Reactants, radial distribution

In this equation g(r) is the equilibrium radial distribution function for a pair of reactants (14), g(r)4irr2dr is the probability that the centers of the pair of reactants are separated by a distance between r and r + dr, and (r) is the (first-order) rate constant for electron transfer at the separation distance r. Intramolecular electron transfer reactions involving "floppy" bridging groups can, of course, also occur over a range of separation distances in this case a different normalizing factor is used. 

In the conventional Debye-Huckel treatment the equilibrium radial distribution function for a pair of reactants g(r) is simply equal to exp(-w/RT) with w given by (15)... 

Unlike premixed flames, which have a very narrow reaction zone, diffusion flames have a wider region over which the composition changes and chemical reactions can take place. Obviously, these changes are principally due to some interdiffusion of reactants and products. Hottel and Hawthorne [5] were the first to make detailed measurements of species distributions in a concentric laminar H2-air diffusion flame. Fig. 6.5 shows the type of results they obtained for a radial distribution at a height corresponding to a cross-section of the overventilated flame depicted in Fig. 6.2. Smyth et al. [2] made very detailed and accurate measurements of temperature and species variation across a Wolfhard-Parker burner in which methane was the fuel. Their results are shown in Figs. 6.6 and 6.7. 

The radial distribution of the reactant concentrations in the spherical catalyst particle is theoretically given as ... 

Because the solvent molecules are usually of a similar size to the reactants, the assumption that reactants diffuse in a structureless and isotropic continuum is not very satisfactory. Liquids possess short-range order. Solvent molecules are several times more likely to be separated by a distance equal to their diameter than separated by about one and a half diameters. More details are revealed by the radial distribution function [see Figs. 38 (p. 216) and 44 (p. 235)]. This implies that there is an... 

Typical forms of the radial distribution function are shown in Fig. 38 for a liquid of hard core and of Lennard—Jones spheres (using the Percus— Yevick approximation) [447, 449] and Fig. 44 for carbon tetrachloride [452a]. Significant departures from unity are evident over considerable distances. The successive maxima and minima in g(r) correspond to essentially contact packing, but with small-scale orientational variation and to significant voids or large-scale orientational variation in the liquid structure, respectively. Such factors influence the relative location of reactants within a solvent and make the incorporation of the potential of mean force a necessity. 

The parametric areas of five regimes are identified for two values of the diffusion ratio. Typical radial concentration profiles associated with each physical picture are also shown. In this case, the boundary for the kinetically controlled regime is given by the value of the Damkohler number so that the effectiveness factor is kept, for example, above 0.9. Since in this case conversion in the channel is negligible, the reactant concentration distribution at the interface with the coating is uniform and close to the inlet value. 

Figure 8.4 shows the optimized TS structure for the Menshutkin reaction in the isolated state and that in aqueous solution obtained by the FEG method. The optimized values of / n-c and l c-ci for TS in solution are 1.97 and 2.07 A, respectively. In comparison with those lengths in the isolated state, it is found that the TS in solution shifts toward the reactant side. Moreover, the distance between NH3 and Cl group of TS in solution (1 n-ci = 4.04 A) becomes larger than that in the isolated state (/ n i = 3.90 A). Such stmctural deformation should enhance the charge separation of the solute complex, and consequently brings about the FE stability of TS. In fact, from the radial distribution functions (RDFs) with respect to... 

If the two competing reactions have the same concentration dependence, then the catalyst pore structure does not influence the selectivity because at each point within the pore structure the two reactions will proceed at the same relative rate, independent of the reactant concentration. However, if the two competing reactions differ in the concentration dependence of their rate expressions, the pore structure may have a significant effect on the product distribution. For example, if V is formed by a first-order reaction and IF by a second-order reaction, the observed yield of V will increase as the catalyst effectiveness factor decreases. At low effectiveness factors there will be a significant gradient in the reactant concentration as one moves radially inward. The lower reactant concentration within the pore structure would then... 

The reactor itself consists of a chamber that is thermally insulated from the surroundings. The reactants, which are a preheated mixture of fuel and air, dilute or concentrated, are injected through numerous radial nozzles and enter the reaction zone as small sonic jets. Because of the high-intensity turbulent mixing, temperature and concentrations can ideally be assumed to be homogeneously distributed. The rapid mixing thus results in sampled compositions that are purely kinetically controlled. The mixture of reactants and products exits through a number of radial ports. 

In general, the effects of mass-transport limitations are not as easy to characterize. The direction of fluid flow, the flow regime, and the local fluid velocity all influence the current distribution. Fluid flow to the rotating disk is unusual in that fluid velocity normal to the disk is dependent only on the normal distance from the disk surface, and not on radial distance. Because the disk surface is uniformly accessible to incoming reactants, mass-transport limitations tend to reduce the current density in regions of high... 

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