Complexation mass balance equation, 90-95 thermodynamics

Thermodynamic data, whether determined through calorimetry or solubility studies, are subject to refinement as more exact values for the components in the reaction scheme, or more complete description of the solution phases, become available. Many of the solubility studies on clays were done before digital-computer chemical equilibrium programs were available. One such program, SOLMNEQ, written by one of the authors ( ) solves the mass-action and mass-balance equations for over 200 species simultaneously. SOLMNEQ was employed in this investigation to convert the chemical analytical data into the activities of appropriate ions, ion pairs, and complexes. 

Empirical Models vs. Mechanistic Models. Experimental data on interactions at the oxide-electrolyte interface can be represented mathematically through two different approaches (i) empirical models and (ii) mechanistic models. An empirical model is defined simply as a mathematical description of the experimental data, without any particular theoretical basis. For example, the general Freundlich isotherm is considered an empirical model by this definition. Mechanistic models refer to models based on thermodynamic concepts such as reactions described by mass action laws and material balance equations. The various surface complexation models discussed in this paper are considered mechanistic models. 

We consider the general balance equations of mass and energy in the absence of chemical reactions, and electrical, magnetic and viscous effects. The partial differential equations of these general balance equations represent the mathematically and thermodynamically coupled phenomena, which may describe some complex behavior due to interactions among various forces and flows within a system. 

Upon involving two or even more variables in connection with spatially inhomogeneous systems, the higher-order non-linearity gives rise to more complex phenomena. The best examples are systems controlled by simultaneous chemical reactions and mass diffusion. From the mathematical point of view, the system becomes localized at the thermodynamic branch and the initially stable solution of the appropriate balance equation bifurcates and new stable solutions suddenly appear often overlapping. One such a possibility is time-symmetry breaking, associated with the merging of time-periodic solutions known as limit... 

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, the thermodynamics of redox reactions, and Monod kinetics, may be omitted. Similarly, by excluding Chapter 4, an instructor can use the text for a course focused only on the water environment. In the case of a more advanced class, the instructor is encomaged 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 chemical equilibrium problems and groundwater transport simulations, and inclusion of case studies. References are provided with each chapter to assist the more advanced student in seeking additional material. 

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