Overall thermodynamic stability constant

The most important property of cyclodextrins is in their ability to accommodate guest molecules within their cavity, which has a volume of 262 per molecule or 157 mL per mol of [3-CD (cavity diameter 6.0-6.5 A). In aqueous solution, this cavity is filled with molecules of water the displacement of which by a less polar guest leads to an overall decrease in free energy. Stability constants and thermodynamic parameters for complexation of a vast number of guest molecules can be found in ref. [3]. 

Conditional (apparent) equilibrium constants - Equilibrium constants that are determined for experimental conditions that deviate from the standard conditions used by convention in - thermodynamics. Frequently, the conditional equilibrium conditions refer to - concentrations, and not to - activities, and in many cases they also refer to overall concentrations of certain species. Thus, the formal potential, i.e., the conditional equilibrium constant of an electrochemical equilibrium, of iron(II)/iron(III) may refer to the ratio of the overall concentrations of the two redox forms. In the case of complex equilibria, the conditional - stability constant of a metal ion Mm+ with a ligand L" refers to the overall concentration of all complex species of Mm+ other than Conditional equilibrium... 

Most of the thermodynamic studies have been performed in aqueous solutions as the cycles and their derivatives are first of all ligands for complexation of water-soluble metal ions. Numerous compounds have been studied and, therefore, only a general overview of trends is given. More information can be find in commercial databases such as NIST Standard Reference Database 46 (Critically Selected Stability Constants of Metal Complexes) or The IUPAC Stability Constants Database (SC-Database) or in reviews <2005PAC1445> (critically evaluated data for DOTA 3 and TETA 4), <1999CCR97> (protonation constants of polyamines) and <2000CCR309> (protonation constants of polyamino-polycarboxylic acids). Overall basicity of the ligands is mostly the main determinant for values of stability constants of metal complexes. 

Solvent extraction, potentiometry, and calorimetry have been used to determine the thermodynamic parameters of the formation of the monofluoride complex of the trivalent lanthanide ions at 25°C. and an ionic strength of IM (NaClOj ). The enthalpies were all endothermic, ranging from 4.0 to 9.5 Kcal./mole consequently, the large, positive entropies, ranging from 25 to 48 cal./°C./mole, explain the high stability constants. This large entropy results from the decrease in overall water structure when the fluoride ion is complexed. The difference in the enthalpies of formation of LnF and LnAc " can possibly be explained by a difference in covalence for Ln-F and Ln-O bonds. 

In this discussion, we shall also meet another closely related type of stability constant, the overall stability constant ((3), which represents the stability for a set of sequential complexation steps, rather than for an individual component step. It allows us to represent, for example, the stability constant for an overall reaction M + L forming ML , rather than just for a single ligand addition step such as M + L forming ML. As for K, the larger is (3, the more thermodynamically stable is the assembly. The overall stability constant is dealt with more fully in Section 5.1.3. 

Silver iodide (K p = 8.51 x 10 ) is less soluble than AgCl in aqueous solution, and so reduction of Ag(I) in the form of solid Agl is thermodynamically less favourable than reduction of AgCl (see problem 7.11 at the end of the chapter). However, Agl is much more soluble in aqueous KI than AgCl is in aqueous KCl solution. The species present in the iodide solution is the complex [Agl3] , the overall stability constant (see Section 6.12) for which is sslO " (equation 7.32). Following a similar procedure to that detailed above, we can use this value to determine that the... 

The reaction between CragOO " " and NO2 appears to be the only documented study of the interaction of a superoxometal complex with NO2. The 0-0 bond in the product CraqOONO + is weak and cleaves in the reverse process, the overall formation constant being 10 M . In comparison, the reaction of NO2 with HO2 is faster in the forward direction, = 1.8x10 M s (190) and slower in the reverse, /j = 0.005-0.05 s (225-227), yielding a much larger equilibrium constant, 7 66 = (3-6 x 10 ° —3.6 x 10 ) The weakening of the N-0 bond upon coordination of peroxynitrate can be traced to increased thermodynamic stability of the metal-superoxo fragment over H02-... 

