Complexes formation coefficient

Min+ and M2"+ differ significantly. The only exception are metal ions of differing charge number whose separation depends on the eluent concentration. If the eluent contains complexing agents such as citric acid or oxalic acid, then the equation for the distribution coefficient of the metal ion M"+ must also take into account the competing equilibrium of the complex formation. The complex formation coefficient may be expressed as follows ... 

Complex formation coefficient [L] Concentration of anionic ligand... 

M(L) Complex formation coefficient [L] Concentration of anionic ligand Bml Formation constant for the equilibrium M" + D" ML"- ... 

As a result the research emphasis in this field focused on efforts to design experiments in which it might be possible to determine to which one of the foregoing three rate equations the observed second-order rate coefficient actually corresponded. More specifically, the objective was to observe one and the same system first under conditions in which complex decomposition (fcp) was rate-determining and then under conditions in which complex formation (kF) was ratedetermining. A system in which either formation or decomposition was subject to some form of catalysis was thus indicated. In displacements with primary and secondary amines the transformation of reactants to products necessarily involves the transfer of a proton at some stage of the reaction. Such reactions are potential-... 

Analytical ultracentrifugation (AUC) Molecular weight M, molecular weight distribution, g(M) vs. M, polydispersity, sedimentation coefficient, s, and distribution, g(s) vs. s solution conformation and flexibility. Interaction complex formation phenomena. Molecular charge No columns or membranes required [2]... 

No new absorption bands are observed in other cases, largely due to the fact that the strong absorptions of the aromatic donors obstruct the UV-spectral measurements. For the complex between CBr4 and TMPD, the quantitative analyses of the temperature and concentration-dependent absorptions of the new band at 380 nm afford the extinction coefficient of ct = 3.2 x 103 M 1 cm x, as well as the thermodynamic parameters for complex formation AH = - 4.5 kcalM x, AS = - 14 e.u., and Kda = 0.3 M x at 295 K. Such thermodynamic characteristics are similar to those of the dihalogen complexes of as well as those of other acceptors with aromatic donors. Similar results are also obtained for CBr4 associates with halide and thio-cyanide anions [5,53]. 

On the other hand, many pericyclic reactions are accelerated by Lewis-acid catalysts. The acceleration has been attributed to a complex formation between the Lewis acid and the polar groups of the reactants that brings about changes in the energies and orbital coefficients of the frontier orbitals.6 The complex formation also stabilizes the enhanced polarized transition state. 

Our discussion of complex formation in electron-ion recombination, field effects, and three-body recombination has perhaps posed more questions than it has answered. In the case of H3 recombination, the experimental observations suggest but do not prove that complex formation is an important mechanism. Three-body recombination involving complex formation is not likely to have much effect on the total recombination coefficients of diatomic ions, but it may alter the yield of minor product channels. Complex formation may be most prevalent in the case of large polyatomic ions, but there is a serious lack of experimental data and theoretical calculations that can be adduced for or against complex formation. 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

All in all, the tritium data present something of a mystery, but at least they set a lower limit for the effective diffusion coefficient in the range 400-500°C, a limit rather higher than some estimates that have been given in the literature for similar temperatures but which we shall not discuss until Section 3 because thay are based on experiments in which hydrogen-acceptor complex formation was clearly important. 

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. 

Table 11.1 Determination of the Distribution Coefficient Kd from Surface Complex Formation (From Schindler, 1984 and Sigg, 1987)...

The selectivity-complex formation function (81) describes the variation of the selectivity coefficient of the transition metal ion versus a non complex forming reference cation with increasing ligand concentration as... 

This amount of thiocyanate is sufficient for both complete reduction and complex formation. Reduction is allowed to proceed for 30 to 45 s after the addition of the thiocyanate. A bright red color can readily be observed at a technetium (VII) concentration of 0.1 ng per ml. Acetone (6 ml) is then added and the volume of the solution mixed and adjusted to 10 ml with distilled water. At this point, the color has generally developed to less than 50% of its final intensity. Quartz 1-cm glass-stoppered cells are filled with the technetiiun solution and placed in a 20 °C water-cooled spectrophotometer. The extinction will approach a maximum intensity in 1 to 3 h. The maximiun extinction occurs at 510 nm with a molar extinction coefficient and standard deviation of 47,500 + 500 in 60 vol. % of the acetone-aqueous medium. An additional examination of the analysis may be carried out by extract-... 

The Pitzer virial coefficient method, see section 6.2.2. Methods 1 and 2 are equivalent and differ only in the form of the denominator in the Debye-Huckel term. Method 3 requires more parameters for the description of the activity factors. These parameters are not available in many cases. This is generally the case for complex formation reactions. 

It can be shown that the virial type of activity coefficient equations and the ionic pairing model are equivalent, provided that the ionic pairing is weak. In these cases, it is in general difficult to distinguish between complex formation and activity coefficient variations unless independent experimental evidence for complex formation is available, e.g., from spectroscopic data, as is the case for the weak uranium(VI) chloride complexes. It should be noted that the ion interaction coefficients evaluated and tabulated by Cia-vatta [10] were obtained from experimental mean activity coefficient data without taking into account complex formation. However, it is known that many of the metal ions listed by Ciavatta form weak complexes with chloride and nitrate ions. This fact is reflected by ion interaction coefficients that are smaller than those for the noncomplexing perchlorate ion (see Table 6.3). This review takes chloride and nitrate complex formation into account when these ions are part of the ionic medium and uses the value of the ion interaction coefficient (m +,cio4) for (M +,ci ) (m +,noj)- Io... 

K over the range 298-398 K. Partition eoeffieients for HFeCU between water and 1-octanol or dibutyl ether depend markedly on HCl and LiCl concentrations. For dibutyl ether as organic phase there is also a dependence of partition coefficient on Fe " " concentration as there is significant polynuclear complex formation in the ether layer. [FeCU] , in the form of its Et3BzN" salt, acts as a bifunctional or phase transfer catalyst for hydrosilylation of phenylacetylene. ... 

Recall that the diffusion coefficient of a molecule will decrease with increasing viscosity of the solvent. Thus, the rate of encounter complex formation will decrease in a viscous medium. Since viscosity is itself temperature dependent, such encounters in solution will have their own activation energy. 

---