Solubility Equilibria PDF

Solubility Equilibria 1 Solution Formation and Equilibrium When dissolution and crystallization occur at the same rate, the solution is in dynamic equilibrium. The quantity of dissolved solute remains constant with time, and the solution is a saturated solution....

Solubility Equilibria 1 Solution Formation and Equilibrium When dissolution and crystallization occur at the same rate, the solution is in dynamic equilibrium. The quantity of dissolved solute remains constant with time, and the solution is a saturated solution. 2  Saturated Solution The concentration of a saturated solution is called the solubility of the solute in the given solvent. Solubility varies with the temperature. A solubility – temperature graph is called a solubility curve. Some typical solubility curves are shown on the next slide. 3 4  Solubility Generally, the solubilities of ionic substances (about 95% of them) increase with increasing temperature. Exceptions tend to be compounds containing the anions SO32-, SO42-, AsO43-, and PO43-. As we add solute to solvent, we start with less solute than would be present in the saturated solution, the solute completely dissolves, and the solution is an unsaturated solution. Alternatively, we can prepare a saturated solution at a high temperature and then cool it down. 5  Supersaturated Solutions Usually, the excess solute crystallizes from solution, but occasionally all the solute may stay in solution. In these cases, because the quantity of solute is greater than in a saturated solution, the solution is supersaturated. A supersaturated solution is unstable, and if a few crystals of solute are added to serve as particles on which crystallization can occur, the excess solute crystallizes. 6  Review of Le Châtelier’s Principle Suppose that a system at equilibrium is subjected to a change that disturbs the system. Le Châtelier’s principle states that the system will spontaneously move back to equilibrium, so the change is offset. Consider the following reaction: for which the equilibrium constant is 7  Review of Le Châtelier’s Principle In one particular equilibrium state of this system, the following concentrations exist: [H+] = 5.0 M; [Cr2O72-] = 0.10 M; [Cr3+] = 0.0030 M [Br-] = 1.0 M; [BrO3-] = 0.043 M Suppose that the equilibrium is disturbed by adding dichromate to the solution to increase the concentration of [Cr2O72-] from 0.10 to 0.20 M. In what direction will the reaction go to come back to equilibrium? According to Le Châtelier’s principle, the reaction will go back to the left to partially offset the increase in dichromate, which is on the right side. 8  Review of Le Châtelier’s Principle We can verify this algebraically by setting up the reaction quotient, Q, which has the same form as the equilibrium constant. The only difference is that Q is evaluated with whatever concentrations happen to exist in the solution. When the system reaches equilibrium, Q = K. For our particular case, Since Q > K, the reaction must go to the left to decrease the numerator and increase the denominator, until Q = K. 9  Review of Le Châtelier’s Principle In general: If a reaction is at equilibrium and products are added (or reactants are removed) the reaction goes to the left. If a reaction is at equilibrium and reactants are added (or products are removed) the reaction goes to the right. If Q > K, the reaction must proceed to the left to reach equilibrium. If Q < K, the reaction must proceed to the right to reach equilibrium. 10  The Solubility Product Constant, Ksp Gypsum, CaSO4.2H2O, is a calcium mineral. It is slightly soluble in water, and groundwater that comes into contact with gypsum often contains some dissolved calcium sulfate. This water cannot be used in certain applications because the calcium sulfate might precipitate from the water and block pipes. The equilibrium between Ca2+(aq) and SO42-(aq) and CaSO4(s) can be represented as 11  The Solubility Product Constant, Ksp We can write the equilibrium constant expression for this equilibrium by including concentration terms for ions that are in solution, but not for the pure solid solute. We represent the equilibrium constant by a special symbol, Ksp. The solubility product constant, Ksp, is the equilibrium constant for the reaction in which a solid salt dissolves to give its constituent ions in solution. 