Chapter 13

Consider two ionic solids, both composed of singly charged ions, that have different lattice energies. (a) Will the solids have the same solubility in water? (b) If not, which solid will be more soluble in water, the one with the larger lattice energy or the one with the smaller lattice energy? Assume that solute-solvent interactions are the same for both solids.

Which two statements about gas mixtures are true? (a) Gases always mix with other gases because the gas particles are too far apart to feel significant intermolecular attractions or repulsions. (b) Just like water and oil don't mix in the liquid phase, two gases can be immiscible and not mix in the gas phase. (c) If you cool a gaseous mixture, you will liquefy all the gases at the same temperature. (d) Gases mix in all proportions in part because the entropy of the system increases upon doing so.

If you compare the solubilities of the noble gases in water, you find that solubility increases from smallest atomic weight to largest, \(\mathrm{Ar}<\mathrm{Kr}<\mathrm{Xe}\). Which of the following statements is the best explanation? (a) The heavier the gas, the more it sinks to the bottom of the water and leaves room for more gas molecules at the top of the water. (b) The heavier the gas, the more dispersion forces it has, and therefore the more attractive interactions it has with water molecules. (c) The heavier the gas, the more likely it is to hydrogenbond with water. (d) The heavier the gas, the more likely it is to make a saturated solution in water.

You take a sample of water that is at room temperature and in contact with air and put it under a vacuum. Right away, you see bubbles leave the water, but after a little while, the bubbles stop. As you keep applying the vacuum, more bubbles appear. A friend tells you that the first bubbles were water vapor, and the low pressure had reduced the boiling point of water, causing the water to boil. Another friend tells you that the first bubbles were gas molecules from the air (oxygen, nitrogen, and so forth) that were dissolved in the water. Which friend is mostly likely to be correct? What, then, is responsible for the second batch of bubbles?

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 \(0.1 \mathrm{M}\) solution of the same solute: Initially, the volume of solution in the balloon is \(0.25 \mathrm{~L}\). 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?

Indicate whether each statement is true or false: (a) A solute will dissolve in a solvent if solute-solute interactions are stronger than solute-solvent interactions. (b) In making a solution, the enthalpy of mixing is always a positive number. (c) An increase in entropy favors mixing.

Indicate whether each statement is true or false: \((\mathbf{a}) \mathrm{NaCl}\) dissolves in water but not in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) because benzene is denser than water. (b) \(\mathrm{NaCl}\) dissolves in water but not in benzene because water has a large dipole moment and benzene has zero dipole moment. (c) NaCl dissolves in water but not in benzene because the water-ion interactions are stronger than benzene-ion interactions.

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 \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right),(\mathbf{b})\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) in water, \((\mathbf{c}) \mathrm{KBr}\) in water, \((\mathbf{d}) \mathrm{HCl}\) 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.

An ionic compound has a very negative \(\Delta H_{\text {soln }}\) in water. (a) Would you expect it to be very soluble or nearly insoluble in water? (b) Which term would you expect to be the largest negative number: \(\Delta H_{\text {solvent }}, \Delta H_{\text {solute }}\), or \(\Delta H_{\operatorname{mix}} ?\)

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

For the dissolution of \(\mathrm{NaCl}\) in water, \(\Delta H_{\mathrm{soln}}=+3 \mathrm{~kJ} / \mathrm{mol}\). Which term would you expect to be the largest negative number: \(\Delta H_{\text {solute }}, \Delta H_{\text {solvent }},\) or \(\Delta H_{\text {mix }} ?\)

Two nonpolar organic liquids, benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) and toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right),\) are mixed. (a) Do you expect \(\Delta H_{\text {soln }}\) to be a large positive number, a large negative number, or close to zero? Explain. (b) Benzene and toluene are miscible with each other in all proportions. In making a solution of them, is the entropy of the system increased, decreased, or close to zero, compared to the separate pure liquids?

\(\mathrm{KBr}\) is relatively soluble in water, yet its enthalpy of solution is \(+19.8 \mathrm{~kJ} / \mathrm{mol}\). Which of the following statements provides the best explanation for this behavior? (a) Potassium salts are always soluble in water. (b) The entropy of mixing must be unfavorable. (c) The enthalpy of mixing must be small compared to the enthalpies for breaking up water-water interactions and K-Br ionic interactions. (d) \(\mathrm{KBr}\) has a high molar mass compared to other salts like \(\mathrm{NaCl}\)

The solubility of alum, \(\mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2} \cdot 12 \mathrm{H}_{2} \mathrm{O},\) in water at is \(44 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water at \(50^{\circ} \mathrm{C}\). A solution of alum in water at \(80^{\circ} \mathrm{C}\) is formed by dissolving \(130 \mathrm{~g}\) in \(100 \mathrm{~g}\) of water. When this solution is slowly cooled to \(50^{\circ} \mathrm{C}\), no precipitate forms. (a) Is the solution that has cooled down to \(50^{\circ} \mathrm{C}\) unsaturated, saturated, or supersaturated? (b) You take a metal spatula and scratch the side of the glass vessel that contains this cooled solution, and crystals start to appear. What has just happened? (c) At equilibrium, what mass of crystals do you expect to form?

