Association constant dependence

According to M. Blander the association constant depends on the change in the Gibbs energy, AG, during exchange of a solvent anion Y", next to a cation of the dissolved salt A+, for an anion of the dissolved salt B according to the relationship... 

Auto-association of A-4-thiazoline-2-thione and 4-alkyl derivatives has been deduced from infrared spectra of diluted solutions in carbon tetrachloride (58. 77). Results are interpretated (77) in terms of an equilibrium between monomer and cyclic dimer. The association constants are strongly dependent on the electronic and steric effects of the alkyl substituents in the 4- and 5-positions, respectively. This behavior is well shown if one compares the results for the unsubstituted compound (K - 1200 M" ,). 4-methyl-A-4-thiazoline-2-thione K = 2200 M ). and 5-methyl-4-r-butyl-A-4-thiazoline-2-thione K=120 M ) (58). 

The functional form for default torsions is the MM-t form with three torsional constants VI, V2, and V3 for 1-fold, 2-fold, and 3-fold contributions. The default values for these constants depend on the particular chemical situation associated with the bond... 

Specific Conductance. The specific conductance depends on the total concentration of the dissolved ioni2ed substances, ie, the ionic strength of a water sample. It is an expression of the abiUty of the water to conduct an electric current. Freshly distilled water has a conductance of 0.5—2 ]lS/cm, whereas that of potable water generally is 50—1500 ]lS/cm. The conductivity of a water sample is measured by means of an a-c Wheatstone-bridge circuit with a null indicator and a conductance cell. Each cell has an associated constant which, when multiphed by the conductance, yields the specific conductance. 

The commonly used method for the determination of association constants is by conductivity measurements on symmetrical electrolytes at low salt concentrations. The evaluation may advantageously be based on the low-concentration chemical model (lcCM), which is a Hamiltonian model at the McMillan-Mayer level including short-range nonelectrostatic interactions of cations and anions [89]. It is a feature of the lcCM that the association constants do not depend on the physical... 

A similar association may result from intermolecular interaction of two growing chains. Of course, the degree of such an association should depend on the concentration of growing polymers, i.e. the observed propagation constant, kobs, is given then by the relation ... 

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

The composition of the electrical effect in the case of the 1,4-benzo-quinones seems to depend upon the degree of substitution. The association constants and charge transfer absorption energies of the 2-substituted-l,4-benzo-quinone-hexamethylbenzene complexes (sets 15-2 and 154) show values of pj of 55 and 44 respectively. Values of p are set forth in Table XVII. 

The aniline-zinc porphyrin interaction has also been exploited to form dimers. Hunter (60) reported the dimerization of porphyrins functionalized at one meso position with ortho or meta aniline groups (47, 48, Fig. 15). Both compounds showed concentration-dependent H NMR spectra with large upfield shifts for the aniline protons. The dimerization constants are 160 and 1080 M-1 respectively for 47 and 48, and these values are an order of magnitude higher than the association constants of simple reference complexes (K — 10 and 130 M 1 respectively), which is indicative of cooperative self-assembly. The complexa-tion-induced changes in chemical shift were used to obtain three-dimensional structures of the dimers. 

Thus, as described by Equation (2.1), the equilibrium dissociation constant depends on the rate of encounter between the enzyme and substrate and on the rate of dissociation of the binary ES complex. Table 2.1 illustrates how the combination of these two rate constants can influence the overall value of Kd (in general) for any equilibrium binding process. One may think that association between the enzyme and substrate (or other ligands) is exclusively rate-limited by diffusion. However, as described further in Chapter 6, this is not always the case. Sometimes conformational adjustments of the enzyme s active site must occur prior to productive ligand binding, and these conformational adjustments may occur on a time scale slower that diffusion. Likewise the rate of dissociation of the ES complex back to the free... 

The noncovalent binding of a series of oxo-squaraine dyes 9a-e to BSA was evaluated by measurement of absorption, emission, and circular dichroism [63]. The magnitude of the association constants (Ks) for the dye-BSA complexes depended on the nature of the side chains and ranged from 34 x 103 to 1 x 107 M-1. Depending on the side chains, the Ks increase in the order [R1 = R2 = butyl-phthalimide] < R1 = R2 = cetyl] <[RJ = R2 = ethyl] <<[R = butyl-phthalimide, R2 = butyl-sulfonate] <<[RJ = R2 = butyl-sulfonate]. These dyes seem to interact mainly with a hydrophobic cavity on BSA. However, the association constants Ks increase substantially when the side chains are selected from butyl sulfonate. 

