Electrostatic Effects in Liquid Solution

The cage effect described above is also referred to as the Franck-Rabinowitch effect (5). It has one other major influence on reaction rates that is particularly noteworthy. In many photochemical reactions there is often an initiation step in which the absorption of a photon leads to homolytic cleavage of a reactant molecule with concomitant production of two free radicals. In gas phase systems these radicals are readily able to diffuse away from one another. In liquid solutions, however, the pair of radicals formed initially is trapped in a cage formed by surrounding solvent molecules and often will recombine before they can diffuse away from one another. This phenomenon is referred to as primary recombination, as opposed to secondary recombination, which occurs when free radicals combine after having previously been separated from one another. The net effect of primary recombination processes is to reduce the photochemical yield of radicals formed in the initiation step for the reaction. 

In dilute solutions it is possible to relate the activity coefficients of ionic species to the composition of the solution, its dielectric properties, the temperature, and certain fundamental constants. Theoretical approaches to the development of such relations trace their origins to classic papers by Debye and Huckel (6-8). For detailed treatments of this subject, refer to standard physical chemistry texts or to treatises on electrolyte solutions [e.g., that by Hamed and Owen (9)]. The Debye-Hiickel theory is useless for quantitative calculations in most of the reaction systems encountered in industrial practice because such systems normally employ concentrated solutions. However, it may be used together with transition state theory to predict the qualitative influence of ionic strength on reaction rate constants. 

For a bimolecular reaction between species A and B, the analysis gives an equation of the form 

If limiting forms of the Debye-Hiickel expression for activity coefficients are used, this equation becomes 

This equation, known as the Br0nsted-Bjerrum equation, may be derived in several ways. It predicts that a plot of log k versus the square root of the ionic strength should be linear over the range of ionic strengths for which the Debye-Hiickel limiting law is applicable. The slopes of such lines are nearly equal to the product of the ionic charges of the reactants Z Zg. 

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