CHEMISTRY THE CENTRAL SCIENCE

13 PROPERTIES OF SOLUTIONS

EXERCISES

VISUALIZING CONCEPTS

13.1 Rank the contents of the following containers in order of increasing entropy: [Section 13.1]

13.2 This figure shows the interaction of a cation with surrounding water molecules.

Would you expect the energy of ion–solvent interaction to be greater for Na+ or Li+? Explain. [Section 13.1]

13.3 How does the lattice energy of an ionic solid affect its solubility in water? [Section 13.1]

13.4 A quantity of the blue solid on the left in Figure 13.7 is placed in an oven and heated for a time. It slowly turns from blue to the white of the solid on the right. What has occurred? [Section 13.1]

13.5 Which of the following is the best representation of a saturated solution? Explain your reasoning. [Section 13.2]

13.6 The solubility of Xe in water at 1 atm pressure and 20 °C is approximately 5 × 10–3M. Compare this with the solubilities of Ar and Kr in water (Table 13.1) and explain what properties of the rare gas atoms account for the variation in solubility. [Section 13.3]

13.7 The structures of vitamins E and B6 are shown below. Predict which is largely water soluble and which is largely fat soluble. Explain. [Section 13.3]

13.8 If you wanted to prepare a solution of CO in water at 25 °C in which the CO concentration was 2.5 mM, what pressure of CO would you need to use? (See FIGURE 13.19.) [Section 13.3]

13.9 The figure shows two identical volumetric flasks containing the same solution at two temperatures.

(a) Does the molarity of the solution change with the change in temperature? Explain.

(b) Does the molality of the solution change with the change in temperature? Explain. [Section 13.4]

13.10 The following diagram shows the vapor-pressure curves of a volatile solvent and a solution of that solvent containing a nonvolatile solute. (a) Which line represents the solution? (b) What are the normal boiling points of the solvent and the solution? [Section 13.5]

13.11 Suppose you had a balloon made of some highly flexible semi-permeable membrane. The balloon is filled completely with a 0.2 M solution of some solute and is submerged in a 0.1 M solution of the same solute:

Initially, the volume of solution in the balloon is 0.25 L. Assuming the volume outside the semipermeable membrane is large, as the illustration shows, what would you expect for the solution volume inside the balloon once the system has come to equilibrium through osmosis? [Section 13.5]

13.12 The molecule n-octylglucoside, shown here, is widely used in biochemical research as a nonionic detergent for “solubilizing” large hydrophobic protein molecules. What characteristics of this molecule are important for its use in this way? [Section 13.6]

THE SOLUTION PROCESS (Section 13.1)

13.13 In general, the attractive intermolecular forces between solvent and solute particles must be comparable or greater than solute–solute interactions for significant solubility to occur. Explain this statement in terms of the overall energetics of solution formation.

13.14 (a) Considering the energetics of solute–solute, solvent–solvent, and solute–solvent interactions, explain why NaCl dissolves in water but not in benzene (C6H6). (b) What factors cause a cation to be strongly hydrated?

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13.15 Indicate the type of solute–solvent interaction (Section 11.2) that should be most important in each of the following solutions: (a) CCl4 in benzene (C6H6), (b) methanol (CH3OH) in water, (c) KBr in water, (d) HCl in acetonitrile (CH3CN).

13.16 Indicate the principal type of solute–solvent interaction in each of the following solutions and rank the solutions from weakest to strongest solute–solvent interaction: (a) KCl in water, (b) CH2Cl2 in benzene (C6H6), (c) methanol (CH3OH) in water.

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13.17 An ionic compound has a very negative ΔHsoln in water. Would you expect it to be very soluble or nearly insoluble in water? Explain in terms of the enthalpy and entropy changes that accompany the process.

13.18 When ammonium chloride dissolves in water, the solution becomes colder. (a) Is the solution process exothermic or endothermic? (b) Why does the solution form?

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13.19 (a) In Equation 13.1 which of the enthalpy terms for dissolving an ionic solid would correspond to the lattice energy? (b) Which energy term in this equation is always exothermic?

