Reaction mechanism equations

Defluorination occurs even with sodium fluoride at 530 °C when tetra-fluorothiolene is converted to 2,5-difluQrothiophene [63], Dehydrofluonnation would be expected at such high temperature, but defluonnation is favored. The product composition also excludes a disproportionation reaction mechanism (equation 32). 

Figure 4. The relative surface coverage of adsorbed hydrogen as a function of electrode potential for acetic acid. The circles are calculated from the second harmonic signal using Equation 1, and the solid line is the theoretical curve predicted from the reaction mechanism (Equations 2 and 3).

As mentioned at the beginning of this Section, computational analyses41,53 have lead to a deeper understanding of the reaction mechanism (equation 49). 

In (2.25a-c), the variables with the asterisk are dimensionless. Substitution into (2.24) yields a dimensionless diffusion-reaction mechanism equation. 

The rearrangement of zinc dialkyldithiophosphate initiated by a double alkyl group migration from oxygen atoms to sulfur atoms (Fuller et al., 1998 Jones and Coy, 1981 Varlot et al., 2000), is believed to be the result of the following reaction mechanism (equation 1.2) ... 

The reaction between 41 and tri-ferf-butylsilyl isocyanate with its bulky substituent leads to the five-membered heterocyclic system 100109. The formation of this ring requires cleavage of the Si=Si multiple bond, but nothing is as yet known about the reaction mechanism (equation 20). 

This is an approximation because the OH concentration does change during the reaction, but since the change is not very great the equation is adequate to illustrate the importance of the two reaction mechanisms. Equation (4.31) is the solution for a reversible reaction that begins with an initial concentration of [C02]° and progresses toward an equilibrium value of [C02]° + BjA. The value represented in A is the reciprocal of the residence time of CO2 with respect to chemical reaction and incorporates both mechanisms of reaction. 

Min investigated the reaction mechanism of this dealumination approach.[24] Breck and Skeels had found that, in the ammonium hexafluorosilicate solution, the extraframework silicon atoms could substitute for the aluminum atoms in the crystal lattice of the zeolite framework, but the mechanism of the whole reaction process was not clear. Through 29Si,27Al-MAS-NMR and IR characterization techniques, Min and coworkers investigated the removal of A1 atoms from the zeolite framework, the chemical environment of the extraframework silicon atoms, and the species of the silicon that can be inserted into the Al-removal framework vacancies during the reaction process, and finally they proposed the reaction mechanism [Equations (6.18)-(6.25)] as follows. 

Using representative reaction paths for reaction mechanisms, the similarities between various reaction mechanisms can be analysed and quantified by direct comparison of their matrix sequences D(p,l), lD(p,2),..., D(p,w). A numerical similarity measure of reaction mechanisms is given by a measure of difierence between the two matrix sequences. A smaller difference between the two matrix sequences implies a greater similarity of the reaction mechanisms. Equation (47) represents the extreme case of similarity the shapewise equivalence of reaction mechanisms. 

These RSSF data are fully consistent with a reaction mechanism (Equation 2) in which covaent bonding occurs to form covalent species along the reaction path (presumably the first tetrahedral intermediate, T], and/or the acyl enzyme intermediate, acyl-E, with release of methanol, Pi), followed by deacylation and formation of the carboxylate ion product (P2). 

Compared with nitrous acid ions, nitric acid ions can be slowly reduced in sodium sulfhydrate. The nitrous acid ions are produced from the hydrolysis of nitrate esters, other than from the reduction of nitric acid ions. Thus, the nitrous acid ions are formed, most likely, by the breakage of bonds between oxygen and nitrogen atoms. The effect of sulfhydrate on the hydrolysis of nitrate esters is to reduce the reactants, as expressed in the following reaction mechanism equations. 

On the basis of the reaction mechanism Equations 4.6—4.11, the reaction rates can be expressed in terms of the different functional groups present in the reactor and the corresponding rate constants [38]. The terms in parentheses denote mole numbers of each component. 

Kinetic plots were linear over 50% of the reaction which though indicative, may be fortuitous. Conadering all of the data which was gathered, Howe and Hiatt [187] postulate the foUowing reaction mechanism, equation (13S). 

The unimolecular dissociation of Mc3Si+ (78) has been studied experimentally . As indicated by CAD studies and isotopic exchange reactions, ion 78 readily interconverts upon excitation to isomer 79 (equation 34). The reaction mechanism for this interesting interconversion has been proposed to proceed via a concerted 1,2-hydrogen/l, 2-methyl migration. This dyotropic rearrangement corresponds to a thermally allowed process. In a similar fashion the ethene elimination from 78 was proposed to proceed via a dyotropic multicenter reaction mechanism (equation 35). 

