Chemistry: The Molecular Nature of Matter

Problem 1

Why do two gases spontaneously mix when they are brought into contact?

David Collins

Numerade Educator

01:27

Problem 2

When substances form liquid solutions, what two factors are involved in determining the solubility of the solute in the solvent?

David Collins

Numerade Educator

Silver chloride is not soluble in water. What are the relative strengths of the inter molecular forces between $\mathrm{Ag}^{+}$ and Cl" ions and water molecules as compared to the inter molecular forces between water molecules and the forces that hold the silver chloride as a solid?

David Collins

Numerade Educator

01:12

Problem 4

Methanol, $\mathrm{CH}_{3} \mathrm{OH},$ and water are miscible in all proportions. What does this mean? Explain how the OH unit in methanol contributes to this.

David Collins

Numerade Educator

01:22

Problem 5

Hexane $\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)$ and water are immiscible. What does this mean? Explain why they are immiscible in terms of structural features of their molecules and the forces of attraction between them.

David Collins

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01:24

Problem 6

Explain how ion-dipole forces help to bring potassium chloride into solution in water.

David Collins

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Problem 7

Explain why potassium chloride will not dissolve in carbon tetrachloride, $\mathrm{CCl}_{4}$

David Collins

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01:40

Problem 8

Water and dichloromethane, $\mathrm{CH}_{2} \mathrm{Cl}_{2}$, are immiscible; however, when enough methanol is added, the three are soluble in each other. What properties of methanol allows the three liquids to form a homogeneous mixture?

David Collins

Numerade Educator

Problem 9

The value of $\Delta H_{\text {soln }}$ for a soluble compound is, say, $+26 \mathrm{~kJ} \mathrm{~mol}^{-1}$, and a nearly saturated solution is prepared in an insulated container (e.g., a coffee cup calorimeter). Will the system's temperature increase or decrease as the solute dissolves?

David Collins

Numerade Educator

01:14

Problem 10

Referring to Question $12.9,$ which value for this compound would be numerically larger, its lattice energy or its hydration energy?

David Collins

Numerade Educator

Problem 11

Which would be expected to have the larger hydration energy, $\mathrm{Al}^{3+}$ or $\mathrm{Li}^{+}$ ? Why? (Both ions are about the same size.)

David Collins

Numerade Educator

01:35

Problem 12

Suggest a reason why the value of $\Delta H_{\text {soln }}$ for a gas such as $\mathrm{CO}_{2},$ dissolving in water, is negative.

David Collins

Numerade Educator

Problem 13

The value of $\Delta H_{\text {saln }}$ for the formation of an acetonewater solution is negative. Explain this in general terms using intermolecular forces of attraction.

David Collins

Numerade Educator

Problem 14

The value of $\Delta H_{\text {soln }}$ for the formation of an ethanolhexane solution is positive. Explain this in general terms that involve intermolecular forces of attraction.

David Collins

Numerade Educator

01:16

Problem 15

When a certain solid dissolves in water, the solution becomes cool. Is $\Delta H_{\text {waln }}$ for this solute positive or negative? Explain your reasoning. Is the solubility of this substance likely to increase or decrease with increasing temperature? Explain your answer using Le Châtelier's principle.

David Collins

Numerade Educator

Problem 16

If the value of $\Delta H_{\text {saln }}$ for the formation of a mixture of two liquids $A$ and $B$ is zero, what does this imply about the relative strengths of $A-A, B-B,$ and $A-B$ intermolecular attractions?

David Collins

Numerade Educator

01:10

Problem 17

What kinds of data would have to be obtained to find out whether a solution of two miscible liquids is almost exactly an ideal solution?

David Collins

Numerade Educator

03:50

Problem 18

If a saturated solution of $\mathrm{NH}_{4} \mathrm{NO}_{3}$ at $75^{\circ} \mathrm{C}$ is cooled to $15^{\circ} \mathrm{C}$, how many grams of solute will separate if the quantity of the solvent is $125 \mathrm{~g}$ ? (Use the data in Figure $12.10 .)$

Susan Hallstrom

Numerade Educator

Problem 19

Anglers know that on hot summer days, the largest fish will be found in deep sinks in lake bottoms. Use the temperature dependence of the density of water and the temperature dependence of the oxygen solubility in water to explain why.

