Bulk rate-determining step

Differentiation of surface and bulk rate-determining step... 

From the above considerations, a plot of hydrogen flow rate as a function of the difference of pressure or the difference of pressure roots should be used to assess the presence of either surface or bulk rate-determining steps. 

Calderbank et al. (C6) studied the Fischer-Tropsch reaction in slurry reactors of 2- and 10-in. diameters, at pressures of 11 and 22 atm, and at a temperature of 265°C. It was assumed that the liquid-film diffusion of hydrogen from the gas-liquid interface is a rate-determining step, whereas the mass transfer of hydrogen from the bulk liquid to the catalyst was believed to be rapid because of the high ratio between catalyst exterior surface area and bubble surface area. The experimental data were not in complete agreement with a theoretical model based on these assumptions. 

In addition, assuming that the rate-determining step is the bulk diffusion (i.e.,ka/(DJt) lholds), we can derive the minimum dissolution current observed after the fluctuation-diffusion current, that is,... 

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

The effectiveness of a crude oil demulsifier is correlated with the lowering of the shear viscosity and the dynamic tension gradient of the oil-water interface. The interfacial tension relaxation occurs faster with an effective demulsifier [1714]. Short relaxation times imply that interfacial tension gradients at slow film thinning are suppressed. Electron spin resonance experiments with labeled demulsifiers indicate that the demulsifiers form reverse micellelike clusters in the bulk oil [1275]. The slow unclustering of the demulsifier at the interface appears to be the rate-determining step in the tension relaxation process. 

Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. 

This dissolution process can be considered to be diffusion-layer controlled. This is best explained by considering the rate of diffusion from the solid surface to the bulk solution through an unstirred liquid film as the rate-determining step. This dissolution process at steady state is described by the Noyes-Whitney equation ... 

Here A(g) and B(g) denote reactant and product in the bulk gas at concentrations CA and Cg, respectively kAg and kBg are mass-transfer coefficients, s is an adsorption site, and A s is a surface-reaction intermediate. In this scheme, it is assumed that B is not adsorbed. In focusing on step (3) as the rate-determining step, we assume kAg and kBg are relatively large, and step (2) represents adsorption-desorption equilibrium. 

The rates of reaction of both enantiomers of amino-acid esters in the presence of (S)-[324] are the same, but with (S)-[323] they are in most cases different. The reactions of L-amino acid esters in the presence of (S)-[323] are faster than those in the presence of (R)-[323] by factors of 9.2 (R = i-Pr), 8.2 (R = C6H5CH2) and 6.0 (R = i-Bu). No difference in rates is observed for L-alanine p-nitrophenyl ester. The results were explained in terms of the formation of diastereomeric tetrahedral intermediates [325] and [326]. The bulk of the group R will determine how much the complex stability of the (D)-complex decreases relative to that of the (L)-complex, which difference is reflected in the activation energy of the rate-determining step. 

Hoftyzer and van Krevelen [100] investigated the combination of mass transfer together with chemical reactions in polycondensation, and deduced the ratedetermining factors from the description of gas absorption processes. They proposed three possible cases for poly condensation reactions, i.e. (1) the polycondensation takes place in the bulk of the polymer melt and the volatile compound produced has to be removed by a physical desorption process, (2) the polycondensation takes place exclusively in the vicinity of the interface at a rate determined by both reaction and diffusion, and (3) the reaction zone is located close to the interface and mass transport of the reactants to this zone is the rate-determining step. 

In many reactions, transfer of the anion across the interface and subsequent diffusion into the bulk of the organic phase will not be the rate-determining step when lipophilic catalysts are used, but the effect of less lipophilic catalysts may be influenced more by the anion and the mechanism of the transfer process. Thus, for example, the reactive anion is frequently produced in base-initiated reactions by proton extraction from the substrate at the two-phase interface and diffusion of the ion-pair contributes to the overall kinetics of the reaction. Additionally, the reactivity of the anion depends on its degree of hydration and on its association with the quaternary ammonium cation. In most situations, the activity of the transferred anion is enhanced, compared with its reactivity in aqueous media, as its degree of hydration is reduced, whereas a relatively weak electrostatic interaction between the two ions resulting from the bulkiness of the cation enhances the reactivity of the anion by making it more available for reaction and will be a major factor in the ratedetermining step. 

