Chapter 13

Which of the following do you expect to be most water soluble, and why? \(\mathrm{C}_{10} \mathrm{H}_{8}(\mathrm{s}), \mathrm{NH}_{2} \mathrm{OH}(\mathrm{s})\) \(\mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{l}), \mathrm{CaCO}_{3}(\mathrm{s})\).

Which of the following is moderately soluble both in water and in benzene \(\left[\mathrm{C}_{6} \mathrm{H}_{6}(1)\right]\), and why? (a) 1 -butanol, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{CH}_{2} \mathrm{OH} ;\) (b) naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8} ;\) (c) hexane, \(\mathrm{C}_{6} \mathrm{H}_{14} ;\) (d) \(\mathrm{NaCl}(\mathrm{s})\)

Two of the substances listed here are highly soluble in water, two are only slightly soluble in water, and two are insoluble in water. Indicate the situation you expect for each one. (a) iodoform, \(\mathrm{CHI}_{3}\) (b) benzoic acid, (c) formic acid, (d) 1-butanol, (e) chlorobenzene, (f) propylene glycol, \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}\)

Explain the observation that all metal nitrates are water soluble but many metal sulfides are not. Among metal sulfides, which would you expect to be most soluble?

A saturated aqueous solution of \(\mathrm{NaBr}\) at \(20^{\circ} \mathrm{C}\) contains \(116 \mathrm{g} \mathrm{NaBr} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\). Express this composition in the more conventional percent by mass, that is, as grams of NaBr per 100 grams of solution.

An aqueous solution with density \(0.988 \mathrm{g} / \mathrm{mL}\) at \(20^{\circ} \mathrm{C}\) is prepared by dissolving \(12.8 \mathrm{mL} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) \((d=0.803 \mathrm{g} / \mathrm{mL})\) in enough water to produce \(75.0 \mathrm{mL}\) of solution. What is the percent \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) expressed as (a) percent by volume; (b) percent by mass; (c) percent (mass/volume)?

A certain brine has \(3.87 \%\) NaCl by mass. A \(75.0 \mathrm{mL}\) sample weighs 76.9 g. How many liters of this solution should be evaporated to dryness to obtain \(725 \mathrm{kg}\) \(\mathrm{NaCl} \)?

You are asked to prepare \(125.0 \mathrm{mL}\) of \(0.0321 \mathrm{M} \mathrm{AgNO}_{3}\) How many grams would you need of a sample known to be \(99.81 \% \mathrm{AgNO}_{3}\) by mass?

A certain vinegar is \(6.02 \%\) acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) by mass. How many grams of \(\mathrm{CH}_{3} \mathrm{COOH}\) are contained in a \(355 \mathrm{mL}\) bottle of vinegar? Assume a density of \(1.01 \mathrm{g} / \mathrm{mL}\).

6.00 M sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\) has a density of \(1.338 \mathrm{g} / \mathrm{mL} .\) What is the percent by mass of sulfuric acid in this solution?

A water sample is found to have 9.4 ppb of chloroform, \(\mathrm{CHCl}_{3} .\) How many grams of \(\mathrm{CHCl}_{3}\) would be found in a glassful \((250 \mathrm{mL})\) of this water?

An aqueous solution is \(6.00 \%\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) by mass, with \(d=0.988 \mathrm{g} / \mathrm{mL} .\) What is the molarity of \(\mathrm{CH}_{3} \mathrm{OH}\) in this solution?

A typical commercial grade aqueous phosphoric acid is \(75 \% \mathrm{H}_{3} \mathrm{PO}_{4}\) by mass and has a density of \(1.57 \mathrm{g} / \mathrm{mL}\) What is the molarity of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) in this solution?

A \(30.00 \%\) -by-mass solution of nitric acid, \(\mathrm{HNO}_{3},\) in water has a density of \(1.18 \mathrm{g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). What is the molarity of \(\mathrm{HNO}_{3}\) in this solution?

What is the molarity of \(\mathrm{CO}_{2}\) in a liter of ocean water at \(25^{\circ} \mathrm{C}\) that contains approximately \(280 \mathrm{ppm}\) of \(\mathrm{CO}_{2} ?\) The density of ocean water is \(1027 \mathrm{kg} / \mathrm{m}^{3}\).

What is the molality of para-dichlorobenzene in a solution prepared by dissolving \(2.65 \mathrm{g} \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2}\) in \(50.0 \mathrm{mL}\) benzene \((d=0.879 \mathrm{g} / \mathrm{mL}) ?\)

How many grams of iodine, \(I_{2}\), must be dissolved in \(725 \mathrm{mL}\) of carbon disulfide, \(\mathrm{CS}_{2}(d=1.261 \mathrm{g} / \mathrm{mL}),\) to produce a \(0.236 \mathrm{m}\) solution?

