gasesgases - weebly · gasesgases solutions manual chemistry: matter and change • chapter 13 253...

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.SOLUTIONS MANUALCHAPTER

GasesGases

Solutions Manual Chemistry: Matter and Change • Chapter 13 253

Section 13.1 The Gas Lawspages 442–451

Practice Problemspage 443

Assume that the temperature and the amount of gas are constant in the following problems.

1. The volume of a gas at 99.0 kPa is 300.0 mL. If the pressure is increased to 188 kPa, what will be the new volume?

158 mL

V2 � V1P1 _ P2

� (300.0 mL)(99.0 kPa)

__ 188 kPa

� 158 mL

2. The pressure of a sample of helium in a 1.00-L container is 0.988 atm. What is the new pressure if the sample is placed in a 2.00-L container?

0.494 atm

P2 � V1P1 _ V2

� (1.00 L)(0.988 atm)

__ 2.00 L

� 0.494 atm

3. Challenge Air trapped in a cylinder fitted with a piston occupies 145.7 mL at 1.08 atm pressure. What is the new volume when the piston is depressed, increasing the pressure by 25%?

117 mL

P2 � 1.08 atm � (1.08 atm � 0.25) � 1.35 atm

V2 �

V1P1 _ P2

� (145.7 mL)(1.08 atm)

__ 1.35 atm

� 117 mL

Problem-Solving Labpage 444

Lungs

Diaphragm

Ribs

1. Apply Boyle’s law to explain why air enters your lungs when you inhale and leaves when you exhale.

Boyle’s Law states that at constant temperature, the volume of a gas varies inversely with pressure. When you inhale, lung volume increases. Pressure decreases and air moves in. When you exhale, lung volume decreases. Pressure increases and air moves out.

2. Explain what happens inside the lungs when a blow to the abdomen knocks the wind out of a person. Use Boyle’s law to determine your answer.

When someone is hit in the abdomen, the diaphragm is temporarily paralyzed. When the diaphragm does not move up and down, lung volume does not change. If the volume does not change, pressure inside the lungs does not change, and air is not drawn in and out of the lungs.

3. Infer Parts of the lungs lose elasticity and become enlarged when a person has emphysema. From what you know about Boyle’s law, why does this condition affect breathing?

If parts of the lungs lose elasticity, it is more difficult to change lung volume. With less change in volume, there is less difference in pressure. With less difference in pressure, it is more difficult for air to enter or exit the lungs.

13

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254 Chemistry: Matter and Change • Chapter 13 Solutions Manual

SOLUTIONS MANUALCHAPTER 13

4. Explain why beginning scuba divers are taught never to hold their breath while ascending from deep water.

As a scuba diver ascends, pressure decreases. A decrease in pressure results in an increase in volume. If a diver holds his or her breath while ascending, air volume in the lungs would increase.

Practice Problemspages 446–450

4. What volume will the gas in the balloon below occupy at 250 K?

4.3 L350 K

3.1 L

V2 � V1T2 _ T1

� (4.3 L)(250 K)

__ 350 K

� 3.1 L

5. A gas at 89ºC occupies a volume of 0.67 L. At what Celsius temperature will the volume increase to 1.12 L?

330°C

T1 � 89°C � 273 � 362 K

T2 � T1V2 _ V1

� (362 K)(1.12 L)

__ 0.67 L

� 605 K

605 � 273 � 332°C � 330°C

6. The Celsius temperature of a 3.00-L sample of gas is lowered from 80.0ºC to 30.0ºC. What will be the resulting volume of this gas?

2.58 L

T1 � 80.0°C � 273 � 353 K

T2 � 30.0°C � 273 � 303 K

V2 � V1T2 _ T1

� (3.00 L)(303 K)

__ 353 K

� 2.58 L

7. Challenge A gas occupies 0.67 L at 350 K. What temperature is required to reduce the volume by 45%?

190 K

V2 � 0.67 L � (0.67 L � 0.45) � 0.37 L

T2 � T1V2 _ V1

� (350 K)(0.37 L )

__ 0.67 L

� 190 K

Assume that the volume and the amount of gas are constant in the following problems.

8. The pressure in an automobile tire is 1.88 atm at 25.0°C. What will be the pressure if the temperature increases to 37.0°C?

1.96 atm

T1 � 25.0°C � 273 � 298 K

T2 � 37.0°C � 273 � 310 K

P2 � P1T2 _ T1

� (1.88 atm)(310 K)

__ 298 K

� 1.96 atm

9. Helium gas in a 2.00-L cylinder is under 1.12 atm pressure. At 36.5ºC, that same gas sample has a pressure of 2.56 atm. What was the initial temperature of the gas in the cylinder?

�138°C

T2 � 36.5°C � 273 � 309.5 K

T1 � T2P1 _ P2

� (309.5 K)(1.12 atm)

__ 2.56 atm

� 135 K

135 K � 273 � �138°C

10. Challenge If a gas sample has a pressure of 30.7 kPa at 0.00ºC, by how many degrees Celsius does the temperature have to increase to cause the pressure to double?

273°C

T1 � 0.00°C � 273 � 273 K

P2 � (30.7 kPa)(2) � 61.4 kPa

T2 � T1P2 _ P1

� (273 K)(61.4 kPa)

__ 30.7 kPa

� 546 K

546 K � 273 � 273°C

The temperature must increase by 273°C.

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Assume that the amount of gas is constant in the following problems.

11. A sample of air in a syringe exerts a pressure of 1.02 atm at 22.0ºC. The syringe is placed in a boiling water-bath at 100.0ºC. The pressure is increased to 1.23 atm by pushing the plunger in, which reduces the volume to 0.224 mL. What was the initial volume?

0.214 mL

T1 � 22.0°C � 273 � 295 K

T2 � 100.0°C � 273 � 373 K

V1 � V2T1P2 _ T2P1

� (0.224 mL)(295 K)(1.23 atm)

___ (373 K)(1.02 atm)

� 0.214 mL

12. A balloon contains 146.0 mL of gas confined at a pressure of 1.30 atm and a temperature of 5.0°C. If the pressure doubles and the temperature decreases to 2.0°C, what will be the volume of gas in the balloon?

72 mL

T1 � 5.0°C � 273 � 278 K

T2 � 2.0°C � 273 � 275 K

V2 � P1T2V1 _ P2T1

� (1.30 atm)(275 K)(146.0 mL)

___ (2.60 atm)(278 K)

� 72 mL

13. Challenge If the temperature in the gas cylinder below increases to 30.0°C and the pressure increases to 1.20 atm, will the cylinder’s piston move up or down?

1.00 atm

30.0 mL

0.00°C

down

T1 � 0.00°C � 273 � 273 K

T2 � 30.0°C � 273 � 303 K

V2 _ V1

� P1T2 _ P2T1

� (1.00 atm)(303 K)

__ (1.20 atm)(273 K)

� 0.92

This is a ratio, so there are no units. 0.92 < 1, so V2 must be less than V1. The final volume is less than the original volume, so the piston will move down.

Section 13.1 Assessmentpage 451

14. State the relationship among pressure, tempera-ture, and volume of a fixed amount of gas.

This relationship is given by the combined gas law. P1V1/T1 � P2V2/T2. For example: when the temperature increases, either the volume or pressure increases (or both).

15. Explain Which of the three variables that apply to equal amounts of gases are directly proportional? Which are inversely proportional?

P and V are directly proportional to T, and P and V are inversely proportional to each other.

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16. Analyze A weather balloon is released into the atmosphere. You know the initial volume, temperature, and air pressure. What informa-tion will you need to predict the volume when it reaches its final altitude? Which law would you use to calculate this volume?