13.20 The schematic diagram of the solution process as the net sum of three steps in Figure 13.4 does not show the relative magnitudes of the three components because these will vary from case to case. For the dissolution of LiCl in water, ΔHsoln = –37 KJ/mol. Which of the three enthalpy changes would you expect to be much more negative than the other two? Explain.

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13.21 When two nonpolar organic liquids such as hexane (C6H14) and heptane (C7H16) are mixed, the enthalpy change that occurs is generally quite small. (a) Use the enthalpy diagram in Figure 13.4 to explain why. (b) Given that ΔHsoln ≈ 0, explain why hexane and heptane spontaneously form a solution.

13.22 The enthalpy of solution of KBr in water is about +198 kJ/mol. Nevertheless, the solubility of KBr in water is relatively high. Why does the solution process occur even though it is endothermic?

SATURATED SOLUTIONS; FACTORS AFFECTING SOLUBILITY (Sections 13.2 and 13.3)

13.23 The solubility of Cr(NO3)3 • 9 H2O in water is 208 g per 100 g of water at 15 °C. A solution of Cr(NO3)3 • 9 H2O in water at 35 °C is formed by dissolving 324 g in 100 g water. When this solution is slowly cooled to 15 °C, no precipitate forms. (a) What term describes this solution? (b) What action might you take to initiate crystallization? Use molecular-level processes to explain how your suggested procedure works.

13.24 The solubility of MnSO4 • H2O in water at 20 °C is 70 g per 100 mL of water. (a) Is a 1.22 M solution of MnSO4 • H2O in water at 20 °C saturated, supersaturated, or unsaturated? (b) Given a solution of MnSO4 • H2O of unknown concentration, what experiment could you perform to determine whether the new solution is saturated, supersaturated, or unsaturated?

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13.25 By referring to Figure 13.18, determine whether the addition of 40.0 g of each of the following ionic solids to 100 g of water at 40 °C will lead to a saturated solution: (a) NaNO3(b) KCl, (c) K2Cr2O7(d) Pb(NO3)2.

13.26 By referring to Figure 13.18, determine the mass of each of the following salts required to form a saturated solution in 250 g of water at 30 °C: (a) KClO3(b) Pb(NO3)2(c) Ce2(SO4)3.

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13.27 Water and glycerol, CH2(OH)CH(OH)CH2OH, are miscible in all proportions. What does this mean? How do the OH groups of the alcohol molecule contribute to this miscibility?

13.28 Oil and water are immiscible. What does this mean? Explain in terms of the structural features of their respective molecules and the forces between them.

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13.29 Common laboratory solvents include acetone (CH3COCH3), methanol (CH3OH), toluene (C6H5CH3), and water. Which of these is the best solvent for nonpolar solutes? Explain.

13.30 Would you expect alanine (an amino acid) to be more soluble in water or in hexane? Explain.

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13.31 (a) Would you expect stearic acid, CH3(CH2)16COOH, to be more soluble in water or in carbon tetrachloride? Explain. (b) Which would you expect to be more soluble in water, cyclohexane or dioxane? Explain.

13.32 Ibuprofen, widely used as a pain reliever, has a limited solubility in water, less than 1 mg/mL. Which feature of the molecule contributes to its low solubility in water, and which feature contributes to its solubility?

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13.33 Which of the following in each pair is likely to be more soluble in hexane, C6H14(a) CCl4 or CaCl2(b) benzene (C6H6) or glycerol, CH2(OH)CH(OH)CH2OH; (c) octanoic acid, CH3CH2CH2CH2CH2CH2CH2COOH, or acetic acid, CH3COOH? Explain your answer in each case.

13.34 Which of the following in each pair is likely to be more soluble in water: (a) cyclohexane (C6H12) or glucose (C6H12O6) (Figure 13.12); (b) propionic acid (CH3CH2COOH) or sodium propionate (CH3CH2COONa); (c) HCl or ethyl chloride (CH3CH2Cl)? Explain in each case.

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13.35 (a) Explain why carbonated beverages must be stored in sealed containers. (b) Once the beverage has been opened, why does it maintain more carbonation when refrigerated than at room temperature?

