The solubility product

Solubility product is the name given to the equilibrium constant that describes the reaction by which a precipitate dissolves in pure water to form its constituent ions, 

The activity of the solid phase can be taken as unity (see Section 3-3). The concentration product, has the same form as the equilibrium constant except that the concentrations of the species in solution are used instead of their activities. Accordingly, 

Assuming that the solution components have activity coefficients of unity and that the solid has an activity of one, - Kso, If the activity coefficients are not equal to unity, so and is a function of ionic 

It is important to differentiate between the terms soJubiJify product and solubility. Solubility product is the colloquial term for the equilibrium constant. Solubility is the amount of a substance in moles/liter or mg/liter that can dissolve in a solution under a given set of conditions. Solubility does not equal the solubility product, but the two quantities are interrelated. 

Calculate the solubility in mg/liter of Cap2 in pure water gt 25°C, neglecting ionic strength effects. 

When solid Mg(OH)2 dissolves in water the chemical reaction is  

Total amount of Mg(OH)2 added Mg2+ concentration in the resulting solution OH concentration in the resulting solution Mass of Mg(OH)2 that does not dissolve 

Choose one of the masses of Mg(OH)2 in the left-hand column of Table 1 and verify that the corresponding number of moles of Mg(OH)2 is correct. 

When 0.20000 grams of Mg(OH)2 are added, how many grams dissolve  

The extent to which a sparingly soluble solid dissolves is expressed by the solubility product. This describes the equilibrium established between the solid and the concentration of its ions in a saturated solution. Consider, for example, the dissolution of goethite in water  

To characterize the solution composition, activities, a , instead of concentrations have to be used (see Chap. 8). At equilibrium the following expression can be formulated  

The Iron Oxides Structure, Propeities, Reactions, Occurences and Uses. R. M. Cornell, U. Schwertmann Copyright 2003 WILEY-VCH Verlag GmbH Co. KGaA,Weinhemi ISBN 3-527-30274-3 

At a given temperature, K is constant and as apeooH the concentration of water are also constant, the three can be combined to give 

Kgo is the solubility product. It applies to iron oxides, hydroxides and oxide hydroxides. 

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Addition of acid will reduce the concentration of ", whilst in alkaline solution the concentration of will increase. Since, in order for precipitation to occur, the solubility product of the sulphide must be exceeded, i.e. 

Aqueous ammonia can also behave as a weak base giving hydroxide ions in solution. However, addition of aqueous ammonia to a solution of a cation which normally forms an insoluble hydroxide may not always precipitate the latter, because (a) the ammonia may form a complex ammine with the cation and (b) because the concentration of hydroxide ions available in aqueous ammonia may be insufficient to exceed the solubility product of the cation hydroxide. Effects (a) and (b) may operate simultaneously. The hydroxyl ion concentration of aqueous ammonia can be further reduced by the addition of ammonium chloride hence this mixture can be used to precipitate the hydroxides of, for example, aluminium and chrom-ium(III) but not nickel(II) or cobalt(II). 

These are practically insoluble in water, are not hydrolysed and so may be prepared by addition of a sufficient concentration of sulphide ion to exceed the solubility product of the particular sulphide. Some sulphides, for example those of lead(II), copper(II) and silver(I), have low solubility products and are precipitated by the small concentration of sulphide ions produced by passing hydrogen sulphide through an acid solution of the metal salts others for example those of zincfll), iron(II), nickel(II) and cobalt(II) are only precipitated when sulphide ions are available in reasonable concentrations, as they are when hydrogen sulphide is passed into an alkaline solution. 

The equilibrium constant for this reaction is called the solubility product, Kjp, and is given as... 

Substituting the equilibrium concentrations into the solubility product expression (equation 6.33)... 

At the equivalence point, we know that the concentrations of Agi" and CL are equal. Using the solubility product expression... 

Before the equivalence point, the concentration of Cr04 is controlled by the solubility product of PbCr04. After the equivalence point, the concentration of Cr04 is determined by the amount of excess titrant added. Considering the reactions controlling the concentration of Cr04 , sketch the expected titration curve of pH versus volume of titrant. 

Potentiometric electrodes are divided into two classes metallic electrodes and membrane electrodes. The smaller of these classes are the metallic electrodes. Electrodes of the first kind respond to the concentration of their cation in solution thus the potential of an Ag wire is determined by the concentration of Ag+ in solution. When another species is present in solution and in equilibrium with the metal ion, then the electrode s potential will respond to the concentration of that ion. Eor example, an Ag wire in contact with a solution of Ck will respond to the concentration of Ck since the relative concentrations of Ag+ and Ck are fixed by the solubility product for AgCl. Such electrodes are called electrodes of the second kind. 

For the most part, the elemental analysis data for the blends are consistent with a weighted average of the individual components. Also shown is the elemental analysis for some of the soluble products form WVGS 13423 in Table 10 As was observed for the WVGS 13421 products, hydrogenation increased the total hydrogen content and decreased the atomic C/H ratio. 

Solubility Product — The solubility product constant commonly referred to as the solubility product provides a convenient method of predicting the solubility of a material in water at equilibrium. Copper hydroxide, for example, dissolves according to the following equilibrium ... 

