Kinetics of the Precipitation

The growth rate is very small during the induction period up to the supersaturated concentration, but then it grows exponentially, as a sigmoidal curve. However, with decreasing solute concentration the rate decreases, as shown in Fig. 7.4. 

The growth can be represented as a rate of first order, namely [1], 

go is the initial rate which corresponds to the saturation, s the supersaturation concentration, and N the number of critical nuclei, corresponding to supersaturation. 

It is possible to induce rapid precipitation, by adding seeds to the solution, which increases the concentration of the solution at the interface. It is a heterogeneous nucleation. The number of crystal particles present in the solution depends on the number of cores or germs in the solution. 

The rate growth around the core depends on the diffusion of ions at the solution-solid interface thus, [1], 

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These relationships are generally determined empirically, because of the complex kinetics of the precipitation polymerization process and the large variations from one reaction system to another. Nevertheless, a review of the literature presents useful guidelines for process design experiments. 

C.J. Perron, D.O. Kwateng and P.F. Duby, Kinetics of the Precipitation of Goethite from Ferrous Sulphate Solutions using Oxygen - Sulphur Dioxide Mixtures , paper presented at the TMS Meetine. New Orleans, Feb. 1991,165-177. 

Alimi, F., Elfil, H. Gadri, A. (2003). Kinetics of the precipitation of calcium sulfate dihydrate in a desalination unit. Desalination, 158(1-3), 9-16. 

G.H. Bogush and C.F. Zukoski IV Studies of the kinetics of the precipitation qfun orm silica particles through the hydrolysis and condensation of silicon alkoxides, J. CoUoid Interface Sci., 142 (1991) 1-18... 

Clearly, Is much larger in the presence than in the absence of silica. From the values for experiments U30 and U31, it turns out that the size of the silica particles does not affect the overall kinetics of the precipitation process. The difference with respect to kj. between experiments U30 and U34 is caused by the higher rate of urea hydrolysis in experiment U30, which itself is brought about by the slightly higher temperature in that experiment. The four-fold difference in initial Mn concentration (experiment U30 versus U34) giving rise to comparable values for kj. - especially when the temperature difference is taken into account - further supports the overall precipitation being adequately described as a first-order process. 

Bulk Polymerization. The bulk polymerization of acrylonitrile is complex. Even after many investigations into the kinetics of the polymerization, it is stiU not completely understood. The complexity arises because the polymer precipitates from the reaction mixture barely swollen by its monomer. The heterogeneity has led to kinetics that deviate from the normal and which can be interpreted in several ways. 

Fig. 19.15 Schematic representation of range of corrosion potentials expected from various chemical tests for sensitisation in relation to the anodic dissolution kinetics of the matrix (Fe-l8Cr-IONi stainless steel) and grain boundary alloy (assumed to be Fe-lOCr-lONi) owing to depletion of Cr by precipitation of Cr carbides of a sensitised steel in a hot reducing acid (after Cowan and Tedmon )...

However, as already noted, the barite content in Kuroko ore inversely correlates to the quartz content and the occurrences of barite and quartz in the submarine hydrothermal ore deposits are different. The discrepancy between the results of thermochemical equilibrium calculations based on the mixing model and the mode of occurrences of barite and quartz in the submarine hydrothermal ore deposits clearly indicate that barite and quartz precipitated from supersaturated solutions under non-equilibrium conditions. Thus, it is considered that the flow rate and precipitation kinetics affect the precipitations of barite and quartz. 

Little is known about the kinetics of dissolution, precipitation, and oxidation-reduction reactions in the natural environment. Consequently, simulating the kinetics of even more complicated injection- zone chemistry is very difficult. 

Other companies (e.g., Hoechst) have developed a slightly different process in which the water content is low in order to save CO feedstock. In the absence of water it turned out that the catalyst precipitates. Clearly, at low water concentrations the reduction of rhodium(III) back to rhodium(I) is much slower, but the formation of the trivalent rhodium species is reduced in the first place, because the HI content decreases with the water concentration. The water content is kept low by adding part of the methanol in the form of methyl acetate. Indeed, the shift reaction is now suppressed. Stabilization of the rhodium species and lowering of the HI content can be achieved by the addition of iodide salts. High reaction rates and low catalyst usage can be achieved at low reactor water concentration by the introduction of tertiary phosphine oxide additives.8 The kinetics of the title reaction with respect to [MeOH] change if H20 is used as a solvent instead of AcOH.9 Kinetic data for the Rh-catalyzed carbonylation of methanol have been critically analyzed. The discrepancy between the reaction rate constants is due to ignoring the effect of vapor-liquid equilibrium of the iodide promoter.10... 