13.36 Explain why pressure substantially affects the solubility of O2 in water but has little effect on the solubility of NaCl in water.

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13.37 The Henry's law constant for helium gas in water at 30 °C is 3.7 × 10–4M/atm and the constant for N2 at 30 °C is 6.0 × 10–4M/atm. If the two gases are each present at 1.5 atm pressure, calculate the solubility of each gas.

13.38 The partial pressure of O2 in air at sea level is 0.21 atm. Using the data in Table 13.1, together with Henry's law, calculate the molar concentration of O2 in the surface water of a mountain lake saturated with air at 20 °C and an atmospheric pressure of 650 torr.

CONCENTRATIONS OF SOLUTIONS (Section 13.4)

13.39 (a) Calculate the mass percentage of Na2SO4 in a solution containing 10.6 g Na2SO4 in 483 g water. (b) An ore contains 2.86 g of silver per ton of ore. What is the concentration of silver in ppm?

13.40 (a) What is the mass percentage of iodine (I2) in a solution containing 0.035 mol I2 in 125 g of CCl4(b) Seawater contains 0.0079 g Sr2+ per kilogram of water. What is the concentration of Sr2+ measured in ppm?

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13.41 A solution is made containing 14.6 g of CH3OH in 184 g H2O. Calculate (a) the mole fraction of CH3OH, (b) the mass percent of CH3OH, (c) the molality of CH3OH.

13.42 A solution is made containing 20.8 g phenol (C6H5OH) in 425 g ethanol (C2H5OH). Calculate (a) the mole fraction of phenol, (b) the mass percent of phenol, (c) the molality of phenol.

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13.43 Calculate the molarity of the following aqueous solutions: (a) 0.540 g Mg(NO3)2 in 250.0 mL of solution, (b) 22.4 g LiClO4 • 3 H2O in 125 mL of solution, (c) 25.0 mL of 3.50 M HNO3 diluted to 0.250 L.

13.44 What is the molarity of each of the following solutions: (a) 15.0 g Al2(SO4)3 in 0.250 mL solution, (b) 5.25 g Mn(NO3)2 • 2 H2O in 175 mL of solution, (c) 35.0 mL of 9.00 M H2SO4 diluted to 0.500 L?

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13.45 Calculate the molality of each of the following solutions: (a) 8.66 g benzene (C6H6) dissolved in 23.6 g carbon tetrachloride (CCl4), (b) 4.80 g NaCl dissolved in 0.350 L of water.

13.46 (a) What is the molality of a solution formed by dissolving 1.12 mol of KCl in 16.0 mol of water? (b) How many grams of sulfur (S8) must be dissolved in 100.0 g naphthalene (C10H8) to make a 0.12 m solution?

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13.47 A sulfuric acid solution containing 571.6 g of H2SO4 per liter of solution has a density of 1.329 g/cm3. Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, (d) the molarity of H2SO4 in this solution.

13.48 Ascorbic acid (vitamin C, C6H8O6) is a water-soluble vitamin. A solution containing 80.5 g of ascorbic acid dissolved in 210 g of water has a density of 1.22 g/mL at 55 °C. Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, (d) the molarity of ascorbic acid in this solution.

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13.49 The density of acetonitrile (CH3CN) is 0.786 g/mL and the density of methanol (CH3OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL CH3OH in 98.7 mL CH3CN. (a) What is the mole fraction of methanol in the solution? (b) What is the molality of the solution? (c)Assuming that the volumes are additive, what is the molarity of CH3OH in the solution?

13.50 The density of toluene (C7H8) is 0.867 g/mL, and the density of thiophene (C4H4S) is 1.065 g/mL. A solution is made by dissolving 8.10 g of thiophene in 250.0 mL of toluene. (a) Calculate the mole fraction of thiophene in the solution. (b) Calculate the molality of thiophene in the solution. (c) Assuming that the volumes of the solute and solvent are additive, what is the molarity of thiophene in the solution?

