Solubilities and Equilibria

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

Generalized computer techniques for calculating vapor-liquid equilibria and solubility relationships in electrolyte systems are not readily available in the metallurgical industry. 

Gases interact with solids at high pressures, either by adsorption to crystal surfaces or by dissolution into amorphous materials, leading to volume changes. An experimental method to study the behavior of solids in the presence of dense gases has been developed. Sorption equilibria and solubilities are determined gravimetrically. Diffusion coefficients are derived with the help of suitable mass-transfer models. The swelling behavior of the solids is observed visually. 

These three approaches have found widespread application to a large variety of systems and equilibria types ranging from vapor-liquid equilibria for binary and multicomponent polymer solutions, blends, and copolymers, liquid-liquid equilibria for polymer solutions and blends, solid-liquid-liquid equilibria, and solubility of gases in polymers, to mention only a few. In some cases, the results are purely predictive in others interaction parameters are required and the models are capable of correlating (describing) the experimental information. In Section 16.7, we attempt to summarize and comparatively discuss the performance of these three approaches. We attempt there, for reasons of completion, to discuss the performance of a few other (mostly) predictive models such as the group-contribution lattice fluid and the group-contribution Flory equations of state, which are not extensively discussed separately. 

Note that it is general practice not to inclnde nnits for the eqnilibrinm constant. In thermodynamics, K is defined as having no nnits because every concentration (molarity) or pressure (atm) term is actually a ratio to a standard value, which is 1 M or 1 atm. This procedure eliminates all units but does not alter the numerical parts of the concentration or pressure. Consequently, K has no units. Later we will extend this practice to acid-base equilibria and solubility equilibria (to be discussed in Chapters 15 and 16). 

From the hydrolysis equilibria and solubility data, the activities of the other potential-determining ions can be calculated. 

The set of species with the lowest overall objective function was considered as the best fit and the results are used in the present hydrolysis model. Sections V.2.1.2, V.3.1 and V.3.2.1.3 detail, respectively, the results obtained from the best fit for the following model paremeters Af/f°(Zr , 298.15K), complex formation equilibria and solubility of Zr02 (mono). 

In this part of your study of general chemistry, it is typical to explore how a chemical system comes to equilibrium and how that equilibrium is represented. Interpretation of equilibrium constants, calculation of concentrations in equilibrium systems, equilibrium in gas phase reactions, relationship of enthalpy to equilibrium, acid-base equilibria, and solubility equilibria all fall into this area of study. 

CHAPTER 16 ACID-BASE EQUILIBRIA AND SOLUBILITY EQUILIBRIA... 

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