Chapter 13

At \(60^{\circ} \mathrm{C}\) the vapor pressure of pure water is \(149.44 \mathrm{mmHg}\) and that above an aqueous sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{12},\) solution is \(119.55 \mathrm{mmHg} .\) Calculate the mole fraction of water and the mass in grams of sucrose in the solution if the mass of water is \(150 . \mathrm{g}\).

At \(60^{\circ} \mathrm{C}\) the vapor pressure of pure water is \(149.44 \mathrm{mmHg}\) and that above an aqueous sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{12},\) solution is \(119.55 \mathrm{mmHg} .\) Calculate the mole fraction of water and the mass in grams of sucrose in the solution if the mass of water is \(150 . \mathrm{g}\).

At \(760 \mathrm{mmHg}\), a solution of \(5.58 \mathrm{~g}\) glycerol in \(40.0 \mathrm{~g}\) water has a boiling point of \(100.777{ }^{\circ} \mathrm{C}\). Calculate the molar mass of glycerol.

The freezing point of \(p\) -dichlorobenzene is \(53.1{ }^{\circ} \mathrm{C},\) and its \(K_{\mathrm{f}}\) is \(-7.10^{\circ} \mathrm{C} \mathrm{kg} / \mathrm{mol}\). A solution of \(1.52 \mathrm{~g}\) of the drug sulfanilamide in \(10.0 \mathrm{~g} p\) -dichlorobenzene freezes at \(46.7^{\circ} \mathrm{C} .\) Calculate the molar mass of sulfanilamide.

Anthracene, a hydrocarbon obtained from coal, has an empirical formula of \(\mathrm{C}_{7} \mathrm{H}_{5} .\) To find its molecular formula you dissolve \(0.500 \mathrm{~g}\) anthracene in \(30.0 \mathrm{~g}\) henzene. The boiling point of the solution is \(80.34{ }^{\circ} \mathrm{C}\). Determine the molar mass and molecular formula of anthracene.

A \(1.00 \mathrm{~mol} / \mathrm{kg}\) aqueous sulfuric acid solution, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), freezes at \(-4.04{ }^{\circ} \mathrm{C}\). Calculate \(i\), the van't Hoff factor, for sulfuric acid in this solution.

The molar mass of a polymer was determined by measuring the osmotic pressure, \(7.6 \mathrm{mmHg},\) of a benzene solution containing \(5.0 \mathrm{~g}\) of the polymer dissolved in \(1.0 \mathrm{~L}\) solution. Calculate the molar mass of the polymer. Assume a temperature of \(298.15 \mathrm{~K}\).

The osmotic pressure at \(25^{\circ} \mathrm{C}\) is 1.79 atm for a solution prepared by dissolving \(2.50 \mathrm{~g}\) sucrose, empirical formula \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), in enough water to give a solution volume of \(100 \mathrm{~mL}\). Use the osmotic pressure equation to show that the empirical formula for sucrose is the same as its molecular formula.

Differentiate between the dispersed phase and the continuous phase of (a) soap suds; (b) milk; (c) airborne pollen grains; (d) margarine.

Differentiate between the dispersed phase and the continuous phase of (a) gelatin; (b) butter; (c) aerosol sprays; (d) mud.

Explain how globular proteins act as hydrophilic colloids in water.

Explain the role of micelles in the cleansing action of soaps.

Shampoos often contain sodium lauryl sulfate, a detergent. Explain why this detergent is an ingredient in shampoos.

Where is most of the fresh water found on Earth?

Some dietitians recommend drinking six 8-oz glasses of water each day. If your drinking water contains the maximum contamination level for arsenic, 0.010 ppm, how much arsenic would you consume in a week following this recommendation?

The U. S. EPA acceptable limit for lead in drinking water is 0.015 ppm. If you drink six 8 -oz. glasses of water each day and do not excrete any lead, calculate how long it would take for you to accumulate \(0.50 \mathrm{mg} \mathrm{Pb}\).

The maximum contamination level (MCL) for chlordane is 0.002 ppm. A sample of well water contained 5 ppb chlordane. Is the sample within the MCL for chlordane?

In a home, hard water containing \(500 . \mathrm{mg} \mathrm{Ca}^{2+} / \mathrm{gal}\) passed through the \(\mathrm{Na}^{+}\) -based ion-exchange water softener. If there was 200 gal. water and the ion-exchange resin operates at \(100 \%\) efficiency, calculate the mass of \(\mathrm{Na}^{+}\) ions displaced from the resin.

How do the lime-soda and ion-exchange processes differ in treating hard water?

Explain how hard water produces "ring around the bathtub."

During municipal drinking water treatment, water is sprayed into the air. Why is this done?

Discuss the risks and benefits of using ozone to treat municipal drinking water.

What is the difference between solubility and miscibility?

If \(5 \mathrm{~g}\) solvent, \(0.2 \mathrm{~g}\) solute \(\mathrm{A},\) and \(0.3 \mathrm{~g}\) solute \(\mathrm{B}\) are mixed to form a solution, calculate the weight percent of \(\mathrm{A} .\)

A chemistry classmate tells you that a supersaturated solution is also saturated. Is the student correct? What would you tell the student about her/his statement?

