Rate constant diffusion-controlled, reactive

Assuming diffusion controlled quenching, the rate constants for deactivation and for reaction of the triplet excited state could be calculated. The rate constant for triplet deactivation kj equals 4.1 10 s l and rate constant for triplet reactivity kj equals 2.2 10 M"ls"l. 

The effect of ionic environment on the rate of diffusion controlled e"aq reactions is revealed when one compares the experimental rate constants with the calculated values. In Table I the highly charged bis-pentacyano cobaltic peroxide (I) is much more reactive than expected for a pentavalent anion (1.11). It has been claimed (19) that polyvalent anions exhibit a lower effective charge in their kinetic behavior than expected from their structural formulae. We have checked the salt effect on the reaction of I + e m and compared it with the NOjf e m reaction. The results presented in Table IV and Figure 1 show that nitrate ions possess a normal salt effect, a result previously obtained by competition kinetics (15, 17). On the other hand, the salt effect of the I + e"aq reaction shows that this bis-pentacyano cobaltic peroxide ion has an... 

K is the reactivity rate constant, D is a constant, and is the critical extent of curing at which the glassy state is attained. Because switching from a reactivity-controlled reaction takes place gradually, the overall rate constant k (x, T) can be expressed using the Rabinovitch model [13] in terms of the Arrhenius rate constant (k) or reactivity rate constant (k ) and diffusion rate constant (k ) as follows [19, 20] ... 

The reactivity of macromonomers in copolymerizalion is strongly dependent on the particular comonomer-macromonomer pair. Solvent effects and the viscosity of the polymerization medium can also be important. Propagation may become diffusion controlled such that the propagation rate constant and reactivity ratios depend on the molecular weight of the macromonomer and the viscosity or, more accurately, the free volume of the medium. 

The sum of all results is consistent with the formation of both the aryl cation and the aryl radical in the aqueous acid system without copper, and with the dominance of the aryl radical in the presence of copper. The product ratios are also qualitatively consistent with the hypothesis that the reactivity of aryl cations with nucleophiles is close to that of a diffusion-controlled process (see Sec. 8.3), and that aryl radicals have arylation rate constants that are about two orders of magnitude smaller than that for diffusion control (0.4-1.7 X 107 m-1s-1 Kryger et al., 1977 Scaiano and Stewart, 1983). Due to the relatively low yields of these dediazoniations in the pentyl nitrite/benzene systems, no conclusions should be drawn from the results. 

Table 12-2 gives some of Sterba s results for 1-naphthol, resorcinol, 1-methoxy-naphthalene, 3-methoxyphenol and 1,3-dimethoxybenzene. The data in the table show that the 1-naphthoxide ion is 108 times more reactive than the undissociated naphthol, which is 102 times more reactive than 1-methoxynaphthalene. The rate ratios for the monoanion of resorcinol relative to resorcinol, 3-methoxyphenol, and 1,3-dimethoxybenzene are of similar magnitudes. The dissociation of both OH groups of resorcinol gives rise to a rate constant (2.83 X 109 m -1 s-1) which, in our opinion, is probably mixing- or diffusion-controlled (see Sec. 12.9). 

A minor component, if truly minute, can be discounted as the reactive form. To continue with this example, were KCrQ very, very small, then the bimolecular rate constant would need to be impossibly large to compensate. The maximum rate constant of a bimolecular reaction is limited by the encounter frequency of the solutes. In water at 298 K, the limit is 1010 L mol-1 s"1, the diffusion-controlled limit. This value is derived in Section 9.2. For our immediate purposes, we note that one can discount any proposed bimolecular step with a rate constant that would exceed the diffusion-controlled limit. 

Several assumptions were made in order to analyze kinetic data in terms of this expression (2). First it was assumed that k 2 m kj, k2 k 3, and kj/k j k /k ( - If). Second it was assumed that the rate constants were independent of the extent of reaction i.e., that all six functional groups were equally reactive and that the reaction was not diffusion controlled. The concentration of polymer hydroxyl functionality was determined experimentally using infrared spectroscopy as described elsewhere (7). A major unknown is the instantaneous concentration of methanol. Fits to the kinetic data were made with a variety of assumptions concerning the methanol concentration. The best fit was achieved by assuming that the concentration of methanol was initally constant but decreased at a rate proportional to the concentration of residual polymer hydroxy groups towards the end of the reaction. As... 

Reaction of nitric oxide with superoxide is undoubtedly the most important reaction of nitric oxide, resulting in the formation of peroxynitrite, one of the main reactive species in free radical-mediated damaging processes. This reaction is a diffusion-controlled one, with the rate constant (which has been measured by many workers, see, for example, Ref. [41]), of about 2 x 109 1 mol-1 s-1. Goldstein and Czapski [41] also measured the rate constant for Reaction (11) ... 

