Equilibrium constant dissolution

Up to this point, we have focused on aqueous equilibria involving proton transfer. Now we apply the same principles to the equilibrium that exists between a solid salt and its dissolved ions in a saturated solution. We can use the equilibrium constant for the dissolution of a substance to predict the solubility of a salt and to control precipitate formation. These methods are used in the laboratory to separate and analyze mixtures of salts. They also have important practical applications in municipal wastewater treatment, the extraction of minerals from seawater, the formation and loss of bones and teeth, and the global carbon cycle. 

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. 

The distribution of metals between dissolved and particulate phases in aquatic systems is governed by a competition between precipitation and adsorption (and transport as particles) versus dissolution and formation of soluble complexes (and transport in the solution phase). A great deal is known about the thermodynamics of these reactions, and in many cases it is possible to explain or predict semi-quantita-tively the equilibrium speciation of a metal in an environmental system. Predictions of complete speciation of the metal are often limited by inadequate information on chemical composition, equilibrium constants, and reaction rates. 

The solubility 5 of magnesium hydroxide (in units of moles per liter) can be computed from the equilibrium constant (the solubility product) for the dissolution of the salt. For 5 equal to the moles per liter of Mg(OH)2 dissolved ... 

Eqn. 16.22) as discussed in Chapter 16. Here, rsio2 is the reaction rate (mol s-1 positive for dissolution), As and k+ are the mineral s surface area (cm2) and rate constant (mol cm-2 s-1), and Q and K are the activity product and equilibrium constant for the dissolution reaction. The reaction for quartz, for example, is... 

The solubility of a compound refers to the concentration of that compound in solution, either as a molarity or as a mass per unit volume. The solubility product constant is the equilibrium constant in terms of concentrations of ions, for the dissolution equilibrium, raised to their appropriate coefficients. 

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). 

The scheme in Fig. 5.5 indicates that the ligand, for example, oxalate, is adsorbed very fast in comparison to the dissolution reaction thus, adsorption equilibrium may be assumed. The surface chelate formed is able to weaken the original Al-oxygen bonds on the surface of the crystal lattice. The detachment of the oxalato-aluminum species is the slow and rate-determining step the initial sites are completely regenerated subsequent to the detachment step provided that the concentrations of the reactants are kept constant, steady state conditions with regard to the oxide surface species are established (Table 5.1). If, furthermore, the system is far from dissolution equilibrium, the back reaction can be neglected, and constant dissolution rates occur. 

Since k2/k 2 corresponds to the equilibrium constant of the redox reaction (redox potential), Eq. (9.12) suggests that the dissolution reaction may depend both on the tendency to bind the reductant to the Fe(III)(hydr)oxide surface and (even if the electron transfer is not overall rate determining), on the redox equilibrium (see Fig. 9.4b). 

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. 

It is necessary to consider a number of equilibrium reactions in an analysis of a hydrometallurgical process. These include complexing reactions that occur in solution as well as solubility reactions that define equilibria for the dissolution and precipitation of solid phases. As an example, in analyzing the precipitation of iron compounds from sulfuric acid leach solutions, McAndrew, et al. (11) consider up to 32 hydroxyl and sulfate complexing reactions and 13 precipitation reactions. Within a restricted pH range only a few of these equilibria are relevant and need to be considered. Nevertheless, equilibrium constants for the relevant reactions must be known. Furthermore, since most processes operate at elevated temperatures, it is essential that these parameters be known over a range of temperatures. The availability of this information is discussed below. 

When excess solid is present in a saturated solution, you can write the equilibrium constant expression for the dissolution of the solid in the same way that you wrote the equilibrium constant expression for a homogeneous equilibrium in Chapter 7. For example, the equilibrium constant expression for barium sulfate is written as follows ... 

Solubility product (K p) The equilibrium constant that describes the dissolution of a solid in a solvent. 

