S 2 P 1 P 2. moles of solute liters of solution M 1 V 1 M 2 V 2. volume of solute 100% volume of solution. mass of solute 100% mass of solution

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1 16 Study Guide 16 Study Guide Study Tip Organize New Information Create flashcards to help you visualize relationships and formulas. Try to integrate what you re studying with what you already know. If your class subscribes to the Interactive Textbook with ChemASAP, your students can go online to access an interactive version of the Student Edition and a self-test. with ChemASAP Key Concepts 16.1 Properties of Solutions Whether or not a substance dissolves depends upon the nature of the solvent and the solute. Factors that determine how fast a substance dissolves are stirring, temperature, and surface area. Solubility is usually expressed in grams of solute per 100 g of solvent. The amount of solute that dissolves in a given solvent depends upon the temperature and pressure Concentrations of Solutions To calculate the molarity of a solution, divide the moles of solute by the volume of the solution in liters. Diluting a solution does not change the total number of moles of solute in Vocabulary boiling-point elevation (p. 490) concentrated solution (p. 480) concentration (p. 480) colligative property (p. 487) dilute solution (p. 480) freezing-point depression (p. 488) Henry's law (p. 476) immiscible (p. 473) miscible (p. 473) molal freezing-point depression constant (K f ) (p. 494) molal boiling-point elevation constant (K b ) (p. 494) molality (m) (p. 491) The concentration of a solution in percent is the ratio of the volume of the solute to the volume of the solution times 100% or the ratio of the mass of the solute to the mass of the solution times 100% Colligative Properties of Solutions Three colligative properties of solutions are vapor-pressure lowering, freezing-point depression, and boiling-point elevation. The magnitude of each colligative property is directly proportional to the number of solute molecules or ions present Calculations Involving Colligative Properties Molality and mole fractions are two additional ways of expressing the concentration of a Freezing-point depression and boiling-point elevation are proportional to molality. molarity (M) (p. 480) mole fraction (p. 492) saturated solution (p. 473) solubility (p. 473) supersaturated solution (p. 474) unsaturated solution (p. 473) Key Equations S Henry's law: 1 S 2 P 1 P 2 Molarity (M ) moles of solute liters of solution M 1 V 1 M 2 V 2 Percent by volume volume of solute 100% volume of solution Percent by mass mass of solute 100% mass of solution Molality moles of solute kilogram of solvent Mole fractions: X A n A n A + n X B n B B n A + n B T f K f m T b K b m 498 Chapter 16 Chapter Resources Print Core Teaching Resources, Chapter 16, Practice Problems, Vocabulary Review, Quiz, Chapter Test A, Chapter Test B Technology Computer Test Bank, Chapter 16 Test Interactive Textbook with ChemASAP, Chapter Chapter 16

2 16 Assessment 16 Assessment Reviewing Content 16.1 Properties of Solutions 42. Name and distinguish between the two components of a 43. Explain why the dissolved component does not settle out of a 44. Define the following terms: solubility, saturated solution, unsaturated solution, miscible, and immiscible. 45. If a saturated solution of sodium nitrate is cooled, what change might you observe? 46. Can a solution with undissolved solute be supersaturated? Explain. 47. What mass of AgNO 3 can be dissolved in 250 g of water at 20 C? Use Table What is the effect of pressure on the solubility of gases in liquids? 49. The solubility of methane, the major component of natural gas, in water at 20 C and 1.00 atm pressure is g/l. If the temperature remains constant, what will be the solubility of this gas at the following pressures? a atm b atm 16.2 Concentrations of Solutions 50. Knowing the molarity of a solution is more meaningful than knowing whether a solution is dilute or concentrated. Explain. 