Chapter 13

(a) Does a \(0.10 \mathrm{~m}\) aqueous solution of \(\mathrm{NaCl}\) have a higher boiling point, a lower boiling point, or the same boiling point as a \(0.10 \mathrm{~m}\) aqueous solution of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) ? (b) The experimental boiling point of the \(\mathrm{NaCl}\) solution is lower than that calculated assuming that \(\mathrm{NaCl}\) is completely dissociated in solution. Why is this the case?

List the following aqueous solutions in order of increasing boiling point: \(0.120 \mathrm{~m}\) glucose, \(0.050 \mathrm{~m}\) 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 \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\).

How many grams of ethylene glycol \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\right)\) must be added to \(1.00 \mathrm{~kg}\) of water to produce a solution that freezes at \(-5.00^{\circ} \mathrm{C} ?\)

What is the freezing point of an aqueous solution that boils at \(105.0^{\circ} \mathrm{C}\) ?

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

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?

A dilute aqueous solution of an organic compound soluble in water is formed by dissolving \(2.35 \mathrm{~g}\) of the compound in water to form \(0.250 \mathrm{~L}\) of solution. The resulting solution has an osmotic pressure of \(0.605\) atm at \(25^{\circ} \mathrm{C}\). Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

The osmotic pressure of a \(0.010 \mathrm{M}\) aqueous solution of \(\mathrm{CaCl}_{2}\) is found to be \(0.674\) atm at \(25^{\circ} \mathrm{C}\). (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.

(a) Do colloids made only of gases exist? Why or why not? (b) In the 1850 's, Michael Faraday prepared ruby-red colloids of gold nanoparticles in water that are still stable today. These brightly colored colloids look like solutions. What experiment(s) could you do to determine whether a given colored preparation is a solution or colloid?

Choose the best answer: A colloidal dispersion of one liquid in another is called (a) a gel, (b) an emulsion, (c) a foam, (d) an aerosol.

An "emulsifying agent" is a compound that helps stabilize a hydrophobic colloid in a hydrophilic solvent (or a hydrophilic colloid in a hydrophobic solvent). Which of the following choices is the best emulsifying agent? (a) \(\mathrm{CH}_{3} \mathrm{COOH}\), (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\), (c) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11} \mathrm{COOH}\), (d) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11} \mathrm{COONa}\).

Aerosols are important components of the atmosphere. Does the presence of aerosols in the atmosphere increase or decrease the amount of sunlight that arrives at the Earth's surface, compared to an "aerosol-free" atmosphere? Explain your reasoning.

Proteins can be precipitated out of aqueous solution by the addition of an electrolyte; this process is called "salting out" the protein. (a) Do you think that all proteins would be precipitated out to the same extent by the same concentration of the same electrolyte? (b) If a protein has been salted out, are the protein-protein interactions stronger or weaker than they were before the electrolyte was added? (c) A friend of yours who is taking a biochemistry class says that salting out works because the waters of hydration that surround the protein prefer to surround the electrolyte as the electrolyte is added; therefore, the protein's hydration shell is stripped away, leading to protein precipitation. Another friend of yours in the same biochemistry class says that salting out works because the incoming ions adsorb tightly to the protein, making ion pairs on the protein surface, which end up giving the protein a zero net charge in water and therefore leading to precipitation. Discuss these two hypotheses. What kind of measurements would you need to make to distinguish between these two hypotheses?

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.

A saturated solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) is made by dissolving excess table sugar in a flask of water. There are \(50 \mathrm{~g}\) 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 \(50 \mathrm{~g}\) 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.

Most fish need at least \(4 \mathrm{ppm}\) dissolved \(\mathrm{O}_{2}\) in water for survival. (a) What is this concentration in \(\mathrm{mol} / \mathrm{L}\) ? (b) What partial pressure of \(\mathrm{O}_{2}\) above water is needed to obtain \(4 \mathrm{ppm} \mathrm{O}_{2}\) in water at \(10^{\circ} \mathrm{C}\) ? (The Henry's law constant for \(\mathrm{O}_{2}\) at this temperature is \(1.71 \times 10^{-3} \mathrm{~mol} / \mathrm{L}\)-atm.)

