Monomolecular reaction schemes

This is a suitable case to outline the method of derivation [21, 22, 25, 147]. Three species are involved in the mass transfer processes, viz. A, O, and R. It will be convenient to define the quantities KA, kA, and DOA by 

The difficulty in solving eqns. (185a) and (185b) is that each of them contains two variable concentrations, cA and cG. Therefore it is helpful to invoke two auxiliary concentration functions, being (simple) combinations of cA and cQ. If we had DA = D0, such functions could be cp = ca + c0 and cQ = cA — KAl cD. If DA D0, a better choice is  

With eqns. (185a) and (185b) valid for cA and cG, it can be shown that, to a quite good approximation, cP and cQ obey the differential equations 

The terms omitted on the right-hand sides are, respectively 

The initial and boundary conditions to eqns. (185c), (187a), and (187b) are 

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With appropriate adaptations, the other monomolecular reaction schemes can be treated by similar procedures. It may suffice, therefore, to give below the resulting Laplace transforms of the interfacial concentrations in terms of parameters, the meanings of which are given in Table 8. Where possible, references to the literature are given. However, notations and formulations are often quite different due to the personal preferences of the authors. 

The results were interpreted on the basis of a mechanism that starts with the photolytic formation of a radical cage consisting of an aryldiazenyl and and arylthiyl (Ar - S ) radical, followed by diffusion of both radicals out of the cage. Three reactions of the aryldiazenyl radical are assumed to occur bimolecular formation of the azoarene and N2, or of biphenyl and N2 (Scheme 8-37), the monomolecular dediazoniation (Scheme 8-38), and recombination with the thiyl radical accompanied by dediazoniation (Scheme 8-39). In addition, two radicals can react to form a di-phenyldisulfide (Scheme 8-40). 

Ionization of 1,5-hexadiene in fluorochloroalkane matrix (Scheme 2.43) represents cation-radical monomolecular reactions. The initially formed cation-radical collapses to the cyclohexane cation-radical, that is, spontaneous cyclization takes place (Williams 1994). Zhu et al. (1998) pointed out that the ring formation from the excited valence isomer in the center of Scheme 2.43 is easier than in the corresponding ground-state dienes. Notably, tandem mass spectrometry revealed the same transformation of 1,5-hexadiene in the gas phase too. This provides ns with a hint that mass spectrometry can serve as a method to express predictions of monomolecnlar transformation of cation-radicals in the condensed phase. A review by Lobodin and Lebedev (2005) discnsses this possibility in more detail. 

The reaction scheme in Fig. 26 gives a detailed picture of the main reactions initiated by the excitation of the dye molecule at the surface of an organic crystal. The rate constants connecting the reactants with the products are given in the dimensions s 1 for monomolecular reactions and in the dimensions cm3 s 1 for biomolecular reactions. Going from left to right in the first line a J describes the... 

The rates of chemical reactions are in linear dependence on thermody namic rushes of the reaction groups of several reactants. When the pertinent kinetic schemes are reducible to a set of the intermediate monomolecular reactions (see Section 1.3.2), the minimization of functional ( Aor ) can be used to find the stationary state of these systems that are far from equilibrium. Let us demonstrate this. 

The overall reaction scheme for the skeletal isomerization of n-butenes (including both the mono- and bimolecular processes) is valid for aU acidic catalysts. However, the relative amounts of the carbenium ion intermediates involved either in the monomolecular or in the bimolecular reaction paths, as well as their relative rates of conversion, can be dramatically different for the various molecular sieve catalysts and can depend crucially on the sizes of the channels and their structural configurations as well as on the acidity of the catalyst. 

The elementary reaction steps of the hydrocarbons considered in this section are summarized in Fig. 8. Tlie occurrence of monomolecular reactions with linear hydrocarbons that produce hydrogen and alkane fragments was first demonstrated by Haag and Dessau [94], For convenience, the zeolite lattice to which the proton is attached is not explicitly shown in the scheme. However, it will become clear later that proton activation cannot be understood properly without explicitly taking into account the interaction of the carbonium and carbenium ion intermediates with the negatively charged zeolite wall. 

