Chapter 13

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

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 \(0.785 \mathrm{g} / \mathrm{mL} .)\)

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?

What mass of \(\mathrm{NaNO}_{3}\) must be added to \(500 . \mathrm{g}\) of water to prepare a solution that is \(0.0512 \mathrm{m}\) in \(\mathrm{NaNO}_{3} ?\) 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, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH},\) in which the mole fraction of solute is \(0.125 .\) What mass of ethylene =glycol, in grams, should you combine with \(955 \mathrm{g}\) -of water? What is the molality of the solution?

Hydrochloric acid is sold as a concentrated aqueous solution. If the concentration of commercial HCl is \(12.0 \mathrm{M}\) 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 \(28 \mathrm{ppb}\) (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 \(\left.1.0 \mathrm{g} / \mathrm{cm}^{3} .\right)\)

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 \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)

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 NaCl in this solution? (See Figure 13.11.) (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.

Butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\), has been suggested as the refrigerant in household compressors such as those found in air conditioners. (a) To what extent is butane soluble in water? Calculate the butane concentration in water if the pressure of the gas is 0.21 atm. \(\left(k_{\mathrm{H}}=\right.\) \(\left.0.0011 \mathrm{mol} / \mathrm{kg} \cdot \text { bar at } 25^{\circ} \mathrm{C}\right)\) (b) If the pressure of butane is increased to 1.0 atm, does the butane concentration increase or decrease?

A 35.0 -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.

An aqueous solution contains \(3.00 \%\) phenylalanine \(\left(\mathrm{C}_{9} \mathrm{H}_{11} \mathrm{NO}_{2}\right)\) by mass. (Phenylalanine is nonionic and nonvolatile.) Find the following: (a) the freezing point of the solution (b) the boiling point of the solution (c) the osmotic pressure of the solution at \(25^{\circ} \mathrm{C}\)

Estimate the osmotic pressure of human blood at \(37^{\circ} \mathrm{C} .\) Assume blood is isotonic with a \(0.154 \mathrm{M}\) NaCl solution, and assume the van't Hoff factor, \(i\), is 1.90 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, \(i_{t}\) is 1.94 for this solution.

You add \(0.255 \mathrm{g}\) of an orange, crystalline compound whose empirical formula is \(\mathrm{C}_{10} \mathrm{H}_{8} \mathrm{Fe}\) to \(11.12 \mathrm{g}\) of benzene. The boiling point of the benzene rises from \(80.10^{\circ} \mathrm{C}\) to \(80.26^{\circ} \mathrm{C} .\) What are the molar mass and molecular formula of the compound?

Benzyl acetate is one of the active components of oil of jasmine. If 0.125 g of the compound is added to \(25.0 \mathrm{g}\) of chloroform \(\left(\mathrm{CHCl}_{3}\right),\) the boiling point of the solution is \(61.82^{\circ} \mathrm{C} .\) What is the molar mass of benzyl acetate?

An aqueous solution contains \(0.180 \mathrm{g}\) of an unknown, nonionic solute in \(50.0 \mathrm{g}\) of water. The solution freezes at \(-0.040^{\circ} \mathrm{C}\). What is the molar mass of the solute?

Aluminon, an organic compound, is used as a reagent to test for the presence of the aluminum ion in aqueous solution. A solution of \(2.50 \mathrm{g}\) of aluminon in \(50.0 \mathrm{g}\) of water freezes at \(-0.197^{\circ} \mathrm{C}\) What is the molar mass of aluminon?

If \(52.5 \mathrm{g}\) of 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 \(2 .\) )

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) \(0.12 m \mathrm{K}_{2} \mathrm{SO}_{4}\) (c) \(0.10 m \mathrm{MgCl}_{2}\) (d) \(0.12 \mathrm{m} \mathrm{KBr}\)

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 are the volume \(\left(V=4 / 3 \pi r^{3}\right)\) and surface area \(\left(A=4 \pi r^{2}\right)\) 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?

(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 \(0.15 m \mathrm{Na}_{7} \mathrm{SO}_{4} ?\)

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) \(0.50 \mathrm{m}\) sugar (c) \(0.20 \mathrm{m} \mathrm{KBr}\) (a strong electrolyte) (d) \(0.20 m \mathrm{Na}_{2} \mathrm{SO}_{4}\) (a strong electrolyte)

Making homemade ice cream is one of life's great pleasures. Fresh milk and cream, sugar, and flavorings are churned in a bucket suspended in an ice-water mixture, the freezing point of which has been lowered by adding salt. One manufacturer of home ice cream freezers recommends adding \(2.50 \mathrm{lb}(1130 \mathrm{g})\) of salt \((\mathrm{NaCl})\) to \(16.0 \mathrm{lb}\) of ice \((7250 \mathrm{g})\) in a \(4-\mathrm{qt}\) freezer. For the solution when this mixture melts, calculate the following: (a) the weight percent of \(\mathrm{NaCl}\) (b) the mole fraction of \(\mathrm{NaCl}\) (c) the molality of the solution

Dimethylglyoxime \(\left[\mathrm{DMG},\left(\mathrm{CH}_{3} \mathrm{CNOH}\right)_{2}\right]\) 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 CANNOT COPY) (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 ^ C? (d) What is the boiling point of the solution? (DMG does not produce ions in solution.) \(\left(K_{\mathrm{bn}} \text { for ethanol }=+1.22^{\circ} \mathrm{C} / \mathrm{m}\right)\)

Concentrated aqueous ammonia has a molarity of \(14.8 \mathrm{mol} / \mathrm{L}\) 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 \(m\) 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) \(0.20 m \mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) (nonvolatile, nonelectrolyte); (ii) 0.10 \(m\) CaCl_i (iii) 0.12 \(m\) 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 g/100. g of water. Calculate the boiling point of this solution. (Assume \(i=1.85\) for NaCl.)

