Stepwise equilibrium constant

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... 

For these reactions, we can write the equilibrium constants (known as stepwise formation or stability constants) as... 

Ki Equilibrium constant for stepwise addition of a ligand in mononuclear complexes... 

Ki Stepwise equilibrium constant for addition of a ligand from the acid... 

The thermodynamic stability of a complex ML formed from an acceptor metal ion M and ligand groups L may be approached in two different but related ways. (The difference between the two approaches lies in the way in which the formation reaction is presented.) Consistent with preceding sections, an equilibrium constant may be written for the formation reaction. This is the formation constant Kv In a simple approach, the effects of the solvent and ionic charges may be ignored. A stepwise representation of the reaction enables a series of stepwise formation constants to be written (Table 3.5). 

Equilibrium constants have been reported for the stepwise conversion of MeRe(NAr)2(PR3)2 to the mixed-phosphine and then the (PR3)2 derivative. Both steric and electronic factors come into play, typical of phosphines. The stability ordering is PMe3 > dmpe>PMe2Ph > P(OMe)2Ph > PEt3 > P(OEt)3 > PMePh2 > P(OEt)Ph2 > PPh3 (58). 

Carbon atoms in organic molecules are most often neutral. Positively charged carbocations have attracted the interest of synthetic organic chemists, because of their use as intermediates in reactions leading to formation of carbon-carbon bonds. Our work on carbocations has focused on defining the stability of these species as intermediates of solvolysis reactions, through the determination of rate and equilibrium constants for these stepwise reactions (Scheme 1). This has led to the development of experimental methods to characterize these parameters for carbocations that are sufficiently stable to form in aqueous solution. 

The equilibrium constants for these stepwise reactions are expressed generally as K ... 

This example illustrates a case of considerable analytical importance, especially for the determination of complex formation constants for hydrophilic complexes, as discussed in section 4.12, when the equilibrium constants for the stepwise metal-organic complexes are of secondary interest. values are tabulated in several reference works. is a conditional constant and only valid provided no other species are formed besides the extracted one. 

The average ligand number can be used to obtain approximate equilibrium constants, as described by [65], assuming that at half integer -values the two adjacent complexes dominate e.g., at = 0.5 the species and MA dominate, while at il = 1.5 MA and MA dominate, etc.. The following expression for the stepwise formation constant is approximately valid at... 

If the equilibrium constant K has a value between 1 and 10, less than a thousandth of the total amount of water formed in the reaction mixture is sufficient to prevent the formation of really high-molecular-weight condensation polymers. Hence it follows that it is extremely important to remove as completely as possible the low-molecular-weight reaction products, for example, water, eliminated during a polycondensation. In principle, these equilibriums are also known in stepwise addition polymerizations (polyaddition) like the back-reactions of urethane groups. Since they mostly occur at higher temperatures only, they can be neglected. 

Due to the absorption of UV radiation by the reactant nucleophiles and the solvent in the zone of interest, application of classical spectrophotometric methods to follow the mechanism of formation of imidazo[4,5-f]-[l,2,5]thiadiazoles 51 from reaction of the parent thiadiazoles 1,1-dioxides 89 and ureas/thioureas was restricted. Consequently, details of the mechanism and equilibrium constants were established by CV <2004JP01091, 2003JP0220>. It was found that the reaction proceeded by a stepwise mechanism with an intramolecular second step as outlined in Scheme 4. In solution, this reaction was reversible, and the equilibrium could be shifted to the side of the reactants by a temperature increase. For example, a 3.54mM solution of 51b in DMF, with a 0.1 M NaC104 as supporting electrolyte, presented a featureless CV between 0.9 and —2.8 V which corroborated with the... 

This method is particularly valuable in two respects (1) It allows the direct determination of reaction rates, say kf and k, from which the equilibrium constant, K2 — kf//c, can be derived. (In some instances, direct determination of the equilibrium constant is also possible.) (2) It is very well suited for the study of stepwise (clustering) solvation processes in the gas phase at temperatures near 298 K. 

The equilibrium constant for the formation of a metal complex is known as its stability constant. (Some authors, however, present the datum as its reciprocal, the instability constant of the complex, by analogy with the dissociation of a weak acid.) There are two kinds of stability constants stepwise (Ad, Ad, Ad,..., Kn) and overall (/ ). We will assume that there are six aqua ligands to be replaced by some other unidentate ligand Xx, in an aqueous solution of Mm+ ... 

Equation 33 is the familiar statistical relation between the equilibrium constants in a series of stepwise equilibria as derived by N. Bjerrum (II) for polyprotic acids and applied by J. Bjerrum (12) to complex ion equilibria. Substituting Equation 33 for K, into Equations 23 and 24 for 0f° and 0o° gives... 

When Z is a simple aquacation, two types of complex are formed depending upon the ionic radius of Z. For alkali, alkaline earth and most transition metal cations the product contains Z"+ in quasi-octahedral coordination. Equilibrium constants for reaction (6) have been determined for Li+, Na+, K+, Mg2+, Ca2+, Sr2+, Ba2+, Mn2+, Fe2+, Co2+, Ni, Cu2+ and Zn2+.93 For the transition metals, log K lies between 3 and 9, and is sensitive both to Z and to the lacunary polyanion involved. Larger cations, Sr24, Ba2+, and tri- and tetra-valent lanthanides and actinides are also able to bind two lacunary ligands in a manner similar to that illustrated in Figure 18. Although the stepwise formation of 1 1 and 2 1 complexes of the... 

Formation constants are the equilibrium constants for complex ion formation. The stepwise formation constants, designated K, are defined as follows ... 

Write the stepwise acid-base reactions for the following ions in water. Write the correct symbol (for example. ATbl) for the equilibrium constant for each reaction. 

The formation of a complex ion is a stepwise process, and each step has its own characteristic equilibrium constant. For formation of Ag(NH3)2+, the reactions are... 

The measured equilibrium constants for this stepwise deprotonation scheme for Mo and W have been collected from the literature in [56]. They show that Mo is more hydrolyzed than W, and that the deprotonation sequence for Mo and W at pH = 1 reaches the neutral species M02(0H)2(H20)2. Assuming the deprotonation processes for the Sg compounds to be similar to those of Mo and W, Equations (6-9), V. Pershina and J.V. Kratz performed fully relativistic density-functional calculations of the electronic structure of the hydrated and hydrolyzed structures for Mo, W, and Sg [56]. By use of the electronic density distribution data, relative values of the free energy changes and by use of the hydrolysis model [29,30], constants of hydrolysis reactions (6-9) were defined [56]. These results show hydrolysis of the cationic species to the neutral species to decrease in the order Mo>W>Sg which is in agreement with the experimental data on hydrolysis of Mo and W, and on Sg [55] for which the deprotonation sequence may end earlier with a cationic species such as SgO(OH)3(H20)2+ that is sorbed on the cation-exchange resin. 

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