Diffusion-controlled rate constant determination

In liquids, collisional energy transfer takes place by multistep diffusion (the rate determining step) followed by an exchange interaction when the pair is very close. The bimolecular-diffusion-controlled rate constant is obtained from Smoluchowski s theory the result, including the time-dependent part, may be written as... 

In practice, the amount of solid molecules on the surface being exposed to the solution is difficult or even impossible to quantify. Instead, the solid surface area to solution volume ratio is often used to quantify the amount of solid reactant. Therefore, experimentally determined second-order rate constants for interfacial reactions have the unit m s h As the true surface area of the solid is very difficult to determine, the BET (Brunauer-Emmett-Teller) surface area is fte-quentiy used. The maximum diffusion-controlled rate constant for a particle suspension containing pm-sized particles is ca 10 m s and for mm-sized particle suspensions the corresponding value is I0 m s h Unfortunately, the discrepancy between the true surface area and the BET surface area and the non-spherical geometry of the solid particles makes it impossible to exactly determine the theoretical diffusion-controlled rate constant. 

For many systems A is of the order 10 L mol s, that is, close to the diffusion-controlled rate constant Ana- This suggests that in these cases quenching is so rapid that the rate-determining step is the actual diffusion of the molecules to form an encounter complex. Thus,... 

Similar radiolytic yields of phenoxyl radicals have been fonnd in CH2CI2 solntions. The radiolysis of this solvent appeared to be simpler than that of CCLj and permitted determination of rate constants for reactions of Cl atoms. Both phenol and p-methoxyphenol react with diffusion-controlled rate constants (2.5 x 10 ° and 5 x... 

Absolute rate constants have been determined for aromatic triplet formation in acetone solutions of several aromatic compounds (5, 30). The formation curves were observed directly for anthracene and naphthalene triplet (5) and for diphenyl triplet. These rate curves were found to fit a first order rate law, and were interpreted as a bimolecular energy transfer process from a state of the solvent molecule which is probably the triplet, that is, by Reaction 11. These rate constants, as well as the triplet yields, are listed in Table VI. The rate constants for anthracene and naphthalene triplet formation appear to correspond to diffusion controlled rate constants. Two further points are of interest, which are in contrast with observations in other systems which will be discussed. In acetone, most of the yield of aromatic triplet (at concentrations of the aromatic compound of 5 X 10"3M or lower) is formed in diffusional processes such as collisional energy transfer. Any fast formation appears... 

The use of this model leads to derived rate constants which exceed the diffusion-controlled limit. Further n.m.r. studies and a reconsideration of earlier published experimental data lead to a new proposal of an associative mechanism for iodide exchange, in which iodide attacks at one end of the tri-iodide. It is possible, from the observed kinetic pattern, that the I so generated has a sufficient lifetime to be considered an intermediate rather than a transition state. A transfer diffusion investigation of the same reaction also culminates in the proposal of an associative mechanism, with a linear transition state. Allowing for the non-spherical nature of the tri-iodide, it is possible to calculate a diffusion-controlled rate constant, which turns out to be the same as the experimentally determined (by this method or from n.m.r.) second-order rate constant. Some calculations on the transition state have been made in connection with this transfer diffusion study of the iodide-tri-iodide exchange reaction. Further study of the iodide-thiocyanate reaction has resulted in an estimate of the association constant for the initial rapid association of the reactants to give the intermediate charge-transfer complex la.SCN-. ... 

Both investigations also reported the pulse radiolysis of solutes dissolved in ionic liquids. Behar et al. studied the effect of the presence of Oj and CCI4 in [bmim][PF6] their results suggested that the latter was a more effective radical scavenger. They also looked at the formation of the radical cations of chlorpromazine (ClPz-+) andN,N,7 r, N -tetramethyl-p-phenylenediamine (TPMD- ) in the same solvent. Finally, the kinetics of oxidation of ClPz in [bmim][PF( ] were studied. The experimentally determined bimolecular rate constant values were corrected for the high viscosity of the ionic liquid by estimation of the values of the diffusion-controlled rate constant, using Equation (5.3),... 

The reaction between nitroxides and carbon-centered radicals occurs at near (but not at) diffusion controlled rates. Rate constants and Arrhenius parameters for coupling of nitroxides and various carbon-centered radicals have been determined.508 311 The rate constants (20 °C) for the reaction of TEMPO with primary, secondary and tertiary alkyl and benzyl radicals are 1.2, 1.0, 0.8 and 0.5x109 M 1 s 1 respectively. The corresponding rate constants for reaction of 115 are slightly higher. If due allowance is made for the afore-mentioned sensitivity to radical structure510 and some dependence on reaction conditions,511 the reaction can be applied as a clock reaction to estimate rate constants for reactions between carbon-centered radicals and monomers504 506"07312 or other substrates.20... 

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. 

D.. .. to here, where the oxidation of I occurs at a diffusion-controlled rate. After a prescribed electrolysis time t, the potential is stepped back to the initial potential, C. Only the reduction of the unreacted carbonium ion II occurs at this potential. The value of the pseudo-first-order rate constant, k[, is then determined from a dimensionless working curve that relates the ratio of the cathodic and anodic currents to k,t. Details for the construction of the working curves (each ratio of tr/t requires a different working curve) and their subsequent use may be found in the literature [8]. 

It is discussed above that the nucleobase radical anions can be proton-ated at a heteroatom and/or carbon. Only the heteroatom-protonated species retains reducing properties, and thus the rate of protonation at carbon determines whether or not an ET to 5BrUra is observed under the given condition. Protonation at carbon is especially fast in the case of Guo, and for this reason an ET to 5BrUra was not observed (Nese et al. 1992). A compilation of the rate constants for such ET reactions is found in Table 10.26. As can be seen from this table, the radical anions transfer an electron to 5BrUra at practically diffusion-controlled rates, while the heteroatom-protonated species react two orders of magnitude more slowly. 

First-order release obeying Fick s first law of diffusion the rate constant a controls the release kinetics, and the dimensionless solubility-dose ratio determines the final fraction of dose dissolved [90]. 

Other electron-transfer reaction rates which have been measured are those between phenothiazine cation-radical (249) and dimethyl- and tetra-methyl-p-phenylenediamines. Electron transfer takes place at the diffusion-controlled rate equilibrium constants were determined which demonstrated the greater stability of the Wurster s radicals over 249. This... 

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