The Most Abundant Surface Intermediate (MASI) Approximation Catalytic transformations may include the formation of many intermediates on the catalyst surface, which are difficult to identify. In these cases, it is impossible to formulate a kinetic model based on all elementary steps. Often, one of the intermediates adsorbs much more strongly in comparison to the other surface species, thus occupying nearly all active sites. This intermediate is called the most abundant surface intermediate masi [24]. For a simple monomolecular reaction, Aj A2, the situation can be illustrated with the following scheme ... 

In this scheme, yH represents the organic compoxmd submitted to pyrolysis, y. stands for the free radical chain carrier which decomposes according to a monomolecular reaction (propagation process 2) and 3. stands for the free radical (or atom) chain carrier which reacts with y H by a bimolecular process, abstracting an H atom and recreating the free radical y. (propagation process 3). Lastly, m and 3H are the major primary products of yH pyrolysis ... 

Reaction scheme (6) is typical in the oxidation of hydrocarbons (A, R, and S) in the presence of a large amount of oxygen. Therefore, the reactions become pseudo-first-order from the viewpoint of hydrocarbons, and the practically constant oxygen partial pressure can be included in the rate constants. The intermediate product, R, represents a partial oxidation product (such as phthalic anhydride in the oxidation of o-xylene or maleic anhydride in the oxidation of benzene), whereas S represents the undesirable byproducts (CO2, H2O). The triangle system (7) represents monomolecular reactions such as isomerizations A, for instance, can be 1-butene, which is subject to an isomerization to ds-2-butene and trflns-2-butene. 

The chemical transformation S - P is just one particular elementary act in the immense set of elementary steps in the scheme (4.3). Of course, in the case of complex reaction, involving the transformation of several components, there may be a number of such elementary acts that represent the catalyzed reaction. However, even in the simplest case of monomolecular reaction the scheme (4.3) is also simplified the sequence of elementary acts on the path from ES to EP may be branching, scheme (4.4). Hence, there are a set of trajectories leading from ES to EP. 

Recently, benzophenone-based initiators with hydrogen donating amine moieties covalently attached via an alkyl spacer were introduced as photoinitiators for vinyl polymerization [101,126-130] (see 1, Table 10). Although also following the general scheme of lype II initiators, the initiation is a monomolecular reaction, as both reactive sites are at the same molecule. Hydrogen transfer is suspected to be an intramolecular reaction. The ionic derivatives (2 and 3) shown in Table 10 are used for polymerization in the aqueous phase [131-133]. With 4,4 -diphenoxybenzophenone (4 in Table 10) in conjunction with tertiary amines, polymerization rates that are by factor of 8 higher than for benzophenone were obtained [134]. 

The interaction of alkyl halides with mercaptans or alkaline mercaptides prodnces thioalkyl derivatives. This is a typical nncleophilic substitution reaction, and one cannot tell by the nature of products whether or not it proceeds through the ion-radical stage. However, the version of the reaction between 5-bromo-5-nitro-l,3-dioxan and sodium ethylmercaptide can be explained only by the intermediate stage involving electron transfer. As found (Zorin et al. 1983), this reaction in DMSO leads to diethyldisulfide (yield 95%), sodium bromide (quantitative yield), and 5,5 -bis(5-nitro-l,3-dioxanyl) (yield 90%). UV irradiation markedly accelerates this reaction, whereas benzene nitro derivatives decelerate it. The result obtained shows that the process begins with the formation of ethylthiyl radicals and anion-radical of the substrate. Ethylthiyl radicals dimerize (diethyldisulfide is obtained), and anion-radicals of the substrate decompose monomolecularly to give 5-nitro-l,3-dioxa-5-cyclohexyl radicals. The latter radicals recombine and form the final dioxanyl (Scheme 4.4). 

The mechanism of the reaction depicted in Scheme 4.6 differs from the Sf.,1 or Sf.,2 mechanism in that it involves the stage of one-electron oxidation-reduction. The impetus of this stage may be the easy detachment of the bromine anion followed by the formation of fluorenyl radical. The latter is unsaturated at position 9 near three benzene rings that stabilize the radical center. The radical formed is intercepted by the phenylthiolate ion. This leads to the anion-radical of the substitution product. Further electron exchange produces the substrate anion-radical and final product in its neutral state. The reaction consists of radical (R)-nucleophilic (N) monomolecular (1) substitution (S), with the combined symbol Sj j l. Reactions of Sj j l type can have both branch-chain and nonchain characters. 

