Stability constants statistically corrected

We now have a sufficient number of conditions to determine the relationship between the measured equilibrium constants, K), K2,-, Km, and the statistically corrected constants, K), K2, ..., Km. The statistical corrections to be applied to the experimental stability constants are shown in Table 19.1 for the most common coordination numbers. 

Many correlations have been made between the stability constants for a series of complexes and other properties. For example, basicity of the ligands, ionic radii, dipole moments, and other properties have been correlated with the stability constants of the complexes. However, before comparisons such as these are made, the stability constants should be corrected statistically to take into account the fact that successive complexes do not have the same probability of forming. 

Note that in the first case, the Cl ion is approaching an aqua complex that carries a + 3 overall charge. In the second case, the Cl is approaching as aquapentachloro complex that already carries a negative charge (—2), which is electrostatically unfavorable. Therefore, even after statistical correction of the stability constants is made, there is a great deal of difference in the likelihood that [M(H20)5C1]2+ and MCI 3 will form (the values of Kt and K6). 

The fact that the stability constants of monodentate ligand complexes of polyion systems are comparable in magnitude with those of the simple molecule resembled, once corrected for the electrostatic effect, is consistent with expectation based on the statistical arguments discussed earlier. The absence of multidentate complex formation is also predictable. Whereas the formation of MA is not affected by the low accessibility of the polyion species, MA and A, their nonideality, and canceling in the mass action expression for the formation of MA (f +/f - = 1), this is not the case for the bidentate species, because f /(f -) = l/f -, the nonideality term for 1/A" remaining uncanceled. The tendency for bidentate complex formation is, on this basis alone, a factor of f - less likely. 

As indicated by the statistically corrected equilibrium constants in Table 1 for the reaction defined in Scheme 8, the values are all >1, revealing that deuterium prefers to be in the C-H site rather than the M-H site due to greater vibrational stabilization. This point has been appreciated by many authors, in particular with respect to both EIEs and KIEs associated with methane loss from M(CH3)H systems. 

The vertical equilibria are hypothetical processes in which the end groups of the monomers are exchanged. The stability of a cyclic -mer does not depend whether its monomeric constituents are of the type A—B or A—A + B—B, thus the equilibrium constant at the right is equal to 1. As to the equilibrium at the left, if we consider a process in which the end groups are statistically scrambled, we obtain at equilibrium 25% A—A, 25% B—B, and 50% A—B, corresponding to an equilibrium constant equal to 2 , thus unequivocally demonstrating the correctness of the factor above. 

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