Quantitative treatment of bimolecular reactions

Although Eqn. 3 is successful in treating unimolecular and micellar inhibited bimolecular reactions it cannot be applied directly to micellar catalyzed bimolecular reactions, because it considers only the distribution of one reactant between aqueous and micellar pseudophases. The rate of a bimolecular reaction will depend on the distribution of both reactants between the two pseudophases [4-6,25,61]. 

A problem in estimating second-order rate constants of solution reactions is that they depend upon the units of concentration, which are chosen arbitrarily. Typically molarity is the chosen unit, because it is a very convenient measure of concentration. However, even in non-micellar systems, assessment of solvent effects upon second-order rate constants depends directly upon our choice of the concentration unit. Relative second-order rate constants in a variety of solvents will, in general, be different if the concentration unit is molarity instead of mole fraction, for example. 

We have exactly the same problem in micellar systems. The important parameter is concentration in the micellar pseudophase, which can be calculated in various ways. One approach is to calculate molarity in terms of moles of reagent per 1 of micelles, and the micellar volume can be estimated from micellar density, which is close to unity. But the micelle is probably not uniform in composition, and if reaction occurs in the Stern layer, at the micelle-water interface, it might be more reasonable to use the volume of that layer, rather than that of the whole micelle. In any event the volumes of the micelle and the Stern layer probably are within a factor 

Another approach, which will be followed here, is to evade the question by defining concentrations in terms of the mole ratio of reagent to micellar head group. This concentration unit is unambiguous, but rate constants so determined cannot be compared directly with those in the bulk solvent which have the units of reciprocal molarity. However, one set of units can be converted into the other using the molar volume of the micelle, or its Stern layer. 

In Eqns. 6 and 7 the quantities in squared brackets are molarities written in terms of total solution volume. 

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