Key Terms, Key Equations, Summaries, and Exercises (Chapter 11)

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Key Terms, Key Equations, Summaries, and Exercises (Chapter 11)

Key Terms

alloy: solid mixture of a metallic element and one or more additional elements

amphiphilic: molecules possessing both hydrophobic (nonpolar) and a hydrophilic (polar) parts

boiling point elevation: elevation of the boiling point of a liquid by addition of a solute

boiling point elevation constant: the proportionality constant in the equation relating boiling point elevation to solute molality; also known as the ebullioscopic constant

colligative property: property of a solution that depends only on the concentration of a solute species

colloid: (also, colloidal dispersion) mixture in which relatively large solid or liquid particles are dispersed uniformly throughout a gas, liquid, or solid

crenation: process whereby biological cells become shriveled due to loss of water by osmosis

dispersed phase: substance present as relatively large solid or liquid particles in a colloid

dispersion medium: solid, liquid, or gas in which colloidal particles are dispersed

dissociation: physical process accompanying the dissolution of an ionic compound in which the compound’s constituent ions are solvated and dispersed throughout the solution

electrolyte: substance that produces ions when dissolved in water

emulsifying agent: amphiphilic substance used to stabilize the particles of some emulsions

emulsion: colloid formed from immiscible liquids

freezing point depression: lowering of the freezing point of a liquid by addition of a solute

freezing point depression constant: (also, cryoscopic constant) proportionality constant in the equation relating freezing point depression to solute molality

gel: colloidal dispersion of a liquid in a solid

hemolysis: rupture of red blood cells due to the accumulation of excess water by osmosis

Henry’s law: the proportional relationship between the concentration of dissolved gas in a solution and the partial pressure of the gas in contact with the solution

hypertonic: of greater osmotic pressure

hypotonic: of less osmotic pressure

ideal solution: solution that forms with no accompanying energy change

immiscible: of negligible mutual solubility; typically refers to liquid substances

ion pair: solvated anion/cation pair held together by moderate electrostatic attraction

ion-dipole attraction: electrostatic attraction between an ion and a polar molecule

isotonic: of equal osmotic pressure

miscible: mutually soluble in all proportions; typically refers to liquid substances

molality (m): a concentration unit defined as the ratio of the numbers of moles of solute to the mass of the solvent in kilograms

nonelectrolyte: substance that does not produce ions when dissolved in water

osmosis: diffusion of solvent molecules through a semipermeable membrane

osmotic pressure (Π): opposing pressure required to prevent bulk transfer of solvent molecules through a semipermeable membrane

partially miscible: of moderate mutual solubility; typically refers to liquid substances

Raoult’s law: the relationship between a solution’s vapor pressure and the vapor pressures and concentrations of its components

saturated: of concentration equal to solubility; containing the maximum concentration of solute possible for a given temperature and pressure

semipermeable membrane: a membrane that selectively permits passage of certain ions or molecules

solubility: extent to which a solute may be dissolved in water, or any solvent

solvation: exothermic process in which intermolecular attractive forces between the solute and solvent in a solution are established

spontaneous process: physical or chemical change that occurs without the addition of energy from an external source

strong electrolyte: substance that dissociates or ionizes completely when dissolved in water

supersaturated: of concentration that exceeds solubility; a nonequilibrium state

suspension: heterogeneous mixture in which relatively large component particles are temporarily dispersed but settle out over time

Tyndall effect: scattering of visible light by a colloidal dispersion

unsaturated: of concentration less than solubility

van’t Hoff factor (i): the ratio of the number of moles of particles in a solution to the number of moles of formula units dissolved in the solution

weak electrolyte: substance that ionizes only partially when dissolved in water

Key Equations

C_{g} = k P_{g}

(P_{A} = X_{A} P_{A}^{*})

P_{solution} = \sum_{i} P_{i} = \sum_{i} X_{i} P_{i}^{*}

P_{solution} = X_{solvent} P_{solvent}^{*}

ΔT_b = K_bm

ΔT_f = K_fm

Π = MRT

Summary

11.1 The Dissolution Process

A solution forms when two or more substances combine physically to yield a mixture that is homogeneous at the molecular level. The solvent is the most concentrated component and determines the physical state of the solution. The solutes are the other components typically present at concentrations less than that of the solvent. Solutions may form endothermically or exothermically, depending upon the relative magnitudes of solute and solvent intermolecular attractive forces. Ideal solutions form with no appreciable change in energy.

