Rate-determining step consecutive reactions

This argument can be extended to consecutive reactions having a rate-determining step. - P The composition of the transition state of the rds is given by the rate equation. This composition includes reactants prior to the rds, but nothing following the rds. Thus, the rate equation may not correspond to the stoichiometric equation. We will consider several examples. In Scheme IV a fast acid-base equilibrium precedes the slow rds. 

Fig. 4. Dependence of relative concentrationa nj/nt of reaction components A, B, and C on time variable r (arbitrary units) in the case of consecutive (— — ) reactions according to scheme (Ha) or parallel (C ) reactions according to scheme (lib). Ads X, Ads A, Des Y denotes that the rate determining step in the overall transformation is adsorption or desorption of the respective substance Des (B + C) denotes that the overall rate is determined by simultaneous desorption of the substance B and C. Ki/Ki = 0.5 for consecutive, and Ki /Ki — 0.5 for parallel reactions, b nxVn. 0 = 2.5 for consecutive reactions Kt = 0.5, and for parallel reactions Ki/Ki — 0.5. c nxVnA0 = 2.5 fcdesBKi Ky/fcdesoXj Kx = 10 [cf. (53)]. d Ki = 1.75 for consecutive, and Ki/Ki = 1.75 for parallel reactions.

This great variety of pathways makes it difficult to decide which of the steps is the rate-determining step. It is most likely that at intermediate current densities the overall reaction rate is determined by the special kinetic features of step (15.24) producing the oxygen-containing species. The slopes of = 0.12 V observed experimentally are readily explained with the aid of this concept. Under different conditions, one of the steps in which these species react further may be the slow step, or several of the consecutive steps may occur with similar kinetic parameters. 

The hydrogens within the octahedral olefin-dihydride intermediate are transferred consecutively with overall cis addition, and the rate-determining step (k9) is olefin insertion to give the alkyl- hydride. Kinetic and thermodynamic parameters for nearly all the steps of Fig. 1 have been estimated for the cyclohexene system. Because the insertion reaction is generally believed to require a cis disposition of the hydride and olefin... 

The overall kinetics of crystal precipitation has to consider that the process consists of a series of consecutive processes in simple cases, the slowest is the rate determining step. Assuming the volume diffusion is not the rate determining step, we still have at least the following reaction sequences ... 

Applying pulse radiolysis to the formation of Cuni(GlyGlyHis) only two consecutive reactions are observed experimentally during its decomposition. A volume of activation of Ah = +14 cm3 mol-1 was measured for the first observable step, which is in accord with the decarboxylation process being the rate determining step in this mechanism. AV = + 8 cm3 mol-1 was obtained for the second observable process in agreement with expectations for the heterolytic. in... 

The simple second-order nature of the kinetics in this system leads to immediate conclusions of some consequence. The rate-determining step is clearly not the heterolytic breaking of a metal-sulfur bond to produce the free R-S group, which then might undergo reaction. Further, the fact that there is no evidence suggesting consecutive processes eliminated the possibility that any such scheme could enter into the total rate except essentially as a pre-equilibrium—e.g., Equations 14 and 15. 

The Rate-Determining Step. Determination of the step that decides the overall rate in a series of consecutive or parallel reactions in heterogeneous catalysis is the most significant part of mechanism determination. It is best to deal with the ideas here in a general way they will be exemplified in three reactions later on in the section. 

It was shown in the pulse radiolysis of the aqueous solution of polyethylene oxide), for example, the peroxy radicals produced by the reaction of 02 combined and formed highly unstable oxyl radicals [73], The LSI decay-curve after the pulse observed with an 02-saturated solution showed two modes. The faster one obeyed a second order kinetics, suggesting that Eq. (17) was the rate determining step in the series of consecutive reactions. This reaction was followed by H-abstraction of OH radical, leading to the main-chain scission. 

In many cases electrode processes involving the transfer of more than one electron take place in consecutive steps. The symmetry of the activation barrier referred to above relates to the rate-determining step. For example, a two-electron transfer involving a pre-equilibrium for the first electron transfer and the second electron transfer as the ratedetermining step leads to (cm) = 1 + 0.5 = 1.5. From this we might calculate or = 0.75, which is not a reflection of the position of the activated complex on the reaction coordinate. Thus extreme care must be... 