Note that the brackets, [ ], refer to the concentration of the species. K,p is the solubility product constant hence [Cu " ] and [OH] are equal to the molar concentrations of copper and hydroxyl ions, respectively. The K p is commonly used in determining suitable precipitation reactions for removal of ionic species from solution. In the same example, the pH for removal of copper to any specified concentration can be determined by substituting the molar concentration into the following equation ... 

By contrast with the water-soluble sulfides of Groups 1 and 2, the corresponding heavy metal sulfides of Groups 11 and 12 are amongst the least-soluble compounds known. Literature values are often wildly discordant, and care should be taken in interpreting the data. Thus, for black HgS the most acceptable value of the solubility product [Hg +][S ] is 10- mol2l-2, i.e. 

The solubility product, [Hg +][S ] = 10 moPdm but the actual solubility is greater than that calculated from this extremely low figure, since the mercury in solution is present not only as Hg + but also as complex species. In acid solution [Hg(SH)2] is probably formed and in alkaline... 

In this example of the corrosion of zinc in a reducing acid of pH = 4, the corrosion product is Zn (aq.), but at higher pHs the thermodynamically stable phase will be Zn(OH)j and the equilibrium activity of Zn will be governed by the solubility product of Zn(OH)j and the pH of the solution at still higher pHs ZnOj-anions will become the stable phase and both Zn and Zn(OH)2 will become unstable. However, a similar thermodynamic approach may be adopted to that shown in this example. 

The data given in Tables 1.9 and 1.10 have been based on the assumption that metal cations are the sole species formed, but at higher pH values oxides, hydrated oxides or hydroxides may be formed, and the relevant half reactions will be of the form shown in equations 2(a) and 2(b) (Table 1.7). In these circumstances the a + will be governed by the solubility product of the solid compound and the pH of the solution. At higher pH values the solid compound may become unstable with respect to metal anions (equations 3(a) and 3(b), Table 1.7), and metals like aluminium, zinc, tin and lead, which form amphoteric oxides, corrode in alkaline solutions. It is evident, therefore, that the equilibrium between a metal and an aqueous solution is far more complex than that illustrated in Tables 1.9 and 1.10. Nevertheless, as will be discussed subsequently, a similar thermodynamic approach is possible. 

Coh ) = concentration (or activity) at the surface which may be obtained from the solubility product of Mg(OH)j, and Aqh- = the mass transport coefficient of hydroxyl ions without chemical reaction and is obtained from ... 

A simple calculation based on the solubility product of ferrous hydroxide and assuming an interfacial pH of 9 (due to the alkalisation of the cathodic surface by reaction ) shows that, according to the Nernst equation, at -0-85 V (vs. CU/CUSO4) the ferrous ion concentration then present is sufficient to permit deposition hydroxide ion. It appears that the ferrous hydroxide formed may be protective and that the practical protection potential ( —0-85 V), as opposed to the theoretical protection potential (E, = -0-93 V), is governed by the thermodynamics of precipitation and not those of dissolution. 

The Ag/AgCl, Cl" electrode, which may be regarded as typical of electrodes of the second kind, consists of AgCl in contact with a soluble chloride, usually KCl. This electrode is essentially an Ag -F e Ag electrode, in which the 0 is controlled by the solubility product of AgCl and by the flci- Thus... 

The membrane consists of a binary compound AVaBVb of constant composition. Ion activities in the solid state are 1. At the membrane surface the activities of A and B in the aqueous phase are given by the solubility product ... 

One way to establish equilibrium between a slightly soluble solid and its ions in solution is to stir the solid with water to form a saturated solution. As you might expect, the solubility of the solid, s, in moles per liter, is related to the solubility product constant, Ksp. In the case of barium sulfate dissolving in water we have... 

Using AG tables in Appendix 1, calculate the solubility product constant, Rsp, for PbCl2 at 25°C. 

Solubility equilibrium constants, such as (20) and (22), are given a special name—the solubility product. It is symbolized K,p. A low value of K,p means the concentrations of ions are low at equilibrium. Hence the solubility must be low. Table 10-11 lists solubility products for some common compounds. 

Write the equation for the dissolving of calcium sulfate, CaSOt, and the solubility product expression. 

The solubility product is learned from measurements of the solubility. In turn, it can be used as a basis for calculations of solubility. Suppose we wish to know how much cuprous chloride, CuCl, will dissolve in one liter of water. We begin by writing the balanced equation for the reaction ... 

Calculate the solubility, in moles per liter, of calcium sulfate in water, using the solubility product given in Table 10-11. 

When two solutions are mixed, a precipitate may form. For example, suppose solutions of calcium chloride, CaCl2, and sodium sulfate, Na2S04, are mixed. The mixture contains both calcium ions, Ca+1, and sulfate ions, S04-2, so solid calcium sulfate may form. The solubility product permits us to predict with confidence whether it will or not. 

Write the solubility product expression for each of the following reactions. 

The solubility product of AgCl is 1.4 x 10-4 at 100°C. Calculate the solubility of silver chloride in boiling water. 

In reaction (7), all of the molecular species involved in the equilibrium are in the solution as dissolved species. Though the equilibrium relationship that exists among the concentrations is a little more complicated than in the solubility product expressions, the guiding principles are the same. 

Although the hydroxides of the alkaline earth elements become more soluble in water as we go down the column, the opposite trend is observed in the solubilities of the sulfates and carbonates. For example, Table 21-VII shows the solubility products of the alkaline earth sulfates. 

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