18 4 Solubility Equilibrium Chapter 18 Reaction Rates

18. 4 Solubility Equilibrium > Chapter 18 Reaction Rates and Equilibrium 18. 1 Rates of Reaction 18. 2 The Progress of Chemical Reactions 18. 3 Reversible Reactions and Equilibrium 18. 4 Solubility Equilibrium 18. 5 Free Energy and Entropy 1 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > CHEMISTRY & YOU How is it possible to ingest a poison without being harmed? Barium sulfate, a poison, can absorb X -rays, so tissues coated with the liquid will appear as light areas in the X-ray images. 2 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant What is the relationship between the solubility product constant and the solubility of a compound? 3 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant • Most ionic compounds containing alkali metals are soluble in water. • For example, more than 35 g of sodium chloride will dissolve in only 100 g of water. 4 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant • Most ionic compounds containing alkali metals are soluble in water. • For example, more than 35 g of sodium chloride will dissolve in only 100 g of water. • By contrast, some ionic compounds are insoluble in water. • For example, compounds that contain phosphate, sulfite, or carbonate ions tend not to dissolve in water. 5 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Interpret Data This table provides some general rules for the solubility of ionic compounds in water. Solubility of Ionic Compounds in Water 6 Compounds Solubility Exceptions Salts of Group 1 A metals and ammonia Soluble Some lithium compounds Ethanoates, nitrates, chlorates, Soluble and perchlorates Few exceptions Sulfates Soluble Compounds of Pb, Ag, Hg, Ba, Sr, and Ca Chlorides, bromides, and iodides Soluble Compounds of Ag and some compounds of Hg and Pb Sulfides and hydroxides Most are insoluble Alkali metal sulfides and hydroxides are soluble. Compounds of Ba, Sr, and Ca are slightly soluble. Carbonates, phosphates, and sulfites Insoluble Compounds of the alkali metals and of ammonium ions Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant Most insoluble ionic compounds will actually dissolve to some extent in water. • These compounds are said to be slightly soluble in water. 7 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant When the “insoluble” compound silver chloride is mixed with water, a very small amount of silver chloride dissolves in the water. Ag. Cl(s) Ag+(aq) + Cl–(aq) An equilibrium is established between the solid and the dissolved ions in the saturated solution. 8 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant When the “insoluble” compound silver chloride is mixed with water, a very small amount of silver chloride dissolves in the water. Ag. Cl(s) Ag+(aq) + Cl–(aq) You can write an equilibriumconstant expression for this process. [Ag+] [Cl–] Keq = [Ag. Cl] 9 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant To compare the solubility of salts, it is useful to have a constant that reflects only the concentrations of the dissolved ions. • This constant is called the solubility product constant (Ksp). • It is equal to the product of the concentrations of the ions each raised to a power equal to the coefficient of the ion in the dissociation equation. Ksp = [A]a [B]b 10 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant The smaller the numerical value of the solubility product constant, the lower the solubility of the compound. 11 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Solubility Product Constant The table below lists the Ksp values for some ionic compounds that are slightly soluble in water. Solubility Product Constants (Ksp) at 25 o. C Ionic compound 12 Ksp Halides Ag. Cl Ag. Br Ag. I Pb. Cl 2 Pb. Br 2 Pb. I 2 Pb. F 2 Ca. F 2 1. 8 10– 10 5. 0 10– 13 8. 3 10– 17 1. 7 10– 5 2. 1 10– 6 7. 9 10– 9 3. 6 10– 8 3. 9 10– 11 Chromates Pb. Cr. O 4 Ag 2 Cr. O 4 1. 8 10– 14 1. 2 10– 12 Ionic compound Ksp Sulfates Pb. SO 4 Ba. SO 4 Ca. SO 4 6. 3 10– 7 1. 1 10– 10 2. 4 10– 5 Sulfides Ni. S Cu. S Ag 2 S Zn. S Fe. S Cd. S Pb. S 4. 0 10– 20 8. 0 10– 37 8. 0 10– 51 3. 