Answer: Write the equations relating boiling-point

Briefly describe the solution process at the molecular level. Use the dissolution of a solid in a liquid as an example.

What is the molality of a solution containing 7.78 g of urea \([(NH_2)_2CO]\) in 203 g of water?

Using Figure 12.3, rank the potassium salts in increasing order of solubility at 40°C.

Explain why the solution process usually leads to an increase in disorder.

Calculate the vapor pressure of a solution made by dissolving 82.4g of urea (molar mass = 60.06 g/mol)in 212 mL of water at 35°C. What is the vapor-pressure lowering?

What does it mean when we say that the osmotic pressure of a sample of seawater is 25 atm at a certain temperature?

A 202-mL benzene solution containing 2.47 g of an organic polymer has an osmotic pressure of 8.63 mmHg at 21°C. Calculate the molar mass of the polymer.

Explain the variations in solubility in water of the alcohols listed here:

The freezing-point depression of a 0.100 m \(\mathrm{MgSO}_{4}\) solution is \(0.225^{\circ} \mathrm{C}\). Calculate the van't Hoff factor of \(\mathrm{MgSO}_{4}\) at this concentration.

The concentrated sulfuric acid we use in the laboratory is 98.0 percent \(\mathrm{H}_{2} \mathrm{SO}_{4}\) by mass. Calculate the molality and molarity of the acid solution. The density of the solution is 1.83 g/mL.

Calculate the molarity and the molality of an \(\mathrm{NH}_{3}\) solution made up of 30.0 g of \(\mathrm{NH}_{3}\) in 70.0 g of water. The density of the solution is 0.982 g/mL.

The density of an aqueous solution containing 10.0 percent of ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) by mass is 0.984 g/mL. (a) Calculate the molality of this solution. (b) Calculate its molarity. (c) What volume of the solution would contain 0.125 mole of ethanol?

A man bought a goldfish in a pet shop. Upon returning home, he put the goldfish in a bowl of recently boiled water that had been cooled quickly. A few minutes later the fish was found dead. Explain what happened to the fish.

A beaker of water is initially saturated with dissolved air. Explain what happens when He gas at 1 atm is bubbled through the solution for a long time.

A miner working 260 m below sea level opened a carbonated soft drink during a lunch break. To his surprise, the soft drink tasted rather “flat.” Shortly afterward, the miner took an elevator to the surface. During the trip up, he could not stop belching. Why?

Explain why molality is used for boiling-point elevation and freezing-point depression calculations and molarity is used in osmotic pressure calculations.

Describe how you would use freezing-point depression and osmotic pressure measurements to determine the molar mass of a compound. Why are boiling-point elevation and vapor-pressure lowering normally not used for this purpose?

The elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesives. inks, and pharmaceuticals) showed that it contained 40.0 percent C, 6.7 percent H, and 53.3 percent O. A solution of 0.650 g of the solid in 27.8 g of the solvent diphenyl gave a freezing- point depression of 1.56°C. Calculate the molar mass and molecular formula of the solid. (\(K_{f}\) for diphenyl is 8.00°C/m.)

How many liters of the antifreeze ethylene glycol \(\left[\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}_{2}(\mathrm{OH})\right]\) would you add to a car radiator containing 6.50 L of water if the coldest winter temperature in your area is ?20°C? Calculate the boiling point of this water-ethylene glycol mixture. (The density of ethylene glycol is 1.11 g/mL.)

A solution is prepared by condensing 4.00 L of a gas, measured at 27°C and 748 mmHg pressure, into 58.0 g of benzene. Calculate the freezing point of this solution.

Consider two aqueous solutions, one of sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)) and the other of nitric acid (\(\mathrm{HNO}_{3}\)). Both solutions freeze at -1.5°C. What other properties do these solutions have in common?

Arrange the following aqueous solutions in order of decreasing freezing point, and explain your reasoning: 0.50 m HCl, 0.50 m glucose, 0.50 m acetic acid.

Water and methanol are miscible with each other but they are immiscible with octane (\(C_{8} H_{18}\)). Which of the following shows the correct picture when equal volumes of these three liquids are mixed in a test tube at 20°C? Assume volumes to be additive. (The densities of the liquids are methanol: 0.792 g/mL; octane: 0.703 g/mL; water: 0.998 g/mL.)

Lysozyme is an enzyme that cleaves bacterial cell walls. A sample of lysozyme extracted from egg white has a molar mass of 13,930 g. A quantity of 0.100 g of this enzyme is dissolved in 150 g of water at 25°C. Calculate the vapor-pressure lowering, the depression in freezing point, the elevation in boiling point, and the osmotic pressure of this solution. (The vapor pressure of water at 25°C is 23.76 mmHg.)

