Chapter 11

What is a semipermeable membrane?

A pure solvent is separated from a solution containing the same solvent by a semipermeable membrane. In which direction does the solvent flow across the membrane, and why?

A dilute solution is separated from a more concentrated solution containing the same solvent by a semipermeable membrane. In which direction does the solvent tend to flow across the membrane, and why?

How is the osmotic pressure of a solution related to its molar concentration and its temperature?

What is reverse osmosis? List the basic components of equipment used to purify seawater by reverse osmosis.

Explain how the minimum pressure for the purification of seawater by reverse osmosis can be estimated from its composition.

Why is it important to know if a substance is a strong electrolyte before predicting its effect on the osmotic pressure of a solution?

Why is the van 't Hoff factor for solutions of acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH},\) slightly greater than 1 but far short of \(i=2 ?\)

Why are theoretical and experimental van 't Hoff factors of electrolytes sometimes different?

Can an experimentally measured value of a van 't Hoff factor be greater than the theoretical value? Why or why not?

The following pairs of aqueous solutions are separated by a semipermeable membrane. In which direction will the solvent flow? a. \(A=1.25 M N_{a} C l ; B=1.50 M K C 1\) b. \(A=3.45 M C_{a} C l_{2} ; B=3.45 M N_{a B r}\) c. \(A=4.68 M\) glucose; \(B=3.00 M N_{a} C 1\)

The following pairs of aqueous solutions are separated by a semipermeable membrane. In which direction will the solvent flow? a. \(A=0.48 M N_{a} C l ; B=55.85 \mathrm{g}\) of \(N a C 1\) dissolved in \(1.00 \mathrm{L}\) of solution b. \(A=100 \mathrm{mL}\) of \(0.982 M \mathrm{CaCl}_{2} ; \mathrm{B}=16 \mathrm{g}\) of \(\mathrm{NaCl}\) in \(100 \mathrm{mL}\) of solution c. \(A=100 \mathrm{mL}\) of \(6.56 \mathrm{mM} \mathrm{MgSO}_{4} ; \mathrm{B}=5.24 \mathrm{g}\) of \(\mathrm{MgCl}_{2}\) in \(250 \mathrm{mL}\) of solution

Calculate the osmotic pressure of each of the following aqueous solutions at \(20^{\circ} \mathrm{C}\) a. \(2.39 M\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) b. \(9.45 \mathrm{mM} \mathrm{MgCl}_{2}\) c. \(40.0 \mathrm{mL}\) of glycerol \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) in \(250.0 \mathrm{mL}\) of aqueous solution (density of glycerol \(=1.265 \mathrm{g} / \mathrm{mL}\) ) d. \(25 \mathrm{g}\) of \(\mathrm{CaCl}_{2}\) in \(350 \mathrm{mL}\) of solution

Calculate the osmotic pressure of each of the following aqueous solutions at \(27^{\circ} \mathrm{C}\) a. \(10.0 \mathrm{g}\) of \(\mathrm{NaCl}\) in \(1.50 \mathrm{L}\) of solution b. \(10.0 \mathrm{mg} / \mathrm{L}\) of \(\mathrm{LiNO}_{3}\) c. \(0.222 M\) glucose d. \(0.00764 M \mathrm{K}_{2} \mathrm{SO}_{4}\)

Determine the molarity of each of the following solutions from its osmotic pressure at \(25^{\circ} \mathrm{C}\). Include the van 't Hoff factor for the solution when the factor is given. a. \(\Pi=0.0259\) atm for a solution of urea \(\left[\mathrm{H}_{2} \mathrm{NC}(\mathrm{O}) \mathrm{NH}_{2}\right]\) b. \(\Pi=1.56\) atm for a solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) c. \(\Pi=0.697\) atm for a solution of \(\mathrm{KI}, i=1.90\)

A 188 mg sample of a nonelectrolyte isolated from throat lozenges is dissolved in enough water to make \(10.0 \mathrm{mL}\) of solution at \(25^{\circ} \mathrm{C} .\) The osmotic pressure of the resulting solution is 4.89 atm. Calculate the molar mass of the compound.

Alpetin is a compound found in Alpinia speciosa, a tropical evergreen used historically for treating cold, flu, fever, flatulence, and indigestion. A \(54.1 \mathrm{mg}\) sample of alpetin is dissolved in \(75.0 \mathrm{mL}\) of water. The osmotic pressure of the solution is 0.0657 atm at \(27^{\circ} \mathrm{C}\) Assuming that alpetin is a nonelectrolyte, calculate the molar mass of alpetin.