You would need to know the final temperature and final pressure to calculate the final volume. Use the combined gas law.

17. Infer why gases such as the oxygen used at hospitals are compressed. Why must compressed gases be shielded from high temperatures? What must happen to compressed oxygen before it can be inhaled?

A greater mass confined to a smaller volume makes transporting and storing of gases easier. Increasing temperature increases pressure, and the cylinders might explode. Before compressed oxygen can be breathed, it must be decompressed.

18. Calculate A rigid plastic container holds 1.00 L of methane gas at 660 torr pressure when the temperature is 22.0°C. How much pressure will the gas exert if the temperature is raised to 44.6°C?

711 torr

T1 � 22.0°C � 273 � 295 K

T2 � 44.6°C � 273 � 318 K

P2 � P1T2 _ T1

� (660 torr)(318 K)

__ 295 K

� 711 torr

19. Design a concept map that shows the relation-ship among pressure, volume, and temperature in Boyle’s, Charles’s, and Gay-Lussac’s laws.

The concept map should show how P, V, and T are proportional to one another. It should also label each pair of variables used in the gas laws.

Constantamount of gas

Temperatureheld constant

Pressureheld constant

Volumeheld constant

P1V1 � P2V2V1 V2T1 T2 T1 T2

�

Boyle’s law Charles’s law Gay-Lussac’slaw

P1 P2�

Section 13.2 The Ideal Gas Lawpages 452–459


20. What size container do you need to hold 0.0459 mol of N2 gas at STP?

1.03 L

0.0459 mol � 22.4 L _ 1 mol

� 1.03 L

21. How much carbon dioxide gas, in grams, is in a 1.0-L balloon at STP?

2.0 g

1.0 L � 1 mol _ 22.4 L

� 0.045 mol

0.045 mol � 44.0 g

_ 1 mol

� 2.0 g

22. What volume in milliliters will 0.00922 g of H2 gas occupy at STP?

102 mL

0.00922 g � 1 mol _ 2.02 g

� 0.00457 mol

0.00457 mol � 22.4 L _ 1 mol

� 0.102 L or 102 mL

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23. What volume will 0.416 g of krypton gas occupy at STP?

0.111 L

0.416 g � 1 mol _ 83.80 g

� 0.00496 mol

0.00496 mol � 22.4 L _ 1 mol

� 0.111 L

24. Calculate the volume that 4.5 kg of ethylene gas (C2H4) will occupy at STP.

3.6 � 103 L

4.5 kg � 1000 g

_ 1 kg

� 1 mol _ 28.00 g

� 22.4 L _ 1 mol

� 3.6 � 103 L

25. Challenge A flexible plastic container contains 0.860 g of helium gas in a volume of 19.2 L. If 0.205 g of helium is removed at constant pressure and temperature, what will be the new volume?

14.6 L

0.860 g � 0.205 g � 0.655 g He remaining

Set up the problem as a ratio.

V _ 0.655 g

� 19.2 L _ 0.860 g

Solve for V.

V � (19.2 L)(0.655 g)

__ 0.860 g

� 14.6 L

26. Determine the Celsius temperature of 2.49 mol of a gas contained in a 1.00-L vessel at a pressure of 143 kPa.

�266°C

143 kPa � 1.00 atm _ 101.3 kPa

� 1.41 atm

T � PV _ nR

� (1.41 atm)(1.00 L)

___ (2.49 mol)(0.0821 L�atm _

mol�K )

� 6.90 K

6.90 K � 273 � �266°C

27. Calculate the volume of a 0.323-mol sample of a gas at 265 K and 0.900 atm.

7.81 L

V � nRT _ P �

(0.323 mol)(0.0821 L�atm _ mol�K

)(265 K) ____

0.900 atm

� 7.81 L

28. What is the pressure, in atmospheres, of a 0.108-mol sample of helium gas at a tempera-ture of 20.0ºC if its volume is 0.505 L?

5.14 atm

T � 20.0°C � 273 � 293 K

P � nRT _ V

� (0.108 mol)(0.0821 L�atm _

mol�K )(293 K)

____ 0.505 L

� 5.14 atm

29. If the pressure exerted by a gas at 25°C in a volume of 0.044 L is 3.81 atm, how many moles of gas are present?

6.9 � 10�3 mol

n � PV _ RT

� (3.81 atm)(0.44 L)

___ (0.0821 L�atm _

mol·K )(298 K)

� 6.9 � 10�3 mol

30. Challenge An ideal gas has a volume of 3.0 L. If the number of moles of gas and the temperature are doubled while the pressure remains constant, what is the new volume?

12 L

PV � nRT

P _ R

� nT _ V

Because P and R are constants, they can

be removed from the equation.

n1T1 _ V1

� n2T2 _ V2

where n2 � 2n1 and T2 � 2T1

n1T1 _ V1

� 2n12T1 _

V2

Multiply both sides by 1 _ n1 and 1 _

T1 .

1 _ V1

� (2)(2)

_ V2

V2 � 4V1

V2 � 4(3.0 L) � 12 L

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Problem-Solving Strategypage 458

Apply the StrategyDerive Boyle’s law, Gay-Lussac’s law, and the combined gas law based on the example above.

Students’ work should use the strategy to show the derivation from the ideal gas law to Boyle’s law (P1V1 � P2V2), Gay-Lussac’s law (P1/T1 � P2/T2), and the combined gas law (P1V1/T1 � P2V2/T2).


31. Explain why Avogadro’s principle holds true for gases that have small particles and for gases that have large particles.

The size of any gas particle is so small compared to the volume of the gas, it is assumed that no particle has any volume of its own.

32. State the equation for the ideal gas law.

PV � nRT

33. Analyze how the ideal gas law applies to real gases using the kinetic-molecular theory.

A real gas behaves most like an ideal gas under conditions that increase the distance and reduce the attractions among gas particles. The best conditions for that are high temperature and low pressure.

34. Predict the conditions under which a real gas might deviate from ideal behavior.

A real gas might deviate from ideal behavior under conditions that decrease the distance and increase the attractions among gas particles, such as low temperature and high pressure.

35. List common units for each variable in the ideal gas law.

P : atm, mm Hg, torr, kPa; V: L, mL; T: K; n: mol

36. Calculate A 2.00-L flask is filled with propane gas (C3H8) at a pressure of 1.00 atm and a temperature of −15.0�C. What is the mass of the propane in the flask?

4.16 g

T � �15°C � 273 � 258 K

n � PV _ RT

� (1.00 atm)(2.00 L)

___ (0.0821 L�atm _

mol�K )(258 K)

� 0.0944 mol

molar mass � (3 � 12.01 g/mol) � (8 � 1.008 g/mol) � 44.09 g/mol

mass � n � M � (0.0944 mol)(44.09 g/mol) � 4.16 g

37. Make and Use Graphs For every 6�C drop in temperature, the air pressure in a car’s tires goes down by about 1 psi (14.7 psi � 1.00 atm). Make a graph illustrating the change in tire pressure from 20�C to �20�C (assume 30.0 psi at 20�C).

-12-14-16-18-20 -8-10 -4-6 -2 0

20

22

2426

28

3032

42 8 10 14 18 206 12 16

Pres

sure

(psi

)

Temperature (°C)

Temperature vs. Pressure

Graph should show air pressure vs. temperature; the resulting plot will be a straight line showing a direct relationship between the variables.

