Chapter 13

(a) Does a 0.10 \(\mathrm{m}\) aqueous solution of NaCl have a higher bolling point, a lower boiling point, or the same boiling point as a 0.10 \(\mathrm{m}\) aqueous solution of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} ?(\mathbf{b})\) The experimental boiling point of the NaCl solution is lower than that calculated assuming that NaCl 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 (\textrm{NaNO} _ { 3 } ) .

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 \(\mathrm{mphenol}\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\)

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 \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) in 0.358 \(\mathrm{L}\) of water at \(25^{\circ} \mathrm{C} ?\)

Seawater contains 34 g of salts for every liter of solution. Assuming that the solute consists entirely of \(\mathrm{NaCl}\) (in fact, over 90\(\%\) of the salt is indeed NaCl), calculate the osmotic pressure of seawater at \(20^{\circ} \mathrm{C}\) .

Adrenaline is the hormone that triggers the release of extra glucose molecules in times of stress or emergency. A solution of 0.64 g of adrenaline in 36.0 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 g of lauryl alcohol in 0.100 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 gof 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 g of the compound in water to form 0.250 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?

(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.

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) Alter 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.

Most fish need at least 4 ppm dissolved \(\mathrm{O}_{2}\) in water for survival. (a) What is this concentration in mol/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 (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 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 9.0- ppb 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 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.)

The normal boiling point of ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH},\) is \(78.4^{\circ} \mathrm{C} .\) When 9.15 \(\mathrm{g}\) of a soluble nonelectrolyte is dissolved in 100.0 \(\mathrm{g}\) of ethanol at that temperature, the vapor pressure of the solution is \(7.40 \times 10^{2}\) torr. What is the molar mass of the solute?

Calculate the freezing point of a 0.100 m aqueous solution of \(\mathrm{K}_{2} \mathrm{SO}_{4},\) (a) ignoring interionic attractions, and (b) taking interionic attractions into consideration by using the van't Hoff factor (Table 13.4 )

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 molar mass of the unknown?

A lithium salt used in lubricating grease has the formula \(\mathrm{LiC}_{n} \mathrm{H}_{2 n+1} \mathrm{O}_{2} .\) The salt is soluble in water to the extent of 0.036 \(\mathrm{g}\) per 100 \(\mathrm{g}\) of water at \(25^{\circ} \mathrm{C}\) . The osmotic pressure of this solution is found to be 57.1 torr. Assuming that molality and molarity in such a dilute solution are the same and that the lithium salt is completely dissociated in the solution, determine an appropriate value of \(n\) in the formula for the salt.

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 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) A sample of hydrogen gas is generated in a closed container by reacting 2.050 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 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)?

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: 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) 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.

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 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 cmc.