Solutions A and B have osmotic pressures of 2.4 atm and 4.6 atm, respectively, at a certain temperature. What is the osmotic pressure of a solution prepared by mixing equal volumes of A and B at the same temperature?

Desalination is a process of removing dissolved salts from seawater. (a) Briefly describe how you would apply distillation and freezing for this purpose. (b) Desalination can also be accomplished by reverse osmosis, which uses high pressure to force water from a more concentrated solution to a less concentrated one. Assuming a sample of seawater is 0.50 M in NaCl, calculate the minimum pressure that needs to be applied for reverse osmosis at \(25^{\circ} \mathrm{C}\). What is the main advantage of reverse osmosis over distillation and freezing?

Fish breathe the dissolved air in water through their gills. Assuming the partial pressures of oxygen and nitrogen in air to be 0.20 atm and 0.80 atm. respectively, calculate the mole fractions of oxygen and nitrogen in water at 298 K. Comment on your results. See Example 12.6 for Henry’s law constants.

Concentrated hydrochloric acid is usually available at a concentration of 37.7 percent by mass. What is its molar concentration? (The density of the solution is 1.19 g/mL.)

Explain each of the following statements: (a) The boiling point of seawater is higher than that of pure water. (b) Carbon dioxide escapes from the solution when the cap is removed from a carbonated soft-drink bottle. (c) Molal and molar concentrations of dilute aqueous solutions are approximately equal. (d) In discussing the colligative properties of a solution (other than osmotic pressure), it is preferable to express the concentration in units of molality rather than in molarity. (e) Methanol (b.p. 65°C) is useful as an antifreeze, but it should be removed from the car radiator during the summer season.

A mixture of NaCl and sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)) of combined mass 10.2 g is dissolved in enough water to make up a 250 mL solution. The osmotic pressure of the solution is 7.32 atm at 23°C. Calculate the mass percent of NaCl in the mixture.

Making mayonnaise involves beating oil into small droplets in water, in the presence of egg yolk. What is the purpose of the egg yolk? (Hint: Egg yolk contains lecithins, which are molecules with a polar head and a long nonpolar hydrocarbon tail.)

A very long pipe is capped at one end with a semipermeable membrane. How deep (in meters) must the pipe be immersed into the sea for freshwater to begin to pass through the membrane? Assume the water to be at 20°C and treat it as a 0.70 M NaCl solution. The density of seawater is 1.03 g/\(c m^{3}\) and the acceleration due to gravity is 9.81 m/\(s^{2}\).

Two beakers, 1 and 2, containing 50 mL of 0.10 M urea and 50 mL of 0.20 M urea, respectively, are placed under a tightly sealed container (see Figure 12.12) at 298 K. Calculate the mole fraction of urea in the solutions at equilibrium. Assume ideal behavior.

The diagram shows the vapor pressure curves for pure benzene and a solution of a nonvolatile solute in benzene. Estimate the molality of the benzene solution.

A common misconception is that adding salt to the water used to cook spaghetti will decrease the cooking time, presumably because it increases the boiling point of the water. Calculate the boiling point of a typical salted water solution used to cook spaghetti. Do you think this increase in temperature will make much difference in the cooking time for spaghetti?

Estimate the volume of the oil droplet that would be formed by the compound sodium stearate shown in Figure 12.19.

Distinguish between an unsaturated solution, a saturated solution, and a supersaturated solution.

Is iodine (\(I_{2}\)) more soluble in water or in carbon disulfide (\(C S_{2}\)).

Which of the following would you expect to be more soluble in benzene than in water: \(\mathrm{C}_4 \mathrm{H}_{10}, \mathrm{HBr}, \mathrm{KNO}_3, \mathrm{P}_4\)?

From which type of solution listed in Question 12.1 does crystallization or precipitation occur? How does a crystal differ from a precipitate?

A sample of \(6.44 \mathrm{~g}\) of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) is dissolved in \(80.1 \mathrm{~g}\) of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\). Calculate the percent by mass of naphthalene in this solution.

A solution is prepared at 200°C and its concentration is expressed in three different units: percent by mass, molality, and molarity. The solution is then heated to 88°C. Which of the concentration units will change (increase or decrease)?

Basing your answer on intermolecular force considerations, explain what “like dissolves like” means.

Calculate the molality of a 5.86 Methanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) solution whose density is 0.927 g/mL.

Which of the following gases has the greatest Henry's law constant in water at 25°C: \(\mathrm{CH}_{4}\), Ne, HCl, \(H_{2}\)?

What is solvation? What factors influence the extent to which solvation occurs? Give two examples of solvation; include one that involves ion-dipole interaction and one in which dispersion forces come into play.

Calculate the molality of a 44.6 percent (by mass) aqueous solution of sodium chloride.