David Collins

Numerade Educator

Problem 20

What is Henry's law?

David Collins

Numerade Educator

Problem 21

Mountain streams often contain fewer living things than equivalent streams at sea level. Give one reason why this might be true in terms of oxygen solubilities at different pressures.

David Collins

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01:23

Problem 22

Why is ammonia so much more soluble in water than nitrogen? Would you expect hydrogen chloride gas to have a high or low solubility in water? Explain your answers to both questions.

David Collins

Numerade Educator

Problem 23

Why does a bottled carbonated beverage fizz when you take the cap off?

David Collins

Numerade Educator

01:17

Problem 24

Some chemical reactions need to be carried out in an atmosphere without oxygen present. One way to remove oxygen is to freeze the solvent, and remove the gas above the solid, then thaw the solvent- the freeze-thaw method. This is repeated three times. Why does this remove the oxygen?

David Collins

Numerade Educator

01:17

Problem 25

Write the definition for each of the following concentration units: (a) mole fraction, (b) mole percent, (c) molality, (d) percent by mass. What are the maximum possible values for the units in (a), (b), and (d)?

David Collins

Numerade Educator

Problem 26

How does the molality of a solution vary with increasing temperature? How does the molarity of a solution vary with increasing temperature?

David Collins

Numerade Educator

01:56

Problem 27

Suppose a $1.0 \mathrm{~m}$ solution of a solute is made using a solvent with a density of $1.15 \mathrm{~g} / \mathrm{mL}$. Will the molarity of this solution be numerically larger or smaller than 1.0 ? Justify your conclusion mathematically.

David Collins

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Problem 28

What specific fact about a physical property of a solution must be true to call it a colligative property?

David Collins

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Problem 29

What is Raoult's law?

David Collins

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01:43

Problem 30

Why does a nonvolatile solute decrease the vapor pressure of a solvent?

David Collins

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01:40

Problem 31

When octane is mixed with methanol, the vapor pressure of the octane over the solution is higher than what we would calculate using Raoult's law. Why? Explain the discrepancy in terms of intermolecular attractions.

David Collins

Numerade Educator

01:18

Problem 32

Will a solution of pentane and hexane have an ideal Raoult's law vapor pressure curve? Explain your answer in terms of intermolecular attractions.

David Collins

Numerade Educator

03:00

Problem 33

Explain why a nonvolatile solute dissolved in water makes the system have (a) a higher boiling point than water, and $(b)$ a lower freezing point than water.

David Collins

Numerade Educator

Problem 34

Why do we call dialyzing and osmotic membranes semipermeable. What is the opposite of permeable?

David Collins

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Problem 35

What is the key difference between dialyzing and osmotic membranes?

David Collins

Numerade Educator

01:34

Problem 36

At a molecular level, explain why, in osmosis, there is a net migration of solvent from the side of the membrane less concentrated in solute to the side more concentrated in solute.

David Collins

Numerade Educator

01:53

Problem 37

Two glucose solutions of unequal molarity are separated by an osmotic membrane. Which solution will lose water, the one with the higher molarity or the one with the lower molarity?

David Collins

Numerade Educator

01:13

Problem 38

Which aqueous solution has the higher osmotic pressure, $10 \%$ glucose, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},$ or $10 \%$ sucrose, $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} ?$
(Both are molecular compounds.)

David Collins

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Problem 39

When a solid is associated in a solution, what does this mean? What difference does it make to expected colligative properties?

David Collins

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Problem 40

What is the difference berween a bypertonic solution and a hypotonic solution?

David Collins

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01:45

Problem 41

Why are colligative properties of solutions of ionic compounds usually more pronounced than those of solutions of molecular compounds of the same molalities?

David Collins

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01:48

Problem 42

What is the van't Hoff factor? What is its expected value for all nondissociating molecular solutes? If its measured value is slightly larger than 1.0 , what does this suggest about the solute? What is suggested by a van't Hoff factor of approximately $0.5 ?$

David Collins

Numerade Educator

Problem 43

Which aqueous solution, if either, is likely to have the higher boiling point, $0.50 \mathrm{~m} \mathrm{Nal}$ or $0.50 \mathrm{~m} \mathrm{Na}_{2} \mathrm{CO}_{3} ?$

David Collins

Numerade Educator

03:05

Problem 44

Determine whether each of the following is likely to be a true solution, a suspension, or a colloidal mixture: (a) orange juice, (b) apple juice, (c) perfume,
(d) tea,
(e) tea with lemon juice, (f) canned gravy. If you have a laser pointer, how can you confirm your answers?

