Equilibria formation constant

The equilibrium formation constant for a metal-ligand complex for a specific set of solution conditions, such as pH. 

At(0) reacts with halogens X2 to produce interhalogen species AtX, which can be extracted into CCI4, whereas halide ions X yield polyhalide ions AtX2 which are not extracted by CCLt but can be extracted into Pr O. The equilibrium formation constants of the various trihalide ions are intercompared in Table 17.28. 

In the simplest case of a competitive uptake of two metals (or a metal and proton) for an identical uptake site under equilibrium conditions, the reduction of the uptake flux of the solute can be quantitatively predicted using the respective equilibrium formation constants (equations (38) (41)). As can be seen in Table 3, for a given study, constants among the trace metals, protons and alkaline earth metals are often sufficiently similar for competition to be important. Nevertheless, competition is likely to be negligible under most environmentally relevant conditions where competition occurs between low concentrations of metals, such that the free carrier concentration remains approximately equal to the total receptor concentration. 

Consider a system in which the membrane ions form stable ion-pairs with both ions, whose equilibrium formation constants are Kj indKy. Then, according to (3.2.10), (3.2.14) converts to... 

The equilibrium formation constants for the 1 1 complexes of Hf with glycine and serine in solutions of pH 2 have been determined as 31 and 18, respectively, and the HfO -amygdalic acid complex, [HfO PhCH(0)- 02)2] , has been obtained in aqueous solutions of pH 7—10.5. The stability constants of the 1 1 complexes of ZrO with iVh/ -ethylenediamine-bis(succinic acid) and Nh/ -ethylenediaminebis(glutaric acid) have been determined. ... 

Data obtained for purified hemocyanin samples in pH 9.6 glycine buffer at various levels of free calcium ion are summarized in Table I. The apparent protein equilibrium (formation) constant Kp (D = dodec-amer or whole molecules and H = hexamer or half molecules) and the degree of dissociation by weight, a, are taken from the ultracentrifuge study of Morimoto and Kegeles (12). 

The triplets p, q, r are known as the stoichiometric coefficients of the chemical components in the formation equation of the complex, and are often quoted as subscripts next to the symbol used for the formation constant, which in this case is (3, so that the equilibrium formation constant would be defined as... 

Mass action equations. The first step in any calculation is to collate the mass action expressions that define the formation of the species. The way in which the formation constants can be used can be illustrated by considering a metal such as aluminium in an aqueous medium. Aluminium ions can undergo a number of hyrolysis reactions in water to form several hydroxy-metal complexes. The reactions can be written as the overall hydrolysis reactions and their associated equilibrium formation constants are shown below. 

NH3)5]"+ (n = 4, 5, or 6) and [(bipy)2ClRu(pyz)RuCl(bipy)2]"4 (n = 2, 3, or 4).50 These studies reveal equivalent metal sites even in the mixed-valency Run-Ru,u species, despite the speed with which ESCA monitors electron distribution (10 17 s). Another investigation shows that the complex [Ru(NH3)5(pyz)]2+ can associate with several aqueous first-row transition-metal ions to form pyrazine-bridged dinuclear complexes.51 Equilibrium formation constants with Ni", Cu , and Zn11 were measured spectroscopically. 

In thermodynamic terms, steady states in multi-faceted reactions occur pretty close to chemical equilibrium. Assuming that the latter is a good approximation for many biological fluids and for many medicines and administered drugs, it is possible to build chemical speciation models based upon the equilibrium formation constants described earlier. 

This compilation of metal complex equilibrium (formation) constants and the corresponding enthalpy and entropy changes represent the authors selection of the most reliable values among those available In the literature. In many cases wide variations in published constants for the same metal complex equilibrium indicate the presence of one or more errors in ligand purity, in the experimental measurements, or in calculations. Usually, the nature of these errors is not readily apparent in the publication, and the reader is frequently faced with uncertainties concerning the correct values. In the course of developing noncritical compilations of stability constants, the authors have long felt that these wide variations in published work constitute a serious Impediment to the use of equilibrium data. Thus these critical tables were developed in order to satisfy what is believed to be an important need in the field of coordination chemistry. 

In general, the complexes formed by chelating ligands (that is, bidentate and polydentate ligands) are more stable than the complexes formed by related monodentate ligands. The equilibrium formation constants for [Ni(NH3)g] and [Ni(en)3] illustrate this observation ... 

Eq. (2.56)] is determined solely by thermodynamic stability of intermediate species, which, in turn, is expressed by the equilibrium formation constant (or, alternatively, the disproportionation equilibrium constant) of the intermediate valence compound. 

Neutral detergents e.g. 2% Triton X 100) increase the equilibrium formation constants and rates of thiocyanate anation of Co -porphyrins in aqueous media by a factor of less than two. ... 

The nature of the solvent influenced the equilibrium formation constant and subsequent rate-determining conversion to products for an intermediate complex, formed between the substrates and PDA these constants were reported for reactions in acetone and benzene. Equations correlating the rates of Py oxidation with the solvent properties are reported the rates are affected by the basicity and polarity, unaffected by polarizability and electrophilicity, and appreciably retarded by added AcOH.234... 

The complex ions cA-[Co(en)2LCl] + with L = aniline or m-toluidine have both been shown readily to lose a proton to form their respective conjugate bases (L = PhNH" or /M-MeCsHjNH-), and rate data for chloride-ion aquation are reported for all four species (Table 3). Above pH 3 significant concentrations of these coryugate bases are present since the equilibrium formation constants are ca. 10 . The enhanced reactivity of the conjugate bases is in line with the now well established S Nlcb mechanism for base hydrolysis. 

Table 14 Comparison of equilibrium formation constants (Ke

In equation (50) is negligible when the observed rate constants are corrected for the side reactions. Values of ki are compared for L = imidazole, ammonia, and pyridine in Table 17. The equilibrium formation constants (ATeq) increase with the increasing t-acceptor capacity of the nitrogen bases, but values of ki vary in the... 

Equilibrium formation constant. Ru Ru Corrected by a statistical factor of 6. 

Equilibrium formation constant. Formation rate constant. In 1 mol l lithium toluene-p-sulphonate. Calculated values from activation parameters = 0.5—1.0moll i. A fast reaction may be due to some high-spin cobalt(ni). f At 348.1 K. 

The most interesting finding, however, was the fact that in copolymerization experiments, the apparent reactivity ratios (rj and r2) are directly related (Fig. 27) to the respective equilibrium formation constants of the corresponding complexes (kf of the monomer—iron complex, as determined independently). In simple words, the monomer which is more strongly bonded to the Mj is incorporated preferentially, even if its rate of insertion is not the higher one. That situation can be summarized as shown in the Scheme. 

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