name date class states of matter 13 - mr. acosta's...

Chapter 13 States of Matter 137

SECTION 13.1 THE NATURE OF GASES (pages 385–389)

This section introduces the kinetic theory and describes how it applies togases. It defines gas pressure and explains how temperature is related to thekinetic energy of the particles of a substance.

Kinetic Theory and a Model for Gases (pages 385–386)

1. The energy an object has because of its motion is called

___________________________________ .

2. Circle the letter of each sentence that is true about the assumptions of thekinetic theory concerning gases.

a. A gas is composed of particles with insignificant volume that are relativelyfar apart from each other.

b. Strong attractive forces exist between particles of a gas.

c. Gases tend to collect near the bottom of a container.

d. The paths of uninterrupted travel of particles in a gas are relatively shortbecause the particles are constantly colliding with each other or with other objects.

3. Is the following statement true or false? According to the kinetic theory,

collisions between particles in a gas are perfectly elastic because kinetic

energy is transferred without loss from one particle to another, and the total

kinetic energy remains constant. ______________________

Gas Pressure (pages 386–387)

4. Gas pressure results from the force exerted by a gas per ____________________________

___________________________________________________________________________ .

5. Simultaneous collisions of billions of particles in a gas with an object

result in ______________________ .

6. What force holds the particles of air in Earth’s atmosphere? _____________________

7. What kind of pressure is measured with a barometer?

Name ___________________________ Date ___________________ Class __________________

STATES OF MATTER13

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kinetic energy

true

gas pressure

gravity

unit surface

area of an object

atmospheric pressure

05_Chem_GRSW_Ch13.SE/TE 6/11/04 3:46 PM 37

Name ___________________________ Date ___________________ Class __________________©

Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.

138 Guided Reading and Study Workbook

CHAPTER 13, States of Matter (continued)

8. Look at Figure 13.2 on page 386. What accounts for the difference in heightof the two mercury columns shown in the figure?

9. Circle the letter next to every name of a unit of pressure.

a. mm Hg d. kPa

b. standard e. atm

c. pascal f. degree

10. Standard temperature and pressure (STP) are defined as _________________________

Kinetic Energy and Temperature (pages 388–389)

11. What happens to the temperature of a substance when the average kineticenergy of its particles increases?

12. Is the following statement true or false. All the particles in a substance at a

given temperature have the same kinetic energy. ___________________

13. The temperature 0K, or �273.15°C, is called _____________________ zero.

Theoretically, particles of matter at this temperature would have no ________________________.

14. On the graph below, write the labels lower temperature and higher temperatureto identify the curve that depicts the kinetic energy distribution of particles ina liquid at a lower temperature and at a higher temperature.

The mercury column on the left is shown at sea level; the one on the right is shown

at an altitude of 9000 m. Because atmospheric pressure decreases as altitude

increases, the column on the right is lower than the one on the left.

of 0°C and a pressure of 101.3 kPa or 1 atm

a temperature

false

kinetic energy

kinetic energy/motion

The temperature of the substance increases.

Kinetic energy

Perc

ent o

f mol

ecul

es

lower temperature

higher temperature

05_Chem_GRSW_Ch13.SE/TE 6/11/04 3:46 PM Page 138

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15. Circle the letter of the temperature scale that correctly completes this sentence. Temperature on the _______ scale is directly proportional to the average kinetic energy of the particles of a substance.

a. Celsius

b. Kelvin

c. Fahrenheit

d. Centigrade

SECTION 13.2 THE NATURE OF LIQUIDS (pages 390–395)

This section describes a model for liquids in terms of kinetic energy and theattractive forces between the particles in a liquid. It also uses kinetic theory to distinguish evaporation from boiling.

A Model for Liquids (page 390)

1. Is the following sentence true or false? The kinetic theory states that there areno attractions between the particles of a liquid.

______________________

2. Circle the letter next to each sentence that is true about the particles of a liquid.

a. Most of the particles in a liquid have enough kinetic energy to escape into agaseous state.

b. Liquids are much denser than gases because intermolecular forces reducethe amount of space between the particles in a liquid.

c. Increasing pressure on a liquid has hardly any effect on its volume.

d. Liquid particles are free to slide past one another.

Evaporation (page 391)

3. The conversion of a liquid to a gas or vapor is called ______________________ .

4. When vaporization occurs at the surface of a liquid that is not boiling, the

process is called ______________________ .

5. As a liquid evaporates, why do only some of the particles break away from thesurface of the liquid? Why does the liquid evaporate faster if the temperature isincreased?


false

vaporization

evaporation

Most of the molecules do not have enough kinetic energy to overcome the attractive

forces. As the temperature is increased, the average kinetic energy increases and

more particles have enough kinetic energy to overcome the forces keeping them in

the liquid state.