David Collins

Numerade Educator

01:39

Problem 45

Can sodium stearate stabilize a water-in-oil emulsion? Explain your conclusion.

David Collins

Numerade Educator

Problem 46

Addition of a neutral salt to a colloidal precipitate such as the $\mathrm{Ba} \mathrm{SO}_{4}(s)$ described in the text allows the crystals to grow in size. Develop a hypothesis on why this occurs.

David Collins

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Problem 47

What is the Tyndall effect?

David Collins

Numerade Educator

01:23

Problem 48

What is a micelle, and why does it form?

David Collins

Numerade Educator

Problem 49

For an ionic compound dissolving in water, $\Delta H_{\text {soln }}=$ $-56 \mathrm{k} \mathrm{J} \mathrm{mol}^{-1}$ and the hydration energy is $-894 \mathrm{~kJ} \mathrm{~mol}^{-1}$ Estimate the lattice energy of the ionic compound.

David Collins

Numerade Educator

Problem 50

Consider the formation of a solution of aqueous potassium chloride. Write the thermochemical equations for (a) the conversion of solid KCl into its gaseous ions and (b) the subsequent formation of the solution by hydration of the ions. The lattice energy of $\mathrm{KCl}$ is $-715 \mathrm{~kJ} \mathrm{~mol}^{-1}$, and the hydration energy of the ions is $-686 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Calculate the enthalpy of solution of $\mathrm{KCl}$ in $\mathrm{kJ} \mathrm{mol}^{-1}$

David Collins

Numerade Educator

Problem 51

The solubility of methane, the chief component of natural gas, in water at $20.0^{\circ} \mathrm{C}$ and 1.0 atm pressure is $0.025 \mathrm{~g} \mathrm{~L}^{-1}$. What is its solubility in water at 1.5 atm and $20.0^{\circ} \mathrm{C}$ ?

David Collins

Numerade Educator

Problem 52

If the solubility of a gas in water is $0.010 \mathrm{~g} \mathrm{~L}^{-1}$ at $25^{\circ} \mathrm{C}$ with the partial pressure of the gas 1. 0 atm, predict the solubility of the gas at the same temperature but at double the pressure.

David Collins

Numerade Educator

01:15

Problem 53

At 740 torr and $20.0^{\circ} \mathrm{C}$, nitrogen has a solubility in water of $0.018 \mathrm{~g} \mathrm{~L}^{-1}$. At 620 torr and $20.0{ }^{\circ} \mathrm{C}$, its solubility is $0.015 \mathrm{~g} \mathrm{~L}^{-1}$. Show that nitrogen obeys Henry's law.

David Collins

Numerade Educator

01:20

Problem 54

Hydrogen gas has a solubility in water of $0.00157 \mathrm{~g} \mathrm{~L}^{-1}$ under 1.00 atm of $H_{2}$ pressure at $25^{\circ} \mathrm{C}$. At 0.85 atm and $25^{\circ} \mathrm{C}$, its solubility is $0.00133 \mathrm{~g} \mathrm{~L}^{-1}$. Does hydrogen gas obey Henry's law?

David Collins

Numerade Educator

02:07

Problem 55

If $100.0 \mathrm{~mL}$ of water is shaken with oxygen gas at $1.0 \mathrm{~atm}$ it will dissolve $0.0039 \mathrm{~g} \mathrm{O}_{2}$. Estimate the Henry's law constant for oxygen gas in water.

Susan Hallstrom

Numerade Educator

01:10

Problem 56

Helium gas can be used to displace other gases from a solvent by bubbling He through the solvent, a process called sparging, and leaving an atmosphere of helium above the solvent. At 760 torr of He, the concentration of He in water is $0.00148 \mathrm{~g} \mathrm{~L}^{-1}$ at $298 \mathrm{~K}$. What is Henry's law constant for $\mathrm{He}$ at $298 \mathrm{~K} ?$

David Collins

Numerade Educator

Problem 57

Muriatic acid is the commercial name for hydrochloric acid that can be purchased from hardware stores as a solution that is $30 \%(\mathrm{w} / \mathrm{w}) \mathrm{HCl}$. What mass of this solution contains $7.5 \mathrm{~g}$ of $\mathrm{HCl}$ ?

