Rate-determining step parallel reactions

The rate-determining step in the reaction of [Fe(bipy)3] +, [Fe(phen)3] +, or [Fe(terpy)2] + with peroxodiphosphate is dissociative - the breaking of an iron-nitrogen bond. It has been recognized for some time that these and related iron(n) complexes react with peroxodisulphate by parallel oxidative and dissociative rate-determining steps the reaction of the [Fe(ppsa)3] + cation mentioned above with peroxodisulphate provides a recent example of this behaviour. It is now apparent that any direct oxidation of this type of iron(n) complex with peroxodiphosphate is so slow that reaction proceeds entirely via rate-determining dissociation, presumably with subsequent rapid oxidation of the products of dissociation. 

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.

In some cases the original reaction with a slow rate-determining step may continue in parallel with the catalyzed reaction. However, the rate is determined by the faster path, which governs the overall rate of formation of products. A very slow elementary reaction does not control the rate if it can be sidestepped by a faster one on an alternative (usually catalyzed) path (Fig. 13.35). 

AU of the remarks above also apply to the case where a given reaction occurs along several parallel pathways. As a result of the principle of independence, the concept of a rate-determining step of the overall reaction becomes meaningless for such a reaction. 

It has been widely accepted that the carbene-transfer reaction using a diazo compound and a transition metal complex proceeds via the corresponding metal carbenoid species. Nishiyama et al. characterized spectroscopically the structure of the carbenoid intermediate that underwent the desired cyclopropanation with high enantio- and diastereoselectivity, derived from (91).254,255 They also isolated a stable dicarbonylcarbene complex and demonstrated by X-ray analysis that the carbene moiety of the complex was almost parallel in the Cl—Ru—Cl plane and perpendicular to the pybox plane (vide infra).255 These results suggest that the rate-determining step of metal-catalyzed cyclopropanation is not carbenoid formation, but the carbene-transfer reaction.254... 

The experimentally observed pseudo-first order rate constant k is increased in the presence of DNA (18,19). This enhanced reactivity is a result of the formation of physical BaPDE-DNA complexes the dependence of k on DNA concentration coincides with the binding isotherm for the formation of site I physical intercalative complexes (20). Typically, over 90% of the BaPDE molecules are converted to tetraols, while only a minor fraction bind covalently to the DNA bases (18,21-23). The dependence of k on temperature (21,24), pH (21,23-25), salt concentration (16,20,21,25), and concentration of different buffers (23) has been investigated. In 5 mM sodium cacodylate buffer solutions the formation of tetraols and covalent adducts appear to be parallel pseudo-first order reactions characterized by the same rate constant k, but different ratios of products (21,24). Similar results are obtained with other buffers (23). The formation of carbonium ions by specific and general acid catalysis has been assumed to be the rate-determining step for both tetraol and covalent adduct formation (21,24). 

The reaction goes faster in more polar solvents (a range of 106 in the rate constant) and parallels carbonium ion rearrangements in that respect. The effect of substituents in the para position of the benzoate group also suggests that the rate-determining step is the formation of an initial ion pair. The reaction is faster with the nitro than with the methoxyl substituent.819 820 The Hammett p value is 1.34. The activation parameters are not known for any but the unsubstituted member of the series however, and hence it is not known to what extent the relative rates depend upon the temperature. 

The zero slope found for transesterification (series 45) can be explained in accordance with the general view on acid-catalyzed reactions of organic acids and esters. The first step is the protonation of the acid or ester, which is followed by interaction with the alcohol (or water in ester hydrolysis). The absence of any observable influence of the alcohol structure on rate indicates that the rate-determining step must be the protonation of the ester. This is in contrast to the homogeneous reaction, in which this step is usually very rapid. The parallel dehydration of the alcohols exhibited a large structure effect on rate (Case 7 from Table II), confirming the independence of the two reaction routes. 

If a particular molecular entity(ies) participates in two or more parallel reactions and the proportion of the resulting products is determined by the relative equilibrium constants for the interconversion of reaction intermediates on or after the rate-determining step(s), then the more prevalent product is said to be thermodynamically controlled (i.e., the more stable product will be the one formed in highest amounts). If the reactions are reversible and the system is allowed to go to equilibrium, the favored product is the thermodynamically controlled species. A synonymous term is equilibrium control. See also Kinetic Control... 

In voltammetric experiments, electroactive species in solution are transported to the surface of the electrodes where they undergo charge transfer processes. In the most simple of cases, electron-transfer processes behave reversibly, and diffusion in solution acts as a rate-determining step. However, in most cases, the voltammetric pattern becomes more complicated. The main reasons for causing deviations from reversible behavior include (i) a slow kinetics of interfacial electron transfer, (ii) the presence of parallel chemical reactions in the solution phase, (iii) and the occurrence of surface effects such as gas evolution and/or adsorption/desorption and/or formation/dissolution of solid deposits. Further, voltammetric curves can be distorted by uncompensated ohmic drops and capacitive effects in the cell [81-83]. 

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. 

Kinetic and equilibrium studies of the sorption of methanol on various coals and on partially acety-lated samples of these coals have been used to elucidate a mechanism for this process. The data are interpreted in terms of partial acetylation blocking surface sites and perhaps interfering with intermolecular hydrogen bonding. It is proposed that the rate-determining step is a set of parallel, competing, second-order reactions involving transfer of methanol from the surface to the interior of the coal. All types of surface sites appear to participate, and the pressure-independent rate constant is considered to be the sum of the rate constants for each type of surface site. The dependence of the experimental rate constant on methanol pressure is a characteristic of the coal rank. 

The author thinks that the use of rate-determining step for photoreactions is misleading, since a photoreaction in principle proceeds via species in their excited state and they undergo both chemical reaction and deactivation (deexcitation). The assumption for rate-determining step is that the reaction proceeds sequentially, not in parallel, such as photoreactions. See Section TV.E. 

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