Chapter 14

Suppose you dissolve \(2.56 \mathrm{g}\) of succinic acid, \(\mathrm{C}_{2} \mathrm{H}_{4}\left(\mathrm{CO}_{2} \mathrm{H}\right)_{2},\) in \(500 .\) mL of water. Assuming that the density of water is \(1.00 \mathrm{g} / \mathrm{cm}^{3},\) calculate the molality, mole fraction, and weight percentage of acid in the solution.

Assume you dissolve \(45.0 \mathrm{g}\) of camphor, \(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O},\) in \(425 \mathrm{mL}\) of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\). Calculate the molality, mole fraction, and weight percent of camphor in this solution. (The density of ethanol is \(0.785 \mathrm{g} / \mathrm{mL}\).)

Fill in the blanks in the table. Aqueous solutions are assumed. $$\begin{array}{llll} \hline & & \text { Weight } & \text { Mole } \\ \text { Compound } & \text { Molality } & \text { Percent } & \text { Fraction } \\\ \hline \mathrm{KN} 0_{3} & & 10.0 & \\ \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H} & 0.0183 & & \\ \mathrm{H} 0 \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} & & 18.0 & \\ \hline \end{array}$$

What mass of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) must you add to \(125 \mathrm{g}\) of water to prepare \(0.200 \mathrm{m} \mathrm{Na}_{2} \mathrm{CO}_{3} ?\) What is the mole fraction of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) in the resulting solution?

You want to prepare a solution that is \(0.0512 \mathrm{m}\) in NaNO \(_{3} .\) What mass of \(\mathrm{NaNO}_{3}\) must be added to \(500 .\) g of water? What is the mole fraction of \(\mathrm{NaNO}_{3}\) in the solution?

You wish to prepare an aqueous solution of glycerol, \(\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3},\) in which the mole fraction of the solute is \(0.093 .\) What mass of glycerol must you add to \(425 \mathrm{g}\) of water to make this solution? What is the molality of the solution?

You want to prepare an aqueous solution of ethylene glycol, HOCH \(_{2} \mathrm{CH}_{2} \mathrm{OH},\) in which the mole fraction of solute is \(0.125 .\) What mass of ethylene glycol, in grams, should you combine with 955 g of water? What is the molality of the solution?

Hydrochloric acid is sold as a concentrated aqueous solution. If the molarity of commercial HCl is 12.0 and its density is \(1.18 \mathrm{g} / \mathrm{cm}^{3},\) calculate the following: (a) the molality of the solution (b) the weight percent of HCl in the solution

Concentrated sulfuric acid has a density of \(1.84 \mathrm{g} / \mathrm{cm}^{3}\) and is \(95.0 \%\) by weight \(\mathrm{H}_{2} \mathrm{SO}_{4} .\) What is the molality of this acid? What is its molarity?

Silver ion has an average concentration of 28 ppb (parts per billion) in U.S. water supplies. (a) What is the molality of the silver ion? (b) If you wanted \(1.0 \times 10^{2} \mathrm{g}\) of silver and could recover it chemically from water supplies, what volume of water in liters, would you have to treat? (Assume the density of water is \(1.0 \mathrm{g} / \mathrm{cm}^{3} .\) )

Which pairs of liquids will be miscible? (a) \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) (b) \(\mathrm{C}_{6} \mathrm{H}_{6}\) (benzene) and \(\mathrm{CCl}_{4}\) (c) \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)

Acetone, \(\mathrm{CH}_{3} \mathrm{COCH}_{3}\), is quite soluble in water. Explain why this should be so. (EQUATION CAN'T COPY)

Use the following data to calculate the enthalpy of solution of sodium perchlorate, \(\mathrm{NaClO}_{4}\): $$\begin{aligned} \Delta H_{f}^{\circ}(\mathrm{s}) &=-382.9 \mathrm{kJ} / \mathrm{mol} \\\ \Delta H_{f}^{\circ}(\mathrm{aq}, 1 m) &=-369.5 \mathrm{kJ} / \mathrm{mol} \end{aligned}$$

You make a saturated solution of \(\mathrm{NaCl}\) at \(25^{\circ} \mathrm{C} .\) No solid is present in the beaker holding the solution. What can be done to increase the amount of dissolved \(\mathrm{NaCl}\) in this solution? (See Figure 14.12.) (a) Add more solid NaCl. (b) Raise the temperature of the solution. (c) Raise the temperature of the solution and add some NaCl. (d) Lower the temperature of the solution and add some NaCl.