A solution contains equal molar amounts of liquids A and B. The vapor pressures of pure A and B are 120 mmHg and 180 mmHg, respectively, at a certain temperature. If the vapor pressure of the solution is 164 mmHg, what can you deduce about the intermolecular forces between A and B molecules compared to the intermolecular forces between A molecules and between B molecules?

As you know, some solution processes are endothermic and others are exothermic. Provide a molecular interpretation for the difference.

Calculate the molar concentration of oxygen in water at 25°C for a partial pressure of 0.22 atm. The Henry's law constant for oxygen is \(1.3 \times 10^{-3}\) mol/L . atm.

Sketch a phase diagram like that shown in Figure 12.10 for nonaqueous solutions such as naphthalene dissolved in benzene. Would the freezing-point depression and boiling-point elevation still apply in this case?

Describe the factors that affect the solubility of a solid in a liquid. What does it mean to say that two liquids are miscible?

Calculate the boiling point and freezing point of a solution containing 478 g of ethylene glycol in 3202 g of water.

Indicate which compound in each of the following groups has a greater tendency to form ion pairs in water: (a) NaCl or \(\mathrm{Na}_{2} \mathrm{SO}_{4}\), (b) \(\mathrm{MgCl}_{2}\) or \(\mathrm{MgSO}_{4}\), (c) LiBr or KBr.

Why is naphthalene (\(\mathrm{C}_{10} \mathrm{H}_{8}\)) more soluble than CsF in benzene?

What is the osmotic pressure (in atm) of a 0.884 M urea solution at 16°C?

The osmotic pressure of blood is about 7.4 atm. What is the approximate concentration of a saline solution (NaCl solution) a physician should use for intravenous injection? Use 37°C for physiological temperature.

Explain why ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) is not soluble in cyclohexane (\(C_{6} H_{12}\)).

A solution of 0.85 g of an organic compound in 100.0 g of benzene has a freezing point of 5.16°C. What are the molality of the solution and the molar mass of the solute?

Arrange the following compounds in order of increasing solubility in water: \(\mathrm{O}_{2}\), LiCl, \(B r_{2}\), methanol (\(\mathrm{CH}_{3} \mathrm{OH}\)).

Define the following concentration terms and give their units: percent by mass, mole fraction, molarity, molality. Compare their advantages and disadvantages.

Outline the steps required for conversion between molarity, molality, and percent by mass.

Calculate the percent by mass of the solute in each of the following aqueous solutions: (a) 5.50 g of NaBr in 78.2 g of solution, (b) 31.0 g of KCl in 152 g of water, (c) 4.5 g of toluene in 29 g of benzene.

Calculate the amount of water (in grams) that must be added to (a) 5.00 g of urea \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\) in the preparation of a 16.2 percent by mass solution, and (b)26.2 g of \(\mathrm{MgCl}_{2}\) in the preparation of a 1.5 percent by mass solution.

Calculate the molality of each of the following solutions: (a) 14.3 g of sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)) in 676 g of water, (b) 7.20 moles of ethylene glycol (\(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\)) in 3546 g of water.

Calculate the molality of each of the following aqueous solutions: (a) 2.50 M NaCl solution (density of solution = 1.08 g/mL), (b) 48.2 percent by mass KBr solution.

For dilute aqueous solutions in which the density of the solution is roughly equal to that of the pure solvent, the molarity of the solution is equal to its molality. Show that this statement is correct for a 0.010 M aqueous urea \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\) solution.

Calculate the molalities of the following aqueous solutions: (a) 1.22 M sugar (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)) solution (density of solution = 1.12 g/mL), (b) 0.87 M NaOH solution (density of solution = 1.04 g/mL), (c) 5.24 M \(\mathrm{NaHCO}_{3}\) solution (density of solution = 1.19 g/mL).

The alcohol content of hard liquor is normally given in terms of the “proof,” which is defined as twice the percentage by volume of ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) present. Calculate the number of grams of alcohol present in 1.00 L of 75-proof gin. The density of ethanol is 0.798 g/mL.

How do the solubilities of most ionic compounds in water change with temperature? With pressure?

Describe the fractional crystallization process and its application.

A 3.20-g sample of a salt dissolves in 9.10 g of water to give a saturated solution at 25°C. What is the solubility (in g salt/100 g of \(\mathrm{H}_{2} \mathrm{O}\)) of the salt?

A 50-g sample of impure \(\mathrm{KClO}_{3}\) (solubility = 7.1 g per 100 g \(\mathrm{H}_{2} \mathrm{O}\) at 20°C) is contaminated with 10 percent of KCl (solubility = 25.5 g per 100 g of \(\mathrm{H}_{2} \mathrm{O}\) at 20°C). Calculate the minimum quantity of 20°C water needed to dissolve all the KCl from the sample. How much \(\mathrm{KClO}_{3}\) will be left after this treatment? (Assume that the solubilities are unaffected by the presence of the other compound.)

Discuss the factors that influence the solubility of a gas in a liquid.

