Dissolution equations

Information about the kinetics of dissolution reactions is provided by Delmon (1969) and by Brown et al. (1980). Dissolution may be either diffusion (i.e., transport) or surface controlled. If diffusion controlled, i. e., if the concentration of dissolved species immediately adjacent to the surface corresponds to the equilibrium solubility (Ce) of the solid phase, the concentration, c, of the dissolved species is diffusion controlled and increases with the square root of time, t, i. e.. 

Gorichev and Kipriyanov (1984, and references therein) found that dissolution of powdered magnetite particles in HCl, H2SO4, H3PO4 and Na2EDTA at temperatures of up to 80 °C displayed sigmoidal dissolution curves that could be described by. 

For hematite and wiistite in the same media, the kinetic curves were deceleratory. 

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Combining alumina dissolution, equation 16, and the anode and cathode reactions, equations 17—19, gives the overall reaction... 

Equation (1) predicts that the rate of release can be constant only if the following parameters are constant (a) surface area, (b) diffusion coefficient, (c) diffusion layer thickness, and (d) concentration difference. These parameters, however, are not easily maintained constant, especially surface area. For spherical particles, the change in surface area can be related to the weight of the particle that is, under the assumption of sink conditions, Eq. (1) can be rewritten as the cube-root dissolution equation ... 

Equation (52) applies to dissolution under sink conditions and no convection. Successful modeling of particle dissolution requires a good understanding of the environment and circumstances for dissolution. Equation (52) describes a relatively simple system (Fig. 11). 

A dissolution model that takes in account the change in particle number and the polydisperse nature of the powder was proposed by de Almeida et al. [25]. The following dissolution equations were used to calculate the decrease in weight of solids with time ... 

Write a balanced dissolution equation and solubility product expression for silver carbonate, Ag2C03. 

The effect of reducing conditions on the solubility of an iron oxide can be found by combining the appropriate dissolution equations with the redox equation to obtain the concentration of the Fe" species released. In the Fe"/Fe oxide system, protons are always involved because the state of hydrolysis of the Fe is changed. For goethite, for example. 

The first of these reactions is a hydrolysis process, the second is a carbonic acid-promoted dissolution, and the third is a proton-promoted dissolution. Equations 3.59b and 3.59c are the forward reactions in Eqs. 3.17 and 3.15, respectively. They provide a mechanistic underpinning for the dependence of kd in Eq. 3.14 on pH or pc0, as discussed in Section 3.1. Indeed, if Eq. 3.7 is applied to the forward reaction in Eq. 3.14 and rate laws for Eq. 3.59 are developed consistently with the hypothesis leading to Eq. 3.7, the result is7,33,34... 

Equations Many dissolution equations are well described in the text. Most of the equation are based on the well-known Fick s law. Figure 16 shows a diagram of the concentration gradient between the matrix tablet and bulk fluid for dissolution. 

Again, reactions 5.10a-c occur in acidic solutions, and reaction 5.10d in a neutral solution. For A1(0H)3, reaction 5.8 yields similar dissolution equations in alkaline regions. 

Table 5.1 displays dissolution reactions for oxides and hydroxides whose ceramics have potential practical applications. Also included is the pH range in which these reactions are valid. The pH range can be derived by the method described above, or as was done in Chapter 4, it can be calculated by equating the two subsequent equations at the transition boundary where these equations are equally valid. This table shows only the dissolution equations that are valid in acidic and neutral pH. For details covering the entire pH range and general discussions, the reader is referred to Ref. [5]. 

Oxide Dissolution Equation pH Range for Dominance of Ions... 

The specific heats of aqueous ions of several metals are not readily available in the literature. As a result, it is difficult to determine the temperature dependence of the thermodynamic quantities and, hence, that of the solubility product constants for these metal oxides. This dependence can be roughly determined from the general dissolution equation... 

Homogeneous Equilibrium. For homogeneous equilibrium including gibbsite, hematite and exchangeable Sr " , the dissolution equation would be... 

It may be that overall montmorillonite equilibrium, whether it be homogeneous or heterogeneous, is not adequately represented by the formulas considered thus far (e.g., 30). However, if equilibrium is carefully approached -from undersaturation and supersaturation over a sufficiently broad range of solution conditions, it whould be possible to accurately determine the slopes of lines similar to those shown in Figures 3 and 4. These slopes represent the coefficients in appropriate dissolution equations. Thus, it seems likely that proper equations can... 

These equations are indistinguishable for rate measurements at a single temperature and pressure, but predict different results for the variation of the rate constant. A , with environmental variables (i.e., r, P, and [Ca ]). Because [Ca ] is not constant in laboratory experiments during the course of dissolution. Equation (10) is normally used to interpret these results (e.g., Morse and Arvidson, 2002 Keir, 1980). In the ocean, where [Ca ] is nearly a constant but K p varies... 

The Crystal Growth of a CaCOj (Calcite) The crystal growth of calcite has been studied by Plummer and et al. (1978), by Kunz and Stumm (1984), and by Chou et al. (1989) to correspond to the reverse of the rate of dissolution (equation 32) ... 

Tabb 1.6 How the parameters of the dissolution equation can be changed to increase (+) or decrease (-) the rate of solution ... 

We know the molar solubility of BaS04. The dissolution equation shows that each formula unit of BaS04 that dissolves produces one Ba ion and one SOy... 

Ammonia. The solubility of NH3 is described in two stages, as dissolution (Equation 2) followed by base dissociation ... 

Many organic compounds are soluble in hquid HF, and in the cases of, for example, amines and carboxylic acids, protonation of the organic species accompanies dissolution (equation 8.38). Proteins react immediately with liquid HF, and it produces very serious skin burns. 

Plan We write the dissolution equation and the ion-product expression. We know K p (6.5X10 ) to find molar solubility (S), we set up a reaction table that expresses [Ca ] and [OH ] in terms of 5, substitute into the ion-product expression, and solve for S. Solution Writing the equation and ion-product expression ... 

Plan We write the balanced dissolution equation and note the anion Weak-acid anions react with H30" and shift the equilibrium position toward more dissolution. Strong-acid anions do not react, so added H3O has no effect. 

Table 9.4. The Effect of Changing Parameters from the Dissolution Equation on the Rate of Solution ...

The Inorganic ion and the dissolution equation of Li20 in ZnO becomes Chemistry of... 

The thickness of passive films at steady state depends on the applied potential and their rate of dissolution (equation 6.37). If chloride ions accelerate the rate of dissolution, a higher chloride concentration in the electrolyte should lead to thinner passive films. This behavior has been confirmed by XPS measurements, as shown in Figure 6.44. This figure presents the effect of several halogen-anions on the thickness of the passive films formed on iron in a phthalate buffer solution (pH 5). In this case, Cr ions have a greater effect than either Br or 1 ions. 

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