51. Define molarity, then calculate the molarity of each a. 1.0 mol KCl in 750 ml of solution b mol MgCl 2 in 1.5 L of solution 52. How many milliliters of 0.500M KCl solution would you need to dilute to make ml of 0.100M KCl? 53. Calculate the moles and grams of solute in each a. 1.0 L of 0.50M NaCl b ml of 2.0M KNO 3 c. 250 ml of 0.10M CaCl Calculate the grams of solute required to make the following solutions. a g of saline solution (0.90% NaCl (m/m)) b kg of 4.0% (m/m) MgCl 2 surround solute particles, reducing the number of solvent molecules that have sufficient energy to escape the solution; relative to the pure solvent, the amount of energy required to cause vaporization or boiling increases. Solutes disrupt the ordering of the solvent structure, so more kinetic energy must be withdrawn from a solution for it to solidify. This lowers the freezing point of the 57. a. sea water b. 1.5M KNO 3 c M MgCl What is the concentration (in % (v/v)) of the following solutions? a. 25 ml of ethanol (C 2 H 5 OH) is diluted to a volume of 150 ml with water. b. 175 ml of isopropyl alcohol (C 3 H 7 OH) is diluted with water to a total volume of 275 ml Colligative Properties of Solutions 56. What are colligative properties? Identify three colligative properties and explain why each occurs. 57. Which has the higher boiling point: a. seawater or distilled water? b. 1.0M KNO 3 or 1.5M KNO 3? c M KCl or 0.100M MgCl 2? 58. Why does a 1m solution of calcium nitrate have a lower freezing point than a 1m solution of sodium nitrate? 59. Explain how a decrease in the vapor pressure of a solution results in an increase in its boiling point. 60. In old-fashioned ice cream makers, a mixture of rock salt (NaCl) and ice is used to cool the creamy mixture as it is stirred. What is the purpose of the salt? 16.4 Calculations Involving Colligative Properties 61. Distinguish between a 1M solution and a 1m 62. Describe how you would make an aqueous solution of methanol (CH 3 OH) in which the mole fraction of methanol is What is the boiling point of each solution? a mol glucose in 1000 g H 2 O b mol NaCl in 1000 g H 2 O 64. What is the freezing point of each solution? a mol Na 2 SO 4 in 1750 g H 2 O b mol MgSO 4 in 100 g H 2 O 65. Determine the freezing points of each 0.20m aqueous a. K 2 SO 4 b. CsNO 3 c. Al(NO 3 ) 3 Assessment The effective molality of the Ca(NO 3 ) 2 solution is 3m. The effective molality of the NaNO 3 solution is 2m. 59. When vapor pressure is lowered relative to pure solvent, more energy must be supplied to reach the boiling point; thus the boiling point is increased relative to pure solvent. 60. The salt lowers the freezing point of the ice-water cooling mixture M solution: 1 mol of solute in 1 L of solution; 1m solution: 1 mol of solute in 1000 g of solvent 42. The solvent is the substance in which the solute is dissolved. 43. Random collisions of the solvent molecules with the solute particles provide enough force to overcome gravity. 44. solubility: the amount of a substance that dissolves in a given quantity of solvent at specified conditions of temperature and pressure to produce a saturated solution; saturated solution: a solution containing the maximum amount of solute for a given amount of solvent at a constant temperature and pressure; unsaturated solution: a solution that contains less solute than a saturated solution at a given temperature and pressure; miscible: describes liquids that dissolve in each other; immiscible: describes liquids that are insoluble in each other 45. Particles of solute crystallize. 46. No; if there were undissolved solute, the excess solute would come out of a supersaturated g AgNO Solubility increases with pressure. 49. a g/l b g/l 50. Dilute and concentrated are relative terms and are not quantitative. Molarity provides the exact number of moles of solute per liter of 51. Molarity is the number of moles of solute dissolved in one liter of a. 1.3M KCl b M MgCl ml 53. a mol NaCl, 29 g NaCl b. 1.0 mol KNO 3, g KNO 3 c mol CaCl 2, 2.8 g CaCl a g NaCl b. 2.0 g MgCl a. 16% (v/v) ethanol b. 63.6% (v/v) isopropyl alcohol 56. Colligative properties are properties of a solution that depend only on the number of solute particles; boiling-point elevation, freezingpoint depression, and vaporpressure lowering. Boiling points are elevated because solvent molecules Solutions 499

