Kinetics removal precipitation

In this chapter we consider how to construct reactions paths that account for the effects of simple reactants, a name given to reactants that are added to or removed from a system at constant rates. We take on other types of mass transfer in later chapters. Chapter 14 treats the mass transfer implicit in setting a species activity or gas fugacity over a reaction path. In Chapter 16 we develop reaction models in which the rates of mineral precipitation and dissolution are governed by kinetic rate laws. 

The reaction rate Rj in these equations is a catch-all for the many types of reactions by which a component can be added to or removed from solution in a geochemical model. It is the sum of the effects of equilibrium reactions, such as dissolution and precipitation of buffer minerals and the sorption and desorption of species on mineral surfaces, as well as the kinetics of mineral dissolution and precipitation reactions, redox reactions, and microbial activity. 

In a simple situation of the type just described, water undersaturated or supersaturated with respect to a mineral invades an aquifer, where the mineral dissolves or precipitates according to a kinetic rate law, adding or removing a species to or from solution. With time, the species concentration along the aquifer approaches a steady state distribution, trending from the unreacted value at the inlet toward the equilibrium concentration. 

Oxidation of Se(0) is unlikely to involve Se isotope fractionation. Se(0) is extremely insoluble and elemental Se precipitates are often found in moderately reducing environments. As solid Se(0) is consumed by an oxidation reaction, any kinetic isotope effect is ultimately negated by mass balance effects. For example, if a strong kinetic isotope effect preferentially removes lighter isotopes from the surface of the solid, the surface becomes enriched in heavier isotopes. Ultimately, the removal of successive layers from the solid requires 100% oxidation of the Se(0) and thus there is no opportunity for any kinetic isotope effect to be expressed. 

Figure 7. Measured and corrected A Fe Fe(ni)-Hem.tite values ( and O, respectively) relative to average hematite precipitation rate for Experiments 5, 7, and 8 of Skulan et al. (2002). The A Fe jj(ni).Hem.tite values are defined as those measured at the termination of the experiments the corrected A Fe i,e(ni).Hem.tite values reflect the estimated correction required to remove any residual kinetic isotope fractionation that was produced early in experiments that was not completely removed hy dissolution and re-precipitation over the long term. Extrapolation of the corrected A Fe jj(ni).Hem.tite values to zero precipitation rates yields an estimate for the equilihrium Fe(III),q-hematite fractionation, A Fci,e(in).hem.tite,...

Crystallization of magnesium hydroxide by a continuous mixed suspension mixed product removal crystallizer was conducted to make clear the characteristics of reactive crystallization kinetics of magnesium hydroxide, which was produced by the precipitation from magnesium chloride with calcium hydroxide. The following operating factors were investigated affecting the crystallization kinetics the initial concentration of feeds, residence time of reactants, feed ratio of reactants, and concentrations of hydroxide and chloride ions. 

Calcium sulfate crystals were precipitated in a Continuous Mixed Suspension Mixed Product Removal (CMSMPR) crystallizer by mixing of calcium phosphate and sulfuric acid feed streams. The formed calcium sulfate hydrate (anhydrite, hemihydrate and dihydrate) mainly depends on the temperature and the solution composition. The uptake of cadmium and phosphate ions in these hydrates has been studied as a function of residence time and solution composition. In anhydrite, also the incorporation of other metal ions has been investigated. The uptake was found to be a function of both thermodynamics and kinetics. 

Houcine et al. (64) used a non-intrusive laser-induced fluorescence method to study the mechanisms of mixing in a 20 dm CSTR with removable baffles, a conical bottom, a mechanical stirrer, and two incoming liquid jet streams. Under certain conditions, they observed an interaction between the flow induced by the stirrer and the incoming jets, which led to oscillations of the jet stream with a period of several seconds and corresponding switching of the recirculation flow between several metastable macroscopic patterns. These jet feedstream oscillations or intermittencies could strongly influence the kinetics of fast reactions, such as precipitation. The authors used dimensional analysis to demonstrate that the intermittence phenomenon would be less problematic in larger CSTRs. 

There are several disadvantages to the batch techniques of Zasoski and Burau (1978), van Riemsdijk and de Haan (1981), and Phelan and Mattigod (1987). A major disadvantage is in not removing desorbed species and difficulty in monitoring desorption kinetics. In studies where desorbed species in the solution phase inhibit further release of adsorbate, such as potassium, or could cause secondary precipitation reactions, these methods may not be suitable. 

Several kinetic models have appeared to describe phosphorus reactions in soils. Enfield (1978) classified models for estimating phosphorus concentrations in percolate waters derived from soil that had been treated with wastewater into three categories (1) empirical models that are not based on known theory (2) two-phase kinetic models that assume a solution phase and some adsorbed phase and (3) multiphase models, which include solution, adsorbed, or precipitated phases. Mansell and Selim (1981) classified models as shown in Table 9.2. The reader is urged to consult this reference for a complete discussion of the phosphorus kinetic models. For the purpose of this discussion, attention will be given to models that assume reversible phosphorus removal from solution, which can occur simultaneously by equilibrium and nonequilibrium reactions, and mechanistic multiphase models for reactions and transport of phosphorus applied to soils. 

Figure 9.2. A schematic representation of six reversible-kinetic reactions that are assumed to control the transfer of applied phosphorus (P) between solution, adsorbed, immobilized (chemisorbed), and precipitated phases within the soil. Sinks are shown for irreversible removal of phosphorus from the soil solution by plant uptake and by leaching. [From Mansell et al, (1977a), with permission.]...

Early protocols to measure ATP from cell cultures involved an acid or alkaline sample extraction step to precipitate proteins and inhibit ATPases (Lundin et al. 1986 Crouch et al. 1993). This was followed by removal of debris by centrifugation or filtration and a step to neutralize the pH of the sample prior to addition of luciferin and firefly luciferase to generate a flash of light proportional to the amount of ATP. Early reagents that created flash kinetics required luminometers with injection capabilities that hindered their use for HTS. 

Many molecular and ionic systems crystallize out of solutions as solvates. This is often a totally unavoidable event because solvent molecules fill the voids of otherwise less dense crystal packings, or the solid solvate precipitates out for kinetic reasons, as solvate nuclei are likely to be formed first with respect to unsolvated ones. The presence of solvent molecules trapped more or less tightly within the crystal structure may be turned to advantage if the solvent can be removed by low-pressure or high-temperature treatments or by other means. An example of polymorphs obtained via desolvation is provided by the hexagonal form of a C6o polymorph that can be obtained from desolvation of cubic 1 1 solvate Cgo grown from dichloromethane [72]. 

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