11.2 Electrolytes

Substances that dissolve in water to yield ions are called electrolytes. Electrolytes may be covalent compounds that chemically react with water to produce ions (for example, acids and bases), or they may be ionic compounds that dissociate to yield their constituent cations and anions, when dissolved. Dissolution of an ionic compound is facilitated by ion-dipole attractions between the ions of the compound and the polar water molecules. Soluble ionic substances and strong acids ionize completely and are strong electrolytes, while weak acids and bases ionize to only a small extent and are weak electrolytes. Nonelectrolytes are substances that do not produce ions when dissolved in water.

11.3 Solubility

The extent to which one substance will dissolve in another is determined by several factors, including the types and relative strengths of intermolecular attractive forces that may exist between the substances’ atoms, ions, or molecules. This tendency to dissolve is quantified as a substance’s solubility, its maximum concentration in a solution at equilibrium under specified conditions. A saturated solution contains solute at a concentration equal to its solubility. A supersaturated solution is one in which a solute’s concentration exceeds its solubility—a nonequilibrium (unstable) condition that will result in solute precipitation when the solution is appropriately perturbed. Miscible liquids are soluble in all proportions, and immiscible liquids exhibit very low mutual solubility. Solubilities for gaseous solutes decrease with increasing temperature, while those for most, but not all, solid solutes increase with temperature. The concentration of a gaseous solute in a solution is proportional to the partial pressure of the gas to which the solution is exposed, a relation known as Henry’s law.

11.4 Colligative Properties

Properties of a solution that depend only on the concentration of solute particles are called colligative properties. They include changes in the vapor pressure, boiling point, and freezing point of the solvent in the solution. The magnitudes of these properties depend only on the total concentration of solute particles in solution, not on the type of particles. The total concentration of solute particles in a solution also determines its osmotic pressure. This is the pressure that must be applied to the solution to prevent diffusion of molecules of pure solvent through a semipermeable membrane into the solution. Ionic compounds may not completely dissociate in solution due to activity effects, in which case observed colligative effects may be less than predicted.

11.5Colloids

Colloids are mixtures in which one or more substances are dispersed as relatively large solid particles or liquid droplets throughout a solid, liquid, or gaseous medium. The particles of a colloid remain dispersed and do not settle due to gravity, and they are often electrically charged. Colloids are widespread in nature and are involved in many technological applications.

Exercises

11.1 The Dissolution Process

1.

How do solutions differ from compounds? From other mixtures?

2.

Which of the principal characteristics of solutions are evident in the solutions of K₂Cr₂O₇ shown in Figure 11.2?

3.

When KNO₃ is dissolved in water, the resulting solution is significantly colder than the water was originally.

(a) Is the dissolution of KNO₃ an endothermic or an exothermic process?

(b) What conclusions can you draw about the intermolecular attractions involved in the process?

(c) Is the resulting solution an ideal solution?

4.

Give an example of each of the following types of solutions:

(a) a gas in a liquid

(b) a gas in a gas

(c) a solid in a solid

5.

Indicate the most important types of intermolecular attractions in each of the following solutions:

(a) The solution in Figure 11.2.

(b) NO(l) in CO(l)

(c) Cl₂(g) in Br₂(l)

(d) HCl(g) in benzene C₆H₆(l)

(e) Methanol CH₃OH(l) in H₂O(l)

6.

Predict whether each of the following substances would be more soluble in water (polar solvent) or in a hydrocarbon such as heptane (C₇H₁₆, nonpolar solvent):

(a) vegetable oil (nonpolar)

(b) isopropyl alcohol (polar)

(c) potassium bromide (ionic)

7.

