Molecular disproportionation, rates

In these cases k is a lower limit for molecular disproportionation rate constants since during the reaction a substantial amount of the donor is converted to tetralin (35b). 

Rates of Molecular Disproportionation. Simple H-atom transfer from a donor molecule to an acceptor molecule (reaction 13, molecular disproportionation) generates two free radicals and can lead to the net transfer of two H atoms by the following reaction sequence. 

To examine the potential importance of molecular disproportionation, a means for estimating ki3 must be found. Estimates of ki3 will be obtained from estimates of both the rate constant for the reverse reaction (radical disproportionation, reaction -13), and the equilibrium constant, Ki3 i.e., ki3 = Ki3 k x3. 

Table V presents a list of estimated enthalpies and half lives for molecular H-atom transfer (disproportionation) from tetralin to a number of unsaturated molecules. At 450°C, and even at 400°C, many structures will undergo rapid molecular disproportionation with tetralin. Approximate relative rates at 400°C for H-atom donation by molecular disproportionation for selected hydrogen donors are estimated below (sources for thermochemistry are given in footnote 1 of Table IV) ...

Estimated rates of molecular disproportionation will now be compared to observed reaction rates of unsaturated molecules in the presence of various hydrogen donors. 

Collins et al. have studied a number of reactions in excess tetralin at 400°C (15). They reported 99% conversion of indene to indane after 1 hour and conversion of cyclohexene and 1-cyclohexenylbenzene to cyclohexane and cyclohexylbenzene after 18 hours. At 400°C values in Table V predict nearly complete (>90%) hydrogenation of both indene and 1-cyclohexenylbenzene after 1 hour and a conversion of cyclohexene to cyclohexane at a rate of 40% per hour. Molecular disproportionation is a feasible pathway for these reactions. 

Virk and Garry (24a) have recently investigated hydrogen transfer from cyclohexanol to anthracene and phenanthrene and have reported well-behaved second-order kinetics. These workers suggest that this reaction may occur by a concerted molecular H2-transfer. Simple second-order kinetic behavior, however, is also consistent with molecular disproportionation (and also with hydride, H, transfer). However, if it is assumed that (k, /k ) = 0.1, predicted rates are only 1/100... 

Virk and co-workers (24b,c) and King and Stock (35b) have reported rates for H2-transfer to anthracene and phenanthrene in solution containing 1,2- and 1,4-dihydronaphthalene and tetralin. Comparisons between reported rate constants and estimated rate constants for bimolecular disproportionation are given in Table VI. In agreement with Stock, this data does not provide evidence for a concerted H2-transfer mechanism. Our calculations indicate that molecular disproportionation may be a major hydrogenation mechanism in these reaction systems. 

Table VI. Comparison of Empirical Rate Constants3 for H2-Transfer from Hydroaromatics, kQbs> Compared to Estimated Molecular Disproportionation Values, k. ...

Formation of Free Radicals by Molecular Disproportionation. A significant conclusion that may be drawn from considerations of rate and equilibrium constants for molecular disproportionation is that this path can provide appreciable concentrations of free radicals in many systems long after most weak chemical bonds have ruptured and bond homolysis has ceased to be a major source of free radicals. In "pure tetralin, for instance, trace concentrations of 1,2-dihydronaphthalene are expected to equilibrate with tetralin and tetralyl radicals,... 

Molecular disproportionation may constitute a major reaction pathway in coal-related systems both for transferring hydrogen and for generating free radicals. Estimated rates of this reaction are shown to often be close to observed reaction rates in model systems. 

Even though the rate of radical-radical reaction is determined by diffusion, this docs not mean there is no selectivity in the termination step. As with small radicals (Section 2.5), self-reaction may occur by combination or disproportionation. In some cases, there are multiple pathways for combination and disproportionation. Combination involves the coupling of two radicals (Scheme 5.1). The resulting polymer chain has a molecular weight equal to the sum of the molecular weights of the reactant species. If all chains are formed from initiator-derived radicals, then the combination product will have two initiator-derived ends. Disproportionation involves the transfer of a P-hydrogen from one propagating radical to the other. This results in the formation of two polymer molecules. Both chains have one initiator-derived end. One chain has an unsaturated end, the other has a saturated end (Scheme 5.1). 