Some lithium chloride, LiCl, is dissolved in 100 mL of water in one beaker and some \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) is dissolved in 100 mL of water in another beaker. Both are at \(10^{\circ} \mathrm{C}\) and both are saturated solutions; some solid remains undissolved in each beaker. Describe what you would observe as the temperature is raised. The following data are available to you from a handbook of chemistry: $$\begin{array}{lll} \hline & \text { Solubility }(\mathrm{g} / 100 \mathrm{mL}) \\ \hline \text { Compound } & 10^{\circ} \mathrm{C} & 40^{\circ} \mathrm{C} \\ \hline \mathrm{Li}_{2} \mathrm{SO}_{4} & 35.5 & 33.7 \\\ \mathrm{LiCl} & 74.5 & 89.8 \\ \hline \end{array}$$

In each pair of ionic compounds, which is more likely to have the more negative heat of hydration? Briefly explain your reasoning in each case. (a) LiF or RbF (b) \(\mathrm{KNO}_{3}\) or \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) (c) \(\operatorname{CsBr}\) or \(\operatorname{CuBr}_{2}\)

When salts of \(\mathrm{Mg}^{2+}, \mathrm{Ca}^{2+},\) and \(\mathrm{Be}^{2+}\) are placed in water, the positive ion is hydrated (as is the negative ion). Which of these three cations is most strongly hydrated? Which one is least strongly hydrated?

The Henry's law constant for \(\mathrm{O}_{2}\) in water at \(25^{\circ} \mathrm{C}\) is 1.66 \(\times 10^{-6} \mathrm{M} / \mathrm{mm}\) Hg. Which of the following is a reasonable constant when the temperature is \(50^{\circ} \mathrm{C}\) ? Explain the reason for your choice. (a) \(8.80 \times 10^{-7} \mathrm{M} / \mathrm{mm} \mathrm{Hg}\) (b) \(3.40 \times 10^{-6} \mathrm{M} / \mathrm{mm} \mathrm{Hg}\) (c) \(1.66 \times 10^{-6} \mathrm{M} / \mathrm{mm} \mathrm{Hg}\) (d) \(8.40 \times 10^{-5} \mathrm{M} / \mathrm{mm} \mathrm{Hg}\)

An unopened soda can has an aqueous \(\mathrm{CO}_{2}\) concentration of \(0.0506 \mathrm{M}\) at \(25^{\circ} \mathrm{C} .\) What is the pressure of \(\mathrm{CO}_{2}\) gas in the can?

A \(35.0-\mathrm{g}\) sample of ethylene glycol, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH},\) is dissolved in \(500.0 \mathrm{g}\) of water. The vapor pressure of water at \(32^{\circ} \mathrm{C}\) is \(35.7 \mathrm{mm}\) Hg. What is the vapor pressure of the water-ethylene glycol solution at \(32^{\circ} \mathrm{C} ?\) (Ethylene glycol is nonvolatile.)

Pure iodine \((105 \mathrm{g})\) is dissolved in \(325 \mathrm{g}\) of \(\mathrm{CCl}_{4}\) at \(65^{\circ} \mathrm{C}\) Given that the vapor pressure of \(\mathrm{CCl}_{4}\) at this temperature is \(531 \mathrm{mm}\) Hg, what is the vapor pressure of the \(\mathrm{CCl}_{4}-\mathrm{I}_{2}\) solution at \(65^{\circ} \mathrm{C} ?\) (Assume that \(\mathrm{I}_{2}\) does not contribute to the vapor pressure.)

