Equilibrium aspects

An acid is a species such as the ammonium ion or the acetic acid molecule which has a tendency to lose a proton. A base (such as the ammonia molecule or the acetate anion) is able to accept a proton. Hence for every acid, HA, there is a conjugate base. A , and for every base, B, there is a conjugate acid, BH.  

Water is both a weak acid and a weak base, Ha O + O H3 O + OH  

The strength of an acid, HA, in aqueous solution is expressed by its dissociation constant, K, where 

It is often convenient to express the strengths of acids and bases in terms of pATa values, where pATa = —log ATj. Extensive compilations of pATa values of organic and inorganic acids and bases are available (Kortiim et al., 1961 Perrin, 1965, 1969, 1972). 

This equation can be regarded as the fundamental relation describing buffer equilibria. However, in assigning values to the concentration terms in this equation it is common to neglect the interaction of the acidic and basic species with the solvent water. This can lead to significant error outside the pH range 3 to 11, and it is tacitly assumed in the remainder of this Chapter that the equation will be used only within these limits. (For a fuller derivation and discussion of the Henderson-Hasselbalch equation, and its limitations, see Appendix IV.) 

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Both the kinetics and the equilibrium aspects of ion exchange involve more than purely surface chemical considerations. Thus, the formal expression for the exchange... 

In the previous section, non-equilibrium behaviour was discussed, which is observed for particles with a deep minimum in the particle interactions at contact. In this final section, some examples of equilibrium phase behaviour in concentrated colloidal suspensions will be presented. Here we are concerned with purely repulsive particles (hard or soft spheres), or with particles with attractions of moderate strength and range (colloid-polymer and colloid-colloid mixtures). Although we shall focus mainly on equilibrium aspects, a few comments will be made about the associated kinetics as well [69, 70]. 

The layout of this article is as follows Section 2 considers the equilibrium aspects of the crystals whilst Sects. 3 and 4 explain the growth theories, divided into nucleation and non-nucleation theories, respectively. Finally, Sect. 5 provides an overview and suggests future lines of investigation. 

Taube H. 1986. Interaction of dioxygen species and metal ions—Equilibrium aspects. Prog Inorg Chem 34 607. 

The fundamentals of the first aspect are dealt with in Sections 4.1 and 4.2, concerning the equilibrium relations and the transport processes, respectively. Furthermore, equilibrium aspects of the emission of hydrogen sulfide from the water phase into the sewer atmosphere are included in Section 4.1 as relevant and illustrative. 

One aspect of the research will examine equilibrium aspects of solvation at hydro-phobic and hydrophilic interfaces. In these experiments, solvent dependent shifts in chromophore absorption spectra will be used to infer interfacial polarity. Preliminary results from these studies are presented. The polarity of solid-liquid interfaces arises from a complicated balance of anisotropic, intermolecular forces. It is hoped that results from these studies can aid in developing a general, predictive understanding of dielectric properties in inhomogeneous environments. 

Ion exchange on soils and soil constituents has been known since Aristotle s time. It was rediscovered as base exchange by soil scientists in the nineteenth century (Thompson, 1850 Way, 1850), and since that time a voluminous amount of research has appeared in the scientific literature. However, most of these studies, particularly in the soil and environmental sciences, have dealt with equilibrium aspects of ion exchange, and only recently have studies appeared on the kinetics and mechanisms of exchange phenomena. 

Besides pesticides, toxic organic substances are of great concern as we attempt to preserve the quality of our environment. Many of these substances have been deposited into aquatic and soil environments. In addition to understanding the equilibrium aspects of these pollutants in soils and sediments, it is imperative that there be an understanding of the rates and mechanisms of retention and mobility. Unfortunately, few of these studies have appeared in the scientific literature. This is most certainly an area of research in the soil and environmental sciences that needs extensive investigation. 

The equilibrium aspect of micelle formation can be considered by application of the second law of thermodynamics. The equilibrium constant for the process represented by Eq. (3) is given by... 

Excess Electrons in Polar SCFs - Equilibrium Aspects... 

A. Ulitski, R. Elber, The thermal equilibrium aspects of the time dependent Hartree and the locally enhanced sapling approximations Formal properties, a correction, and computational examples for rare gas clusters, J. Chem. Phys. 98 (1993), 3380. 

Adsorption from solution is discussed by Adamson, but with emphasis on the equilibrium aspects, rather than the kinetics. The subject can conveniently be divided into adsorption of non-electrolytes and adsorption of electrolytes. The former can be treated for dilute solutions, in a similar manner to adsorption of gases on solid surfaces. Multilayer adsorption has been observed however, so that... 

The crystallization of a liquid is a change of phase in which symmetry is broken a spatially periodic state arises from one that was invariant under translations. A full description of such a phase change would involve three components (1) an understanding of the equilibrium aspects of the transition (at what temperature and pressure it takes place, what changes in thermodynamic properties such as volume and entropy accompany it), (2) a micro-... 

The equilibrium aspect here is referred to as the sorption isotherm. The calculation can be conducted according to empirical expressions such as Langmuir and Freundlich equations and IX theories. The aim of the calculations is to determine the treatment results and the operational conditions (e.g., mass of IXR applied). 

Taube, Henry, Interaction of Dioxygen Species and Metal Ions—Equilibrium Aspects. 34 607... 

A polymer s usefulness and lifetime are often determined by the rate at which a minor chemical constituent is released by the polymer. Obvious examples are the desorption of antioxidants and plasticizers. To quantitatively describe this phenomenon requires a knowledge of the diffusants transport and thermodynamic properties within the polymer and in the environmental fluid phase. The main objective of this paper is to examine the thermodynamic or equilibrium aspect of this problem. 

Hippel, P. H. von, Revzin, A., Gross, C. A., Wang, A. C. (1974). Non-specific DNA binding of genome regulating proteins as a biological control mechanism I. The lac operon Equilibrium aspects. Proc. Natl. Acad. Sci. USA 71,4808-4812. 

Some authors have taken a different approach by studying the kinetics, rather than the equilibrium aspects, of cation exchanges and a short summary of the background to these follows. 

In the preceding chapter we learned the equilibrium aspects of radiation, including emissive power and surface properties. In the present chapter we proceed to the nonequilibrium or transport aspects of radiation. 

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