12 The Solubility Product Constant, Ksp The concentration of the solid is omitted from the equilibrium constant because the solid is in its standard state. 1 Consider the dissolution of mercurous chloride in water. The reaction is for which the solubility product Ksp is 13 The Solubility Product Constant, Ksp A solution containing excess, undissolved solid is said to be saturated with that solid. The solution contains all the solid capable of being dissolved under the prevailing conditions. What will be the concentration of Hg22+ in a solution saturated with Hg2Cl2? In the reaction (previous slide) we see that 2 Cl- ions are produced for each Hg22+ ion. If the concentration of dissolved Hg22+ is x M, the concentration of dissolved Cl- must be 2x M. Putting these values of concentration into the solubility product gives 14 The Solubility Product Constant, Ksp The concentration of Hg22+ is 6.7 x 10-7 M, and the concentration of Cl- is (2)(6.7 x 10-7) = 13.4 x 10-7 M. The physical meaning of the solubility product is this: If an aqueous solution is left in contact with excess solid Hg2Cl2, the solid will dissolve until the condition [Hg22+][Cl-]2 = Ksp is satisfied. After that, the amount of undissolved solid stays constant. 15 The Solubility Product Constant, Ksp Unless excess solid remains, there is no guarantee that [Hg22+][Cl-]2 = Ksp. If Hg22+ and Cl- are mixed together (with appropriate counterions) such that the product [Hg22+][Cl-]2 exceeds Ksp, then Hg2Cl2 will precipitate. The amount of excess solid present has no effect on the equilibrium position. Having a small amount of excess solid will not cause a different solubility than having a large amount of excess solid. 16  The Mercurous Ion Mercury has three common oxidation states. 1. Hg(0) is metallic mercury. Hg is one of only two elements (the other being Br) that is a liquid at 298 K (room temperature). 2. Hg(I) is the mercurous ion which is a dimer with a bond length close to 250 pm (0.250 nm). [Hg-Hg]2+ When mercurous salts dissolve, they do not give monatomic Hg+ in solution. Hg22+ remains present as a diatomic ion. 3. Hg(II) is the mercuric ion, which exists as Hg2+. 17  Solubility vs. Solubility Product It is very important to distinguish between the solubility of a given solid and its solubility product, Ksp. The solubility product is an equilibrium constant and has only one value for a given solid at a given temperature. Solubility, on the other hand, is an equilibrium position. In pure water at a specific temperature a given salt has a particular solubility. On the other hand, if a common ion is present in the solution, the solubility varies according to the concentration of the common ion. However, in all cases the product of the ion concentrations must satisfy the Ksp expression. 18 The Relationship Between Solubility and Ksp Is there a relationship between the solubility product constant, Ksp, of a solute and the solute’s molar solubility – its molarity in a saturated aqueous solution? As we will see in the following examples, there is a definite relationship between them. 2, 3, 4, 5, 6 19  Relative Solubilities A salt’s Ksp value gives us information about its solubility. However, we must be careful in using Ksp values to predict the relative solubilities of a group of salts. That is, you might ask the question “Is a solute with a larger value of Ksp always more soluble than one with a smaller value?” To answer this, there are two possible cases: 1. The salts being compared produce the same number of ions. For example, consider AgI(s) Ksp = 1.5 x 10-16 CuI(s) Ksp = 5.0 x 10-12 CaSO4(s) Ksp = 6.1 x 10-5 20  Relative Solubilities Each of these solids dissolves to produce two ions: If x is the solubility in mol/L, then at equilibrium 21  Relative Solubilities Therefore, in this case we can compare the solubilities for these solids by comparing the Ksp values: 22  Relative Solubilities 2. The salts being compared produce different numbers of ions. For example, consider CuS(s) Ksp = 8.5 x 10-45 Ag2S(s) Ksp = 1.6 x 10-49 Bi2S3(s) Ksp = 1.1 x 10-73 Because these salts produce different numbers of ions when they dissolve, the Ksp values cannot be compared directly to determine relative solubilities. In fact, if we calculate the solubilities (as we’ve done in the examples) we get the results shown on the next slide. 