Rate-determining step— An overall chemical reaction usually involves several consecutive steps, e.g.,... 

At the same time, the rate determining step features the maximum dif ference of thermodynamic rushes (or the maximum difference of chemical potentials) between the reacting partners in the process under consider ation. Indeed, in the consecutive transformations, the stationary rates are identical through aU of the reaction channels ... 

In systems of consecutive reactions it may sometimes occur that there is one step which is very much slower than all the subsequent steps leading to product. Then the rate of production of product may depend on the rates of all the steps preceding the last slow step but will not depend on any of the subsequent steps, all of which are rapid compared to the last slow step. Such a last slow step has been called, somewhat misleadingly, the rate-determining step of the reaction. 

Electrochemical reactions on electrodes involve consecutive reactions with several steps. Knowledge of the reactants and products in each step may provide a valuable piece of evidence by means of which the pathway—and sometimes even the rate-determining step—can be identified. 

Although Misono and coworkers [63] agreed with the consecutive mechanism, they suggested a different rate determining step to Taufiq-Yap and coworkers [64]. By determining kinehc data for the reaction of n-butane, 1-butene and 1, 3-butadiene over VPP, they concluded that the initial dehydrogenation of butane was rate determining. The mechanism for this H abstraction has been studied in more detail by Millet [201]. 

When a reaction occurs in several consecutive steps, the rate of all steps must be equal at steady state (otherwise the system would not be at steady state). This rate is determined by the slowest step in the sequence, which we refer to as the rate-determining step (rds). In the preceding example, if k (e), the specific rate constant for step 8F, is much smaller than k (E), the specific rate constant for step 9F, the rate of the second step will effectively be limited by the supply of adsorbed intermediates Cl, namely, by the rate of the first step. 

With or without additives in the electrolyte, the charge-transfer Cu/Cu2+ occurs in two consecutive one-electron steps, with Cu+ being formed as an intermediate (Eq. (20)). The reduction of cupric ion is a slow reaction, whereas the reduction of cuprous ion to metallic copper is a fast one. This means that without additives the formation of Cu(I) ions is the rate-determining step. 

This mechanism assumes that the first step is very rapid and the second step is the rate determining step (which could proceed in a series of consecutive chain reactions). 

Most oxygen transfer reactions, such as CO -f HjO = CO2 + H2 or 2CO -h O2 = 2CO2 involve several consecutive steps. Thus, it is especially relevant to investigate reactions involving a single rate-determining step, e.g., the isotope exchange reactions... 

When it is necessary for a reaction to proceed through several successive elementary steps before the product is formed, the rate of the reaction is determined by the rates of all these steps. If one of these reactions is much slower than any of the others, then the rate will depend on the rate of this single slowest step. The slow step is the rate-determining step. The situation is analogous to water flowing through a series of pipes of different diameters. The rate of delivery of the water will depend on the rate at which it can pass through the narrowest pipe. An apt illustration of this feature of consecutive reactions is offered by the Lindemann mechanism of activation for unimolecular decompositions. 

This last reaction, the hydrolysis of coordinated nitriles, has been extensively studied by Ford and co-workers acidic hydrolysis of [Rh(NH3)5NCO] has been used as an alternate route to the hexaammine (equation 113). The reaction was shown to go through a carbamic acid intermediate, which was isolated and characterized. The kinetic study of the hexaammine formation was complicated by the presence of these two consecutive reactions, and by two different reaction paths. The mechanism proposed for the hydrolysis of the coordinated cyanate is shown in Scheme 14 at low acid concentrations (0.005 to 0.025 M) the rate determining step is HjO attack of the protonated species leading to a rate expression which is first-order in [H ] rate = ky [RhlfH" ]. At higher acid concentrations (0.2 to 1.0 M), decomposition of the carbamic acid complex is rate determining, and... 

For the adsorption of intermediates, involved in the consecutive reaction path, the type of isotherm is particularly important because it determines the relation of the kinetic parameter to the path and rate-determining step. 

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