What is thermal pollution? Why is it harmful to aquatic life?

What is Henry’s law? Define each term in the equation, and give its units. How would you account for the law in terms of the kinetic molecular theory of gases? Give two exceptions to Henry’s law.

A student is observing two beakers of water. One beaker is heated to 30°C, and the other is heated to 100°C. In each case, bubbles form in the water. Are these bubbles of the same origin? Explain.

The solubility of \(N_{2}\) in blood at 37°C and at a partial pressure of 0.80 atm is \(5.6 \times 10^{-4}\) mol/L. A deep-sea diver breathes compressed air with the partial pressure of \(N_{2}\) equal to 4.0 atm. Assume that the total volume of blood in the body is 5.0 L. Calculate the amount of \(N_{2}\) gas released (in liters at 373C and 1 atm) when the diver returns to the surface of the water, where the partial pressure of \(N_{2}\) is 0.80 atm.

What are colligative properties? What is the meaning of the word “colligative” in this context?

Write the equation representing Raoult’s law, and express it in words.

Use a solution of benzene in toluene to explain what is meant by an ideal solution.

Write the equations relating boiling-point elevation and freezing-point depression to the concentration of the solution. Define all the terms, and give their units.

How is vapor-pressure lowering related to a rise in the boiling point of a solution?

Use a phase diagram to show the difference in freezing points and boiling points between an aqueous urea solution and pure water.

What is osmosis? What is a semipermeable membrane?

A solution is prepared by dissolving 396 g of sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)) in 624 g of water. What is the vapor pressure of this solution at 30°C? (The vapor pressure of water is 31.8 mmHg at 30°C.)

How many grams of sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)) must be added to 552 g of water to give a solution with a vapor pressure 2.0 mmHg less than that of pure water at 20°C? (The vapor pressure of water at 20°C is 17.5 mmHg.)

The vapor pressure of benzene is 100.0 mmHg at 26.1°C. Calculate the vapor pressure of a solution containing 24.6 g of camphor (\(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}\)) dissolved in 98.5 g of benzene. (Camphor is a low-volatility solid.)

The vapor pressure of ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) at 20°C is 44 mmHg, and the vapor pressure of methanol (\(\mathrm{CH}_{3} \mathrm{OH}\)) at the same temperature is 94 mmHg. A mixture of 30.0 g of methanol and 45.0 g of ethanol is prepared (and can be assumed to behave as an ideal solution). (a) Calculate the vapor pressure of methanol and ethanol above this solution at 20°C. (b) Calculate the mole fraction of methanol and ethanol in the vapor above this solution at 20°C. (c) Suggest a method for separating the two components of the solution.

How many grams of urea [\(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\)] must be added to 450 g of water to give a solution with a vapor pressure 2.50 mmHg less than that of pure water at 30°C? (The vapor pressure of water at 30°C is 31.8 mmHg.)

An aqueous solution contains the amino acid glycine (\(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\)). Assuming that the acid does not ionize in water, calculate the molality of the solution if it freezes at ?1.1°C.

Pheromones are compounds secreted by the females of many insect species to attract males. One of these compounds contains 80.78 percent C, 13.56 percent H, and 5.66 percent O. A solution of 1.00 g of this pheromone in 8.50 g of benzene freezes at 3.37°C. What are the molecular formula and molar mass of the compound? (The normal freezing point of pure benzene is 5.50°C.)

A solution of 2.50 g of a compound having the empirical formula \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{P}\) in 25.0 g of benzene is observed to freeze at 4.3°C. Calculate the molar mass of the solute and its molecular formula.

A quantity of 7.480 g of an organic compound is dissolved in water to make 300.0 mL of solution. The solution has an osmotic pressure of 1.43 atm at 27°C. The analysis of this compound shows that it contains 41.8 percent C, 4.7 percent H, 37.3 percent O, and 16.3 percent N. Calculate the molecular formula of the compound.

Problem 66P A solution of 6.85 g of a carbohydrate in 100.0 g of water has a density of 1.024 g/mL and an osmotic pressure of 4.61 atm at 20.0°C. Calculate the molar mass of the carbohydrate.

What is the van’t Hoff factor? What information does it provide?

What are the normal freezing points and boiling points of the following solutions? (a) 21.2 g NaCl in 135 mL of water and (b) 15.4 g of urea in 66.7 mL of water

At 25°C the vapor pressure of pure water is 23.76 mmHg and that of seawater is 22.98 mmHg. Assuming that seawater contains only NaCl, estimate its molal concentration.

Both NaCl and \(\mathrm{CaCl}_{2}\) are used to melt ice on roads and sidewalks in winter. What advantages do these substances have over sucrose or urea in lowering the freezing point of water?

