Thermodynamic stability relations

The energy representation of the fundamental equation reveals that U-S diagrams at constant volume and composition provide complete thermodynamic information about a system. Since 

Isotherms on an A-V diagram are useful to illustrate the origin of p-V diagrams, superheated liquids and subcooled vapors in metastable states, unstable states between the spinodal points, critical points, and the requirement of mechanical stability. It is reasonable to assume that the slope of A vs. V at constant temperamre and composition is negative, because 

However, this is subject to controversy because negative pressure is not disallowed, even though negative absolute temperature is not possible. Several references that add fuel to the fire are Hayward (1971), Richards and Trevena (1976), and Sedgewick and Trevena (1976). 

The curvature condition that ensures single-phase behavior is 

Spinodal points represent the boundary between positive and negative curvature of A-V isotherms. An equilibrium state on the spinodal curve is defined by (9p/9V)7 ,au JV = 0. Regions between the spinodal points are intrinsically unstable and violate the criterion of mechanical stability. 

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It follows from the second law of thermodynamics, the Onsager relation Ltj = Lji, the thermodynamic stability condition (G3)... 

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)... 

Primarily connected to corrosion concepts, Pourbaix diagrams may be used within the scope of prediction and understanding of the thermodynamic stability of materials under various conditions. Park and Barber [25] have shown this relevance in examining the thermodynamic stabilities of semiconductor binary compounds such as CdS, CdSe, CdTe, and GaP, in relation to their flat band potentials and under conditions related to photoelectrochemical cell performance with different redox couples in solution. 

The (photo)electrochemical behavior of p-InSe single-crystal vdW surface was studied in 0.5 M H2SO4 and 1.0 M NaOH solutions, in relation to the effect of surface steps on the crystal [183]. The pH-potential diagram was constructed, in order to examine the thermodynamic stability of the InSe crystals (Fig. 5.12). The mechanism of photoelectrochemical hydrogen evolution in 0.5 M H2SO4 and the effect of Pt modification were discussed. A several hundred mV anodic shift of the photocurrent onset potential was observed by depositing Pt on the semiconductor electrode. 

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) ... 

Complexation of Cd with a series of polyamine macrocycles, but also related open-chain polyamines, comprising or attached to the 2,2 -bipyridine (bipy) and 1,10-phenanthroline (phen) moieties, has been studied by combined UV/vis spectrometry and potentiometry.24 Formation constants and distribution diagrams of the species present have been evaluated. As a result the thermodynamic stabilities, i.e., the formation constants, are lower for the bipy- and phen-contain-ing ligands than those for Cd complexes with aliphatic oligoaza macrocycles containing the same number of N donors. The probable reason is loss of flexibility of the ligands caused by the size and stiffness of the inserted heteroaromatic moieties. 

Another concept that may cause confusion is that of stability. Here, the term thermodynamic stability is used in relation to populations, while the term kinetic stability is used in relation to average lifetimes. Thus, the thermodynamically most stable conformer is the most populated one, while the kinetically most stable conformer is the one with the longest average lifetime. Whether these are necessarily the same is discussed on the basis of the examples. 

Knowledge of the 90 chemical elements and their properties in compounds led to the construction, by man, of a unique table of elements, the Periodic Table, of 18 Groups in six periods in a pattern fully explained by quantum theory, described in Chapter 2. There is then a huge variety of chemical combinations possible on the Earth and limitations on what is observable are related to element position in this Table. It also relates to the thermodynamic and/or kinetic stability of particular combinations of them in given physical circumstances (Table 11.3). The initial state of the surface of the Earth with which we are concerned was a dynamic water layer, the sea, covering a crust mainly of oxides and some sulfides and with an atmosphere of NH3, HCN, N2, C02(C0, CH4), H20, with some H2 but no 02. This combination of phases and their contents then produced an aqueous solution layer of particular components in which there were many concentration restrictions between it and the components of the other two layers due to thermodynamic stability, equilibria, or kinetic stability of the chemicals trapped in the phases. It is the case that equilibrium... 

It is therefore assumed that the p-variation in hydration comes only from a thermodynamic effect, related to a Y-dependent change in the stability of the intermediate, whereas in bromination, a transition-state shift adds to this latter effect, as expressed by (49) and (52), where log kY expresses the reactivity of PhCY=CH2. The second term in (52) is probably negligible in hydration... 

Table 6.1 summarizes the thermodynamic parameters relating to the macrocyclic effect for the high-spin Ni(n) complexes of four tetraaza-macrocyclic ligands and their open-chain analogues (the open-chain derivative which yields the most stable nickel complex was used in each case) (Micheloni, Paoletti Sabatini, 1983). Clearly, the enthalpy and entropy terms make substantially different contributions to complex stability along the series. Thus, the small macrocyclic effect which occurs for the first complex results from a favourable entropy term which overrides an unfavourable enthalpy term. Similar trends are apparent for the next two systems but, for these, entropy terms are larger and a more pronounced macrocyclic effect is evident. For the fourth (cyclam) system, the considerable macrocyclic effect is a reflection of both a favourable entropy term and a favourable enthalpy term. 

This conditional stability constant, K, is related to the thermodynamic stability constant (KM]J by (133) ... 

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). 

If the metals bound in complexes exchange with biological ligands, the dissociation kinetics of these complexes, the ligand-exchange kinetics and the association kinetics with the biological ligands must be considered. Simple dissociation kinetics of complexes are related to their thermodynamic stability constants by the relationship ... 

The amorphous phase is not usually a desirable state for the API because the formation process is more random and difficult to control than a crystallization. A second dispersed liquid phase is usually formed just prior to freezing and may coalesce or disperse under the influence of hydrodynamic forces in the crystallizer, making the process sensitive to micro-mixing effects on scale up. Amorphous solids also have significantly lower thermodynamic stability than related crystalline material and may subsequently crystallize during formulation and storage. Because of the non-uniformity of the amorphous solid it can more easily incorporate molecules other than the API, making purification less effective. 

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