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13.51 Calculate the number of moles of solute present in each of the following aqueous solutions: (a) 600 mL of 0.250 M SrBr2(b) 86.4 g of 0.180 m KCl, (c) 124.0 g of a solution that is 6.45% glucose (C6H12O6) by mass.

13.52 Calculate the number of moles of solute present in each of the following solutions: (a) 255 mL of 1.50 M HNO3(aq), (b) 50.0 mg of an aqueous solution that is 1.50 m NaCl, (c) 75.0 g of an aqueous solution that is 1.50% sucrose (C12H22O11) by mass.

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13.53 Describe how you would prepare each of the following aqueous solutions, starting with solid KBr: (a) 0.75 L of 1.5 × 10–2M KBr, (b) 125 g of 0.180 m KBr, (c) 1.85 L of a solution that is 12.0% KBr by mass (the density of the solution is 1.10 g/mL), (d) a 0.150 M solution of KBr that contains just enough KBr to precipitate 16.0 g of AgBr from a solution containing 0.480 mol of AgNO3.

13.54 Describe how you would prepare each of the following aqueous solutions: (a) 1.50 L of 0.110 M (NH4)2SO4 solution, starting with solid (NH4)2SO4(b) 225 g of a solution that is 0.65 m in Na2CO3, starting with the solid solute; (c) 1.20 L of a solution that is 15.0% Pb(NO3)2 by mass (the density of the solution is 1.16 g/mL), starting with solid solute; (d) a 0.50 M solution of HCl that would just neutralize 5.5 g of Ba(OH)2 starting with 6.0 M HCl.

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13.55 Commercial aqueous nitric acid has a density of 1.42 g/mL and is 16 M. Calculate the percent HNO3 by mass in the solution.

13.56 Commercial concentrated aqueous ammonia is 28% NH3 by mass and has a density of 0.90 g/mL. What is the molarity of this solution?

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13.57 Brass is a substitutional alloy consisting of a solution of copper and zinc. A particular sample of red brass consisting of 80.0% Cu and 20.0% Zn by mass has a density of 8750 kg/m3(a) What is the molality of Zn in the solid solution? (b) What is the molarity of Zn in the solution?

13.58 Caffeine (C8H10N4O2) is a stimulant found in coffee and tea. If a solution of caffeine in chloroform (CHCl3) as a solvent has a concentration of 0.0500 m, calculate (a) the percent caffeine by mass, (b) the mole fraction of caffeine.

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13.59 During a typical breathing cycle, the CO2 concentration in the expired air rises to a peak of 4.6% by volume. Calculate the partial pressure of the CO2 at this point, assuming 1 atm pressure. What is the molarity of the CO2 in air at this point, assuming a body temperature of 37 °C?

13.60 Breathing air that contains 4.0% by volume CO2 over time causes rapid breathing, throbbing headache, and nausea, among other symptoms. What is the concentration of CO2 in such air in terms of (a) mol percentage, (b) molarity, assuming 1 atm pressure and a body temperature of 37 °C?

COLLIGATIVE PROPERTIES (Section 13.5)

13.61 List four properties of a solution that depend on the total concentration but not the type of particle or particles present as solute. Write the mathematical expression that describes how each of these properties depends on concentration.

13.62 How does increasing the concentration of a nonvolatile solute in water affect the following properties: (a) vapor pressure, (b) freezing point, (c) boiling point; (d) osmotic pressure?

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13.63 Consider two solutions, one formed by adding 10 g of glucose (C6H12O6) to 1 L of water and the other formed by adding 10 g of sucrose (C12H22O11) to 1 L of water. Are the vapor pressures over the two solutions the same? Why or why not?

13.64 (a) What is an ideal solution(b) The vapor pressure of pure water at 60 °C is 149 torr. The vapor pressure of water over a solution at 60 °C containing equal numbers of moles of water and ethylene glycol (a nonvolatile solute) is 67 torr. Is the solution ideal according to Raoult's law? Explain.

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13.65 (a) Calculate the vapor pressure of water above a solution prepared by adding 22.5 g of lactose (C12H22O11) to 200.0 g of water at 338 K. (Vapor-pressure data for water are given in Appendix B.) (b) Calculate the mass of propylene glycol (C3H8O2) that must be added to 0.340 kg of water to reduce the vapor pressure by 2.88 torr at 40 °C.