6. Is the following sentence true or false? Evaporation is a cooling process

because the particles in a liquid with the highest kinetic energy tend to escape

first, leaving the remaining particles with a lower average kinetic energy and,

thus, a lower temperature. ______________________

Questions 7, 8, 9, and 10 refer to either container A or container B below. Think ofeach container as a system involving both liquid water and water vapor.

(a) (b)

7. From which of the containers are water molecules able to escape? ____

8. In which container can a dynamic equilibrium between water molecules in

the liquid state and water molecules in the vapor state be established? ____

9. In which container will the water level remain constant? ____

10. From which container is it possible for all of the liquid water to disappear

through evaporation? ____

11. What causes the chill you may feel after stepping out of a swimming pool on awarm, windy day?


Name ___________________________ Date ___________________ Class __________________©


true

Wind causes water on the skin to evaporate, which is a cooling process.

b

a

a

b



Vapor Pressure (pages 392–393)

12. Circle the letter next to each sentence that is true about vapor pressure.

a. Vapor pressure arises when particles of a liquid in a closed, partly filledcontainer vaporize and collide with the walls of the container.

b. After a time in a closed, partly filled container, a liquid will evaporate andits vapor will condense at equal rates.

c. Look at Figure 13.6b on page 391. Condensation on the inside of theterrarium indicates that there is not a liquid-vapor equilibrium in thesealed terrarium.

d. When the temperature of a contained liquid increases, its vapor pressureincreases.

13. Look at Figure 13.7 on page 393. How does the vapor pressure of the ethanol inthe manometer change when the temperature is increased from 0°C to 20°C?Circle the letter of the correct answer.

a. The vapor pressure decreases by more than 4 kPa.

b. The vapor pressure remains constant.

c. The vapor pressure increases by more than 4 kPa.

d. There is no way to detect a change in vapor pressure with a manometer.

Boiling Point (pages 393–395)

14. The boiling point of a liquid is the temperature at which the vapor

pressure of the liquid is just equal to the ______________________________________ .

15. Look at Figure 13.8 on page 394. Why does the boiling point decrease asaltitude increases?

16. Use Figure 13.9 on page 394. At approximately what temperature wouldethanol boil atop Mount Everest, where the atmospheric pressure is 34 kPa?Circle the letter next to the best estimate.

a. 50°C b. 100°C c. 0°C d. 85°C

17. Is the following sentence true or false? After a liquid reaches its boiling point,

its temperature continues to rise until all the liquid vaporizes.

Name ___________________________ Date ___________________ Class __________________©

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external pressure

At higher altitudes, atmospheric pressure is lower than it is at sea level. Because

boiling occurs when vapor pressure is equal to atmospheric pressure, a liquid boils

at a lower temperature.

false


Name ___________________________ Date ___________________ Class __________________©




SECTION 13.3 THE NATURE OF SOLIDS (pages 396–399)

This section describes the highly organized structures of solids, distinguishes between acrystal lattice and a unit cell, and explains how allotropes of an element differ.

A Model for Solids (page 396)

1. Is the following sentence true or false? Although particles in solids have

kinetic energy, the motion of particles in solids is restricted to

vibrations about fixed points. ______________________

2. A solid melts when _____________________________________________________.

3. Is the following sentence true or false? The temperature at which the liquid

and solid states of a substance are in equilibrium is the same as the

melting point and the freezing point of the substance. ______________________

Crystal Structure and Unit Cells (pages 396–399)

4. How are particles arranged in a crystal?

5. What type of solid has a relatively low melting point?

6. Do all solids melt when heated? Explain.

7. Circle the letter next to each sentence that is true about solids.

a. Most solid substances are not crystalline.

b. All crystals have sides, or faces, that intersect at angles that arecharacteristic for a given substance.

c. There are seven groups, or crystal systems, into which all crystals may beclassified.

d. The orderly array of sodium ions and chloride ions gives crystals of tablesalt their regular shape.

true

true

A molecular solid has a relatively low melting point.

No; some solids, such as wood, decompose.

They are arranged in an orderly, repeating, three-dimensional pattern.

Writing a summary can help you remember what you have read. When you write a summary,include only the most important points. Write a summary of the discussion of boiling point on pages 393–395. Do your work on a separate sheet of paper.

Reading Skill Practice

Students’ summaries should include a definition of boiling point and normal boiling point. They shouldalso include the effects of pressure on the temperature of a boiling liquid.

the organization of its particles breaks down



Identify the unit cell in each figure below as simple cubic, body-centered cubic, orface-centered cubic.

8. ______________________ 9. ______________________ 10. _____________________

11. Is the following sentence true or false? Some solid substances can exist inmore than one form. Give an example to support your answer.

12. Two or more different molecular forms of the same element in the same

physical state are called ______________________ .