The solubility of ammonium formate, \(\mathrm{NH}_{4} \mathrm{CHO}_{2}\) in \(100 .\) g of water is 102 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 \(\mathrm{NH}_{4} \mathrm{CHO}_{2}\) precipitates? (Assume that no water evaporates and that the solution is not supersaturated.)

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.

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 \(2.0 \mathrm{mol}\) of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right) .\) The vapor pressures of the pure solvents are \(22 \mathrm{mm} \mathrm{Hg}\) and \(75 \mathrm{mm} \mathrm{Hg},\) 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?

A solution is \(4.00 \%\) (by mass) maltose and \(96.00 \%\) water. It freezes at \(-0.229^{\circ} \mathrm{C}\) (a) Calculate the molar mass of maltose (which is not an ionic compound). (b) The density of the solution is \(1.014 \mathrm{g} / \mathrm{mL}\). Calculate the osmotic pressure of the solution.

A tree is \(10.0 \mathrm{m}\) tall. (a) What must be the total molarity of the solutes if sap rises to the top of the tree by osmotic pressure at \(20^{\circ} \mathrm{C} ?\) Assume the groundwater outside the tree is pure water and that the density of the sap is \(1.0 \mathrm{g} / \mathrm{mL} .\left(1 \mathrm{mm} \mathrm{Hg}=13.6 \mathrm{mm} \mathrm{H}_{2} \mathrm{O} .\right)\) (b) If the only solute in the sap is sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11},\) what is its percent by mass?

A \(2.00 \%\) solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in water freezes at \(-0.796^{\circ} \mathrm{C}\) (a) Calculate the van't Hoff factor, \(i\) (b) Which of the following best represents sulfuric acid in a dilute aqueous solution: \(\mathrm{H}_{2} \mathrm{SO}_{4}\) \(\mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{HSO}_{4}^{-},\) or \(2 \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{SO}_{4}^{2-2}\)

A compound is known to be a potassium halide, KX. If 4.00 g of the salt is dissolved in exactly \(100 \mathrm{g}\) of water, the solution freezes at \(-1.28^{\circ} \mathrm{C}\) Identify the halide ion in this formula.

Nitrous oxide, \(\mathrm{N}_{2} \mathrm{O},\) laughing gas, is used as an anesthetic. Its Henry's law constant is \(2.4 \times 10^{-2} \mathrm{mol} /\) kg \cdotbar. Determine the mass of \(\mathrm{N}_{2} \mathrm{O}\) that will dissolve in \(500 .\) mL of water, under an \(\mathrm{N}_{2} \mathrm{O}\) pressure of 1.00 bar. What is the concentration of \(\mathrm{N}_{2} \mathrm{O}\) in this solution, expressed in ppm \(\left(d\left(\mathrm{H}_{2} \mathrm{O}\right)=1.00 \mathrm{g} / \mathrm{mL}\right) ?\)

If a carbonated beverage is bottled under 1.5 bar \(\mathrm{CO}_{2}\) pressure, what will be the concentration of dissolved \(\mathrm{CO}_{2}\) in that beverage? \((k_{\mathrm{H}} \text { for } \mathrm{CO}_{2}\) is \(0.034 \mathrm{mol} / \mathrm{kg}\) bar. After the pressure is released, what fraction of the dissolved gas will escape before equilibrium with the \(\mathrm{CO}_{2}\) in the atmosphere is reached?

You are given a flask filled with a colored liquid. Suggest several tests that would allow you to determine whether this is a solution or a colloid.

If one is very careful, it is possible to float a needle on the surface of water. (If the needle is magnetized, it will turn to point north and south and become a makeshift compass.) What would happen to the needle if a drop of liquid soap is added to the solution? Explain the observation.

In a police forensics lab, you examine a package that may contain heroin. However, you find the white powder is not pure heroin but a mixture of heroin \(\left(\mathrm{C}_{21} \mathrm{H}_{23} \mathrm{O}_{5} \mathrm{N}\right)\) and lactose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) .\) To determine the amount of heroin in the mixture, you dissolve \(1.00 \mathrm{g}\) of the white powdery mixture in water in a 100.0 -mL volumetric flask. You find that the solution has an osmotic pressure of \(539 \mathrm{mm}\) Hg at \(25^{\circ} \mathrm{C}\). What is the composition of the mixture?

An organic compound contains carbon \((71.17 \%)\) hydrogen \((5.12 \%)\) with the remainder nitrogen. Dissolving 0.177 g of the compound in \(10.0 \mathrm{g}\) of benzene gives a solution with a vapor pressure of \(94.16 \mathrm{mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C} .\) (The vapor pressure of pure benzene at this temperature is \(95.26 \mathrm{mm}\) Hg. What is the molecular formula for the compound?