13.66 (a) Calculate the vapor pressure of water above a solution prepared by dissolving 28.5 g of glycerin (C3H8O3) in 125 g of water at 343 K. (The vapor pressure of water is given in Appendix B.) (b) Calculate the mass of ethylene glycol (C2H6O2) that must be added to 1.00 kg of ethanol (C2H5OH) to reduce its vapor pressure by 10.0 torr at 35 °C. The vapor pressure of pure ethanol at 35 °C is 1.00 × 102 torr.

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[13.67] At 63.5 °C the vapor pressure of H2O is 175 torr, and that of ethanol (C2H5OH) is 400 torr. A solution is made by mixing equal masses of H2O and C2H5OH. (a) What is the mole fraction of ethanol in the solution? (b) Assuming ideal-solution behavior, what is the vapor pressure of the solution at 63.5 °C? (c) What is the mole fraction of ethanol in the vapor above the solution?

[13.68] At 20 °C the vapor pressure of benzene (C6H6) is 75 torr, and that of toluene (C7H8) is 22 torr. Assume that benzene and toluene form an ideal solution. (a) What is the composition in mole fractions of a solution that has a vapor pressure of 35 torr at 20 °C? (b) What is the mole fraction of benzene in the vapor above the solution described in part (a)?

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13.69 (a) Why does a 0.10 m aqueous solution of NaCl have a higher boiling point than a 0.10 m aqueous solution of C6H12O6(b) Calculate the boiling point of each solution. (c) The experimental boiling point of the NaCl solution is lower than that calculated, assuming that NaCl is completely dissociated in solution. Why is this the case?

13.70 Arrange the following aqueous solutions, each 10% by mass in solute, in order of increasing boiling point: glucose (C6H12O6), sucrose (C12H22O11), sodium nitrate (NaNO3).

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13.71 List the following aqueous solutions in order of increasing boiling point: 0.120 m glucose, 0.050 m LiBr, 0.050 m Zn(NO3)2.

13.72 List the following aqueous solutions in order of decreasing freezing point: 0.040 m glycerin (C3H8O3), 0.020 m KBr, 0.030 m phenol (C6H5OH).

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13.73 Using data from Table 13.3, calculate the freezing and boiling points of each of the following solutions: (a) 0.22 m glycerol (C3H8O3) in ethanol, (b) 0.240 mol of naphthalene (C10H8) in 2.45 mol of chloroform, (c) 1.50 g NaCl in 0.250 kg of water, (d) 2.04 g KBr and 4.82 g glucose (C6H12O6) in 188 g of water.

13.74 Using data from Table 13.3, calculate the freezing and boiling points of each of the following solutions: (a) 0.25 m glucose in ethanol; (b) 20.0 g of decane, C10H22, in 50.0 g CHCl3(c) 3.50 g NaOH in 175 g of water, (d) 0.45 mol ethylene glycol and 0.15 mol KBr in 150 g H2O.

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13.75 How many grams of ethylene glycol (C2H6O2) must be added to 1.00 kg of water to produce a solution that freezes at –5.00 °C?

13.76 What is the freezing point of an aqueous solution that boils at 105.0 °C?

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13.77 What is the osmotic pressure formed by dissolving 44.2 mg of aspirin (C9H8O4) in 0.358 L of water at 25 °C?

13.78 Seawater contains 3.4 g of salts for every liter of solution. Assuming that the solute consists entirely of NaCl (over 90% is), calculate the osmotic pressure of seawater at 20 °C.

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13.79 Adrenaline is the hormone that triggers the release of extra glucose molecules in times of stress or emergency. A solution of 0.64 g of adrenaline in 36.0 g of CCl4 elevates the boiling point by 0.49 °C. Is the molar mass of adrenaline calculated from the boiling-point elevation in agreement with the following structural formula?