13. What is an amorphous solid?

14. Circle the letter next to each solid that is an amorphous solid.

a. table salt c. plastic

b. rubber d. glass

15. How are glasses different from crystalline solids?

SECTION 13.4 CHANGES OF STATE (pages 401–404)

This section describes the process of sublimation. It also explains phase changesbetween solid, liquid, and vapor states and how to interpret a phase diagram.

Sublimation (page 401)

1. The process by which wet laundry dries on an outdoor clothesline in winter

is called ______________________ .

2. Is the following sentence true or false? Solids have vapor pressure because

some particles near the surface of a solid substance have enough kinetic

energy to escape directly into the vapor phase. ______________________

Name ___________________________ Date ___________________ Class __________________©

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face-centered cubic

allotropes

body-centered cubic simple cubic

True. The element carbon has at least three solid forms: graphite, diamond, and

buckminsterfullerene.

The internal structures of glasses are intermediate between free-flowing liquids

and crystalline solids. Glasses do not have a definite melting point, but soften

when heated. Glass breaks into irregular, jagged pieces when shattered.

An amorphous solid lacks an ordered internal structure.

true

sublimation



Phase Diagrams (pages 402–403)

3. What does a phase diagram show?

4. What is the triple point of a substance?

5. In the phase diagram for water shown below, label the melting point andboiling point at normal atmospheric pressure, and the triple point.

6. Use the phase diagram above to answer the following question. Why is alaboratory required to produce the conditions necessary for observing water atthe triple point?


Name ___________________________ Date ___________________ Class __________________©


A phase diagram shows the temperature and pressure conditions at which a

substance exists in the solid, liquid, and vapor phases.

The triple point represents the only conditions of temperature and pressure at

which three phases of a substance can exist in equilibrium.

From the diagram, the triple point of water is at a pressure of 0.61 kPa, far below

atmospheric pressure. Laboratory equipment is necessary to achieve pressures this low.

101.3

0.61

Solid Liquid Vapor

0 0.016 100 Temperature (�C)

Pres

sure

(kPa

)

Normal boiling point

Normal melting point

Triple point


1. What causes air pressure in a closed container?

2. What is the speed of gas particles?

3. What is the distance between gas particles?

4. What happens when gas particles collide with each other?

. Read pages 327-328. Ben has a deflated soccer ball. He takes a hand pump and pumps it up.

1. What happens to the number of particles in the ball?

2. Would the pressure increase, decrease, stay the same?

3. If Ben puts in twice as many particles, would the pressure increase, decrease, stay thesame? By how much?

Name

4. Rose buys a small canister of compressed helium gas to fill balloons for a party. Shedecides she wants a really large balloon, so she keeps adding helium to the balloon.What do you predict will happen to the balloon? Why?

5. The canister of helium gas is not very large but she can fill about fifty 9 inch balloons.Compare the volume of the canister of gas with the volume of the 50 balloons.

6. After several days, the helium balloons are almost deflated. What is happening?

7. As a demonstration for chemistry class, the chemistry teacher inserts a balloon into alarge container of liquid nitrogen (-196 Cº). What happens to the volume of the balloon?Why?

You can buy a can of Office Duster™ 3. The can holds 10 ounces of a pressurized gas. The company decides to sell a 20 ounce pray can. The pressure will remain the same as the smaller can.

8. What will the volume of the can have to be?

9. Why does the gas in the can leave the can when the nozzle is depressed? (Hint; think ofhigh pressure versus low pressure.)

10. You use the Office Duster™ 3 to remove the dust on your computer keyboard, whathappens to the pressure in the can?

11. Is the can “empty” when no more gas is released when the nozzle is depressed? Why orwhy not?

12. When the gas is released from the can, why does it feel cold?

13. The instructions on the can say, “Do not puncture container”. Why this warning?

14. The instructions also say, “Do not incinerate.” Why this warning?

15. The can also says “Do not expose to heat, use near open flame, or store at temperaturesover 120ºF. Store in a cool place out of direct sunlight.” What could happen if the canwas left in a car parked in the sun on a July day when the temperature is in the 90’s?

© John Erickson, 2005 WS14-1BoylesLaw

example

A gas occupies a volume of 5.4 L at a pressure of 1.06 atm. What volume will the gas occupy if when the pressure is increased to 1.52 atm? Assume the temperature does not change.

