Chapter 13

Why do ionic substances with higher lattice energies tend to be less soluble in water than those with lower lattice energies? [Section 13.1]

Suppose you had a balloon made of some highly flexible semipermeable 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:

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.

(a) Considering the energetics of solute-solute, solventsolvent, and solute- solvent interactions, explain why \(\mathrm{NaCl}\) dissolves in water but not in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right) .\) (b) What factors cause a cation to be strongly hydrated?

Indicate the type of solute-solvent interaction (Section 11.2) that should be most important in each of the following solutions: (a) \(\mathrm{CCl}_{4}\) in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\),(b) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) in water, (c) \(\mathrm{KBr}\) in water, (d) \(\mathrm{HCl}\) in acetonitrile \(\left(\mathrm{CH}_{3} \mathrm{CN}\right)\).

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) \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\), (c) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) in water.

The enthalpy of solution of \(\mathrm{KBr}\) in water is about \(+198 \mathrm{~kJ} / \mathrm{mol}\). Nevertheless, the solubility of \(\mathrm{KBr}\) in water is relatively high. Why does the solution process occur even though it is endothermic?

The solubility of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\) in water is \(208 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water at \(15^{\circ} \mathrm{C}\). A solution of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\) in water at \(35^{\circ} \mathrm{C}\) is formed by dissolving \(324 \mathrm{~g}\) in \(100 \mathrm{~g}\). water. When this solution is slowly cooled to \(15^{\circ} \mathrm{C}\), 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.

The solubility of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20{ }^{\circ} \mathrm{C}\) is \(70 \mathrm{~g}\) per \(100 \mathrm{~mL}\) of water. (a) \(\mathrm{ls}\) a \(1.22 \mathrm{M}\) solution of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20^{\circ} \mathrm{C}\) saturated, supersaturated, or unsaturated? (b) Given a solution of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) of unknown concentration, \(w\) hat experiment could you perform to determine whether the new solution is saturated, supersaturated, or unsaturated?

Water and glycerol, \(\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}\), are mis- cible in all proportions. What does this mean? How do the OH groups of the alcohol molecule contribute to this miscibility?

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.

(a) Would you expect stearic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{COOH}\), 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.

Consider a series of carboxylic acids whose general formula is \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{n} \mathrm{COOH}\). How would you expect the solubility of these compounds in water and in hexane to change as \(n\) increases? Explain.

Which of the following in each pair is likely to be more soluble in hexane, \(\mathrm{C}_{6} \mathrm{H}_{14}:\) (a) \(\mathrm{CCl}_{4}\) or \(\mathrm{CaCl}_{2}\); (b) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) or glycerol, \(\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH} ;\) (c) octanoic acid, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\), or acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\). Explain your answer in each case.

Which of the following in each pair is likely to be more soluble in water: (a) cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) or glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) (Figure 13.12); (b) propionic acid \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\right)\) or sodium propionate \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COONa}\right) ;\) (c) \(\mathrm{HCl}\) or ethyl chloride \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}\right) ?\) Explain in each case.

(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?

Explain why pressure affects the solubility of \(\mathrm{O}_{2}\) in water, but not the solubility of \(\mathrm{NaCl}\) in water.

The Henry's law constant for helium gas in water at \(30^{\circ} \mathrm{C}\) is \(3.7 \times 10^{-4} \mathrm{M} / \mathrm{atm}\) and the constant for \(\mathrm{N}_{2}\) at \(30{ }^{\circ} \mathrm{C}\) is \(6.0 \times 10^{-4} \mathrm{M} / \mathrm{atm} .\) If the two gases are each present at \(1.5\) atm pressure, calculate the solubility of each gas.

(a) Calculate the mass percentage of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in a solution containing \(10.6 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}\) in \(483 \mathrm{~g}\) water. (b) An ore contains \(2.86 \mathrm{~g}\) of silver per ton of ore. What is the concentration of silver in ppm?

(a) What is the mass percentage of iodine \(\left(\mathrm{I}_{2}\right)\) in a solution containing \(0.035 \mathrm{~mol} \mathrm{I}_{2}\) in \(115 \mathrm{~g}\) of \(\mathrm{CCl}_{4} ?\) (b) Seawater contains \(0.0079 \mathrm{~g} \mathrm{Sr}^{2+}\) per kilogram of water. What is the concentration of \(\mathrm{Sr}^{2+}\) measured in \(\mathrm{ppm} ?\)

A solution is made containing \(14.6 \mathrm{~g}\) of \(\mathrm{CH}_{3} \mathrm{OH}\) in \(184 \mathrm{~g}\) \(\mathrm{H}_{2} \mathrm{O} .\) Calculate (a) the mole fraction of \(\mathrm{CH}_{3} \mathrm{OH},(\mathrm{b})\) the mass percent of \(\mathrm{CH}_{3} \mathrm{OH}\), (c) the molality of \(\mathrm{CH}_{3} \mathrm{OH}\).

