Chapter 13

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 \(20^{\circ} \mathrm{C} ?\) (b) What is the mole fraction of benzene in the vapor above the solution described in part (a)?

(a) Does a \(0.10 \mathrm{~m}\) aqueous solution of \(\mathrm{KCl}\) have a higher freezing point, a lower freezing point, or the same freezing point as a \(0.10 \mathrm{~m}\) aqueous solution of urea \(\left(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\right)\), (b) The experimental freezing point of the KCl solution is higher than that calculated assuming that \(\mathrm{KCl}\) is completely dissociated in solution. Why is this the case?

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 \(\left(\mathrm{NaNO}_{3}\right)\).

List the following aqueous solutions in order of increasing boiling point: \(0.080 \mathrm{~m} \mathrm{KBr}, 0.130 \mathrm{~m}\) urea \(\left(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\right)\), \(0.080 \mathrm{~m} \mathrm{Mg}\left(\mathrm{NO}_{2}\right)_{2}\) \(0.030 \mathrm{~m}\) phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\)

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

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 \(50.0 \mathrm{mg}\) of acetylsalicylic acid \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) in \(0.100 \mathrm{~L}\) of water at \(37^{\circ} \mathrm{C} ?\)

Adrenaline is the hormone that triggers the release of extra glucose molecules in times of stress or emergency. A solution of \(0.64 \mathrm{~g}\) of adrenaline in \(36.0 \mathrm{~g}\) of \(\mathrm{CCl}_{4}\) elevates the boiling point by \(0.49^{\circ} \mathrm{C}\). Calculate the approximate molar mass of adrenaline from this data.

Lauryl alcohol is obtained from coconut oil and is used to make detergents. A solution of \(5.00 \mathrm{~g}\) of lauryl alcohol in \(0.100 \mathrm{~kg}\) of benzene freezes at \(4.1^{\circ} \mathrm{C}\). What is the molar mass of lauryl alcohol from this data?

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 \(0.127 \mathrm{kPa}\) at \(25^{\circ} \mathrm{C}\). What is the molar mass of lysozyme?

A dilute aqueous solution of fructose in water is formed by dissolving \(1.25 \mathrm{~g}\) of the compound in water to form \(0.150 \mathrm{~L}\) of solution. The resulting solution has an osmotic pressure of \(112.8 \mathrm{kPa}\) at \(20^{\circ} \mathrm{C}\). 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 \(68.3 \mathrm{kPa}\) at \(25^{\circ} \mathrm{C}\). Calculate the van't Hoff factor, \(i\), for the solution.

(a) Do colloids made only of gases exist? Why or why not? (b) In the 1850s, 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 \((\mathbf{a})\) a gel, \((\mathbf{b})\) an emulsion, \((\mathbf{c})\) 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) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11}\) 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?

Soaps consist of compounds such as sodium stearate, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{16} \mathrm{COO}^{-} \mathrm{Na}^{+},\) that have both hydrophobic and hydrophilic parts. Consider the hydrocarbon part of sodium stearate to be the "tail" and the charged part to be the "head." (a) Which part of sodium stearate, head or tail, is more likely to be solvated by water? (b) Grease is a complex mixture of (mostly) hydrophobic compounds. Which part of sodium stearate, head or tail, is most likely to bind to grease? (c) If you have large deposits of grease that you want to wash away with water, you can see that adding sodium stearate will help you produce an emulsion. What intermolecular interactions are responsible for this?

A supersaturated solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) is made by dissolving sucrose in hot water and slowly letting the solution cool to room temperature. After a long time, the excess sucrose crystallizes out of the solution. Indicate whether each of the following statements is true or false: (a) After the excess sucrose has crystallized out, the remaining solution is saturated. (b) After the excess sucrose has crystallized out, the system is now unstable and is not in equilibrium. (c) After the excess sucrose has crystallized out, the rate of sucrose molecules leaving the surface of the crystals to be hydrated by water is equal to the rate of sucrose molecules in water attaching to the surface of the crystals.

Some soft drinks contain up to 85 ppm oxygen. (a) What is this concentration in mol/L? (b) What partial pressure of \(\mathrm{O}_{2}\) above water is needed to obtain \(85 \mathrm{ppm} \mathrm{O}_{2}\) in water at \(10^{\circ} \mathrm{C} ?\) (The Henry's law constant for \(\mathrm{O}_{2}\) at this temperature is \(\left.1.69 \times 10^{-5} \mathrm{~mol} / \mathrm{m}^{3}-\mathrm{Pa} .\right)\)

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 15.2 kPa pressure of the gas over the water at \(30^{\circ} \mathrm{C}\) is \(0.109 \mathrm{M},\) what is the Henry's law constant for radon in water at this temperature? (b) A sample consisting of various gases contains 4.5 -ppm radon (mole fraction). This gas at a total pressure of 5.07 MPa 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 ppt (parts per trillion) and 50 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 ppb. (a) Calculate the molarity of lead in a 9.0ppb solution. (b) How many grams of lead are in a swimming pool containing 9.0 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 \(1.80 \mathrm{M}\) 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 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 \(1.07 \mathrm{kPa}\) of ethanol vapor pressure at \(35^{\circ} \mathrm{C}\) ? The vapor pressure of pure ethanol at \(35^{\circ} \mathrm{C}\) is \(13.3 \mathrm{kPa}\).

