Activity coefficients basic concepts

A fundamental concept in all theories for determining activity coefficients is that ionic interactions are involved. These interactions cause a deviation in the free energy associated with the ions from what it would be if they did not occur. Consequently, at the limit of an infinitely dilute solution, activity coefficients go to 1 because there are no ionic interactions. This basic consideration also leads to the idea that as the concentration of ions increases, their extent of interaction must also increase. Ionic strength is a measure of the overall concentration of ions in a solution and the fact that more highly charged ions exert a greater influence on ionic interactions. It is calculated as ... 

In this chapter, we introduced the reader to some basic principles of solution chemistry with emphasis on the C02-carbonate acid system. An array of equations necessary for making calculations in this system was developed, which emphasized the relationships between concentrations and activity and the bridging concept of activity coefficients. Because most carbonate sediments and rocks are initially deposited in the marine environment and are bathed by seawater or modified seawater solutions for some or much of their history, the carbonic acid system in seawater was discussed in more detail. An example calculation for seawater saturation state was provided to illustrate how such calculations are made, and to prepare the reader, in particular, for material in Chapter 4. We now investigate the relationships between solutions and sedimentary carbonate minerals in Chapters 2 and 3. 

Hydrogeochemical models are dependent on the quality of the chemical analyses, the boundary conditions presumed by the program, theoretical concepts (e.g. calculation of activity coefficients) and the thermodynamic data. Therefore it is vital to check the results critically. For that, a basic knowledge about chemical and thermodynamic processes is required and will be outlined briefly in the following chapters on hydrogeochemical equilibrium (chapter 1.1), kinetics (chapter 1.2), and transport (chapter 1.3). Chapter 2 gives an overview on standard... 

The seasoned Debye-Hiickel (D-H) theory, put forth in 1923 [33,34] takes into account the contribution of the ionic electrostatic interactions to the free energy of a solution and provides a quantitative expression for the activity coefficients. The basic concept of the D-H theory is that the long-range Coulomb interaction between two individual ions bathed in a salt solution is mediated by mobile ions from the solution. The effective charges of a certain ion are decreased as the result of charge screening by the mobile counterions it follows that, at sufficient distance, the interaction between two ions decays exponentially. We briefly outline the main considerations and assumptions of the D-H model ... 

Depending on the nature of the class, the instructor may wish to spend more time with the basics, such as the mass balance concept, chemical equilibria, and simple transport scenarios more advanced material, such as transient well dynamics, superposition, temperature dependencies, activity coefficients, redox energetics, and Monod kinetics, can be skipped. Similarly, by omitting Chapter 4, an instructor can use the text for a water-only course. In the case of a more advanced class, the instructor is encouraged to expand on the material suggested additions include more rigorous derivation of the transport equations, discussions of chemical reaction mechanisms, introduction of quantitative models for atmospheric chemical transformations, use of computer software for more complex groundwater transport simulations, and inclusion of case studies and additional exercises. References are provided... 

J. Pharma Set., 74, pp. 807-814 (1985)] to estimate infinite-dilution partition ratios for solute distributed between water and an organic solvent. The model uses 36 generalized parameters and four solvatochromic parameters to characterize a given solute. The solvatochromic parameters are a (acidity), p (basicity), K (polarity), and 6 (polarizability). Another method utilizing LSER concepts is the SPACE model for estimating infinite-dilution activity coefficients [Hait et al., Ind. Eng. Chem. Res., 32(11), pp. 2905-2914 (1993)]. Also see Abraham, IbnSiim, and Zissi-mos, J. Chromatography, 1037, pp. 29-47 (2004). 

These basic concepts and techniques were further extended in the fifties and sixties by Russell and coworkers [8] to structure reactivity relationships for aromatic compounds, by Mayo et al. [9] to copolymerization of oxygen with many vinyl monomers, and by Ingold and Howard to extensive measurements of absolute rate coefficients for peroxy and alkoxy radicals [10]. During this same period, an active group in the Soviet Union including Emanuel et al. [11] examined many complex oxidation systems. 

Activity coefficient models. Prausnitz, Lichtenthaler, and de Azevedo (1986) provide an excellent presentation of activity coefficient models and theories of solutions extensively in Chapters 6 and 7 of their book. Here, we briefly review the basic concepts beyond various activity coefficient models. 

The basic assumption of the Hammett method is that the activity coefficient ratio /bh+//b is independent of the nature of B at any given solvent composition. This seems to be a reasonably good assumption for a closely related series of bases, such as the primary anilines, but may not be true for bases of different structural types. This has led to the proposal of many different types of acidity function, and to much controversy as to the meaning and usefulness of the Hammett and related acidity functions. This subject has been extensively reviewed elsewhere [16]. Although it now appears that the concept of the acidity function is perhaps not as generally useful as was originally believed, at the present time we do not have any more reliable method of assessing the acidities of superacid media. 

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