Chapter 10

The freezing point of \(t\) -butanol is \(25.50^{\circ} \mathrm{C}\) and \(K_{\mathrm{f}}\) is \(9.1^{\circ} \mathrm{C} \cdot \mathrm{kg} /\) mol. Usually \(t\) -butanol absorbs water on exposure to air. If the freezing point of a 10.0 -g sample of \(t\) -butanol is \(24.59^{\circ} \mathrm{C},\) how many grams of water are present in the sample?

Reserpine is a natural product isolated from the roots of the shrub Rauwolfia serpentina. It was first synthesized in 1956 by Nobel Prize winner R. B. Woodward. It is used as a tranquilizer and sedative. When 1.00 g reserpine is dissolved in \(25.0 \mathrm{g}\) camphor, the freezing-point depression is \(2.63^{\circ} \mathrm{C}(K_{\mathrm{f}}\) for camphor is \(40 .^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol})\) Calculate the molality of the solution and the molar mass of reserpine.

A solution contains \(3.75 \mathrm{g}\) of a nonvolatile pure hydrocarbon in \(95 \mathrm{g}\) acetone. The boiling points of pure acetone and the solution are \(55.95^{\circ} \mathrm{C}\) and \(56.50^{\circ} \mathrm{C},\) respectively. The molal boilingpoint constant of acetone is \(1.71^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol} .\) What is the molar mass of the hydrocarbon?

a. Calculate the freezing-point depression and osmotic pressure at \(25^{\circ} \mathrm{C}\) of an aqueous solution containing \(1.0 \mathrm{g} / \mathrm{L}\) of a protein (molar mass \(=9.0 \times 10^{4} \mathrm{g} / \mathrm{mol}\) ) if the density of the solution is \(1.0 \mathrm{g} / \mathrm{cm}^{3} .\) b. Considering your answer to part a, which colligative property, freezing- point depression or osmotic pressure, would be better used to determine the molar masses of large molecules? Explain.

Erythrocytes are red blood cells containing hemoglobin. In a saline solution they shrivel when the salt concentration is high and swell when the salt concentration is low. In a \(25^{\circ} \mathrm{C}\) aqueous solution of \(\mathrm{NaCl}\), whose freezing point is \(-0.406^{\circ} \mathrm{C},\) erythrocytes neither swell nor shrink. If we want to calculate the osmotic pressure of the solution inside the erythrocytes under these conditions, what do we need to assume? Why? Estimate how good (or poor) of an assumption this is. Make this assumption and calculate the osmotic pressure of the solution inside the erythrocytes.

An aqueous solution of 10.00 g of catalase, an enzyme found in the liver, has a volume of \(1.00 \mathrm{L}\) at \(27^{\circ} \mathrm{C}\). The solution's osmotic pressure at \(27^{\circ} \mathrm{C}\) is found to be 0.745 torr. Calculate the molar mass of catalase.

A 0.15 -g sample of a purified protein is dissolved in water to give \(2.0 \mathrm{mL}\) of solution. The osmotic pressure is found to be 18.6 torr at \(25^{\circ} \mathrm{C} .\) Calculate the protein's molar mass.

How would you prepare \(1.0 \mathrm{L}\) of an aqueous solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) having an osmotic pressure of 15 atm at a temperature of \(22^{\circ} \mathrm{C} ?\) Sucrose is a nonelectrolyte.

How would you prepare 1.0 L of an aqueous solution of sodium chloride having an osmotic pressure of 15 atm at \(22^{\circ} \mathrm{C} ?\) Assume sodium chloride exists as \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\) ions in solution.

Consider the following solutions: \(0.010 m \mathrm{Na}_{3} \mathrm{PO}_{4}\) in water \(0.020 \mathrm{m} \mathrm{CaBr}_{2}\) in water \(0.020 \mathrm{m} \mathrm{KCl}\) in water \(0.020 \mathrm{m}\) HF in water (HF is a weak acid.) a. Assuming complete dissociation of the soluble salts, which solution(s) would have the same boiling point as \(0.040 \mathrm{m}\) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) in water? \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) is a nonelectrolyte. b. Which solution would have the highest vapor pressure at \(28^{\circ} \mathrm{C} ?\) c. Which solution would have the largest freezing-point depression?

