Dissolution-precipitation equilibrium

Solubility equilibria resemble the equilibria between volatile liquids (or solids) and their vapors in a closed container. In both cases, particles from a condensed phase tend to escape and spread through a larger, but limited, volume. In both cases, equilibrium is a dynamic compromise in which the rate of escape of particles from the condensed phase is equal to their rate of return. In a vaporization-condensation equilibrium, we assumed that the vapor above the condensed phase was an ideal gas. The analogous starting assumption for a dissolution-precipitation reaction is that the solution above the undissolved solid is an ideal solution. A solution in which sufficient solute has been dissolved to establish a dissolution-precipitation equilibrium between the solid substance and its dissolved form is called a saturated solution. 

The interfacial properties of colloidal suspensions are determined by the chemical reactions (e.g. protonation) and adsorption of solutes. Additionally, the interface can be affected by the dissolution-precipitation equilibrium of the particle phase. This is because precipitation changes the surface morphology (Vigil et al. 1994) or leads to phase transition (Lefevre et al. 2002 Carrier et al. 2007). In addition, dissolution means degradation of the particles and may result in the loss of the finest particle fractions (i.e. Ostwald ripening). For this reason, it is necessary to understand the factors governing the dissolution of solid particles. 

Occlusions are minimized by maintaining the precipitate in equilibrium with its supernatant solution for an extended time. This process is called digestion and may be carried out at room temperature or at an elevated temperature. During digestion, the dynamic nature of the solubility-precipitation equilibrium, in which the precipitate dissolves and re-forms, ensures that occluded material is eventually exposed to the supernatant solution. Since the rate of dissolution and reprecipitation are slow, the chance of forming new occlusions is minimal. 

The principle we have applied here is called microscopic reversibility or principle of detailed balancing. It shows that there is a link between kinetic rate constants and thermodynamic equilibrium constants. Obviously, equilibrium is not characterized by the cessation of processes at equilibrium the rates of forward and reverse microscopic processes are equal for every elementary reaction step. The microscopic reversibility (which is routinely used in homogeneous solution kinetics) applies also to heterogeneous reactions (adsorption, desorption dissolution, precipitation). 

Let us consider the dissolution-precipitation process in seawater in the following example. The normal concentrations of calcium and of carbonate in the near-surface oceanic waters are about [Ca2+] = 0.01 and [C032-] 2 x lO"4 M. The CaC03 in solution is metastable and roughly 2U0% saturated (1). Should precipitation occur due to an abundance of nuclei, TC032-] will drop to 10-4 M but [Ca2+] will change by no more than 2%. Therefore, the ionic strength of the ionic medium seawater will remain essentially constant at 0.7 M. The major ion composition will also remain constant. We shall see later what the implications are for equilibrium constants. 

In contrast to these we have the equilibrium processes of sublimation, absorption, dissolution, precipitation, evaporation, and condensation, throngh which the physical states of solid, Uqnid, and gas are connected. For example, the common crystallization of salts from sea water involves all three phases. Distillation, which is essential for prodncing organic solvents, is a two-step evaporation (liquid => gas) condensation (gas => Uqnid) process. 

Naturally, the principles of chemical equilibrium can be applied to any reaction or process. When a solid substance, such as CaSO, is dissolved in water, the reaction initially proceeds towards the right side. As a result, the concentrations of ions in the solvent increase. But, as time passes, the reverse reaction will start to occur and an equilibrium (dissolution-precipitation) is established. 

Dissolution-precipitation reactions often exhibit characteristic time scales that are much larger than those for complexation reactions in aqueous solution. When this is true, the aqueous species in a soil solution will come to mutual equilibrium long before they equilibrate with the solid phase via the reaction in l-q. 3.1. It is possible under these circumstances to define two useful criteria for dissolution precipiialionequilibrium, the ion activity product (IAP) ... 

The situation becomes much less problematic if the reaction in Eq. 3.1 is considered only at equilibrium. Equilibrium states are steady states in which the net reaction fluxes to produce products or reactants, regardless of the reaction pathway, are equal and opposite. From the perspective of chemical thermodynamics, equilibrium states are unique and independent of thermodynamic path. Thus these states can be described by a unique set of chemical species irrespective of the intermediate steps of their formation. Dissolution- precipitation reactions and the chemical species that affect them at equilibrium can be described by an extension of the methodology discussed in Section 2.4 (cf. Fig. 