Heat is released when some solutions form; heat is absorbed when other solutions form. Provide a molecular explanation for the difference between these two types of spontaneous processes.

8.

Solutions of hydrogen in palladium may be formed by exposing Pd metal to H₂ gas. The concentration of hydrogen in the palladium depends on the pressure of H₂ gas applied, but in a more complex fashion than can be described by Henry’s law. Under certain conditions, 0.94 g of hydrogen gas is dissolved in 215 g of palladium metal (solution density = 10.8 g cm³).

(a) Determine the molarity of this solution.

(b) Determine the molality of this solution.

(c) Determine the percent by mass of hydrogen atoms in this solution.

11.2 Electrolytes

9.

Explain why the ions Na⁺ and Cl⁻ are strongly solvated in water but not in hexane, a solvent composed of nonpolar molecules.

10.

Explain why solutions of HBr in benzene (a nonpolar solvent) are nonconductive, while solutions in water (a polar solvent) are conductive.

11.

Consider the solutions presented:

(a) Which of the following sketches best represents the ions in a solution of Fe(NO₃)₃(aq)?

(b) Write a balanced chemical equation showing the products of the dissolution of Fe(NO₃)₃.

12.

Compare the processes that occur when methanol (CH₃OH), hydrogen chloride (HCl), and sodium hydroxide (NaOH) dissolve in water. Write equations and prepare sketches showing the form in which each of these compounds is present in its respective solution.

13.

What is the expected electrical conductivity of the following solutions?

(a) NaOH(aq)

(b) HCl(aq)

(c) C₆H₁₂O₆(aq) (glucose)

(d) NH₃(aq)

14.

Why are most solid ionic compounds electrically nonconductive, whereas aqueous solutions of ionic compounds are good conductors? Would you expect a liquid (molten) ionic compound to be electrically conductive or nonconductive? Explain.

15.

Indicate the most important type of intermolecular attraction responsible for solvation in each of the following solutions:

(a) the solutions in Figure 11.7

(b) methanol, CH₃OH, dissolved in ethanol, C₂H₅OH

(c) methane, CH₄, dissolved in benzene, C₆H₆

(d) the polar halocarbon CF₂Cl₂ dissolved in the polar halocarbon CF₂ClCFCl₂

(e) O₂(l) in N₂(l)

11.3 Solubility

16.

Suppose you are presented with a clear solution of sodium thiosulfate, Na₂S₂O₃. How could you determine whether the solution is unsaturated, saturated, or supersaturated?

17.

Supersaturated solutions of most solids in water are prepared by cooling saturated solutions. Supersaturated solutions of most gases in water are prepared by heating saturated solutions. Explain the reasons for the difference in the two procedures.

18.

Suggest an explanation for the observations that ethanol, C₂H₅OH, is completely miscible with water and that ethanethiol, C₂H₅SH, is soluble only to the extent of 1.5 g per 100 mL of water.

19.

Calculate the percent by mass of KBr in a saturated solution of KBr in water at 10 °C. See Figure 11.16 for useful data, and report the computed percentage to one significant digit.

20.

Which of the following gases is expected to be most soluble in water? Explain your reasoning.

(a) CH₄

(b) CCl₄

(c) CHCl₃

21.

At 0 °C and 1.00 atm, as much as 0.70 g of O₂ can dissolve in 1 L of water. At 0 °C and 4.00 atm, how many grams of O₂ dissolve in 1 L of water?

22.

Refer to Figure 11.10.

(a) How did the concentration of dissolved CO₂ in the beverage change when the bottle was opened?

(b) What caused this change?

(c) Is the beverage unsaturated, saturated, or supersaturated with CO₂?

23.

The Henry’s law constant for CO₂ is 3.4 $\times$ 10⁻² M/atm at 25 °C. Assuming ideal solution behavior, what pressure of carbon dioxide is needed to maintain a CO₂ concentration of 0.10 M in a can of lemon-lime soda?

24.