From the following: pure water solution of \(\mathbf{C}_{12} \mathbf{H}_{22} \mathbf{O}_{11}(m=0.01)\) in water solution of \(\mathrm{NaCl}(m=0.01)\) in water solution of \(\mathrm{CaCl}_{2}(m=0.01)\) in water Choose the one with the a. highest freezing point. b. lowest freezing point. c. highest boiling point. d. lowest boiling point. e. highest osmotic pressure.

A water desalination plant is set up near a salt marsh containing water that is 0.10 \(M\) NaCl. Calculate the minimum pressure that must be applied at \(20 .^{\circ} \mathrm{C}\) to purify the water by reverse osmosis. Assume \(\mathrm{NaCl}\) is completely dissociated.

Use the following data for three aqueous solutions of \(\mathrm{CaCl}_{2}\) to calculate the apparent value of the van't Hoff factor. $$\begin{array}{lc} \text { Molality } & \text { Freezing-Point Depression }\left(^{\circ} \mathrm{C}\right) \\ \hline 0.0225 & 0.110 \\ 0.0910 & 0.440 \\ 0.278 & 1.330 \end{array}$$

The freezing-point depression of a 0.091-m solution of CsCl is \(0.320^{\circ} \mathrm{C} .\) The freezing-point depression of a \(0.091-m\) solution of \(\mathrm{CaCl}_{2}\) is \(0.440^{\circ} \mathrm{C}\). In which solution does ion association appear to be greater? Explain.

In the winter of \(1994,\) record low temperatures were registered throughout the United States. For example, in Champaign, Illinois, a record low of \(-29^{\circ} \mathrm{F}\) was registered. At this temperature can salting icy roads with \(\mathrm{CaCl}_{2}\) be effective in melting the ice? a. Assume \(i=3.00\) for \(\mathrm{CaCl}_{2}\) b. Assume the average value of \(i\) from Exercise 87 (The solubility of \(\mathrm{CaCl}_{2}\) in cold water is \(74.5 \mathrm{g}\) per \(100.0 \mathrm{g}\) water.

A 0.500 -g sample of a compound is dissolved in enough water to form \(100.0 \mathrm{mL}\) of solution. This solution has an osmotic pressure of 2.50 atm at \(25^{\circ} \mathrm{C}\). If each molecule of the solute dissociates into two particles (in this solvent), what is the molar mass of this solute?

The solubility of benzoic acid \(\left(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\right)\) is \(0.34 \mathrm{g} / 100 \mathrm{mL}\) in water at \(25^{\circ} \mathrm{C}\) and is \(10.0 \mathrm{g} / 100 \mathrm{mL}\) in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) at \(25^{\circ} \mathrm{C}\). Rationalize this solubility behavior. (Hint: Benzoic acid forms a dimer in benzene.) Would benzoic acid be more or less soluble in a 0.1-M NaOH solution than it is in water? Explain.

In a coffee-cup calorimeter, \(1.60 \mathrm{g} \mathrm{NH}_{4} \mathrm{NO}_{3}\) was mixed with \(75.0 \mathrm{g}\) water at an initial temperature \(25.00^{\circ} \mathrm{C}\). After dissolution of the salt, the final temperature of the calorimeter contents was \(23.34^{\circ} \mathrm{C}\) a. Assuming the solution has a heat capacity of \(4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\) and assuming no heat loss to the calorimeter, calculate the enthalpy of solution \(\left(\Delta H_{\text {soln }}\right)\) for the dissolution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in units of kJ/mol. b. If the enthalpy of hydration for \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is \(-630 . \mathrm{kJ} / \mathrm{mol}\), calculate the lattice energy of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\)

Explain the following on the basis of the behavior of atoms and/or ions. a. Cooking with water is faster in a pressure cooker than in an open pan. b. Salt is used on icy roads. c. Melted sea ice from the Arctic Ocean produces fresh water. d. \(\mathrm{CO}_{2}(s)\) (dry ice) does not have a normal boiling point under normal atmospheric conditions, even though \(\mathrm{CO}_{2}\) is a liquid in fire extinguishers. e. Adding a solute to a solvent extends the liquid phase over a larger temperature range.

