of toluene [29] or methyl radicals [30], and of bimolecular reactions such as the reaction of CO with HO2 to CO2 and OH,... 

These are the reverse of unimolecular decomposition reactions. The decomposition reaction can be analyzed by the means discussed above, and then the rate constant for the association reaction can be obtained using the equilibrium constant. When doing this, it is important to check that the rate of the association reaction does not substantially exceed the gas-kinetic collision rate. If it does, then there is probably a problem with the decomposition rate constant, the equilibrium constant, or both. 

Photoinduced unimolecular decomposition reactions are among the simplest reactions which can be studied experimentally and theoretically. One such reaction which has received considerable attention is the vibrational predissociation of small isolated van der Waals (vdW) clusters for which one molecule is a chromophore and the other is a small "solvent" molecule. Two dynamical events may transpire in such a system following the initial photoexcitation to Si vibronic levels vibrational energy may be redistributed to modes other than the optically accessed zero order chromophore states and at sufficient energies the cluster may dissociate. The fundamental theoretical understanding of these two kinetic processes should be accessible in terms of Fermi s golden rulel and unimolecular reaction rate2 concepts. 

The form of equation 7.6 or 7.7 is also suitable for unimolecular decomposition reactions provided that additional sites are not required for the decomposition products for example, an appropriate sequence would be ... 

However, if in a unimolecular decomposition reaction at least one additional active site is required in the RDS (or any step preceding it), then a different rate expression is obtained. Consider again A decomposing to B + C, but now ... 

It was mentioned in Chapter 7.1 that if more than one active site is required in a unimolecular decomposition reaction, the denominator must be raised to a power greater than unity. Now, if a RDS does not exist, the derivation can become more complicated. An example of this is provided by a study of ammonia decomposition on a 4.8% Ru/carbon catalyst with a dispersion near unity [60]. Using a power rate law of the form rm = values... 

Historically, the theory of the termolecular reaction mentioned in the previous paragraph has been developed through the unimolecular reaction theory. This paragraph describes unimolecular decomposition reacticms in some detail. The chemical formula for the unimolecular decomposition reactions corresponding to the Lindemann mechanism can be shown as... 

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