13.80 Lauryl alcohol is obtained from coconut oil and is used to make detergents. A solution of 5.00 g of lauryl alcohol in 0.100 kg of benzene freezes at 4.1 °C. What is the approximate molar mass of lauryl alcohol?

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13.81 Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing 0.150 g of this enzyme in 210 mL of solution has an osmotic pressure of 0.953 torr at 25 °C. What is the molar mass of lysozyme?

13.82 A dilute aqueous solution of an organic compound soluble in water is formed by dissolving 2.35 g of the compound in water to form 0.250 L of solution. The resulting solution has an osmotic pressure of 0.605 atm at 25 °C. Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

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[13.83] The osmotic pressure of a 0.010 M aqueous solution of CaCl2 is found to be 0.674 atm at 25 °C. (a) Calculate the van't Hoff factor, i, for the solution. (b) How would you expect the value of i to change as the solution becomes more concentrated? Explain.

[13.84] Based on the data given in Table 13.4, which solution would give the larger freezing-point lowering, a 0.030 m solution of NaCl or a 0.020 m solution of K2SO4? How do you explain the departure from ideal behavior and the differences observed between the two salts?

COLLOIDS (Section 13.6)

13.85 (a) Why is there no colloid in which both the dispersed substance and the dispersing substance are gases? (b) Michael Faraday first prepared ruby-red colloids of gold particles in water that were stable indefinitely. To the unaided eye these brightly colored colloids are not distinguishable from solutions. How could you determine whether a given colored preparation is a solution or colloid?

13.86 (a) Many proteins that remain homogeneously distributed in water have molecular masses in the range of 30,000 amu and larger. In what sense is it appropriate to consider such suspensions to be colloids rather than solutions? Explain. (b) What general name is given to a colloidal dispersion of one liquid in another? What is an emulsifying agent?

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13.87 Indicate whether each of the following is a hydrophilic or a hydrophobic colloid: (a) butterfat in homogenized milk, (b) hemoglobin in blood, (c) vegetable oil in a salad dressing, (d) colloidal gold particles in water.

13.88 Explain how each of the following factors helps determine the stability or instability of a colloidal dispersion: (a) particulate mass, (b) hydrophobic character, (c) charges on colloidal particles.

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13.89 Colloidal dispersions of proteins, such as a gelatin, can often be caused to separate into two layers by addition of a solution of an electrolyte. Given that protein molecules may carry electrical charges on their outer surface as illustrated in Figure 13.30, what do you believe happens when the electrolyte solution is added?

13.90 Explain how (a) a soap such as sodium stearate stabilizes a colloidal dispersion of oil droplets in water; (b) milk curdles upon addition of an acid.

ADDITIONAL EXERCISES

13.91 Butylated hydroxytoluene (BHT) has the following molecular structure:

It is widely used as a preservative in a variety of foods, including dried cereals. Based on its structure, would you expect BHT to be more soluble in water or in hexane (C6H14)? Explain.

13.92 A saturated solution of sucrose (C12H22O11) is made by dissolving excess table sugar in a flask of water. There are 50 g of undissolved sucrose crystals at the bottom of the flask in contact with the saturated solution. The flask is stoppered and set aside. A year later a single large crystal of mass 50 g is at the bottom of the flask. Explain how this experiment provides evidence for a dynamic equilibrium between the saturated solution and the undissolved solute.

13.93 Most fish need at least 4 ppm dissolved O2 for survival. (a) What is this concentration in mol/L? (b) What partial pressure of O2 above the water is needed to obtain this concentration at 10 °C? (The Henry's law constant for O2 at this temperature is 1.71 × 10–3 mol/L-atm.)

13.94 The presence of the radioactive gas radon (Rn) in well water obtained from aquifers that lie in rock deposits presents a possible health hazard in parts of the United States. (a) Assuming that the solubility of radon in water with 1 atm pressure of the gas over the water at 30 °C is 7.27 × 10–3M, what is the Henry's law constant for radon in water at this temperature? (b) A sample consisting of various gases contains 3.5 × 10–6 mole fraction of radon. This gas at a total pressure of 32 atm is shaken with water at 30 °C. Calculate the molar concentration of radon in the water.

