Chapter 13

Describe the differences among solutions that are unsaturated, saturated, and supersaturated in terms of amount of solute, and in terms of \(Q\) and \(K_{\mathrm{c}}\).

State Henry's law. Name three factors that govern the solubility of a gas in a liquid.

In general, how does the water solubility of most ionic compounds change as the temperature is increased?

How does the solubility of gases in liquids change with increased temperature? Explain why.

Define molality. How does it differ from molarity?

Explain the difference between the mass fraction and the mole fraction of solute in a solution.

Explain why the vapor pressure of a solvent is lowered by the presence of a nonvolatile solute.

Explain why the vapor pressure of a solvent is lowered by the presence of a nonvolatile solute.

Explain how reverse osmosis works.

How do colloids differ from suspensions?

Explain why the Tyndall effect is not observed with solutions.

Why would the same solid readily dissolve in one liquid and be almost insoluble in another liquid? Give an example of such behavior.

Which of these general types of substances would you expect to dissolve readily in water? Explain why. (a) Alcohols (b) Hydrocarbons (c) Metals (d) Nonpolar molecules (e) Polar molecules (f) Salts

Beakers (a), (b), and (c) are representations of tiny sections (not to scale) of mixtures made from pure glycerol and pure cyclohexane. Select which beaker gives proper representation of the result when the two pure substances are mixed.

Simple acids such as formic acid, \(\mathrm{HCOOH},\) and acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH},\) are very soluble in water; however, fatty acids such as stearic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{COOH},\) and palmitic acid, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{14} \mathrm{COOH},\) are water- insoluble. Based on what you know about the solubility of alcohols, explain the solubility of these organic acids.

If a solution of a certain salt in water is saturated at some temperature and a few crystals of the salt are added to the solution, what happens? What happens if the same quantity of the same salt crystals is added to an unsaturated solution of the salt?

The lattice energy of \(\mathrm{CaCl}_{2}\) is \(-2258 \mathrm{~kJ} / \mathrm{mol}\), and the total enthalpy of hydration of its ions is \(-2175 \mathrm{~kJ} / \mathrm{mol}\). Determine whether the process of dissolving \(\mathrm{CaCl}_{2}\) in water is endothermic or exothermic.

Calculate the enthalpy of solution of \(\mathrm{CaBr}_{2}\) given that its lattice energy is \(-1984 \mathrm{~kJ} / \mathrm{mol}\) and the total enthalpy of hydration of its ions is \(-1827 \mathrm{~kJ} / \mathrm{mol}\).

Given these data, calculate the enthalpy of hydration of \(\mathrm{I}^{-}\). Lattice energy of \(\mathrm{LiI}=-759 \mathrm{~kJ} / \mathrm{mol}\); enthalpy of solution of \(\mathrm{LiI}=-63.3 \mathrm{~kJ} / \mathrm{mol} ;\) hydration enthalpy of \(\mathrm{Li}^{+}=-558 \mathrm{~kJ} / \mathrm{mol}\).

Describe what happens when an ionic solid dissolves in water. Sketch an illustration that includes at least three positive ions, three negative ions, and a dozen or so water molecules in the vicinity of the ions.

A saturated solution of \(\mathrm{NH}_{4} \mathrm{Cl}\) was prepared by adding solid \(\mathrm{NH}_{4} \mathrm{Cl}\) to water until no more solid \(\mathrm{NH}_{4} \mathrm{Cl}\) would dissolve. The resulting mixture felt very cold and had a layer of undissolved \(\mathrm{NH}_{4} \mathrm{Cl}\) on the bottom. When the mixture reached room temperature, no solid \(\mathrm{NH}_{4} \mathrm{Cl}\) was present. Explain what happened. Was the solution still saturated? Explain your answer.

The partial pressure of \(\mathrm{O}_{2}\) in your lungs is about \(100 \mathrm{mmHg} .\) Calculate the concentration of \(\mathrm{O}_{2}\) (in grams per liter) that can dissolve in water at \(37^{\circ} \mathrm{C}\) when the \(\mathrm{O}_{2}\) partial pressure is \(100 . \mathrm{mmHg} .\) The Henry's law constant for \(\mathrm{O}_{2}\) at \(37{ }^{\circ} \mathrm{C}\) is \(1.5 \times 10^{-6} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{mmHg}^{-1}\).

The Henry's law constant for nitrogen in blood serum is approximately \(8 \times 10^{-7} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{mmHg}^{-1}\). Calculate the \(\mathrm{N}_{2}\) concentration in a diver's blood at a depth where the total pressure is 2.5 atm. The air the diver is breathing is \(78 \% \mathrm{~N}_{2}\) by volume.