A drawback of Gran plots is the fact that all deviations from the theoretical slope value cause an error and that side reactions are not considered. The method was modified by Ingman and Still [63], who considered side reactions to a certain degree, but the equilibrium constants and the concentrations of the components involved must be known. The Gran method is, however, advantageous for determinations in the vicinity of the determination limit The extrapolation of the linear dependence yields the sum + c, where c, is the residual concentration of the test component produced by impurities, dissolution of the ISE membrane, etc. 

For comparison, a telechelic sulfonated polystyrene with a functionality f = 1.95 was prepared. In cyclohexane the material forms a gel independent of the concentration. At high concentrations the sample swells. When lower concentrations were prepared, separation to a gel and sol phase was observed. Thus, dilution in cyclohexane does not result in dissolution of the gel even at elevated temperatures. Given the high equilibrium constant determined for the association of the mono functional sample, the amount of polymer in the sol phase can be neglected. Hence, the volume fraction of polymer in the gel phase can be calculated from the volume ratio of the sol and gel phases and the total polymer concentration. The plot in Figure 9 shows that the polymer volume fraction in the gel is constant over a wide range of concentrations. 

The Henry s law and equilibrium constants are from Sillen and Martell, 1964.) In such cases, the Henry s law constant reflects only the physical solubility (i.e., reaction (1, -1). A pseudo-Henry s law constant, H, is often defined to take into account the increased uptake compared to that expected based on simple dissolution of the gas without further reaction. With C02 as an example, this pseudo-Henry s law constant is defined by Eq. (A) ... 

There is an eqnilibrinm constant for the dissolution of hydrogen in each solid phase, Ka and Kb, respectively. Similarly, the activity of hydrogen at the interface, is related to the concentration at the interface and equilibrium constants, Cj = Kaci and c = Kbu, so that Eq. (4.88) becomes... 

Person 1 Calculate the equilibrium constant for the dissolution of hydrogen in nickel,... 

The solubility product is the equilibrium constant for the dissolution of a solid salt into its constituent ions in aqueous solution. The common ion effect is the observation that, if one of the ions of that salt is already present in the solution, the solubility of a salt is decreased. Sometimes, we can selectively precipitate one ion from a solution containing other ions by adding a suitable counterion. At high concentration of ligand, a precipitated metal ion may redissolve by forming soluble complex ions. In a metal-ion complex, the metal is a Lewis acid (electron pair acceptor) and the ligand is a Lewis base (electron pair donor). 

The equilibrium constant for dissolution in water of a nonionic compound, such as diethyl ether (CH3CH2OCH2CH3), can be written... 

If the saturated solution is prepared by a method other than dissolution of CaF2 in pure water, there are no separate restrictions on [Ca2+] and [F—] the only restriction on the ion concentrations is that the equilibrium constant expression [Ca2+][F-]2 must equal the Ksp. That condition is satisfied by an infinite number of combinations of [Ca2+] and [F-], and therefore we can prepare many different solutions that are saturated with respect to CaF2. For example, if [F-] is 1.0 X 10 2 M, then [Ca2+] must be 1.5 x 10 6 M ... 

The solubility product, Ksp, for an ionic compound is the equilibrium constant for dissolution of the compound in water. The solubility of the compound and Ksp are related by the equilibrium equation for the dissolution reaction. The solubility of an ionic compound is (1) suppressed by the presence of a common ion in the solution (2) increased by decreasing the pH if the compound contains a basic anion, such as OH-, S2-, or CO32- and (3) increased by the presence of a Lewis base, such as NH3, CN-, or OH-, that can bond to the metal cation to form a complex ion. The stability of a complex ion is measured by its formation constant, Kf. 

Write a balanced net ionic equation for each of the following dissolution reactions, and use the appropriate Ksp and Kf values in Appendix C to calculate the equilibrium constant for each. 

In an ideal solution, the maximum solubility of a drug substance is a function of the solid phase in equilibrium with a speciLed solvent system at a given temperature and pressure. Solubility is an equilibrium constant for the dissolution of the solid into the solvent, and thus depends on the strengths of solute solvent interactions and solute solute interactions. Alteration of the solid phase of the drug substance can inLuence its solubility and dissolution properties by affecting the solute solutc molecular interactions. 

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