13.95 Glucose makes up about 0.10% by mass of human blood. Calculate the concentration in (a) ppm, (b) molality. What further information would you need to determine the molarity of the solution?

13.96 The concentration of gold in seawater has been reported to be between 5 ppt (parts per trillion) and 50 ppt. Assuming that seawater contains 13 ppt of gold, calculate the number of grams of gold contained in 1.0 × 103 gal of seawater.

13.97 The maximum allowable concentration of lead in drinking water is 9.0 ppb. (a) Calculate the molarity of lead in a 9.0-ppb solution. What assumption did you have to make in your calculation? (b) How many grams of lead are in a swimming pool containing 9.0 ppb lead in 60m3of water?

13.98 Acetonitrile (CH3CN) is a polar organic solvent that dissolves a wide range of solutes, including many salts. The density of a 1.80 M LiBr solution in acetonitrile is 0.826 g/cm3. Calculate the concentration of the solution in (a) molality, (b) mole fraction of LiBr, (c) mass percentage of CH3CN.

13.99 A “canned heat” product used to warm chafing dishes consists of a homogeneous mixture of ethanol (C2H5OH) and paraffin that has an average formula of C24H50. What mass of C2H5OH should be added to 620 kg of the paraffin in formulating the mixture if the vapor pressure of ethanol at 35 °C over the mixture is to be 8 torr? The vapor pressure of pure ethanol at 35 °C is 100 torr.

13.100 A solution contains 0.115 mol H2O and an unknown number of moles of sodium chloride. The vapor pressure of the solution at 30 °C is 25.7 torr. The vapor pressure of pure water at this temperature is 31.8 torr. Calculate the number of moles of sodium chloride in the solution. (Hint: Remember that sodium chloride is a strong electrolyte.)

[13.101] Two beakers are placed in a sealed box at 25 °C. One beaker contains 30.0 mL of a 0.050 M aqueous solution of a nonvolatile nonelectrolyte. The other beaker contains 30.0 mL of a 0.035 M aqueous solution of NaCl. The water vapor from the two solutions reaches equilibrium. (a) In which beaker does the solution level rise, and in which one does it fall? (b) What are the volumes in the two beakers when equilibrium is attained, assuming ideal behavior?

13.102 A car owner who knows no chemistry has to put antifreeze in his car's radiator. The instructions recommend a mixture of 30% ethylene glycol and 70% water. Thinking he will improve his protection he uses pure ethylene glycol. He is saddened to find that the solution does not provide as much protection as he hoped. Why not?

13.103 Calculate the freezing point of a 0.100 m aqueous solution of K2SO4(a) ignoring interionic attractions, and (b) taking interionic attractions into consideration by using the van't Hoff factor (Table 13.4).

13.104 Carbon disulfide (CS2) boils at 46.30 °C and has a density of 1.261 g/mL. (a) When 0.250 mol of a nondissociating solute is dissolved in 400.0 mL of CS2, the solution boils at 47.46 °C. What is the molal boiling-point-elevation constant for CS2(b) When 5.39 g of a nondissociating unknown is dissolved in 50.0 mL of CS2, the solution boils at 47.08 °C. What is the molecular weight of the unknown?

[13.105] A lithium salt used in lubricating grease has the formula LiCnH2n+1O2. The salt is soluble in water to the extent of 0.036 g per 100 g of water at 25 °C. The osmotic pressure of this solution is found to be 57.1 torr. Assuming that molality and molarity in such a dilute solution are the same and that the lithium salt is completely dissociated in the solution, determine an appropriate value of n in the formula for the salt.

INTEGRATIVE EXERCISES

13.106 Fluorocarbons (compounds that contain both carbon and fluorine) were, until recently, used as refrigerants. The compounds listed in the following table are all gases at 25 °C, and their solubilities in water at 25 °C and 1 atm fluorocarbon pressure are given as mass percentages.(a) For each fluorocarbon, calculate the molality of a saturated solution. (b) Explain why the molarity of each of the solutions should be very close numerically to the molality. (c) Based on their molecular structures, account for the differences in solubility of the four fluorocarbons. (d) Calculate the Henry's law constant at 25 °C for CHClF2, and compare its magnitude to that for N2(6.8 × 10–4 mol/L-atm). Can you account for the difference in magnitude?