Consider water and glycerol, \(\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}\). (a) Would you expect them to be miscible in all proportions? (b) List the intermolecular attractions that occur between a water molecule and a glycerol molecule.

Oil and water are immiscible. Which is the most likely reason? (a) Oil molecules are denser than water. (b) Oil molecules are composed mostly of carbon and hydrogen. (c) Oil molecules have higher molar masses than water. (d) Oil molecules have higher vapor pressures than water. (e) Oil molecules have higher boiling points than water.

Common laboratory solvents include acetone \(\left(\mathrm{CH}_{3} \mathrm{COCH}_{3}\right),\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right),\) toluene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\right),\) and water. Which of these is the best solvent for nonpolar solutes?

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

(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? (b) Which would you expect to be more soluble in water, cyclohexane or dioxane?

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 \(\mathrm{CaCl}_{2},(\mathbf{b})\) 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: \((\mathbf{a})\) cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) or glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right),\) (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) HCl or ethyl chloride ( \(\left.\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}\right)\) ? Explain in each case.

Indicate whether each statement is true or false: (a) The higher the temperature, the more soluble most gases are in water. (b) The higher the temperature, the more soluble most ionic solids are in water. (c) As you cool a saturated solution from high temperature to low temperature, solids start to crystallize out of solution if you achieve a supersaturated solution. (d) If you take a saturated solution and raise its temperature, you can (usually) add more solute and make the solution even more concentrated.

Indicate whether each statement is true or false: (a) If you compare the solubility of a gas in water at two different temperatures, you find the gas is more soluble at the lower temperature. (b) The solubility of most ionic solids in water decreases as the temperature of the solution increases. (c) The solubility of most gases in water decreases as the temperature increases because water is breaking its hydrogen bonding to the gas molecules as the temperature is raised. (d) Some ionic solids become less soluble in water as the temperature is raised.

The Henry's law constant for hydrogen gas \(\left(\mathrm{H}_{2}\right)\) in water at \(25^{\circ} \mathrm{C}\) is \(7.7 \times 10^{-6} \mathrm{M} / \mathrm{kPa}\) and the constant for argon \((\mathrm{Ar})\) at \(25^{\circ} \mathrm{C}\) is \(1.4 \times 10^{-5} \mathrm{M} / \mathrm{kPa}\). If the two gases are each present at 253 kPa pressure, calculate the solubility of each gas.

(a) Calculate the mass percentage of \(\mathrm{NaNO}_{3}\) in a solution containing \(13.6 \mathrm{~g}\) of \(\mathrm{NaNO}_{3}\) in \(834 \mathrm{~g}\) of water. (b) An alloy contains \(2.86 \mathrm{~g}\) of chromium per \(100 \mathrm{~kg}\) of alloy. What is the concentration of chromium in ppm?

(a) What is the mass percentage of iodine in a solution containing \(0.035 \mathrm{~mol} \mathrm{I}_{2}\) in \(125 \mathrm{~g}\) of \(\mathrm{CCl}_{4} ?\) (b) Seawater contains \(0.0079 \mathrm{~g}\) of \(\mathrm{Sr}^{2+}\) per kilogram of water. What is the concentration of \(\mathrm{Sr}^{2+}\) in \(\mathrm{ppm}\) ?

A solution is made containing \(50.0 \mathrm{~g}\) of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) in \(1000 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) Calculate \((\mathbf{a})\) the mole fraction of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) (b) the mass percent of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},(\mathbf{c})\) the molality of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\).

A solution is made containing \(20.8 \mathrm{~g}\) of phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) in \(425 \mathrm{~g}\) of ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right) .\) Calculate \((\mathbf{a})\) the mole fraction of phenol, \((\mathbf{b})\) the mass percent of phenol, (c) the molality of phenol.

What is the molarity of each of the following solutions: (a) \(15.0 \mathrm{~g}\) of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) in \(0.250 \mathrm{~mL}\) solution, (b) \(5.25 \mathrm{~g}\) of \(\mathrm{Mn}\left(\mathrm{NO}_{3}\right)_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) in \(175 \mathrm{~mL}\) of solution, \((\mathbf{c}) 35.0 \mathrm{~mL}\) of \(9.00 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) diluted to \(0.500 \mathrm{~L} ?\)

(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 \(\left(S_{8}\right)\) must be dissolved in \(100.0 \mathrm{~g}\) of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) to make a \(0.12 \mathrm{~m}\) solution?

A sulfuric acid solution containing \(697.6 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) per liter of solution has a density of \(1.395 \mathrm{~g} / \mathrm{cm}^{3} .\) Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, \((\mathbf{d})\) the molarity of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in this solution.

