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

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 \(0.0512 m\) in \(\mathrm{NaNO}_{3}\) 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,\(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\), in which the mole fraction of solute is \(0.125 .\) What mass of ethylene glycol, in grams, should you combine with 955 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 CANNOT COPY)

Use the following data to calculate the enthalpy of solution of sodium perchlorate, \(\mathrm{NaClO}_{4}\) \(\Delta_{f} H^{\circ}(\mathrm{s})=-382.9 \mathrm{kJ} / \mathrm{mol} \quad\) and $$ \Delta_{f} H^{\circ}(\mathrm{aq}, 1 \mathrm{m})=-369.5 \mathrm{kJ} / \mathrm{mol} $$

A 35.0 -g sample of ethylene glycol, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\), is dissolved in 500.0 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 \(531 \mathrm{mm} \mathrm{Hg},\) 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.)

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 1.90 for 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 \(0^{\circ} \mathrm{C}\). Assume the van't Hoff factor, \(i\), is 1.94 for this solution.

Butylated hydroxyanisole (BHA) is used in margarine and other fats and oils. (It is used as an antioxidant and prolongs the shelf life of the food.) What is the molar mass of BHA if \(0.640 \mathrm{g}\) of the compound, dissolved in \(25.0 \mathrm{g}\) of chloroform, produces a solution whose boiling point is \(62.22^{\circ} \mathrm{C} ?\)

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 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?

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?

The organic compound called aluminon 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?

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 \(1.85 .\) )

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) \(0.20 m\) ethylene glycol (nonvolatile, nonelectrolyte) (b) \(0.12 m\) \(\mathrm{K}_{2} \mathrm{SO}_{4}\) (c) \(0.10 m\) \(\mathrm{MgCl}_{2}\) (d) \(0.12 m\) \(m \mathrm{KBr}\)

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?

Phenylcarbinol is used in nasal sprays as a preservative. A solution of \(0.52 \mathrm{g}\) of the compound in \(25.0 \mathrm{g}\) of water has a melting point of \(-0.36^{\circ} \mathrm{C} .\) What is the molar mass of phenylcarbinol?

(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) \(0.35 m\) \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) (a nonvolatile solute) (b) \(0.50 m\) sugar (c) \(0.20 m\) \(\mathrm{KBr}\) (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 rock salt. One manufacturer of home ice cream freezers recommends adding \(2.50 \mathrm{lb}(1130 \mathrm{g})\) of rock salt \((\mathrm{NaCl})\) to 16.0 lb of ice \((7250 \mathrm{g})\) in a 4 -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

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 mol/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 \(0.100 \mathrm{m}\) 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) \(0.20\) \(m\) \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) (nonvolatile, nonelectrolyte); (ii) \(0.10\) \(m\) \(\mathrm{CaCl}_{2}\); (iii) \(0.12\) \(m\) \(\mathrm{KBr}\) ; and (iv) \(0.12\) \(m\) \(\mathrm{Na}_{2} \mathrm{SO}_{4}\). (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 \(0.10 \mathrm{m} \mathrm{Na}_{2} \mathrm{CO}_{3} ?\)

Instead of using NaCl to melt the ice on your sidewalk, you decide to use \(\mathrm{CaCl}_{2}\). If you add \(35.0 \mathrm{g}\) of \(\mathrm{CaCl}_{2}\) to 150. g of water, what is the freezing point of the solution? (Assume \(i=2.7\) for \(\mathrm{CaCl}_{2 .}\) )

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

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.

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?

A tree is exactly \(10 \mathrm{m}\) 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, \(\mathbf{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) what is its percent by mass?

A compound is known to be a potassium halide, KX. If \(4.00 \mathrm{g}\) 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.

The Henry's law constant for \(\mathrm{N}_{2} \mathrm{O}\) is \(2.4 \times 10^{-2}\) \(\mathrm{mol} / \mathrm{kg} \cdot\) bar. (Nitrous oxide, \(\mathrm{N}_{2} \mathrm{O},\) laughing gas, is used as an anesthetic). 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? \(\left(k_{\mathrm{H}} \text { for } \mathrm{CO}_{2} \text { is } 0.034 \mathrm{mol} / \mathrm{kg} \text { bar. }\right)\) 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?

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 \(539 \mathrm{mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C} .\) What is the composition of the mixture?

A newly synthesized compound containing boron and fluorine is \(22.1 \%\) boron. Dissolving \(0.146 \mathrm{g}\) of the compound in \(10.0 \mathrm{g}\) of benzene gives a solution with a vapor pressure of \(94.16 \mathrm{mm}\) Hg at \(25^{\circ} \mathrm{C} .\) (The vapor pressure of pure benzene at this temperature is 95.26 mm Hg.) In a separate experiment, it is found that the compound does not have a dipole moment. (a) What is the molecular formula for the compound? (b) Draw a Lewis structure for the molecule, and suggest a possible molecular structure. Give the bond angles in the molecule and the hybridization of the boron atom.

In chemical research we often send newly synthesized compounds to commercial laboratories for analysis. These laboratories determine the weight percent of \(\mathrm{C}\) and \(\mathrm{H}\) by burning the compound and collecting the evolved \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} .\) They determine the molar mass by measuring the osmotic pressure of a solution of the compound. Calculate the empirical and molecular formulas of a compound, \(\mathrm{C}_{x} \mathrm{H}_{y}\) Cr, given the following information: (a) The compound contains \(73.94 \%\) C and \(8.27 \%\) H; the remainder is chromium. (b) At \(25^{\circ} \mathrm{C},\) the osmotic pressure of a solution containing 5.00 mg of the unknown dissolved in exactly \(100 \mathrm{mL}\) of chloroform solution is \(3.17 \mathrm{mm}\) Hg.

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?

Explain why a cucumber shrivels up when it is placed in a concentrated solution of salt.

If you dissolve equal molar amounts of NaCl and \(\mathrm{CaCl}_{2}\) in water, the CaCl, lowers the freezing point of the water almost 1.5 times as much as the NaCl. Why?