The Henry’s law constant for O₂ is 1.3 $\times$ 10⁻³ M/atm at 25 °C. Assuming ideal solution behavior, what mass of oxygen would be dissolved in a 40-L aquarium at 25 °C, assuming an atmospheric pressure of 1.00 atm, and that the partial pressure of O₂ is 0.21 atm?

25.

Assuming ideal solution behavior, how many liters of HCl gas, measured at 30.0 °C and 745 torr, are required to prepare 1.25 L of a 3.20-M solution of hydrochloric acid?

11.4 Colligative Properties

26.

Which is/are part of the macroscopic domain of solutions and which is/are part of the microscopic domain: boiling point elevation, Henry’s law, hydrogen bond, ion-dipole attraction, molarity, nonelectrolyte, nonstoichiometric compound, osmosis, solvated ion?

27.

What is the microscopic explanation for the macroscopic behavior illustrated in Figure 11.14?

28.

Sketch a qualitative graph of the pressure versus time for water vapor above a sample of pure water and a sugar solution, as the liquids evaporate to half their original volume.

29.

A solution of potassium nitrate, an electrolyte, and a solution of glycerin (C₃H₅(OH)₃), a nonelectrolyte, both boil at 100.3 °C. What other physical properties of the two solutions are identical?

30.

What are the mole fractions of H₃PO₄ and water in a solution of 14.5 g of H₃PO₄ in 125 g of water?

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

31.

What are the mole fractions of HNO₃ and water in a concentrated solution of nitric acid (68.0% HNO₃ by mass)?

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

32.

Calculate the mole fraction of each solute and solvent:

(a) 583 g of H₂SO₄ in 1.50 kg of water—the acid solution used in an automobile battery

(b) 0.86 g of NaCl in 1.00 $\times$ 10² g of water—a solution of sodium chloride for intravenous injection

(c) 46.85 g of codeine, C₁₈H₂₁NO₃, in 125.5 g of ethanol, C₂H₅OH

(d) 25 g of I₂ in 125 g of ethanol, C₂H₅OH

33.

Calculate the mole fraction of each solute and solvent:

(a) 0.710 kg of sodium carbonate (washing soda), Na₂CO₃, in 10.0 kg of water—a saturated solution at 0 °C

(b) 125 g of NH₄NO₃ in 275 g of water—a mixture used to make an instant ice pack

(c) 25 g of Cl₂ in 125 g of dichloromethane, CH₂Cl₂

(d) 0.372 g of tetrahydropyridine, C₅H₉N, in 125 g of chloroform, CHCl₃

34.

Calculate the mole fractions of methanol, CH₃OH; ethanol, C₂H₅OH; and water in a solution that is 40% methanol, 40% ethanol, and 20% water by mass. (Assume the data are good to two significant figures.)

35.

What is the difference between a 1 M solution and a 1 m solution?

36.

What is the molality of phosphoric acid, H₃PO₄, in a solution of 14.5 g of H₃PO₄ in 125 g of water?

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

37.

What is the molality of nitric acid in a concentrated solution of nitric acid (68.0% HNO₃ by mass)?

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

38.

Calculate the molality of each of the following solutions:

(a) 583 g of H₂SO₄ in 1.50 kg of water—the acid solution used in an automobile battery

(b) 0.86 g of NaCl in 1.00 $\times$ 10² g of water—a solution of sodium chloride for intravenous injection

(c) 46.85 g of codeine, C₁₈H₂₁NO₃, in 125.5 g of ethanol, C₂H₅OH

(d) 25 g of I₂ in 125 g of ethanol, C₂H₅OH

39.

Calculate the molality of each of the following solutions:

(a) 0.710 kg of sodium carbonate (washing soda), Na₂CO₃, in 10.0 kg of water—a saturated solution at 0°C

(b) 125 g of NH₄NO₃ in 275 g of water—a mixture used to make an instant ice pack

(c) 25 g of Cl₂ in 125 g of dichloromethane, CH₂Cl₂

(d) 0.372 g of tetrahydropyridine, C₅H₉N, in 125 g of chloroform, CHCl₃

40.