- list the variables: V1 = 5.4 L P1 = 1.06 atm P2 = 1.52 atm

- substitute into the equation: 2211 VPVP ×=× 2atm) 52.1(L) 4.5(atm) 06.1( V×=×

- solve: atm 52.1

atm) 52.1(atm 52.1

L) 4.5(atm) 06.1( 2V×=× L 8.32 =V

USEFUL EQUATIONS

P1 × V1 = P2 × V2 1.00 atm = 760 mmHg 1.00 atm = 101300 Pa 1.00 atm = 760 torr 1.00 atm = 101.3 kPa 1.00 atm = 14.7 psi

Robert Boyle observed the relationship between the pressure and volume for a gas sample. These two variables are inversely proportional. This means that when the pressure goes up the volume goes down. This is expressed in the equation P1 × V1 = P2 × V2, which is known as Boyle’s Law. The relationship between pressure and volume is only observed when the temperature and amount of gas particles do not change. The graph below shows this relationship.

Solve the following problems.

1. According to the graph, when the pressure of a gas sample is decreased what happens to the volume?

2. The gas in a 600 mL balloon has a pressure of 1.20 atm. If the temperature remains constant, what will bethe pressure of the gas in the balloon when it is compressed to 400 mL?

3. An oxygen container has a volume of 48 mL and a pressure of 420 kPa. What is the volume of this gas whenthe pressure is 105 kPa?

4. A tank of compressed CO2 has a pressure of 850 psi and a volume of 150 mL. What is the volume of thisgas when the pressure is 45 psi?

5. A scuba tank has a pressure of 19,300 kPa and a volume of 10.3 L. What would be the pressure of the gas ifit were transferred to a 50.0 L container?

6. Air fills a room with a volume of 5600 L. Atmospheric pressure is 740 torr. What will be the pressure if allof the gas is pumped into an 80 L tank? Convert this pressure to kPa.

7. A sample of 24 L of helium gas is stored in a cylinder at a pressure of 110 lb/in2. The helium is transferredto a container with a volume of 15 L. Assuming the temperature has not changed what will be the pressure?

8. An air compressor has a volume of 110 L. What volume of gas is pumped into the tank if the pressure goesfrom 750 torr to a pressure of 145 psi?

Name ________________ Boyle’s Law Chem Worksheet 14-1

Boyle's Law

0

10

20

30

40

50

60

0 0.5 1 1.5 2 2.5 3 3.5

Pressure (atm)

Vol

ume

(mL)

© John Erickson, 2005 WS14-2CharlesLaw

USEFUL EQUATIONS

2

2

1

1

TV

TV

= TK = TC + 273

1 mL = 1 cm3 ( )3295 −= fc TT

1 L = 1000 mL

Solve the following problems. Assume that the pressure does not change.

1. According to the graph, when the Kelvin temperature of a gas is doubled, what happens to the volume?

2. Using the graph, estimate the Kelvin temperature that the gas sample would reach a volume of 140 L.

3. A 240 mL sample of argon gas at 270 K is cooled until the volume is 180 mL. What is the new temperature?

4. A container of oxygen with a volume of 60 L is heated from 300 K to 400 K. What is the new volume?

5. When a piston with a volume of 35 mL is heated from 25ºC to 323ºC it expands. Assuming the pressure on the piston remains the same, determine the new volume of the cylinder.

6. A balloon with a volume of 5.3 L is taken from an indoor temperature of 24ºC to the outdoors. The volume of the balloon outside is 4.9 L. Determine the Celsius temperature outside.

7. A movable piston contains a sample of 680 mL of neon gas with a temperature of -5ºC. When the piston is heated the sample expands to a volume of 1.32 L. What is the new temperature of the neon gas?

8. A helium balloon has a volume of 2600 cm3 when the temperature is 21ºC. What is the volume of the balloon when it’s placed in a freezer with a temperature of -15ºC?

9. The Kelvin temperature of sample of 650 cm3 sample of ammonia gas is doubled. What is the new volume of the gas? Assume that the pressure stays constant.

10. A movable piston is allowed to cool from 392ºF to 104ºF. If the initial volume is 105 mL, what will be the new volume?

Name ________________ Charles’ Law Chem Worksheet 14-2

Charles' Law

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600

Temperature (K)

Vol

ume

(L)

example

A gas sample with a volume of 35 mL is heated from 25ºC to 425ºC. What is the new volume? Assume a constant pressure.

- list the variables: V1 = 35 mL T1 = 25ºC = 298 K T2 = 425ºC = 698 K - substitute into the equation:

2

2

1

1

TV

TV

= K 698K 298

mL 35 21 V=

- solve by cross-multiplying: K) 298(K) (698ml) 35( 2 ×=× V

K 298K)298(

K 298K) (698ml) 35( 2 ×=× V mL 822 =V

Jacques Charles made the observation the volume of a gas is directly proportional to the Kelvin temperature of the gas. If the Kelvin temperature is doubled, the volume also doubles. The equation for this relationship is

2

2

1

1

TV

TV

= , where V represents volume and T represents temperature. The volume of a gas can be measured in liters, milliliters, cubic meters, or a variety of other units, but the temperature must be converted to kelvins. This relationship is only observed when the pressure remains constant.