3 16 Assessment continued 62. Add 27.0 g H 2 O to 32.0 g CH 3 OH. 63. a C b C 64. a C b. 2.2 C 65. a. 1.1 C b C c. 1.5 C 66. a.the freezing-point depression is twice as great for solute B; solute B must provide twice as many particles in b. Solute A probably forms a saturated 67. T f = 9.60 C; T b = C 68. Each gram of acetone requires 0.93 g of water. 69. The mole fraction of NaHCO 3 is 0.020; of water is The solution is 1.1m. 70. The mole fraction of NaCl is ; the mole fraction of H 2 O is Add one crystal of KNO 3. If the solution is supersaturated, crystallization occurs. If it is saturated, the crystal does not dissolve; if unsaturated, the crystal dissolves. 72. Solubility CO 2 (g 100 g H 2 O) Assessment continued 66. Different numbers of moles of two different solutes, A and B, were added to identical quantities of water. The graph shows the freezing point of each of the solutions formed. Understanding Concepts Freezing Point of Solutions Moles of solute (mol) a. Explain the relative slopes of the two lines between 0 and 2 mol of solute added. b. Why does the freezing point for solution A not continue to drop as amounts of solute A are added beyond 2.4 mol? 67. Calculate the freezing- and boiling-point changes for a solution containing 12.0 g of naphthalene (C 10 H 8 ) in 50.0 g of benzene. 68. Describe how you would prepare an aqueous solution of acetone (CH 3 COCH 3 ) in which the mole fraction of acetone is The solubility of sodium hydrogen carbonate (NaHCO 3 ) in water at 20 C is 9.6 g/100 g H 2 O. What is the mole fraction of NaHCO 3 in a saturated solution? What is the molality of the solution? 70. A solution is labeled 0.150m NaCl. What are the mole fractions of the solute and solvent in this solution? 71. You are given a clear aqueous solution containing KNO 3. How would you determine experimentally if the solution is unsaturated, saturated, or supersaturated? 72. Plot a graph of solubility versus temperature for the three gases listed in Table Chapter 16 Freezing point A Freezing point B 73. A mixture of ethylene glycol (EG) and water is used as antifreeze in automobile engines. The freezing point and specific gravity of the mixture vary with the percent by mass of (EG) in the mixture. On the following graph, point A represents 20% (EG) by mass; point B, 40%; and point C, 60%. Freezing point ( C) Freezing Point vs. Specific Gravity A B 20% (EG) by mass 40% (EG) by mass 60% (EG) by mass C Specific gravity a. What is the specific gravity of the antifreeze mixture that freezes at 25 C? b. What is the freezing point of a mixture that has a specific gravity of 1.06? c. Estimate the freezing point of a mixture that is 30% by mass (EG). 74. Calculate the freezing point and the boiling point of a solution that contains 15.0 g of urea (CH 4 N 2 O) in 250 g of water. Urea is a covalently bonded compound. 75. Calculate the mole fractions in a solution that is 25.0 g of ethanol (C 2 H 5 OH) and 40.0 g of water. 76. Estimate the freezing point of an aqueous solution of 20.0 g of glucose (C 6 H 12 O 6 ) dissolved in g of water. 77. The solubility of KCl in water is 34.0 g KCl/100 g H 2 O at 20 C. A warm solution containing 50.0 g KCl in 130 g H 2 O is cooled to 20 C. a. How many grams of KCl remain dissolved? b. How many grams came out of solution? 78. How many moles of ions are present when 0.10 mol of each compound is dissolved in water? a. K 2 SO 4 b. Fe(NO 3 ) 3 c. Al 2 (SO 4 ) 3 d. NiSO Solubility O 2 (g 100 g H 2 O) Solubility H 2 (g 100 g H 2 O) a. about 1.14 b. about 7.2 C c. about 9.5 C 74. fp = 1.86 C; bp = C 75. X C 2 H 5 OH = 0.20; X H 2 O = C 77. a g KCl b. 5.8 g KCl 78. a mol b mol c mol d mol 500 Chapter 16