Section 13.3 Gas Stoichiometrypages 460–464


38. How many liters of propane gas (C3H8) will undergo complete combustion with 34.0 L of oxygen gas?

6.80 L C3H8

C3H8(g) � 5O2(g) 0 3CO2(g) � 4H2O(g)

34.0 L O2 � 1 L C3H8 _ 5 L O2

� 6.80 L C3H8

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39. Determine the volume of hydrogen gas needed to react completely with 5.00 L of oxygen gas to form water.

10.0 L H2

2H2(g) � O2(g) 0 2H2O(g)

5.00 L O2 � 2 L H2 _ 1 L O2

� 10.0 L H2

40. What volume of oxygen is needed to completely combust 2.36 L of methane gas (CH4)?

4.72 L O2

CH4(g) � 2O2(g) 0 CO2(g) � 2H2O(g)

2.36 L CH4 � 2 L O2 _ 1 L CH4

� 4.72 L O2

41. Challenge Nitrogen and oxygen gases react to form dinitrogen monoxide gas (N2O). What volume of O2 is needed to produce 34 L of N2O?

17 L O2

N2 � O2 � N2O

2N2 � O2 � 2N2O

34 L N2O � 1 L O2 _ 2 L N2O

� 17 L O2

42. Ammonium nitrate is a common ingredient in chemical fertilizers. Use the reaction shown to calculate the mass of solid ammonium nitrate that must be used to obtain 0.100 L of dini-trogen monoxide gas at STP.

NH4NO3(s) 0 N2O(g) � 2H2O(g)

0.357 g NH4NO3

0.100 L N2O � 1 mol _ 22.4 L

� 0.00446 mol N2O

0.00446 mol N2O � 1 mol NH4NO3 __

1 mol N2O

� 0.00446 mol NH4NO3

0.00446 mol NH4NO3 � 80.03 g/mol � 0.357 g NH4NO3

43. When solid calcium carbonate (CaCO3) is heated, it decomposes to form solid calcium oxide (CaO) and carbon dioxide gas (CO2). How many liters of carbon dioxide will be produced at STP if 2.38 kg of calcium carbonate reacts completely?

533 L CO2

CaCO3 0 CaO � CO2

2.38 kg � 1000 g

_ 1 kg

� 1 mol CaCO3 __

100.09 g �

1 mol CO2 __

1 mol CaCO3 � 22.4 L _

1 mol � 533 L CO2

44. When iron rusts, it undergoes a reaction with oxygen to form iron(III) oxide.

4Fe(s) � 3O2(g) 0 2Fe2O3(s)

Calculate the volume of oxygen gas at STP that is required to completely react with 52.0 g of iron.

15.6 L O2

52.0 g Fe � 1 mol Fe _ 55.85 g Fe

� 3 mol O2 _ 4 mol Fe

� 22.4 L _ 1 mol

� 15.6 L O2

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45. Challenge An excess of acetic acid is added to 28 g of sodium bicarbonate at 25°C and 1 atm pressure. During the reaction, the gas cools to 20°C. What volume of carbon dioxide will be produced? The balanced equation for the reaction is shown below.

NaHCO3(aq) � CH3COOH(aq) 0

NaCH3COO(aq) � CO2(g) � H2O(l)

7.9 L CO2

Molecular mass of sodium bicarbonate � 83.9 g/mole

28 g NaHCO3 � 1 mol NaHCO3 __

83.9 g

� 0.33 mol NaHCO3

For each mole of sodium bicarbonate, one mole of CO2 is produced, so 0.33 mol NaHCO3 will produce 0.33 mol CO2.

For an ideal gas, molar volume is 22.4 L at 273 K and 1 atm.

T � 20°C � 273 � 293 K

0.33 mol CO2 � 22.4 L _ 1 mol

� 293 K _ 273 K

� 7.9 L of CO2


46. Explain When fluorine gas combines with water vapor, the following reaction occurs.

2F2(g) � 2H2O(g) 0 O2(g) � 4HF(g)

If the reaction starts with 2 L of fluorine gas, how many liters of water vapor react with the fluorine, and how many liters of oxygen and hydrogen fluoride are produced?

2 L H2O, 1 L O2, and 4 L HF

2 L F2 � 2 L H2O

_ 2 L F2

� 2 L H2O

2 L F2 � 1 L O2 _ 2 L F2

� 1 L O2

2 L F2 � 4 L HF _ 2 L F2

� 4 L HF

47. Analyze Is the volume of a gas directly or indirectly proportional to the number of moles of a gas at constant temperature and pressure? Explain.

Directly proportional; as the amount of gas increases, so does volume.

48. Calculate One mole of a gas occupies a volume of 22.4 L at STP. Calculate the tempera-ture and pressure conditions needed to fit 2 mol of a gas into a volume of 22.4 L.

Student answers may vary. Temperature can be halved or pressure doubled or a combination of lowering temperature and increasing pressure.

49. Interpret Data Ethene gas (C2H4) reacts with oxygen to form carbon dioxide and water. Write a balanced equation for this reaction, then find the mole ratios of substances on each side of the equation.

C2H4(g) � 3O2(g) 0 2CO2 � 2H2O

1:3 2:2

Chapter 13 Assessmentpages 468–471

Section 13.1

Mastering Concepts 50. State Boyle’s law, Charles’s law, Gay-Lussac’s

law, and the combined gas law in words and equations.

Boyle’s law: the volume of a given amount of gas held at a constant temperature varies inversely with pressure, P1V1 � P2V2; Charles’s law: the volume of a given mass of gas is directly proportional to its kelvin temperature at constant pressure, V1/T1 � V2/T2; Gay-Lussac’s law: the pressure of a given mass of gas varies directly with the kelvin temperature when the volume remains constant, P1/T1 � P2/T2; combined gas law: states the relationship among pressure, volume, and temperature of a fixed amount of gas, P1V1/T1 � P2V2/T2

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51. If two variables are inversely proportional, what happens to the value of one as the value of the other increases?

One variable always decreases as the other increases.

52. If two variables are directly proportional, what happens to the value of one as the value of the other increases?

One variable always increases as the other increases.

53. List the standard conditions for gas measurements.

T � 0.00°C (273 K) and P � 1.00 atm

54. Identify the units most commonly used for P, V, and T.

atm for pressure, kelvin for temperature, and L for volume

Mastering Problems

500 100 150 250 300 400350200

Volu

me

(mL)

800

700

600

500

400

300

200

100

0

Temperature (K)

(100 K, 200 mL)

(300 K, 600 mL)

(200 K, 400 mL)

Temperature and Volume Data

55. Use Charles’s law to determine the accuracy of the data plotted in Figure 13.13.

Charles’s law states that the volume of a given mass of gas is directly proportional to temperature. The graphed data follow this law because doubling the temperature doubles the volume, so the data are accurate.

56. Weather Balloons A weather balloon is filled with helium that occupies a volume of 5.00 × 10 4 L at 0.995 atm and 32.0°C. After it is released, it rises to a location where the pressure is 0.720 atm and the temperature is �12.0°C. What is the volume of the balloon at the new location?

5.91 � 10 4 L

T1 � 32.0°C � 273 � 295 K

T2 � �12°C � 273 � 261 K

V2 � P1V1T2 _ T1P2

� (0.995 atm)(5.00 � 10 4 L)(261 K)

___ (305 K)(0.720 atm)

� 5.91 � 10 4 L

57. Use Boyle’s, Charles’s, or Gay-Lussac’s law to calculate the missing value in each of the following.

a. V1 � 2.0 L, P1 � 0.82 atm, V2 � 1.0 L, P2 � ?