Gay-Lussac’s Law

1. What is Gay-Lussac’s Law?

2. A gas has a pressure of 6.58 kPa at 539 K. What will be the pressure at 211 K? Volume is constant.

3. A gas with a pressure of 1.00 x103 kPa at 20.0°C is heated until its temperature is 50.0°C. What is the new pressure?

4. Determine the pressure change when a constant volume of gas at 101.3 kPa is heated from 20.0 °C to 30.0 °C.

5. A gas has a pressure of 37.5 kPa at 50.0 °C. What is the pressure at standard temperature?

6. A gas has a pressure of 105.6 kPa Hg at 40.0 °C. What is the temperature at standard pressure?

7. If a gas is cooled from 323.0 K to 273.15 K and the volume is kept constant what final pressure would result if the original pressure was 99.9 kPa?

8. If a gas in a closed container is pressurized from 1520 kPa to 1621 kPa and its original temperature was 25.0 °C, what would the final temperature of the gas be?

9. A 30.0 L sample of nitrogen inside a rigid, metal container at 20.0 °C is placed inside an oven whose temperature is 50.0 °C. The pressure inside the container at 20.0 °C was at 303.9 kPa. What is the pressure of the nitrogen after its temperature is increased?

© John Erickson, 2005 WS14-3CombinedGasLaw

USEFUL EQUATIONS

2

22

1

11

TVP

TVP

= TK = TC + 273


1. A canister containing air has a volume of 85 cm3 and a pressure of 1.45 atm when the temperature is 310 K.What is the pressure when the volume is increased to 180 cm3 and the temperature is reduced to 280 K?

2. Air is transferred from a 75 L tank where the pressure is 125 psi and the temperature is 288 K to a tire with avolume of 6.1 L and a pressure of 25 psi. What is the new temperature?

3. A helium balloon at 28ºC has a volume of 1.8 L and a pressure of 102 kPa. What is the volume of theballoon when is rises into the atmosphere where the pressure is 85 kPa and the temperature is 4ºC?

4. The pressure of a piston with a volume of 650 cm3 and 85ºC is 830 torr. It is heated to 350ºC andcompressed to a volume of 65 cm3. What is the new pressure?

5. A gas tank has a volume of 28.1 m3 and a pressure of 18.4 atm. The temperature of the gas is 32ºC. What isthe Celsius temperature when the gas is put in an 11.2 m3 tank with a pressure of 22.7 atm?

6. A metal can is able to withstand 3800 kPa before is bursts. The gas in the can has a volume of 235 mL andthe pressure is 110 kPa at 25ºC. If the can is crushed to a volume of 8.5 mL and the temperature does notchange will it burst? What is the pressure of the gas in the can?

Name ________________ Combined Gas Law Chem Worksheet 14-3

Boyle’s law shows that the pressure and volume of a gas are inversely related. Charles’ law shows that the kelvin temperature and volume of a gas are directly related. These two relationships can be combined into a single equation known as the combined gas law. The formula for the combined gas law

is: 2

22

1

11

TVP

TVP

= This equation could be memorized instead of memorizing Boyle’s law, Charles’ law, and Guy-Lussac’s law. Each of these other gas laws can be derived from the combined gaslaw by canceling out the variable that does not change.

example

A 28 L sample of gas has a pressure of 25 psi when the temperature is 45ºC. What is the volume of the gas if the pressure is increased to 175 psi and the temperature is increased to 320ºC?

- list the variables: V1 = 28 L P1 = 25 psi T1 = 45ºC = 313 K V2 = ? P2 = 175 psi T2 = 320ºC = 593 K

- substitute into the equation: 2

22

1

11

TVP

TVP

=K) 593(

)(psi) 175(K) 313(

)L 28(psi) 25( 2V=

- cross-multiply and simplify: K) 313)(( psi) 175(K) 593( L) psi)(28 25( 2V= K) psi)(313 175(

K) 313)((psi) 175( K) (313 psi) 175(K) 593L)( psi)(28 25( 2V

=

- solve: L 6.72 =V

Law Equation Constant Variable

Boyle’s Law 2

22

1

11

TVP

TVP

= temperature

Charles’ Law 2

22

1

11

TVP

TVP

= pressure

Guy-Lussac’s Law 2

22

1

11

TVP

TVP

= volume

© John Erickson, 2005 WS14-4IdealGasLaw

The ideal gas law is an equation that relates the volume, temperature, pressure and amount of gas particles to a constant. The ideal gas constant is abbreviated with the variable R and has the value of 0.0821 atm·L/mol·K. The ideal gas law can be used when three of the four gas variables are known. When using this equation it is important that the units for pressure are atmospheres (atm), volume is in liters (L), and temperature is converted to kelvins (K). The amount of gas is measured in units called moles (mol).


