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CHAPTER 13 SOLUTIONS MANUAL Gases

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Section 13.1 The Gas Laws

pages 442?451

Practice Problems

page 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)(99.0 188 kPa

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 2.00 L

atm)

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 1.35 atm

atm)

117

mL

Problem-Solving Lab

page 444

Ribs

Lungs

Diaphragm

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.

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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 Problems

pages 446?450

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

4.3 L 350 K

3.1 L

_ __ V2

V1T2 T1

(4.3 L)(250 350 K

K)

3.1

L

5. A gas at 89?C 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 0.67 L

L)

605

K

605 273 332?C 330?C

6. The Celsius temperature of a 3.00-L sample of gas is lowered from 80.0?C to 30.0?C. 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)(303 353 K

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 0.67 L

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)(310 298 K

K)

1.96

atm

9. Helium gas in a 2.00-L cylinder is under 1.12 atm pressure. At 36.5?C, 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 0.00?C, 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.

254 Chemistry: Matter and Change ? Chapter 13

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SOLUTIONS MANUAL

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 22.0?C. The syringe is placed in a boiling water-bath at 100.0?C. 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 (2.60 atm)(278 K)

mL)

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?

0.00?C

1.00 atm

30.0 mL

down T1 0.00?C 273 273 K T2 30.0?C 273 303 K

_ _ __ V2 P1T2 (1.00 atm)(303 K) 0.92

V1 P2T1 (1.20 atm)(273 K) 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 Assessment

page 451

14. State the relationship among pressure, temperature, 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 information 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)(318 295 K

K)

711

torr

19. Design a concept map that shows the relationship 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.

Constant amount of gas

Temperature held constant

Pressure held constant

Volume held constant

P1V1 P2V2 Boyle's law

V1 T1

V2 T2

Charles's law

P1 T1

P2 T2

Gay-Lussac's

law

Section 13.2 The Ideal Gas Law

pages 452?459

Practice Problems

pages 453?455

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 1.03 L 1 mol

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 0.045 mol 22.4 L

_ 44.0 g

0.045 mol

2.0 g

1 mol

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

102 mL

_ 0.00922 g 1 mol 0.00457 mol 2.02 g

_ 0.00457 mol 22.4 L 0.102 L or 102 mL 1 mol

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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 0.00496 mol 83.80 g

_ 0.00496 mol 22.4 L 0.111 L 1 mol

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 mol 22.4 L 3.6 103 L 1 kg 28.00 g 1 mol

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 19.2 L

0.655 g 0.860 g

Solve for V.

__ V (19.2 L)(0.655 g) 14.6 L 0.860 g

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 1.41 atm 101.3 kPa

_ ___ _ T

PV nR

(1.41 atm)(1.00 L)

(2.49

mol)(0.0821

Latm molK

)

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

(0.323

mol)(0.0821

Latm molK

)(265

K)

P

0.900 atm

7.81 L

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

5.14 atm

T 20.0?C 273 293 K

_ ___ __ P

nRT

(0.108

mol)(0.0821

Latm molK

)(293

K)

V

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?

6.9 103 mol

_ __ __ n

PV RT

(3.81 (0.0821

atm)(0.44 L)

Latm mol?K

)(298

K)

6.9 103 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 nT Because P and R are constants, they can

R V be removed from the equation.

_ _ n1T1

V1

n2T2 V2

where

n2

2n1

and

T2

2T1

_ _ n1T1 2n12T1

V1

V2

_ _ Multiply

both

sides

by

1 n1

and

1 T1

.

_ _ 1 (2)(2)

V1

V2

V2 4V1

V2 4(3.0 L) 12 L

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SOLUTIONS MANUAL

Pressure (psi)

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Problem-Solving Strategy

page 458

Apply the Strategy Derive 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).

Section 13.2 Assessment

page 459

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

258 Chemistry: Matter and Change ? Chapter 13

36. Calculate A 2.00-L flask is filled with propane gas (C3H8) at a pressure of 1.00 atm and a temperature of -15.0C. 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

Latm molK

)(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 6C 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 20C to 20C (assume 30.0 psi at 20C).

Temperature vs. Pressure

32 30 28 26 24 22 20

-20 -18-16-14-12-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 Temperature (?C)

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 Stoichiometry

pages 460?464

Practice Problems

pages 461?463

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 1

L L

H2 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 dinitrogen 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 mol CaCO3

1 kg

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 3 mol O2 22.4 L 55.85 g Fe 4 mol Fe 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

293 273

K K

7.9

L

of

CO2

Section 13.3 Assessment

page 464

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 temperature 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 Assessment

pages 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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