Chemical reaction, model dissolution

The just-suspended state is defined as the condition where no particle remains on the bottom of the vessel (or upper surface of the liquid) for longer than 1 to 2 s. At just-suspended conditions, all solids are in motion, but their concentration in the vessel is not uniform. There is no solid buildup in comers or behind baffles. This condition is ideal for many mass- and heat-transfer operations, including chemical reactions and dissolution of solids. At jnst-snspended conditions, the slip velocity is high, and this leads to good mass/heat-transfer rates. The precise definition of the just-suspended condition coupled with the ability to observe movement using glass or transparent tank bottoms has enabled consistent data to be collected. These data have helped with the development of reliable, semi-empirical models for predicting the just-suspended speed. Complete suspension refers to nearly complete nniformity. Power requirement for the just-suspended condition is mnch lower than for complete snspension. 

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. Many efforts have been made to describe the crystal dissolution behavior. A variety of empirical or semi-empirical models have been used to describe drug dissolution or release from formulations [1-6]. Noyes and Whitney published the first quantitative study of the dissolution process in 1897 [7]. They found that the dissolution process is diffusion controlled and involves no chemical reaction. The Noyes-Whitney equation simply states that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration ... 

Both models apply the same chemical scheme of mercury transformations. It is assumed that mercury occurs in the atmosphere in two gaseous forms—gaseous elemental HgO, gaseous oxidized Hg(II) particulate oxidized Hgpart, and four aqueous forms—elemental dissolved HgO dis, mercury ion Hg2+, sulphite complex Hg(S03)2, and aggregate chloride complexes HgnClm. Physical and chemical transformations include dissolution of HgO in cloud droplets, gas-phase and aqueous-phase oxidation by ozone and chlorine, aqueous-phase formation of chloride complexes, reactions of Hg2+ reduction through the decomposition of sulphite complex, and adsorption by soot particles in droplet water. 

Electrostatic vs. Chemical Interactions in Surface Phenomena. There are three phenomena to which these surface equilibrium models are applied regularly (i) adsorption reactions, (ii) electrokinetic phenomena (e.g., colloid stability, electrophoretic mobility), and (iii) chemical reactions at surfaces (precipitation, dissolution, heterogeneous catalysis). 

The FREZCHEM model is a chemical equilibrium model. For a reaction such as gypsum dissolution... 

Changes in the state of the adsorbent-adsorbate system which, at the atomic-molecular level, is described by the lattice-gas model are caused by variations in the occupancy of its individual sites as a result of the elementary processes. The following elementary processes occur on the adsorbent surface adsorption and desorption of the gaseous phase molecules, reaction between the adspecies, migration of the adspecies over the surface and their dissolution inside the solid. The solid s atoms are capable of participating in the chemical reactions with the gaseous phase molecules, as well as migrating inside the solid or on its surface. 

Correlations of the kind that appear in Fig. 3.4 must be tempered, however, with the reminder that Eqs. 3.1 and 3.7 always represent hypotheses about dissolution and precipitation processes. If the rates of these processes are controlled by how quickly aqueous-solution species can approach the surface of the solid phase transport control), then a rate law based solely on an assumed chemical reaction at the surface reaction control) is quite irrelevant. This issue cannot be decided simply by fitting rate data to models like that in Eq. 3.7, but instead must be resolved through direct experimentation (e.g., by comparing the temperature dependence of the reaction with that for aqueous species transport,... 

Thermodynamics is the basis of all chemical transformations [1], which include dissolution of chemical components in aqueous solutions, reactions between two dissolved species, and precipitation of new products formed by the reactions. The laws of thermodynamics provide conditions in which these reactions occur. One way of determining such conditions is to use thermodynamic potentials (i.e., enthalpy, entropy, and Gibbs free energy of individual components that participate in a chemical reaction) and then apply the laws of thermodynamics. In the case of CBPCs, this approach requires relating measurable parameters, such as solubility of individual components of the reaction, to the thermodynamic parameters. Thermodynamic models not only predict whether a particular reaction is likely to occur, but also provide conditions (measurable parameters such as temperature and pressure) in which ceramics are formed out of these reactions. The basic thermodynamic potentials of most constituents of the CBPC products have been measured at room temperature (and often at elevated temperatures) and recorded in standard data books. Thus, it is possible to compile these data on the starter components, relate them to their dissolution characteristics, and predict their dissolution behavior in an aqueous solution by using a thermodynamic model. The thermodynamic potentials themselves can be expressed in terms of the molecular behavior of individual components forming the ceramics, as determined by a statistical-mechanical approach. Such a detailed study is beyond the scope of this book. 

In summary, the two models of Figs. 27 and 28 provide new insights into the pH dependence of the surface topography of Si(l 11) in fluoride solutions (see Fig. 21). With increasing pH the uptake of the chemical reaction with water enhances the anisotropy of the dissolution since the chemical route depends critically on the atom coordination in contrast to the electrochemical one [122, 123 b]. 

D Me-S surface alloy and/or 3D Me-S bulk alloy formation and dissolution (eq. (3.83)) is considered as either a heterogeneous chemical reaction (site exchange) or a mass transport process (solid state mutual diffusion of Me and S). In site exchange models, the usual rate equations for the kinetics of heterogeneous reactions of first order (with respect to the species Me in Meads and Me t-S>>) are applied. In solid state diffusion models, Pick s second law and defined boundary conditions must be solved using Laplace transformation. 

In modeling this acid buildup, we might begin with the chemical reactions expected to produce soil acidity internally. This was shown earlier in this chapter to be due in part to the dissolution of biologically generated CO2 (or organic acids) in water. The relevant reactions of CO2 with water are discussed in Chapter 3 (see equations 3.55 and 3.56). The equilibrium expressions from these reactions are ... 

This work is not meant to be a basic kinetic study of the mechanism of the reaction. Rather it has as a goal the development of a simple kinetic rate expression which can be used in an overall model of oxidation including the complicating effects of solid dissolution and gas absorption. The goal is to accumulate kinetic data necessary to design a scrubber undergoing oxidation rather than to explore the mechanism of the complicated chemical reactions. 

A model has been developed for oxidation of calcium sulfite in a three-phase, semibatch reactor, The overall rate of conversion to sulfate depends on the rates of solid dissolution and liquid phase chemical reaction. In this first treatment of the problem, gas-liquid mass transfer resistance did not affect the overall rate of oxidation. 

Modeling of the Slurry Oxidation. In 1969 Ramachandran and Sharma(18) first proposed a film model for gas absorption accompanied by a fast chemical reaction in a slurry containing sparingly soluble, fine particles. A first case assumed that the solid dissolution in the liquid film next to the gas-liquid interface was unimportant. The second case assumed that it was important. Numerical solutions were given for the second case which indicated hat the specific rate of absorption of gas in the presence of fine particles could be considerably higher than in the absence of solids. 

The first case is calcium sulfite dissolution without chemical reaction. Using a film model will allow the calculation of the surface concentrations of all the species and the rate of dissolution. With a knowledge of the particle population and solution concentrations, most of the variables are known when the experiment starts. To specify all the starting values of the variables, the conditions at the particle surface are required. From the consideration of saturation concentration In the previous section during dissolution, the bulk liquid must obey ... 

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