An aqueous solution is \(34.0 \% \mathrm{H}_{3} \mathrm{PO}_{4}\) by mass and has a density of \(1.209 \mathrm{g} / \mathrm{mL}\). What are the molarity and molality of this solution?

A \(10.00 \%\) -by-mass solution of ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) in water has a density of \(0.9831 \mathrm{g} / \mathrm{mL}\) at \(15^{\circ} \mathrm{C}\) and \(0.9804 \mathrm{g} / \mathrm{mL}\) at \(25^{\circ} \mathrm{C} .\) Calculate the molality of the ethanol-water solution at these two temperatures. Does the molality differ at the two temperatures (that is, at 15 and \(25^{\circ} \mathrm{C}\) )? Would you expect the molarities to differ? Explain.

A solution is prepared by mixing \(1.28 \mathrm{mol} \mathrm{C}_{7} \mathrm{H}_{16}\) \(2.92 \mathrm{mol} \mathrm{C}_{8} \mathrm{H}_{18},\) and \(2.64 \mathrm{mol} \mathrm{C}_{9} \mathrm{H}_{20} .\) What is the (a) mole fraction and (b) mole percent of each component of the solution?

Calculate the mole fraction of solute in the following aqueous solutions: (a) \(21.7 \% \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH},\) by mass; (b) \(0.684 m \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\) (urea).

Calculate the mole fraction of the solute in the following aqueous solutions:(a) \(0.112 \mathrm{M} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) \((d=1.006 \mathrm{g} / \mathrm{mL})\) (b) \(3.20 \%\) ethanol,by volume \((d=0.993 \mathrm{g} / \mathrm{mL}\) pure \(\left.\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}, d=0.789 \mathrm{g} / \mathrm{mL}\right)\).

What volume of glycerol,\(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}\) \((d=1.26 \mathrm{g} / \mathrm{mL})\)must be added per kilogram of water to produce a solution with 4.85 mol \% glycerol?

Two aqueous solutions of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11},\) are mixed. One solution is \(0.1487 \mathrm{M} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) and has \(d=1.018 \mathrm{g} / \mathrm{mL} ;\) the other is \(10.00 \% \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) by mass and has \(d=1.038 \mathrm{g} / \mathrm{mL} .\) Calculate the mole percent \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) in the mixed solution.

The Environmental Protection Agency has a limit of 15 ppm for the amount of lead in drinking water. If a \(1.000 \mathrm{mL}\) sample of water at \(20^{\circ} \mathrm{C}\) contains \(15 \mathrm{ppm}\) of lead, how many lead ions are there in this sample of water? What is the mole fraction of lead ion in solution?

Under an \(\mathrm{O}_{2}(\mathrm{g})\) pressure of \(1.00 \mathrm{atm}, 28.31 \mathrm{mL}\) of \(\mathrm{O}_{2}(\mathrm{g})\) dissolves in \(1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) at \(25^{\circ} \mathrm{C} .\) What will be the molarity of \(\mathrm{O}_{2}\) in the saturated solution at \(25^{\circ} \mathrm{C}\) when the \(\mathrm{O}_{2}\) pressure is 3.86 atm? (Assume that the solution volume remains at \(1.00 \mathrm{L}\).)

Natural gas consists of about \(90 \%\) methane, \(\mathrm{CH}_{4}\) Assume that the solubility of natural gas at \(20^{\circ} \mathrm{C}\) and 1 atm gas pressure is about the same as that of \(\mathrm{CH}_{4}\) \(0.02 \mathrm{g} / \mathrm{kg}\) water. If a sample of natural gas under a pressure of 20 atm is kept in contact with \(1.00 \times 10^{3} \mathrm{kg}\) of water, what mass of natural gas will dissolve?

At 1.00 atm, the solubility of \(\mathrm{O}_{2}\) in water is \(2.18 \times 10^{-3} \mathrm{M}\) at \(0^{\circ} \mathrm{C}\) and \(1.26 \times 10^{-3} \mathrm{M}\) at \(25^{\circ} \mathrm{C}\) What volume of \(\mathrm{O}_{2}(\mathrm{g}),\) measured at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm},\) is expelled when \(515 \mathrm{mL}\) of water saturated with \(\mathrm{O}_{2}\) is heated from 0 to \(25^{\circ} \mathrm{C}\) ?

