Kirkwood-Westheimer equation

That values of yj and 7r vary with the reaction and the reaction conditions is readily seen from the results reported in Table XLVIII for the rrans-vinylene group. Values of yj for this group range from 1.01 to 3.28. That the value of yj is dependent upon the reaction is no surprise. Charton has shown (251,252) that the yj values may be calculated from the Kirkwood-Westheimer equation in the form... 

A substantial amount of structural and acidity data on pentaammineruthenium(III) complexes with purines and similar ligands has been correlated through the modification of the Kirkwood-Westheimer equation given in Eq.(l). Such a correlation can only be expected to hold when dealing with the same metal ion similarly coordinated to the identical tautomeric form of a rigid ligand for which the pK value is known. In addition, this relationship is valid only over a fairly narrow range of r (between 3.3 and 5.6 A). 

It should be noted that Kirkwood s formula does not appear in his first publication [240] in the form of Eq. (5-86). Nevertheless, it is this form of Kirkwood s formula which is widely known, representing only one of the terms of a more complex equation given in reference [240] with n= Kirkwood s theory was further developed in papers by Kirkwood, Westheimer, and Tanford [241], Laidler and Landskroener [242], and Hiromi [243]. 

Clearly, if one takes a smaller value of D, one gets a higher value of IVj j, for a given distance Rufj. Kirkwood and Westheimer (1938), Westheimer and Kirkwood (1938), and Westiieimer and Shookhoff (1939) indeed argued that one should take a much smaller dielectric constant, since the intervening medium between the two protons more closely resembles a hydrocarbon liquid rather than water. In fact, for any dicarboxylic acid one can define an effective dielectric constant to fit the experimental value of W, by an equation of the form (4.8.13), with Dg being dependent on the proton-proton distance, the type and size of the acid and the solvent. 

In a major contribution to the understanding of transmission of substituent effects in organic molecules, Westheimer and co-workers (Kirkwood and Westheimer, 1938 Westheimer and Kirkwood, 1938 Westheimer and Shookhoff, 1939 Westheimer et al., 1942) pointed out that the electrostatic field of a charged or dipolar substituent is at least partially transmitted through the molecule itself. Because the dielectric constant of an organic molecule is much smaller than that of a polar solvent such as water, substituent effects are attenuated with increasing distance to a much smaller extent than predicted by Equations (5) and (6). Kirkwood and Westheimer described methods for computation of the effective dielectric constant for a molecule-solvent system. The use of the effective dielectric constant (Dea) in place of the solvent s dielectric constant (D) in Equations (5) and (6) greatly improved the quantitative capabilities of electrostatic models of substituent effects. 

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