Diffusion-controlled reaction rate constant

However, there is another operative timescale in solution. This is that timescale for reaction with other photolytically generated species or with added reactants. This reaction cannot take place faster than the diffusion-limited reaction rate which is concentration dependent (59). Typical diffusion-controlled reaction rate constants are 109-1010 dm3 mol"1 second-1. By comparison, a typical gas-kinetic rate con-... 

This is obviously incorrect as, on chemical grounds, the o-Ps and p-Ps reaction rate constants cannot be different the statistical spin substate factor should not appear in the rate at which the reaction occurs but rather, as in reaction XI, in the yield of the products of the reaction. Formally, reaction schemes XI and XII lead to exactly the same type of kinetic equations to describe the PALS parameters, particularly, A,3. However, if one wishes to compare the experimentally determined k with some theoretical expression such as the diffusion-controlled reaction rate constant, reaction XII will lead to a value of k which is 4 times lower than that yielded by reaction XI if o-... 

Table 4.4 Comparison between experimental Ps reaction rate constants (k ) and diffusion-controlled reaction rate constants calculated from eq. (18) by using either the bubble (kDd, Rb) or the free Ps (kD, RPs = 0.053 nm) radius, (a), unpublished results (b), [82] (c) [61] (d), [84], ox = oxidation sp = spin conversion bs = bound-state formation. The rate constants are in M W. NDMA N-dimethylacetamide 0-NO2 ...

We have already mentioned that Dorfman and collaborators have developed a versatile technique to observe ort-lived carbenium ions in solution generated by dissociative pulse radiolysis. This novel approach to the characterisation of transient species has also allowed this schod to measure the rate constants of many electrophilic reactions between carbenium ions (the benzylium ion in particular) and various nucleophiles. In the first paper of the series Jones and Dorfman reported the rate constants of the benzylium ion reaction with methanol, ethanol, the bromide and the iodide ions in ethylene chloride at 24 C. Values of about 5 x 10 sec were obtained for the halide ions and of around 10 sec for the alcohols. Later studies confirmed that the reaction of halide ions vrith benzylium, diphenyl-methylium and triphenylmethylium ions is at the limit of diffusion control. Reaction rate constants of these three carbenium ions with amines and alcdiols were also reported in the same paper. More recently, these studies have been extended to include cyclopropylphenylmetiiylium ion as electrophile, ammonia as nucleophile and methylene chloride and trichloroethane as solvents These results are extremely... 

Dependence of the intermacromolecular diffusion-controlled reaction rate constant for polystyrene samples of varying degree of polymerization and in several solvents... 

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

The diffusion-controlled reaction rate constant kx,y can be calculated as... 

In these circumstances a decision must be made which of two (or more) kinet-ically equivalent rate terms should be included in the rate equation and the kinetic scheme (It will seldom be justified to include both terms, certainly not on kinetic grounds.) A useful procedure is to evaluate the rate constant using both of the kinetically equivalent forms. Now if one of these constants (for a second-order reaction) is greater than about 10 ° M s-, the corresponding rate term can be rejected. This criterion is based on the theoretical estimate of a diffusion-controlled reaction rate (this is described in Chapter 4). It is not physically reasonable that a chemical rate constant can be larger than the diffusion rate limit. 

Quantitative data on rates of reaction have been obtained for some of the triplet reactions. Assuming triplet quenching to be approximately diffusion controlled, the rate constants for the reactions between excited species and nucleophile are 10 -10 1 mole s . The data show that in comparing and interpreting quantum yields—even in the case of related systems—one should proceed to determine separately rate constants as well as intersystem crossing efficiencies and lifetimes of the reacting excited species. 

The hydrated electron, if the major reducing species in water. A number of its properties are important either in understanding or measuring its kinetic behavior in radiolysis. Such properties are the molar extinction coefficient, the charge, the equilibrium constant for interconversion with H atoms, the hydration energy, the redox potential, the reaction radius, and the diffusion constant. Measured or estimated values for these quantities can be found in the literature. The rate constants for the reaction of Bag with other products of water radiolysis are in many cases diffusion controlled. These rate constants for reactions between the transient species in aqueous radiolysis are essential for testing the "diffusion from spurs" model of aqueous radiation chemistry. 

The crystallisation reaction is surface-controlled rather than volume diffusion-controlled. The rate constant was found to be independent of the stirring speed and the apparent activation energy for growth was deter-... 

A wide variety of molecules act as collisional quenchers. Molecular oxygen is one such quencher, possessing diffusion-controlled reaction rates (see Section 14.2.4). In the presence of a quenching agent, the lifetime (x) of a reactive intermediate is inversely proportional to the collisional quenching constant (Kq) and the concentration of the quencher, [Q], when the quenching reaction is diffusion controlled (Lakowicz, 1983) ... 

For all alcohols studied, a diffusion-controlled transfer rate constant of about 3 X 109M 1 sec. 1 was found in alkaline solution. In less basic solutions, however, where the alcohol radical was not dissociated, the transfer rate constant for the reaction... 

Determining the effect of solvent on the rate or course of a reaction can often provide insight into the reaction mechanism. One solvent property that may be important in extremely fast reactions is viscosity. If a reaction is encounter-controlled (also termed diffusion-controlled), the rate constant for the reaction is limited by the ability of the reacting species to reach other. For example, in aqueous solution, the second-order rate constant for the encoxmter of two species is ca. 10 °Lmol In such cases, changing fromalower viscosity... 

Comparatively little work has been done on the kinetics of complex formation between the alkali metal ions and simple ligands in view of the high rate constants and low stability constants involved. Atkinson has recently studied the ultrasonic absorption of the five alkali metal sulfates in water in the frequency range 25-250 MHz, where he found only one relaxation for each salt. The results are analyzed in terms of the normal two-step mechanism (the fast formation of an outer-sphere complex followed by rapid conversion to the inner-sphere complex) in which the rates of the two steps approach each other as the concentration of the solution decreases. (The concentrations were in the range 0.3-1.0 mol dm". ) As expected, the reactions are nearly diffusion controlled the rate constants for inner-sphere complex formation at 0.5 mol dm and 25°C are 1.0 x 10 s for Li, Na, Rb, and Cs sulfates but 2.0 x 10 s for the potassium salt. 

An important use of Brownian dynamics is for computation of the diffusionTControlled bimolecular rate constant. The diffusion equations can be related to the reaction rate via the flux at the r ctive surface. Smoluchowski showed that, for two spherical reactants with no interparticle forces, the analytical result for the diffusion-controlled bimolecular rate constant k is... 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

The reaction kinetics approximation is mechanistically correct for systems where the reaction step at pore surfaces or other fluid-solid interfaces is controlling. This may occur in the case of chemisorption on porous catalysts and in affinity adsorbents that involve veiy slow binding steps. In these cases, the mass-transfer parameter k is replaced by a second-order reaction rate constant k. The driving force is written for a constant separation fac tor isotherm (column 4 in Table 16-12). When diffusion steps control the process, it is still possible to describe the system hy its apparent second-order kinetic behavior, since it usually provides a good approximation to a more complex exact form for single transition systems (see Fixed Bed Transitions ). 

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