David Collins

Numerade Educator

01:06

Problem 58

Hydrofluoric acid dissolves glass and must be stored in plastic containers. What mass of a $45 \%(\mathrm{w} / \mathrm{w})$ solution of $\mathrm{HF}(a q)$ contains $1.5 \mathrm{~g}$ of $\mathrm{HF}$ ?

David Collins

Numerade Educator

02:22

Problem 59

What mass of a 0.853 molal solution of iron(III) nitrate is needed to obtain (a) 0.0200 moles of iron(III) nitrate,
(b) 0.0500 moles of $\mathrm{Fe}^{3+}$ ions,
(c) 0.00300 moles of nitrate ions?

David Collins

Numerade Educator

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Problem 60

In order to conduct three experiments that required different amounts of chloride ions, what mass of a $0.150 \mathrm{~m}$ $\mathrm{NaCl}$ solution is needed to obtain (a) $0.00100 \mathrm{~mol} \mathrm{Cl}^{-}$ (b) $0.00500 \mathrm{~mol} \mathrm{Cl}$, (c) $0.0200 \mathrm{~mol} \mathrm{Cl}^{-}$ ?

David Collins

Numerade Educator

Problem 61

What is the molality of $\mathrm{NaCl}$ in a solution that is $3.000 \mathrm{M}$ $\mathrm{NaCl}$, with a density of $1.07 \mathrm{~g} \mathrm{~mL}^{-1}$ ?

David Collins

Numerade Educator

01:21

Problem 62

A solution of acetic acid, $\mathrm{CH}_{3} \mathrm{COOH}$, has a concentration of $0.143 M$ and a density of $1.00 \mathrm{~g} \mathrm{~mL}^{-1}$. What is the molality of this solution?

David Collins

Numerade Educator

Problem 63

The mole fraction of neon in the air is about $2.6 \times 10^{-5}$. If the average molar mass of air is $28.96 \mathrm{~g} / \mathrm{mol}$, what is the concentration of neon in air in $\mathrm{ppm}$ ?

David Collins

Numerade Educator

Problem 64

Botulinum toxin is one of the most acutely toxic substances known, with a lethal dose at about $140 \mathrm{ng}$ for a 150 lb person. What would this concentration be in ppb?

David Collins

Numerade Educator

01:54

Problem 65

A solution of fructose, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},$ a sugar found in many fruits, is made by dissolving $24.0 \mathrm{~g}$ of fructose in $1.00 \mathrm{~kg}$ of water. For this solution, what are (a) the molal con-
centration, (b) the mole fraction, (c) the mass percent, and (d) the molarity of fructose if the density of the solution is $1.0078 \mathrm{~g} / \mathrm{mL}$

David Collins

Numerade Educator

02:28

Problem 66

If you dissolved $11.5 \mathrm{~g}$ of $\mathrm{NaCl}$ in $1.00 \mathrm{~kg}$ of water, $(\mathrm{a})$ what would be its molal concentration? (b) What are the mass percent $\mathrm{NaCl}$ and the mole percent $\mathrm{NaCl}$ in the solution? The volume of this solution is virtually identical to the original volume of the $1.00 \mathrm{~kg}$ of water.
(c) What is the molar concentration of $\mathrm{NaCl}$ in this solution?
(d) What would have to be true about any solvent for one of its dilute solutions to have essentially the same molar and molal concentrations?

David Collins

Numerade Educator

01:14

Problem 67

A solution of ethanol, $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH},$ in water has a concentration of $1.25 \mathrm{~m}$. Calculate the mass percent of ethanol.

David Collins

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Problem 68

A solution of $\mathrm{NaCl}$ in water has a concentration of 19.5\%. Calculate the molality of the solution.

David Collins

Numerade Educator

01:35

Problem 69

A solution of $\mathrm{NH}_{3}$ in water has a concentration of $7.50 \%$ by mass. Calculate the mole percent $\mathrm{NH}_{3}$ in the solution. What is the molal concentration of the $\mathrm{NH}_{3}$ ?