The following entry defines the commonly used stability constants (stepwise, overall, conditional, association, dissociation, and pK) and relates the values to a rigorous thermodynamic definition of equilibrium constants. In addition, the article briefly outlines experimental techniques (potentiometric titration, spectroscopic methods involving ultraviolet/visible, infrared, Raman, fluorescence. and nuclear magnetic resonance spectroscopy), together with the numerical methods and computer programs that can be used to derive stability constants from such experimental data. 

The thermodynamic stabilities of coordination compounds are typically measured using stability or formation constants, as shown in Equations(l5.l)-(l5.4) for Cu(NH3)4+. The tetraaquacopper(ll) cation is used as the starting material in Equation (15.1) because the hydration enthalpy Is so negative that most metal ions cannot exist as naked cations in aqueous solution. It is not always possible for the stepwise constants to be measured individually, so typically only the overall formation constant is reported, where n is the number of ligands attached to the metal ion. If the stepwise stability constants do happen to be known, then the overall constant can be determined from the product of each individual formation constant. The stepwise formation constants for coordination compounds usually decrease in magnitude as the value of n increases. This is an entropic effect that has to do with the number of available substitutions. Thus, for example, addition of NH3 to [Cu(H20)4] " in Equation (15.1) has four possible positions available for substitution, whereas addition of NH3 to [Cu(NH3)3(H20)] in Equation (15.4) has only one possible position available for substitution. 

The thermodynamic stability of a metal complex may be represented by a stepwise formation constant (or stability constant) K or an overall stability constant P . The formation of a complex between a metal ion, M, and a ligand, L, is usually a substitution reaction. For example, metal ions in aqueous solution will be present as aqua ions. The reaction for the formation of the first complex could be written as ... 

The effect of the amine on the overall equilibrium constants of condensation reactions of carbonyl compounds and amines has been discussed above (see section II.A) where it was pointed out that the thermodynamic stability of the C=N— linkage increases with the type of amine used, in the order NH3 < aliphatic amines < aromatie amines < amines containing an adjacent electronegative atom with a free electron pair. In contrast to the overall equilibrium constants, the rate and equilibrium constants for addition compound formation appear to be dependent on the basicity of the amine. In studies in which different amines have been reacted with the same earbonyl compound under the same conditions, the following observations have been made. The equilibrium constants for addition compound formation with -chlorobenzaldehyde were found to be 21 7, 9-11, 4 14 1/mole for hydroxylamine (pJiTa = 6-0) methoxyamine (pA =... 

From this description of ion transport, several interesting questions arise. Is there a rate-limiting step in the overall reaction sequence, or do all reactions take place at comparable rates Is the ion specificity of the carrier determined by thermodynamic factors alone (stability constant of the complex MS ), or also by kinetic parameters (rate constants) To answer these questions, a detailed kinetic analysis of the carrier system must be made. Such an analysis appears difficult at first because of the need to determine not only the four rate constants, Kr, Kd, Ks, and Kms, but also the concentration of the carrier in the bilayer. The analysis becomes possible, however, by combining measurement of steady-state conductance with results obtained from electrical relaxation experiments [328]. 

If we consider how easily the [Fe (EDTA)] complex forms as a function of the experimental conditions, in particular and overall as a function of pH, we realize that an acidic medium favors its formation in accordance with the last reaction. This is not necessarily true, because, simultaneously, the acidic medium induces the protonation of EDTA, as relations (25.12)-(25.15) indicate. Therefore, it is difficult to predict which of the two effects is more important. Only the stability constant knowledge of all the superimposing equilibria allows this prediction, at least on thermodynamic grounds. To reinforce these considerations, weTl mention the fact that the [Fe(EDTA)] complex is also a diacid since it may accept two hydroxide ions (it is a Werner diacid) ... 

Thermodynamic Parameters From the calculated stability constants, the overall constants relatingto reaction (2.5) (M = PaO, / = 1, = 1 -3) can be derived. The calculated overall stability constants for the higher monomeric hydrolysis species are... 

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