Diffusion-limited, bimolecular elementary

Solution reactions that are much slower than diffusion-limited reactions are called activation-limited reactions. After an encounter occurs, the molecules undergo numerous collisions inside a cage of other molecules before finally reacting. The rate of collisions is very large (see Example 9.12), but only a small fraction of them will lead to reaction. If this fraction depends only on the temperature, the rate will be proportional to the number of encounters as well as to the fraction of collisions that lead to reaction. Since the number of 2-3 encounters is proportional to the number of type 2 molecules and the number of type 3 molecules, an activation-limited bimolecular elementary reaction is first order with respect to each reactant and second order overall, just as with a diffusion-limited reaction and a gas-phase reaction. The rate of a reaction between molecules of the same substance is second order with respect to that substance, and its temperature dependence should be similar to that of a gas-phase reaction. 

Instead of concentrating on the diffusion limit of reaction rates in liquid solution, it can be instructive to consider the dependence of bimolecular rate coefficients of elementary chemical reactions on pressure over a wide solvent density range covering gas and liquid phase alike. Particularly amenable to such studies are atom recombination reactions whose rate coefficients can be easily investigated over a wide range of physical conditions from the dilute-gas phase to compressed liquid solution [3, 4]. 

Diffusion-Controlled Encounter. Elementary bimolecular reaction mechanisms require diffiisional encovmter before the reaction. If the intrinsic kinetics are fast, and/or the viscosity of the solution is high, diffusion-controlled encounter may occur. In a homogeneous medium, a rate constant /jdiff can be evaluated which reflects the effective bulk-averaged rate constant associated with bimolecular encounters (45). Diffusional bimolecular encounter should be considered in the appropriate context. If Areact is the intrinsic bimolecular rate constant and djff is the differential rate constant defined above, then the observed rate constant for the bimolecular reaction is given by equation (11) (46). The limiting cases of this equation can be readily identified that is when the rate constant is very large, the observed rate constant corresponds to the diffusional rate constant. 

A theory for the rate of a bimolecular elementary diffusion-limited process was developed by Smoluchowski. The first version of the theory was based on the assumption that molecules of type 2 are diffusing toward stationary molecules of type 3. On the average, the motion of type 2 molecules toward the fixed molecules of type 3... 

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