The resting state of the propanoate catalysts may well be an acyl complex [60,61], while the attack of alcohol at the acylpalladium complex is considered to be the rate-determining step. It is probably more precise to say that fast preequilibria exist between the acyl complex and other complexes en route to it and that the highest barrier is formed by the reaction of alcohol and acylpalladium complex. The precise course of the reaction is still not known presumably deprotonation of the coordinating alcohol and the migratory elimination are concerted processes, accelerated by the steric bulk of the bidentate ligand. Toth and Elsevier showed that the reaction of an acetylpalladium complex and sodium methoxide is very fast and occurs already at low temperature to give methyl acetate and a palladium(I) hydride dimer [46]. 

The success of the Potts-Guy equation led many authors to advocate a single mechanism as the rate determining step for permeation through the skin barrier for all or at least a wide range of solutes diffusion was assumed to occur primarily via the interkeratinocyte lipids of the stratum corneum, a mixture of ceramides, fatty acids, and sterols. While from a macroscopic point of view these lipids may be modeled as a bulk solvent, on a microscopic scale they... 

The kinetics of MeOH oxidation of a 1 1 PfRu in an MEA has been well established by Vidakovic, Christov, and Sundmacher. At low overpotentials, the MeOH oxidation reaction was found to be zero order in MeOH concentration, indicating that CO oxidation is the rate-determining step. A Tafel slope of 50-60 mV dec was found at 60°C. At higher overpotentials, positive reaction orders were found, suggesting that MeOH adsorption becomes rate determining. An activation energy of 55 kj moP was found this agrees well with the values found for similar bulk PtRu electrodes. 

Electrode reactions are analogous to the growth of tarnishing (corrosion) layers (Weppner and Huggins, 1977). Assuming that bulk transport is the rate determining step, the growth rate of the reaction product is inversely proportional to the instantaneous thickness L... 

Since perchlorate ions, and more generally the majority of anions used in common electrolyte systems, are known to move rapidly in liquid solutions, it is reasonable to assume that the rate determining step in controlling the kinetics of the overall process is the ion diffusion throughout the polymer fibrils. This conclusion has been experimentally confirmed. For example, the diffusion coefficient of electrolyte counterions in bulk polyacetylene has been determined (Will, 1985) to be seven orders of magnitude lower than in liquid electrolytes, namely about 10 cm s vs 10 cm s ... 

Equations 2.26 and 2.27 carmot be solved analytically except for a series of limiting cases considered by Bartlett and Pratt [147,192]. Since fine control of film thickness and organization can be achieved with LbL self-assembled enzyme polyelectrolyte multilayers, these different cases of the kinetic case-diagram for amperometric enzyme electrodes could be tested [147]. For the enzyme multilayer with entrapped mediator in the mediator-limited kinetics (enzyme-mediator reaction rate-determining step), two kinetic cases deserve consideration in this system in both cases I and II, there is no substrate dependence since the kinetics are mediator limited and the current is potential dependent, since the mediator concentration is potential dependent. Since diffusion is fast as compared to enzyme kinetics, mediator and substrate are both approximately at their bulk concentrations throughout the film in case I. The current is first order in both mediator and enzyme concentration and k, the enzyme reoxidation rate. It increases linearly with film thickness since there is no... 

Case 3 There are two interfacial rate-determining steps, consisting of 1) formation of an interfacial complex between the interfacially adsorbed molecules of the extractant and the metal ion and (2) transfer of the interfacial complex from the interface to the bulk organic phase and simultaneous replacement of the interfacial vacancy with bulk organic molecules of the extractant. For this mechanism, we distinguish two possibilities. The first (case 3.1) describes the reaction with the dissociated anion of the extracting reagent, B"(ad). The second (case 3.2) describes the reation with the undissociated extractant, BH(ad). 

Adsorption of chlorobenzene on pc-Au electrode has been studied by Czerwinsld and Sobkowski [316] as early as in 1980, using a radiotracer technique. The rate-determining step of this adsorption was diffusion of the reactant. Chlorobenzene was adsorbed in multilayers at sufficiently high bulk concentration. The adsorbed molecules were probably oriented vertically with respect to the Au surface and bounded to it via a Cl atom. 

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