Erich Koenigsberger

The standard equilibrium constant, K⊖(T), for a chemical reaction is a dimensionless quantity defined by K⊖(T)=exp{−ΔrG⊖(T)/RT}, where ΔrG⊖(T) is the change in the standard molar Gibbs energy due to the reaction. The value of K⊖(T) depends on the choice of the standard state, which must be specified. The standard equilibrium constant is, like all standard thermodynamic quantities, independent of pressure and composition (Ewing et al. 1994; Cohen et al. 2008).

Solubility phenomena (i.e. dissolution and precipitation reactions) are the physicochemical basis of numerous biological processes. These include, for instance: • gas solubilities in respiratory and photosynthetic processes; the solubility of volatile anaesthetics; • the crystallisation, both in biologically controlled and pathological processes, of biogenic minerals in a variety of body fluids; the resorption of mineralised tissue; • the accumulation, due to their higher solubility, of lipophilic substances, such as pesticides, in liquid fat contained, e.g. in adipose tissue or human milk; • the incorporation of metal ions such as strontium (including the radioactive 90Sr isotope) in bone, by co-precipitation and solid-solution formation. Since Sr stabilises bone apatite crystals (i.e. decreases solubility), it may retard the resorption of the calcified matrix and thus have therapeutic potential in the prevention and treatment of osteopenic disorders [1]. In dental enamel, a combination of strontium and fluoride was reported to be more effective in stabilising the apatetic structure than each element alone [2]. This results in an improved crystal resistance to degradation by bacterial acids and hence may be useful for the prevention of dental caries [3]. All of these solubility phenomena are governed by the laws of thermodynamics and kinetics. The human body is essentially an isothermal system (a notable exception, related to gout, has been reported in the literature – see below). Thus, the pertinent in vitro measurements have almost always been performed at 37_C. However, reactions in body fluids are complicated by the presence of organic complexing agents which affect the speciation of metal ions (i.e. their distribution among these complexes). Computer speciation modelling of biofluids, which has a long history [4], has also to be considered in the modelling of solubility equilibria. The presence of organic macromolecules such as proteins provides templates or matrices which control the crystallisation of biogenic minerals and modify their morphologies. The mineral phase in organic/inorganic composites (such as teeth or bone) may form nanosized crystals, which exhibit unusual dissolution and crystallisation behaviour [5]. A new biomineralisation mechanism invoking liquid precursors and their importance for normal and pathological biomineralisation processes has been proposed [6]. These and other aspects of normal and pathological biomineralisation processes have been reviewed recently [7].

(Book Overview) This new book discusses important topics on one of the most basic of thermodynamic properties, namely Solubility - a property which underlies most industrial processes. The objective of the book is to bring together new, exciting and disparate topics, all related to Solubility, in a single volume, so that readers can extend their horizons and relate hitherto unrelated topics, leading to innovative and creative ideas.

Biomineralization, which refers to the complex processes by which organisms form minerals, is frequently associated with a high degree of regulation on different hierarchical levels [1,2]. ‘Biologically controlled’ mineralization, in which extra-, inter- and intracellular activities direct the nucleation, growth and morphology of minerals that form ‘normal’ biomaterials such as bone and teeth [1,2], is fundamentally different from ‘biologically induced’ mineralization, which occurs as a result of interactions between biological activity (affecting e.g. the pH and composition of secretion products) and the environment [1,2]. Since there is little control of the biological system over the type and habit of minerals deposited, these vary as greatly as the environments in which they form and are often poorly defined, heterogeneous and porous [1,2]. Biologically induced mineralization is commonly associated with various bacterial activities and with epicellular mineralization in marine environments, occasionally leading to the complete encrustation of organisms, that sink subsequently and form sediments [1,2]. However, its characteristic features are also typical for uncontrolled ‘pathological’ crystallization resulting in painful or even life threatening conditions such as calculi formation (renal, biliary, pancreatic or sublingual), development of gout or arteriosclerosis, tissue calcification associated with cancer, etc.

Solubilities in aqueous media of sparingly soluble ionic compounds or homogeneous solid mixtures play an important role in chemical processes, whether carried out on a laboratory or an industrial scale. The respective solubility phenomena, i.e. dissolution and precipitation reactions, frequently control procedures for preparing, separating and purifying chemicals. Moreover, the interactions of the hydrological cycle with the cycle of rocks, the naturally occurring dissolution of minerals in water, as well as their precipitation on the ocean floor and in the sediments of rivers and lakes, can often be simply described iii terms of solubility equilibria, although gigantic quantities of material may be involved. Solid—solute equilibrium chemistry has usually been restricted to pure solids, whereas most minerals are solid solutions. Consequently, this chapter also deals with homogeneous solid mixtures or solid solutions, whose solubilities not only depend on those of the respective end members but also on the excess Gibbs energies of mixing.

It is often believed that macroscopically observable properties of electrolyte systems, like thermodynamic quantities or solubilities, can be derived from solid-solute-solvent interactions once computers have become powerful enough to solve complicated equations in order to calculate ‘everything’ from first principles. In contrast, holism claims that completely new qualities emerge in macroscopic systems, and simple reductionism is a fundamentally wrong concept because microscopic and macroscopic properties are complementary to each other in the sense of Niels Bohr’s famous concept. In fact, all molecular-level theories, but also empirical models, have failed so far to predict, for instance, solubilities of ionic solids over wide ranges of temperature, pressure, and composition in sufficient accuracy for industrial, geochemical, or environmental applications.

The following definitions and examples are based on recent recommendations by the Union of Pure and Applied Chemistry (Ewing et aZ., 1994; cf. also the recommendations given in Mills et ai., 1993). Further details can be found in textbooks on chemical thermodynamics (e.g. McGlashan, 1979). According to IUPAC, all standard chemical potentials and standard equilibrium constants are defined in terms of an arbitrarily chosen standard pressure. Alternative definitions with explicit pressure dependencies of these quantities are possible for reactions in condensed phases (e.g. Wood and Battino, 1990). This, however, requires different relationships for reactions in condensed and gaseous phases, because for the latter the standard thermodynamic quantities are usually defined for a standard pressure of 1 bar.

Thermodynamically, a solution is a special description of a homogeneous mixture for which it is convenient to distinguish between the solvent A on the one hand and the solutes B, C, ... , on the other hand. This asymmetrical description arises from a different choice of the standard states, i.e. the thermodynamic functions of solvent and solutes are referred to the states of the pure substance and infinite dilute solution, respectively. A solid solution, however, usually consists of components which are thermodynamically treated in the same way, i.e. with the states of the pure substances as reference states. In some textbooks on chemical thermodynamics (e.g. McGlashan, 1979) they are therefore referred to as homogeneous solid mixtures. The term solid solution, which implicitly suggests mixing at the scale of single crystals, is nevertheless the common expression used in geochemical literature. This article focuses on physicochemical fundamentals and comparatively simple models of solid solutions. Several other, more complicated models have been described in literature. Related concepts are ordering models or the thermodynamics of defect structures (see Mineral defects).