A solution is made containing \(25.5 \mathrm{~g}\) phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) in \(425 \mathrm{~g}\) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\). Calculate (a) the mole fraction of phenol, (b) the mass percent of phenol, (c) the molality of phenol.

Calculate the molarity of the following aqueous solutions: (a) \(0.540 \mathrm{~g} \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) in \(250.0 \mathrm{~mL}\) of solution, (b) \(22.4 \mathrm{~g} \mathrm{LiClO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}\) in \(125 \mathrm{~mL}\) of solution, (c) \(25.0 \mathrm{~mL}\) of \(3.50 \mathrm{M} \mathrm{HNO}_{3}\) diluted to \(0.250 \mathrm{~L}\).

What is the molarity of each of the following solutions: (a) \(15.0 \mathrm{~g} \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) in \(0.350 \mathrm{~L}\) solution, (b) \(5.25 \mathrm{~g}\) \(\mathrm{Mn}\left(\mathrm{NO}_{3}\right)_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) in \(175 \mathrm{~mL}\) of solution, (c) \(35.0 \mathrm{~mL}\) of \(9.00 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) diluted to \(0.500 \mathrm{~L} ?\)

Calculate the molality of each of the following solutions: (a) \(8.66 \mathrm{~g}\) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) dissolved in \(23.6 \mathrm{~g}\) carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\), (b) \(4.80 \mathrm{~g} \mathrm{NaCl}\) dissolved in \(0.350 \mathrm{~L}\) of water.

(a) What is the molality of a solution formed by dissolving \(1.25\) mol of \(\mathrm{KCl}\) in \(16.0\) mol of water? (b) How many grams of sulfur \(\left(\mathrm{S}_{8}\right)\) must be dissolved in \(100.0 \mathrm{~g}\) naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) to make a \(0.12 \mathrm{~m}\) solution?

A sulfuric acid solution containing \(571.6 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) per Jiter of solution has a density of \(1.329 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, (d) the molarity of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in this solution.

Ascorbic acid (vitamin \(\mathrm{C}\), \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\) ) is a water-soluble vitamin. A solution containing \(80.5 \mathrm{~g}\) of ascorbic acid dissolved in \(210 \mathrm{~g}\) of water has a density of \(1.22 \mathrm{~g} / \mathrm{mL}\) at \(55^{\circ} \mathrm{C}\). Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, (d) the molarity of ascorbic acid in this solution.

The density of acetonitrile \(\left(\mathrm{CH}_{3} \mathrm{CN}\right)\) is \(0.786 \mathrm{~g} / \mathrm{mL}\) and the density of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) is \(0.791 \mathrm{~g} / \mathrm{mL}\). A solution is made by dissolving \(22.5 \mathrm{~mL} \mathrm{CH}_{3} \mathrm{OH}\) in \(98.7 \mathrm{~mL}\) \(\mathrm{CH}_{3} \mathrm{CN}\). (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 \(\mathrm{CH}_{3} \mathrm{OH}\) in the solution?

The density of toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)\) is \(0.867 \mathrm{~g} / \mathrm{mL}\), and the density of thiophene \(\left(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{~S}\right)\) is \(1.065 \mathrm{~g} / \mathrm{mL}\). A solution is made by dissolving \(9.08 \mathrm{~g}\) of thiophene in \(250.0 \mathrm{~mL}\) 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?

Calculate the number of moles of solute present in each of the following aqueous solutions: (a) \(600 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{SrBr}_{2}\), (b) \(86.4 \mathrm{~g}\) of \(0.180 \mathrm{~m} \mathrm{KCl}\), (c) \(124.0 \mathrm{~g}\) of a solution that is \(6.45 \%\) glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) by mass.

Calculate the number of moles of solute present in each of the following solutions: (a) \(185 \mathrm{~mL}\) of \(1.50 \mathrm{M}\) \(\mathrm{HNO}_{3}(a q)\), (b) \(50.0 \mathrm{mg}\) of an aqueous solution that is \(1.25 \mathrm{~m} \mathrm{NaCl}\), (c) \(75.0 \mathrm{~g}\) of an aqueous solution that is \(1.50 \%\) sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) by mass.

Describe how you would prepare each of the following aqueous solutions, starting with solid KBr: (a) \(0.75 \mathrm{~L}\) of \(1.5 \times 10^{-2} M \mathrm{KBr}\), (b) \(125 \mathrm{~g}\) of \(0.180 \mathrm{~m} \mathrm{KBr}\) (c) \(1.85 \mathrm{~L}\) of a solution that is \(12.0 \% \mathrm{KBr}\) by mass (the density of the solution is \(1.10 \mathrm{~g} / \mathrm{mL}\) ), (d) a \(0.150 \mathrm{M}\) solution of \(\mathrm{KBr}\) that contains just enough \(\mathrm{KBr}\) to precipitate \(16.0 \mathrm{~g}\) of \(\mathrm{AgBr}\) from a solution containing \(0.480 \mathrm{~mol}\) of \(\mathrm{AgNO}_{3}\)

