Solvent Effects on Polar and Ionic Reactions

Equations will be presented for three cases—the second-order reactions of two polar molecules, two ions, and one of each. The result in each case suggests a linear relation between the logarithm of the rate constant and the inverse of the dielectric constant of the solvent. 

The first case to be taken up is that for polar molecules. Kirkwood8 has developed an expression for the free energy of transfer of a polar molecule from a medium of unit dielectric constant to one with a value e. If the dipole moment of the molecule is denoted as jx and its radius as r, AGtr is 

One then assumes that the predominant kinetic factor arises from electrostatic interactions between the solute and solvent. They are the result of the dipole-dipole forces described by Eq. (9-28). The rate constant is thus 

An alternative electrostatic model9 leads to a similar expression  

Here kref corresponds to e = , a change from that used in Eqs. (9-29)—(9-30). Because (e - l)/(2e + 1) is proportional to 1/e, except at very low e (see Problem 9-5), these formulations are equivalent. An example of these treatments is presented in Fig. 9-1, which shows the data from Table 9-2, for reaction (9-2). The slope of the plot of ln k versus 1/e is negative, which is consistent with the obvious fact that the transition state is more polar than the reagents. The agreement is not spectacular, but it rarely is in this correlation. The problem is that dipole-dipole interactions are rather small, and other forces (van der Waals and repulsive interactions) are not entirely negligible. 

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