23  Relative Solubilities The order of solubilities is Which is opposite to the order of the Ksp values. 24  Relative Solubilities Remember that relative solubilities can be predicted by comparing Ksp values only for salts that produce the same total number of ions. 25  Will a Precipitate Form? Silver iodide’s solubility equilibrium is AgI(s) Ag+(aq) + I-(aq) Ksp = [Ag+][I-] = 1.5 x 10-16 What if we mix solutions of AgNO3(aq) and KI(aq) to get a mixed solution that has [Ag+] = 0.010 M and [I-] = 0.015 M? Is this solution unsaturated, saturated, or supersaturated? In the past, we have used the reaction quotient, Q. It has the same form as the equilibrium constant expression but uses initial concentrations rather than equilibrium concentrations. 26  Will a Precipitate Form? Initially, Q = [Ag+]init[I-]init = (0.010)(0.015) = 1.5 x 10-4 > Ksp The fact that Q > Ksp indicates that the concentrations of Ag+ and I- are already higher than they would be in a saturated solution and that a net change should occur to the left. The solution is supersaturated. As is generally the case with supersaturated solutions, excess AgI should precipitate from solution. If we had found Q < Ksp, the solution would have been unsaturated. Then no precipitate would have formed. 27  Criterion for Precipitation When applied to solubility equilibria, Q is generally called the ion product because its form is that of the product of ion concentrations raised to appropriate powers. The criteria for determining whether ions in a solution will combine to form a precipitate requires us to compare the ion product with Ksp. – Precipitation should occur if Q > Ksp. – Precipitation cannot occur if Q < Ksp. – A solution is just saturated if Q = Ksp. 7,8 28 Criterion for Precipitation 29  Is Precipitation Complete? Precipitation of a solute is considered to be complete only if the amount remaining in solution is very small. An arbitrary rule of thumb is that precipitation is complete if 99.9% or more of a particular ion has precipitated, leaving less than 0.1% of the ion in solution. In example 9, we will calculate the concentration of Mg2+ that remains in a solution from which Mg(OH)2(s) has precipitated. We will compare this remaining [Mg2+] to the initial [Mg2+] to determine the completeness of the precipitation. 9 30  Common Ion Effect So far we have considered ionic solids dissolved in pure water. We will now see what happens when the water contains an ion in common with the dissolving salt. E.g., consider the solubility of solid silver chromate (Ag2CrO4, Ksp = 9.0 x 10-12) in a 0.100 M solution of AgNO3. Before any Ag2CrO4 dissolves, the solution contains the major species Ag+, NO3-, and H2O, with solid Ag2CrO4 on the bottom of the container. 31  Common Ion Effect The relevant initial concentrations (before any Ag2CrO4 dissolves) are [Ag+]0 = 0.100 M (from the dissolved AgNO3) [CrO42-]0 = 0 The system comes to equilibrium as the solid Ag2CrO4 dissolves according to the reaction Ag2CrO4 (s) ⇄ 2Ag+(aq) + CrO42-(aq) Ksp = [Ag+]2[CrO42-] = 9.0 x 10-12 We assume that x mol/L of Ag2CrO4 dissolves to reach equilibrium, which means that x mol/L Ag2CrO4(s) → 2x mol/L Ag+(aq) + x mol/L CrO42-(aq) 32  Common Ion Effect Now we can specify the equilibrium concentrations in terms of x: [Ag+] = [Ag+]0 + change = 0.100 + 2x [CrO42-] = [CrO42-]0 + change = 0 + x = x Substituting these concentrations into the expression for Ksp gives 9.0 x 10-12 = [Ag+]2[CrO42-] = (0.100 + 2x)2(x) This is a cubic equation, but we can make a simplifying assumption. Since the Ksp for Ag2CrO4 is small, x is expected to be small compared with 0.100 M. Therefore, 0.100 + 2x  0.100. 33  Common Ion Effect 9.0 x 10-12 = (0.100 + 2x)2(x)  (0.100)2(x) Then x  9.0 x 10-12 = 9.0 x 10-10 mol/L (0.100)2 Since x is much less than 0.100 M, our assumption is valid. This (x) is the solubility of Ag2CrO4 in 0.100 M AgNO3. Let’s compare the solubilities of Ag2CrO4 in pure water and in 0.100 M AgNO3. – Solubility of Ag2CrO4 in pure water = 1.3 x 10-4 M – Solubility of Ag2CrO4 in 0.100 M AgNO3 = 9.0 x 10-10 M Note that the solubility of Ag2CrO4 is much less in the presence of Ag+ ions from AgNO3. The solubility of a solid is lowered if the solution already contains ions common to the solid. 