1.6 atm

P2 � P1V1 _ V2

� (0.82 atm)(2.0 L)

__ (1.0 L)

� 1.6 atm

b. V1 � 250 mL, T1 � ?, V2 � 400 mL, T2 � 298 K

200 K

T1 � T2V1 _ V2

� (298 K)(250 mL)

__ (400 mL)

� 186 K � 200 K

c. V1 � 0.55 L, P1 � 740 mm Hg, V2 � 0.80 L, P2 � ?

510 mm Hg

P2 � P1V1 _ V2

� (740 mm Hg)(0.55 L)

__ (0.80 L)

� 510 mm Hg

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58. Hot-Air Balloons A sample of air occupies 2.50 L at a temperature of 22.0°C. What volume will this sample occupy inside a hot-air balloon at a temperature of 43.0°C? Assume that the pressure inside the balloon remains constant.

2.68 L

T1 � 22.0°C � 273 � 295 K

T2 � 43.0°C � 273 � 316 K

V2 � V1T2 _ T1

� (2.50 L)(316 K)

__ (295 K)

� 2.68 L

59. What is the pressure of a fixed volume of hydrogen gas at 30.0°C if it has a pressure of 1.11 atm at 15.0°C?

1.17 atm

T1 � 15.0°C � 273 � 288 K

T2 � 30.0°C � 273 � 303 K

P2 � P1T2 _ T1

� (1.11 atm)(303 K)

__ (288 K)

� 1.17 atm

V1 = 500 mLP1 = 108 KPaT1 = 10.0°C

V2 = 750 mLT2 = 21.0°C

N2

N2

60. A sample of nitrogen gas is transferred to a large flask, as shown in Figure 13.14. What is the pressure of nitrogen in the second flask?

74.8 kPa

T1 � 10.0°C � 273 � 283 K

T2 � 21.0°C � 273 � 294 K

P2 � P1V1T2 _ T1V2

� (108 kPa)(500.0 mL)(294 K)

___ (283 K)(750.0 mL)

� 74.8 kPa

Section 13.2

Mastering Concepts 61. State Avogadro’s principle.

At a fixed temperature and pressure, equal volumes of any ideal gas contain equal numbers of particles.

62. State the ideal gas law.

The ideal gas law describes the physical behavior of an ideal gas in terms of the pressure, volume, temperature, and number of moles of gas present.

63. What volume is occupied by one mol of a gas at STP? What volume does 2 mol occupy at STP?

22.4 L; 44.8 L

64. Define the term ideal gas, and explain why there are no true ideal gases in nature.

An ideal gas is one whose particles take up no space and have no intermolecular attractive forces, and it follows the gas laws under all conditions of temperature and pressure. No gas is truly ideal because all gas particles have some volume and are subject to intermolecular interactions.

65. List two conditions under which a gas is least likely to behave ideally.

high pressure and low temperature

66. What units must be used to express the temper-ature in the equation for the ideal gas law? Explain.

Kelvin units; V is not directly proportional to Celsius temperature.

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Mastering Problems 67. Home Fuel Propane (C3H8) is a gas

commonly used as a home fuel for cooking and heating.

a. Calculate the volume that 0.540 mol of propane occupies at STP.

12.1 L

0.540 mol � 22.4 L _ 1 mol

� 12.1 L

b. Think about the size of this volume and the amount of propane that it contains. Why do you think propane is usually liquefied before it is transported?

Propane occupies a much smaller volume when liquefied.

68. Careers in Chemistry A physical chemist measured the lowest pressure achieved in a laboratory—about 1.0 � 10�15 mm Hg. How many molecules of gas are present in a 1.00-L sample at that pressure if the sample’s tempera-ture is 22.0ºC?

3.3 � 10 4 molecules

T � 22.0°C � 273 � 295 K

n � PV _ RT

� (1.0 � 10�15 mm Hg)(1.00 L)

___ (62.4

L�mm Hg _

mol�K )(295 K)

� 5.4 � 10 �20 mol

5.4 � 10�20 mol � 6.02 � 10 23 molecules ___ 1 mol

� 3.3 � 10 4 molecules

69. Calculate the number of moles of O2 gas held in a sealed, 2.00-L tank at 3.50 atm and 25.0°C. How many moles would be in the tank if the temperature was raised to 49.0°C and the pres-sure remained constant?

0.286 mol; 0.265 mol

T � 25.0°C � 273 � 298 K

n � PV _ RT

� (3.50 atm)(2.00 L)

___ (0.0821 L�atm _

mol�K )(298 K)

� 0.286 mol

T � 49.0°C � 273 � 322 K

n � PV _ RT

� (3.50 atm)(2.00 L)

___ (0.0821 L�atm _

mol�K )(322 K)

� 0.265 mol

70. Perfumes Geraniol is a compound found in rose oil that is used in perfumes. What is the molar mass of geraniol if its vapor has a density of 0.480 g/L at a temperature of 260.0°C and a pressure of 0.140 atm?

1.50 � 10 2 g/mol

Assume 1 mol of geraniol.

T � 260.0°C � 273 � 533 K

V � nRT _ P �

(1 mol)(0.0821 L�atm _ mol�K

)(533 K) ___

0.140 atm � 313 L

mass � density � volume � (0.480 g/L)(313 L) � 1.50 � 10 2 g in 1 mole

71. Find the volume that 42 g of carbon monoxide gas occupies at STP.

34 L

n � 42 g CO � 1 mol CO __ 28.01 g CO

� 1.5 mol CO

V � 1.5 mol � 22.4 L _ 1 mol

� 34 L

72. Determine the density of chlorine gas at 22.0°C and 1.00 atm.

2.93 g/L

Molar mass Cl2 � 70.90 g/mol

T � 22.0°C � 273 � 295 K

D � MP _ RT

� (70.90 g/mol)(1.00 atm)

___ (0.0821 L atm/mol · K)(295 K)

� 2.93 g/L

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NitrogenN2

PropaneC3H8

Mass of C3H80.52 kg

Mass of N20.38 kg

73. Which of the gases in Figure 13.15 occupies the greatest volume at STP? Explain your answer.

The N2 occupies the greatest volume at STP. The N2 occupies 310 L, while the C3H8 occupies only 260 L.

0.52 kg C3H8 � 1000 g

_ 1 kg

� 1 mol _ 44.1 g

� 11.8 mol C3H8

11.8 mol � 22.4 L _ 1 mol

� 260 L C3H8

0.38 kg N2 � 1000 g

_ 1 kg

� 1 mol _ 28.0 g

� 13.6 mol N2

13.6 mol � 22.4 L _ 1 mol

� 310 L N2

74. If the containers in Figure 13.15 each hold 4.00 L, what is the pressure inside each? Assume ideal behavior.

propane: 66.1 atm; nitrogen: 76.2 atm

PV � nRT

propane:

P � nRT _ V

� (11.8 mol C3H8)(0.0821 L�atm _

mol�K )(273 K)

____ 4.00 L

� 66.1 atm

nitrogen:

P � nRT _ V

� (13.6 mol N2)(0.0821 L�atm _

mol�K )(273 K)

____ 4.00 L

� 76.2 atm

Atm

2.0 3.0

1.0

0.0

4.0 5.0

P = 1.08 atmT = 15.0°C

75. A 2.00-L flask is filled with ethane gas (C2H6) from a small cylinder, as shown in Figure 13.16. What is the mass of the ethane in the flask?

2.75 g

T � 15°C � 273 � 288 K

n � PV _ RT

� (1.08 atm)(2.00 L)

___ (0.0821 L�atm _

mol�K )(288 K)

� 0.0914 mol

molar mass � (2 � 12.01 g/mol) �(6 � 1.008 g/mol) � 30.07 g/mol

mass � n � M � (0.0914 mol)(30.07 g/mol) � 2.75 g

76. What is the density of a sample of nitrogen gas (N2) that exerts a pressure of 5.30 atm in a 3.50-L container at 125°C?

