Non-elementary steps

In the bromate-iron clock reaction, there is an autocatalytic cycle involvmg the species intennediate species HBrO. This cycle is comprised of the following non-elementary steps ... 

In stark contrast to the transport considerations, typical time-scales for elementary and non-elementary steps in organometallic chemistry and homogeneous catalysis range from vibrational motions of ca. 10 s or less [44], to ca. hours or even days for the formation of products and side products. Moreover, the three pri-... 

Note 3.7.- Everything we have just discussed concerning opposite reactions and the energy diagram in Figure 3.1 apphes to elementary reactions alone. Arty use, especially the interpretation of a so-called activation energy for non-elementary steps, is the result of a fast extrapolation without any foundation. 

One of the possibilities is to study experimentally the coupled system as a whole, at a time when all the reactions concerned are taking place. On the basis of the data obtained it is possible to solve the system of differential equations (1) simultaneously and to determine numerical values of all the parameters unknown (constants). This approach can be refined in that the equations for the stoichiometrically simple reactions can be specified in view of the presumed mechanism and the elementary steps so that one obtains a very complex set of different reaction paths with many unidentifiable intermediates. A number of procedures have been suggested to solve such complicated systems. Some of them start from the assumption of steady-state rates of the individual steps and they were worked out also for stoichiometrically not simple reactions [see, e.g. (8, 9, 5a)]. A concise treatment of the properties of the systems of consecutive processes has been written by Noyes (10). The simplification of the treatment of some complex systems can be achieved by using isotopically labeled compounds (8, 11, 12, 12a, 12b). Even very complicated systems which involve non-... 

Pj release occurs at a relatively apparent slow rate (kobs = 0.005 s" ), so that the transient intermediate F-ADP-Pj in which P is non-covalently bound, has a life time of 2-3 minutes (Carlier and Pantaloni, 1986 Carlier, 1987). While the y-phosphate cleavage step is irreversible as assessed by 0 exchange studies (Carlier et al., 1987), the release of Pi is reversible. Binding of H2PO4 (Kp 10 M) causes the stabilization of actin filaments and the rate of filament growth varies linearly with the concentration of actin monomer in the presence of Pi (Carlier and Pantaloni, 1988). Therefore, Pi release appears as the elementary step responsible for the destabilization of actin-actin interactions in the filament. 

From these data, some key information can be drawn in both cases, the couple methane/pentane as well as the couple ethane/butane have similar selectivities. This implies that each couple of products (ethane/butane and methane/pentane) is probably formed via a common intermediate, which is probably related to the hexyl surface intermediate D, which is formed as follows cyclohexane reacts first with the surface via C - H activation to produce a cyclohexyl intermediate A, which then undergoes a second C - H bond activation at the /-position to give the key 1,3-dimetallacyclopentane intermediate B. Concerted electron transfer (a 2+2 retrocychzation) leads to a non-cychc -alkenylidene metal surface complex, C, which under H2 can evolve towards a surface hexyl intermediate D. Then, the surface hexyl species D can lead to all the observed products via the following elementary steps (1) hydrogenolysis into hexane (2) /1-hydride elimination to form 1-hexene, followed by re-insertion to form various hexyl complexes (E and F) or (3) a second carbon-carbon bond cleavage, through a y-C - H bond activation to the metallacyclic intermediate G or H (Scheme 40). Under H2, intermediate G can lead either to pentane/methane or ethane/butane mixtures, while intermediate H would form ethane/butane or propane. 

In the foregoing it has been discus.sed how a metal can dissociate H2. Fig. 3.6 explains the principle of catalysis with an example of the hydrogenation of ethylene, for which dissociative chemisorption of hydrogen is an elementary step in the catalytic cycle. The adsorption of alkenes, on the other hand, is non-dissociative. 

Shibata M, Furuya N, Watanabe M. 1987. Electrocatalysis by ad-atoms. Part XXL Catal3ftic effects on the elementary steps in methanol oxidation by non-oxygen-adsorbing ad-atoms. J Electroanal Chem 229 385-394. 

The experimental evidence, first based on spectroscopic studies of coadsorption and later by STM, indicated that there was a good case to be made for transient oxygen states being able to open up a non-activated route for the oxidation of ammonia at Cu(110) and Cu(lll) surfaces. The theory group at the Technische Universiteit Eindhoven considered5 the energies associated with various elementary steps in ammonia oxidation using density functional calculations with a Cu(8,3) cluster as a computational model of the Cu(lll) surface. At a Cu(lll) surface, the barrier for activation is + 344 k.I mol 1, which is insurmountable copper has a nearly full d-band, which makes it difficult for it to accept electrons or to carry out N-H activation. Four steps were considered as possible pathways for the initial activation (dissociation) of ammonia (Table 5.1). 

Juwekar and Sharma [1] described the kinetics of the above reactions. The formation of calcium carbonate is non elementary reaction which involves the number of elementary steps as shown in Scheme 7.2, steps (iv) and (v) assumed to be instantaneous. Absorption of C02 gas and dissolution of Ca(OH)2 affects the nucleation step, both are considered as rate controlling steps. 