The monomolecular conversion of three components has also been considered in some detail by Kallo (30). Rate equations based on Langmuir adsorption were developed assuming a number of different mechanistic schemes including steps in which surface adsorption was not at equilibrium. Since the rate equations developed became complicated, practical application was devoted to cases in which only initial reaction rates were observed, so... 

Scheme 5.3 (a) Mechanism of ester and anilide ethanolysis catalyzed by dinuclear complexes, showing productive (II) and non-productive (I and III) species and (b) the corresponding intermolecular model reaction based on monomolecular complexes. 

In Scheme 4.1 the mechanisms of typical monomolecular (SnI) and bimolecular (Sn2) nucleophilic substitutions at a neutral electrophile with an anionic nucleophile are sketched. SnI reactions usually occur when the electrophile is sterically... 

The skeletal isomerization of butane to isobutane is a typical reaction catalyzed by superacidity. Early in the history of this work, S04/Fe203, S04/Ti02, and S04/Zr02, were termed superacids owing to their ability to isomerize butane at room temperature or below [32, 37, 39] The formation of isobutane from butane, however, does not necessarily require superacidic strength. A bimolecular reaction pathway based on the intermediacy of butane is energetically lower than a monomolecular mechanism [129-133]. The monomolecular and bimolecular mechanisms are shown in Schemes 17.1 and 17.2, respectively, using pentane as a model. 

The assumption of uniformity is in fact justified for some realistic kinetic schemes, such as Langmuir isotherm catalyzed reactions, Michaelis-Menten kinetics, and others (Aris, 1989 Cicarelli et al, 1992). The assumption bears a more than superficial analogy with those systems termed pseudo-monomolecular by Wei and Prater (1962). Mathematically, it is a very powerful assumption By crossing out the dependence of F[ ] on x, its value has been reduced from an infinite-dimensional vector (a function of x) to a scalar. This simplification makes Eq. (102) a quasilinear one, and it can be integrated explicitly by introducing a warped time scale t(0. (0) = 0. The solution, as can be verified by inspection, is... 

Table I 4) a) shows that allyl iodide decomposes much more readily than any of those previously described. At 494 decomposition was almost 60 %, so that in order to obtain more moderate decomposition lower temperatures had to be chosen. Exps. 77-78 show the absence of any effect of iodide-pressure on the rate. The comparison of these results with Exp. 80 reveals a fourfold increase of Ai caused by a twelvefold reduction of the contact time. Exps. 84, 78, 82 and 86, carried out at the lower temperature of about 356° again show Aj as independent of the iodide pressure. Comparing Exp. 84 with Exps. 78, 82 and 86, and the latter with Exps. 89 and 81, we see also that the rise of Aj with diminishing contact time has become less marked— if not altogether negligible. With a further lowering of the temperature to about 298° (Exps. 83, 79, 85, 88) the dependence of Ai on contact time becomes quite imperceptible. Thus with decreasing temperature the kinetics of the reaction appear to conform increasingly well to the monomolecular scheme. Extrapolating the rate of pyrolysis of -propyl iodide down to 298°, the ratio of Aj for -propyl allyl can be calculated at about i 14000.

The theoretical scheme took into account the reaction of chain propagation limitation by transfer to the Al-organic compound, monomer, and hydrogen, as well as the chain termination following the monomolecular mechanism (spontaneous termination or the immurement of active center). 

REACTION PRODUCTS AND ORGANOMETALLIC INTERMEDIATES WITH NICKEL(0) COMPLEXES. Nickel(O) complexes such as (Cod)2Ni, show a striking parallel with lithium(0) complexes in their reactions with diphenylacetylene a sequence of monomolecular reduction bimolecular, stereospecific reduction and cyclotrimerization (Scheme IX). Consonant with the suggestion that nickel(0) forms nickelirene (26) and nickelole (27) intermediates in the course of cyclotrimerization of diphenylacetylene is the isolation of (Z)-l,2-di-phenylethene (28) and (E,E)-1,2,3,4-tetraphenyl-l,3-butadiene (29) upon hydrolysis. Furthermore, when DC1 was used in the workup, both 28 and 29... 

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