Ascorbic acid (vitamin 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, \((\mathbf{b})\) the mole fraction, \((\mathbf{c})\) the molality, \((\mathbf{d})\) 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 \(25.0 \mathrm{~mL}\) of \(\mathrm{CH}_{3} \mathrm{OH}\) in \(100 \mathrm{~mL}\) of \(\mathrm{CH}_{3} \mathrm{CN}\). (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 \(8.10 \mathrm{~g}\) 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) \(750 \mathrm{~mL}\) of \(0.120 \mathrm{M}\) \(\operatorname{SrBr}_{2},(\mathbf{b}) 70.0 \mathrm{~g}\) of \(0.200 \mathrm{~m} \mathrm{KCl},(\mathbf{c}) 150.0 \mathrm{~g}\) of a solution that is \(5.75 \%\) 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) \(255 \mathrm{~mL}\) of \(1.50 \mathrm{M} \mathrm{HNO}_{3}(a q)\) (b) \(50.0 \mathrm{mg}\) of an aqueous solution that is \(1.50 \mathrm{~m} \mathrm{NaCl}\), (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 \(0.180 m \mathrm{KBr},(\mathbf{c}) 1.85 \mathrm{~L}\) 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 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) \(225 \mathrm{~g}\) 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 \(0.50 M\) solution of HCl that would just neutralize \(5.5 \mathrm{~g}\) of \(\mathrm{Ba}(\mathrm{OH})_{2}\) starting with \(6.0 \mathrm{MHCl}\).

Commercial aqueous nitric acid has a density of \(1.12 \mathrm{~g} / \mathrm{mL}\) and is 3.7 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?

Caffeine \(\left(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\right)\) is a stimulant found in coffee and tea. If a solution of caffeine in the solvent chloroform \(\left(\mathrm{CHCl}_{3}\right)\) has a concentration of \(0.0500 \mathrm{~m},\) calculate \((\mathbf{a})\) the percentage of caffeine by mass, (b) the mole fraction of caffeine in the solution.

During a person's typical breathing cycle, the \(\mathrm{CO}_{2}\) concentration in the expired air rises to a peak of \(4.6 \%\) by volume. (a) Calculate the partial pressure of the \(\mathrm{CO}_{2}\) in the expired air at its peak, assuming \(101.3 \mathrm{kPa}\) pressure and a body temperature of \(37^{\circ} \mathrm{C}\). (b) What is the molarity of the \(\mathrm{CO}_{2}\) in the expired air at its peak, 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 \((\mathbf{a})\) mol percentage, \((\mathbf{b})\) molarity, assuming 101.3 kPa pressure and a body temperature of \(37^{\circ} \mathrm{C} ?\)

You make two solutions of a nonvolatile solute with a liquid solvent, \(0.01 M\) and \(1.00 M .\) Indicate whether each of the following statements is true or false. (a) The vapor pressure of the concentrated solution is higher than that of the diluted solution. (b) The osmotic pressure of the concentrated solution is higher than that of the diluted solution. (c) The boiling point of the concentrated solution is higher than that of the diluted solution. (d) The freezing point of the concentrated solution is higher than that of the diluted solution.

You make a solution of a nonvolatile solute with a liquid solvent. Indicate if each of the following statements is true or false. (a) The freezing point of the solution is unchanged by addition of the solvent. (b) The solid that forms as the solution freezes is nearly pure solute. (c) The freezing point of the solution is independent of the concentration of the solute. (d) The boiling point of the solution increases in proportion to the concentration of the solute. \((\mathbf{e})\) At any temperature, the vapor pressure of the solvent over the solution is lower than what it would be for the pure solvent.

The vapor pressure of pure water at \(70^{\circ} \mathrm{C}\) is \(31.2 \mathrm{kPa}\). The vapor pressure of water over a solution at \(70^{\circ} \mathrm{C}\) containing equal numbers of moles of water and glycerol \(\left(\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3}\right.\), a nonvolatile solute) is \(13.3 \mathrm{kPa}\). Is the solution ideal according to Raoult's law?

At \(63.5^{\circ} \mathrm{C},\) the vapor pressure of \(\mathrm{H}_{2} \mathrm{O}\) is \(23.3 \mathrm{kPa},\) and that of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is \(53.3 \mathrm{kPa}\). 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 idealsolution behavior, what is the vapor pressure of the solution at \(63.5^{\circ} \mathrm{C} ?(\mathbf{c})\) 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 \(10 \mathrm{kPa}\), and that of toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)\) is \(2.9 \mathrm{kPa}\). Assume that benzene and toluene form an ideal solution. (a) What is the composition in mole fraction of a solution that has a vapor pressure of \(4.7 \mathrm{kPa}\) at \(20^{\circ} \mathrm{C} ?(\mathbf{b})\) What is the mole fraction of benzene in the vapor above the solution described in part (a)?

Arrange the following aqueous solutions, each \(10 \%\) by mass in solute, in order of increasing boiling point: glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right),\) sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),\) sodium nitrate \(\left(\mathrm{NaNO}_{3}\right)\).