4.55 g/L

D � MP _ RT

� (28.0

g _

mol )(5.30 atm)

___ (0.0821 L�atm _

mol�K )(398 K)

� 4.55 g/L

77. How many moles of helium gas (He) would be required to fill a 22-L container at a tempera-ture of 35°C and a pressure of 3.1 atm?

2.7 mol

T � 35°C � 273 � 308 K

n � PV _ RT

� (3.1 atm)(22 L)

___ (0.0821 L�atm _

mol�K )(308 K)

� 2.7 mol

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78. Before a reaction, two gases share a container at a temperature of 200 K. After the reaction, the product is in the same container at a tempera-ture of 400 K. If both V and P are constant, what must be true of n?

With a constant volume and pressure and doubling of the temperature, the number of moles would be half the initial number of moles.

Section 13.3

Mastering Concepts 79. Why must an equation be balanced before using

it to determine the volumes of gases involved in a reaction?

Equation coefficients represent ratios among gas volumes in the reaction.

80. It is not necessary to consider temperature and pressure when using a balanced equation to determine relative gas volume. Why?

Temperature and pressure are the same for each gas involved in the reaction. These conditions affect each gas in the same way.

81. What information do you need to solve a volume-mass problem that involves gases?

balanced equation, at least one mass or volume value for a reactant or product, and P and T conditions under which gas volumes have been measured

82. Explain why the coefficients in a balanced chemical equation represent not only molar amounts but also relative volumes for gases.

Avogadro’s principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles (or an equal number of moles). Therefore, the coefficients also represent the relative volumes of the gases.

83. Do the coefficients in a balanced chemical equation represent volume ratios for solids and liquids? Explain.

No, this relationship only applies to gases that behave like ideal gases.

Mastering Problems 84. Ammonia Production Ammonia is often

formed by reacting nitrogen and hydrogen gases. How many liters of ammonia gas can be formed from 13.7 L of hydrogen gas at 93.0°C and a pressure of 40.0 kPa?

9.13 L NH3

N2 � 3H2 0 2NH3

13.7 L H2 � 2 L NH3 _ 3 L H2

� 9.13 L NH3

85. A 6.5-L sample of hydrogen sulfide is treated with a catalyst to promote the reaction shown below.

2H2S(g) � O2(g) 0 2H2O(g) � 2S(s)

If the H2S reacts completely at 2.0 atm and 290 K, how much water vapor, in grams, is produced?

9.7 g

Determine volume ratios from the balanced

chemical equation: 2 volumes H2S

__ 2 volumes H2O

6.5 L H2S ( 2 L H2O _

2 L H2S ) � 6.5 L H2O

n � PV _ RT

n � (2.0 atm)(6.5 L H2O)

___ (0.0821 L�atm _

mol�K )(290 K)

� 0.54 mol

molar mass � (2 � 1.008 g/mol) � (1 � 15.999 g/mol) � 18.015 g/mol

mass � n � M � (0.54 mol)(18.015 g/mol) � 9.7 g

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86. To produce 15.4 L of nitrogen dioxide at 310 K and 2.0 atm, how many liters of nitrogen gas and oxygen gas are required?

N2 gas: 7.7 L; O2 gas: 15.4 L

Write a balanced chemical equation: N2 � 2O2 0 2NO2

The molar relationship between O2 and NO2 is 1:1 based on the balanced chemical equation. Therefore, the volume of O2 gas is 15.4 L. The molar relationship between N2 and NO2 is 1:2.

(15.4 L NO2) � 1 L N2 _

2 L NO2 � 7.7 L N2

87. Use the reaction shown below to answer these questions.

2CO(g) + 2NO(g) 0 N2(g) + 2CO2(g)

a. What is the volume ratio of carbon monoxide to carbon dioxide in the balanced equation?

1:1

b. If 42.7 g of CO is reacted completely at STP, what volume of N2 gas will be produced?

17.1 L

nCO � 42.7 g CO � 1 mol CO __ 28.01 g CO

� 1.52 mol CO

nN2 � 1.52 mol CO �

1 mol N2 _ 2 mol CO

� 0.762 mol N2

VN2 � (0.762 mol) � (22.4 L/mol) � 17.1 L

88. When 3.00 L of propane gas is completely combusted to form water vapor and carbon dioxide at 350°C and 0.990 atm, what mass of water vapor results?

4.2 g

2C3H8 � 10O2 0 6CO2 � 8H2O

3.00 L C3H8 � 8 L H2O

_ 2 L C3H8

� 12.0 L H2O

T � 350°C � 273 � 623 K

n � PV _ RT

� (0.990 atm)(12.0 L)

___ (0.0821 L�atm _

mol�K )(623 K)

� 0.232 mol H2O

mass � 0.232 mol H2O � 18.02 g H2O

__ 1 mol H2O

� 4.2 g H2O

89. When heated, solid potassium chlorate (KClO3) decomposes to form solid potassium chloride and oxygen gas. If 20.8 g of potassium chlorate decomposes, how many liters of oxygen gas will form at STP?

5.70 L

2KClO3 0 2KCl � 3O2

molar mass KClO3 � 39.10 g/mol � 35.45 g/mol � (3 � 16.00 g/mol) � 122.55 g/mol

nKClO3 � 20.8 g KClO3 �

1 mol KClO3 __ 122.55 g KClO3

� 0.170 mol KClO3

nO2 � 0.170 mol KClO3 �

3 mol O2 __ 2 mol KClO3

� 0.255 mol O2

V � 0.255 mol � 22.4 L _ 1 mol

� 5.70 L O2

90. Acetylene The gas acetylene, often used for welding, burns according to the following equation.

2C2H2(g) � 5O2(g) 0 2H2O(g) � 4CO2(g)

If you have a 10.0-L tank of acetylene at 25.0°C and 1.00 atm pressure, how many moles of CO2 will be produced if you burn all the acetylene in the tank?

0.817 mol

(10.0 L C2H2) � 4 volumes CO2 __ 2 volumes C2H2

� 20.0 L CO2

T � 25°C � 273 � 298 K

n � PV _ RT

� (1.00 atm)(20.0 L)

___ (0.0821 L�atm _

mol�K )(298 K)

� 0.817 mol CO2

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Mixed Review 91. Gaseous methane (CH4) undergoes complete

combustion by reacting with oxygen gas to form carbon dioxide and water vapor.

a. Write a balanced equation for this reaction.

CH4(g) � 2O2(g) 0 CO2(g) � 2H2O(g)

b. What is the volume ratio of methane to water in this reaction?

1:2

Atm

2.0 3.0

1.0

0.0

4.05.0

125°C

7.0 L

92. Calculate the amount of water vapor, in grams, contained in the vessel shown in Figure 13.17.

3.9 g

T � 125°C � 273 � 398 K

m � MPV _ RT

� (18.015

g _

mol )(1.0 atm)(7.0 L)

___ (0.0821 L�atm _

mol�K )(398 K)

� 3.9 g

93. Television Determine the pressure inside a television picture tube with a volume of 3.50 L that contains 2.00 � 10�5 g of nitrogen gas at 22.0°C.

