Mechanism bimolecular models

It would be reasonable to expect that the decomposition of the N,N-dimethylimino ester chlorides proceeds via a bimolecular mechanism already demonstrated for the thermal decomposition of simple imino ester salts (79). In the carbohydrate series, where an isolated secondary hydroxyl group is involved, such a process would result in chlorodeoxy sugar derivatives with overall inversion of configuration, provided that the approach of the chloride ion is not sterically hindered. Further experiments are in progress in this laboratory utilizing additional model substance to establish the scope and stereochemical course of the chlorination reaction. 

Michael reactions and, 895 Beta-keto ester, 851 alkylation of, 859-860 cyclic, 892-893 decarboxylation of, 857, 860 Michael reactions and. 895 pKd of, 852 synthesis of, 892-893 Beta-lactam antibiotics, 824-825 Beta oxidation pathway, 1133-1137 mechanism of, 1133-1136 Beta-pleated sheet (protein), 1038 molecular model of, 1039 secondary protein structure and, 1038-1039 Betaine, 720 Bextra. structure of, 544 BHA, synthesis of, 629 BHT, synthesis of. 629 Bicycloalkane. 129 Bijvoet. J. M., 299 Bimolecular, 363... 

Alternative mechanisms have been recently proposed [78,79] based on a kinetic investigation of NO reduction by n-octane under isothermal (200°C) and steady-state conditions in the presence of H2. The authors built up a mathematical model based on supposed reaction pathways, which account for molecular adsorption of NO and CO and dissociative ones for H2 and 02. The elementary steps, which have been considered for modelling their results are reported in Table 10.3. Interesting kinetic information can be provided by the examination of this mechanism scheme in particular the fast bimolecular... 

The heat of decomposition (238.4 kJ/mol, 3.92 kJ/g) has been calculated to give an adiabatic product temperature of 2150°C accompanied by a 24-fold pressure increase in a closed vessel [9], Dining research into the Friedel-Crafts acylation reaction of aromatic compounds (components unspecified) in nitrobenzene as solvent, it was decided to use nitromethane in place of nitrobenzene because of the lower toxicity of the former. However, because of the lower boiling point of nitromethane (101°C, against 210°C for nitrobenzene), the reactions were run in an autoclave so that the same maximum reaction temperature of 155°C could be used, but at a maximum pressure of 10 bar. The reaction mixture was heated to 150°C and maintained there for 10 minutes, when a rapidly accelerating increase in temperature was noticed, and at 160°C the lid of the autoclave was blown off as decomposition accelerated to explosion [10], Impurities present in the commercial solvent are listed, and a recommended purification procedure is described [11]. The thermal decomposition of nitromethane under supercritical conditions has been studied [12], The effects of very high pressure and of temperature on the physical properties, chemical reactivity and thermal decomposition of nitromethane have been studied, and a mechanism for the bimolecular decomposition (to ammonium formate and water) identified [13], Solid nitromethane apparently has different susceptibility to detonation according to the orientation of the crystal, a theoretical model is advanced [14], Nitromethane actually finds employment as an explosive [15],... 

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... 

It has been generally accepted that the thermal decomposition of paraffinic hydrocarbons proceeds via a free radical chain mechanism [2], In order to explain the different product distributions obtained in terms of experimental conditions (temperature, pressure), two mechanisms were proposed. The first one was by Kossiakoff and Rice [3], This R-K model comes from the studies of low molecular weight alkanes at high temperature (> 600 °C) and atmospheric pressure. In these conditions, the unimolecular reactions are favoured. The alkyl radicals undergo successive decomposition by [3-scission, the main primary products are methane, ethane and 1-alkenes [4], The second one was proposed by Fabuss, Smith and Satterfield [5]. It is adapted to low temperature (< 450 °C) but high pressure (> 100 bar). In this case, the bimolecular reactions are favoured (radical addition, hydrogen abstraction). Thus, an equimolar distribution ofn-alkanes and 1-alkenes is obtained. 

A mechanism is determined from these data by choosing one which is consistent with the overall equilibrium behavior and which correctly matches the rate relationships derived for the postulated mechanism e.g., assuming the bimolecular adsorption/desorption reaction mechanism, as given in Equation 1, and using the kinetic model described above, the following relationship between xp and reactant and product concentrations can be derived (see Appendix C) ... 

If this mechanism is consistent with the experimental relaxation data, then a plot of xp versus the expression in the brackets of Equation 35 will give a straight line with a slope of kjnt and an intercept at the origin. As shown in Figure 11, the data fit this proposed mechanism quite well. Values for i i0, reactant and product concentrations, and K nt input into Equation 35 are from the equilibrium modeling results calculated at each pH value for which kinetic runs were made. Normally a variety of different mechanisms are tested against the experimental data. Several other more complex mechanisms were tested, including those postulated for metal ion adsorption onto y-A O (7) however, only the above mechanism was consistent with the experimental data. Hence it was concluded that the bimolecular adsorption/desorption reaction was the most plausible mechanism for Pb2+ ion adsorption onto a-FeOOH. 