The presence of the radioactive gas radon \((\mathrm{Rn})\) in well water 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 \(30^{\circ} \mathrm{C}\) is \(7.27 \times 10^{-3} \mathrm{M}\), what is the Henry's law constant for radon in water at this temperature? (b) A sample consisting of various gases contains \(3.5 \times 10^{-6}\) mole fraction of radon. This gas at a total pressure of 32 atm is shaken with water at \(30^{\circ} \mathrm{C}\). Calculate the molar concentration of radon in the water.

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

The concentration of gold in seawater has been reported to be between \(5 \mathrm{ppt}\) (parts per trillion) and \(50 \mathrm{ppt}\). Assuming that seawater contains 13 ppt of gold, calculate the number of grams of gold contained in \(1.0 \times 10^{3}\) gal of seawater.

The maximum allowable concentration of lead in drinking water is \(9.0 \mathrm{ppb}\). (a) Calculate the molarity of lead in a 9.0\(\mathrm{ppb}\) solution. (b) How many grams of lead are in a swimming pool containing \(9.0 \mathrm{ppb}\) lead in \(60 \mathrm{~m}^{3}\) of water?

Acetonitrile \(\left(\mathrm{CH}_{3} \mathrm{CN}\right)\) is a polar organic solvent that dissolves a wide range of solutes, including many salts. The density of a \(1.80 \mathrm{M} \mathrm{LiBr}\) solution in acetonitrile is \(0.826 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the concentration of the solution in (a) molality, (b) mole fraction of \(\mathrm{LiBr}\), (c) mass percentage of \(\mathrm{CH}_{3} \mathrm{CN}\).

A "canned heat" product used to warm buffet dishes consists of a homogeneous mixture of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and paraffin, which has an average formula of \(\mathrm{C}_{24} \mathrm{H}_{50}\). What mass of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) should be added to \(620 \mathrm{~kg}\) of the paraffin to produce 8 torr of ethanol vapor pressure at \(35^{\circ} \mathrm{C}\) ? The vapor pressure of pure ethanol at \(35^{\circ} \mathrm{C}\) is 100 torr.

A solution contains \(0.115 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) and an unknown number of moles of sodium chloride. The vapor pressure of the solution at \(30^{\circ} \mathrm{C}\) is \(25.7\) torr. The vapor pressure of pure water at this temperature is \(31.8\) torr. Calculate the number of grams of sodium chloride in the solution. (Hint: Remember that sodium chloride is a strong electrolyte.)

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, which is a liquid at room temperature. He is saddened to find that the solution does not provide as much protection as he hoped. The pure ethylene glycol freezes solid in his radiator on a very cold day, while his neighbor, who did use the \(30 / 70\) mixture, has no problem. Suggest an explanation.

Carbon disulfide \(\left(\mathrm{CS}_{2}\right)\) boils at \(46.30^{\circ} \mathrm{C}\) and has a density of \(1.261 \mathrm{~g} / \mathrm{mL}\). (a) When \(0.250 \mathrm{~mol}\) of a nondissociating solute is dissolved in \(400.0 \mathrm{~mL}\) of \(\mathrm{CS}_{2}\), the solution boils at \(47.46^{\circ} \mathrm{C}\). What is the molal boiling-point-elevation constant for \(\mathrm{CS}_{2}\) ? (b) When \(5.39 \mathrm{~g}\) of a nondissociating unknown is dissolved in \(50.0 \mathrm{~mL}\) of \(\mathrm{CS}_{2}\), the solution boils at \(47.08^{\circ} \mathrm{C}\). What is the molecular weight of the unknown?

At ordinary body temperature \(\left(37^{\circ} \mathrm{C}\right)\), the solubility of \(\mathrm{N}_{2}\) in water at ordinary atmospheric pressure ( \(1.0 \mathrm{~atm})\) is \(0.015 \mathrm{~g} / \mathrm{L}\). Air is approximately \(78 \mathrm{~mol} \% \mathrm{~N}_{2}\). (a) Calculate the number of moles of \(\mathrm{N}_{2}\) dissolved per liter of blood, assuming blood is a simple aqueous solution. (b) At a depth of \(100 \mathrm{ft}\) in water, the external pressure is \(4.0 \mathrm{~atm}\). What is the solubility of \(\mathrm{N}_{2}\) from air in blood at this pressure? (c) If a scuba diver suddenly surfaces from this depth, how many milliliters of \(\mathrm{N}_{2}\) gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood?