David Collins

Numerade Educator

02:05

Problem 70

An aqueous solution of isopropyl alcohol, $\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}, \mathrm{rub}=$ bing alcohol, has a mole fraction of alcohol equal to $0.250 .$ What is the percent by mass of alcohol in the solution? What is the molality of the alcohol?

David Collins

Numerade Educator

02:17

Problem 71

Sodium nitrate, $\mathrm{NaNO}_{3},$ is sometimes added to tobacco to improve its burning characteristics. An aqueous solution of $\mathrm{NaNO}_{3}$ has a concentration of $0.363 \mathrm{~m}$. Its density is $1.0185 \mathrm{~g} \mathrm{~mL}^{-1}$. Calculate the molar concentration of $\mathrm{NaNO}_{3}$ and the mass percent of $\mathrm{NaNO}_{3}$ in the solution. What is the mole fraction of $\mathrm{NaNO}_{3}$ in the solution?

David Collins

Numerade Educator

02:23

Problem 72

In an aqueous solution of sulfuric acid, the concentration is $1.89 \mathrm{~mol} \%$ of acid. The density of the solution is $1.0645 \mathrm{~g} \mathrm{~mL}^{-1}$. Calculate the following:
(a) the molal concentration of $\mathrm{H}_{2} \mathrm{SO}_{4},$ (b) the mass percent of the acid, and (c) the molarity of the solution.

David Collins

Numerade Educator

01:17

Problem 73

At $25^{\circ} \mathrm{C}$, the vapor pressure of water is 23.8 torr. What is the vapor pressure of a solution prepared by dissolving $65.0 \mathrm{~g}$ of $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ (a nonvolatile solute) in $150 \mathrm{~g}$ of water? (Assume the solution is ideal.)

David Collins

Numerade Educator

01:11

Problem 74

The vapor pressure of water at $20^{\circ} \mathrm{C}$ is 17.5 torr. A $35 \%$ solution of the nonvolatile solute ethylene glycol, $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{OH})_{2},$ in water is prepared. Estimate the vapor pressure of the solution.

David Collins

Numerade Educator

01:24

Problem 75

At $25^{\circ} \mathrm{C}$ the vapor pressures of benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)$ and toluene $\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)$ are 93.4 and 26.9 torr, respectively. A solution made by mixing $35.0 \mathrm{~g}$ of benzene and $65.0 \mathrm{~g}$ of toluene is prepared. What is the vapor pressure of this solution?

David Collins

Numerade Educator

01:22

Problem 76

Pentane $\left(\mathrm{C}_{5} \mathrm{H}_{12}\right)$ and heptane $\left(\mathrm{C}_{7} \mathrm{H}_{16}\right)$ are two hydrocarbon liquids present in gasoline. At $20.0^{\circ} \mathrm{C}$, the vapor pressure of pentane is 422 torr and the vapor pressure of heptane is 36.0 torr. What will be the total vapor pressure (in torr) of a solution prepared by mixing equal masses of the two liquids?

David Collins

Numerade Educator

01:13

Problem 77

Benzene and toluene help achieve good engine performance from lead-free gasoline. At $40{ }^{\circ} \mathrm{C}$, the vapor pressure of benzene is 184 torr and that of toluene is 58 torr. Suppose you wished to prepare a solution of these liquids that will have a total vapor pressure of 96 torr at $40^{\circ} \mathrm{C}$. What must be the mole percent concentrations of each in the solution?

David Collins

Numerade Educator

Problem 78

The vapor pressure of pure methanol, $\mathrm{CH}_{3} \mathrm{OH}$, at $33^{\circ} \mathrm{C}$ is 164 torr. How many grams of the nonvolatile solute glycerol, $\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3},$ must be added to $105 \mathrm{~g}$ of methanol to obtain a solution with a vapor pressure of 145 torr?

David Collins

Numerade Educator

01:15

Problem 79

A solution containing $8.3 \mathrm{~g}$ of a nonvolatile, nondissociating substance dissolved in $1.00 \mathrm{~mol}$ of chloroform, $\mathrm{CHCl}_{3},$ has a vapor pressure of 511 torr. The vapor pressure of pure $\mathrm{CHCl}_{3}$ at the same temperature is 526 torr. Calculate (a) the mole fraction of the solute, (b) the number of moles of solute in the solution, and (c) the molecular mass of the solute.