The above reaction mechanism (Equation 10) has also been used to describe the influence of hydrogen sulphide [l], alkali metal ions [15], and halide ions [16,17]. 

Irradiation of dioxane solutions of MA gives dimer 2, accompanied by oligomer containing about four units derived from monomer and one dioxane unit per polymer molecule. Mass spectroscopy, NMR, IR, elemental, and other analytical studies support a complex reaction mechanism (equations 1-8), consisting of monomer excimer, ionic intermediates, dioxanyl radical, and other intermediates formation during photoexcitation. 

The above equations can apply when the rate-determining step is first order even though the complete reaction mechanism is complicated. Thus for the reac-... 

The system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... 

General first-order kinetics also play an important role for the so-called local eigenvalue analysis of more complicated reaction mechanisms, which are usually described by nonlinear systems of differential equations. Linearization leads to effective general first-order kinetics whose analysis reveals infomiation on the time scales of chemical reactions, species in steady states (quasi-stationarity), or partial equilibria (quasi-equilibrium) [M, and ]. 

Vibrational motion is thus an important primary step in a general reaction mechanism and detailed investigation of this motion is of utmost relevance for our understanding of the dynamics of chemical reactions. In classical mechanics, vibrational motion is described by the time evolution and l t) of general internal position and momentum coordinates. These time dependent fiinctions are solutions of the classical equations of motion, e.g. Newton s equations for given initial conditions and I Iq) = Pq. 

Thus far we have considered systems where stirring ensured homogeneity witliin tire medium. If molecular diffusion is tire only mechanism for mixing tire chemical species tlien one must adopt a local description where time-dependent concentrations, c r,f), are defined at each point r in space and tire evolution of tliese local concentrations is given by a reaction-diffusion equation... 

For a proposed reaction mechanism to be valid the sum of its elementary steps must equal the equation for the overall reaction and the mechanism must be consistent with all experimental observations The S l mechanism set forth m Figure 4 6 satisfies the first criterion What about the second d... 

Much of the language used for empirical rate laws can also be appHed to the differential equations associated with each step of a mechanism. Equation 23b is first order in each of I and C and second order overall. Equation 23a implies that one must consider both the forward reaction and the reverse reaction. The forward reaction is second order overall the reverse reaction is first order in [I. Additional language is used for mechanisms that should never be apphed to empirical rate laws. The second equation is said to describe a bimolecular mechanism. A bimolecular mechanism implies a second-order differential equation however, a second-order empirical rate law does not guarantee a bimolecular mechanism. A mechanism may be bimolecular in one component, for example 2A I. 

Absorption of Nitrogen Oxides. There have been numerous studies and reports on the reaction mechanisms and rate-controlling steps for the absorption of nitrogen oxides into water (43—46). The overall reaction to form nitric acid may be represented by equation 14, where Ai/298 K kJ/mol ofNO consumed. 

Reaction Mechanisms. There is considerable difference of opinion concerning the specific cell reactions that occur ia the silver—ziac battery. Equations that are readily acceptable are... 

The total concentration or amount of chlorine-based oxidants is often expressed as available chorine or less frequendy as active chlorine. Available chlorine is the equivalent concentration or amount of Cl needed to make the oxidant according to equations 1—4. Active chlorine is the equivalent concentration or amount of Cl atoms that can accept two electrons. This is a convention, not a description of the reaction mechanism of the oxidant. Because Cl only accepts two electrons as does HOCl and monochloramines, it only has one active Cl atom according to the definition. Thus the active chlorine is always one-half of the available chlorine. The available chlorine is usually measured by iodomettic titration (7,8). The weight of available chlorine can also be calculated by equation 5. 

A -Halogenated compounds such as iV-chlorotnfluoroacetamide, A -chloro-imidosulfuryl fluonde and N N dichlorotnfluoromethylamine add across C=C bonds to form saturated amides [14] tmidosulfury I fluorides [15] and amines [16], respectively Allylic halogenation also occurs with the use of A-bromo- or A-chIo roperfluoroamides The primary amine A,A-dichlorotrifluororaethylamine selectively affords 11 or 2 1 adducts with either tetrafluoroethylene or chlorotrifluoroethylene [16] (equation 7) The reaction mechanism is believed to involve thermal free radicals, with control achieved principally by reaction temperature The 1 1 adduct is formed even in the presence of a large excess of olefin... 

The generally accepted mechanism for this reaction is presented as a series of three equations in Figure 4.6. We say generally accepted because a reaction mechanism can never be proved to be conect. A mechanism is our best present assessment of how a reaction proceeds and must account for all experimental observations. If new experimental data appear that conflict with the mechanism, the mechanism must be modified to accommodate them. If the new data are consistent with the proposed mechanism, our confidence grows that the mechanism is likely to be conect. 

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