A 0.86 percent by mass solution of NaCl is called “physiological saline” because its osmotic pressure is equal to that of the solution of blood cells. Calculate the osmotic pressure of this solution at normal body temperature (37°C). Note that the density of the saline solution is 1.005 g/mL.

The osmotic pressure of 0.010 M solutions of \(\mathrm{CaCl}_{2}\) and urea at 25°C are 0.605 atm and 0.245 atm, respectively. Calculate the van’t Hoff factor for the \(\mathrm{CaCl}_{2}\) solution.

Calculate the osmotic pressure of a 0.0500 M \(\mathrm{MgSO}_{4}\) solution at 25°C. (Hint: See Table 12.3.)

What are colloids? Referring to Table 12.4, why is there no colloid in which both the dispersed phase and the dispersing medium are gases?

Describe how hydrophilic and hydrophobic colloids are stabilized in water.

Aqueous solutions A and B both contain urea at different concentrations. On standing exposed to air, the vapor pressure of A remains constant while that of B gradually decreases. (a) Which solution has a higher boiling point? (b) Eventually the two solutions have the same vapor pressure. Explain.

A cucumber placed in concentrated brine (salt water) shrivels into a pickle. Explain.

Two liquids A and B have vapor pressures of 76 mmHg and 132 mmHg, respectively, at 25°C. What is the total vapor pressure of the ideal solution made up of (a) 1.00 mole of A and 1.00 mole of B and (b) 2.00 moles of A and 5.00 moles of B?

Calculate the van't Hoff factor of \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) in a 0.40 m solution whose freezing point is -2.6°C.

A 262-mL sample of a sugar solution containing 1.22 g of the sugar has an osmotic pressure of 30.3 mmHg at 35°C. What is the molar mass of the sugar?

An aqueous solution of a 0.10 M monoprotic acid HA has an osmotic pressure of 3.22 atm at 25°C. What is the percent ionization of the acid at this concentration?

Calculate the mass of naphthalene (\(C_{10} H_{8}\)) that must be added to 250 g of benzene (\(C_{6} H_{6}\)) to give a solution with a freezing point 2.00°C below that of pure benzene.

Consider the three mercury manometers shown here. One of them has 1 mL of water on top of the mercury, another has 1 mL of a 1 m urea solution on top of the mercury, and the third one has 1 mL of a 1 m NaCl solution placed on top of the mercury. Which of these solutions is in the tube labeled X, which is in Y, and which is in Z?

A forensic chemist is given a white powder for analysis. She dissolves 0.50 g of the substance in 8.0 g of benzene. The solution freezes at 3.9°C. Can the chemist conclude that the compound is cocaine (\(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}\))? What assumptions are made in the analysis?

“Time-release” drugs have the advantage of releasing the drug to the body at a constant rate so that the drug concentration at any time is not too high as to have harmful side effects or too low as to be ineffective. A schematic diagram of a pill that works on this basis is shown below. Explain how it works.

Hydrogen peroxide with a concentration of 3.0 percent (3.0 g of \(\mathrm{H}_{2} \mathrm{O}_{2}\) in 100 mL of solution) is sold in drugstores for use as an antiseptic. For a 10.0-mL 3.0 percent \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution, calculate (a) the oxygen gas produced (in liters) at STP when the compound undergoes complete decomposition and (b) the ratio of the volume of \(\mathrm{O}_{2}\) collected to the initial volume of the \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution.

Two beakers, one containing a 50-mL aqueous 1.0 M glucose solution and the other a 50-mL aqueous 2.0 M glucose solution, are placed under a tightly sealed bell jar at room temperature. What are the volumes in these two beakers at equilibrium?

In the apparatus shown here, what will happen if the membrane is (a) permeable to both water and the \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\) ions, (b) permeable to water and \(\mathrm{Na}^{+}\) ions but not to \(\mathrm{Cl}^{-}\) ions, (c) permeable to water but not to \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\) ions?

Explain why it is essential that fluids used in intravenous injections have approximately the same osmotic pressure as blood.

A 1.32-g sample of a mixture of cyclohexane (\(\mathrm{C}_{6} \mathrm{H}_{12}\)) and naphthalene (\(\mathrm{C}_{10} \mathrm{H}_{8}\)) is dissolved in 18.9 g of benzene (\(\mathrm{C}_{6} \mathrm{H}_{6}\)). The freezing point of the solution is 2.2°C. Calculate the mass percent of the mixture. (See Table 12.2 for constants.)

The concentration of commercially available concentrated sulfuric acid is 98.0 percent by mass, or 18 M. Calculate the density and the molality of the solution.

For ideal solutions, the volumes are additive. This means that if 5 mL of A and 5 mL of B form an ideal solution, the volume of the solution is 10 mL. Provide a molecular interpretation for this observation. When 500 mL of ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)) are mixed with 500 mL of water, the final volume is less than 1000 mL. Why?

