Rate constants for diffusion-controlled reactions

Note that the rate constant for diffusion controlled reactions between a proton and.a base decreases by a factor of 0.3 to 0.5 for each positive charge added to the base. 

Starting with Fick s first law, one can calculate for a solution of two reactants A and B the frequency of A-B encounters, which is in effect the reaction rate constant for diffusion-controlled reactions. This is given by the following, in units of L mol 1 s-1 ... 

Rate constants for diffusion-controlled reactions can be calculated from the laws of diffusion [18, 869]. For a simple cage reaction A -I- B AB, in which A reacts with B every time the two approach one another to within a distance R, the following equation can be derived,... 

As is known, rate constants for diffusion-controlled reactions can be described by the Debye-Smoluchowski equation ... 

The process of energy transfer requires that the excited donor diffuse to the proximity of an acceptor within the time period of its excited lifetime. This is subject to the viscosity of the medium and the efficiently of the collision process and the range r in which the collisions can occur. The observed rate constant for energy transfer et is governed by the molecular rate constant for diffusion-controlled reaction. This is defined by the Debye equation ... 

Bimolecular association rate constant Rate constant for dissociation Rate constant for Dexter energy transfer Rate constant for diffusion-controlled reactions Rate constant for fluorescence... 

Theory of rate constants for diffusion-controlled reactions... 

Separation of an ion-pair to free ions, with rate constant d, has been used as a clock for other reactions of the ion pair. Estimates of d can be obtained from the simple relationship between the association constant for ion-pair formation (Xas, equation (2)) and the rate constant for diffusion-controlled encounter... 

Thus, bimolecular rate constant depends only on the viscosity and the temperature of the solvent. The calculated rate constants for diffusion-controlled bimolecular reactions in solution set the upper limit for such reactions. 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

The last comprehensive review of reactions between carbon-centered radicals appeared in 1973.142 Rate constants for radical-radical reactions in the liquid phase have been tabulated by Griller.14 The area has also been reviewed by Alfassi114 and Moad and Solomon.145 Radical-radical reactions arc, in general, very exothermic and activation barriers are extremely small even for highly resonance-stabilized radicals. As a consequence, reaction rate constants often approach the diffusion-controlled limit (typically -109 M 1 s"1). 

The Smoluchowski theory for diffusion-controlled reactions, when combined with the Stokes-Einstein equation for the diffusion coefficient, predicts that the rate constant for a diffusion-controlled reaction will be inversely proportional to the solution viscosity.16 Therefore, the literature values for the bimolecular electron transfer reactions (measured for a solution viscosity of r ) were adjusted by multiplying by the factor r 1/r 2 to obtain the adjusted value of the kinetic constant... 

The rate constants for reaction of Bu3SnH with the primary a-alkoxy radical 24 and the secondary ce-alkoxy radical 29 are in reasonably good agreement. However, one would not expect the primary radical to react less rapidly than the secondary radical. The kinetic ESR method used to calibrate 24 involved a competition method wherein the cyclization reactions competed with diffusion-controlled radical termination reactions, and diffusional rate constants were determined to obtain the absolute rate constants for the clock reactions.88 The LFP calibrations of radical clocks... 

A reaction whose rate is limited (or controlled) only by the speed with which reactants diffuse to each other. For a ligand binding to a protein, the bimolecular rate constant for diffusion-limited association is around 10 M s. The enzyme acetylcholinesterase has an apparent on-rate constant of 1.6 x 10 M s with its natural cationic substrate acetylcholine, and the on-rate constant of about 6 X 10 with acetylselenoylcholine and about... 

It is natural to conclude that the high rate constants for electron attachment reactions in nonpolar liquids are associated with the high mobility of electrons. Early studies [96,104,105] of attachment to biphenyl and SFg emphasized the dependence of on mobility. This relationship is apparent if the expression for the rate constant for a diffusion-controlled reaction ... 

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. 

Favorable proton transfers between electronegative atoms such as O, N, and S are extremely fast. The bimolecular rate constants are generally diffusion-controlled, being 1010 to 10" s-1 A/-1 (Table 4.2). For example, the rate constant for the transfer of a proton from H30+ to imidazole, a favorable transfer since imidazole is a stronger base than H20, is 1.5 X 1010 s 1 M l (Table 4.3). The rate constant for the reverse reaction, the transfer of a proton from the imidazolium ion to water, may be calculated from the difference in their p a s by using the following equations ... 

Values of for chloride ions have been determined by combining a rate constant for solvolysis ksoiv (for reactions for which the ionization step is ratedetermining) with a rate constant for the reverse reaction corresponding to recombination of cation and nucleophile. The latter constant may be found (a) by generating the cation by photolysis and measuring directly rate constants for reactions with nucleophiles or (b) from common ion rate depression of the solvolysis reaction coupled with diffusion-controlled trapping by a competing nucleophile used as a clock. 

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. 

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