1. A tank contains 115 moles of neon gas. It has a pressure of 57 atm at a temperature of 45ºC. Calculate thevolume of the tank.

2. A scuba tank has a pressure of 195 atm at a temperature of 10ºC. The volume of the tank is 350 L. Howmany moles of air are in the tank?

3. A helium-filled balloon has a volume of 208 L and it contains 9.95 moles of gas. If the pressure of theballoon is 1.26 atm, determine the temperature in Celsius degrees.

4. A tank of oxygen has a volume of 1650 L. The temperature of the gas inside is 35ºC. If there are 9750 molesof oxygen in the tank what is the pressure in PSI?

5. A canister of acetylene has a volume of 42 L. The temperature of the acetylene is 305 K and the pressure is780 torr. Determine the amount (moles) of gas in the canister.

6. Calculate the volume of a CO2 cartridge that has a pressure of 850 PSI at a temperature of 21ºC. Thecartridge contains 0.273 mol of CO2.

7. A tank contains 2500 L of argon gas. The pressure is13790 kPa and the temperature is 25ºC. How manymoles of argon are in the tank?

Name ________________ Ideal Gas Law Chem Worksheet 14-4

Unknown Equation Known Variables

pressure V

nRTP = amount, temp., volume

volume P

nRTV = amount, temp., pressure

temperature nRPV

T = pressure, volume, amount

amount RTPV

n = pressure, volume, temp.

KmolLatm

⋅⋅

example

The pressure exerted by 2.8 moles of argon gas at a temperature of 85ºC is 420 torr. What is the volume of this sample?

- list the variables: P = 420 torr V = ? n = 2.8 mol R = 0.0821 T = 85ºC

- convert the variables: atm 553.0 torr760

atm 11 torr420

=× T = 85ºC + 273 = 358 K

- substitute into the equation: P

nRTV = L 82

atm 553.0

K) 358)(08206.0)(mol 8.2(KmolLatm

== ⋅⋅

V

USEFUL EQUATIONS

PV = nRT 1.00 atm = 101300 Pa R = 0.0821 1.00 atm = 101.3 kPa TK = TC + 273 1.00 atm = 760 mmHg 1 cm3 = 1 mL 1.00 atm = 760 torr 1 L = 1000 mL 1.00 atm = 14.7 psi

KmolLatm

⋅⋅

© John Erickson, 2005 WS14-6PartialPressures

USEFUL EQUATIONS

1.00 atm = 760 torr PV = nRT R = 0.0821

Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the individual pressures. In other words, mixtures of gases behave the same as a single gas would. In a mixture of gases each individual gas contributes its own pressure, known as the partial pressure, to the total pressure. The pressure of each gas is determined by the number of moles of gas, its volume and temperature. The sum of each gas pressure equals to the total pressure. The equation for this law is

Ptotal = P1 + P2 + P3 + . . .Pn


1. A canister contains 425 kPa of carbon dioxide, 750 kPa of nitrogen, and 525 kPa of oxygen. Whatis the total pressure of the container?

2. A tank containing ammonia and argon has a total pressure equal to 1.8 atm. The pressure of theammonia is 1.2 atm. What is the pressure of the argon gas?

3. A sample of gas contains 3 moles of argon and 5 moles of krypton. If the argon exerts a pressure of210 torr, what is the pressure of the krypton? What is the total pressure?

A 32.6 mL sample of hydrogen gas is collected over water using a technique known as water displacement. The temperature of the gas is 295 K. The total pressure of the mixture (hydrogen and water vapor) is 785.2 torr.

4. At 295 K the vapor pressure of water is 19.8 torr. Find the pressure of the hydrogen gas alone.

5. Using the volume and temperature given above, calculate the number of moles of hydrogenpresent.

6. Using the volume and temperature above, determine the number of moles of water vapor present.

The tank shown below contains helium, nitrogen, and oxygen gas and it has a volume of 425 L. Each marker in the container represents a mole of gas in the mixture. The container is at room temperature (20ºC).

7. Count the number of moles of helium in the sample. Repeat fornitrogen and oxygen.

8. Determine the fraction of each of the three gases.

9. Calculate the pressure of each gas. Use the volume and temperaturelisted above for each calculation.

10. Find the total pressure inside the container by adding the partialpressures for each gas.

Name ________________ Partial Pressures of Gas Chem Worksheet 14-6

KmolLatm

⋅⋅

heliumnitrogenoxygen

Chemistry WS14-5GasStoich

Use your knowledge of Stoichiometry and the Ideal Gas Law to solve the following problems. The chemical equations given are all balanced.