A solution contains \(0.50 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) and an unknown number of moles of sodium chloride. The vapor pressure of the solution at \(29^{\circ} \mathrm{C}\) is \(3.85 \mathrm{kPa}\). The vapor pressure of pure water at this temperature is \(4.05 \mathrm{kPa}\). Calculate the number of grams of sodium chloride in the solution. (Hint: Remember that sodium chloride is a strong electrolyte.)

The normal boiling point of ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH},\) is \(78.4^{\circ} \mathrm{C}\). When \(3.26 \mathrm{~g}\) of a soluble nonelectrolyte is dissolved in \(100.0 \mathrm{~g}\) of ethanol at that temperature, the vapor pressure of the solution is \(100 \mathrm{kPa}\). What is the molar mass of the solute?

Benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) boils at \(80.1^{\circ} \mathrm{C}\) and has a density of \(0.876 \mathrm{~g} / \mathrm{mL} .\) (a) When \(0.100 \mathrm{~mol}\) of a nondissociating solute is dissolved in \(500 \mathrm{~mL}\) of \(\mathrm{C}_{6} \mathrm{H}_{6}\), the solution boils at \(79.52^{\circ} \mathrm{C}\). What is the molal boiling-point-elevation constant for \(\mathrm{C}_{6} \mathrm{H}_{6} ?\) (b) When \(10.0 \mathrm{~g}\) of a nondissociating unknown is dissolved in \(500 \mathrm{~mL}\) of \(\mathrm{C}_{6} \mathrm{H}_{6}\), the solution boils at \(79.23^{\circ} \mathrm{C}\). What is the molar mass 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 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 \(30.5 \mathrm{~m}\) in water, the external pressure is \(405 \mathrm{kPa}\). 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) A sample of hydrogen gas is generated in a closed container by reacting \(1.750 \mathrm{~g}\) of zinc metal with \(50.0 \mathrm{~mL}\) of \(1.00 \mathrm{M}\) hydrochloric 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 150 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 \(7.7 \times 10^{-6} \mathrm{~mol} / \mathrm{m}^{3}-\mathrm{Pa}\). 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)?

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 101.3 kPa. (a) What volume of \(\mathrm{CH}_{4}(g)\) under standard conditions of temperature and pressure is contained in \(4.0 \mathrm{~L}\) of a saturated solution at \(25^{\circ} \mathrm{C} ?\) (b) The solubilities (in water) of the hydrocarbons are as follows: methane \(<\) ethane \(<\) ethylene. Is this because ethylene is the most polar molecule? (c) What intermolecular interactions can these hydrocarbons have with water? (d) Draw the Lewis dot structures for the three hydrocarbons. Which of these hydrocarbons possess \(\pi\) bonds? Based on their solubilities, would you say \(\pi\) bonds are more or less polarizable than \(\sigma\) bonds? (e) Explain why NO is more soluble in water than either \(\mathrm{N}_{2}\) or \(\mathrm{O}_{2} .\) (f) \(\mathrm{H}_{2} \mathrm{~S}\) is more water-soluble than almost all the other gases in table. What intermolecular forces is \(\mathrm{H}_{2} \mathrm{~S}\) likely to have with water? \((\mathbf{g}) \mathrm{SO}_{2}\) is by far the most water-soluble gas in table. What intermolecular forces is \(\mathrm{SO}_{2}\) likely to have with water? $$ \begin{array}{lc} \hline \text { Gas } & \text { Solubility (mM) } \\ \hline \mathrm{CH}_{4} \text { (methane) } & 1.3 \\ \mathrm{C}_{2} \mathrm{H}_{6} \text { (ethane) } & 1.8 \\ \mathrm{C}_{2} \mathrm{H}_{4} \text { (ethylene) } & 4.7 \\ \mathrm{~N}_{2} & 0.6 \\ \mathrm{O}_{2} & 1.2 \\ \mathrm{NO} & 1.9 \\ \mathrm{H}_{2} \mathrm{~S} & 99 \\ \mathrm{SO}_{2} & 1476 \\ \hline \end{array} $$

At \(35^{\circ} \mathrm{C}\) the vapor pressure of acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO},\) is 47.9 \(\mathrm{kPa}\), and that of carbon disulfide, \(\mathrm{CS}_{2}\), is \(66.7 \mathrm{kPa}\). A solution composed of an equal number of moles of acetone and carbon disulfide has a vapor pressure of \(86.7 \mathrm{kPa}\) at \(35^{\circ} \mathrm{C} .(\mathbf{a})\) What would be the vapor pressure of the solution if it exhibited ideal behavior? (b) Based on the behavior of the solution, predict whether the mixing of acetone and carbon disulfide is an exothermic \(\left(\Delta H_{\text {soln }}<0\right)\) or endothermic \(\left(\Delta H_{\text {soln }}>0\right)\) process.

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 cmc depends on the substance, the solvent, and the temperature. At and above the \(\mathrm{cmc}\), the properties of the solution vary drastically. (a) The turbidity (the amount of light scattering) of solutions increases dramatically at the \(\mathrm{cmc}\). Suggest an explanation. (b) The ionic conductivity of the solution dramatically changes at the \(\mathrm{cmc}\). 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 \(\mathrm{cmc}\).