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) \(\mathrm{A}\) salt such as \(\mathrm{NaBr}\) is insoluble in most polar nonaqueous solvents such as acetonitrile \(\left(\mathrm{CH}_{3} \mathrm{CN}\right)\) or nitromethane \(\left(\mathrm{CH}_{3} \mathrm{NO}_{2}\right)\), but salts of large cations, such as tetramethylammonium bromide \(\left[\left(\mathrm{CH}_{3}\right)_{4} \mathrm{NBr}\right]\), 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.

(a) A sample of hydrogen gas is generated in a closed container by reacting \(2.050 \mathrm{~g}\) of zinc metal with \(15.0 \mathrm{~mL}\) of \(1.00 \mathrm{M}\) 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 in the container is \(122 \mathrm{~mL}\). Calculate the partial pressure of the hydrogen gas in this volume at \(25^{\circ} \mathrm{C}\), ignoring any solubility of the gas in the solution. (c) The Henry's law constant for hydrogen in water at \(25^{\circ} \mathrm{C}\) is \(7.8 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\)-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 \(25^{\circ} \mathrm{C}\) under a total pressure of gas and water vapor of \(1 \mathrm{~atm}\). (a) What volume of \(\mathrm{CH}_{4}(\mathrm{~g})\) under standard conditions of temperature and pressure is contained in \(4.0 \mathrm{~L}\) of a saturated solution at \(25^{\circ} \mathrm{C}\) ? (b) Explain the variation in solubility among the hydrocarbons listed (the first three compounds), based on their molecular structures and intermolecular forces. (c) Compare the solubilities of \(\mathrm{O}_{2}, \mathrm{~N}_{2}\), and \(\mathrm{NO}\), and account for the variations based on molecular structures and intermolecular forces. (d) Account for the much larger values observed for \(\mathrm{H}_{2} \mathrm{~S}\) and \(\mathrm{SO}_{2}\) as compared with the other gases listed. (e) Find several pairs of substances with the same or nearly the same molecular masses (for example, \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{N}_{2}\) ), and use intermolecular interactions to explain the differences in their solubilities.

A small cube of lithium (density \(=0.535 \mathrm{~g} / \mathrm{cm}^{3}\) ) measuring \(1.0 \mathrm{~mm}\) on each edge is added to \(0.500 \mathrm{~L}\) of water. The following reaction occurs: $$ 2 \mathrm{Li}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{LiOH}(a q)+\mathrm{H}_{2}(g) $$ What is the freezing point of the resultant solution, assuming that the reaction goes to completion?

At \(35^{\circ} \mathrm{C}\) the vapor pressure of acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\), is 360 torr, and that of chloroform, \(\mathrm{CHCl}_{3}\), is 300 torr. Acetone and chloroform can form very weak hydrogen bonds between one another; the chlorines on the carbon give the carbon a sufficient partial positive charge to enable this behavior: CC(=O)NC(Cl)(Cl)Cl A solution composed of an equal number of moles of acetone and chloroform has a vapor pressure of 250 torr at \(35^{\circ} \mathrm{C}\). (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 \(\left(\Delta H_{\text {soln }}<0\right.\) ) or endothermic \(\left(\Delta H_{\text {soln }}>0\right)\) process. (d) Would you expect the same vaporpressure behavior for acetone and chloromethane \(\left(\mathrm{CH}_{3} \mathrm{Cl}\right)\) ? Explain.

Compounds like sodium stearate, called "surfactants" in general, can form structures known as micelles in water, once the solution concentration reaches the value known as the critical micelle concentration (cmc). Micelles contain dozens to hundreds of molecules. The cme depends on the substance, the solvent, and the temperature. At and above the cmc, the properties of the solution vary drastically. (a) The turbidity (the amount of light scattering) of solutions increases dramatically at the cmc. Suggest an explanation. (b) The ionic conductivity of the solution dramatically changes at the cme. Suggest an explanation. (c) Chemists have developed fluorescent dyes that glow brightly only when the dye molecules are in a hydrophobic environment. Predict how the intensity of such fluorescence would relate to the concentration of sodium stearate as the sodium stearate concentration approaches and then increases past the cme.