18.3 Solubility Equilibrium 18.3 FOCUS. Guide for Reading INSTRUCT. The Solubility Product. Section Resources

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1 Solubility Equilibrium 1 FOCUS Objectives Describe the relationship between the solubility product constant and the solubility of a compound Predict whether precipitation will occur when two salt solutions are mixed. Guide for Reading Build Vocabulary Paraphrase Make sure students understand the difference between the terms solubility and solubility product. Have them write the definitions in their own words. Reading Strategy Summarize After reading this section, ask students to summarize what they learned about solubility product constants and the common ion effect. Suggest that they use an equation to illustrate their summary. 2 INSTRUCT Guide for Reading Key Concepts What is the relationship between the solubility product constant and the solubility of a compound? How can you predict whether precipitation will occur when two salt solutions are mixed? Vocabulary solubility product constant common ion common ion effect Reading Strategy Predicting Based on what you know about equilibrium and the dissociation of ionic compounds in aqueous solution, predict the form of the equilibrium constant expression for the dissolving of an ionic compound in water. After you read the section, check the accuracy of your prediction and clarify any misconceptions you may have had. Cl X-rays allow physicians to make observations of bones and internal organs without invasive surgery. Sometimes chemical substances are used to improve the clarity of the X-ray image. Barium sulfate is ingested by a patient before X-ray images of the digestive tract are taken. Barium sulfate absorbs the X-rays, thereby producing light areas on the developed X-ray film. However, barium salts are usually toxic. In this section, you will learn why patients can ingest this poisonous substance without harm. The Solubility Product Constant Ionic compounds differ in their solubilities. Most salts of the alkali metals are soluble in water. More than 35 g of sodium chloride will dissolve in only 100 g of water. Many classes of ionic compounds, however, are insoluble. For example, compounds that contain phosphate, sulfide, sulfite, or carbonate ions are often insoluble. Exceptions are compounds in which these ions are combined with ammonium ions or alkali metal ions. Table 18.1 summarizes the solubilities of many ionic compounds in water. Most insoluble salts will actually dissolve to some extent in water. These salts are said to be slightly, or sparingly, soluble in water. For example, Figure shows what happens when the insoluble salt silver chloride is mixed with water. A very small amount of silver chloride actually dissolves in the water. AgCl(s) m Ag (aq) Cl (aq) You can write an equilibrium expression for this process. K eq 3Ag+ 4 3Cl - 4 3AgCl4 As long as some undissolved AgCl (solid) is present, the concentration of the AgCl is a constant. Thus the concentration of AgCl, a constant, can be combined with the equilibrium constant to form a new constant. Ask, Why is BaSO 4 ingested by a patient before having an X-ray taken of the stomach? (Soft tissues don't show up well in X-rays.) Why is the digestive system well suited to this type of image enhancement? (Chemicals are easily brought into the system and easily removed.) The Solubility Product Constant Any ionic solid placed in water establishes an equilibrium between its dissociated ions in solution and the solid that is undissolved. The solubility product constant is an equilibrium constant that describes the equilibrium between a solid and its ions in solution. Ag 560 Chapter 18 Section Resources Print Guided Reading and Study Workbook, Section 18.3 Core Teaching Resources, Section 18.3 Review Transparencies, T203 T205 Laboratory Manual, Lab 39 K eq [AgCl] [Ag ] [Cl ] K sp Figure Silver chloride is slightly soluble in water. Predicting Would adding solid silver chloride to this test tube disturb the equilibrium? Technology Interactive Textbook with ChemASAP, Problem-Solving 18.17, 18.19; Assessment 18.3 Go Online, Section Chapter 18

2 Table 18.1 This new constant, called the solubility product constant (K sp ), equals the product of the concentrations of the ions each raised to a power equal to the coefficient of the ion in the dissociation equation. The coefficients for the dissociation of silver chloride are each 1. The value of K sp for silver chloride at 25 C is What does the size of the solubility product constant tell you about the solubility of the compound? The smaller the numerical value of the solubility product constant, the lower the solubility of the compound. The solubility product constants for some common sparingly soluble salts are given in Table 18.2 on the next page. The mineral deposits around sink drains, such as the one shown in Figure 18.17, are composed of compounds such as calcium carbonate (K sp ). The low solubility of such compounds makes them difficult to remove. Checkpoint Solubilities of Ionic Compounds in Water Compounds Solubility Exceptions Salts of Group 1A metals and ammonia Soluble Some lithium compounds