Thermodynamics, of equilibria between

We shall see later (Frames 35, 37, 38, 39) that G and G° can, under certain circumstances, be replaced by chemical potentials, fj, and and that these relationships and that of (20.12) are really key equations when considering the thermodynamics of equilibria between phases (Frame 35). 

Thermodynamics of equilibria between water vapor and saline hydrates non-stoichiometric hydrates... 

Controlled oxidation of mixtures of both rubidium and cesium metals leads under equilibrium conditions only to the cesium clusters CsnOa in the form of the compounds [CsnOaJCsio-xRbx, [CsnOajRbv-xCSx, or [CsiiOajCsi-xRbx. Only after the consumption of all the cesium can the rubidium partially replace the cesium in the clusters. This feature indicates the presence of equilibria between actual chemical species with different relative thermodynamic stabilities. The ionization energy of cesium is lower than that of rubidium. This feature appears to be determinant in the relative stability of the suboxides, higher for CsuOa than for Rb902, deduced from the experiments discussed above. 

The thermochromic behavior of some metallic complexes in solution stems from the existence of equilibria between different configurations of the complexes (of different colors) at different temperatures (7,8). These equilibria thus have specific thermodynamic and spectral characteristics. Practical problems are often encountered in the experimental determination of these characteristic parameters. The present study was designed to ... 

The importance of the Gibbs free energy and the chemical potential is very great in chemical thermodynamics. Any thermodynamic discussion of chemical equilibria involves the properties of these quantities. It is therefore worthwhile considering the derivation of equation 20.180 in some detail, since it forms a prime link between the thermodynamics of a reaction (AG and AG ) and its chemistry. 

Table 8.1 is a thermodynamic acidity scale and applies only to positions of equilibria. For the distinction between thermodynamic and kinetic acidity, see p. 228. 

Liquid-Fluid Equilibria Nearly all binary liquid-fluid phase diagrams can be conveniently placed in one of six classes (Prausnitz, Licntenthaler, and de Azevedo, Molecular Thermodynamics of Fluid Phase Blquilibria, 3d ed., Prentice-Hall, Upper Saddle River, N.J., 1998). Two-phase regions are represented by an area and three-phase regions by a line. In class I, the two components are completely miscible, and a single critical mixture curve connects their criticsu points. Other classes may include intersections between three phase lines and critical curves. For a ternary wstem, the slopes of the tie lines (distribution coefficients) and the size of the two-phase region can vary significantly with pressure as well as temperature due to the compressibility of the solvent. 

The discussion of moisture uptake by hygroscopic materials must include a description of the thermodynamics of vapor-liquid equilibria. For gas (g) and liquid (1) phases to be in equilibrium, the infinitesimal transfer of molecules between phases (dng and dn ) must lead to a free energy change of zero. 

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... 

The theory of equilibrium is treated on the basis of thermodynamics considering only the initial and final states. Time or intermediate states have no concern. However, there is a close relationship between the theory of rates and the theory of equilibria, in spite of there being no general relation between equilibrium and rate of reaction. A good approximation of equilibrium can be regarded between the reactants and activated state and the concentration of activated complex can, therefore, be calculated by ordinary equilibrium theory and probability of decomposition of activated complex and hence the rate of reaction can be known. 

We begin with a discussion of the vapor pressure isotope effect (VPIE). To do so we compare the equilibria between condensed and vapor phase for samples of two isotopomers. At equilibrium, condensed(c) = vapor(v), the partial molar free energies, a(v), and p,(c), of the two phases are equal this, in fact, is the thermodynamic... 

Design of extraction processes and equipment is based on mass transfer and thermodynamic data. Among such thermodynamic data, phase equilibrium data for mixtures, that is, the distribution of components between different phases, are among the most important. Equations for the calculations of phase equilibria can be used in process simulation programs like PROCESS and ASPEN. 

A phase diagram is often considered as something which can only be measured directly. For example, if the solubility limit of a phase needs to be known, some physical method such as microscopy would be used to observe the formation of the second phase. However, it can also be argued that if the thermodynamic properties of a system could be properly measured this would also define the solubility limit of the phase. The previous sections have discussed in detail unary, single-phase systems and the quantities which are inherent in that sjrstem, such as enthalpy, activity, entropy, etc. This section will deal with what happens when there are various equilibria between different phases and includes a preliminary description of phase-diagram calculations. 

Except for some anionic/cationic surfactant mixtures which form ion pairs, in a typical surfactant solution, the concentration of the surfactant components as monomeric species is so dilute that no significant interactions between surfactant monomers occur. Therefore, the monomer—mi celle equilibria is dictated by the tendency of the surfactant components to form micelles and the interaction between surfactants in the micelle. Prediction of monomer—micelle equilibria reduces to modeling of the thermodynamics of mixed micelle formation. 

The earliest work in this area assumed that particles in the atmosphere were solid and that the uptake of SOC involved adsorption to a solid or solid-like surface. It was subsequently recognized that many atmospheric particles are liquid or have liquid-like outer layers, and hence the uptake of gases could be treated as absorption into a liquid. These approaches are summarized in the following. It should be noted that these treat the equilibria between the gas- and condensed-phase species i.e., it is assumed that thermodynamics rather than kinetics controls the distribution between the phases. The implications of this assumption are discussed later. 

Clark and Odell have found (39) that the susceptibility varies with temperature in a way that can be explained very well on the basis of temperature-dependent equilibria between diamagnetic and paramagnetic forms. This is valid equally for pyridine and for inert solvents. Thermodynamic quantities calculated from these measurements show that the paramagnetic forms have the lower enthalpies, and that there are relatively large increases of entropy on going from the paramagnetic to the diamagnetic forms. 

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