The aqueous solubility at \(20^{\circ} \mathrm{C}\) of \(\mathrm{Ar}\) at \(1.00 \mathrm{atm}\) is equivalent to \(33.7 \mathrm{mL} \mathrm{Ar}(\mathrm{g}),\) measured at STP, per liter of water. What is the molarity of Ar in water that is saturated with air at 1.00 atm and \(20^{\circ} \mathrm{C}\) ? Air contains \(0.934 \%\) Ar by volume. Assume that the volume of water does not change when it becomes saturated with air.

The aqueous solubility of \(\mathrm{CO}_{2}\) at \(20^{\circ} \mathrm{C}\) and 1.00 atm is equivalent to \(87.8 \mathrm{mL} \mathrm{CO}_{2}(\mathrm{g}),\) measured at STP, per \(100 \mathrm{mL}\) of water. What is the molarity of \(\mathrm{CO}_{2}\) in water that is at \(20^{\circ} \mathrm{C}\) and saturated with air at 1.00 atm? The volume percent of \(\mathrm{CO}_{2}\) in air is \(0.0360 \% .\) Assume that the volume of the water does not change when it becomes saturated with air.

What are the partial and total vapor pressures of a solution obtained by mixing 35.8 g benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\) and \(56.7 \mathrm{g}\) toluene, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3},\) at \(25^{\circ} \mathrm{C} ? \mathrm{At} 25^{\circ} \mathrm{C}\) the vapor pressure of \(\mathrm{C}_{6} \mathrm{H}_{6}=95.1 \mathrm{mm} \mathrm{Hg} ;\) the vapor pressure of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}=28.4 \mathrm{mmHg}\).

Calculate the vapor pressure at \(25^{\circ} \mathrm{C}\) of a solution containing \(165 \mathrm{g}\) of the nonvolatile solute, glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) in \(685 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\). The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is \(23.8 \mathrm{mmHg}\).

Calculate the vapor pressure at \(20^{\circ} \mathrm{C}\) of a saturated solution of the nonvolatile solute, urea, \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2},\) in methanol, \(\mathrm{CH}_{3} \mathrm{OH} .\) The solubility is \(17 \mathrm{g}\) urea/100 \(\mathrm{mL}\) methanol. The density of methanol is \(0.792 \mathrm{g} / \mathrm{mL}\), and its vapor pressure at \(20^{\circ} \mathrm{C}\) is \(95.7 \mathrm{mmHg}\).

Styrene, used in the manufacture of polystyrene plastics, is made by the extraction of hydrogen atoms from ethylbenzene. The product obtained contains about \(38 \%\) styrene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}=\mathrm{CH}_{2}\right)\) and \(62 \%\) ethylbenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{CH}_{3}\right),\) by mass. The mixture is separated by fractional distillation at \(90^{\circ} \mathrm{C} .\) Determine the composition of the vapor in equilibrium with this \(38 \%-62 \%\) mixture at \(90^{\circ} \mathrm{C}\). The vapor pressure of ethylbenzene is \(182 \mathrm{mmHg}\) and that of styrene is \(134 \mathrm{mmHg}\).

A benzene-toluene solution with \(x_{\text {benz }}=0.300\) has a normal boiling point of \(98.6^{\circ} \mathrm{C}\). The vapor pressure of pure toluene at \(98.6^{\circ} \mathrm{C}\) is \(533 \mathrm{mm} \mathrm{Hg}\). What must be the vapor pressure of pure benzene at \(98.6^{\circ} \mathrm{C} ?\) (Assume ideal solution behavior.)

A 0.72 g sample of polyvinyl chloride (PVC) is dissolved in \(250.0 \mathrm{mL}\) of a suitable solvent at \(25^{\circ} \mathrm{C}\). The solution has an osmotic pressure of \(1.67 \mathrm{mm} \mathrm{Hg}\). What is the molar mass of the PVC?

When the stems of cut flowers are held in concentrated \(\mathrm{NaCl}(\mathrm{aq}),\) the flowers wilt. In a similar solution a fresh cucumber shrivels up (becomes pickled). Explain the basis of these phenomena.

Some fish live in saltwater environments and some in freshwater, but in either environment they need water to survive. Saltwater fish drink water, but freshwater fish do not. Explain this difference between the two types of fish.

In what volume of water must \(1 \mathrm{mol}\) of a nonelectrolyte be dissolved if the solution is to have an osmotic pressure of 1 atm at 273 K? Which of the gas laws does this result resemble?