4 Critical Thinking 79. A solution contains 26.5 g NaCl in 75.0 g H 2 O at 20 C. Determine if the solution is unsaturated, saturated, or supersaturated. (The solubility of NaCl at 20 C is 36.0 g/100 g H 2 O.) 80. An aqueous solution freezes at 2.47 C. What is its boiling point? 81. Hydrogen peroxide is often sold commercially as a 3.0% (m/v) aqueous a. If you buy a 250-mL bottle of 3.0% H 2 O 2 (m/v), how many grams of hydrogen peroxide have you purchased? b. What is the molarity of this solution? 82. How many grams of NaNO 3 will precipitate if a saturated solution of NaNO 3 in 200 g H 2 O at 50 C is cooled to 20 C? 83. What is the molar mass of a nondissociating compound if 5.76 g of the compound in 750 g of benzene gives a freezing-point depression of C? 84. The molality of an aqueous solution of sugar (C 12 H 22 O 11 ) is 1.62m. Calculate the mole fractions of sugar and water. 85. Why might calcium chloride spread on icy roads be more effective at melting ice than an equal amount of sodium chloride? 86. The following table lists the most abundant ions in seawater and their molal concentrations. Calculate the mass in grams of each component ion contained in 5.00 L of seawater. The density of sea water is g/ml. Molality Ion (m) Chloride Sodium Magnesium Sulfate Calcium Potassium Hydrogen carbonate Which will have a greater boiling point elevation: 3.00 g Ca(NO 3 ) 2 in 60.0 g of water, or 6.00 g Ca(NO 3 ) 2 in 30.0 g of water? Concept Challenge 88. When an excess of zinc is added to 800 ml of a hydrochloric acid solution, the solution evolves 1.21 L of hydrogen gas measured over water at 21 C and mm Hg. What was the molarity of the acid? The vapor pressure of water at 21 C is 18.6 mm Hg. 89. How many milliliters of 1.50M HNO 3 contain enough nitric acid to dissolve an old copper penny with a mass of 3.94 g? 3Cu 8HNO 3 3Cu(NO 3 ) 2 2NO 4H 2 O 90. One way to express the solubility of a compound is in terms of moles of compound that will dissolve in 1 kg of water. Solubility depends on temperature. Plot a graph of the solubility of potassium nitrate (KNO 3 ) from the following data. Temperature (C ) Solubility (mol/kg) From your graph estimate a. the solubility of KNO 3 at 76 C and at 33 C. b. the temperature at which its solubility is 17.6 mol/kg of water. c. the temperature at which the solubility is 4.24 mol/kg of water. 91. A 250-mL sample of Na 2 SO 4 is reacted with an excess of BaCl 2. If 5.28 g BaSO 4 is precipitated, what is the molarity of the Na 2 SO 4 solution? 92. Suppose you have an unknown compound and want to identify it by means of its molar mass. Design an experiment that uses the concept of freezing-point depression to obtain the molar mass. What laboratory measurements would you need to make? What calculations would be needed? Assessment unsaturated C 81. a. 7.5 g H 2 O 2 b M g NaNO g/mol 84. X H2 O = 0.972; X C 12 H 22 O 11 = CaCl 2 produces three particles upon dissolving; NaCl produces only two particles. Freezing-point depression depends on the number of solute particles in the solvent. 86. To solve this problem: (1) For each ion, multiply molar mass by molality to find mass per 1000 g of solvent. (2) Sum the masses from (1) and add to 1000 g. (3) Calculate the percent mass of each ion by dividing each answer in (1) by answer (2). (4) Multiply the percent mass of each ion by the mass of 5.00 L of sea water (5120 g). chloride: g sodium: g magnesium: 7.1 g sulfate: g calcium: 2.3 g potassium: 2.0 g hydrogen carbonate: g 87. The solution with the higher concentration of ions will have the greater boiling point elevation; 6.00 g Ca(NO 3 ) 2 in 30 g of water M HCl ml HNO a. 76 C: 15 mol/kg; 33 C: 5 mol/kg b. 82 C c. 30 C M Na 2 SO Determine the freezing point of a suitable solvent. Dissolve a known mass of the unknown molecular compound in a known mass of the solvent. Determine the freezing point of the This gives the freezing point depression. Use T f = K f m to find the molality of the Use the molality to find the moles of solute. Use the moles of solute and the measured mass of solute to calculate the molar mass. g solute 1000 g solvent 1 kg solvent g solute = g solvent 1 kg solvent 1 mol solute 1 mol solute The molar mass obtained is valid only for an undissociating molecular solute. Solutions 501

