Carbonic diffusion-limitation

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

It has been shown that the development of wormholes in carbonate rocks is a consequence of diffusion-limited (mass-transfer-limited) kinetics of attack (6). Such kinetics prevail in most of these rocks, i.e. limestones and dolomites, providing that, for the latter, the temperature is larger than about 200°F (90°C) (7-8). 

The book focuses on three main themes catalyst preparation and activation, reaction mechanism, and process-related topics. A panel of expert contributors discusses synthesis of catalysts, carbon nanomaterials, nitric oxide calcinations, the influence of carbon, catalytic performance issues, chelating agents, and Cu and alkali promoters. They also explore Co/silica catalysts, thermodynamic control, the Two Alpha model, co-feeding experiments, internal diffusion limitations. Fe-LTFT selectivity, and the effect of co-fed water. Lastly, the book examines cross-flow filtration, kinetic studies, reduction of CO emissions, syncrude, and low-temperature water-gas shift. 

During conventional polymerizations of both HEMA and DEGDMA, complications resulting from diffusion limitations to termination and propagation are observed. Features such as autoacceleration, autodeceleration and incomplete conversion of double bonds characterize the rate behavior of these polymerizations. As TED is added to the reacting system, the carbon-DTC radical termination reaction is introduced. Diffusion limitations to carbon-DTC radical combination are lower than those to carbon-carbon radical termination as the DTC radical is smaller and much more mobile than a typical polymeric carbon radical. As a result, the cross-... 

It can be observed that the initial rate of polymerization decreases and the autoacceleration peak is suppressed as the TED concentration is increased. The TED molecules generate dithiocarbamyl (DTC) radicals upon initiation. As a result, termination may occur by carbon-carbon combination which leads to a dead polymer and by carbon-DTC radical reaction which produces a reinitiatable ( living ) polymer. The cross-termination of carbon-DTC radicals occurs early in the reaction (with the carbon-carbon radical termination), and this feature is observed by the suppression of the initial rate of polymerization. As the conversion increases, the viscosity of the system poses mass transfer limitations to the bimolecular termination of carbon radicals. As has been observed in Figure 3, this effect results in a decrease in the ktCC. However, as the DTC radicals are small and mobile, the crosstermination does not become diffusion limited, i.e., the kinetic constant for termination of carbon-DTC radicals, ktCS, does not decrease. Therefore, the crosstermination becomes the dominant reaction pathway. This leads to a suppression of the autoacceleration peak as the carbon-DTC radical termination limits the carbon radical concentration to a low value, thus limiting the rate of polymerization. This observation is in accordance with results of previous studies (10) with XDT and TED, where it was found that when there was an excess of DTC radicals, the carbon radical concentration was lower and the cross-termination reaction was the dominant termination pathway. 

In this paper, the kinetics and polymerization behavior of HEMA and DEGDMA initiated by a combination of DMPA (a conventional initiator) and TED (which produces DTC radicals) have been experimentally studied. Further, a free volume based kinetic model that incorporates diffusion limitations to propagation, termination by carbon-carbon radical combination and termination by carbon-DTC radical reaction has been developed to describe the polymerization behavior in these systems. In the model, all kinetic parameters except those for the carbon-DTC radical termination were experimentally determined. The agreement between the experiment and the model is very good. 

Whichever mechanism operates, it appears to be generally true that singlet aromatic carbenes react with the lower alcohols to form ethers at rates approaching the diffusion limit. On the other hand, aromatic carbenes that are clearly triplets do not give any ether at all from reaction with alcohols. Instead, these triplets behave as is expected of biradicals and abstract a hydrogen atom from the oxygen bearing carbon of the alcohol. The stable products of this reaction are those due to the combination and disproportionation (10) of the pair of radicals (Lapin et al., 1984). The more com-... 

The reaction of FL with methyl alcohol gives the ether (92%). This process plays a pivotal role in the analysis of the properties of this carbene. The results are analysed within the spin-specific reaction framework where the ether is taken to be the product of the singlet carbene and this reaction rate is approximately diffusion limited (as it is for JXA). It is further assumed that 3FL will react with methyl alcohol as does 3BA, i.e., by hydrogen-atom abstraction from carbon, a relatively slow process in comparison with reaction of the singlet carbene (see Table 7). 

In combustion of solids such as charcoal, a reaction occurs between carbon and O2 from the air in diffusion-limited reactions. More than 1000 years ago the Chinese found that when... 

