Dissolution with chemical reaction, model

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 ... 

The dissolution of most minerals due to hydrolysis is a very complex, multistep and not always completely studied process. Currently it became obvious that it is associated with surface complexing. And in recent times ever more attention is devoted to what is going on on the surface of the mineral and within the inner layer Helmholtz layer. In 1970-2000 were simultaneously proposed several models of surface complexation participation in dissolution, which try to tie in properties of minerals with chemical reactions on their surface taking into account mass action law, balance of the substance and of the charge. Without discussing details of this mechanism we will only review its balance. 

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. 

Carbonate minerals are among the most chemically reactive common minerals under Earth surface conditions. Many important features of carbonate mineral behavior in sediments and during diagenesis are a result of their unique kinetics of dissolution and precipitation. Although the reaction kinetics of several carbonate minerals have been investigated, the vast majority of studies have focused on calcite and aragonite. Before examining data and models for calcium carbonate dissolution and precipitation reactions in aqueous solutions, a brief summary of the major concepts involved will be presented. Here we will not deal with the details of proposed reaction mechanisms and the associated complex rate equations. These have been examined in extensive review articles (e.g., Plummer et al., 1979 Morse, 1983) and where appropriate will be developed in later chapters. 

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,... 

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 ... 

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. 

A major problem with Equation 2.13 is that it leads to the heat of mixing being positive, that is, always endothermic, absorbing heat. Many solutions are exothermic, that is, heat is evolved when the solution is formed. There have been various efforts to model exothermic heats of mixing. These are generally dated to Dolezalek (34) who considered dissolution to represent processes similar to chemical reactions. 

With the emergence of a mineral, processes of its dissolution and formation run on its smface. The mechanisms of these processes include similar elemental reactions, which nm in opposite directions. Both include diffusion, ion exchange, adsorption and desorption and chemical reactions in the Helmholtz layer. Both are accompanied by absorption or release of heat. As a result, the solution s temperature changes. That is why, despite a guarantee of their mechanisms total identity, in modeling at the level of elemental reactions is acceptable and the principle of microsccopic reversibility of reactions introduced in 1924 by Richard Chace Tolman (188-1948) is used. It is assumed under this principle that the processes of dissolution and minerogenesis run through a series of the same elemental reactions (in trail) but in the opposite directions and maybe described by one common equation ... 

Propylene dissolves in two modes, a physical dissolution mode in the matrix and a binding mode resulting from a reversible chemical reaction with metal complexes. Henry s law commonly expresses the physical dissolution mode for small molecules, while the Langmuir model adequately describes the reversible binding mode, as shown in Eq. (9-2). Mathematically, a Langmuir adsorption isotherm for a small molecule in a porous media is identical to the expression of the olefin concentration bound to the metal complex. 

Fig. 4.20 shows schematically the accommodation along the x-axis. Mass accommodation occurs when a gas molecule strikes the particle surface for solid particles adsorption and surface chemistry almost occurs and for hydrometeors absorption (dissolution) and aqueous phase chemistry must be considered (Fig. 4.19). The uptake of molecules into droplets lowers the surface concentration ((Cat)o < cN)g < (ctv) J and results in a subsequent gas phase diffusion to the surface because of the concentration gradient. The mass accommodation coefficient a is the probability that a molecule that strikes the particle surface is adsorbed or enters the liquid. In a further application of the resistance model, we split the net uptake into two processes in series adsorption and dissolution (with possibly aqueous phase chemical reaction see later). Poschl et al. (2005) proposed the term surface accommodation coefficient for a.

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