The concentration of glucose, C₆H₁₂O₆, in normal spinal fluid is $\frac{75 mg}{100 g} .$ What is the molality of the solution?

41.

A 13.0% solution of K₂CO₃ by mass has a density of 1.09 g/cm³. Calculate the molality of the solution.

42.

Why does 1 mol of sodium chloride depress the freezing point of 1 kg of water almost twice as much as 1 mol of glycerin?

43.

Assuming ideal solution behavior, what is the boiling point of a solution of 115.0 g of nonvolatile sucrose, C₁₂H₂₂O₁₁, in 350.0 g of water?

(a) Outline the steps necessary to answer the question

(b) Answer the question

44.

Assuming ideal solution behavior, what is the boiling point of a solution of 9.04 g of I₂ in 75.5 g of benzene, assuming the I₂ is nonvolatile?

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

45.

Assuming ideal solution behavior, what is the freezing temperature of a solution of 115.0 g of sucrose, C₁₂H₂₂O₁₁, in 350.0 g of water?

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

46.

Assuming ideal solution behavior, what is the freezing point of a solution of 9.04 g of I₂ in 75.5 g of benzene?

(a) Outline the steps necessary to answer the following question.

(b) Answer the question.

47.

Assuming ideal solution behavior, what is the osmotic pressure of an aqueous solution of 1.64 g of Ca(NO₃)₂ in water at 25 °C? The volume of the solution is 275 mL.

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

48.

Assuming ideal solution behavior, what is osmotic pressure of a solution of bovine insulin (molar mass, 5700 g mol⁻¹) at 18 °C if 100.0 mL of the solution contains 0.103 g of the insulin?

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

49.

Assuming ideal solution behavior, what is the molar mass of a solution of 5.00 g of a compound in 25.00 g of carbon tetrachloride (bp 76.8 °C; K_b = 5.02 °C/m) that boils at 81.5 °C at 1 atm?

(a) Outline the steps necessary to answer the question.

(b) Solve the problem.

50.

A sample of an organic compound (a nonelectrolyte) weighing 1.35 g lowered the freezing point of 10.0 g of benzene by 3.66 °C. Assuming ideal solution behavior, calculate the molar mass of the compound.

51.

A 1.0 m solution of HCl in benzene has a freezing point of 0.4 °C. Is HCl an electrolyte in benzene? Explain.

52.

A solution contains 5.00 g of urea, CO(NH₂)₂, a nonvolatile compound, dissolved in 0.100 kg of water. If the vapor pressure of pure water at 25 °C is 23.7 torr, what is the vapor pressure of the solution (assuming ideal solution behavior)?

53.

A 12.0-g sample of a nonelectrolyte is dissolved in 80.0 g of water. The solution freezes at −1.94 °C. Assuming ideal solution behavior, calculate the molar mass of the substance.

54.

Arrange the following solutions in order by their decreasing freezing points: 0.1 m Na₃PO₄, 0.1 m C₂H₅OH, 0.01 m CO₂, 0.15 m NaCl, and 0.2 m CaCl₂.

55.

Calculate the boiling point elevation of 0.100 kg of water containing 0.010 mol of NaCl, 0.020 mol of Na₂SO₄, and 0.030 mol of MgCl₂, assuming complete dissociation of these electrolytes and ideal solution behavior.

56.

How could you prepare a 3.08 m aqueous solution of glycerin, C₃H₈O₃? Assuming ideal solution behavior, what is the freezing point of this solution?

57.

A sample of sulfur weighing 0.210 g was dissolved in 17.8 g of carbon disulfide, CS₂ (K_b = 2.34 °C/m). If the boiling point elevation was 0.107 °C, what is the formula of a sulfur molecule in carbon disulfide (assuming ideal solution behavior)?

58.

In a significant experiment performed many years ago, 5.6977 g of cadmium iodide in 44.69 g of water raised the boiling point 0.181 °C. What does this suggest about the nature of a solution of CdI₂?