34 Common Ion Effect 10,11 35  Limitations of the Ksp Concept We have used the term slightly soluble in describing the solutes for which we have written Ksp expressions. Can we write Ksp expressions for moderately or highly soluble ionic compounds, such as NaCl, KNO3, and NaOH? The answer is yes, but the Ksp must be based on activities rather than on concentrations. In ionic solutions of moderate to high concentrations, activities and concentrations are generally far from equal. If we cannot use molarities in place of activities, much of the simplicity of the Ksp concept is lost. Thus Ksp values are usually limited to slightly soluble (essentially insoluble) solutes, and ion molarities are used in place of activities. 36 Diverse (“Uncommon”) Ion Effect: The Salt Effect We have seen the effect of common ions on a solubility equilibrium, but what effect do ions different from those involved in the equilibrium have on solute solubilities? The effect of “uncommon” ions, or diverse ions, is not as striking as the common ion effect. Uncommon ions tend to increase rather than decrease solubility. As the total ionic concentration of a solution increases, interionic attractions become more important. Activities (effective concentrations) become smaller than the stoichiometric or measured concentrations. 37 Diverse (“Uncommon”) Ion Effect: The Salt Effect For the ions involved in the solution process, this means that higher concentrations must appear in solution before equilibrium is established – the solubility increases. The diverse ion effect is more commonly called the salt effect. As a result of the salt effect, the numerical value of a Ksp based on molarities will vary depending on the ionic atmosphere. Most tabulated values of Ksp are based on activities rather than on molarities, thus avoiding the problem of the salt effect. 38 Common Ion and Diverse Ion Effects 39 Incomplete Dissociation of Solute into Ions In doing calculations involving Ksp values and solubilities, we have assumed that all the dissolved solute appears in solution as separated cations and anions. This assumption is often not valid. The solute might not be 100% ionic, and some of the solute might go into solution in molecular form. Or, some ions in solution might join together into ion pairs. 40 Incomplete Dissociation of Solute into Ions An ion pair is two oppositely charged ions that are held together by the electrostatic attraction between the ions. For example, in a saturated solution of magnesium fluoride, although most of the solute exists as Mg2+ and F- ions, some exists as the ion pair MgF+. 41 Incomplete Dissociation of Solute into Ions To the extent that a solution contains cations and anions of a solute as ion pairs, the concentrations of the dissociated ions are reduced from the stoichiometric expectations. Thus, although the measured solubility of MgF2 is about 4 x 10-3 M, we cannot safely assume that [Mg2+] = 4 x 10-3 M and that [F-] = 8 x 10-3 M, because some of the Mg2+ and F- ions are involved in ion pairing. This means that additional solute must be present for the product of ion concentrations to equal Ksp of the solute, making the true solubility of the solute greater than expected on the basis of Ksp. The degree of ion-pair formation increases as mutual electrostatic attraction of the cation and anion increases. Ion-pair formation is increasingly likely when the cations or anions in solution carry multiple charges (e.g., Mg2+ or SO42-). 42  Simultaneous Equilibria The reversible reaction between a solid solute and its ions in aqueous solution is never the only process occurring. At the very least, the autoionization of water also goes on, although we can generally ignore it. Other equilibrium processes that can occur include reactions between solute ions and other solution species. Two possibilities are acid-base reactions and complex-ion formation. Calculations based on the Ksp expression may be in error if we fail to take into account other equilibrium processes that happen simultaneously with solution equilibrium. 43  The Limitations of Ksp Back in Example 2, we calculated the Ksp for CaSO4 on the basis of its measured solubility. We calculated Ksp to be 2.3 x 10-4. This value is almost 10 times larger than the value listed in Appendix 2 of your textbook, which is Ksp = 2.4 x 10-5. These conflicting results for CaSO4 are understandable. The Ksp value listed in the table is based on ion activities, whereas the Ksp value calculated from experimentally determined solubility is based on ion concentrations, assuming complete dissociation of the solute into ions and no ion-pair formation. 