4.94 � 10�6 atm

n � 2.00 � 10�5 g N2 � 1 mol N2 __

28.02 g N2

� 7.14 � 10�7 mol

T � 22.0°C � 273 � 295 K

P � nRT _ V

� (7.14 � 10�7 mol)(0.0821 L�atm _

mol�K )(295 K)

____ 3.50 L

� 4.94 � 10�6 atm

94. Determine how many liters 8.80 g of carbon dioxide gas would occupy at:

n � 8.80 g CO2 � 1 mol CO2 __

44.01 g CO2

� 0.200 mol CO2

a. STP

4.48 L

V � 0.200 mol � 22.4 L _ 1 mol

� 4.48 L

b. 160°C and 3.00 atm

2.37 L

T � 160°C � 273 � 433 K

V � nRT _ P

� (0.200 mol)(0.0821 L�atm _

mol�K )(433 K)

____ 3.00 atm

� 2.37 L

c. 288 K and 118 kPa

4.06 L

V � nRT _ P �

(0.200 mol)(8.314 L�kPa _ mol�K

)(288 K) ____

118 kPa

� 4.06 L

95. Oxygen Consumption If 5.00 L of hydrogen gas, measured at a temperature of 20.0ºC and a pressure of 80.1 kPa, is burned in excess oxygen to form water, what mass of oxygen will be consumed? Assume temperature and pressure remain constant.

2.63 g

2H2(g) � O2(g) 0 2H2O(g)

VO2 � 5.00 L H2 �

1 L O2 _ 2 L H2

� 2.50 L O2

T � 20.0°C � 273 � 293 K

n � PV _ RT

� (80.1 kPa)(2.50 L)

__ (8.314 L�kPa _

mol�K )(293 K)

� 0.0822 mol O2

mass � 0.0822 mol O2 � 32.00 g O2 __ 1 mol O2

� 2.63 g O2

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96. A fixed amount of oxygen gas is held in a 1.00-L tank at a pressure of 3.50 atm. The tank is connected to an empty 2.00-L tank by a tube with a valve. After this valve has been opened and the oxygen is allowed to flow freely between the two tanks at a constant tempera-ture, what is the final pressure in the system?

1.17 atm

P2 � P1V1 _ V2

� (3.50 atm)(1.00 L)

__ 3.00 L

� 1.17 atm

97. If 2.33 L of propane at 24°C and 67.2 kPa is completely burned in excess oxygen, how many moles of carbon dioxide will be produced?

0.19 mol

C3H8 � 5O2 0 3CO2 � 4H2O

2.33 L C3H8 � 3 L CO2 _ 1 L C3H8

� 6.99 L CO2

T � 24°C � 273 � 297 K

n � PV _ RT

� (67.2 kPa)(6.99 L)

__ (8.314 L�kPa _

mol�K )(297 K)

� 0.190 mol CO2

98. Respiration A human breathes about 0.50 L of air during a normal breath. Assume the conditions are at STP.

a. What is the volume of one breath on a cold day atop Mt. Everest? Assume �60ºC and 253 mm Hg pressure.

1.2 L

n � PV _ RT

� (760 mm Hg)(0.50 L)

___ (62.4

L�mm Hg _

mol�K ) (273 K)

� 0.022 mol

T � �60°C � 273 � 213 K

V � nRT _ P �

(0.022 mol)(62.4 L�mm Hg

_ mol�K

)(213 K) ____

253 mm Hg

� 1.2 L

b. Air normally contains about 21% oxygen. If the O2 content is about 14% atop Mt. Everest, what volume of air does a person need to breathe to supply the body with the same amount of oxygen?

0.75 L

21% _ 14%

� 100 � 1.5

0.50 L � 1.5 � 0.75 L

Think Critically 99. Apply An oversized helium balloon in a

floral shop must have a volume of at least 3.8 L to rise. When 0.1 mol is added to the empty balloon, its volume is 2.8 L. How many grams of He must be added to make it rise? Assume constant T and P.

0.56 g

n1 _ n2

� V1 _ V2

n2 � n1V2 _ V1

� (0.1 mol)(3.8 L)

__ 2.8 L

� 0.14 mol

0.14 mol � 4.003 g _

mol � 0.56 g

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100. Calculate A toy manufacturer uses tetrafluo-roethane (C2H2F4) at high temperatures to fill plastic molds for toys.

a. What is the density (in g/L) of C2H2F4 at STP?

4.55 g/L

molar mass � (2 � 12.011 g/mol) � (2 � 1.008 g/mol) � (4 � 18.998 g/mol) � 102 g/mol

D � MP _ RT

� (102

g _

mol ) (1.00 atm)

___ (0.0821 L�atm _

mol�K ) (273 K)

� 4.55 g/L

b. Find the molecules per liter of C2H2F4 at 220°C and 1.0 atm.

1.51 � 10 22 molecules per liter

n � PV _ RT

� (1.0 atm) (1.0 L)

___ (0.0821 L�atm _

mol�K ) (493 K)

n � 0.025 mol

1 L of C2H2F4 contains 0.025 mol

1 mole � 6.023 � 1023 molecules

0.025 mol � 6.023 � 1023 molecules ___ 1 mol

� 1.51 � 10 22 molecules

101. Analyze A solid brick of dry ice (CO2) weighs 0.75 kg. Once the brick has fully sublimated into CO2 gas, what would its volume be at STP?

381 L

0.75 kg � 750 g

750 g

_ 44

g _

mol � 17.0 moles

22.4 L _ 1 mol

� 17.0 mol � 381 L

102. Apply Calculate the pressure of 4.67 � 10 22 molecules of CO gas mixed with 2.87 � 10 24 molecules of N2 gas in a 6.00-L container at 34.8°C.

20.4 atm

nCO � 4.67 � 10 22 molecules

� 1 mol ___ 6.02 � 10 23 molecules

� 0.0776 mol CO

nN2 � 2.87 � 10 24 molecules

� 1 mol ___ 6.02 � 10 23 molecules

� 4.77 mol N2

ntotal � 0.0776 mol CO � 4.77 mol N2 � 4.85 mol

T � 34.8°C � 273 � 307.8 K

P � nRT _ V

� (4.85 mol) (0.0821 L�atm _

mol�K ) (307.8 K)

____ 6.00 L

� 20.4 atm

103. Apply When nitroglycerin (C3H5N3O9) explodes, it decomposes into the following gases: CO2, N2, NO, and H2O. If 239 g of nitroglycerin explodes, what volume will the mixture of gaseous products occupy at 1.00 atm pressure and 2678°C?

1850 L

molar mass C3H5N3O9 � (3 � 12.01) � (5 � 1.008) � (3 � 14.01) � (9 � 16.00) � 227.10 g/mol

n � 239 g C3H5N3O9 � 1 mol C3H5N3O9 __

227.10 g C3H5N3O9

� 1.05 mol C3H5N3O9

4C3H5N3O9(s) 0 12CO2(g) � 5N2(g) � 2NO(g) � 10H2O(g)

1.05 mol C3H5N3O9 � 29 mol gas products

__ 4 mol C3H5N3O9

� 7.61 mol gas products

V � nRT _ P

� (7.61 mol) (0.0821 L�atm _

mol�K ) (2951 K)

____ 1.00 atm

� 1850 L

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104. Make and Use Graphs The data in Table 13.3 show the volume of hydrogen gas collected at several different temperatures. Illustrate these data with a graph. Use the graph to complete the table. Determine the temperature at which the volume will reach a value of 0 mL. What is this temperature called?

Volume of H2 Collected

Trial T(°C) V(mL)

1 300 48

2 175 37

3 110 32

4 0 22

5 �100 15

6 �150 11

�300 �200 �100 0 100 200 3000

10

20

30

40

50Volume vs. Temperature

Temperature (°C)

Vo

lum

e (m

L)

Extrapolating the graph to a volume of 0 mL intersects the temperature axis at approximately �273°C, the temperature called absolute zero.

