Equilibrium constants precipitates

As we have noted, the solubility product is an equilibrium constant precipitation of an ionic componnd from solution occurs whenever the ion product exceeds for that substance. In a saturated solution of AgCl, for example, the ion product [Ag ][CP] is, of course, equal to Furthermore, simple stoichiometry teUs us that [Ag+] = [CP]. But this equality does not hold in all situations. 

Several types of reactions are commonly used in analytical procedures, either in preparing samples for analysis or during the analysis itself. The most important of these are precipitation reactions, acid-base reactions, complexation reactions, and oxidation-reduction reactions. In this section we review these reactions and their equilibrium constant expressions. 

Group III sulfides are much more difficult to precipitate than those of Group II. Compare, for example, the equilibrium constant for the reaction... 

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. 

Sometimes it is important to know under what conditions a precipitate will form. For example, if we are analyzing a mixture of ions, we may want to precipitate only one type of ion to separate it from the mixture. In Section 9.5, we saw how to predict the direction in which a reaction will take place by comparing the values of J, the reaction quotient, and K, the equilibrium constant. Exactly the same techniques can be used to decide whether a precipitate is likely to form when two electrolyte solutions are mixed. In this case, the equilibrium constant is the solubility product, Ksp, and the reaction quotient is denoted Qsp. Precipitation occurs when Qsp is greater than Ksp (Fig. 11.17). 

One of the most useful applications of standard potentials is in the calculation of equilibrium constants from electrochemical data. The techniques that we develop here can be applied to any kind of reaction, including neutralization and precipitation reactions as well as redox reactions, provided that they can be expressed as the difference of two reduction half-reactions. 

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 equilibrium constant for this reaction is large, indicating that nearly all of the aqueous ions end up as solid precipitate. 

Again, we use the standard approach to an equilibrium calculation. In this case the reaction is a precipitation, for which the equilibrium constant is quite large. Thus, taking the reaction to completion by applying limiting reactant stoichiometry is likely to be the appropriate approach to solving the problem. 

The wastewater contains Cd +, so an anion must also be present in the solution to balance the charge of the cadmium ions. Other species may exist as well. The problem asks only about the cadmium in the wastewater, so assume that any other ions are spectators. The sodium hydroxide solution contains Na and OH, so the major species in the treated wastewater include B.2 O, Cd ", OH", and Na. The equilibrium constant for the precipitation reaction is the inverse of for Cd (OH)2 ... 

Now set up a concentration table. The equilibrium constant for precipitation is very large, so imagine the precipitation in two steps (see Example ). First, take the reaction to completion by applying limiting reactant stoichiomehy. Then switch on the solubility equilibrium ... 

A relatively large amount of calcium ions are required for precipitation while only a very small amount of copper ions are needed. This observation has been attributed to the existence of an equilibrium constant between free and bound cations which will be much less important for Ca than for Cu [18]. The same feature has been observed, in the same solvent whatever the DE as it is shown in Figures 3 and 4, and also in water. 

By convention, [HA(s)] = [B(s)] = 1. Eqs. (6.1) represent the precipitation equilibria of the uncharged species, and are characterized by the intrinsic solubility equilibrium constant, Sq. The zero subscript denotes the zero charge of the precipitating species. In a saturated solution, the effective (total) solubility S, at a particular pH is defined as the sum of the concentrations of all the compound species dissolved in the aqueous solution ... 

The fluoride ion is the only inorganic ligand to form a complete substitution series, Be(H20)4 flFJ(2 1 (n = 1-4), though there is considerable variation in the equilibrium constants that have been reported. The most reliable values are probably those of Anttila et al. (117) who used both glass and fluoride-ion selective electrodes and also took account of the competing hydrolysis reactions. They did not, however, make measurements in the conditions where BeF2 would have been formed. A speciation diagram based on reported equilibrium constants is shown in Fig. 12. It can be seen that the fluoride ion competed effectively with hydroxide at pH values up to 8, when Be(OH)2 precipitates. 

Displacement of the bound ketone by H2 was directly observed by NMR (Eq. (37)), and an approximate equilibrium constant was determined. The cationic tungsten complex can also be used for catalytic hydrosilylation of ketones. In the case of catalytic hydrosilylation of abphatic substrates using HSiEt3, the catalyst precipitates at the end of the reaction, facilitating recycle and reuse [66],... 

The [solute] term may, in fact, comprise several component parts if the solute is ionic, or precipitation involves agglomeration. This equilibrium constant is not written as a fraction because the effective concentration of the undissolved solute [solute] (S) can be taken to be unity. 

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). 

Equilibrium composition of solutions in contact with freshly precipitated, Al(OH)3 and Fe(OH)3, calculated, using representative values for the equilibrium constants for solubility and hydrolysis equilibria. Shaded areas are approximate operating regions in water treatment practice coagulation in these systems occurs under conditions of oversaturation with respect to the metal hydroxide. 

Besides, the foregoing facts another vital aspect to be taken into consideration is the solubility product that plays a major role in such titration. Hence, the equilibrium constant of the reaction giving the precipitate of AgCl may be expressed as ... 

In the precipitation reaction involving chloride and silver nitrate, the addition of even a small quantity of the latter shall effect precipitation of AgCl provided that Ksp has been exceeded significantly. At this juncture, the concentrations of both Ag+ and Cl are related by the solubility-product equilibrium constant thus, we have ... 

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. 

The two-state model was used to test whether characteristics of the low-temperature cryosolvent cause the equilibrium constant for complex formation, K(T), to fall precipitously as the temperature is lowered through T ij. In this case, the slow phase that appears below 250 K would correspond to un-complexed ZnCcP. This interpretation fails because within the transition range the fraction, f(T), is unaffected by a ten-fold reduction in the ratio, R = [Cc]/[CcP], whereas use of K(T) calculated from f(T) would predict a larger shift of f(T). Alternatively, the two-state model would apply if a low-temperature form of the complex were created by a change in ligation of either ZnP or FeP. 

The hydrated metal hydroxy complex in Eq. (1.10) is a soluble species. However, if the pH is sufficiently high, the metal hydroxide, which is relatively insoluble for most metals (apart from the alkali group metals) will precipitate. The pH value at which hydroxide precipitation occurs can be related to the acidity of the cation and is approximately equal to the pK of the cation, where the pK is minus the logarithm of the equilibrium constant of Eq. (1.10). 

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