Equilibrium constant stability

Re—O—Re linkage.The complexing of rhenium(iv) with thiourea (L) has been studied in HCl solutions in the presence of tin(ii) by a cation-exchange method, and equilibrium stability constants Pj—P4 for [ReOL4] -t- nCl" [ReOCl L4 -I- nh determined.The complexing of rhenium(iv) with thiocyanate ions in HCl solutions in the presence of SnClj has also been investigated and the formation of a 1 1 Re -SCN" complex confirmed. ° ... 

A measure of the thermodynamic stability of ML is given by the equilibrium stability constant... 

These rate constants are dependent on ligand structure and, for the disjunctive pathway, on pH. The rate constant for the disjunctive pathway is determined by the rate constant for reaction of the incoming metal with the steady-state concentration of the free or protonated ligand intermediate. It is thus inversely proportional to the conditional equilibrium stability constant for the initial metal complex and directly proportional to the formation rate constant for the final metal complex. The adjunctive rate constant is more dependent on ligand structure since either formation or dissociation of the intermediate dinuclear complex can be rate-limiting. Specifically ... 

Comparison of areas under individual peaks in the H NMR spectrum of dienPd(II)-nucleoside and nucleotide complexes permits evaluation of equilibrium stability constants for complex formation. Figure 5 shows the species distribution in a nearly equimolar solution of dienPd(II) and 5 -GMP and Figure 6 does the same for 5 -AMP. The difference between the distributions in Figure 5 and 6 results largely from the different absolute... 

The hole-size relationship between cations and crown ethers has been a part of the lore in the cation binding area for nearly two decades. Although, to our knowledge, no formal definition of this principle has ever been offered, the general concept seems to be that cation binding will be optimized when the cation diameter and macrocycle cavity size are identical. A simple consequence of this concept is the notion that 15-crown-5 is selective (binds more strongly) for Na+ over K+. We have measured the homogeneous (equilibrium) stability constants for the reaction... 

EPR spectroscopy was employed by Rockenbauer et al [Ro 72] to study the equilibrium stability constants of low-spin cobalt(II) mixed complexes. They determined the equilibrium constants of formation of the mixed complexes of the bis(dimethylglyoximato)cobalt(II) parent complex with pyridine ligands, in methanol. It was shown that in a methanolic solution of the parent complex, two methanol molecules are coordinated along the z axis, and these methanol molecules can be replaced stepwise with pyridine. 

For certain compounds, e.g., Ni(NCS)2 and Ni(CF3COO)2, an almost linear correlation is found between the equilibrium stability constant and the Gutmann donicity of the solvent [Ma 75]. 

Thus, as we have already found out, the data of chronopotentiometric experiments cannot be presented in simple form such as Eq. (2.9) or (2.10) to calculate the equilibrium stability constants of LVIs by a standard routine. In our opinion, this method is more appropriate for the studies of intervalence reaction kinetics (see the next chapter) rather than equilibrium. However, some information on the intervalence equilibria also can be obtained in certain cases. For example, equilibrium disproportionation constant may be estimated from the shape of the wave, as was pointed out above, ii K > A and the plot in semi-logarithmic coordinates is typically S-shaped as in Fig. 2.10. 

Table 1 (below) contains the slope of each line (concentration of ACT against concentration of CD), as calculated by linear regression, and the equilibrium (stability) constant for each interaction. 

Gold complexes, with a few exceptions, are either 2-coordinated with the two ligand molecules bonded to the central Au+ ion in linear configuration or 4-coordinated with the ligand molecules bonded to the central Au + ion in a square-planar configuration. Complex stability in aqueous solution is assessed by determining the equilibrium stability constant of the complex formation reaction. The formation of an n-coordinated complex of a z-valent metal cation with a ligand species... 

The equilibrium constant for the formation of a complex ion is called a formation constant (or stability constant) and given the symbol Kf. A typical example is... 

The equilibrium constants Kl,K2,...,Kn are referred to as stepwise stability constants. 

The equilibrium constants pi,p2,...,p are called the overall stability constants and are related to the stepwise stability constants by the general expression... 

A knowledge of stability constant values is of considerable importance in analytical chemistry, since they provide information about the concentrations of the various complexes formed by a metal in specified equilibrium mixtures this is invaluable in the study of complexometry, and of various analytical separation procedures such as solvent extraction, ion exchange, and chromatography.2,3... 

It can be shown from a consideration of the overall stability constants of the ions [Ni( CN)4] 2 " (1027) and [ Ag( CN)2 ] (1021) that the equilibrium constant for the above ionic reaction is 1015, i.e. the reaction proceeds practically completely to the right. An interesting exercise is the analysis of a solid silver halide, e.g. silver chloride. 

The size of the EDTA ring structure complex (not too big or too small), plus the multiple points of attachment, provides a very stable complex (high stability constant) that overcomes reaction tendencies to reach equilibrium via the lowest possible energy state or maximum state of disorder (entropy). 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

Four anthocyanin species exist in equilibrium under acidic conditions at 25°C/ according to the scheme in Figure 4.3.3. The equilibrium constant values determine the major species and therefore the color of the solution. If the deprotonation equilibrium constant, K, is higher than the hydration constant, Kj, the equilibrium is displaced toward the colored quinonoidal base (A), and if Kj, > the equilibrium shifts toward the hemiacetalic or pseudobase form (B) that is in equilibrium with the chalcone species (C), both colorless." - Therefore, the structure of an anthocyanin is strongly dependent on the solution pH, and as a consequence so is its color stability, which is highly related to the deprotonation and hydration equilibrium reaction constant values (K and Kj,). 

Table 6. Free calcium concentrations in equilibrium with common complexing agents. A low free calcium concentration implies effective complexation, whether the complex formed is soluble or insoluble. The data were derived from either stability constants (soluble complexes) or solubility products (insoluble complexes).

The vertical spring and mass is an example of a stable system and by definition this means that an arbitrary small external force does not cause the mass to depart far from the position of equilibrium. Correspondingly, the mass vibrates at small distances from the position of equilibrium. Stability of this system directly follows from Equation (3.102) as long as the mechanical sensitivity has a finite value, and it holds for any position of the mass. First, suppose that at the initial moment a small impulse of force is applied, delta function, then small vibrations arise and the mass returns to its original position due to attenuation. If the external force is small and constant then the mass after small oscillations occupies a new position of equilibrium, which only differs slightly from the original one. In both cases the elastic force of the spring is directed toward the equilibrium and this provides stability. Later we will discuss this subject in some detail. 

Adding protons or hydroxide ions to the system will influence the position of the chelation equilibrium. The stability constant of a complex is thus influenced by the pH of... 

Note The above potentials, E, are for pH 7 at equal concentrations of oxidised and reduced species. These equilibrium values are as important as stability constants and solubility products for an understanding of cellular chemical systems. These are free energy changes in volts, E, and where n3E is in kilocalories. The [Fe3+]/[Fe2+] is related to an equilibrium constant, K (see Section 4.17). 

The thermodynamic stability of an ML complex is expressed by the equilibrium constant of the formation reaction, A1ML, called the the stability constant ... 

Complex stability constants are most often determined by pH-potentiometric titration of the ligand in the presence and absence of the metal ion.100 This method works well when equilibrium is reached rapidly (within a few minutes), which is usually the case for linear ligands. For macrocyclic compounds, such as DOTA and its derivatives, complex formation is very slow, especially for low pH values where the formation is not complete, therefore a batch method is... 

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