The term proof is defined as twice the percent by volume of pure ethanol in solution. Thus, a solution that is \(95 \%\) (by volume) ethanol is 190 proof. What is the molarity of ethanol in a 92 proof ethanol-water solution? Assume the density of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) is \(0.79 \mathrm{g} / \mathrm{cm}^{3}\) and the density of water is \(1.0 \mathrm{g} / \mathrm{cm}^{3}\)

At \(25^{\circ} \mathrm{C},\) the vapor in equilibrium with a solution containing carbon disulfide and acetonitrile has a total pressure of 263 torr and is 85.5 mole percent carbon disulfide. What is the mole fraction of carbon disulfide in the solution? At \(25^{\circ} \mathrm{C},\) the vapor pressure of carbon disulfide is 375 torr. Assume the solution and vapor exhibit ideal behavior.

A solution is made by mixing \(50.0 \mathrm{g}\) acetone \(\left(\mathrm{CH}_{3} \mathrm{COCH}_{3}\right)\) and 50.0 g methanol (CH_OH). What is the vapor pressure of this solution at \(25^{\circ} \mathrm{C} ?\) What is the composition of the vapor expressed as a mole fraction? Assume ideal solution and gas behavior. (At \(25^{\circ} \mathrm{C}\) the vapor pressures of pure acetone and pure methanol are 271 and 143 torr, respectively.) The actual vapor pressure of this solution is 161 torr. Explain any discrepancies.

An unknown compound contains only carbon, hydrogen, and oxygen. Combustion analysis of the compound gives mass percents of \(31.57 \%\) C and \(5.30 \%\) H. The molar mass is determined by measuring the freezing-point depression of an aqueous solution. A freezing point of \(-5.20^{\circ} \mathrm{C}\) is recorded for a solution made by dissolving \(10.56 \mathrm{g}\) of the compound in \(25.0 \mathrm{g}\) water. Determine the empirical formula, molar mass, and molecular formula of the compound. Assume that the compound is a nonelectrolyte.

What stabilizes a colloidal suspension? Explain why adding heat or adding an electrolyte can cause the suspended particles to settle out.

Patients undergoing an upper gastrointestinal tract laboratory test are typically given an X-ray contrast agent that aids with the radiologic imaging of the anatomy. One such contrast agent is sodium diatrizoate, a nonvolatile water-soluble compound. A \(0.378-m\) solution is prepared by dissolving 38.4 g sodium diatrizoate (NaDTZ) in \(1.60 \times 10^{2} \mathrm{mL}\) water at \(31.2^{\circ} \mathrm{C}\) (the density of water at \(31.2^{\circ} \mathrm{C}\) is \(0.995 \mathrm{g} / \mathrm{cm}^{3}\) ). What is the molar mass of sodium diatrizoate? What is the vapor pressure of this solution if the vapor pressure of pure water at \(31.2^{\circ} \mathrm{C}\) is 34.1 torr?

A solution is prepared by dissolving 52.3 g cesium chloride in \(60.0 \mathrm{g}\) water. The volume of the solution is \(63.3 \mathrm{mL}\). Calculate the mass percent, molarity, molality, and mole fraction of the CsCl solution.

The lattice energy of \(\mathrm{NaCl}\) is \(-786 \mathrm{kJ} / \mathrm{mol}\), and the enthalpy of hydration of 1 mole of gaseous \(\mathrm{Na}^{+}\) and 1 mole of gaseous \(\mathrm{Cl}^{-}\) ions is \(-783 \mathrm{kJ} / \mathrm{mol} .\) Calculate the enthalpy of solution per mole of solid NaCl.