105. Apply What is the numerical value of the ideal gas constant (R) in

cm3�Pa _ mol�K

?

8.314 � 106 cm3 �Pa _ mol�K

R � 8.314 L�kPa __ mol�k

� 1000 cm3 _

1 L � 1000 Pa _

1 kPa

� 8.314 � 10 6 cm3�Pa _ mol�K

106. Infer At very high pressures, will the ideal gas law calculate a pressure that is higher or lower than the actual pressure exerted by a sample of gas? How will the calculated pressure compare to the actual pressure at low temperatures? Explain your answers.

At high pressures and low temperatures, the ideal gas law will calculate a pressure that is higher than the gas actually exerts. Under these conditions, the effects of intermolecular forces become more important. Attractions between particles will lower the force of the collisions with the container wall, resulting in an actual pressure that is lower than the pressure calculated by the ideal gas law.

Challenge Problem107. Baking A baker uses baking soda as the

leavening agent for his pumpkin-bread recipe. The baking soda decomposes according to two possible reactions.

2NaHCO3(s) 0 Na2CO3(s) � H2O(l) � CO2(g)

NaHCO3(s) � H�(aq) 0 H2O(l) � CO2(g) � Na�(aq)

Calculate the volume of CO2 that forms per gram of NaHCO3 by each reaction process. Assume the reactions take place at 210°C and 0.985 atm.

2NaHCO3(s) 0 Na2CO3(s) � H2O(l) � CO2(g) � 0.24 L per gram

NaHCO3(s) � H� (aq) 0 H2O(l) � CO2(g) � Na�(aq) � 0.48 L per gram

(1) 2NaHCO3(s) 0 Na2CO3(s) � H2O(l) � CO2(g)

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Molar ratio between NaHCO3 and CO2: 2:1

V � nRT _ P �

(1.0 mol) (0.0821 L�atm _ mol � K

) (483 K) ___

0.985 atm

V � 40.2 L of CO2

2 mol of NaHCO3 produces 40.2 L of CO2

2 mol � 84.2 g/mole � 168 g of NaHCO3

168 g of NaHCO3 produces 40.2 L of CO2

40.2 L/168 g � 0.24 L/g

(2) NaHCO3(s) � H�(aq) → H2O(l) � CO2(g) � Na�(aq)

Molar ratio between NaHCO3 and CO2: 1:1

V � nRT _ P �

(1.0 mol) (0.0821 L � atm _ mol� K

) (483 K) ___

0.985 atm

V � 40.2 L of CO2

1 mol of NaHCO3 produces 40.2 L of CO2

84 g of NaHCO3 produces 40.2 L of CO2

40.2 L/84 g � 0.48 L/g

Cumulative Review108. Convert each mass measurement to its equivalent

in kilograms. (Chapter 2)

a. 247 g

0.247 kg

247 g � 1 kg

_ 103 g

� 0.247 kg

b. 53 mg

5.3 � 10 4 kg

53 mg � 1 g _

103 mg �

1 kg _

103 g � 5.3 � 10�5 kg

c. 7.23 mg

7.23 � 103 kg

7.23 mg � 1 g _

103 mg �

1 kg _

103 g � 7.23 � 10�6 kg

d. 975 mg

9.75 � 10�4 kg

975 mg � 1 g _

103 mg �

1 kg _

103 g � 9.75 � 10�4 kg

109. Write the electron configuration for each atom. (Chapter 5)

a. iodine

[Kr] 4d10 5s2 5p5

b. boron

[He] 2s2 2p1

c. chromium

[Ar] 3d5 4s1

d. krypton

[Ar] 3d10 4s2 4p6

e. calcium

[Ar] 4s2

f. cadmium

[Kr] 4d10 5s2

110. For each element, tell how many electrons are in each energy level and write the electron dot structure. (Chapter 5)

a. Kr

2, 8, 18, 8; Kr

b. Sr

2, 8, 18, 8, 2; Sr

c. P

2, 8, 5; P

d. B

2, 3; B

e. Br

2, 8, 18, 7; Br

f. Se

2, 8, 18, 6; Se

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111. How many atoms of each element are present in five formula units of calcium permanga-nate? (Chapter 7)

5 formula units Ca(MnO4)2: 5Ca, 10Mn, 40 O

112. You are given two clear, colorless aqueous solutions. One solution contains an ionic compound, and one contains a covalent compound. How could you determine which is an ionic solution and which is a covalent solution? (Chapter 8)

The ionic solution will conduct electricity. The covalent solution will not conduct electricity.

113. Write a balanced equation for the following reactions. (Chapter 9)

a. Zinc displaces silver in silver chloride.

Zn(s) � 2AgCl(aq) 0 ZnCl2(aq) � 2Ag(s)

b. Sodium hydroxide and sulfuric acid react to form sodium sulfate and water.

2NaOH(aq) � H2SO4(aq) 0 Na2SO4(aq) � 2H2O(l)

114. Terephthalic acid is an organic compound used in the formation of polyesters. It contains 57.8% C, 3.64% H, and 38.5% O. The molar mass is approximately 166 g/mol. What is the molecular formula of terephthalic acid? (Chapter 10)

C8H6O4

57.8 g C � 1 mol C _ 12.01 g C

� 4.81 mol C

3.64 g H � 1 mol H _ 1.01 g H

� 3.60 mol H

38.5 g O � 1 mol O _ 16.00 g O

� 2.41 mol O

4.81 mol C __ 2.41

� 2.00 mol C

3.60 mol H __ 2.41

� 1.50 mol H

2.41 mol O __ 2.41

� 1.00 mol O

empirical formula: C4H3O2

molar mass C4H3O2 � (4 � 12.01 g/mol) � (3 � 1.01 g/mol) � (2 � 16.00 g/mol)

� 83.07 g/mol

n � 166

g _

mol _

83.07 g _

mol � 2.00

molecular formula: C8H6O4

115. The particles of which gas have the highest average speed? The lowest average speed? (Chapter 12)

a. carbon monoxide at 90°Cb. nitrogen trifluoride at 30°Cc. methane at 90°Cd. carbon monoxide at 30°C

c, b

Average speed is greater at higher temperature and lower at greater molar mass

Additional Assessment

Writing in Chemistry 116. Hot-Air Balloons Many early balloonists

dreamed of completing a trip around the world in a hot-air balloon, a goal not achieved until 1999. Write about what you imagine a trip in a balloon would be like, including a description of how manipulating air temperature would allow you to control altitude.

Student answers should include a description of how the difference in density of hot air and cold air is what allows hot-air balloons to stay aloft, and how manipulating the rate of heating of air allows a balloonist to ascend and descend.

117. Scuba Investigate and explain the function of the regulators on the air tanks used by scuba divers.

Student answers should include the overall function of the air tank regulator, a device that changes air pressure levels and delivers air. The first stage regulator is the regulator attached to the scuba tank, and it lowers the tank pressure to ambient pressure plus a predetermined pressure (e.g., ambient � 140 psi). The second stage regulator follows the first stage regulator in line, and it delivers compressed air to the diver.

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Document-Based Questions

The Haber Process Ammonia (N H 3 ) is used in the production of fertilizer, refrigerants, dyes, and plas-tics. The Haber process is a method of producing ammonia through a reaction of molecular nitrogen and hydrogen. The equation for the reversible reaction is:

N2(g) � 3H2(g) a 2 NH3(g) � 92 kJ

Figure 13.18 shows the effect of temperature and pressure on the amount of ammonia produced by the Haber process.