Together with acid-base reactions, where a proton transfer occurs (pH-dependent dissolution/ precipitation, sorption, complexation) redox reactions play an important role for all interaction processes in aqueous systems. Redox reactions consist of two partial reactions, oxidation and reduction, and can be characterized by oxygen or electron transfer. Many redox reactions in natural aqueous systems can actually not be described by thermodynamic equilibrium equations, since they have slow kinetics. If a redox reaction is considered as a transfer of electrons, the following general reaction can be derived ... 

Solute movement through soil is a complex process. It depends on convective-dispersive properties as influenced by pore size, shape, continuity, and a number of physicochemical reactions such as sorption-desorption, diffusion, exclusion, stagnant and/or double-layer water, interlayer water, activation energies, kinetics, equilibrium constants, and dissolution-precipitation. Miscible displacement is one of the best approaches for determining the factors in a given soil responsible for the transport behavior of any given solute. 

The dissolution-precipitation equilibria are characterized by the thermodynamic equilibrium constants and similarly to potential-pH diagrams (Figures 1.4 and 1.5), stability diagrams can be constructed. The axes of the stability diagrams show the concentration of the relevant species, including pH (the concentration [activity]... 

Equilibrium calculations based on mineral saturation indices also show how the concentration of solutes that are present in trace amounts are influenced by mineral dissolution/ precipitation reactions. Eor example, the concentration of barium in groundwater appears to be buffered by the saturation index of barite (BaS04) (Eigure 2). 

Solubility and speciation. Minimum requirements for reliable thermodynamic solubility studies include (i) solution equilibrium conditions (ii) effective and complete phase separation (iii) well-defined solid phases and (iv) knowledge of the speciation/oxidation state of the soluble species at equilibrium. Ideally, radionuclide solubilities should be measured in both oversaturation experiments, in which radionuclides are added to a solution untU a solid precipitates, and undersaturation experiments, in which a radionuchde solid is dissolved in aqueous media. Due to the difference in solubilities of crystalline versus amorphous solids and different kinetics of dissolution, precipitation, and recrystalhzation, the results of these two types of experiments rarely agree. In some experiments, the maximum concentrahon of the radionuchde source term in specific water is of interest, so the sohd that is used may be SF or nuclear waste glass rather than a pure radionuclide solid phase. 

Hypothetical reaction pathways chosen to model the L2 leachate-Uinta Sandstone system are illustrated in Figure 5. As a first approximation, dissolution/precipitation reactions affecting the mass balance of Na, K, Mo, SO4, and Cl were not considered. Instead, based upon the solubility controls discussed in the previous sections of this paper, the working hypothesis for the simulations is that the recarbonation of L2 leachate drives the reactions toward equilibrium. Along the path toward equilibrium, recarbonation is accompanied by the precipitation and dissolution of sepiolite, calcite, and an inferred hydrated magnesium carbonate mineral such as hydromagnesite. 

A number of anions form slightly soluble precipitates with certain metal ions and can be titrated with the metal solutions for example, chloride can be titrated with silver ion and sulfate with barium ion. The precipitation equilibrium may be affected by pH or by the presence of complexing agents. The anion of the precipitate may be derived from a weak acid and therefore combine with protons in acid solution to cause the precipitate to dissolve. On the other hand, the metal ion may complex with a ligand (the complexing agent) to shift the equilibrium toward dissolution. Silver ion will complex with ammonia and cause silver chloride to dissolve. 

Figure2 Ohnishi et al. (1985) and Chijimatsu et al. (2000)) and reactive-mass transport model (inside the box named Chemical in Figure 2). This is a system of governing equations composed of Equations (l)-(9), which couple heat flow, fluid flow, deformation, mass transport and geochemical reaction in terms of following primary variables temperature T, pressure head y/, displacement u total dissolved concentration of the n master species C< > and total dissolved and precipitated concentration of the n" master species T,. Here we set master species as the linear independent basis for geochemical reactions, and speciation in solution and dissolution/precipitation of minerals are calculated by a series of governing equations for geochemical reaction. Now we adopt equilibrium model for geochemical reaction (Parkhurst et al. (1980)), mainly because of reliability and abundance of thermodynamic data for geochemical reaction.

In this chapter, we present various equilibrium-based geochemical modeling approaches that can be used for the analysis of leaching of various species from contaminated media. We focus on two important processes that can chemically limit the concentration of the contaminant released or leached dissolution/precipitation and adsorption. We progress from a simpler approach based on aqueous speciation of chemicals to more complicated approaches that in addition require dissolution/precipitation and/or adsorption calculations. Examples for applications of the geochemical modehng approaches discussed in this chapter are provided in Table 1. 

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