44  The Limitations of Ksp We will continue to use molarities instead of activities of ions, and the case of CaSO4 simply suggests that some of our results, although of the appropriate magnitude (i.e., within a factor of 10 or 100), may not be highly accurate. These order-of-magnitude results, however, still let us make some correct predictions and to apply the Ksp concept in useful ways. 45  Fractional Precipitation If a large excess of AgNO3 is added to a solution containing the ions CrO42- and Br-, a mixed precipitate of Ag2CrO4(s) and AgBr(s) is obtained. There is a way of adding AgNO3, however, that will cause AgBr(s) to precipitate but leave CrO42- in solution. The way to do that is called fractional precipitation or selective precipitation. Fractional precipitation is a technique in which two or more ions in solution, each capable of being precipitated by the same reagent, are separated by the proper use of that reagent. The key to the technique is the slow addition of a concentrated solution of the precipitating reagent to the solution from which precipitation is to occur, as from a burette. 46 Fractional Precipitation 12,13 47  Solubility and pH The pH of a solution can affect the solubility of a salt to a large degree. That is especially true when the anion of the salt is the conjugate base of a weak acid or the base OH- itself. An example is the highly insoluble Mg(OH)2, which, when suspended in water, is the popular antacid known as milk of magnesia. Hydroxide ions from the dissolved magnesium hydroxide react with hydronium ions (in stomach acid) to form water. 48  Solubility and pH Mg(OH)2 Mg2+(aq) + 2OH-(aq) (1) OH-(aq) + H3O+(aq) → 2H2O(l) (2) According to Le Châtelier’s principle, we expect reaction (1) to be driven to the right – that is, additional Mg(OH)2 dissolves to replace OH- ions drawn off by the neutralization reaction (2). We can get the overall net ionic equation by doubling equation (2) and adding it to equation (1). 49  Solubility and pH The large value of K for this reaction shows that the reaction goes essentially to completion and that Mg(OH)2 is highly soluble in acidic solution. Other slightly soluble solutes having basic anions (such as ZnCO3, MgF2, and CaC2O4) also become more soluble in acidic solutions. For these solutes, we can write overall net ionic equations for solubility equilibria and corresponding K values based on Ksp for the solutes and Ka for the conjugate acids of the anions. 50  Solubility and pH Although Mg(OH)2 is soluble in acidic solution, in moderately or strongly basic solutions it is not. In example 14, we calculate [OH-] in a solution of the weak base NH3 and then use the criterion for precipitation to see if Mg(OH)2(s) will precipitate. In example 15, we find how to adjust [OH-] to prevent precipitation of Mg(OH)2(s). This adjustment is made by adding NH4+ to the NH3(aq), thereby converting it to a buffer solution. 14,15 51  Solubility and pH This idea also applies to salts with other types of anions. For example, the solubility of silver phosphate (Ag3PO4) is greater in acid than in pure water because the PO43- ion is a strong base that reacts with H+ to form the HPO42- ion. The reaction H+ + PO43- → HPO42- occurs in acidic solution, thus lowering the concentration of PO43- and shifting the solubility equilibrium Ag3PO4(s) ⇄ 3Ag+(aq) + PO43- (aq) to the right. This increases the solubility of silver phosphate. 52  Solubility and pH Silver chloride (AgCl), however, has the same solubility in acid as in pure water. Why? Since the Cl- ion is a very weak base (that is HCl is a very strong acid), no HCl molecules are formed. Thus the addition of H+ to a solution containing Cl- does not affect [Cl-] and has no effect on the solubility of a chloride salt. The general rule is that if the anion X- is an effective base – that is, if HX is a weak acid – the salt MX will show increased solubility in an acidic solution. 53  Solubility and pH Examples of common anions that are effective bases are OH-, S2-, CO32-, C2O42-, and CrO42-. Salts containing these anions are much more soluble in an acidic solution than in pure water. 54