5 16 Assessment continued 16 Assessment continued Cumulative Review 93. a g H 2 O b mg H 2 O c kg H 2 O 94. a kg b kg c kg d kg 95. Rutherford s model contains a nucleus. 96. a. manganese, Mn b. indium, In c. francium, Fr d. polonium, Po 97. Calcium permanganate is Ca(MnO 4 ) 2. Four formula units contain 4 Ca atoms, 8 Mn atoms, and 32 O atoms. 98. C 8 H 6 O a g Fe, g Cu, g Hg, g S b. Each sample contains atoms. c mol Fe, mol Cu, mol Hg, mol S L 101. a. combination b. decomposition c. single-replacement d. combustion e. single-replacement f. double-replacement H + (aq) + S 2 (aq) H 2 S(g) 103. a. NH 4 Cl(s) NH + 4 (aq) + Cl (aq) b.cu(no 3 ) 2 (s) Cu 2+ (aq) + 2NO 3 (aq) c. HNO 3 (aq) H + (aq) + NO 3 (aq) d. HC 2 H 3 O 2 (l) H + (aq) + C 2 H 3 O 2 (aq) e. Na 2 SO 4 (s) 2Na + (aq)+ SO 2 4 (aq) f. HgCl 2 (s) Hg 2+ (aq) + 2Cl (aq) L O a. I b. Te c. Sb d. Sr kpa 107. The particles in an ideal gas have no volume and there are no attractions between particles Unbalanced intermolecular attractions between molecules at the surface of the liquid and those below the surface create an inward pull, or force, that minimizes the surface area to create surface tension. 502 Chapter A cylindrical vessel, 28.0 cm in height and 3.00 cm in diameter, is filled with water at 50 C. The density of water is g/cm 3 at this temperature. Express the mass of water in the vessel in the following units. (Chapter 3) a. grams b. milligrams c. kilograms 94. Convert each of the following mass measurements to its equivalent in kilograms. (Chapter 3) a. 347 g b. 73 mg c mg d. 877 mg 95. What is the most significant difference between the Thomson model of the atom and the Rutherford model? (Chapter 5) 96. Name and give the symbol for the element in the following positions in the periodic table. (Chapter 6) a. Group 7B, period 4 b. Group 3A, period 5 c. Group 1A, period 7 d. Group 6A, period How many atoms of each element are present in four formula units of calcium permanganate? (Chapter 6) 98. Terephthalic acid is an organic compound used in the synthesis of polyesters. Terephthalic acid contains 57.8 percent C, 3.64 percent H, and 38.5 percent O. The molar mass is approximately 166 g/mol. What is the molecular formula of terephthalic acid? (Chapter 10) 99. The photograph shows one mole each of iron, copper, mercury, and sulfur. (Chapter 10) a. What is the mass of each element? b. How many atoms are in each sample? c. How many moles is 25.0 g of each element? 502 Chapter The very polar hydrogen chloride molecule produces hydronium ions (H 3 O + ) and chloride ions (Cl ) that are stabilized by becoming surrounded by water molecules in aqueous Hydrogen chloride does not dissociate in nonpolar benzene. Polar compounds generally have low solubility in nonpolar solvents a solution, if the soap mixture is very dilute; More concentrated mixtures of soap in water form colloids What is the volume occupied by 1500 g of hydrogen gas (H 2 ) at STP? (Chapter 10) 101. Identify the type of chemical reaction. (Chapter 11) a. H 2 (g) Cl 2 (g) 2HCl(g) b. 2H 2 O(l) O 2 (g) 2H 2 (g) c. 2K(s) 2H 2 O(l) 2KOH(aq) H 2 (g) d. C 2 H 6 O(l) 3O 2 (g) 2CO 2 (g) 3H 2 O(l) e. Cl 2 (aq) 2KBr(aq) 2KCl(aq) Br 2 (aq) f. Pb(NO 3 ) 2 (aq) 2NaCl(aq) PbCl 2 (s) 2NaNO 3 (aq) 102. Write the net ionic equation for the following reaction. (Chapter 11) 2HI(aq) Na 2 S(aq) H 2 S(g) 2NaI(aq) 103. Indicate by simple equations how the following substances ionize or dissociate in water. (Chapter 11) a. NH 4 Cl b. Cu(NO 3 ) 2 c. HNO 3 d. HC 2 