Ammonia (\(\mathrm{NH}_{3}\)) is very soluble in water, but nitrogen trichloride (\(\mathrm{NCl}_{3}\)) is not. Explain.

Acetic acid is a polar molecule and can form hydrogen bonds with water molecules. Therefore, it has a high solubility in water. Yet acetic acid is also soluble in benzene (\(\mathrm{C}_{6} \mathrm{H}_{6}\)), a nonpolar solvent that lacks the ability to form hydrogen bonds. A solution of 3.8 g of \(\mathrm{CH}_{3} \mathrm{COOH}\) in 80 g \(\mathrm{C}_{6} \mathrm{H}_{6}\) has a freezing point of 3.5°C. Calculate the molar mass of the solute and suggest what its structure might be. (Hint: Acetic acid molecules can form hydrogen bonds between themselves.)

Problem 127P Two beakers are placed in a closed container. Beaker A initially contains 0.15 mole of naphthalene (C10H8) in 100 g of benzene (C6H6) and beaker B initially contains 31 g of an unknown compound dissolved in 100 g of benzene. At equilibrium, beaker A is found to have lost 7.0 g of benzene. Assuming ideal behavior, calculate the molar mass of the unknown compound. State any assumptions made.

Use Henry’s law and the ideal gas equation to prove the statement that the volume of a gas that dissolves in a given amount of solvent is independent of the pressure of thè gas. (Hint: Henry’s law can be modified as n = kP, where n is the number of moles of the gas dissolved in the solvent.)

(a) Derive the equation relating the molality (m) of a solution to its molarity (M) where d is the density of the solution (g/mL) and ? is the molar mass of the solute (g/mol). (Hint: Start by expressing the solvent in kilograms in terms of the difference between the mass of the solution and the mass of the solute.) (b) Show that, for dilute aqueous solutions, m is approximately equal to M.

At 298 K, the osmotic pressure of a glucose solution is 10.50 atm. Calculate the freezing point of the solution. The density of the solution is 1.16 g/mL.

A student carried out the following procedure to measure the pressure of carbon dioxide in a soft drink bottle. First, she weighed the bottle (853.5 g). Next, she carefully removed the cap to let the \(\mathrm{CO}_{2}\) gas escape. She then reweighed the bottle with the cap (851.3 g). Finally, she measured the volume of the soft drink (452.4 mL). Given that Henry’s law constant for \(\mathrm{CO}_{2}\) in water at 25°C is \(3.4 \times 10^{-2}\) mol/L · atm, calculate the pressure of \(\mathrm{CO}_{2}\) in the original bottle. Why is this pressure only an estimate of the true value?

Here is an after-dinner trick. With guests still sitting at the table, the host provided each of them with a glass of water containing an ice cube floating on top and a piece of string about 2–3 in. in length. He then asked them to find a way to lift the ice cube without touching it by hand or using any other objects such as a spoon or fork. Explain how this task can be accomplished. (Hint: The table had not been cleared so the salt and pepper shakers were still there.)

The molecule drawn here has shown promise as an agent for cleaning up oil spills in water. Instead of dispersing the oil into water as soap molecules would do (see Figures 12.19 and 12.20), these molecules bind with the oil to form a gel, which can be easily separated from the body of water. Suggest an explanation for the ability of this compound to remove oil from water.

The Henry’s law constant of oxygen in water at 25°C is \(1.3 \times 10^{-3}\) mol/L atm. Calculate the molarity of oxygen in water under 1 atmosphere of air Comment on the prospect for our survival without hemoglobin molecules. (Recall from previous problems that the total volume of blood in an adult human is about 5 L.)

The diagram here shows the vapor pressure curves of two liquids A and B and a solution of the two liquids. Given that A is more volatile than B, match the curves with the pure liquids and the solution.

The solubility of \(\mathrm{KNO}_{3}\) is 155 g per 100 g of water at 75°C and 38.0 g at 25°C. What mass (in grams) of \(\mathrm{KNO}_{3}\) will crystallize out of solution if exactly 100 g of its saturated solution at 75°C is cooled to 25°C?

The solubility of \(\mathrm{CO}_{2}\) in water at 25°C and 1 atm is 0.034 mol/L. What is its solubility under atmospheric conditions? (The partial pressure of \(\mathrm{CO}_{2}\) in air is 0.0003 atm.) Assume that \(\mathrm{CO}_{2}\) obeys Henry’s law.

Write the equation relating osmotic pressure to the concentration of a solution. Define all the terms and specify their units.

The vapor pressure of ethanol \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) and l-propanol \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\) at 35°C are 100 mmHg and 37.6 mmHg, respectively. Assume ideal behavior and calculate the partial pressures of ethanol and l-propanol at 35°C over a solution of ethanol in l-propanol, in which the mole fraction of ethanol is 0.300.

