Encounter-controlled rate

A reaction velocity equal to the rate of encounter of reacting molecular entities (also known as diffusion-con-trolled rate). For a bimolecular reaction in aqueous solutions at 25°C, the corresponding second-order rate constant for the encounter-controlled rate is typically about 10 ° M s See Diffusion Control for Bimolecular Collisions in Solution... 

ENCOUNTER-CONTROLLED RATE DIFFUSION-LIMITED REACTION CHEMICAL KINETICS DIFFUSION OF LIGAND TO RECEPTOR DIFFUSION OF MOLECULES INTO A PORE... 

STEREOCHEMICAL TERMINOLOGY, lUPAC RECOMMENDATIONS ENANTIOSELECTIVE REACTION ASYMMETRIC INDUCTION ENCOUNTER COMPLEX ENCOUNTER-CONTROLLED RATE DIFFUSION CONTROL FOR BIMOLECULAR COLLISIONS ENDERGONIC PROCESS ENDO-a (or j8)-N-ACETYLGALACTOSAMI-NIDASE... 

ENCOUNTER-CONTROLLED RATE SECOND-ORDER REACTiON CHEMICAL KINETICS ORDER OF REACTION NOYES EQUATION MOLECULARITY AUTOCATALYSIS FIRST-ORDER REACTION... 

An example of the application of this test to a compound that nitrates as its free base is provided by pyridine 1-oxide. Under an identical set of conditions, nitration of this N-oxide had a half life of 20 min, whilst 1-methoxypyridinium gave no nitro compound in 144 h. Two further criteria have been used to provide confirmatory evidence, namely comparison of the rate of nitration for the reactive species with the encounter controlled rate, and by determination of the Arrhenius parameters. 

On the assumptions that the triplet TMB biradical 37 is the reactive intermediate and that its reaction with O2 occurs at the encounter-controlled rate, the authors estimated that the triplet is more stable than the singlet by at least 4-5 kcal/mol, or more if the diffusion-limited trapping rate assumed is actually lower. 

Encounter complex (or precursor complex) — is a complex of -> molecular entities produced at an - encounter-controlled rate, and which occurs as an intermediate in a reaction mechanism. If the complex is formed from two molecular entities, it is called an encounter pair . A distinction between encounter pairs and (larger) encounter complexes may be relevant in some cases, e.g., for mechanisms involving pre-association. 

Encounter-controlled rate — A -> reaction rate corresponding to the rate of encounter of the reacting -> molecular entities. This rate is also known as diffusion-controlled rate since rates of encounter are themselves controlled by -> diffusion rates (which in turn depend on the - viscosity of the medium and the dimensions of the reactant molecular entities). For a bi-molecular reaction between solutes in water at 25 °C an encounter-controlled rate is calculated to have a second-order rate constant of about 1010 dm3 mol-1 s 1. 

For a bimolecular reaction between solutes in water at 25°C, an encounter-controlled rate is calculated to have a second-order rate constant of about 1010 dm3 mol-1 sec-1. 

If (hypothetically) a bimolecular reaction in a homogeneous medium occurred instantaneously when two reactant molecular entities made an encounter, the rate of reaction would be an encounter-controlled rate, determined solely by rates of diffusion of reactants. Such a hypothetical fully diffusion-con-trolled rate is also said to correspond to total microscopic diffusion control and represents the asymptotic limit of the rate of reaction as the RATE constant for the chemical conversion of the encounter pair into product (or products) becomes large relative to the rate constant for separation (or dissociation) of the encounter pair. 

Consider a dilute solution of two reactant molecules, A and B. Inevitably an A molecule and a B molecule will undergo an encounter, the frequency of such encounters depending upon the concentrations of A and B. If, upon each encounter of A and B, they undergo bimolecular reaction, then the rate of this reaction is determined solely by the rate of encounter of A and B that is, the rate is not controlled by the chemical requirement that an energy barrier be overcome. One way to find this rate is to treat the problem as one of classical diffusion, and so this maximum possible rate of reaction is often called the diffusion-controlled rate. This problem was solved by Smoluchowski. In the following development no provision is made for attractive forces between the molecules. ... 

This value, often approximated as 1010 L mol"1 s 1, is referred to as the diffusion-controlled rate constant. It is rather insensitive to the chemical species that participate in the reaction. A larger molecule diffuses more slowly than a smaller one, but that effect is roughly compensated by a higher probability of encounter given its larger radius. 

Following Noyes (1961), one may write (fe))1 = kdif + and kj = T km, where fedifr is the diffusion-controlled rate, is the rate of final the chemical step, and t) is the reaction efficiency in that step. Denoting the first electronO-scavenger encounter probability from an initial separation rg by P(rg), the pair reaction prob-abilty in given by... 

Alkyl radicals react in solution very rapidly. The rate of their disappearance is limited by the frequency of their encounters. This situation is known as microscopic diffusion control or encounter control, when the measured rate is almost exactly equal to the rate of diffusion [230]. The rate of diffusion-controlled reaction of free radical disappearance is the following (the stoichiometric coefficient of reaction is two [233]) ... 

The discrepancy between calculated and experimental AHf° value of 162 was resolved as it turned out that the latter has to be considered as the upper limit resulting from the assumption of the interception of 162 by 302 under encounter control. However, the numerical simulation of the experimental rate data was also perfectly successful by imposing an activation barrier of 7 kcal mol-1 on the trapping step [13], This brought the AH/ of 162 down to 78 kcal mol-1 above that of benzene [13], in good agreement with calculated values [13,116,117]. 

For bimolecular second-order reactions and for trimolecular reactions, if the reaction rate is very high compared to the rate to bring particles together by diffusion (for gas-phase and liquid-phase reactions), or if diffusion is slow compared to the reaction rate (for homogenous reaction in a glass or mineral), or if the concentrations of the reactants are very low, then the reaction may be limited by diffusion, and is called an encounter-controlled reaction. 

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. ... 

A somewhat unusual approach is encountered when high-speed motion picture cameras of the Hycam type are used as a streak camera. This is accomplished by filming through the camera s viewfinder which bypasses the prism system that normally cuts up the scene into frames or pictures. After nearly one-fourth of the film has run through the camera the voltage-controlled rate of film travel is reasonably steady and can be used for velocity measurements. 

Such bimolecular quenching reactions occur at diffusion controlled rates. A probability P for reaction per encounter may be included. The rate constant terms in (5.61) become... 

In Chaps. 3 and 4, estimates of encounter distances and mutual diffusion coefficients from similar experiments to those of Buxton et al. [18] are discussed. The complications to the analysis of diffusion-controlled rate processes in solution when the reactants interact strongly with one another or the reaction can occur over distances much larger than typical encounter distances do not lead to markedly different time-dependent rate coefficient expressions to the Smoluchowski form. Indeed, replacing R in eqn. (29) by an effective encounter distance, Reff, allows the compactness of the Smoluchowski rate coefficient to be extended to other situations. Means of estimating Reff are discussed in Chaps. 3, 4, 5 (Sect. 4.3), 8 (Sect. 2.6) and 9 (Sects. 4 and 6). 

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