As a result of that reductive process, a deposit of copper metal (denoted in Eq. 2.2 by s for solid ) is formed on the carbon electrode surface. The prominent anodic peak recorded in the reverse scan corresponds to the oxidative dissolution of the deposit of copper metal previously formed. The reason for the very intense anodic peak current is that the copper deposit is dissolved in a very small time range (i.e., potential range) because, in the dissolution of the thin copper layer, practically no diffusion limitations are involved, whereas in the deposition process (i.e., the cathodic peak), the copper ions have to diffuse through the expanding diffusion layer from the solution to the electrode surface. These processes, labeled as stripping processes, are typical of electrochemically deposited metals such as cadmium, copper, lead, mercury, zinc, etc., and are used for trace analysis in solution [84]. Remarkably, the peak profile is rather symmetrical because no solution-like diffusive behavior is observed. 

The studies of Hasinoff [53] on the recombination rate of carbon monoxide and the heme units after photodissociation of carboxy ferrous microperioxidase come close to satisfying the requirements for observing the effects of anisotropic reactivity and rotational diffusion on the rate of a translational diffusion-limited reaction. In Chap. 2, Sect. 5.6, the details of this study were briefly mentioned. Hasinoff found that the rate of recombination was substantially diffusion-limited in all three aqueous solvents used at 260 K, but at higher temperatures, the rate of reaction of the encounter pair, feact, was a significant factor in determining the overall rate of recombination (see Fig. 9). The observed rate coefficient of recombination, feobs, was separated into the rate coefficient of diffusive formation of encounter pairs, feD, and the rate coefficient of reaction of encounter pairs, fcact, with the Collins and Kimball expression, eqn. (26)... 

Since M0 is greater than Mc, the displacement of the carbon atom should be initially greater than the displacement of the oxygen atom which in turn should be greater than the displacement of the C.M. Since 1 — is positive for t > 0, the above order of displacements should persist for all time. That is, provided the translational-rotational term can be neglected. In the diffusion limit, or equivalently, for long times we have... 

In order for an interventional catalyst to have an effect on the rate, it must accelerate the net rate of diffusion (the physical process of diffusion will not change but the reversion will be slowed). It must either make carbon dioxide or the carbanion less reactive. Since the process that slows reversion must compete with diffusion, it cannot itself be diffusion-limited. This can be achieved by the reaction being intramolecular or by the catalyst being associated with the reactant prior to the formation of the initial products, a process known as pre-association.11 16... 

Carbonic anhydrase II, present in human red blood cells (RBCs), catalyzes the reversible hydration of C02. It is one of the most efficient enzymes and only diffusion-limited in its turnover numbers. The catalytic Zn11 is ligated by three histidine residues and OH this ZnOH+ structure renders the zinc center an efficient nucleophile which is able to attack the C02 molecule and capture it in an adjacent hydrophobic pocket. The catalytic mechanism is shown in Figure 9.5. 

Reactions of carbocations with free CN- occur preferentially at carbon, and not nitrogen as predicted by the principle of hard and soft acids and bases.69 Isocyano compounds (N-attack) are only formed with highly reactive carbocations where the reaction with cyanide occurs without an activation barrier because the diffusion limit has been reached. A study with the nitrite nucleophile led to a similar observation.70 This led to a conclusion that the ambident reactivity of nitrite in terms of charge control versus orbital control needs revision. In particular, it is proposed that SNl-type reactions of carbocations with nitrite only give kinetically controlled products when these reactions proceed without activation energy (i.e. are diffusion controlled). Activation controlled combinations are reversible and result in the thermodynamically more stable product. The kinetics of the reactions of benzhydrylium ions with alkoxides dissolved in the corresponding alcohols were determined.71 The order of nucleophilicities (OH- MeO- < EtO- < n-PrCT < / -PrO ) shows that alkoxides differ in reactivity only moderately, but are considerably more nucleophilic than hydroxide. 

The reaction of cyanide ion with substituted benzhydryl carbenium ions to form nitriles and isocyanides is controlled by the rates of reaction at carbon and nitrogen.124 In slow reactions, far from the diffusion limit, the attack is completely at the cyanide carbon. Very fast reactions, with little or no reaction barrier reacting at the diffusion-controlled limit, occur at both the N and the C of the cyanide ion. XN2 reactions occur almost exclusively at carbon regardless of the substrate or source of the cyanide ion. The HSAB principle cannot predict the products of these reactions. 

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