A 10.0 -M aqueous solution of \(\mathrm{NaOH}\) has a density of \(1.33 \mathrm{~g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C}\). Calculate the weight percent of \(\mathrm{NaOH}\) in the solution.

Concentrated aqueous ammonia is \(14.8 \mathrm{M}\) and has a density of \(0.90 \mathrm{~g} / \mathrm{cm}^{3} .\) Calculate the weight percent of \(\mathrm{NH}_{3}\) in the solution.

(a) Calculate the molality of a solution made by dissolving \(115.0 \mathrm{~g}\) ethylene glycol, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH},\) in \(500 . \mathrm{mL}\) water. The density of water at this temperature is \(0.978 \mathrm{~g} / \mathrm{mL}\) (b) Calculate the molarity of the solution.

Dimethylglyoxime (DMG) reacts with nickel(II) ion in aqueous solution to form a bright red compound. However, DMG is insoluble in water. To get it into aqueous solution where it can encounter \(\mathrm{Ni}^{2+}\) ions, it must first be dissolved in a suitable solvent, such as ethanol. Suppose you dissolve \(45.0 \mathrm{~g} \mathrm{DMG}\left(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{~N}_{2} \mathrm{O}_{2}\right)\) in \(500 . \mathrm{mL}\) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} ;\right.\) density \(\left.=0.7893 \mathrm{~g} / \mathrm{mL}\right) .\) Determine the molality and weight percent of DMG in this solution.

Arrange these aqueous solutions in order of decreasing freezing point. (Assume theoretical values for \(i\).) (a) \(0.20 \mathrm{~mol}\) ethylene \(\mathrm{glycol} / \mathrm{kg}\) (b) \(0.12 \mathrm{~mol} \mathrm{Na}_{2} \mathrm{SO}_{4} / \mathrm{kg}\) (c) \(0.10 \mathrm{~mol} \mathrm{NaBr} / \mathrm{kg}\) (d) \(0.12 \mathrm{~mol} \mathrm{KI} / \mathrm{kg}\)

Arrange these aqueous solutions in order of increasing boiling point. (Assume theoretical values for \(i\).) (a) \(0.20 \mathrm{~mol}\) ethylene \(\mathrm{glycol} / \mathrm{kg}\) (b) \(0.12 \mathrm{~mol} \mathrm{~K}_{2} \mathrm{SO}_{4} / \mathrm{kg}\) (c) \(0.10 \mathrm{~mol} \mathrm{BaCl}_{2} / \mathrm{kg}\) (d) \(0.12 \mathrm{~mol} \mathrm{KBr} / \mathrm{kg}\)

The organic salt \(\left[\left(\mathrm{C}_{4} \mathrm{H}_{9}\right)_{4} \mathrm{~N}\right]\left[\mathrm{ClO}_{4}\right]\) consists of the ions \(\left(\mathrm{C}_{4} \mathrm{H}_{9}\right)_{4} \mathrm{~N}^{+}\) and \(\mathrm{ClO}_{4}^{-}\). The salt dissolves in chloroform. What mass (in grams) of the salt must have been dissolved if the boiling point of a solution of the salt in \(25.0 \mathrm{~g}\) chloroform is \(63.20^{\circ} \mathrm{C} ?\) The normal boiling point of chloroform is \(61.70{ }^{\circ} \mathrm{C}\) and \(K_{\mathrm{b}}=3.63{ }^{\circ} \mathrm{C} \mathrm{kg} \mathrm{mol}^{-1}\). Assume that the salt dissociates completely into its ions in solution.

A solution, prepared by dissolving \(9.41 \mathrm{~g} \mathrm{NaHSO}_{3}\) in \(1.00 \mathrm{~kg}\) water, freezes at \(-0.33{ }^{\circ} \mathrm{C}\). From these data, decide which of these equations is the correct expression for the dissociation of the salt. (a) \(\mathrm{NaHSO}_{3}(\mathrm{aq}) \longrightarrow \mathrm{Na}^{+}(\mathrm{aq})+\mathrm{HSO}_{3}^{-}(\mathrm{aq})\) (b) \(\mathrm{NaHSO}_{3}(\mathrm{aq}) \longrightarrow \mathrm{Na}^{+}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{SO}_{3}^{2-}(\mathrm{aq})\)

A \(0.250-\mathrm{M}\) sodium sulfate solution is added to a \(0.200-\mathrm{M}\) barium nitrate solution and \(0.700 \mathrm{~g}\) barium sulfate precipitates. (a) Write the balanced equation for this reaction. (b) Calculate the minimum volume of barium nitrate solution that was used. (c) Calculate the minimum volume of sodium sulfate needed to precipitate \(0.700 \mathrm{~g}\) barium sulfate. Assume \(100 \%\) yield.