What are the boiling point and freezing point of a 2.47 m solution of naphthalene in benzene? (The boiling point and freezing point of benzene are 80.1°C and 5.5°C, respectively.)

The molar mass of benzoic acid \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\) determined by measuring the freezing-point depression in benzene is twice what we would expect for the molecular formula \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}\). Explain this apparent anomaly.

What is the osmotic pressure (in atm) of a \(1.36 M\) aqueous solution of urea \(\left[\left(\mathrm{NH}_2\right)_2 \mathrm{CO}\right]\) at \(22.0^{\circ} \mathrm{C}\)?

A solution containing 0.8330 g of a polymer of unknown structure in 170.0 mL of an organic solvent was found to have osmotic pressure of 5.20 mmHg at 25°C. Determine the molar mass of the polymer.

What are ion pairs? What effect does ion-pair formation have on the colligative properties of a solution? How does the ease of ion-pair formation depend on (a) charges on the ions, (b) size of the ions, (c) nature of the solvent (polar versus non-polar), (d) concentration?

Which of the following aqueous solutions has (a) the higher boiling point, (b) the higher freezing point, and (c) the lower vapor pressure: 0.35 m \(\mathrm{CaCl}_{2}\) or 0.90 m urea? Explain. Assume \(\mathrm{CaCl}_{2}\) to undergo complete dissociation.

Arrange the following solutions in order of decreasing freezing point: 0.10 m \(N a_{3} P_{4}\), 0.35 m NaCl, 0.20 m \(\mathrm{MgCl}_{2}\), 0.15 m \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), 0.15 m \(\mathrm{CH}_{3} \mathrm{COOH}\).

A solution of 1.00 g of anhydrous aluminum chloride, \(\mathrm{AlCl}_{3}\), in 50.0 g of water freezes at -1.11°C. Does the molar mass determined from this freezing point agree with that calculated from the formula? Why?

A protein has been isolated as a salt with the formula \(N a_{20} P\) (this notation means that there are 20 \(\mathrm{Na}^{+}\) ions associated with a negatively charged protein \(P^{20-}\)). The osmotic pressure of a 10.0-ml solution containing 0.225 g of the protein is 0.257 atm at 25.0°C. (a) Calculate the molar mass of the protein from these data. (b) Calculate the actual molar mass of the protein.

A nonvolatile organic compound Z was used to make up two solutions. Solution A contains 5.00 g of Z dissolved in 100 g of water, and solution B contains 2.31 g of Z dissolved in 100 g of benzene. Solution A has a vapor pressure of 754.5 mmHg at the normal boiling point of water, and solution B has the same vapor pressure at the normal boiling point of benzene. Calculate the molar mass of Z in solutions A and B and account for the difference.

State which of the alcohols listed in Problem 12.12 you would expect to be the best solvent for each of the following substances, and explain why: (a) \(I_{2}\), (b) KBr, (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\).

Before a carbonated beverage bottle is sealed, it is pressurized with a mixture of air and carbon dioxide. (a) Explain the effervescence that occurs when the cap of the bottle is removed. (b) What causes the fog to form near the mouth of the bottle right after the cap is removed?

Iodine (\(I_{2}\)) is only sparingly soluble in water (left photo). Yet upon the addition of iodide ions (for example, from KI), iodine is converted to the triiodide ion, which readily dissolves (right photo): \(I_{2}(s)+I^{-}(a q) \rightleftharpoons I_{3}^{-}(a q)\) Describe the change in solubility of \(I_{2}\) in terms of the change in intermolecular forces.

A 0.050 M hydrofluoric acid (HF) solution is 11 percent ionized at 25°C. Calculate the osmotic pressure of the solution.

Shown here is a plot of vapor pressures of two liquids A and B at different concentrations at a certain temperature. Which of the following statements are false? (a) The solutions exhibit negative deviation from Raoult's law. (b) A and B molecules attract each other more weakly than they do their own kind. (c) \(\Delta H_{s o l n}\) is positive. (d) At \(X_{A}=0.20\), the solution has a higher boiling point than liquid B and a lower boiling point than liquid A.

How does each of the following affect the solubility of an ionic compound? (a) Lattice energy, (b) solvent (polar versus nonpolar), (c) enthalpies of hydration of cation and anion.

A solution contains two volatile liquids A and B. Complete the following table, in which the symbol ? indicates attractive intermolecular forces.

The concentration of commercially available concentrated nitric acid is 70.0 percent by mass, or 15.9 M. Calculate the density and the molality of the solution.

A mixture of ethanol and l-propanol behaves ideally at 36°C and is in equilibrium with its vapor. If the mole fraction of ethanol in the solution is 0.62, calculate its mole fraction in the vapor phase at this temperature. (The vapor pressures of pure ethanol and l-propanol at 36°C are 108 mmHg and 40.0 mmHg, respectively.)