0 10– 23 8. 0 10– 19 1. 0 10– 27 3. 0 10– 28 Ionic compound Ksp Hydroxides Al(OH)3 Zn(OH)2 Ca(OH)2 Mg(OH)2 Fe(OH)2 3. 0 10– 34 3. 0 10– 16 6. 5 10– 6 7. 1 10– 12 7. 9 10– 16 Carbonates Ca. CO 3 Sr. CO 3 Zn. CO 3 Ag 2 CO 3 Ba. CO 3 4. 5 10– 9 9. 3 10– 10 1. 0 10– 10 8. 15 10– 12 5. 0 10– 9 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 6 Finding the Ion Concentrations in a Saturated Solution What is the concentration of lead ions and chromate ions in a saturated solution of lead(II) chromate at 25 o. C? (Ksp = 1. 8 10– 14) 13 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 6 1 Analyze List the knowns and the unknowns. Write the expression for Ksp. Then modify it so that there is a single unknown. KNOWNS Ksp = 1. 8 10– 14 Pb. Cr. O 4(s) Pb 2+(aq) + Cr. O 42–(aq) UNKNOWN [Pb 2+] = ? M [Cr. O 42–] = ? M 14 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 6 2 Calculate Solve for the unknowns. • Start with the general expression for the solubility product constant. The exponent for a b Ksp = [A] [B] each ion is 1. • Use the chemical equation to write the correct expression for Ksp for the reaction. Ksp = [Pb 2+] [Cr. O 42–] = 1. 8 10– 14 15 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 6 2 Calculate Solve for the unknowns. Substitute [Pb 2+] for [Cr. O 42–] in the expression to get an equation with one unknown. At equilibrium, [Pb 2+] = [Cr. O 42–]. Ksp = [Pb 2+]2 = 1. 8 10– 14 16 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 6 2 Calculate Solve for the unknowns. Solve for [Pb 2+] = 1. 8 10– 14 [Pb 2+] = [Cr. O 42–] = 1. 3 10– 7 M 17 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 6 3 Evaluate Does the result make sense? • Calculate [Pb 2+] [Cr. O 42–] to evaluate the answers. • The result is 1. 7 10– 14, which is close to the value of Ksp. • The result varies slightly from the actual value because the answers were rounded to two significant figures. 18 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Which of the following compounds is o least soluble at 25 C? A. Pb. F 2 B. Zn. S C. Sr. CO 3 D. Ca. SO 4 19 o Ksp at 25 C Ionic compound Ksp Ca. SO 4 2. 4 10– 5 Pb. F 2 3. 6 10– 8 Sr. CO 3 9. 3 10– 10 Zn. S 3. 0 10– 23 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Which of the following compounds is o least soluble at 25 C? A. Pb. F 2 B. Zn. S C. Sr. CO 3 D. Ca. SO 4 20 o Ksp at 25 C Ionic compound Ksp Ca. SO 4 2. 4 10– 5 Pb. F 2 3. 6 10– 8 Sr. CO 3 9. 3 10– 10 Zn. S 3. 0 10– 23 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Common Ion Effect How can you predict whether precipitation will occur when two solutions are mixed? 21 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Common Ion Effect In a saturated solution of lead(II) chromate, an equilibrium is established between the solid lead(II) chromate and its ions in solution. Pb. Cr. O 4(s) Pb 2+(aq) + Cr. O 42–(aq) What would happen if you added some lead nitrate to this solution? 22 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Common Ion Effect Pb. Cr. O 4(s) Pb 2+(aq) + Cr. O 42–(aq) • Lead(II) nitrite is soluble in water, so adding Pb(NO 3)2 causes the concentration of lead ion to increase. • The addition of lead ions is a stress on the equilibrium. • Applying Le Châtelier’s principle, the stress can be relieved if the reaction shifts to the left. 23 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Common Ion Effect The yellow solid in the test tube, which is Pb. Cr. O 4, cannot dissolve because the solution is saturated with Pb 2+ and Cr. O 42– ions. 24 When some Pb(NO 3)2 is added, the excess lead ions combine with the chromate ions in solution to form additional solid Pb. Cr. O 4. Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Common Ion Effect In this example, the lead ion is a common ion. • A common is an ion that is found in both ionic compounds in a solution. • The lowering of the solubility of an ionic compound as a result of the addition of a common is called the common ion effect. 25 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > CHEMISTRY & YOU The Ksp of Ba. SO 4 is 1. 1 10– 10. Why can a patient ingest the toxic Ba. SO 4 without being harmed? 