The Henry's law constant for \(\mathrm{N}_{2}\) in water at \(25^{\circ} \mathrm{C}\) is \(8.4 \times 10^{-7} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{mmHg}^{-1}\). Calculate the solubility of \(\mathrm{N}_{2}\) in \(\mathrm{mol} / \mathrm{L}\) if its partial pressure is \(1520 \mathrm{mmHg}\). Calculate the solubility when the \(\mathrm{N}_{2}\) partial pressure is 20. mmHg.

Which is the highest solute concentration: \(50 \mathrm{ppm}\), \(500 \mathrm{ppb},\) or \(0.05 \%\) by weight?

Show mathematically how 1 ppb is equivalent to \(1 \mu \mathrm{g} / 1 \mathrm{~kg}\).

Show mathematically how 1 ppm is equivalent to \(1 \mathrm{mg} / 1 \mathrm{~kg}\).

Calculate the mass (g) of ethanol in \(750 . \mathrm{mL}\) of a \(12 \%\) ethanol solution. (Assume its density is the same as that of water.)

Calculate the mass (g) of sucrose in \(1.0 \mathrm{~kg}\) of a \(0.25 \%\) sucrose solution.

A sample of water contains 0.010 ppm lead ions, \(\mathrm{Pb}^{2+}\). (a) Calculate the mass of lead ions per liter in this solution. (Assume the density of the water solution is \(1.0 \mathrm{~g} / \mathrm{mL}\).) (b) Calculate the mass fraction of lead in ppb.

A liquid sample of lead-based paint contains 60.5 ppm lead. The density of the paint is \(10.0 \mathrm{lb} / \mathrm{gal}\). Calculate the mass of lead (in grams) that would be present in \(50 . \mathrm{gal}\) of this paint.

Calculate the mass in grams of solute required to prepare each of these solutions. (a) \(750 \cdot \mathrm{mL}\) of \(4.00-\mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) (b) \(1.50 \mathrm{~L}\) of \(0.750-\mathrm{M} \mathrm{KCl}\) (c) \(150 . \mathrm{mL}\) of \(0.350-\mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\)

Calculate the mass in grams of solute needed to prepare each of these solutions. (a) \(250 . \mathrm{mL}\) of \(0.50-\mathrm{M} \mathrm{NaCl}\) (b) \(0.50 \mathrm{~L}\) of 0.15 -M sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) (c) \(200 . \mathrm{mL}\) of \(0.20-\mathrm{M} \mathrm{NaHCO}_{3}\)

Calculate the molarity of the solute in a solution containing (a) \(14.2 \mathrm{~g} \mathrm{KCl}\) in \(250 . \mathrm{mL}\) solution. (b) \(5.08 \mathrm{~g} \mathrm{~K}_{2} \mathrm{CrO}_{4}\) in \(150 . \mathrm{mL}\) solution. (c) \(0.799 \mathrm{~g} \mathrm{KMnO}_{4}\) in \(400 . \mathrm{mL}\) solution. (d) \(15.0 \mathrm{~g} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) in \(500 . \mathrm{mL}\) solution.

Calculate the molarity of the solute in a solution containing (a) \(6.18 \mathrm{~g} \mathrm{MgNH}_{4} \mathrm{PO}_{4}\) in \(250 . \mathrm{mL}\) solution. (b) \(16.8 \mathrm{~g} \mathrm{NaCH}_{3} \mathrm{COO}\) in \(300 . \mathrm{mL}\) solution. (c) \(2.50 \mathrm{~g} \mathrm{CaC}_{2} \mathrm{O}_{4}\) in \(750 . \mathrm{mL}\) solution. (d) \(2.20 \mathrm{~g}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) in \(400 . \mathrm{mL}\) solution.

Concentrated sulfuric acid has a density of \(1.84 \mathrm{~g} / \mathrm{cm}^{3}\) and is \(18 \mathrm{M}\). Calculate the weight percent of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in the solution.

Concentrated nitric acid is a \(70.0 \%\) solution of nitric acid, \(\mathrm{HNO}_{3},\) in water. The density of the solution is \(1.41 \mathrm{~g} / \mathrm{mL}\) at \(25^{\circ} \mathrm{C} .\) Calculate the molarity of nitric acid in this solution.

A 0.6-mL teardrop contains \(4 \mathrm{mg} \mathrm{NaCl}\). Calculate the molarity of \(\mathrm{NaCl}\) in the teardrop.

Consider a \(13.0 \%\) solution of sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), whose density is \(1.090 \mathrm{~g} / \mathrm{mL}\). (a) Calculate the molarity of this solution. (b) To what volume should \(100 . \mathrm{mL}\) of this solution be diluted to prepare a 1.10 -M solution?

You want to prepare a \(1.0 \mathrm{~mol} / \mathrm{kg}\) solution of ethylene glycol, \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{OH})_{2},\) in water. Calculate the mass of ethylene glycol you would need to mix with \(950 . \mathrm{g}\) water.