Ethanoates, nitrates, chlorates, and Soluble Few exceptions perchlorates 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 K sp 3Ag + 4 3Cl - 4 K sp What does the solubility product constant expression consist of? Figure Scale, formed by the precipitation of slightly soluble salts, often builds up around kitchen and bathroom faucets. Applying Concepts Why are insoluble substances hard to remove? CLASS Activity Solubility Tables Purpose Students illustrate the solubilities of salts containing various anions. Materials Calculator, paper, pencil Procedure Divide the class into groups of four students. Ask the groups to create color-coded tables illustrating the solubilities of salts containing various anions. For example, students can design separate tables for nitrates, sulfates, chlorides, sulfides, hydroxides, and carbonates. Have them use different colors in each table to show which elements form soluble compounds containing a given anion and which form insoluble compounds. Students should divide the tasks of looking up solubilities, designing the tables, and drawing the final tables. Use Visuals Table 18.1 Have students reread the Connecting to Your World on page 560. Ask them if Table 18.1 helps them understand why barium sulfate can be used in humans for X-ray imaging. (because it isn't soluble in human tissues) Explain that the solubility product constant is closely related to the equilibrium constant that students learned about in Section Point out similarities in the equations for these two quantities. Write the example problems on the board and carry out the solutions for the solubility product, K sp. Focus on how to set up the algebraic expression. Section 18.3 Solubility Equilibrium 561 Answers to... Figure No, because the concentration of AgCl is constant. Figure because they don t dissolve in a solvent such as water. Checkpoint The product of the two ions raised to a power equal to their respective coefficients in the dissociation equation. Reaction Rates and Equilibrium 561

3 Section 18.3 (continued) TEACHER Demo Common Ion Effect Purpose Students hypothesize the result of mixing silver nitrate and silver chloride Materials silver chloride, silver nitrate, 2 test tubes Procedure Prepare saturated solutions of silver chloride and silver nitrate in two test tubes. Write the solubility product constant expression for silver chloride on the board. K sp = [Ag + ] [Cl ] = Have students hypothesize what would occur if a few drops of the silver nitrate solution were added to the test tube containing the silver chloride. Add the drops of silver nitrate solution and ask students what they observe. (A precipitate, silver chloride, comes out of solution.) Explain that the value of [Ag + ] increases in the K sp expression as the silver nitrate is added, so that silver chloride must precipitate until the solubility product again equals K sp. Sample Problem 18.3 Answers M M Practice Problems Plus What is the concentration of barium and sulfate ions in a saturated barium sulfate solution at 25 C? K sp = ( M) Table 18.2 Solubility Product Constants (K sp ) at 25 C Salt K sp Salt K sp Salt K sp Halides Sulfates Hydroxides AgCl PbSO Al(OH) AgBr BaSO Zn(OH) AgI CaSO Ca(OH) PbCl Sulfides Mg(OH) PbBr NiS Fe(OH) PbI CuS Carbonates PbF Ag 2 S CaCO CaF ZnS SrCO Chromates FeS ZnCO PbCrO CdS Ag 2 CO Ag 2 CrO PbS BaCO The chromate ion is responsible for the brilliant yellow color of lead(ii) chromate. Problem Solving Solve Problem 17 with the help of an interactive guided tutorial. withchemasap SAMPLE PROBLEM 18.3 Finding the Ion Concentrations in a Saturated Solution What is the concentration of lead ions and chromate ions in a saturated lead chromate solution at 25 C? (K sp ) Analyze List the knowns and the unknowns. Knowns K sp K sp [Pb ] [CrO 4 ] PbCrO 4 (s) m Pb (aq) CrO 4 (aq) 3Pb CrO M Practice Problems Unknowns [Pb ]? M [CrO 4 ]? M For each Pb ion formed, one CrO 4 ion is formed. Calculate Solve for the unknowns. K sp [Pb ] [CrO 4 ] At equilibrium [Pb ] [CrO 4 ]. Substitute [Pb ] for [CrO 4 ] in the expression for K sp to get an equation with one unknown. K sp [Pb ] [Pb ] [Pb ] Solve for [Pb ]. Evaluate Does the result make sense? The product [Pb ] [CrO 4 ] is close to the value of K sp. The answer should have two significant figures. 17. Lead(II) sulfide (PbS) has a K sp of What is the concentration of lead(ii) ions in a saturated solution of PbS? 18. What is the concentration of calcium ions in a saturated calcium carbonate solution at 25 C? (K sp ) 562 Chapter Chapter 18