According to the model, a perturbation at one site is transmitted to all the other sites, but the key point is that the propagation occurs via all the other molecules as a collective process as if all the molecules were connected by a network of springs. It can be seen that the model stresses the concept, already discussed above, that chemical processes at high pressure cannot be simply considered mono- or bimolecular processes. The response function X representing the collective excitations of molecules in the lattice may be viewed as an effective mechanical susceptibility of a reaction cavity subjected to the mechanical perturbation produced by a chemical reaction. It can be related to measurable properties such as elastic constants, phonon frequencies, and Debye-Waller factors and therefore can in principle be obtained from the knowledge of the crystal structure of the system of interest. A perturbation of chemical nature introduced at one site in the crystal (product molecules of a reactive process, ionized or excited host molecules, etc.) acts on all the surrounding molecules with a distribution of forces in the reaction cavity that can be described as a chemical pressure. 

For Examples 5, 8, 12, 21, and 28, all first order, the logL values for Steps 1, 4, and 6 are too large. With Examples 8 and 12 one can obtain reasonable logL values by postulating (as was done in connection with similar examples listed in Table V) that the gas molecule does not lose all of its entropy upon adsorption. For Example 28 Kuriacose and Jewur (56) postulated a bimolecular surface mechanism, that is. Step 4. The L value for that step is very large the authors claimed that an intermediate is ferric acetate. If this is correct, one would indeed expect the L calculation to indicate that the reaction is more complex than any of our models. For... 

All the preceding mechanisms of the carrier packet spread and transit time dispersion imply that charge transport is controlled by traps randomly distributed in both energy and space. This traditional approach completely disregards the occurrence of long-range potential fluctuations. The concept of random potential landscape was used by Tauc [15] and Fritzsche [16] in their models of optical absorption in amorphous semiconductors. The suppressed rate of bimolecular recombination, which is typical for many amorphous materials, can also be explained by a fluctuating potential landscape. 

A useful application of digital simulation to the problems discussed above is that it can be invoked to check the validity of several approximations. In addition, it is indispensable for the solution of more complex models, e.g. the bimolecular mechanisms reviewed in Sect. 7.1 [152, 155-158]. 

As it was mentioned in Section 2.1.1, the concentration oscillations could be simulated quite well by a set of even two ordinary differential equations of the first order but paying the price of giving up the rigid condition imposed on interpretation of mechanisms of chemical reactions namely that they are based on mono- and bimolecular stages only (remember the Hanusse theorem [19]) An example of what Smoes [7] called the heuristic-topological model is the well-known Brusselator [2], Its scheme was discussed in Section 2.1.1 see equations (2.1.33) to (2.1.35). 

A comparative study was done by Kevrekidis and published as I. G. Kevrekidis, L. D. Schmidt, and R. Aris. Some common features of periodically forced reacting systems. Chem. Eng. Sci. 41,1263-1276 (1986). See also two papers by the same authors Resonance in periodically forced processes Chem. Eng. Sci. 41, 905-911 (1986) The stirred tank forced. Chem. Eng. Sci. 41,1549-1560 (1986). A full study of the Schmidt-Takoudis vacant site mechanism is to be found in M. A. McKamin, L. D. Schmidt, and R. Aris. Autonomous bifurcations of a simple bimolecular surface-reaction model. Proc. R. Soc. Lond. A 415,363-387 (1988) Forced oscillations of a self-oscillating bimolecular surface reaction model. Proc. R. Soc. Lond. A 415,363-388 (1988). 

The second model results from a bimolecular surface reaction, A + B — products, with competitive Langmuir-Hinshelwood kinetics, which occurs in a heterogeneous differential reactor with perfectly mixed gas phase. The reaction is first order in both adsorbed A and B, and two vacant sites are required in the reaction mechanism. If the reaction products desorb immediately, the... 

In both these cases there is an autocatalytic element, i.e. one which is both the product of the reaction and which tends to increase its rate. This is the substance B in the first case and heat in the second. It is this element of feedback that is the source of the interesting behaviour. The first two terms in both of these equations represent the access to the site of reaction, in this case the stirred tank, in accordance with the criterion of actuality. The feasibility of these simple reaction schemes can be established by showing that they can be embedded in a fully reversible mechanism and the simple system recovered by limiting processes that do not violate the laws of thermodynamics or kinetics (for example, the Wegscheider condition). Yablonskii and his coworkers (Bykov et al. 1978,1979a, b, c Yablonskii Bykov 1979 Gol dshtein et al. 1986) have considered a number of simple models from which it is clear that the autocatalytic feature is essential. In the bimolecular surface reaction the autocatalytic role is played by the vacant sites which are indeed the product of the main reaction which releases those previously held by adsorbate and, at the same time, are a positive influence on the rate of reaction. 

Model Equations to Predict Reaction Rate. A final constitutive relation is needed for the reaction rate r(rxt). If the mechanism for the formation of ZnS is assumed to be a bimolecular reaction between adsorbed Zn and S (22), as given by... 

Kannebley 30) and Sorokin et al. 31,32) obtained second-order rate constants for the relevant model bimolecular reactions whereas Arnold 19) and Doszlop et al.37) consider curing of epoxy resin with anhydride or reactions of monoepoxides with various proton-donor compounds to be first order (Table 1). Considering the mechanism of individual reactions which proceed during curing or in the non-catalyzed... 

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