Anthracene, a hydrocarbon obtained from coal, has an empirical formula of \(\mathrm{C}_{7} \mathrm{H}_{5} .\) To find its molecular formula you dissolve \(0.500 \mathrm{g}\) in \(30.0 \mathrm{g}\) of benzene. The boiling point of the pure benzene is \(80.10^{\circ} \mathrm{C},\) whereas the solution has a boiling point of \(80.34^{\circ} \mathrm{C} .\) What is the molecular formula of anthracene?

The melting point of pure biphenyl \(\left(\mathrm{C}_{12} \mathrm{H}_{10}\right)\) is found to be \(70.03^{\circ} \mathrm{C} .\) If \(0.100 \mathrm{g}\) of naphthalene is added to \(10.0 \mathrm{g}\) of biphenyl, the freezing point of the mixture is \(69.40^{\circ} \mathrm{C} .\) If \(K_{\mathrm{fp}}\) for biphenyl is \(-8.00^{\circ} \mathrm{C} / \mathrm{m},\) what is the molar mass of naphthalene?

If \(52.5 \mathrm{g}\) of \(\mathrm{LiF}\) is dissolved in \(306 \mathrm{g}\) of water, what is the expected freezing point of the solution? (Assume the van't Hoff factor, \(i\), for LiF is \(2 .\) )

To make homemade ice cream, you cool the milk and cream by immersing the container in ice and a concentrated solution of rock salt (NaCl) in water. If you want to have a water-salt solution that freezes at \(-10 .^{\circ} \mathrm{C},\) what mass of NaCl must you add to \(3.0 \mathrm{kg}\) of water? (Assume the van't Hoff factor, \(i,\) for \(\mathrm{NaCl}\) is \(1.85 .\) )

List the following aqueous solutions in order of increasing melting point. (The last three are all assumed to dissociate completely into ions in water.) (a) \(0.1 \mathrm{m}\) sugar (b) \(0.1 \mathrm{m} \mathrm{NaCl}\) (c) \(0.08 \mathrm{m} \mathrm{CaCl}_{2}\) (d) \(0.04 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4}\)

Arrange the following aqueous solutions in order of decreasing freezing point. (The last three are all assumed to dissociate completely into ions in water.) (a) \(0.20 \mathrm{m}\) ethylene glycol (nonvolatile, nonelectrolyte) (b) \(0.12 \mathrm{m} \mathrm{K}_{2} \mathrm{SO}_{4}\) (c) \(0.10 \mathrm{mgCl}_{2}\) (d) \(0.12 \mathrm{m} \mathrm{KBr}\)

Estimate the osmotic pressure of human blood at \(37^{\circ} \mathrm{C}\) Assume blood is isotonic with a \(0.154 \mathrm{M} \mathrm{NaCl}\) solution, and assume the van't Hoff factor, \(i,\) is 1.9 for \(\mathrm{NaCl}\).

An aqueous solution containing \(1.00 \mathrm{g}\) of bovine insulin (a protein, not ionized) per liter has an osmotic pressure of \(3.1 \mathrm{mm}\) Hg at \(25^{\circ} \mathrm{C} .\) Calculate the molar mass of bovine insulin.

Calculate the osmotic pressure of a \(0.0120 \mathrm{M}\) solution of NaCl in water at \(0^{\circ}\) C. Assume the van't Hoff factor, \(i\), is 1.94 for this solution.

When solutions of \(\mathrm{BaCl}_{2}\) and \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) are mixed, the mixture becomes cloudy. After a few days, a white solid is observed on the bottom of the beaker with a clear liquid above it. (a) Write a balanced equation for the reaction that occurs. (b) Why is the solution cloudy at first? (c) What happens during the few days of waiting?