David Collins

Numerade Educator

Problem 80

At $21.0^{\circ} \mathrm{C},$ a solution of $18.26 \mathrm{~g}$ of a nonvolatile, nonpolar compound in $33.25 \mathrm{~g}$ of ethyl bromide, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Br}$, had a vapor pressure of 336.0 torr. The vapor pressure of pure ethyl bromide at this temperature is 400.0 torr. Assuming an ideal solution, what is the molecular mass of the compound?

David Collins

Numerade Educator

Problem 81

How many grams of sucrose $\left(\mathrm{C}_{2} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ are needed to lower the freezing point of $125 \mathrm{~g}$ of water by $3.00^{\circ} \mathrm{C} ?$

David Collins

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01:28

Problem 82

To make sugar candy, a concentrated sucrose solution is boiled until the temperature reaches $272^{\circ} \mathrm{F}$. What are the molality and the mole fraction of sucrose in this mixture?

David Collins

Numerade Educator

Problem 83

A solution of $12.00 \mathrm{~g}$ of an unknown nondissociating compound dissolved in $200.0 \mathrm{~g}$ of benzene freezes at $3.45^{\circ} \mathrm{C}$. Calculate the molecular mass of the unknown.

David Collins

Numerade Educator

01:06

Problem 84

A solution of $14 \mathrm{~g}$ of a nonvolatile, nondissociating compound in $0.10 \mathrm{~kg}$ of benzene boils at $81.7{ }^{\circ} \mathrm{C}$. Calculate the molecular mass of the unknown.

David Collins

Numerade Educator

01:19

Problem 85

What are the molecular mass and molecular formula of a nondissociating molecular compound whose empirical formula is $\mathrm{C}_{4} \mathrm{H}_{2} \mathrm{~N}$ if $3.84 \mathrm{~g}$ of the compound in $0.500 \mathrm{~kg}$ of benzene gives a freezing point depression of $0.307^{\circ} \mathrm{C}$ ?

David Collins

Numerade Educator

02:43

Problem 86

Benzene reacts with hot concentrated nitric acid dissolved in sulfuric acid to give chiefly nitrobenzene, $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NO}_{2}$ A by-product is often obtained, which consists of $42.86 \%$ C, $2.40 \% \mathrm{H},$ and $16.67 \% \mathrm{~N}$ (by mass). The boiling point of a solution of $5.5 \mathrm{~g}$ of the by-product in $45 \mathrm{~g}$ of benzene was $1.84{ }^{\circ} \mathrm{C}$ higher than that of benzene.
(a) Calculate the empirical formula of the by-product.
(b) Calculate a molecular mass of the by-product and determine its molecular formula.

David Collins

Numerade Educator

01:50

Problem 87

(a) Show that the following equation is true.
Molar mass of solute $=\frac{\text { (grams of solute) } R T}{\Pi \mathrm{V}}$ (b) An aqueous solution of a compound with a very high molecular mass was prepared in a concentration of $2.0 \mathrm{~g} \mathrm{~L}^{-1}$ at $25^{\circ} \mathrm{C}$. Its osmotic pressure was 0.021 torr. Calculate the molecular mass of the compound.

David Collins

Numerade Educator

01:14

Problem 88

A saturated solution is made by dissolving $0.400 \mathrm{~g}$ of a polypeptide (a substance formed by joining together in a chainlike fashion a number of amino acids) in water to give $1.00 \mathrm{~L}$ of solution. The solution has an osmotic pressure of 3.74 torr at $27{ }^{\circ} \mathrm{C}$. What is the approximate molecular mass of the polypeptide?

David Collins

Numerade Educator

Problem 89

The vapor pressure of water at $20.0^{\circ} \mathrm{C}$ is 17.5 torr. $\mathrm{At}$ that temperature, what would be the vapor pressure of solution made by dissolving $23.0 \mathrm{~g}$ of $\mathrm{NaCl}$ in $0.100 \mathrm{~kg}$ of water? (Assume complete dissociation of the solute and an ideal solution.)

