Thermodynamic stability defined

For the use as a contrast agent the stability of the complex in vivo is most important. It depends significantly on the thermodynamic stability defined by Eq.(l). 

As with all determinations of thermodynamic stability, we comihehce by defining all stable phases possible, and their standard, chemical, potentials. For inost, metals there are many such phases, including oxides, hydroxides and dissolved ions. For brevity, here, only the minimum number of phases is Considered. The siriiplest system is a metal, ilf, which can oxidise lo form a stable dissolved pro,duct, (qorrpsipn), or to form a stable oxide MO (passivation), lit aqueous environments thfbe equilibria Can thereby be... 

In general, thermodynamic stability of a mixed-valence dinuclear complex, which is denoted as a combination of reduced (Red) and oxidized (Ox) sites, Red-Ox, is exhibited as a difference in redox potentials AE° = E°(Ox-Ox/Red-Ox) - °(Red-Ox/Red -Red). This difference is related to the comproportionation constant, Kc, defined in Eq. (1) ... 

The stability of a trivial assembly is simply determined by the thermodynamic properties of the discrete intermolecular binding interactions involved. Cooperative assembly processes involve an intramolecular cyclization, and this leads to an enhanced thermodynamic stability compared with the trivial analogs. The increase in stability is quantified by the parameter EM, the effective molarity of the intramolecular process, as first introduced in the study of intramolecular covalent cyclization reactions (6,7). EM is defined as the ratio of the binding constant of the intramolecular interaction to the binding constant of the corresponding intermolecular interaction (Scheme 2). The former can be determined by measuring the stability of the self-assembled structure, and the latter value is determined using simple monofunctional reference compounds. 

This is a situation that must rise where the alternative products are mutually interconvertible under the conditions of the reaction, either by direct isomerisation or by reversal of the reaction to form the starting material which then undergoes new attack to yield a more thermodynamically stable isomer. It is important to emphasise that the relative proportions of alternative products formed will be defined by their relative thermodynamic stabilities under the conditions of the reaction, which may possibly differ from those of the isolated molecules. Thus if m-dimethylbenzene is heated at 82° with HF and a catalytic amount of BF3 the proportions of the three isomeric dimethylbenzenes in the product resemble very closely those calculated thermodynamically ... 

Figure 2. The potential-pH (Pourbaix) diagram for aluminum in aqueous medium, defining regions of thermodynamic stability of the different species.

Solution equilibria for gadolinium imaging agents have been studied with consideration for pharmacokinetic, protein binding, elimination, and safety aspects of the dmgs. The thermodynamic stability constant, Kq defined by equation 7.4 must be large for clinically viable agents. Some Kq l data are listed in Table 7.3. 

As a measure of their thermodynamic stability, the pAfR+ values for the carbocation salts were determined spectrophotometrically in a buffer solution prepared in aqueous solution of acetonitrile. The KR+ scale is defined by the equilibrium constant for the reaction of a carbocation with water molecule (/CR+ = [R0H][H30+]/[R+]). Therefore, the larger p/CR+ index indicates higher stability for the carbocation. However, the neutralization of these cations was not completely reversible. This is attributable to instability of the neutralized products. The instability of the neutralized products should arise from production of unstable polyolefinic substructure by attack of the base at the aromatic core. 

Let us now consider redox limits for the thermodynamic stability of aqueous solutions. Maximum oxidation is defined by the dissociation of water molecules, with the formation of hydrogen ions and gaseous oxygen—i.e.,... 

The maximum reduction limit for the thermodynamic stability of water is defined by the reduction of hydrogen ions in solution with the formation of diatomic gaseous molecules H2 (normal hydrogen electrode) ... 

The stability constants are defined here in terms of concentrations and hence have dimensions. True thermodynamic stability constants K° and (3° would be expressed in terms of activities (Section 2.2), and these constants can be obtained experimentally by extrapolation of the (real) measurements to (hypothetical) infinite dilution. Such data are of limited value, however, as we cannot restrict our work to extremely dilute solutions. At practical concentrations, the activities and concentrations of ions in solution differ significantly, that is, the activity coefficients are not close to unity worse still, there is no thermodynamically rigorous means of separating anion and cation properties for solutions of electrolytes. Thus, single-ion activity coefficients are not experimentally accessible, and hence, strictly speaking, one cannot convert equations such as 13.6 or 13.8 to thermodynamically exact versions. 

Aromaticity has been long recognized as one of the most useful theoretical concepts in organic chemistry. It is essential in understanding the reactivity, structure and many physico-chemical characteristics of heterocyclic compounds. Aromaticity can be defined as a measure of the basic state of cyclic conjugated TT-electron systems, which is manifested in increased thermodynamic stability, planar geometry with non-localized cyclic bonds, and the ability to sustain an induced ring current. In contrast to aromatic compounds there exist nonaromatic and antiaromatic systems. Thus, pyrazine (69)... 

A stereoselective reaction on the other hand is one in which the stereo-electronic requirement of the reaction mechanism is such that two equally valid alternative pathways are available for the same mechanistic interaction between reactant and reagent. However, either the free energies of activation of the alternative reactions or the thermodynamic stabilities of the products differ, so that one isomer is formed in preference to the other selection has occurred. An example is provided by the reduction of cholestan-3-one (32). Equatorial attack (i) or axial attack (ii) of the hydride ion is mechanistically equally feasible and stereoelectronically defined. However, steric interactions between the hydride ion source and the conformationally fixed steroid molecule, together with considerations as to whether the reaction was under kinetic or thermodynamic control, would determine that the reaction is proceeding in a stereoselective manner. 

The corresponding (thermodynamic) stability constant K and the (thermodynamic) cumulative stability constant (P) are, according to Sillen and Martell (1964, 1971), defined as ... 

The difficulty to transform CO2 into other organic compounds lies in its high thermodynamic stability. Typical activation energies for the dissociation and recombination ofC02 are of 535 and 13 kJ/mol, respectively [5], The activation can occur by photochemical or electrochemical processes, by catalytic fixation or by metal-ligand insertion mechanisms. As documented in different reviews, organometallic compounds, metallo-enzyme sites and well defined metallic surfaces are able to activate carbon dioxide [6-16],... 

In addition to the linear free energy studies discussed, there have been many attempts to estimate the thermodynamic stabilities of electrophilic species, such as carbocations.7 The pKr+ values for carbocations reveal trends in relative stability and is defined as, according to the equilibrium established between the carbinol... 

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