[13.107] At ordinary body temperature (37 °C) the solubility of N2 in water in contact with air at ordinary atmospheric pressure (1.0 atm) is 0.015 g/L. Air is approximately 78 mol % N2. Calculate the number of moles of N2 dissolved per liter of blood, which is essentially an aqueous solution. At a depth of 100 ft in water, the pressure is 4.0 atm. What is the solubility of N2 from air in blood at this pressure? If a scuba diver suddenly surfaces from this depth, how many milliliters of N2 gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood?

[13.108] Consider the following values for enthalpy of vaporization (kJ/mol) of several organic substances:

(a) Use variations in the intermolecular forces operating in these organic substances to account for their variations in heats of vaporization. (b) How would you expect the solubilities of these substances to vary in hexane as solvent? In ethanol? Use intermolecular forces, including hydrogen-bonding interactions where applicable, to explain your responses.

[13.109] A textbook on chemical thermodynamics states, “The heat of solution represents the difference between the lattice energy of the crystalline solid and the solvation energy of the gaseous ions.” (a) Draw a simple energy diagram to illustrate this statement. (b) A salt such as NaBr is insoluble in most polar nonaqueous solvents such as acetonitrile (CH3CN) or nitromethane (CH3NO2), but salts of large cations, such as tetramethylammonium bromide [(CH3)4NBr], are generally more soluble. Use the thermochemical cycle you drew in part (a) and the factors that determine the lattice energy (Section 8.2) to explain this fact.

13.110 (a) A sample of hydrogen gas is generated in a closed container by reacting 2.050 g of zinc metal with 15.0 mL of 1.00 M sulfuric acid. Write the balanced equation for the reaction, and calculate the number of moles of hydrogen formed, assuming that the reaction is complete.(b) The volume over the solution is 122 mL. Calculate the partial pressure of the hydrogen gas in this volume at 25 °C, ignoring any solubility of the gas in the solution. (c) The Henry's law constant for hydrogen in water at 25 °C is 7.8 × 10–4 mol/L-atm. Estimate the number of moles of hydrogen gas that remain dissolved in the solution. What fraction of the gas molecules in the system is dissolved in the solution? Was it reasonable to ignore any dissolved hydrogen in part (b)?

[13.111] The following table presents the solubilities of several gases in water at 25 °C under a total pressure of gas and water vapor of 1 atm. (a) What volume of CH4(g) under standard conditions of temperature and pressure is contained in 4.0 L of a saturated solution at 25 °C? (b)Explain the variation in solubility among the hydrocarbons listed (the first three compounds), based on their molecular structures and inter-molecular forces. (c) Compare the solubilities of O2, N2, and NO, and account for the variations based on molecular structures and intermolecular forces. (d) Account for the much larger values observed for H2S and SO2 as compared with the other gases listed. (e) Find several pairs of substances with the same or nearly the same molecular masses (for example, C2H4 and N2), and use intermolecular interactions to explain the differences in their solubilities.

13.112 A small cube of lithium (density = 0.535 g/cm3) measuring 1.0 mm on each edge is added to 0.500 L of water. The following reaction occurs:

What is the freezing point of the resultant solution?

[13.113] At 35 °C the vapor pressure of acetone, (CH3)2CO, is 360 torr, and that of chloroform, CHCl3, is 300 torr. Acetone and chloroform can form very weak hydrogen bonds between one another as follows:

A solution composed of an equal number of moles of acetone and chloroform has a vapor pressure of 250 torr at 35 °C. (a) What would be the vapor pressure of the solution if it exhibited ideal behavior? (b) Use the existence of hydrogen bonds between acetone and chloroform molecules to explain the deviation from ideal behavior. (c) Based on the behavior of the solution, predict whether the mixing of acetone and chloroform is an exothermic (ΔHsoln < 0) or endothermic (ΔHsoln > 0) process.