David Collins

Numerade Educator

01:52

Problem 90

How many grams of $\mathrm{AlCl}_{3}$ would have to be dissolved in $0.150 \mathrm{~L}$ of water to give a solution that has a vapor pressure of 38.7 torr at $35^{\circ} \mathrm{C}$ ? Assume complete dissociation of the solute and ideal solution behavior. (At $35^{\circ} \mathrm{C}$, the vapor pressure of pure water is 42.2 torr.)

David Collins

Numerade Educator

01:45

Problem 91

What is the osmotic pressure, in torr, of a $2.0 \%$ solution of $\mathrm{NaCl}$ in water when the temperature of the solution is $25^{\circ} \mathrm{C} ?$

David Collins

Numerade Educator

01:18

Problem 92

Below are the concentrations of the most abundant ions in seawater. Use these data to estimate the osmotic pressure of seawater at $25^{\circ} \mathrm{C}$ in units of atm. What is the minimum pressure in atm needed to desalinate seawater by reverse osmosis?

David Collins

Numerade Educator

01:10

Problem 93

What is the expected freezing point of a $0.20 \mathrm{~m}$ solution of $\mathrm{CaCl}_{2}$ ? (Assume complete dissociation.)

David Collins

Numerade Educator

02:10

Problem 94

The freezing point of a $0.10 \mathrm{~m}$ solution of mercury(I) nitrate is approximately $-0.27^{\circ} \mathrm{C}$. Show that these data suggest that the formula of the mercury $(\mathrm{I})$ ion is $\mathrm{Hg}_{2}^{2+}$.

David Collins

Numerade Educator

Problem 95

The van't Hoff factor for the solute in $0.100 \mathrm{~m} \mathrm{NiSO}_{4}$ is 1.19. What would this factor be if the solution behaved as if it were $100 \%$ dissociated?

David Collins

Numerade Educator

Problem 96

What is the expected van't Hoff factor for $\mathrm{K}_{2} \mathrm{SO}_{4}$ in an aqueous solution, assuming $100 \%$ dissociation?

David Collins

Numerade Educator

02:51

Problem 97

Vodka from the European Union must be at least $37.5 \%$ alcohol by volume or 75 proof. If the density of water is $1.00 \mathrm{~g} \mathrm{~mL}^{-1}$ and the density of ethanol is $0.789 \mathrm{~g} \mathrm{~mL}^{-1},$ what are the molarity, mole fraction, and mass percent of alcohol in vodka?

David Collins

Numerade Educator

01:58

Problem 98

The "bends" is a medical emergency caused by the formation of tiny bubbles in the blood vessels of divers who rise too quickly to the surface from a deep dive. At $37^{\circ} \mathrm{C}$ (normal body temperature), the solubility of $\mathrm{N}_{2}$ in water is $0.015 \mathrm{~g} \mathrm{~L}^{-1}$ when its pressure over the solution is 1 atm. Air is approximately $78 \mathrm{~mol} \% \mathrm{~N}_{2}$. How many moles of $\mathrm{N}_{2}$ are dissolved per liter of blood (essentially an aqueous solution) when a diver inhales air at a pressure of 1 atm? How many moles of $\mathrm{N}_{2}$ dissolve per liter of blood when the diver is submerged to a depth of approximately $100 \mathrm{ft}$, where the total pressure of the air being breathed is 4 atm? If the diver suddenly surfaces, how many milliliters of $\mathrm{N}_{2}$ gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood (at $37^{\circ} \mathrm{C}$ and $\left.1 \mathrm{~atm}\right)$ ?

David Collins

Numerade Educator

01:19

Problem 99

In order for mosquitos to survive the cold winter, they produce glycerol, $\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} .$ What molality and mass fraction of glycerol is needed to keep water from freezing at $0^{\circ} \mathrm{F} ?$

David Collins

Numerade Educator

Problem 100

The vapor pressure of a mixture of $0.400 \mathrm{~kg}$ of carbon tetrachloride and $43.3 \mathrm{~g}$ of an unknown compound is 137 torr at $30^{\circ} \mathrm{C}$. At the same temperature, the vapor pressure of pure carbon tetrachloride is 143 torr, while that of the pure unknown is 85 torr. What is the approximate molecular mass of the unknown? Will our estimate of the molecular mass be too high or too low if the heat of solution is exothermic?

