Relationships Involving Equilibrium Constants

The pioneering work of Gilkerson and co-workers [122-130] and Huyskens and colleagues [131,132] allows the determination of the corresponding equilibrium constants from conductivity measurements. If all equilibria, Eq. (4)-(6), are involved, the association constants of an electrolyte without (K l) and with (KA ) addition of the ligand at concentration cL of the ligand L are given by the relationship [132]... 

It should be apparent that the larger the equilibrium constants for these reactions, the more unstable the complexes. Consequently, the equilibrium constants for these reactions are called dissociation or instability constants. One must remember that the first step in the dissociation of ABm corresponds to the reverse of the last step in the formation of the complex. Thus, if we represent the instability constants as fc and a total of six steps are involved, the relationships between the fe, and K values are as follows. 

Quantitative structure-chemical reactivity relationships (QSRR). Chemical reactivities involve the formation and/or cleavage of chemical bonds. Examples of chemical reactivity data are equilibrium constants, rate constants, polarographic half wave potentials and oxidation-reduction potentials. 

Equations (65) and (66) show that a linear logarithmic relationship involving the effect of a change in chain length on the kinetic EM and the equilibrium EM of the same cyclisation reaction is impossible, unless 0AH° is a constant throughout the series. 

While ki2 in AN is tenfold higher than in DE, k2i in AN is only three times its value in DE. These findings are in accordance with the relationship between the formation constant of hexachloroantimonate and the donicity of the utilized solvent, as has been stated in Sect. 3.1. The values for the equilibrium constants [SbCle]" obtained from the kinetic measurements are in agreement102 with those found from equilibrium studies4 in the respective solvents (Fig. 17). In solvents of very low donicity the /f[SbCl6 ] values are lower than expected on the basis of the DN-Ai[SbCl6 ]" plot. This may be attributed to the presence of polymeric SbCl5 units, and thus to the involvement of a second equilibrium. 

Examining the relationship between the hydrolysis rate constants (A ,) and the equilibrium constant (Aj) for a series of reactions of the type (4.28) and (4.29) involving charged ligands X" has been very helpful in delineating the type of / mechanism. 

In this latter case, although we have made use of the equality between forward and reverse rate, which only holds at equilibrium, the resulting relationship /cu//c u = /c, /k-, = Kc only involves (rate and equilibrium) constants and therefore holds in general. 

The reactions of poly(styryl)lithium in benzene with an excess of diphenyl-ethylene 272) and bis[4-(l-phenylethenyl)phenyl]ether158) also were found to proceed by a first order process. However, the reactions of poly(styryl)lithium with the double diphenylethylenes l,4-bis(l-phenylethenyl)benzene and 4,4 bis(l-phenyl-ethenyl)l,l biphenyl gave l58) non-linear first order plots with the gradients decreasing with time. This curvature was attributed to departure from a geometric mean relationship between the three dimerization equilibrium constants (Ka, Kb and Kab). The respective concentrations of the various unassociated, self-associated and cross-associated aggregates involved in the systems described by Equations (49) to (51) are dependent upon the relative concentrations of the two active centers and the respective rate constants which govern the association-dissociation events. 

In this section, two types of structure-metal binding ability relationships will be described. The first one concerns empirical linear correlations between equilibrium constants of complexation or extraction and some descriptors. In most cases, these correlations are obtained for relatively small datasets (less than 20 molecules) without any validation. We do not intend to analyze them in detail only their general characteristics will be reported. The second type of relationships were obtained in regular QSPR studies involving the selection of pertinent descriptors from their large initial pools, and the stage of the models, validation on external test set(s). 

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