The effect of crystal size of these zeolites on the resulted toluene conversion can be ruled out as the crystal sizes are rather comparable, which is particularly valid for ZSM-5 vs. SSZ-35 and Beta vs. SSZ-33. The concentrations of aluminum in the framework of ZSM-5 and SSZ-35 are comparable, Si/Al = 37.5 and 39, respectively. However, the differences in toluene conversion after 15 min of time-on-stream (T-O-S) are considerable being 25 and 48.5 %, respectively. On the other hand, SSZ-35 exhibits a substantially higher concentration of strong Lewis acid sites, which can promote a higher rate of the disproportionation reaction. Two mechanisms of xylene isomerization were proposed on the literature [8] and especially the bimolecular one involving the formation of biphenyl methane intermediate was considered to operate in ZSM-5 zeolites. Molecular modeling provided the evidence that the bimolecular transition state of toluene disproportionation reaction fits in the channel intersections of ZSM-5. With respect to that formation of this transition state should be severely limited in one-dimensional (1-D) channel system of medium pore zeolites. This is in contrast to the results obtained as SSZ-35 with 1-D channels system exhibits a substantially higher... 

Diffusion of particles in the polymer matrix occurs much more slowly than in liquids. Since the rate constant of a diffusionally controlled bimolecular reaction depends on the viscosity, the rate constants of such reactions depend on the molecular mobility of a polymer matrix (see monographs [1-4]). These rapid reactions occur in the polymer matrix much more slowly than in the liquid. For example, recombination and disproportionation reactions of free radicals occur rapidly, and their rate is limited by the rate of the reactant encounter. The reaction with sufficient activation energy is not limited by diffusion. Hence, one can expect that the rate constant of such a reaction will be the same in the liquid and solid polymer matrix. Indeed, the process of a bimolecular reaction in the liquid or solid phase occurs in accordance with the following general scheme [4,5] ... 

The results of adsorption and desorption of CO mentioned above suggest that for the reaction at low temperature, the sites for relatively weakly chemisorbed CO are covered by the deposited carbon and the reaction occurs between molecularly adsorbed CO and oxygen on the carbon-free sites which are the sites for relatively strongly chemisorbed CO. Therefore, the definition of the turnover rate at 445 K remains as given in Equation 1. For the reaction at 518 K, however, this definition becomes inappropriate for the smaller particles. Indeed, to obtain the total number of Pd sites available for reaction, we now need to take into consideration the number Trp of CO molecules under the desorption peak. Furthermore, let us assume that disproportionation of CO takes place through reaction between two CO molecules adsorbed on two adjacent sites, and let us also assume that the coverage is unity for the CO molecules responsible for the LT desorption peak, since this was found to be approximately correct on 1.5 nm Pd on 1012 a-A O (1). Then, the number Np of palladium sites available for reaction at 518 K is given by HT/0 + NC0 LT s nce t ie co molecules under the LT desorption peak count only half of the available sites. Consequently, the turnover rate at 518 K should be defined as ... 

Small alkylperoxy and alkoxy radicals can decompose uni-molecularly, though their rate constants are often in the second-order region. They abstract hydrogen atoms from alkanes, aldehydes, esters, and acids, add to olefins, and may react with 02. Furthermore, interactions with other radicals can lead to disproportionation or combination. These reactions are reviewed, and particular attention is given to CH 02 and CH30 a number of rate constants are estimated. 

Because the rates of this reaction are very rapid, normal sampling techniques were not satisfactory and an infrared technique was used. This esterification reaction was shown to be about 100 times faster than the disproportionation reaction and inter-intra-molecular assistance was also found to be important. This assistance seems to be a common pattern in acid-catalysed processes of oligosiloxanols in inert solvents. In dioxane solvent the redistribution kinetics can be interpreted in terms of an unzipping mechanism. The ratedetermining step is terminal silanol cleavage by water forming dimethylsilanediol which rapidly reacts with other substrate silanols (Scheme 4). 

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