David Collins

Numerade Educator

02:49

Problem 101

Ethylene glycol, $\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2},$ is used in many antifreeze mixtures. Protection against freezing to as low as $-45^{\circ} \mathrm{F}$ is sought.
(a) How many moles of solute are needed per kilogram of water to ensure this protection?
(b) The density of ethylene glycol is $1.11 \mathrm{~g} \mathrm{~mL}^{-1} . \mathrm{To}$ how many milliliters of solute does your answer to part (a) correspond?
(c) Calculate the number of quarts of ethylene glycol that should be mixed with each quart of water to get the desired protection.

Crystal Wang

Numerade Educator

01:38

Problem 102

What is the osmotic pressure in torr of a $0.010 \mathrm{M}$ aqueous solution of a molecular compound at $25^{\circ} \mathrm{C}$ ?

David Collins

Numerade Educator

05:48

Problem 103

The osmotic pressure of a dilute solution of a slightly soluble polymer (a compound composed of large molecules formed by linking many smaller molecules together) in water was measured using the osmometer in Figure 12.22 . The difference in the heights of the liquid levels was determined to be $1.26 \mathrm{~cm}$ at $25^{\circ} \mathrm{C}$. Assume the solution has a density of $1.00 \mathrm{~g} \mathrm{~mL}^{-1}$.
(a) What is the osmotic pressure of the solution in torr?
(b) What is the molarity of the solution?
(c) At what temperature would the solution be expected to freeze?
(d) On the basis of the results of these calculations, explain why freezing point depression cannot be used to determine the molecular masses of compounds composed of very large molecules.

Ronald Prasad

Numerade Educator

01:27

Problem 104

A solution of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$, in water has a concentration of $4.613 \mathrm{~mol} \mathrm{~L}^{-1}$. At $20.0^{\circ} \mathrm{C}$, its density is $0.9677 \mathrm{~g} \mathrm{~mL}^{-1}$. Calculate the following:
(a) the molality of the solution and (b) the mass percentage of the alcohol in the mixture.

David Collins

Numerade Educator

01:53

Problem 105

Consider an aqueous $1.00 \mathrm{~m}$ solution of $\mathrm{Na}_{3} \mathrm{PO}_{4}, \mathrm{a}$ compound with useful detergent properties.
(a) Calculate the boiling point of the solution on the assumption that it does not ionize at all in solution.
(b) Do the same calculation, assuming that the van't Hoff factor for $\mathrm{Na}_{3} \mathrm{PO}_{4}$ reflects $100 \%$ dissociation into its ions.
(c) The $1.00 \mathrm{~m}$ solution boils at $100.183{ }^{\circ} \mathrm{C}$ at $1 \mathrm{~atm}$. Calculate the van't Hoff factor for the solute in this solution.

David Collins

Numerade Educator

08:30

Problem 106

A $2.50 \mathrm{~g}$ sample of aluminum chloride and sodium sulfate has a freezing point depression of $2.65^{\circ} \mathrm{C}$. Assuming complete dissociation of all ions, what are the molarities of aluminum chloride and sodium sulfate?

A. Elizabeth Hildreth

Numerade Educator

Problem 107

A $0.118 \mathrm{~m}$ solution of $\mathrm{LiCl}$ has a freezing point of $-0.415^{\circ} \mathrm{C}$. What is the van't Hoff factor for this solute at this concentration? What is the approximate osmotic pressure of a $0.118 \mathrm{~m}$ solution of $\mathrm{LiCl}$ at $10^{\circ} \mathrm{C}$ ? Express the answer in torr.

David Collins

Numerade Educator

11:20

Problem 108

A sample containing only iron(II) nitrate and potassium chloride is dissolved in water and the boiling point of the mixture is $104.6^{\circ} \mathrm{C}$. That same solution is reacted with $36.3 \mathrm{~mL}$ of $0.220 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ solution that completely converts the iron(II) to iron(III). What are the molarities of iron(II) nitrate and potassium chloride in the original solution? The density of the mixture is $1.032 \mathrm{~g} / \mathrm{mL},$ and we assume all soluble species are completely dissociated.

Susan Hallstrom

Numerade Educator