In this chapter we consider the problem of the kinetics of the heterogeneous reactions by which minerals dissolve and precipitate. This topic has received a considerable amount of attention in geochemistry, primarily because of the slow rates at which many minerals react and the resulting tendency of waters, especially at low temperature, to be out of equilibrium with the minerals they contact. We first discuss how rate laws for heterogeneous reactions can be integrated into reaction models and then calculate some simple kinetic reaction paths. In Chapter 26, we explore a number of examples in which we apply heterogeneous kinetics to problems of geochemical interest. 

The first class, discussed in detail in Chapter 6, was reaction between a fluid and the minerals it contacts. The kinetics of the reactions by which minerals dissolve and precipitate was the subject of the preceding chapter (Chapter 16). The second class of reactions commonly observed to be in disequilibrium in natural waters, as discussed in Chapter 7, is redox reactions. The subject of this chapter is modeling the rates at which redox reactions proceed within the aqueous solution, or when catalyzed on a mineral surface or by the action of an enzyme. In the following chapter (Chapter 18), we consider the related question of how rapidly redox reactions proceed when catalyzed in the geosphere by the action of microbial life. 

Comparing the development here to the accounting for the kinetics of mineral precipitation and dissolution presented in the previous chapter (Chapter 16), we see the mass transfer coefficients v and so on serve a function parallel to the coefficients v , etc., in Reaction 16.1. The rates of change in the mole number of each basis entry, accounting for the effect of each kinetic redox reaction carried in the simulation, for example,... 

Given a specific application, we might also include precipitation kinetics in our calculations, as described in Chapter 16. Wat et al. (1992) present a brief study of the kinetics of barite formation, including the effects of scale inhibitors on precipitation rates. For a variety of reasons (see Section 16.2), however, it remains difficult to construct reliable models of the kinetics of scale precipitation. 

A simple method to analyze binding equilibria with slow association and dissociation kinetics is the precipitation of one binding partner with an antibody or... 

The mobilization of arsenic from the tailings material seems to be a slow and continuos process attributed to reduction of iron phases. The seepage water of the middle source contains arsenite as well as arsenate in high concentrations and seems to be the only water source in contact with the tailings material. The concentrations of arsenic downstream are still high and the immobilization process by precipitation of iron hydroxide and coprecipitation or sorption of arsenic is incomplete. A reason for this may be the slow kinetics of the oxidation process and the transport of fine grained hydroxide particles. These particles are mobile and can bind the arsenic (mainly as arsenate) too. 

Part of this objection to the calcium pectate as a means of following the hydrolysis of pectic materials can be met by using the simple procedure developed by Fellers and Rice" for the estimation of pectic substances as pectic acid. This approximate method measures the volume of the pectic acid which can be produced from a sample of soluble pectic material and will therefore show the loss of colloidality by the rapidly decreasing volume even if the weight of the precipitate remains the same. Unfortunately the Fellers-Rice method is not sufficiently accurate for exact kinetic studies. 

Abstract. Auto-accelerated polymerization is known to occur in viscous reaction media ("gel-effect") and also when the polymer precipitates as it forms. It is generally assumed that the cause of auto-acceleration is the arising of non-steady-state kinetics created by a diffusion controlled termination step. Recent work has shown that the polymerization of acrylic acid in bulk and in solution proceeds under steady or auto-accelered conditions irrespective of the precipitation of the polymer. On the other hand, a close correlation is established between auto-acceleration and the type of H-bonded molecular association involving acrylic acid in the system. On the basis of numerous data it is concluded that auto-acceleration is determined by the formation of an oriented monomer-polymer association complex which favors an ultra-fast propagation process. Similar conclusions are derived for the polymerization of methacrylic acid and acrylonitrile based on studies of polymerization kinetics in bulk and in solution and on evidence of molecular associations. In the case of acrylonitrile a dipole-dipole complex involving the nitrile groups is assumed to be responsible for the observed auto-acceleration. 

The Ostwald Step Rule, or the rule of stages postulates that the precipitate with the highest solubility, i.e., the least stable solid phase will form first in a consecutive precipitation reaction. This rule is very well documented mineral formation via precursors and intermediates can be explained by the kinetics of the nucleation process. The precipitation sequence results because the nucleation of a more soluble... 

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