Concentration association constants

Ion-pairing between the paramagnetic [Co(tdt)2] monoanion and nine different cations was examined by Tsao and Lim.105 The cations belong to either of two classes, quaternary ammonium or substituted V-octylpyridinium ions. By recording the H NMR spectra as a function of concentration (nitrobenzene, 307 K), the concentration association constants (Kas) were obtained. Substituent effects were found to influence the ion-pair geometry, as deduced from the isotropic shifts of the cationic protons and their shift ratios. In low dielectric constant solvents, speculation consistent with the magnetic anisotropy and the relation between the cationic proton shifts and concentration was tendered for cylindrically shaped aggregates. 

As in any other cases, the reviewed constants may be thermodynamic (for activities) and concentration (for concentrations). Overall thermodynamic and concentration association constants tied between themselves by equation... 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

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. 

Cussler studied diffusion in concentrated associating systems and has shown that, in associating systems, it is the size of diffusing clusters rather than diffusing solutes that controls diffusion. is a reference diffusion coefficient discussed hereafter is the activity of component A and iC is a constant. By assuming that could be predicted by Eq. (5-223) with P = 1, iC was found to be equal to 0.5 based on five binaiy systems and vahdated with a sixth binaiy mixture. The limitations of Eq. (5-225) using and K defined previously have not been explored, so caution is warranted. Gurkan showed that K shoiild actually be closer to 0.3 (rather than 0.5) and discussed the overall results. 

MW) is the molar concentration of methanol/water associate, and (k) is the "association" constant... 

Different samples of aqueous solution containing radionuclides of Co and Eu were prepared at different copper sulphate concentrations and constant polymer concentrations (pAM) of 15 mg/1. The addition of salt to the system was done to reduce both the repulsion forces between the radionuclides and the interaction between the polymeric chains [7]. The polymer efficiency for the prepared samples was determined, results are shown in Fig. 15. It is clear that the polymer efficiency for Eu " is higher than for Co. This can be explained by the difference in the tightly bound structured water associated with different cationic species [14,107]. On this basis, we expect that Co is more hydrated than Eu. This is due to the difference in the ionic size. The hydra-... 

Equilibrium (dissociation) constant, reciprocal of the association constant and affinity characterizes the binding of a molecule to a receptor. Specifically, it is the ratio of the rate of offset of the molecule away from the receptor divided by the rate of onset toward the receptor. It also is a molar concentration that binds to 50% of the receptor population. 

Purification of solvents and salts is essential for reliable electrochemical studies and measurements. A water content of 20ppm already corresponds to a 10 3molL solution. This is in the concentration range of dilute solutions used in conductivity studies for the determination of association constants (see Sec.7.3.2). Traces of water may affect chemical equilibria and therefore act on specific conductivities and limiting ion conductivities. For example, addition of 30 ppm water to a 2xl0-4 mol LT1 solution of LiBF4 in THF at 15 °C increases its conductivity by 4.4 percent (precision of measurements about 0.02 percent) 380 ppm water causes an increase by 51.7 percent see Fig. 3 [20J. 

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... 

Conductivity measurements yield molar conductivities A (Scm2 mol-1) at salt concentration c (mol L-1). A set of data pairs (Af, c,), is evaluated with the help of non linear fits of equations [89,93,94] consisting of the conductivity equation, Eq. (7), the expression for the association constant, Eq. (3), and an equation for the activity coefficient of the free ions in the solution, Eq.(8) the activity coefficient of the ion pair is neglected at low concentrations. 

At low salt concentrations and very high association constants, the ratio of association constants can be approximated by... 

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]... 

Recent developments of the chemical model of electrolyte solutions permit the extension of the validity range of transport equations up to high concentrations (c 1 mol L"1) and permit the representation of the conductivity maximum Knm in the framework of the mean spherical approximation (MSA) theory with the help of association constant KA and ionic distance parameter a, see Ref. [87] and the literature quoted there in. 

In contrast to points (l)-(3) of discussion, the effect of ion association on the conductivity of concentrated solutions is proven only with difficulty. Previously published reviews refer mainly to the permittivity of the solvent or quote some theoretical expressions for association constants which only take permittivity and distance parameters into account. Ue and Mori [212] in a recent publication tried a multiple linear regression based Eq. (62)... 

This reaction reduces the concentration of the free polystyryl anions, the only species capable of propagating the reaction in this system. The association constant of the above reaction deduced from the kinetics of retardation 78) agrees well with that reported previously 79) based on the results of conductance studies. 

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. 

A polymeric structure can be generated by intermolecular coordination of a metalloporphyrin equipped with a suitable ligand. Fleischer (18,90) solved the crystal structure of a zinc porphyrin with one 4-pyridyl group attached at the meso position. In the solid state, a coordination polymer is formed (75, Fig. 30). The authors reported that the open polymer persists in solution, but the association constant of 3 x 104 M 1 is rather high, and it seems more likely, in the light of later work on closed macrocycles (see above), that this system forms a cyclic tetramer at 10-3 M concentrations in solution (71,73). 

Hunter (60) reported a self-assembled open polymer formed by a zinc porphyrin bearing one para-aniline substituent at the meso position. The ortho- and mela-analogs discussed above form closed dimers, but the geometry of the para-derivative precludes this, and polymerization is the only alternative (76, Fig. 31). Although the dilution experiments could be fitted to a non-cooperative polymerization model with a pairwise association constant (K = 190 M 1) practically identical to that found for simple aniline-zinc porphyrin complexes (K = 130 M 1), broadening of the 4H NMR spectrum at high concentrations is characteristic of oligomerization. 

Because association is reversed by the dissociation reaction, one does not ever achieve complete conversion of free E and I to the El complex. Rather, the system approaches an equilibrium with respect to the concentrations of E, /, and EL We can define an equilibrium association constant as the ratio of products to reactants, or as the ratio of the forward to reverse rate constants ... 

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