Rate determining step diffusion

Diffusion-limited rate control at high basicity may set in. This is more eommonly seen in a true Br nsted plot. If the rate-determining step is a proton transfer, and if this is diffusion controlled, then variation in base strength will not affect the rate of reaction. Thus, 3 may be zero at high basicity, whereas at low basicity a dependence on pK may be seen. ° Yang and Jencks ° show an example in the nucleophilic attack of aniline on methyl formate catalyzed by oxygen bases. 

In contrast to the influence of velocity, whose primary effect is to increase the corrosion rates of electrode processes that are controlled by the diffusion of reactants, temperature changes have the greatest effect when the rate determining step is the activation process. In general, if diffusion rates are doubled for a certain increase in temperature, activation processes may be increased by 10-100 times, depending on the magnitude of the activation energy. 

At medium and high temperatures copper ultimately follows the parabolic law " . It has been shown " using radioactive tracers that the diffusion of copper ions in cuprous oxide is the rate-determining step at 8(X)-1 000°C, and there is considerable evidence in favour of the view that metal moves outwards through the film by means of vacant sites in the oxide lattice . 

Even though the absolute rate constant for reactions between propagating species may be determined largely by diffusion, this does not mean that there is no specificity in the termination process or that the activation energies for combination and disproportionation are zero or the same. It simply means that this chemistry is not involved in the rate-determining step of the termination process. 

However, while it is generally accepted that the rate of radical-radical reaction is dependent on how fast the radical centers of the propagating chains (Pp and Pj ) come together, there remains some controversy as to the diffusion mechanism(s) and/or what constitutes the rate-determining step in the diffusion process. The steps in the process as postulated by North and coworkers30 3" arc shown conceptually in Scheme 5.5. 

Center of mass or translational diffusion is believed to be the rate-determining step for small radicals33 and may also be important for larger species. However, other diffusion mechanisms are operative and are required to bring ihe chain ends together and these will often be the major term in the termination rate coefficient for the case of macromolecular species. These include ... 

Values of 0 required to fit the rate of copolymerization by the chemical control model were typically in the range 5-50 though values <1 are also known. In the case of S-MMA copolymerization, the model requires 0 to be in the range 5-14 depending on the monomer feed ratio. This "chemical control" model generally fell from favor wfith the recognition that chain diffusion should be the rate determining step in termination. 

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. 

Pai Vemeker and Kannan [1273] observe that data for the decomposition of BaN6 single crystals fit the Avrami—Erofe ev equation [eqn. (6), n = 3] for 0.05 < a < 0.90. Arrhenius plots (393—463 K) showed a discontinuous rise in E value from 96 to 154 kJ mole-1 at a temperature that varied with type and concentration of dopant present Na+ and CO2-impurities increased the transition temperature and sensitized the rate, whereas Al3+ caused the opposite effects. It is concluded, on the basis of these and other observations, that the rate-determining step in BaN6 decomposition is diffusion of Ba2+ interstitial ions rather than a process involving electron transfer. 

RCS (.sec Rate-controlling step) Racemization, 49, 95 Rate constant calculation of. 17 composite, 161-164 diffusion-controlled, 200-201 Rate-controlling step, 9, 82-86 Rate-determining step (see Ratecontrolling step)... 

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,... 

Independently of this, chronoabsorptiometric measurements by Genies et al. have proved that PPy films grow in timer linear to t and not to j/t. In the opinion of the authors this implies that the rate-determining step during film growth is a radical ion coupling and not the diffusion of the uncharged monomer towards the electrode surface. The attested phenomenon that PPy polymerizes... 

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... 

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. 

Note that Eqs. (4) and (5) implicitly consider the transfer across the interface as the rate-determining step in the ion transfer processes [51], and neglect other steps involved in the process such as the ion transport across the diffusion boundary layers [55] and across the diffuse electrical double layer [50]. 

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 ... 

Methods for quantifying both the transcellular diffusion and concurrent metabolism of drugs and the unusual transcellular diffusion of membrane-interactive molecules coupled with the influence of protein binding are described in detail. To demonstrate the utility of cultured cell monolayers as a tool for basic science investigations, a subsection is devoted to the elucidation of rate-determining steps and factors in the passive diffusion of peptides across biological membranes. The chapter concludes with a discussion on the judicious use of in vitro cell monolayer results to predict in vivo results. 

Previously, the rate-determining step in the Caco-2 cell transmonolayer/ Transwell flux of testosterone was shown to be convective diffusion across the ABLs. Using the values for the 50 rpm situation in Table 11, Eqs. (78) and (79) become... 

In the second stage, substantial amounts of alkali and unfixed dyes are desorbed and diffuse from the fibre pores into the liquor phase. This is the diffusion stage and the rate-determining step is diffusion of the labile dye molecules out of the fibre phase. This takes time and is accelerated by higher temperatures and perhaps by mechanical agitation of the substrate. 

In liquids, collisional energy transfer takes place by multistep diffusion (the rate determining step) followed by an exchange interaction when the pair is very close. The bimolecular-diffusion-controlled rate constant is obtained from Smoluchowski s theory the result, including the time-dependent part, may be written as... 

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