Aluminum sulfate \(\left[\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\right]\) is sometimes used in municipal water treatment plants to remove undesirable particles. Explain how this process works.

Acetic acid is a weak acid that ionizes in solution as follows: \(\mathrm{CH}_{3} \mathrm{COOH}(a q) \rightleftharpoons \mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{H}^{+}(a q)\) If the freezing point of a 0.106 m \(\mathrm{CH}_{3} \mathrm{COOH}\) solution is -0.203°C, calculate the percent of the acid that has undergone ionization.

A 2.6-L sample of water contains 192 ????g of lead. Does this concentration of lead exceed the safety limit of 0.050 ppm of lead per liter of drinking water? [Hint: 1 ????g = \(1 \times 10^{-6}\) g. Parts per million (ppm) is defined as (mass of component/mass of solution) \(\times 10^{6}\).]

Certain fishes in the Antarctic Ocean swim in water at about -2°C. (a) To prevent their blood from freezing, what must be the concentration in molality) of the blood? Is this a reasonable physiological concentration? (b) In recent years scientists have discovered a special type of protein in these fishes' blood which, although present in quite low concentrations (? 0.001 m), has the ability to prevent the blood from freezing. Suggest a mechanism for its action.

As we know, if a soft drink can is shaken and then opened, the drink escapes violently. However, if after shaking the can we tap it several times with a metal spoon, no such "explosion" of the drink occurs. Why?

Why are ice cubes (for example, those you see in the trays in the freezer of a refrigerator) cloudy inside?

Two beakers are placed in a closed container. Beaker A initially contains 0.15 mole of naphthalene (\(C_{10} H_{8}\)) in 100 g of benzene (\(C_{6} H_{6}\)) and beaker B initially contains 31 g of an unknown compound dissolved in 100 g of benzene. At equilibrium, beaker A is found to have lost 7.0 g of benzene. Assuming ideal behavior, calculate the molar mass of the unknown compound. State any assumptions made.

At 27°C, the vapor pressure of pure water is 23.76 mmHg and that of an urea solution 22.98 mmHg. Calculate the molality of solution.

An example of the positive deviation shown in Figure 12.8(a) is a solution made of acetone \(\left(\mathrm{CH}_3 \mathrm{COCH}_3\right)\) and carbon disulfide (C \(\left.\mathrm{S}_2\right)\). (a) Draw Lewis structures of these molecules. Explain the deviation from ideal behavior in terms of intermolecular forces. (b) A solution composed of 0.60 mole of acetone and 0.40 mole of carbon disulfide has a vapor pressure of 615mmHg at \(35.2^{\circ} \mathrm{C}\). What would be the vapor pressure if the solution behaved ideally? The vapor pressure of the pure solvents at the same temperature are: acetone: 349mmHg; carbon disulfide: 501mmHg}. (c) Predict the sign of \(\Delta H_{\text {soln }}\).

Liquids A (molar mass 100 g/mol) and B (molar mass 110 g/mol ) form an ideal solution. At \(55^{\circ} \mathrm{C}\), A has a vapor pressure of 95 mmHg and B has a vapor pressure of 42 mmHg. A solution is prepared by mixing equal masses of A and B. (a) Calculate the mole fraction of each component in the solution. (b) Calculate the partial pressures of A and B over the solution at \(55^{\circ} \mathrm{C}\). (c) Suppose that some of the vapor described in (b) is condensed to a liquid in a separate container. Calculate the mole fraction of each component in this liquid and the vapor pressure of each component above this liquid at \(55^{\circ} \mathrm{C}\).

A mixture of liquids A and B exhibits ideal behavior. At 84°C, the total vapor pressure of a solution containing 1.2 moles of A and 2.3 moles of B is 331 mmHg. Upon the addition of another mole of B to the solution, the vapor pressure increases to 347 mmHg. Calculate the vapor pressures of pure A and B at 84°C.

Valinomycin is an antibiotic. It functions by binding \(K^{+}\) ions and transporting them across the membrane into cells to offset the ionic balance. The molecule is represented here by its skeletal structure in which the end of each straight line corresponds to a carbon atom (unless a N or an O atom is shown at the end of the line). There are as many H atoms attached to each C atom as necessary to give each C atom a total of four bonds. Use the "like dissolves like" guideline to explain its function. (Hint: The -\(\mathrm{CH}_{3}\) groups at the two ends of the Y shape are nonpolar.)

Often the determination of the molar mass of a compound by osmotic pressure measurement is carried out at several different concentrations to get a more reliable average value. From the following data for the osmotic pressure of poly(methyl methacrylate) in toluene at 25°C, determine graphically the molar mass of the polymer. [Hint: Rearrange Equation (12.8) so that ???? is expressed in terms of c, which is the number of grams of the solute per liter of solution.]