The results obtained in Ref 30 for partially diffusion-controlled recombination show that the field dependence of the recombination rate constant is affected by both the reaction radius R and the reactivity parameter p [cf. Eq. (33)]. Depending on their relative values, the rate constant can be increased or decreased by the electric field. The latter effect predominates at low values of p, where the reactants staying at the encounter distance are forced to separate by the electric field. 

In this case of uncharged, nonpolar reactions, there is little interaction between the reactants and the solvent. As a result, the solvent does not play an important role in the kinetics per se, except through its role in determining the solubility of reactive species and cage effects. The rate constants for such reactions therefore tend to be similar to those for the same reactions occurring in the gas phase. Thus, as we saw earlier, diffusion-controlled reactions in the gas phase have rate constants of 10-ll) cm3 molecule-1 s-1, which in units of L mol-1 s-1 corresponds to 6 X 1010 L mol-1 s-1, about equal to (usually slightly greater than) that for diffusion-controlled reactions in solution. 

Aryl radical additions to anions are generally very fast, with many reactions occurring at or near the diffusion limit. For example, competition studies involving mixtures of nucleophiles competing for the phenyl radical showed that the relative reactivities were within a factor of 10, suggesting encounter control,and absolute rate constants for additions of cyanophenyl and 1-naphthyl radicals to thiophenox-ide, diethyl phosphite anion, and the enolate of acetone are within an order of magnitude of the diffusional rate constant. ... 

At higher concentrations in solution, the photodimerization of tS has been studied by means of picosecond electronic absorption spectroscopy. The 5i state of tS in benzene at 22°C is quenched with a diffusion-controlled rate constant of 2.03 X lO M s to give a new reactive intermediate exhibiting an absorption maximum at 480 nm. This new species decays unimolecularly with a rate constant of (2.40 0.37) X 10 s. It has tentatively been assigned to either the excimer or a biradicaloid species located at the pericyclic minimum. 

Rate constants for the reaction of each purine nucleoside, fcnuc, were estimated based on the known values of kj for 75n and 75o that had previously been determined under identical solvent and temperature conditions. The results indicate that k uc levels off at ca. 2.0 x 10 M s for the most reactive purine nucleosides (Table 3). It was suggested that this was the approximate diffusion-controlled limit for reaction of these ions with purine nucleosides. 

Rate constants for the reaction of hydroxyl radicals with different compounds were determined by Haag and Yao (1992) and Chramosta et al. (1993). In the study of Haag and Yao (1992) all hydroxyl radical rate constants were determined using competition kinetics. The measured rate constants demonstrate that OH0 is a relatively nonselective radical towards C-H bonds, but is least reactive with aliphatic polyhalogenated compounds. Olefins and aromatics react with nearly diffusion-controlled rates. Table 4-3 gives some examples comparing direct (kD) and indirect (kR) reaction rate constants of important micropollutants in drinking water. 

The extension of equilibrium measurements to normally reactive carbocations in solution followed two experimental developments. One was the stoichiometric generation of cations by flash photolysis or radiolysis under conditions that their subsequent reactions could be monitored by rapid recording spectroscopic techniques.3,4,18 20 The second was the identification of nucleophiles reacting with carbocations under diffusion control, which could be used as clocks for competing reactions in analogy with similar measurements of the lifetimes of radicals.21,22 The combination of rate constants for reactions of carbocations determined by these methods with rate constants for their formation in the reverse solvolytic (or other) reactions furnished the desired equilibrium constants. 

Choride ion is considerably less reactive than the azide ion. Thus, although values of kc 1/ kn2o have been quite widely available from mass law effects of chloride ion on the solvolysis of aralkyl halides, normally the reaction of the chloride ion cannot be assumed to be diffusion controlled and the value of kn2o cannot be inferred, except for relatively unstable carbocations (p. 72). Mayr and coworkers251 have measured rate constants for reaction of chloride ion with benzhydryl cations in 80% aqueous acetonitrile and their values of logk are plotted together with a value for the trityl cation19 in Fig. 7. There is some scatter in the points, possibly because of some steric hindrance to reaction of the trityl cations. However, it can be seen that chloride ion is more... 

The dilemma presented by these conflicting results was resolved by TaShma and Rappoport.265 They pointed out that the apparent dependence of kAz/ knl0 upon the reactivity of the carbocation arose because even the most stable cation reacting with azide ion did so at the limit of diffusion control. Thus while kn2o remained dependent on the stability of the cation in the manner illustrated in Fig. 7 the rate constant for the azide ion remained unchanged. Thus the most stable cation formed in the solvolysis reactions was the trityl ion, for which direct measurements of kn2o = 1 -5 x 105 s 1 and kAz = 4.1 x 109 now show that even for this ion the reaction with azide ion is diffusion controlled.22... 

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