Chapter 13

(a) Calculate the vapor pressure of water above a solution prepared by adding \(22.5 \mathrm{~g}\) 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 benzene and toluene form an ideal solution. (a) What is the composition in mole fractions 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)?

(a) Why does a \(0.10 m\) aqueous solution of NaCl have a higher boiling point than a \(0.10 \mathrm{~m}\) aqueous solution of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} ?\) (b) Calculate the boiling point of each solution. (c) 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?

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: \(0.120 \mathrm{~m}\) glucose, \(0.050 \mathrm{~m} \mathrm{LiBr}, 0.050 \mathrm{~m}\) \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}\)

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

Using data from Table \(13.3,\) calculate the freezing and boiling points of each of the following solutions: (a) \(0.25 \mathrm{~m}\) glucose in ethanol; (b) \(20.0 \mathrm{~g}\) of decane, \(\mathrm{C}_{10} \mathrm{H}_{22}\), in \(50.0 \mathrm{~g} \mathrm{CHCl}_{3} ;\) (c) \(3.50 \mathrm{~g}\) \(\mathrm{NaOH}\) in \(175 \mathrm{~g}\) of water, (d) 0.45 mol ethylene glycol and \(0.15 \mathrm{~mol} \mathrm{KBr}\) in \(150 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\)

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

Seawater contains \(3.4 \mathrm{~g}\) of salts for every liter of solution. Assuming that the solute consists entirely of \(\mathrm{NaCl}\) (over \(90 \%\) is), 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 \(0.64 \mathrm{~g}\) of adrenaline in \(36.0 \mathrm{~g}\) of \(\mathrm{CCl}_{4}\) elevates the boiling point by \(0.49^{\circ} \mathrm{C}\). Is the molar mass of adrenaline calculated from the boiling-point elevation in agreement with the following structural formula?

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 approximate molar mass of lauryl alcohol?

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 \(25^{\circ}\) 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) Why is there no colloid in which both the dispersed substance and the dispersing substance are gases? (b) Michael Faraday first prepared ruby-red colloids of gold particles in water that were stable indefinitely. To the unaided eye these brightly colored colloids are not distinguishable from solutions. How could you determine whether a given colored preparation is a solution or colloid?

(a) Many proteins that remain homogeneously distributed in water have molecular masses in the range of 30,000 amu and larger. In what sense is it appropriate to consider such suspensions to be colloids rather than solutions? Explain. (b) What general name is given to a colloidal dispersion of one liquid in another? What is an emulsifying agent?

Indicate whether each of the following is a hydrophilic or a hydrophobic colloid: (a) butterfat in homogenized milk, (b) hemoglobin in blood, (c) vegetable oil in a salad dressing, (d) colloidal gold particles in water.

Explain how each of the following factors helps determine the stability or instability of a colloidal dispersion: (a) particulate mass, (b) hydrophobic character, (c) charges on colloidal particles.

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

The presence of the radioactive gas radon \((\mathrm{Rn})\) in well water obtained from aquifers that lie in rock deposits 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 the concentration in (a) ppm, (b) molality. 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 \(9.0 \mathrm{ppb}\). (a) Calculate the molarity of lead in a 9.0-ppb solution. What assumption did you have to make in your calculation? (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 \(\mathrm{LiBr},(\mathrm{c})\) mass percentage of \(\mathrm{CH}_{3} \mathrm{CN}\).

A "canned heat" product used to warm chafing dishes consists of a homogeneous mixture of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and paraffin that 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 in formulating the mixture if the vapor pressure of ethanol at \(35^{\circ} \mathrm{C}\) over the mixture is to be 8 torr? 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 moles of sodium chloride in the solution. (Hint: Remember that sodium chloride is a strong electrolyte.)

Two beakers are placed in a sealed box at \(25^{\circ} \mathrm{C}\). One beaker contains \(30.0 \mathrm{~mL}\) of a \(0.050 \mathrm{M}\) aqueous solution of a nonvolatile nonelectrolyte. The other beaker contains \(30.0 \mathrm{~mL}\) of a \(0.035 \mathrm{M}\) aqueous solution of \(\mathrm{NaCl}\). The water vapor from the two solutions reaches equilibrium. (a) In which beaker does the solution level rise, and in which one does it fall? (b) What are the volumes in the two beakers when equilibrium is attained, assuming ideal behavior?

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. He is saddened to find that the solution does not provide as much protection as he hoped. Why not?

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 molecular weight 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.

Fluorocarbons (compounds that contain both carbon and fluorine) were, until recently, used as refrigerants. The compounds listed in the following table are all gases at \(25^{\circ} \mathrm{C},\) and their solubilities in water at \(25^{\circ} \mathrm{C}\) and 1 atm fluorocarbon pressure are given as mass percentages. (a) For each fluorocarbon, calculate the molality of a saturated solution. (b) Explain why the molarity of each of the solutions should be very close numerically to the molality. (c) Based on their molecular structures, account for the differences in solubility of the four fluorocarbons. (d) Calculate the Henry's law constant at \(25^{\circ} \mathrm{C}\) for CHClF \(_{2}\), and compare its magnitude to that for \(\mathrm{N}_{2}\left(6.8 \times 10^{-4} \mathrm{~mol} / \mathrm{L}-\mathrm{atm}\right) .\) Can you account for the difference in magnitude?

At ordinary body temperature \(\left(37^{\circ} \mathrm{C}\right)\) the solubility of \(\mathrm{N}_{2}\) in water in contact with air at ordinary atmospheric pressure \((1.0 \mathrm{~atm})\) is \(0.015 \mathrm{~g} / \mathrm{L}\). Air is approximately \(78 \mathrm{~mol} \% \mathrm{~N}_{2}\). Calculate the number of moles of \(\mathrm{N}_{2}\) dissolved per liter of blood, which is essentially an aqueous solution. At a depth of \(100 \mathrm{ft}\) in water, the pressure is \(4.0 \mathrm{~atm}\). What is the solubility of \(\mathrm{N}_{2}\) from air in blood at this pressure? 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) A salt such as 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 \(M\) 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 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)?

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 atm. (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) 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. $$ \begin{array}{lc} \hline \text { Gas } & \text { Solubility }(\mathrm{m} M) \\ \hline \mathrm{CH}_{4}(\text { methane }) & 1.3 \\ \mathrm{C}_{2} \mathrm{H}_{6} \text { (ethane) } & 1.8 \\ \mathrm{C}_{2} \mathrm{H}_{4} \text { (ethylene) } & 4.7 \\ \mathrm{~N}_{2} & 0.6 \\ \mathrm{O}_{2} & 1.2 \\ \mathrm{NO} & 1.9 \\ \mathrm{H}_{2} \mathrm{~S} & 99 \\ \mathrm{SO}_{2} & 1476 \end{array} $$

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 as follows: 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.