For each of the following pairs, predict which substance is more soluble in water. a. \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) or \(\mathrm{NH}_{3}\) b. \(\mathrm{CH}_{3} \mathrm{CN}\) or \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) c. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) or \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\) d. \(\mathrm{CH}_{3} \mathrm{OH}\) or \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) e. \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CCH}_{2} \mathrm{OH}\) or \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{6} \mathrm{OH}\) f. \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\) or \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)

The normal boiling point of methanol is \(64.7^{\circ} \mathrm{C} .\) A solution containing a nonvolatile solute dissolved in methanol has a vapor pressure of 556.0 torr at \(64.7^{\circ} \mathrm{C}\). What is the mole fraction of methanol in this solution?

A solution is prepared by mixing 1.000 mole of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) and 3.18 moles of propanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right) .\) What is the composition of the vapor (in mole fractions) at \(40^{\circ} \mathrm{C} ?\) At \(40^{\circ} \mathrm{C},\) the vapor pressure of pure methanol is 303 torr, and the vapor pressure of pure propanol is 44.6 torr.

A \(4.7 \times 10^{-2}\) mg sample of a protein is dissolved in water to make \(0.25 \mathrm{mL}\) of solution. The osmotic pressure of the solution is 0.56 torr at \(25^{\circ} \mathrm{C}\). What is the molar mass of the protein?

The vapor pressure of pure benzene is 750.0 torr and the vapor pressure of toluene is 300.0 torr at a certain temperature. You make a solution by pouring "some" benzene with "some" toluene. You then place this solution in a closed container and wait for the vapor to come into equilibrium with the solution. Next, you condense the vapor. You put this liquid (the condensed vapor) in a closed container and wait for the vapor to come into equilibrium with the solution. You then condense this vapor and find the mole fraction of benzene in this vapor to be 0.714. Determine the mole fraction of benzene in the original solution assuming the solution behaves ideally.

Liquid A has vapor pressure \(x,\) and liquid B has vapor pressure y. What is the mole fraction of the liquid mixture if the vapor above the solution is \(30 . \%\) A by moles? \(50 . \%\) A? \(80 . \%\) A? (Calculate in terms of \(x\) and \(y .\) ) Liquid A has vapor pressure \(x,\) liquid B has vapor pressure y. What is the mole fraction of the vapor above the solution if the liquid mixture is \(30 . \%\) A by moles? \(50 . \%\) A? \(80 . \%\) A? (Calculate in terms of \(x\) and \(y .\) )

Plants that thrive in salt water must have internal solutions (inside the plant cells) that are isotonic with (have the same osmotic pressure as) the surrounding solution. A leaf of a saltwater plant is able to thrive in an aqueous salt solution (at \(25^{\circ} \mathrm{C}\) ) that has a freezing point equal to \(-0.621^{\circ} \mathrm{C}\). You would like to use this information to calculate the osmotic pressure of the solution in the cell. a. In order to use the freezing-point depression to calculate osmotic pressure, what assumption must you make (in addition to ideal behavior of the solutions, which we will assume)? b. Under what conditions is the assumption (in part a) reasonable? c. Solve for the osmotic pressure (at \(25^{\circ} \mathrm{C}\) ) of the solution in the plant cell. d. The plant leaf is placed in an aqueous salt solution (at \(\left.25^{\circ} \mathrm{C}\right)\) that has a boiling point of \(102.0^{\circ} \mathrm{C}\). What will happen to the plant cells in the leaf?

You make \(20.0 \mathrm{g}\) of a sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) and NaCl mixture and dissolve it in \(1.00 \mathrm{kg}\) water. The freezing point of this solution is found to be \(-0.426^{\circ} \mathrm{C}\). Assuming ideal behavior, calculate the mass percent composition of the original mixture, and the mole fraction of sucrose in the original mixture.

An aqueous solution is \(1.00 \%\) NaCl by mass and has a density of \(1.071 \mathrm{g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\). The observed osmotic pressure of this solution is 7.83 atm at \(25^{\circ} \mathrm{C}\) a. What fraction of the moles of NaCl in this solution exist as ion pairs? b. Calculate the freezing point that would be observed for this solution.