H 3 O 2 e. Na 2 SO 4 f. HgCl The equation for the combustion of methanol (CH 3 OH) is the following: 2CH 3 OH(l) 3O 2 (g) 2CO 2 (g) 4H 2 O(l) What volume of oxygen, measured at STP, is required to completely burn 35.0 g of methanol? (Chapter 12) 105. Write electron dot structures for the following atoms. (Chapter 13) a. I b. Te c. Sb d. Sr 106. A cylinder of nitrogen gas at 25 C and 10l.3 kpa is heated to 45 C. What is the new pressure of the gas? (Chapter 14) 107. Why does an ideal gas not exist? (Chapter 14) 108. What relationship exists between surface tension and intermolecular attractions in a liquid? (Chapter 15) 109. The solubility of hydrogen chloride gas in the polar solvent water is much greater than its solubility in the nonpolar solvent benzene. Why? (Chapter 15) 110. When soap is shaken with water, is a solution, a suspension, or a colloid formed? Explain. (Chapter 15)

6 Standardized Test Prep Test-Taking Tip Interpreting Data Tables Tables present a large amount of data in a small space. They allow you to make comparisons and to analyze the information present. Start by reading the title (if there is one). Then read the headings. Try to figure out the relationship between the different columns and rows of information. Ask yourself some questions: What information is related in the table? How are the relationships represented? Select the choice that best answers each question or completes each statement. 1. An aqueous solution is 65% (v/v) rubbing alcohol. How many milliliters of water are in a 95-mL sample of this solution? a. 62 ml b. 1.5 ml c. 33 ml d. 30 ml 2. Which of these actions will cause more sugar to dissolve in a saturated sugar water solution? I. Add more sugar while stirring. II. Add more sugar and heat the III. Grind the sugar to a powder; then add while stirring. a. I only b. II only c. III only d. I and II only e. II and III only 3. When 2.0 mol of methanol is dissolved in 45 g of water, the mole fraction of methanol is a b c d The lettered choices below refer to Questions 4 7. A lettered choice may be used once, more than once, or not at all. A. moles/liter of solution B. grams/mole C. moles/kilogram of solvent D. C/molal E. no units Which of the above units is appropriate for each measurement? 4. molality 5. mole fraction 6. molar mass 7. molarity Use the description and the data table to answer Questions A student measured the freezing points of three different aqueous solutions at five different concentrations. The data table summarizes the data. Freezing Point Depression ( C) Molarity (M) NaCl CaCl 2 C 2 H 5 OH Graph the data for all three solutes on the same graph, using molarity as the independent variable. 9. Summarize the relationship between molarity and freezing-point depression. 10. Compare the slopes of the three lines and explain any difference. 11. If you collected similar data for KOH and added a fourth line to your graph, which existing line would the new line approximate? Use the atomic windows to answer Questions The windows show water and two aqueous solutions with different concentrations. The red spheres represent the solute particles; the blue spheres represent water. a. b. c. 12. Which solution has the highest vapor pressure? 13. Which solution has the lowest vapor pressure? 14. Which solution has the lowest boiling point? Write a brief essay to answer Question Describe how you would prepare 100 ml of 0.50M KCl starting with a stock solution that is 2.0M KCl. Standardized Test Prep 1. c 2. b 3. a 4. C 5. E 6. B 7. A 8. Freezing Point Depression ( C) Molarity (M) sodium chloride calcium chloride ethanol 9. As the molarity increases, the freezing-point depression increases. 10. The slopes are an approximate 1:2:3 ratio that reflects the relative number of particles per mole of each solute in 11. NaCl 12. b 13. a 14. b 15. Transfer 25 ml of the stock solution to a 100-ml volumetric flask and add water to make 100 ml of Standardized Test Prep 503 Solutions 503