The molecular mass of hemoglobin is \(6.86 \times 10^{4} \mathrm{u}\) What mass of hemoglobin must be present per \(100.0 \mathrm{mL}\) of a solution to exert an osmotic pressure of \(7.25 \mathrm{mmHg}\) at \(25^{\circ} \mathrm{C} ?\)

At \(25^{\circ} \mathrm{C}\) a \(0.50 \mathrm{g}\) sample of polyisobutylene (a polymer used in synthetic rubber) in \(100.0 \mathrm{mL}\) of benzene solution has an osmotic pressure that supports a \(5.1 \mathrm{mm}\) column of solution \((d=0.88 \mathrm{g} / \mathrm{mL}) .\) What is the molar mass of the polyisobutylene? (For \(\mathrm{Hg}\), \(d=13.6 \mathrm{g} / \mathrm{mL} .)\)

Use the concentration of an isotonic saline solution, \(0.92 \% \mathrm{NaCl}(\mathrm{mass} / \text { volume }),\) to determine the osmotic pressure of blood at body temperature, \(37.0^{\circ} \mathrm{C}\). [Hint: Assume that \(\mathrm{NaCl}\) is completely dissociated in aqueous solutions.]

Adding \(1.00 \mathrm{g}\) of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) to \(80.00 \mathrm{g}\) cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12},\) lowers the freezing point of the cyclohexane from 6.5 to \(3.3^{\circ} \mathrm{C}\). (a) What is the value of \(K_{f}\) for cyclohexane? (b) Which is the better solvent for molar mass determinations by freezing- point depression, benzene or cyclohexane? Explain.

Thiophene \(\left(\mathrm{fp}=-38.3 ; \mathrm{bp}=84.4^{\circ} \mathrm{C}\right)\) is a sulfur containing hydrocarbon sometimes used as a solvent in place of benzene. Combustion of a \(2.348 \mathrm{g}\) sample of thiophene produces \(4.913 \mathrm{g} \mathrm{CO}_{2}, 1.005 \mathrm{g} \mathrm{H}_{2} \mathrm{O},\) and \(1.788 \mathrm{g} \mathrm{SO}_{2} .\) When a \(0.867 \mathrm{g}\) sample of thiophene is dissolved in \(44.56 \mathrm{g}\) of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right),\) the freezing point is lowered by \(1.183^{\circ} \mathrm{C} .\) What is the molecular formula of thiophene?

An important test for the purity of an organic compound is to measure its melting point. Usually, if the compound is not pure, it begins to melt at a lower temperature than the pure compound.(a) Why is this the case, rather than the melting point being higher in some cases and lower in others?(b) Are there any conditions under which the melting point of the impure compound is higher than that of the pure compound? Explain.

Predict the approximate freezing points of \(0.10 \mathrm{m}\) solutions of the following solutes dissolved in water: (a) \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(\text { urea }) ;(\mathrm{b}) \mathrm{NH}_{4} \mathrm{NO}_{3} ;(\mathrm{c}) \mathrm{HCl} ;(\mathrm{d}) \mathrm{CaCl}_{2}\) (e) \(\mathrm{MgSO}_{4} ;\) (f) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) (ethanol); \((\mathrm{g}) \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) (acetic acid).

Calculate the van't Hoff factors of the following weak electrolyte solutions: (a) \(0.050 \mathrm{m}\) HCHO \(_{2}\), which begins to freeze at \(-0.0986^{\circ} \mathrm{C}\).(b) \(0.100 \mathrm{M} \mathrm{HNO}_{2},\) which has a hydrogen ion (and nitrite ion) concentration of \(6.91 \times 10^{-3} \mathrm{M}\).

\(\mathrm{NH}_{3}(\mathrm{aq})\) conducts electric current only weakly. The same is true for acetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(\mathrm{aq}) .\) When these solutions are mixed, however, the resulting solution conducts electric current very well. Propose an explanation.

An isotonic solution is described as \(0.92 \%\) NaCl (mass/volume). Would this also be the required concentration for isotonic solutions of other salts, such as \(\mathrm{KCl}, \mathrm{MgCl}_{2},\) or \(\mathrm{MgSO}_{4} ?\) Explain.

An aqueous solution has \(109.2 \mathrm{g} \mathrm{KOH} / \mathrm{L}\) solution. The solution density is \(1.09 \mathrm{g} / \mathrm{mL} .\) Your task is to use \(100.0 \mathrm{mL}\) of this solution to prepare \(0.250 \mathrm{m}\) KOH. What mass of which component, \(\mathrm{KOH}\) or \(\mathrm{H}_{2} \mathrm{O}\), would you add to the \(100.0 \mathrm{mL}\) of solution?