A \(1.60-\mathrm{g}\) sample of a mixture of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) and anthracene \(\left(\mathrm{C}_{14} \mathrm{H}_{10}\right)\) is dissolved in \(20.0 \mathrm{g}\) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right) .\) The freezing point of the solution is \(2.81^{\circ} \mathrm{C} .\) What is the composition as mass percent of the sample mixture? The freezing point of benzene is \(5.51^{\circ} \mathrm{C}\) and \(K_{\mathrm{f}}\) is \(5.12^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol}\)

A solid mixture contains \(\mathrm{MgCl}_{2}\) and \(\mathrm{NaCl}\). When \(0.5000 \mathrm{g}\) of this solid is dissolved in enough water to form 1.000 L of solution, the osmotic pressure at \(25.0^{\circ} \mathrm{C}\) is observed to be 0.3950 atm. What is the mass percent of \(\mathrm{MgCl}_{2}\) in the solid? (Assume ideal behavior for the solution.)

Formic acid (HCO_A) is a monoprotic acid that ionizes only partially in aqueous solutions. A 0.10-M formic acid solution is \(4.2 \%\) ionized. Assuming that the molarity and molality of the solution are the same, calculate the freezing point and the boiling point of 0.10 \(M\) formic acid.

You have a solution of two volatile liquids, \(A\) and \(B\) (assume ideal behavior). Pure liquid A has a vapor pressure of 350.0 torr and pure liquid B has a vapor pressure of 100.0 torr at the temperature of the solution. The vapor at equilibrium above the solution has double the mole fraction of substance A that the solution does. What is the mole fraction of liquid A in the solution?

In some regions of the southwest United States, the water is very hard. For example, in Las Cruces, New Mexico, the tap water contains about \(560 \mu \mathrm{g}\) of dissolved solids per milliliter. Reverse osmosis units are marketed in this area to soften water. A typical unit exerts a pressure of 8.0 atm and can produce 45 L water per day. a. Assuming all of the dissolved solids are \(\mathrm{MgCO}_{3}\) and assuming a temperature of \(27^{\circ} \mathrm{C},\) what total volume of water must be processed to produce 45 L pure water? b. Would the same system work for purifying seawater? (Assume seawater is 0.60 \(M\) NaCl.)

Creatinine, \(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{N}_{3} \mathrm{O},\) is a by-product of muscle metabolism, and creatinine levels in the body are known to be a fairly reliable indicator of kidney function. The normal level of creatinine in the blood for adults is approximately \(1.0 \mathrm{mg}\) per deciliter (dL) of blood. If the density of blood is \(1.025 \mathrm{g} / \mathrm{mL},\) calculate the molality of a normal creatinine level in a 10.0 -mL blood sample. What is the osmotic pressure of this solution at \(25.0^{\circ} \mathrm{C} ?\)

An aqueous solution containing 0.250 mole of Q, a strong electrolyte, in \(5.00 \times 10^{2} \mathrm{g}\) water freezes at \(-2.79^{\circ} \mathrm{C}\). What is the van't Hoff factor for Q? The molal freezing-point depression constant for water is \(1.86^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol} .\) What is the formula of \(\mathrm{Q}\) if it is \(38.68 \%\) chlorine by mass and there are twice as many anions as cations in one formula unit of Q?

Anthraquinone contains only carbon, hydrogen, and oxygen. When \(4.80 \space \mathrm{mg}\) anthraquinone is burned, \(14.2 \space \mathrm{mg}\space \mathrm{CO}_{2}\) and \(1.65 \space \mathrm{mg} \space \mathrm{H}_{2} \mathrm{O}\) are produced. The freezing point of camphor is lowered by \(22.3^{\circ} \mathrm{C}\) when \(1.32 \mathrm{g}\) anthraquinone is dissolved in 11.4 g camphor. Determine the empirical and molecular formulas of anthraquinone.