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. [Section 13.1\(]\)

Which two statements about gas mixtures are true [Section 13.1\(]\) (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, Ar \(<\mathrm{Kr}<\mathrm{Xe} .\) Which of the following statements is the best explanation? [ Section 13.3\(]\) (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 hydrogen-bond with water. (d) The heavier the gas, the more likely it is to make a saturated solution in water.

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 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\(]\)

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: (a) NaCl dissolves in water but not in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) because benzene is denser than water. (b) 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 \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right),\) , ( b ) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) in water, (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 \(\Delta H_{\text { mix }}\) ?

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

Two nonpolar organic liquids, hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) and heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right),\) 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) Hexane and heptane 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-Brionic interactions. (d) KBr has a high molar mass compared to other salts like NaCl.

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 \(\mathrm{g}\) of water. When this solution is slowly cooled to \(15^{\circ} \mathrm{C},\) no precipitate forms. (a) Is the solution that has cooled down to \(15^{\circ}\) Cunsaturated, 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?

The solubility of MnSO_ \(\cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20^{\circ} \mathrm{C}\) is 70 \(\mathrm{g}\) per 100 \(\mathrm{mL}\) of water. (a) Is 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 MnSO_ \(\cdot \mathrm{H}_{2} \mathrm{O}\) of unknown concentration, what experiment could you perform to determine whether the new solution is saturated, supersaturated, or unsaturated?

Consider water and glycerol, 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.

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, \(\mathrm{C}_{6} \mathrm{H}_{14} :(\mathbf{a}) \mathrm{CCl}_{4}\) or \(\mathrm{CaCl}_{2},(\mathbf{b})\) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) or glycerol, \(\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH},(\mathbf{c})\) octanoic \(\mathrm{acid}, \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH},\) 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 (C. \(\mathrm{H}_{12}\) ) 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 \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COONa}\right),(\mathbf{c}) \mathrm{HCl}\) 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 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.

The partial pressure of \(\mathrm{O}_{2}\) 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 \(\mathrm{O}_{2}\) in the surface water of a mountain lake saturated with air at \(20^{\circ} \mathrm{C}\) and an atmospheric pressure of 650 torr.

(a) Calculate the mass percentage of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in a solution containing 10.6 \(\mathrm{g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in 483 \(\mathrm{g}\) of 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 in a solution containing 0.035 \(\mathrm{mol}_{2}\) in 125 \(\mathrm{g}\) of \(\mathrm{CCl}_{4} ?\) (b) Seawater contains 0.0079 \(\mathrm{g}\) of Sr \(^{2+}\) per kilogram of water. What is the concentration of \(\mathrm{Sr}^{2+}\) in ppm?

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

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 (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 \(\mathrm{g}\) of Mg \(\left(\mathrm{NO}_{3}\right)_{2}\) in 250.0 \(\mathrm{mL}\) of solution, \((\mathbf{b}) 22.4 \mathrm{gof}\) \(\mathrm{LiClO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}\) in 125 \(\mathrm{mL}\) of solution, \((\mathrm{c}) 25.0 \mathrm{mL}\) 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 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 \(\mathrm{L} ?\)

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

(a) What is the molality of a solution formed by dissolving 1.12 mol of \(\mathrm{KCl}\) in 16.0 \(\mathrm{mol}\) of water? (b) How many grams of sulfur \(\left(S_{8}\right)\) must be dissolved in 100.0 g of 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 liter 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, ( \mathbf{d} ) ~ t h e ~ m o l a r i t y ~ o f ~ \(\mathrm{H}_{2} \mathrm{SO}_{4}\) 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, ( \(\mathbf{d}\) ) 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 \(\mathrm{g} / \mathrm{mL} . \mathrm{A}\) solution is made by dissolving 22.5 \(\mathrm{mL}\) of \(\mathrm{CH}_{3} \mathrm{OH}\) in 98.7 \(\mathrm{mL}\) 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 molefraction 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 \(M \operatorname{SrBr}_{2},(\mathbf{b}) 86.4 \mathrm{g}\) of \(0.180 \mathrm{m} \mathrm{KCl},(\mathrm{c}) 124.0 \mathrm{g}\) 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) 255 \(\mathrm{mL}\) of \(1.50 \mathrm{MNO}_{3}(a q),\) (b) 50.0 \(\mathrm{mg}\) of an aqueous solution that is 1.50 \(\mathrm{m} \mathrm{NaCl}_{1}\) (c) 75.0 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 L of \(1.5 \times 10^{-2} M \mathrm{KBr},\) (b) 125 \(\mathrm{g}\) of \(0.180 \mathrm{m} \mathrm{KBr},(\mathbf{c}) 1.85 \mathrm{L}\) of a solution that is 12.0\(\% \mathrm{KBr}\) by mass (the density of the solution is 1.10 \(\mathrm{g} / \mathrm{mL}\) , ( \(\mathrm{d}\) ) a 0.150 \(\mathrm{M}\) solution of \(\mathrm{KBr}\) that contains just enough KBr to precipitate 16.0 \(\mathrm{g}\) of AgBr from a solution containing 0.480 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 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; (\boldsymbol{d} ) ~ a ~ 0.50 \(\mathrm{M}\) solution of HCl that would just neutralize 5.5 \(\mathrm{g}\) of \(\mathrm{Ba}(\mathrm{OH})_{2}\) starting with 6.0 \(\mathrm{M} \mathrm{HCl}\) .

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 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 CO \(_{2}\) in the expired air at its peak, assuming 1 atm 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 (a) mol percentage, (b) molarity, assuming 1 atm pressure and a body temperature of \(37^{\circ} \mathrm{C} ?\)

You make a solution of a nonvolatile solute with a liquid solvent. Indicate whether each of the following statements is true or false. (a) The freezing point of the solution is higher than that of the pure solvent. (b) The freezing point of the solution is lower than that of the pure solvent. (c) The boiling point of the solution is higher than that of the pure solvent. (d) The boiling point of the solution is lower than that of the pure solvent.

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. ( \(\mathbf{d}\) ) The boiling point of the solution increases in proportion to the concentration of the solute. (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 \(60^{\circ} \mathrm{C}\) 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?

(a) Calculate the vapor pressure of water above a solution prepared by adding 22.5 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 ben- benzene and toluene form an ideal solution. (a) What is the composition in mole fraction 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)?