Controlled Reactions of Uncharged Nonpolar Species in Solution

Diffusion-Controlled Reactions of Uncharged Nonpolar Species in Solution 

Let us first consider a very fast reaction between uncharged nonpolar reactants in solution. In this case, the rate is controlled by the number of encounters. Once A and B diffuse into the same solvent cage, they will react hence the rate of these diffusion-controlled reactions is determined by how fast A and B diffuse together in solution. 

Fick s first law describes the rate of diffusion of a species A in solution across an area E in the direction 

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  

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. 

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