Reactions of Charged Species in Solution

If the reactants are ionic with opposite charges, the rate constant can be greater than 1010 L mol -1 s-1 due to the favorable attractive forces. For example, the rate constant for the reaction of H+ with OH- in aqueous solutions at 25°C is 10n L mol-1 s-1. On the other hand, the electrostatic repulsion between ions of like sign can significantly slow their reaction. Similarly, if the reactants are polar molecules, electrostatic forces between them and the solvent may come into play. 

For ions and polar molecules, the nature of the solvent is an important factor in solution-phase reactions. Following the derivation of Laidler and Meiser (1982), we first consider the reaction between two ions A and B with charges ZAe and ZL e, respectively, where e is unit electronic charge and ZA and Zu are the number of unit charges on the ions, i.e., are whole positive or negative numbers. The electrostatic force (F) between these two ions separated by a distance r in a vacuum is given by Coulomb s law, 

As seen in Section A.3.b, the transition state form of the rate constant is given by 

The free energy of activation AG0 for bringing two ions to the necessary distance dAU in order to react is given by equation (KK). Thus the natural logarithm of the rate constant becomes 

Equation (LL) predicts that the rate constant for the reaction between two ions in solution will depend on the dielectric constant e, and hence the nature of the solvent. A plot of In k against 1 /e should be a straight line with slope of — (ZAZ13e2/4 7T 0 7A1Jk7 ). From the slope, dA]i can be obtained. Experimentally, it is found that Eq. (LL) is indeed followed in many cases. 

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