26 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > CHEMISTRY & YOU The Ksp of Ba. SO 4 is 1. 1 10– 10. Why can a patient ingest the toxic Ba. SO 4 without being harmed? Barium sulfate is not very soluble. Therefore, very little of it can dissolve in bodily fluids and be absorbed as a toxin. 27 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 7 Finding Equilibrium Ion Concentrations in the Presence of a Common Ion Small amounts of silver bromide can be added to the lenses used for eyeglasses. The silver bromide causes the lenses to darken in the presence of large amounts of UV light. The Ksp of silver bromide is 5. 0 10– 13. What is the concentration of bromide ion in a 1. 00 -L saturated solution of Ag. Br to which 0. 020 mol of Ag. NO 3 is added? 28 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 7 1 Analyze List the knowns and the unknown. Use one unknown to express both [Ag+] and [Br–]. Let x be the equilibrium concentration of bromide ion and x + 0. 020 be the equilibrium concentration of silver ion. KNOWNS Ksp = 5. 0 UNKNOWN [Br–] = ? M 10– 13 moles of Ag. NO 3 added = 0. 020 mol Ag. Br(s) 29 Ag+(aq) + Br–(aq) Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 7 2 Calculate Solve for the unknown. • Write the expression for Ksp = [Ag+] [Br–] • Substitute x for [Br–] in the solubility product expression. Ksp = [Ag+] x 30 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 7 2 Calculate Solve for the unknown. • Rearrange the equation to solve for x. Ksp x = [Ag+] • Substitute the values for Ksp and [Ag+] in the expression and solve. (5. 0 10– 13) x = 0. 020 [Br–] = 2. 5 10– 11 M 31 Based on the small value of Ksp, you can assume that x will be very small compared to 0. 020. Thus, [Ag+] ≈ 0. 020 M. Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Sample Problem 18. 7 3 Evaluate Does the result make sense? • The concentration of Br– in a saturated solution of Ag. Br is 7. 0 10– 7 M (the square root of the Ksp). • It makes sense that the addition of Ag. NO 3 – would lower the concentration of Br because the presence of a common ion, Ag+, causes Ag. Br to precipitate from solution. 32 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > The Common Ion Effect A precipitate will form if the product of the concentrations of two ions in the mixture is greater than the Ksp value for the compound formed from the ions. As solutions of barium nitrate and sodium sulfate are mixed, a precipitate of Ba. SO 4 is formed. 33 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Does a precipitate form when 1 L of 0. 034 M Na 2 SO 4 is mixed with 1 L of 0. 0012 M Ba(NO 3)2? The Ksp for Ba. SO 4 is 1. 1 10– 10. 34 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Does a precipitate form when 1 L of 0. 034 M Na 2 SO 4 is mixed with 1 L of 0. 0012 M Ba(NO 3)2? The Ksp for Ba. SO 4 is 1. 1 10– 10. [Ba 2+] [SO 42–] = (0. 0006 M) (0. 014 M) = 8. 4 10– 6 The result is larger than the Ksp value for Ba. SO 4, so a precipitate will form. 35 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Key Concepts and Key Equation The smaller the value of the solubility product constant, the lower the solubility of the compound. A precipitate will form if the product of the concentrations of two ions in the mixture is greater than the Ksp value of the compound formed from the ions. Ksp = [A]a × [B]b 36 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > Glossary Terms • solubility product constant: an equilibrium constant applied to the solubility of electrolytes; it is equal to the product of the concentrations of the ions each raised to a power equal to the coefficient of the ion in the dissociation equation • common ion: an ion that is common to both salts in a solution; in a solution of silver nitrate and silver chloride, Ag+ would be a common ion • common ion effect: a decrease in the solubility of an ionic compound caused by the addition of a common ion 37 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.

18. 4 Solubility Equilibrium > END OF 18. 4 38 Copyright © Pearson Education, Inc. , or its affiliates. All Rights Reserved.