It may also happen that an association equilibrium exists between the luminescent indicator and the quencher. Non-associated indicator molecules will be quenched by a dynamic process however, the paired indicator dye will be instantaneously deactivated after absorption of light (static quenching). Equation 2 still holds provided static quenching is the only luminescence deactivation mechanism (i.e. no simultaneous dynamic quenching occurs) but, in this case, Ksv equals their association constant (Kas). However, if both mechanisms operate simultaneously (a common situation), the Stem-Volmer equation adopts more complicated forms, depending on the stoichiometry of the fluorophore quencher adduct, the occurrence of different complexes, and their different association constants. For instance, if the adduct has a 1 1 composition (the simplest case), the Stem-Volmer equation is given by equation 3 ... 

Equation (4) demonstrates that the relationship between the association constant K, which is sensitive to the ionic strength (16,17,21,25), and the level of covalent binding, f v, is a complex one. It is known that fcov decreases upon the addition of NaCl or MgCl2, and this effect has been taken as evidence that physical intercalation complexes play a role in the covalent binding reaction (17,22,26). While this conclusion may still be correct, such evidence is insufficient since it has been shown that not only K, but also k3 (21,25), and the branching ratio kc/k (21) in Equation (4) depend on the salt concentration. 

Dependence of tt complex binding constants upon nucleoside ionization potentials for ( ) uridine, ( ) thymidine, (A) cytidine, (o) adenosine, (O) guanosine, and (A) N,N,-dimethyladenosine. Panel A shows association constants for the binding of nucleosides to riboflavin. Panel B shows association constants for the self association of nucleosides. (Reproduced from Ref. 82. Copyright 1981, American Chemical Society.)... 

In theory, the two diastereomeric complexes will have different association constants. The evaluation of any chiral discrimination will depend upon measurement of the different proportions of the diastereoisomers formed. For example, nmr experiments have been successful in determining the degree of complex formation by each enantiomer. Alternatively, an extraction procedure has been employed this involves the interaction... 

For a binding reaction we can pick whether we show the reaction as favorable or unfavorable by picking the substrate concentration we use. Association constants have concentration units (M-1)- The equilibrium position of the reaction (how much ES is present) depends on what concentration we pick for the substrate. At a concentration of the substrate that is much less than the dissociation constant for the interaction, most of the enzyme will not have substrate bound, the ratio[ES]/[E] will be small, and the apparent equilibrium constant will also be small. This all means that at a substrate concentration much less than the dissociation constant, the binding of substrate is unfavorable. At substrate concentrations higher than the dissociation constant, most of the enzyme will have substrate bound and the reaction will be shown as favorable (downhill). (See also the discussion of saturation behavior in Chap. 8.)... 

Condensation reactions are conveniently written as carbanion reactions, and yet it is clear that the metallic cation is important too. For example, sodium and lithium give quite different results in the condensation of acetophenone and tert-butyl acetate.422 The various rate and equilibrium constants depend on the nature of the associated metal. Lithium, zinc, and magnesium, which give the aldol condens-... 

As a general statement, the reaction rate in each direction follows second-order kinetics for all the rhenium compounds studied. Moreover, the rate constants depend on the identities of L and Ly. Both findings argue for an associative (displacement) mechanism, which is also supported by the large and negative values of AS, that often reach —120 J K-1 mol-1 (39). 

The equilibrium constant for reaction 5 depends on the complex formation constant, the association constant of C in the membrane and on the distribution coefficients of H+, and ions between the organic membrane phase and aqueous sample solution, e.g. 

The reactions involved are unimolecular, and the cyclohexenyl derivative 3 undergoes solely the spontaneous heterolysis while both spontaneous heterolysis and ligand coupling occur with the iodane 14. The relative contributions of the two reactions of 14 depend on the solvent polarity. The results summarized in Table I show that the iodonium ion and the counteranion are in equilibrium with the hypervalent adduct, X3-iodane. The equilibrium constants depend on the identity of the anion and the solvent employed, and the iodane is less reactive than the free iodonium ion as the k /k2 raios demonstrate. Spontaneous heterolysis of 3 occurs more than 100 times as fast as th t of the adduct 14 as observed in methanol the leaving ability of the iodonid group is lowered by association by more than 100 times. 

Both the absolute and the relative values of the association constants of crown-ether complexes with cations are dependent on the type of solvent used. 

A comparison of experimental results with those calculated from the Fuoss (2) theory is presented in Table I. The theory 1s only valid approximately so that the order of magnitude agreement is fairly good, except in the cases of MgC03° and CaC03 . Stoichiometric association constants K are then obtained from the activity coefficients, expressions for K, and from equations for the conservation of mass. The latter express the total concentration of a given ion as the sum of the concentrations of the free ion and of the ion-pairs. Values of K and of the activity coefficients of free ions in ionic media depend only upon the effective ionic strength as is shown later. 

The value of (feobsd caic) at a given concentration of bromide anion depends on the association constant for formation of the ion pair from free ions (Ai s = and on the relative reactivity of the ion-pair and free carbocation toward addition of solvent For example, if is small, then the concentration of the ion-pair... 

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