0 100 300 400200

Perc

ent

yiel

d of

am

mon

ia

70 350°C

400°C

450°C

500°C

550°C

50

60

40

30

20

10

0

Pressure (atm)

The Haber Process

118. Explain how the percent yield of ammonia is affected by pressure and temperature.

Ammonia yield is increased by very high pressures. Yield decreases at very high temperatures.

119. The Haber process is typically run at 200 atm and 450°C, a combination proven to yield a substantial amount of ammonia in a short time.

a. What effect would running the reaction above 200 atm have on the temperature of the containment vessel?

Increasing the pressure above 200 atm raises the temperature.

b. How do you think lowering the temperature of this reaction below 450°C would affect the amount of time required to produce ammonia?

Lowering the temperature of this reaction slows the rate of reaction, increasing the amount of time required to produce ammonia.

Standardized Test Practicepages 472–473

Use the graph below to answer Questions 1 and 2.

200 250 300 350 400 450

Pres

sure

(kPa

)

1200

1000

800

600

400

200

0

Gas A

Gas B

Gas C

Gas D

Temperature (K)

Pressures of Four Gasesat Different Temperatures

1. Which is evident in the graph above?

a. As temperature increases, pressure decreases.

b. As pressure increases, volume decreases.c. As temperature increases, the number of

moles decreases.d. As pressure decreases, temperature

decreases.

d

2. Which behaves as an ideal gas?

a. Gas Ab. Gas Bc. Gas Cd. Gas D

d

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Use the graph below to answer Question 3.

0.80 1.00 1.20 1.40

Tem

pera

ture

(°C) 200

160

120

80

40

0

Density (kg/m3)

Density of Air

3. The graph shows data from an experiment which analyzed the relationship between temperature and air density. What is the inde-pendent variable in the experiment?

a. densityb. massc. temperatured. time

c

4. Hydrofluoric acid (HF) is used in the manu-facture of electronics equipment. It reacts with calcium silicate (CaSi O 3), a component of glass. What type of property prevents hydro-fluoric acid from being transported or stored in glass containers?

a. chemical propertyb. extensive physical propertyc. intensive physical propertyd. quantitative property

a

5. Sodium hydroxide (NaOH) is a strong base found in products used to clear clogged plumbing. What is the percent composition of sodium hydroxide?

a. 57.48% Na, 60.00% O, 2.52% Hb. 2.52% Na, 40.00% O, 57.48% Hc. 57.48% Na, 40.00% O, 2.52% Hd. 40.00% Na, 2.52% O, 57.48% H

c

Determine the molar mass.

1 mol Na � 22.99 g Na

__ 1 mol Na

� 22.99 g Na

1 mol O � 16.00 g O

_ 1 mol O

� 16.00 g O

1 mol H � 1.008 g H

_ 1 mol H

� 1.008 g H

Total molar mass � 22.99 g � 16.00 g � 1.008 g � 39.998 g � 40.00 g/mol NaOH

Determine percent by mass.

percent Na � 22.99 g/mol

__ 40.00 g/mol

� 100 � 57.48%

percent O � 16.00 g/mol __ 40.00 g/mol

� 100 � 40.00%

percent H � 1.008 g/mol __ 40.00 g/mol

� 100 � 2.52%

Use the circle graph below to answer Question 6.

Hydrogen4.21%

Oxygen66.81%

Lithium28.98%

6. What is the empirical formula for this compound?

a. LiOHb. Li2OHc. Li3OHd. LiOH2

a

Assume a 100 g sample. Determine the number of moles.

66.81 g O � 1 mol O _ 16.00 g O

� 4.176 mol O

28.98 g Li � 1 mol Li _ 6.941 g Li

� 4.175 mol Li

4.21 g H � 1 mol H _ 1.008 g H

� 4.177 mol H

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Calculate the simplest ratio of moles.

4.176 mol O __ 4.175

� 1.000

4.175 mol Li __ 4.175

� 1.000

4.177 mol H __ 4.175

� 1.000

The empirical formula is LiOH.

7. While it is on the ground, a blimp is filled with 5.66 � 106 L of He gas. The pressure inside the grounded blimp, where the temperature is 25°C, is 1.10 atm. Modern blimps are nonrigid, which means that their volumes can change. If the pressure inside the blimp remains the same, what will be the volume of the blimp at a height of 2300 m, where the temperature is 12°C?

a. 2.72 � 106 Lb. 5.40 � 106 Lc. 5.66 � 106 Ld. 5.92 � 106 L

b

V1 _ T1

� V2 _ T2

T1 � 25°C � 273 � 298 K

T2 � 12°C � 273 � 285 K

V2 � (5.66 � 106 L)(285 K)

__ 298 K

� 5.4 � 106 L

8. Describe several observations that provide evidence that a chemical change has occurred.

Evidence of chemical change includes temperature change, color change, the production of an odor or a gas, and the precipitation of a solid.

9. Identify seven diatomic molecules that occur naturally, and explain why the atoms in these molecules share one pair of electrons.

Hydrogen (H2), oxygen (O2), nitrogen (N2), fluorine (F2), chlorine (Cl2), bromine (Br2), and iodine (I2) occur naturally. By sharing a pair of electrons, both atoms achieve noble gas configurations, resulting in atomic stability

10. The diagram below shows the Lewis structure for the polyatomic ion nitrate (NO3�). Define the term polyatomic ion, and give examples of ions of this type.

NO

O OA polyatomic ion is an ion made up of more than one atom that acts as a single unit with a net charge. Other examples include hydroxide (OH�), chlorite (ClO2

�), and cyanide (CN�).

Use the table below to answer Question 11.

Radon Levels August 2004 through July 2005

DateRadon Level

(mJ/m3) Date

Radon Level

(mJ/m3)

8/04 0.15 2/05 0.05

9/04 0.03 3/05 0.05

10/04 0.05 4/05 0.06

11/04 0.03 5/05 0.13

12/04 0.04 6/05 0.05

1/05 0.02 7/05 0.09

11. Radon is a radioactive gas produced when radium in soil and rock decays. It is a known carcinogen. The data above show radon levels measured in a community in Australia. Select a method for graphing these data. Explain the reasons for your choice, and graph the data.

Students should choose a bar or line graph for the data, with justification that each data point can be represented on the graph.

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12. Which diagram shows the relationship between volume and pressure for a gas at constant temperature?

V

P

V

P

V

P

V

P

V

P

a. d.

b. e.

c.

d

13. The reaction that provides blowtorches with their intense flame is the combustion of acety-lene (C2H2) with oxygen to form carbon dioxide and water vapor. Assuming that the pressure and temperature of the reactants are the same, what volume of oxygen gas is required to completely burn 5.60 L of acetylene?

a. 2.24 Lb. 5.60 Lc. 8.20 Ld. 11.2 Le. 14.0 L

e

Balance the chemical equation: 2C2H2 � 5O2 0 4CO2 � 2H2O

Determine the volume ratio: 5 volumes O2 __

2 volumes C2H2

VO2 � 5.60 L C2H2 �

5 LO2 _ 2 L C2H2

� 14.0 L O2

14. Assuming ideal behavior, how much pressure will 0.0468 g of ammonia (N H3) gas exert on the walls of a 4.00-L container at 35.0°C?

a. 0.0174 atmb. 0.296 atmc. 0.0126 atmd. 0.00198 atme. 0.278 atm

a

P � nRT _ V

� (0.00275 mol )(0.0821 L atm/mol K)(308.0 K) ____ 4.00 L

= 0.0174 atm

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