Describe how you would prepare each of the following aqueous solutions: (a) \(1.50 \mathrm{~L}\) of \(0.110 \mathrm{M}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) solution, starting with solid \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} ;\) (b) \(120 \mathrm{~g}\) of a solution that is \(0.65 \mathrm{~m}\) in \(\mathrm{Na}_{2} \mathrm{CO}_{3}\), starting with the solid solute; (c) \(1.20 \mathrm{~L}\) of a solution that is \(15.0 \% \mathrm{~Pb}\left(\mathrm{NO}_{3}\right)_{2}\) by mass (the density of the solution is \(1.16 \mathrm{~g} / \mathrm{mL}\) ), starting with solid solute; (d) a \(0.50 \mathrm{M}\) solution of \(\mathrm{HCl}\) that would just neutralize \(5.5 \mathrm{~g}\) of \(\mathrm{Ba}(\mathrm{OH})_{2}\) starting with \(6.0\) M HCl.

Commercial aqueous nitric acid has a density of \(1.42 \mathrm{~g} / \mathrm{mL}\) and is \(16 \mathrm{M}\). Calculate the percent \(\mathrm{HNO}_{3}\) by mass in the solution.

Commercial concentrated aqueous ammonia is \(28 \% \mathrm{NH}_{3}\) by mass and has a density of \(0.90 \mathrm{~g} / \mathrm{mL}\). What is the molarity of this solution?

During a typical breathing cycle the \(\mathrm{CO}_{2}\) concentration in the expired air rises to a peak of \(4.6 \%\) by volume. Calculate the partial pressure of the \(\mathrm{CO}_{2}\) at this point, assuming 1 atm pressure. What is the molarity of the \(\mathrm{CO}_{2}\) in air at this point, assuming a body temperature of \(37^{\circ} \mathrm{C} ?\)

Breathing air that contains \(4.0 \%\) by volume \(\mathrm{CO}_{2}\) over time causes rapid breathing, throbbing headache, and nausea, among other symptoms. What is the concentration of \(\mathrm{CO}_{2}\) in such air in terms of (a) mol percentage, (b) molarity, assuming 1 atm pressure, and a body temperature of \(37^{\circ} \mathrm{C} ?\)

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.

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?

Consider two solutions, one formed by adding \(10 \mathrm{~g}\) of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) to \(1 \mathrm{~L}\) of water and the other formed by adding \(10 \mathrm{~g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) to \(1 \mathrm{~L}\) of water. Are the vapor pressures over the two solutions the same? Why or why not?

(a) What is an ideal solution? (b) The vapor pressure of pure water at \(60^{\circ} \mathrm{C}\) is 149 torr. The vapor pressure of water over a solution at \(60^{\circ} \mathrm{C}\) 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.

(a) Calculate the vapor pressure of water above a solution prepared by adding \(22.5 \mathrm{~g}\) of lactose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) to \(200.0 \mathrm{~g}\) of water at \(338 \mathrm{~K}\). (Vapor-pressure data for water are given in Appendix B.) (b) Calculate the mass of propylene glycol \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{2}\right)\) that must be added to \(0.340 \mathrm{~kg}\) of water to reduce the vapor pressure by \(2.88\) torr at \(40^{\circ} \mathrm{C}\).

At \(63.5^{\circ} \mathrm{C}\) the vapor pressure of \(\mathrm{H}_{2} \mathrm{O}\) is 175 torr, and that of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is 400 torr. A solution is made by mixing equal masses of \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\). (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 \(63.5^{\circ} \mathrm{C} ?\) (c) What is the mole fraction of ethanol in the vapor above the solution?

At \(20^{\circ} \mathrm{C}\) the vapor pressure of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is 75 torr, and that of toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)\) 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 \(20^{\circ} \mathrm{C} ?\) (b) What is the mole fraction of benzene in the vapor above the solution described in part (a)?

List the following aqueous solutions in order of increasing boiling point: \(0.120 \mathrm{~m}\) glucose, \(0.050 \mathrm{~m} \mathrm{LiBr}, 0.050 \mathrm{~m}\) \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}\).

List the following aqueous solutions in order of decreasing freezing point: \(0.040 \mathrm{~m}\) glycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right), 0.020 \mathrm{~m}\) \(\mathrm{KBr}, 0.030 \mathrm{~m}\) phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\).

What is the osmotic pressure formed by dissolving \(44.2 \mathrm{mg}\) of aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) in \(0.358 \mathrm{~L}\) of water at \(25^{\circ} \mathrm{C} ?\)

Seawater contains \(3.4 \mathrm{~g}\) of salts for every liter of solution. Assuming that the solute consists entirely of \(\mathrm{NaCl}\) (over \(90 \%\) is), calculate the osmotic pressure of seawater at \(20^{\circ} \mathrm{C}\).

Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing \(0.150 \mathrm{~g}\) of this enzyme in \(210 \mathrm{~mL}\) of solution has an osmotic pressure of \(0.953\) torr at \(25^{\circ} \mathrm{C}\). What is the molar mass of lysozyme?