After \(100.0 \mathrm{mL}\), of a solution of physiological saline \((0.90 \%\) NaCl by mass) is diluted by the addition of \(250.0 \mathrm{mL}\) of water, what is the osmotic pressure of the final solution at \(37^{*} \mathrm{C} ?\) Assume that \(\mathrm{NaCl}\) dissociates completely into \(\mathrm{Na}^{+}(a q)\) and \(\mathrm{Cl}^{+}(a q)\).

An unknown compound \((152 \mathrm{mg})\) is dissolved in water to make \(75.0 \mathrm{mL}\) of solution. The solution does not conduct electricity and has an osmotic pressure of 0.328 atm at \(27^{\circ} \mathrm{C} .\) Elemental analysis reveals the substance to be \(78.90 \% \mathrm{C}, 10.5996 \mathrm{H},\) and \(10.5196 \mathrm{O}\). Determine the molecular formula of this compound.

Use kinetic molecular theory to explain why the vapor pressure of a liquid increases with increasing temperature.

Generally speaking, how is the vapor pressure of a liquid affected by the strength of intermolecular forces?

Is vapor pressure an intensive or extensive property of a volatile substance?

Rank the following compounds in order of increasing vapor pressure at \(298 \mathrm{K}:\) (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH},\) (b) \(\mathrm{CH}_{3} \mathrm{OCH}_{3},\) and (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\).

What physical property of the components of crude oil is used to separate them?

What is the difference between simple distillation and fractional distillation?

In an equimolar mixture of \(\mathrm{C}_{5} \mathrm{H}_{12}\) and \(\mathrm{C}_{7} \mathrm{H}_{16},\) which compound is present in higher concentration in the vapor above the solution?

Why does the boiling point of a mixture of volatile hydrocarbons increase over time during a distillation?

At \(20^{\circ} \mathrm{C},\) the vapor pressure of ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)\) is 45 torr and the vapor pressure of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) is 92 torr. What is the vapor pressure at \(20^{\circ} \mathrm{C}\) of a solution prepared by mixing \(25 \mathrm{g}\) of methanol and \(75 \mathrm{g}\) of ethanol?

A bottle is half-filled with a 50: 50 (by moles) mixture of heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right)\) and octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) at \(25^{\circ} \mathrm{C} .\) What is the mole ratio of heptane vapor to octane vapor in the air space above the liquid in the bottle? The vapor pressures of heptane and octane at \(25^{\circ} \mathrm{C}\) are 31 torr and 11 torr, respectively.

A dam separates the freshwater of the Charles River from the seawater of Boston Harbor. If the two bodies of water are at the same temperature, which one evaporates faster on a hot summer day?

What is the difference between molarity and molality?

As a solution of NaCl becomes more concentrated, does the difference between its molarity and its molality increase or decrease?

Why does seawater freeze at a lower temperature than normal saline?

The thermostat in a refrigerator filled with cans of soft drinks malfunctions and the temperature of the refrigerator drops below \(0^{\circ} \mathrm{C}\). The contents of the cans of diet soft drinks freeze, rupturing many of the cans and causing an awful mess. However, none of the cans containing regular, nondiet soft drinks freeze and rupture. Why?

A solution contains 4.5 mol of water, 0.3 mol of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),\) and 0.2 mol of glucose. Sucrose and glucose are nonvolatile. What is the mole fraction of water in the solution? What is the vapor pressure of the solution at \(35^{\circ} \mathrm{C},\) given that the vapor pressure of pure water at \(35^{\circ} \mathrm{C}\) is 42.2 torr?

Calculate the molality of each of the following solutions: a. 0.875 mol of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) in \(1.5 \mathrm{kg}\) of water b. 11.5 mmol of acctic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) in \(65 \mathrm{g}\) of water c. 0.325 mol of baking soda \(\left(\mathrm{NaHCO}_{3}\right)\) in \(290.0 \mathrm{g}\) of water

Calculate the molality of each of the following solutions: a. \(11.7 \mathrm{g}\) of \(\mathrm{NaCl}\) in \(1.0 \mathrm{kg}\) of water b. \(4.99 \mathrm{g}\) of \(\mathrm{CuSO}_{4}\) in \(265 \mathrm{g}\) of water c. \(6.41 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{OH}\) in \(375 \mathrm{g}\) of water