1. What volume of O2 is producedwhen 28.5 g of hydrogen peroxide(H2O2) decomposes to form waterand oxygen at 150°C and 2.0 atm?

2H2O2 (aq) →→→→ 2H2O (l) + O2 (g)

2. This reaction uses 18.2 g of copper(I) sulfide (Cu2S). What volume ofsulfur dioxide gas would becollected at 237°C and 10.7 atm?

2Cu2S (s) + 3O2 (g) →→→→ 2Cu2O (s) + 2SO2 (g)

3. When 62.7-g nitrogen and excessoxygen react they generate nitrogendioxide. If the NO2 is collected at625 K and 0.724 atm, what volumewill it occupy?

N2 (g) + 2O2 (g) →→→→ 2NO2 (g)

4. What volume of hydrogen gas isevolved from a reaction between0.52 g of Na and water? The gas iscollected at 20.°C and 745 mmHg.

2Na (s) + 2H2O (l) →→→→ 2NaOH (aq) + H2 (g)

5. At what pressure is the nitrogen gassample that is collected when 48.4 gof NaN3 decomposes? Thetemperature of the gas is 25°C andthe volume is 18.4 L.

2NaN3 (s) →→→→ 2Na (s) + 3N2 (g)

6. When 2.4-g zinc is added tohydrochloric acid, 450 mL ofhydrogen gas forms at a temperatureof 32°C. What is the pressure of thegas?

Zn (s) + 2HCl (aq) →→→→ ZnCl2 (aq) + H2 (g)

7. The following reaction forms 6.41 Lof oxygen at a temperature of 18.7°Cand a pressure of 731 torr, what massof KClO3 must have decomposed?

2KClO3 (s) →→→→ 2KCl (s) + 3O2 (g)

8. What mass of CaSO3 must have beenpresent initially to produce 14.5 L ofSO2 gas at a temperature of 12.5°Cand a pressure of 1.10 atm?

CaSO3 (s) →→→→ CaO (s) + SO2 (g)

Name ________________ Gas Stoichiometry Chem Worksheet 14-5

9

Dalton’s Law of Partial Pressures, Ideal Gas Law, Combined Gas Law, & Gas Stoich

1. A metal tank contains three gases: oxygen, helium, and nitrogen. If the partial pressures of

the three gases in the tank are 35 atm of O2, 5 atm of N2, and 25 atm of He, what is the total

pressure inside of the tank?

2. Blast furnaces give off many unpleasant and unhealthy gases. If the total air pressure is 0.99

atm, the partial pressure of carbon dioxide is 0.05 atm, and the partial pressure of hydrogen

sulfide is 0.02 atm, what is the partial pressure of the remaining air?

3. If the air from problem 2 contains 22% oxygen, what is the partial pressure of oxygen near a

blast furnace?

4. If four moles of a gas at a pressure of 5.4 atmospheres have a volume of 120 liters, what is the

temperature?

10

5. If I initially have a gas with a pressure of 84 kPa and a temperature of 350 ⁰C and I heat it an

additional 230 degrees, what will the new pressure be? Assume the volume of the container is

constant.

6. My car has an internal volume of 2600 liters. If the sun heats my car from a temperature of

200 ⁰C to a temperature of 550 ⁰C, what will the pressure inside my car be? Assume the

pressure was initially 760 mm Hg.

7. How many moles of gas are in my car in problem #3?

8. A toy balloon filled with air has an internal pressure of 1.25 atm and a volume of 2.50 L. If I

take the balloon to the bottom of the ocean where the pressure is 95 atmospheres, what will the

new volume of the balloon be? How many moles of gas does the balloon hold? (Assume T = 285

K)

11

9. For the reaction 2 H2(g) + O2(g) 2 H2O(g), how many liters of water can be made from 5 L of

oxygen gas and an excess of hydrogen?

10. How many liters of water can be made from 55 grams of oxygen gas and an excess of

hydrogen at STP?

11. How many liters of water can be made from 55 grams of oxygen gas and an excess of

hydrogen at a pressure of 12.4 atm and a temperature of 850 C?

12. How many liters of water can be made from 34 grams of oxygen gas and 6.0 grams of

hydrogen gas at STP? What is the limiting reactant for this reaction?

CHEMISTRY GAS LAW’S WORKSHEET

Combines Boyle’s, Charles’, and the Temperature-Pressure relationship into one equation. Each of these laws can be derived from this law.

Guy-Lassac's Law

PV

T= k

V1P1T2 = V2P2T1

P1V1

T1

=P2V2

T2

P

T= k

P1T2 = P2T1

P1

T1

=P2

T2

V

T= k

V1T2 = V2T1

V1

T1

=V2

T2

Combined Gas LawBoyle’s Law

PV = k

P1V1 = P2V2

The pressure of a gas is directly proportional to the Kelvin temperature if the volume is kept constant.

The volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.

Charles’ Law

For a given mass of gas at constant temperature, the volume of a gas varies inversely with pressure

The Ideal Gas Law relates the pressure, temperature, volume, and mass of a gas through the gas constant “R”.

Rate A

RateB

=molar massB

molar massA

PV = nRTPtotal = P1 + P2 + P3 + ...Pn

The rate of effusion/diffusion of two gases (A and B) are inversely proportional to the square roots of their formula masses. [It can be a ratio of molecular speeds, effusion /diffusion times, distance traveled by molecules, or amount of gas effused]

At constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the pressures exerted by each gas,

Graham’s LawIdeal Gas LawDalton’s Law

Subscript (1) = old condition or initial conditionSubscript (2) = new condition or final conditionTemperature must be in Kelvinsn = number of moles = grams/Molar massR = 8.31 L-kPa/ mol-K = 0.0821 L-atm/mol-K =62.4 L-Torr/mol-KYou must have a common set of units in the problem

0°C = 273 K1.00 atm = 760.0 mm Hg = 76 cm Hg =101.325 kPa = 101, 325 Pa = 29.9 in Hg

K = °C + 273

Fo = 1.8Co + 32

Co =Fo −32

1.81 cm3 (cubic centimeter) = 1 mL (milliliter)1 dm3 (cubic decimeter) = 1 L (liter) = 1000 mL

atm = atmospheremm Hg = millimeters of mercurytorr = another name for mm HgPa = Pascal kPa = kilopascalK = Kelvin°C = degrees Celsius

Gas Law’s Equation Symbols

Standard Conditions

Conversions

Abbreviations


5. A sample of gas has a volume of 215 cm3 at 23.5 °Cand 84.6 kPa. What volume will the gas occupy at STP?

4. 8.98 dm3 of hydrogen gasis collected at 38.8 °C. Find the volume the gas will occupyat -39.9 °C if the pressure remains constant.

3. A sample of nitrogen gas has a volume of 478 cm3 and a pressure of 104.1 kPa. Whatvolume would the gas occupy at 88.2 kPa if the temperature remains constant?

2. Convert the following temperatures to C.

a) 67 Kb) 1671 K

1. Convert the following temperatures to K.

a) 104 Cb) -3 C


10. A sample of gas occupies avolume of 450.0 mL at 740 mm Hg and 16°C. Determine the volume of this sample at 760 mm Hg and 37°C.

9. A sample of gas is transferred from a 75 mL vessel to a 500.0 mL vessel. Ifthe initial pressure of the gas is145 atm and if the temperature is held constant, what is the pressure of the gas sample in the 500.0 mL vessel?

8. 495 cm3 of oxygen gas and 877 cm3 of nitrogen gas, both at 25.0 °C and 114.7 kPa, are injected into an evacuated 536 cm3 flask. Find the total pressure in the flask, assuming the temperature remains constant.

7. Find the relative rate of diffusion for the gases chlorine, Cl2 and ethane, C2H6.

6. At a certain temperature, molecules of methane gas, CH4 have an average velocity of 0.098 m/s. What is the average velocity of carbon dioxide molecules at this same temperature?


15. At what temperature Celsius will 19.4 g of molecular oxygen, O2, exert a pressure of 1820 mm Hg in a 5.12 L cylinder?

14. A bubble of helium gas hasa volume of 0.650 mL near the bottom of a large aquarium where the pressure is 1.54 atm and the temperature is 12°C. Determine the bubble’s volumeupon rising near the top where the pressure is 1.01 atm and 16°C.

13. Air in a closed cylinder is heated from 25°C to 36°C. If the initial pressure is 3.80 atm, what is the final pressure?

12. Convert a pressure of 0.0248 mm Hg to the equivalent pressure in pascals (Pa).

11. One mole of H2S gas escapes from a container by effusion in 77 seconds. How long would it take one mole of NH3 gas to escape from the same container?


20. Determine the molar mass of a gas that has a density of 2.18 g/L at 66°C and 720 mm Hg.

(Hint: the number of moles of a substance is its mass/molecular mass and density is mass/volume.)

19. What is the pressure in atmexerted by 2.48 moles of a gas in a 250.0 mL container at 58°C?

18. To what temperature must 32.0 ft3 of a gas at 2°C be heated for it to occupy 1.00 x 102 ft3 at the same pressure?

17. What is the pressure in mm of Hg , of a gas mixture that contains 1g of H2, and 8.0 g of Ar in a 3.0 L container at 27°C.

16. A sample of nitrogen gas, N2, is collected in a100 mL container at a pressure of 688 mm Hg and a temperature of 565 °C. How many grams of nitrogen gas are present in this sample?

name date class states of matter 13 - mr. acosta's...

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