A martini is a \(5-\mathrm{oz}(142-\mathrm{g})\) cocktail containing \(30 \%\) by mass of alcohol. When the martini is consumed, about \(15 \%\) of it passes directly into the bloodstream (blood volume \(=7.0 \mathrm{~L}\) in an adult). Consider an adult who drinks two martinis with lunch. Estimate the blood alcohol concentration in this person after the two martinis have been consumed. An adult with a blood alcohol concentration of \(3.0 \times 10^{-4} \mathrm{~g} / \mathrm{mL}\) or more is considered intoxicated. Is the person intoxicated?

What happens on the molecular level when a liquid freezes? What effect does a nonvolatile solute have on this process? Comment on the purity of water obtained by melting an iceberg.

In your own words, explain why (a) seawater has a lower freezing point than fresh water. (b) salt is added to the ice in an ice cream maker to freeze the ice cream faster.

Criticize these statements. (a) A saturated solution is always a concentrated one. (b) A \(0.10-\mathrm{mol} / \mathrm{kg}\) sucrose solution and a \(0.10-\mathrm{mol} / \mathrm{kg} \mathrm{KCl}\) solution have the same osmotic pressure.

In chemical research, newly synthesized compounds are often sent to commercial laboratories for analysis that determines the weight percent of \(\mathrm{C}\) and \(\mathrm{H}\) by burning the compound and collecting the evolved \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) ( Sec. \(3-9\) ). The molar mass is determined by measuring the osmotic pressure of a solution of the compound. Calculate the empirical and molecular formulas of a compound, \(\mathrm{C}_{x} \mathrm{H}_{y} \mathrm{Cr}\), given this information: (a) The compound contains \(73.94 \% \mathrm{C}\) and \(8.27 \% \mathrm{H} ;\) the remainder is chromium. (b) At \(25^{\circ} \mathrm{C}\), the osmotic pressure of \(5.00 \mathrm{mg}\) of the unknown dissolved in \(100 . \mathrm{mL}\) of chloroform solution is \(3.17 \mathrm{mmHg}\)

An osmotic pressure of 5.15 atm is developed by a solution containing \(4.80 \mathrm{~g}\) dioxane (a nonelectrolyte) dissolved in \(250 . \mathrm{mL}\) water at \(15.0^{\circ} \mathrm{C}\). The empirical formula of dioxane is \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O} .\) Use the osmotic pressure data to show that the empirical formula and the molecular formula of dioxane are not the same.

The osmotic pressure of human blood at \(37^{\circ} \mathrm{C}\) is 7.63 atm. Calculate what the molarity of a glucose solution should be if it is to be safely administered intravenously.

Consider these data for aqueous solutions of ammonium chloride, \(\mathrm{NH}_{4} \mathrm{Cl}\). $$\begin{array}{cc}\hline \text { Molality }(\mathrm{mol} / \mathrm{kg}) & \text { Freezing Point }\left({ }^{\circ} \mathrm{C}\right) \\\\\hline 0.0050 & -0.0158 \\\0.020 & -0.0709 \\\0.20 & -0.678 \\\1.0 & -3.33\end{array}$$ (a) Plot these data and from the graph determine the freezing point of a \(0.50 \mathrm{~mol} / \mathrm{kg}\) ammonium chloride solution. (b) Calculate the van't Hoff \(i\) factor for each concentration. Explain any trend that you see. (c) Calculate the percent dissociation of ammonium chloride in each solution.

Maple syrup sap is \(3 \%\) sugar (sucrose) and \(97 \%\) water by mass. Maple syrup is produced by heating the sap to evaporate a certain amount of the water. (a) Describe what happens to the composition and boiling point of the solution as evaporation takes place. (b) A rule of thumb among maple syrup producers is that the finished syrup should boil about \(4{ }^{\circ} \mathrm{C}\) higher than the original sap being boiled. Explain the chemistry behind this guideline. (c) If the finished product boils \(4^{\circ} \mathrm{C}\) higher than the original sap, calculate the concentration of sugar in the final product. Assume that sugar is the only solute and the operation is done at 1 atm pressure.

A \(0.63 \%\) by weight aqueous tin(II) fluoride, \(\mathrm{SnF}_{2},\) solution is used as an oral rinse in dentistry to decrease tooth decay. (a) Calculate the \(\mathrm{SnF}_{2}\) concentration in ppm and ppb. (b) Calculate the molarity of \(\mathrm{SnF}_{2}\) in the solution. (c) Tin(II) fluoride is produced commercially by a series of steps that begin with reduction of cassiterite, \(\mathrm{SnO}_{2}\), the principal tin ore, with carbon.$$\mathrm{SnO}_{2}(\mathrm{~s})+2 \mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{Sn}(\mathrm{s})+2 \mathrm{CO}(\mathrm{g})$$ Once purified, the tin is reacted with hydrogen fluoride vapor to produce \(\mathrm{SnF}_{2}\). Consider that one metric ton of cassiterite ore is reduced with sufficient carbon to tin metal in \(80 \%\) yield. The tin is purified and reacted with sufficient hydrogen fluoride to produce \(\mathrm{SnF}_{2}\) in \(94 \%\) yield. Calculate how many \(250 .-\mathrm{mL}\) bottles of \(0.63 \%\) \(\mathrm{SnF}_{2}\) solution could be prepared from the one metric ton of cassiterite by these steps.