One of the most efficient approaches allowing us to investigate in a reasonable time a catalytic cycle on non-periodic materials in combination with reliable DFT functional is a cluster approach. The present study is devoted to the investigation of the effect of the cluster size on the energetic properties of the (p-oxo)(p-hydroxo)di-iron metal active site. As a first step, we have studied the stability of the [Fen(p-0)(p-0H)Fen]+ depending on the A1 position and cluster size. Then, we compared the energetics for the routes involving the first two elementary steps of the N20 decomposition catalytic process i.e. the adsorption and dissociation of one N20 molecule. 

In order to illustrate the non-elementary reaction case, consider the two-step (/ = 2) reaction... 

In this review, we shall mainly consider the electrochemical behavior of sulfur and polysulfide ions (i.e. the reduced forms of sulfur) in solution. Recent works (see Sect. 8.3.1) gave a better understanding of the elementary steps leading from sulfur Sg to polysulfide ions S (or S ) in non-aqueous solvents. This has been achieved by using spectroscopic techniques for the identification of chemical species, the direct coupling of spectroscopic and electrochemical techniques, and by using digital simulation calculations for the validation of the proposed models. 

The Bodenstein approximation recognises that, after a short initial period in the reaction, the rate of destruction of a low concentration intermediate approximates its rate of formation, with the approximation improving as the maximum concentration of intermediate decreases (see Chapters 3 and 4). Equating rates of formation and destruction of a non-accumulating intermediate allows its concentration to be written in terms of concentrations of observable species and rate constants for the elementary steps involved in its production and destruction. This simplifies the kinetic expressions for mechanisms involving them, and Scheme 9.3 shows the situation for sequential first-order reactions. The set of differential equations... 

Operating within the framework of the Chauvin mechanism, the main consideration for the reaction mechanism is the order of events in terms of addition, loss and substitution of ligands around the ruthenium alkylidene centre. Additionally, there is a need for two pathways (see above), both being first order in diene, one with a first-order dependence on [Ru] and the other (which is inhibited by added Cy3P) with a half-order dependence on [Ru]. From the analysis of the reaction kinetics and the empirical rate equation thus derived, the sequence of elementary steps via two pathways was proposed, one non-dissociative (I) and the other dissociative (II), as shown in Scheme 12.20. The mechanism-derived rate equation is also shown in the scheme and it can thus be seen how the constants A and B relate to elementary forward rate constants and equilibria in the proposed mechanism. 

For linear mechanisms we have obtained structurized forms of steady-state kinetic equations (Chap. 4). These forms make possible a rapid derivation of steady-state kinetic equations on the basis of a reaction scheme without laborious intermediate calculations. The advantage of these forms is, however, not so much in the simplicity of derivation as in the fact that, on their basis, various physico-chemical conclusions can be drawn, in particular those concerning the relation between the characteristics of detailed mechanisms and the observable kinetic parameters. An interesting and important property of the structurized forms is that they vividly show in what way a complex chemical reaction is assembled from simple ones. Thus, for a single-route linear mechanism, the numerator of a steady-state kinetic equation always corresponds to the kinetic law of the overall reaction as if it were simple and obeyed the law of mass action. This type of numerator is absolutely independent of the number of steps (a thousand, a million) involved in a single-route mechanism. The denominator, however, characterizes the "non-elementary character accounting for the retardation of the complex catalytic reaction by the initial substances and products. 

Let us analyze the structure of eqn. (70). Its numerator can be written as K+ [A] - K [B], where K+ = Aq 2 3 and K = k 1k 2k 3. In this form, it corresponds to the brutto-equation of the reaction A = B obtained by adding all the steps of the detailed mechanism with unit stoichiometric numbers. The numerator is a kinetic equation for the brutto-reaction A = B considered to be elementary and fitting the mass action law. The denominator accounts for the "non-elementary character due to the inhibition of the complex catalytic reaction rate by the initial substances and products. 

As has been shown above, the cyclic characteristics is a kinetic equation for the brutto-reaction as if it were a simple step. But the denominator SjD, accounts for the "non-elementary character of this reaction and indicates the rate retardation by catalyst surface intermediates. 

This Rh(I)-based mechanism does not properly explain the pronounced rate acceleration observed on addition of HC1. Rather, we suggest that the well-known propensity of Rh(I) to oxidatively add HC1 evokes a different, Rh(III)-based mechanism. The elementary steps along such a pathway (/3-hydride insertion then C-C reductive elimination) differ substantially from those depicted in Scheme 4. Despite this uncertainty, our current mechanistic understanding of the non-H+ mediated reaction constitutes a satisfactory model because it has led to the successful refinement and expansion of our initial findings. 

This electron-richness of N-heterocyclic carbenes has an impact on many elementary steps of catalytic cycles, for example, facilitating the oxidative addition step. Therefore, NHC metal complexes are well suited for crosscoupling reactions of non-activated aryl chlorides—substrates that challenge the catalyst with a difficult oxidative addition step [28]. Furthermore, as a consequence of their strong electron-donor property, N-heterocyclic carbenes are considered to be higher field as well as higher trans effect ligands than phosphines. 

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