The dispersed phase of a certain colloidal dispersion consists of spheres of diameter \(1.0 \times 10^{2} \mathrm{nm}\) (a) What is the volume \(\left(V=\frac{4}{3} \pi r^{3}\right)\) and surface area \((A=\) \(\left.4 \pi r^{2}\right)\) of each sphere? (b) How many spheres are required to give a total volume of \(1.0 \mathrm{cm}^{3} ?\) What is the total surface area of these spheres in square meters?

Which salt, \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) or \(\mathrm{Cs}_{2} \mathrm{SO}_{4}\), is expected to have the more exothermic heat of hydration? Explain briefly.

(a) Which aqueous solution is expected to have the higher boiling point: \(0.10 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4}\) or \(0.15 \mathrm{m}\) sugar? (b) For which aqueous solution is the vapor pressure of water higher: \(0.30 \mathrm{m} \mathrm{NH}_{4} \mathrm{NO}_{3}\) or \(0.15 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4} ?\)

Arrange the following aqueous solutions in order of (i) increasing vapor pressure of water and (ii) increasing boiling point. (a) \(0.35 \mathrm{m} \mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) (a nonvolatile solute) (b) \(0.50 m\) sugar (c) \(0.20 \mathrm{m}\) KBr (a strong electrolyte) (d) \(0.20 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4}\) (a strong electrolyte)

Dimethylglyoxime [DMG, (CH \(\left._{3} \mathrm{CNOH} \text { ) }_{2}\right]\) is used as a reagent to precipitate nickel ion. Assume that \(53.0 \mathrm{g}\) of DMG has been dissolved in \(525 \mathrm{g}\) of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) (IMAGE CAN'T COPY) The red, insoluble compound formed between nickel(II) ion and dimethylglyoxime (DMG) is precipitated when DMG is added to a basic solution of \(\mathrm{Ni}^{2+}(\mathrm{aq})\) (a) What is the mole fraction of DMG? (b) What is the molality of the solution? (c) What is the vapor pressure of the ethanol over the solution at ethanol's normal boiling point of \(78.4^{\circ} \mathrm{C} ?\) (d) What is the boiling point of the solution? (DMG does not produce ions in solution.) \(\left(K_{\mathrm{bp}} \text { for ethanol }=\right.\) \(\left.+1.22^{\circ} \mathrm{C} / m\right)\)

A \(10.7 \mathrm{m}\) solution of \(\mathrm{NaOH}\) has a density of \(1.33 \mathrm{g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). Calculate the following: (a) the mole fraction of \(\mathrm{NaOH}\) (b) the weight percent of \(\mathrm{NaOH}\) (c) the molarity of the solution

Concentrated aqueous ammonia has a molarity of 14.8 and a density of \(0.90 \mathrm{g} / \mathrm{cm}^{3} .\) What is the molality of the solution? Calculate the mole fraction and weight percent of \(\mathrm{NH}_{3}.\)

If you dissolve \(2.00 \mathrm{g}\) of \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) in \(750 \mathrm{g}\) of water, what is the molality of \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} ?\) What is the total molality of ions in solution? (Assume total dissociation of the ionic solid.)

If you want a solution that is \(0.100 \mathrm{m}\) in ions, what mass of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) must you dissolve in \(125 \mathrm{g}\) of water? (Assume total dissociation of the ionic solid.)

Consider the following aqueous solutions: (i) \(0.20 \mathrm{m}\) \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) (nonvolatile, nonelectrolyte); (ii) \(0.10 \mathrm{m}\) \(\mathrm{CaCl}_{2} ;\) (iii) \(0.12 \mathrm{m} \mathrm{KBr} ;\) and (iv) \(0.12 \mathrm{m} \mathrm{Na}_{2} \mathrm{SO}_{4}.\) (a) Which solution has the highest boiling point? (b) Which solution has the lowest freezing point? (c) Which solution has the highest water vapor pressure?