4 a b Figure Lead(II) chromate is slightly soluble in water. a A saturated solution of PbCrO 4 is pale yellow. b When a few drops of lead nitrate (Pb(NO 3 ) 2 ) are added to the solution, it becomes cloudy as more lead(ii) chromate precipitates. Applying Concepts Explain what happened in b by considering the addition of lead nitrate as a stress on the PbCrO 4 equilibrium. The Common Ion Effect Point out that the common ion effect is not a new concept, but an example of Le Châtelier s principle at work. Explain that adding an ion to an equilibrium system containing that ion will cause the equilibrium to shift in the direction that uses up the ion. 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. PbCrO 4 (s) m Pb (aq) CrO 4 (aq) K sp What do you think would happen if you added some lead nitrate to this solution? The concentration of lead ion would increase. Immediately, the product of [Pb ] and [CrO 4 ] would be greater than K sp. Applying Le Châtelier s principle, the stress of the additional Pb can be relieved if the reaction shifts to the left. Figure demonstrates that lead ions combine with chromate ions in solution to form additional solid PbCrO 4. Lead chromate continues to precipitate from the solution until the product of [Pb ] and [CrO 4 ] once again equals K sp for the original solution: [Pb ][CrO 4 ] K sp after addition of Pb(NO 3 ) 2 : [Pb ][CrO 4 ] In this example, the lead ion is called a common ion. A common ion is an ion that is found in both salts in a solution. Adding lead nitrate to a saturated solution of PbCrO 4 causes the solubility of PbCrO 4 to decrease. The lowering of the solubility of an ionic compound as a result of the addition of a common ion is called the common ion effect. Adding sodium chromate to the solution of PbCrO 4 would also produce the common ion effect. The additional chromate ion, a different common ion, would similarly cause the solubility equilibrium to shift to the left and produce more PbCrO 4. Recall from Connecting to Your World that patients must ingest toxic barium sulfate (BaSO 4 ) when having an X-ray taken. Table 18.2 shows that the K sp of barium sulfate is Considering this low value, it is understandable that barium cannot harm the patient because so little of it is in solution and able to enter the bloodstream. The solubility can be further reduced by adding sodium sulfate (Na 2 SO 4 ), a nontoxic soluble compound that provides the common ion SO 4. For: Links on the Common Ion Effect Visit: Web Code: cdn-1182 Download a worksheet on the Common Ion Effect for students to complete, and find additional teacher support from NSTA SciLinks. Checkpoint What is the common ion effect? Section 18.3 Solubility Equilibrium 563 Facts and Figures Other Compounds in Radiology Barium sulfate is just one of many compounds used as contrast materials in radiology. Barium compounds are used to look at gastrointestinal areas. Water-soluble iodinated compounds are contrast materials injected to make blood vessels, urinary tract, and spinal canal visible in X-rays. Naturally placed or injected air also functions as a contrast material. Answers to... Figure An increase in Pb 2+ (aq) shifts the equilibrium to the left creating more PbCrO 4 (s). Checkpoint The lowering of the solubility of an ionic compound as a result of the addition of one of the ions in the compound Reaction Rates and Equilibrium 563

5 Section 18.3 (continued) Relate Tiny crystals or grains of silver bromide are immersed in a gelatinous emulsion on the surface of unexposed photographic film. When photons enter a camera and strike the film, the energy of the photons causes some bromide ions to lose an electron and some silver ions to gain an electron. These grains of silver bromide are said to be activated. In the developing process, only silver ions in activated grains are converted to silver atoms to form the image. Sample Problem 18.4 Answers M M Math Handbook For a math refresher and practice, direct students to algebraic equations, page R69. Math Handbook For help with algebraic equations, go to page R69. SAMPLE PROBLEM 18.4 Finding Equilibrium Ion Concentrations in the Presence of a Common Ion Photographic film is covered with a light-sensitive emulsion containing silver bromide. The K sp of silver bromide is What is the bromide-ion concentration of a 1.00-L saturated solution of AgBr to which mol of AgNO 3 is added? Analyze List the knowns and the unknown. Knowns K sp moles of AgNO 3 added mol volume of solution 1 L AgBr(s) m Ag (aq) Br (aq) K sp [Ag ] [Br ] Practice Problems Unknown [Br ]? M Express the concentrations of the two ions in one unknown. Let the equilibrium concentration of bromide ion from the dissociation be x. Then the equilibrium concentration of silver ion is x Calculate Solve for the unknown. Because of the small value of K sp, you can make a simplifying assumption: x will be negligibly small compared to Thus the [Ag ] at equilibrium is approximately equal to 0.020M. Solve for x and substitute these values into the K sp expression. K sp [Ag ] [Br ] [Ag ] x x K sp Practice Problems 3Ag Ag + 4 ( ) [Br ] M The equilibrium concentration of bromide ion is M. Evaluate Does the result make sense? Because the [Ag ] is so high, [Br ] should be very low, approaching the numerical value for K sp. The answer should have two significant figures, and the simplifying assumption was justified. Problem Solving Solve Problem 19 with the help of an interactive guided tutorial. withchemasap 19. What is the concentration of sulfide ion in a 1.0-L solution of iron(ii) sulfide to which 0.04 mol of iron(ii) nitrate is added? The K sp of FeS is The K sp of SrSO 4 is What is the equilibrium concentration of sulfate ion in a 1.0-L solution of strontium sulfate to which 0.10 mol of Sr(CH 3 CO 2 ) 2 has been added? 564 Chapter 18 Differentiated Instruction Less Proficient Readers Pair students who have trouble with word problems with those who are proficient at algebra and problem solving. Have each pair work through the practice problems, taking turns being the lead solver. The lead student should explain the process being used to arrive at the solution. 564 Chapter 18