Calculate the molality of each of the following aqueous solutions: a. \(1.30 M \mathrm{CaCl}_{2}(d=1.113 \mathrm{g} / \mathrm{mL})\) b. \(2.02 M\) fructose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}, d=1.139 \mathrm{g} / \mathrm{mL}\right)\) c. \(8.94 M\) ethylene glycol (antifreeze, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\), \(d=1.069 \mathrm{g} / \mathrm{mL})\) d. \(1.97 M\) LiCl \((d=1.046 \mathrm{g} / \mathrm{mL})\)

What mass of the following solutions contains 0.100 mol of solute? (a) \(0.334 \mathrm{m} \mathrm{NH}_{4} \mathrm{NO}_{3} ;\) (b) \(1.24 \mathrm{m}\) ethylene glycol, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH} ;(\mathrm{c}) 5.65 \mathrm{m} \mathrm{CaCl}_{2}\)

How many moles of solute are there in the following solutions? a. \(0.150 \mathrm{m}\) glucose solution made by dissolving the glucose in \(100.0 \mathrm{kg}\) of water b. \(0.028 m \mathrm{Na}_{2} \mathrm{CrO}_{4}\) solution made by dissolving the \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) in \(1000.0 \mathrm{g}\) of water c. \(0.100 \mathrm{m}\) urea solution made by dissolving the urea in \(500.0 \mathrm{g}\) of water

High concentrations of ammonia (NH \(_{3}\) ), nitrite ion, and nitrate ion in water can kill fish. Lethal concentrations of these species for rainbow trout are \(1.1 \mathrm{mg} / \mathrm{L}, 0.40 \mathrm{mg} / \mathrm{L},\) and \(1361 \mathrm{mg} / \mathrm{L},\) respectively. Express these concentrations in molality units, assuming a solution density of \(1.00 \mathrm{g} / \mathrm{mL}\).

The concentrations of six important elements in a sample of river water are \(0.050 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Al}^{3+}, 0.040 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Fe}^{3+}, 13.4 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Ca}^{2+}, 5.2 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Na}^{+}, 1.3 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{K}^{+}\), and \(3.4 \mathrm{mg} / \mathrm{kg}\) of \(\mathrm{Mg}^{2+} .\) Express each of these concentrations in molality units.

Cinnamon owes its flavor and odor to cinnamaldehyde (C \(_{9} \mathrm{H}_{8} \mathrm{O}\) ). Determine the freezing point of a solution of 75 mg of cinnamaldehyde dissolved in \(1.00 \overline{\mathrm{g}}\) of benzene \(\left(K_{f}=4.3^{\circ} \mathrm{C} / \mathrm{m} ; \text { normal freezing point }=5.5^{\circ} \mathrm{C}\right)\).

Determine the boiling point elevation of a solution of 125 mg of carvone \(\left(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O},\) oil of spearmint) \right. dissolved in \(1.50 \mathrm{g}\) of carbon disulfide \(\left(K_{\mathrm{b}}=2.34^{\circ} \mathrm{C} / \mathrm{m}\right)\).

What molality of a nonvolatile, nonelectrolyte solute is needed to lower the melting point of camphor by \(1.000^{\circ} \mathrm{C}\) \(\left(K_{f}=39.7^{\circ} \mathrm{C} / m\right) ?\)

What molality of a nonvolatile, nonelectrolyte solute is needed to raise the boiling point of water by \(7.60^{\circ} \mathrm{C}\) \(\left(K_{\mathrm{b}}=0.52^{\circ} \mathrm{C} / \mathrm{m}\right) ?\)

Determine the boiling point of an aqueous solution that is \(2.50 \mathrm{m}\) ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right) ; K_{\mathrm{b}}\) for water is \(0.52^{\circ} \mathrm{C} / \mathrm{m} .\) Assume that the boiling point of pure water is \(100.00^{\circ} \mathrm{C}\).

Which aqueous solution has the lowest freezing point: \(0.5 \mathrm{m}\) glucose, \(0.5 \mathrm{m} \mathrm{NaCl},\) or \(0.5 \mathrm{m} \mathrm{CaCl}_{2} ?\)

Which aqueous solution has the highest boiling point: \(0.5 \mathrm{m}\) glucose, \(0.5 \mathrm{m} \mathrm{NaCl},\) or \(0.5 \mathrm{m} \mathrm{CaCl}_{2} ?\)

Which one of the following aqueous solutions should have the highest boiling point: \(0.0400 \mathrm{m} \mathrm{NH}_{4} \mathrm{NO}_{3}, 0.0165 \mathrm{m}\) LiCl, or \(0.0105 \mathrm{m} \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} ?\)