Diffusion rate constants

In solution the reaction of alkyl radical with dioxygen occurs extremely rapidly with a diffusion rate constant (see Table 2.4). The data on solubility of dioxygen in different organic solvents are collected in Table 2.2. 

Disproportionation of sterically nonhindered semiquinone radicals occurs with diffusion rate constants. On the other hand, sterically hindered semiquinone radicals react by several orders of magnitude more slowly (see Table 15.11). 

The efficiency and specificity of this method depends on the irreversibility of the whole process due to a high rate constant and favorable thermodynamics of Reaction (10) [4] and a high rate of subsequent Reaction (11) (which is the recombination of a free radical anion and a free radical cation with the diffusion rate constant of about 109 1 mol-1 s ). 

For complexation/dissociation reactions, ji corresponds with the average distance that M can travel following dissociation of ML (and prior to reassociation) [40,46]. Complexes are dynamic when M frequently changes from its free to complexed state during its diffusion time to the membrane surface or, in other words, if the first-order dissociation rate constant, k(, and the pseudo first-order formation rate constant, kf[L], are much larger than their effective diffusion rate constants (D/<52) [325,326]. Thus, for conditions of planar diffusion, complexes are labile if ... 

The ko, for free radical-02 reactions is found to be nearly equal to the diffusion rate constant (kdiff). For example, ko = 2.4 x 10 sec for the benzyl radical-02 reaction is... 

A comparison was made between the diffusion rate constant and that of hydroxyl disappearance at the wall. It was found that determinations corresponded to the kinetic range such that diffusion of radicals may be neglected. 

There are also certain data on electron tunneling in electron transfer reactions in liquids. The ideas about electron tunneling have been used by Anbar and Hart [75] to interpret the anomalously large rate constants for the diffusion controlled reactions of hydrated electrons with some inorganic anions in aqueous solution. Table 5 represents the data on the largest values of the rate constants, ke, observed for the reactions of eaq with various inorganic anions and cations. Theoretical diffusion rate constants, kA, for... 

The rate constants of reactions of hydrated electrons with some accep-tors-anions substantially exceed the diffusion rate constants calculated with the help of the Debye equation [Chap. 2, eqn. (45)l(see Chap. 2, Sect. 4). This excess is usually attributed to the capture of electrons by acceptors via tunneling at distances exceeding the sum of the reagents [28,89,111,1201- In this case, the tunneling distance can be estimated from experimental rate constants for reactions of eaq with acceptors [109] by means of the expression... 

Thus, the results of direct measurements of diffusion rate constants for reactions of etr with acceptors in water-alkaline matrices in the vicinity of the temperature of their devitrification corroborate the conclusion that long-range electron tunneling is the main channel of performing these reactions at low temperatures. 

A mathematical model has been developed to describe the kinetics of multicomponent adsorption. The model takes into account diffusional processes in both the solid and fluid phases, and nonlinear adsorption equilibrium. Comparison of model predictions with binary rate data indicates that the model predictions are in excellent for solutes with comparable diffusion rate characteristics. For solutes with markedly different diffusion rate constants, solute-solute interactions appear to affect the diffusional flows. In all cases, the total mixture concentration profiles predicted compares well with experimental data. 

Here X is the rate constant that would occur without diffusion limitation d is the diffusion rate constant which characterizes the catalyst and the reaction conditions. For X Xrf no diffusion limitation occurs and Xoxp = X. For X Xdiffusion-limited and Xexp = sjXX,j. 

Kinetic Models Including Diffusion Rate Constants... 

Although different models of diffusion rate constants have been proposed in the literature, one must bear in mind that it is very difficult to capture the evolution of the system in the glassy state with a simple mathematical model. The main problem is the physical aging that occurs in parallel with the advance in conversion. Physical aging produces a densifica-tion of the glass, which brings two consequences ... 

A simpler semiempirical relationship was proposed by Chern and Poehlein (1987), based on free volume considerations. The diffusion rate constant is defined as... 

We note that the effective rate constant k is determined by both the diffusion rate constant kp and the reaction rate constant k s. Let us consider two limits. If k D -c then the effective rate constant is seen to be k kp, that is, the rate constant is... 

The square of this number represents the ratio between the maximum reaction rate of ozone near the water interface (film thickness) and the maximum physical absorption rate (i.e., the absorption without reaction). In Eq. (9), kD and kL are parameters representing the chemical reaction and physical diffusion rate constants, that is, the rate constant of the ozone-compound reaction and water phase mass transfer coefficient, respectively. Their values are indicative of the importance of both the physical and chemical steps in terms of their rates. However, two additional parameters, as shown in Eq. (9), are also needed the concentration of the compound, CM, and the diffusivity of ozone in water, Z)0i. The ozone diffusivity in water can be calculated from empirical equations such as those of Wilke and Chang [55], Matrozov et al. [56], and Johnson and Davies [57] from these equations, at 20°C, D0 is found to be 1.62xl0 9, 1.25xl0-9, and 1.76xl0 9 m2 s 1, respectively. 

The chemical significance of the Bunzl rate law can be appreciated by examining the roles played by the parameters it contains. Its principal dependence on the film diffusion mechanism, for example, is epitomized in the film diffusion rate constant (Eq. 4.66)... 

Depending on the distribution chosen, as few as three fitting parameters may be required to define a distribution of diffusion rates. In some cases, a single distribution was used to describe both fast and slow rates of sorption and desorption, and in other cases fast and slow mass transfer were captured with separate distributions of diffusion rates. For example, Werth et al. [42] used the pore diffusion model with nonlinear sorption to predict fast desorption, and a gamma distribution of diffusion rate constants to describe slow desorption. 

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