6 The solubility product (K sp ) can be used to predict whether a precipitate will form when solutions are mixed. If the product of the concentrations of two ions in the mixture is greater than the K sp of the compound formed from the ions, a precipitate will form. After precipitation, the solution will be saturated with the precipitated compound. If the product of the concentrations is less than the K sp, no precipitate will form and the solution is unsaturated. Suppose you have 0.50 L of 0.002M Ba(NO 3 ) 2 and mix it with 0.50 L of M Na 2 SO 4. You then have one liter of solution. The insoluble compound that could precipitate is barium sulfate. To predict whether a precipitate of BaSO 4 will form, you need to determine the concentration of the ions after the dilution that occurs on mixing. Precipitation will occur if the product of the concentrations of the two ions (Ba and SO 4 ) exceeds the K sp of BaSO 4, which is Because each solution was diluted with an equal volume of the other solution, the concentrations of both Ba and SO 4 after mixing will be half of their original concentrations. Thus in the combined solution, [Ba ] 0.001M and [SO 4 ] 0.004M. These concentrations can now be multiplied together as a trial product and the result compared with the K sp. [Ba ] [SO 4 ] (0.001M) (0.004M) The K sp of barium sulfate is , so the trial product is larger than the K sp. A precipitate will form. Barium sulfate will precipitate until the product of the concentrations of the ions remaining in solution equals Figure shows the mixing of the solutions and the precipitation of barium sulfate Section Assessment 21. Key Concept What is the relationship between the solubility product constant and the solubility of a compound? 22. Key Concept How can you predict whether a precipitate will form when two salt solutions are mixed? 23. Write the solubility product expression for Ag 2 CO What is the concentration of lead ions and sulfide ions in a saturated solution of lead sulfide (PbS) solution at 25 C? (K sp ) 25. The K sp of barium sulfate is What is the sulfate-ion concentration of a 1.00 L saturated solution of BaSO 4 to which mol of Ba(NO 3 ) 2 is added? 26. Would precipitation occur when 500 ml of a 0.02M solution of AgNO 3 is mixed with 500 ml of a 0.001M solution of NaCl? Explain. Figure A precipitate of barium sulfate forms as barium nitrate (Ba(NO 3 ) 2 ) and sodium sulfate (Na 2 SO 4 ) solutions are mixed. Applying Concepts What is the product of the concentrations of barium ion and sulfate ion after precipitation is complete? 27. Which compound, FeS (K sp ) or CuS (K sp ), has the higher solubility? 28. What is the K sp of nickel(ii) sulfide if the equilibrium concentrations of Ni and S in a saturated solution of NiS are each M? Spectator Ions Refer to the discussion of spectator ions and net ionic equations in Section In a precipitation reaction, would the addition of a spectator ion lead to the formation of more precipitate because of the common ion effect? Explain. Assessment 18.3 Test yourself on the concepts in Section withchemasap Have students hypothesize how the common ion effect could be used to identify ions in solution. Suggest that they use Table 18.1 to find a common property of salts listed in Table 18.2 (insolubility). Explain that saturated solutions of many of the salts in Table 18.2 can be used to test for the presence of different ions in solution. If a precipitate forms when a few drops of an unknown solution is added to a known saturated solution, the unknown solution must have an ion in common with the known solution. 3 ASSESS Evaluate Understanding Have students classify the salts in Table 18.2 on the basis of solubility. Ask, What is the relationship between the solubility product constant and the relative solubility of a salt?(the larger the solubility product constant, the more soluble the salt) Reteach Project a transparency of Table Point out some salient features, for example, water is the solvent, the last column is for exceptions to the first column. Ask students to look in Table 18.2 for examples of ions described as lowsolubility in Table Sketch a graph of the relationship between solubility product constants and solubility. Connecting Concepts Spectator ions don t participate in the reaction. They stay in solution and don't precipitate. Section 18.3 Solubility Equilibrium the smaller the K sp, the lower the solubility of the compound 22. If the product of the concentrations of two ions in a mixture is greater than the K sp of the compound formed from the ions, a precipitate will form. 23. [Ag + ] 2 [CO 3 2 ] = K sp Section 18.3 Assessment M M 26. yes; the product [Ag + ] [Cl ] = 0.01M M = >> K sp AgCl = FeS If your class subscribes to the Interactive Textbook, use it to review key concepts in Section with ChemASAP Answers to... Figure (K sp ) Reaction Rates and Equilibrium 565