Reactions pseudo-diffusion

However, among reactions of radical recombination, Ifaere are isuch reactions for which exp ko but t), i.e., they are not limited by the translatory diffusion of reactants but depend, nevertheless, on the molecular mobility of the environment. They were named pseudo-diffusion reactions. They are the recombination of 2,6-disubstituted phenoxyls, whose substituents are phenyl, methoxy, and rer/-butyl groups. They are characterized by proportionality but xp is by 1, 2 or 3... 

If the data in Figure 13 are replotted against a.t0.3 as a pseudo Thiele-modulus, a single curve describing all the catalysts (Figure 15) results. Thus, the para-selectivity of a catalyst can be readily predicted from this empirical correlation and a knowledge of two basic catalyst properties, activity and diffusion time. Furthermore, these data are in full agreement with the model advanced above, which describes para-selectivity in terms of a classical diffusion-reaction interplay. 

Diffusion, reaction and the pseudo-steady-state hypothesis (with C. Georgakis). Math. Bioscl 25, 237-258 (1975). 

As is shown in Figure 2, in the two-phase model the fluid bed reactor is assumed to be divided into two phases with mass transfer across the phase boundary. The mass transfer between the two phases and the subsequent reaction in the suspension phase are described in analogy to gas/liquid reactors, i.e. as an absorption of the reactants from the bubble phase with pseudo-homogeneous reaction in the suspension phase. Mass transfer from the bubble surface into the bulk of the suspension phase is described by the film theory with 6 being the thickness of the film. D is the diffusion coefficient of the gas and a denotes the mass transfer coefficient based on unit of transfer area between the two phases. 6 is given by 6 = D/a. 

In this way, the diffusion/reaction equations are reduced to trial and error algebraic relationships which are solved at each integration step. The progress of conversion can therefore be predicted for a particular semi-batch experiment, and also the interfacial conditions of A,B and T are known along with the associated influence of the film/bulk reaction upon the overall stirred cell reactor behaviour. It is important to formulate the diffusion reaction equations incorporating depletion of B in the film, because although the reaction is close to pseudo first order initially, as B is consumed as conversion proceeds, consumption of B in the film becomes significant. 

Pore Mouth (or Shell Progressive) Poisoning This mechanism occurs when the poisoning of a pore surface begins at the mouth of the pore and moves gradmuly inward. This is a moving boundary problem, and the pseudo-steady-state assumption is made that the boundary moves slowly compared with diffusion of poison and reactants and reaction on the active surface. P is the fraction of the pore that is deactivated. The poison diffuses through the dead zone and deposits at the interface between the dead and active zones. The reactants diffuse across the dead zone without reaction, followed by diffusion-reaction in the active zone. 

The mean squared displacement and the diffusion coefficient are not always the most useful parameters to calculate. For instance, in cases where we are interested in a chemical reaction. Suppose we wish to calculate the time development of the concentration of a molecule A, free to move within a fractal space in which a great number of fixed molecules B have been scattered at random. Although they do not move, the B molecules can react with the A molecules. In chemical kinetics, this constitutes a pseudo-monomolecular reaction. In more simple terms, we are dealing with a survival problem in the presence of traps. What is the survival probability u N) for an A molecule after N steps If p is the probability that a site is occupied by a trap (so p is the number of traps divided by the number of sites) and if A reacts instantaneously with B as soon as they are juxtaposed on the same site,... 

Analysis of the transport and kinetics must be approached on two levels the first is essentially macroscopic. The steady-state Ficksian diffusion/reaction equation must be solved for the substrate in the bounded diffusion space of the film of extent L. This type of analysis has been discussed in previous sections of Chapter 2. From this analysis the pseudo first-order rate constant k for substrate reaction can be derived however the analysis must be taken a step further. We must also adopt a microscopic approach. In this case the spherical geometry of the microparticle must be considered, and the steady-state spherical diffusion of the substrate to the microparticle must be examined. We must then relate the macroscopic rate constant k for substrate reaction to the spherical diffusion and reaction at each microparticle. 

The heterogeneous catalytic reforming reactions are supposed to take place on the gas-solid interface. In heterogeneous catalysis no species enter into the solid phase, hence for this process the species mass balance are solved only in the gas phase. For the adsorption process the reaction actually takes place within the solid adsorbent material. However, in the modeling approach employed by Wang et al. [161] a pseudo-homogeneous reaction model was adopted so that the CO2 capture reaction was approximated by a particle surface reaction thus the overall diffusion... 

Cholanic acid also possesses the ability of transporting cations across a lipophilic membrane but the selectivity is not observed because it contains no recognition sites for specific cations. In the basic region, monensin forms a lipophilic complex with Na+, which is the counter ion of the carboxylate, by taking a pseudo-cyclic structure based on the effective coordination of the polyether moiety. The lipophilic complex taken up in the liquid membrane is transferred to the active region by diffusion. In the acidic region, the sodium cation is released by the neutralization reaction. The cycle is completed by the reverse transport of the free carboxylic ionophore. 

The rate of photolytic transformations in aquatic systems also depends on the intensity and spectral distribution of light in the medium (24). Light intensity decreases exponentially with depth. This fact, known as the Beer-Lambert law, can be stated mathematically as d(Eo)/dZ = -K(Eo), where Eo = photon scalar irradiance (photons/cm2/sec), Z = depth (m), and K = diffuse attenuation coefficient for irradiance (/m). The product of light intensity, chemical absorptivity, and reaction quantum yield, when integrated across the solar spectrum, yields a pseudo-first-order photochemical transformation rate constant. 

The cyclohexadienyl radicals decay by second-order kinetics, as proven by the absorption decay, with almost diffusion-controlled rate (2k = 2.8 x 109 M 1 s 1). The cyclohexyl radicals 3 and 4 decay both in pseudo-first-order bimolecular reaction with the 1,4-cyclohexadiene to give the cyclohexadienyl radical 5 and cyclohexene (or its hydroxy derivative) (equation 15) and in a second order bimolecular reaction of two radicals. The cyclohexene (or its hydroxy derivative) can be formed also in a reaction of radical 3 or... 

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