59.

Lysozyme is an enzyme that cleaves cell walls. A 0.100-L sample of a solution of lysozyme that contains 0.0750 g of the enzyme exhibits an osmotic pressure of 1.32 $\times$ 10⁻³ atm at 25 °C. Assuming ideal solution behavior, what is the molar mass of lysozyme?

60.

The osmotic pressure of a solution containing 7.0 g of insulin per liter is 23 torr at 25 °C. Assuming ideal solution behavior, what is the molar mass of insulin?

61.

The osmotic pressure of human blood is 7.6 atm at 37 °C. What mass of glucose, C₆H₁₂O₆, is required to make 1.00 L of aqueous solution for intravenous feeding if the solution must have the same osmotic pressure as blood at body temperature, 37 °C (assuming ideal solution behavior)?

62.

Assuming ideal solution behavior, what is the freezing point of a solution of dibromobenzene, C₆H₄Br₂, in 0.250 kg of benzene, if the solution boils at 83.5 °C?

63.

Assuming ideal solution behavior, what is the boiling point of a solution of NaCl in water if the solution freezes at −0.93 °C?

64.

The sugar fructose contains 40.0% C, 6.7% H, and 53.3% O by mass. A solution of 11.7 g of fructose in 325 g of ethanol has a boiling point of 78.59 °C. The boiling point of ethanol is 78.35 °C, and K_b for ethanol is 1.20 °C/m. Assuming ideal solution behavior, what is the molecular formula of fructose?

65.

The vapor pressure of methanol, CH₃OH, is 94 torr at 20 °C. The vapor pressure of ethanol, C₂H₅OH, is 44 torr at the same temperature.

(a) Calculate the mole fraction of methanol and of ethanol in a solution of 50.0 g of methanol and 50.0 g of ethanol.

(b) Ethanol and methanol form a solution that behaves like an ideal solution. Calculate the vapor pressure of methanol and of ethanol above the solution at 20 °C.

(c) Calculate the mole fraction of methanol and of ethanol in the vapor above the solution.

66.

The triple point of air-free water is defined as 273.16 K. Why is it important that the water be free of air?

67.

Meat can be classified as fresh (not frozen) even though it is stored at −1 °C. Why wouldn’t meat freeze at this temperature?

68.

An organic compound has a composition of 93.46% C and 6.54% H by mass. A solution of 0.090 g of this compound in 1.10 g of camphor melts at 158.4 °C. The melting point of pure camphor is 178.4 °C. K_f for camphor is 37.7 °C/m. Assuming ideal solution behavior, what is the molecular formula of the solute? Show your calculations.

69.

A sample of HgCl₂ weighing 9.41 g is dissolved in 32.75 g of ethanol, C₂H₅OH (K_b = 1.20 °C/m). The boiling point elevation of the solution is 1.27 °C. Is HgCl₂ an electrolyte in ethanol? Show your calculations.

70.

A salt is known to be an alkali metal fluoride. A quick approximate determination of freezing point indicates that 4 g of the salt dissolved in 100 g of water produces a solution that freezes at about −1.4 °C. Assuming ideal solution behavior, what is the formula of the salt? Show your calculations.

11.5 Colloids

71.

Identify the dispersed phase and the dispersion medium in each of the following colloidal systems: starch dispersion, smoke, fog, pearl, whipped cream, floating soap, jelly, milk, and ruby.

72.

Distinguish between dispersion methods and condensation methods for preparing colloidal systems.

73.

How do colloids differ from solutions with regard to dispersed particle size and homogeneity?

74.

Explain the cleansing action of soap.

75.

How can it be demonstrated that colloidal particles are electrically charged?

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Key Terms

Key Equations

Summary

11.1 The Dissolution Process

11.2 Electrolytes

11.3 Solubility

11.4 Colligative Properties

11.5Colloids

Exercises

11.1 The Dissolution Process

11.2 Electrolytes

11.3 Solubility

11.4 Colligative Properties

11.5 Colloids

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