Dissolution, solids

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

Physical Ionic solid Dissolution is based on hydration Sodium chloride in water NaCl + (x + y)H20—>Na(H20)J + C1(H20) ... 

Chemical Partially-ionic- covalent-bond solids Dissolution is based on neutralization Aluminum hydroxide in acid or base Al(OH)3 + 3 H+ Al3+ + 3 H20 A1(0H)3 + 0H-->A10(0H)2 (aq) + H20... 

Electro- chemical Conducting solids Dissolution is based on redox process Iron in acid Fe + 2 H+ — Fe2+ + H2... 

As an alternative to film models, McNamara and Amidon [6] included convection, or mass transfer via fluid flow, into the general solid dissolution and reaction modeling scheme. The idea was to recognize that diffusion was not the only process by which mass could be transferred from the solid surface through the boundary layer [7], McNamara and Amidon constructed a set of steady-state convective diffusion continuity equations such as... 

Other researchers used flow between two parallel plates as the experimental and theoretical system to incorporate diffusion plus convection into their dissolution modeling and avoid film model approximations [10]. Though they did not consider adding reactions to their model, these workers did show that convection was an important phenomenon to consider in the mass transfer process associated with solid dissolution. In fact, the dissolution rate was found to correlate with flow as... 

The difficulty here is that the ion-activity product includes not only the Gibbs energy change in a solid dissolution process but also the activity of the solid itself. Consider, as a simple example, the dissolution of CdCOjis), for which the ion-activity product (IAP) is (12) ... 

Although, as described by Bjerle et alS13 liquid jet-type absorbers are also used, one relatively recent application of mass transfer in agitated tanks with chemical reaction is the absorption of pollutants from flue gases and, in particular, the scrubbing of sulphur dioxide by a slurry containing fine limestone particles. In this case, the concentration of sulphur dioxide is usually very low and the mechanism of the absorption is complicated due to the presence of solids in the liquid phase where the rate of solid dissolution may significantly affect the absorption rate. 

Studies on the dissolution of solids in the liquid phase include that of Hixson and Baum(74) whose correlation of data in terms of Reynolds, Sherwood and Schmidt numbers, discussed in detail in Section 10.2 in connection with mass transfer during leaching, is one of the most frequently used methods for calculating the mass transfer coefficient for the solid dissolution. 

Novak CF, Lake LW (1989) Diffusion and solid dissolution/precipitation in permeable media. AIChE 135 1057-1072... 

Scale-up based on the mass-transfer rate between phases is directly related to liquid turbulence and motion at the interface. Scale-up of solids dissolution rate or mass transfer between liquid phases is adequately handled utilizing 2/3 as an exponent... 

In general, the following steps can occur in an overall liquid-solid extraction process solvent transfer from tile bulk of the solution to the surface of the solid penetration or diffusion of the solvent into the pores of the solid dissolution of the solvent into the solute solute diffusion lo ihe surface of the particle and solute transfer to the bulk of the solution. Any one of the five basic processes may be responsible for limiting the extraction rale. 

Advantages of Using Metastable Solids Dissolution Rate Improvement... 

Solid Dissolution. The dissolution rate of a solid, whether it be a nondisintegrating compact or a powder, generally decreases with time because of the reduction in surface area as the dissolution proceeds. The familiar cube-root law for dissolution of solids was derived by Hixson and Crowell (1 on the basis of diffusion away from the surface of a spherically-shaped solid. The convex surface of a sphere decreases in area as solid mass is lost from the surface so that the dissolution rate decreases in proportion to the decrease in area until the solid is completely dissolved. By including shape factors, this model has been extended to describe the dissolution of various prismatic forms (2). As in the case of spherical particles, the dissolution rates decrease with time as the dissolution process progresses because of the decrease in area. 

Case A Small concentration of solids or large particle size compared to the thickness of liquid film In this case, solid dissolution during diffusion of species C in the liquid film can be neglected. The solid dissolution and chemical reaction can be assumed to be processes in series. 

The solid dissolution and chemical reaction in the liquid film occur in parallel steps. The effect of solid dissolution in the film is to increase the local concentration of the reactive species in the film, thereby enhancing the rate of absorption. 

In the analysis of Ramchandran and Sharma,139 it was assumed that the solid dissolution process increases the absorption rate of the gaseous reactant. If we consider another case, where the rate of dissolution of the solid is also enhanced by the reaction between the absorbed gas and the dissolved solid species in the liquid film between x = 0 and x = A, then the material balance for the diffusing gas for 0 < x < A is given by the following equation ... 

Due to the presence of the absorbed gas A in this region, the rate of solid dissolution is enhanced by the value of 1 + ZADa/CsDc- Since the reaction is assumed to be instantaneous, no B exists between 0 < x < A. For A < x < S, no A exists and the material balance on C gives... 

From the above inequality, it can be seen that the term KsasDi/4klDc represents the extent to which the solid dissolution in the film is capable of increasing the rate of absorption. 

The first necessary condition [6.21] to be taken into account in all particularization cases is the use of general mixing parameters (factors related to the geometry of agitation, the properties of liquid media, the type of agitators and rotation speed) as well as the use of the specific factors of the studied application. For example, in the case of suspended solid dissolution, we can consider the mass transfer coefficient for dissolving suspended solids, the mean dimension of the suspended solid particles, and the diffusion coefficient of the dissolved species in the liquid. 

The individual elements produced various results. Additions of antimony oxide, tin(ll) oxide, and samarium oxide gave no evidence of reactions with the nitrate melt or solubility. The addition of zirconyl nitrate resulted in the evolution of nitrogen dioxide from the melt and the formation of a white insoluble precipitate. Addition of palladium nitrate to the melt produced a black melt and black insoluble solids. Dissolution of the cooled and solidified salt cake with distilled water indicated that a palladium mirror had formed at the meniscus of the melt. Niobium was added as potassium hexaniobate, KgNb Oj I6H2O. 

The precipitation process, the reverse of solid dissolution, is dictated by solution thermodynamics. The solution reaches saturation state when the dissolution rate equals the precipitation rate. Nucleation starts when the solution concentration exceeds the saturation concentration. The solution concentration affects the crystallite size of the precipitated catalyst. For example, diluted solution is beneficial to crystal growth due to slow nucleation and the presence of a few nuclei. In contrast, submicrometer- or even nano-sized amorphous gel or sol can be formed starting with a more concentrated solution. 

Figure 9.10 shows energy-dissipation contours for four impellers. The numbers represent fractions of the average energy input. It is important to understand energy distribution because it affects all processes requiring intensive mixing. This includes fast multipath chemical reactions, bubble and drop dispersion, and solids dissolution. Subsequent sections review these topics. 

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