You need a \(0.050 \mathrm{~mol} / \mathrm{kg}\) aqueous solution of methanol, \(\mathrm{CH}_{3} \mathrm{OH}\). Calculate the mass of methanol you would need to dissolve in \(500 . \mathrm{g}\) water to make this solution.

A \(23.2 \%\) by weight aqueous solution of sucrose has a density of \(1.127 \mathrm{~g} / \mathrm{mL}\). Calculate the molarity of sucrose in this solution.

Calculate the mass \((\mathrm{g})\) of \(\mathrm{KI}\) required to prepare \(100 . \mathrm{mL}\) of \(0.0200-\mathrm{M}\) KI. How many milliliters of this solution are required to produce \(250 . \mathrm{mL}\) of \(0.00100-\mathrm{M} \mathrm{KI} ?\)

A 12 -oz \((355-\mathrm{mL})\) Pepsi contains \(38.9 \mathrm{mg}\) caffeine (molar mass \(=194.2 \mathrm{~g} / \mathrm{mol}\) ). Assume that the Pepsi, mainly water, has a density of \(1.01 \mathrm{~g} / \mathrm{mL}\). For such a Pepsi, calculate: (a) its caffeine concentration in ppm; (b) its molarity of caffeine; and (c) the molality of caffeine.

Calculate the mass fraction and the weight percent of the solute in each of these solutions: (a) \(20.7 \mathrm{~g} \mathrm{NaCl}\) in \(175 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\). (b) \(1.45 \mathrm{~g}\) ethanol in \(10.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\). (c) \(20.0 \mathrm{~g} \mathrm{CS}_{2}\) in \(45.0 \mathrm{~g} \mathrm{CHCl}_{3} .\) (d) \(4.00 \mathrm{~mL}\) benzene \((d=0.877 \mathrm{~g} / \mathrm{mL})\) in \(120 . \mathrm{g}\) diethyl ether.

Calculate the mass fraction and the weight percent of the solute in each of these solutions: (a) \(14.0 \mathrm{~g} \mathrm{~K}_{2} \mathrm{CrO}_{4}\) in \(225 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\). (b) \(4.56 \mathrm{~g}\) ethanol in \(50.0 \mathrm{~g}\) benzene. (c) \(15.0 \mathrm{~g}\) methanol in \(89.0 \mathrm{~g}\) ethanol. (d) \(14.5 \mathrm{~mL}\) ethylene glycol \((d=1.11 \mathrm{~g} / \mathrm{mL})\) in \(200 . \mathrm{g} \mathrm{H}_{2} \mathrm{O}\).

Calculate the boiling point of a solution containing \(0.200 \mathrm{~mol}\) of a nonvolatile nonelectrolyte solute in 100. g benzene. The normal boiling point of benzene is \(80.10{ }^{\circ} \mathrm{C},\) and \(K_{\mathrm{b}}=2.53{ }^{\circ} \mathrm{C} \mathrm{kg} / \mathrm{mol}\)

List these aqueous solutions in order of decreasing freezing point. (a) \(0.10 \mathrm{~mol}\) methanol/kg (b) \(0.10 \mathrm{~mol} \mathrm{KCl} / \mathrm{kg}\) (c) \(0.080 \mathrm{~mol} \mathrm{BaCl}_{2} / \mathrm{kg}\) (d) \(0.040 \mathrm{~mol} \mathrm{Na}_{2} \mathrm{SO}_{4} / \mathrm{kg}\) (Assume that all of the salts dissociate completely into their ions in solution.)

Place these aqueous solutions in order of increasing boiling point. (a) \(0.10 \mathrm{~mol} \mathrm{KCl} / \mathrm{kg}\) (b) \(0.10 \mathrm{~mol}\) glucose \(/ \mathrm{kg}\) (c) \(0.080 \mathrm{~mol} \mathrm{MgCl}_{2} / \mathrm{kg}\) (Assume that all of the salts dissociate completely into their ions in solution.)

Calculate the boiling point and the freezing point of these solutions at \(760 \mathrm{mmHg}\). (a) \(20.0 \mathrm{~g}\) citric acid, \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\), in \(100.0 \mathrm{~g}\) water (b) \(3.00 \mathrm{~g} \mathrm{CH}_{3} \mathrm{I}\) in \(20.0 \mathrm{~g}\) benzene \(\left(K_{\mathrm{b}}\right.\) benzene \(=\) \(2.53^{\circ} \mathrm{C} \mathrm{kg} / \mathrm{mol} ; K_{\mathrm{f}} \text { benzene } \left.=-5.10^{\circ} \mathrm{C} \mathrm{kg} / \mathrm{mol}\right)\)