(a) Which solution is expected to have the higher boiling point: \(0.20 \mathrm{m}\) KBr or \(0.30 \mathrm{m}\) sugar? (b) Which aqueous solution has the lower freezing point: \(0.12 \mathrm{m} \mathrm{NH}_{4} \mathrm{NO}_{3}\) or \(0.10 \mathrm{m} \mathrm{Na}_{2} \mathrm{CO}_{3} ?\)

The solubility of NaCl in water at \(100^{\circ} \mathrm{C}\) is \(39.1 \mathrm{g} / 100 .\) g of water. Calculate the boiling point of this solution. (Assume \(i=1.85\) for \(\mathrm{NaCl}.\)

Hexachlorophene has been used in germicidal soap. What is its molar mass if \(0.640 \mathrm{g}\) of the compound, dissolved in \(25.0 \mathrm{g}\) of chloroform, produces a solution whose boiling point is \(61.93^{\circ} \mathrm{C} ?\)

The solubility of ammonium formate, \(\mathrm{NH}_{4} \mathrm{CHO}_{2},\) in \(100 \mathrm{g}\) of water is \(102 \mathrm{g}\) at \(0^{\circ} \mathrm{C}\) and \(546 \mathrm{g}\) at \(80^{\circ} \mathrm{C} .\) A solution is prepared by dissolving \(\mathrm{NH}_{4} \mathrm{CHO}_{2}\) in \(200 \mathrm{g}\) of water until no more will dissolve at \(80^{\circ} \mathrm{C}\). The solution is then cooled to \(0^{\circ} \mathrm{C} .\) What mass of \(\mathrm{NH}_{4} \mathrm{CH} \mathrm{O}_{2}\) precipitates? (Assume that no water evaporates and that the solution is not supersaturated.)

Cigars are best stored in a "humidor" at \(18^{\circ} \mathrm{C}\) and \(55 \%\) relative humidity. This means the pressure of water vapor should be \(55 \%\) of the vapor pressure of pure water at the same temperature. The proper humidity can be maintained by placing a solution of glycerol \(\left[\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3}\right]\) and water in the humidor. Calculate the percent by mass of glycerol that will lower the vapor pressure of water to the desired value. (The vapor pressure of glycerol is zero.)

Vinegar is a \(5 \%\) solution (by weight) of acetic acid in water. Determine the mole fraction and molality of acetic acid. What is the concentration of acetic acid in parts per million (ppm)? Explain why it is not possible to calculate the molarity of this solution from the information provided.

Calculate the enthalpies of solution for \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) and \(\mathrm{K}_{2} \mathrm{SO}_{4}\) Are the solution processes exothermic or endothermic? Compare them with LiCl and KCI. What similarities or differences do you find? $$\begin{array}{lll} \hline & \Delta H_{f}^{\circ}(\mathrm{s}) & \Delta H_{f}^{\circ}(\mathrm{aq}, 1 \mathrm{m}) \\ \text { Compound } & (\mathrm{kJ} / \mathrm{mol}) & (\mathrm{kJ} / \mathrm{mol}) \\ \hline \mathrm{Li}_{2} \mathrm{SO}_{4} & -1436.4 & -1464.4 \\\ \mathrm{K}_{2} \mathrm{SO}_{4} & -1437.7 & -1414.0 \\ \hline \end{array}$$

A Water at \(25^{\circ} \mathrm{C}\) has a density of \(0.997 \mathrm{g} / \mathrm{cm}^{3} .\) Calculate the molality and molarity of pure water at this temperature.

A If a volatile solute is added to a volatile solvent, both substances contribute to the vapor pressure over the solution. Assuming an ideal solution, the vapor pressure of each is given by Raoult's law, and the total vapor pressure is the sum of the vapor pressures for each component. A solution, assumed to be ideal, is made from 1.0 mol of toluene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\right)\) and 2.0 mol of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right) .\) The vapor pressures of the pure solvents are \(22 \mathrm{mm}\) Hg and \(75 \mathrm{mm}\) Hg, respectively, at \(20^{\circ} \mathrm{C}\). What is the total vapor pressure of the mixture? What is the mole fraction of each component in the liquid and in the vapor?