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418 Chapter 14
Gases
CHAPTER 14
What Yoursquoll LearnYou will use gas laws to cal-culate how pressure tem-perature volume andnumber of moles of a gaswill change when one ormore of these variables isaltered
You will compare propertiesof real and ideal gases
You will apply the gas lawsand Avogadrorsquos principle tochemical equations
Why Itrsquos ImportantFrom barbecuing on a gas grillto taking a ride in a hot-airballoon many activitiesinvolve gases It is importantto be able to predict whateffect changes in pressuretemperature volume oramount will have on theproperties and behavior ofa gas
Firefighters breathe air that hasbeen compressed into tanks thatthey can wear on their backs
Visit the Glencoe Chemistry Website at chemistrymccom to findlinks about gases
null
11493906
null
52663124
141 The Gas Laws 419
DISCOVERY LAB
Objectivesbull State Boylersquos law Charlesrsquos
law and Gay-Lussacrsquos law
bull Apply the three gas laws toproblems involving the pres-sure temperature and vol-ume of a gas
VocabularyBoylersquos lawCharlesrsquos lawGay-Lussacrsquos law
Section 141 The Gas Laws
The manufacturer of the air tank in the photo on the opposite page had tounderstand the nature of the gases the tank contains Understanding gases didnot happen accidentally The work of many scientists over many years hascontributed to our present knowledge of the nature of gases The work of threescientists in particular was valuable enough that laws describing gas behav-ior were named in their honor In this section yoursquoll study three importantgas laws Boylersquos law Charlesrsquos law and Gay-Lussacrsquos law Each of theselaws relates two of the variables that determine the behavior of gasesmdashpres-sure temperature volume and amount of gas present
Kinetic TheoryYou canrsquot understand gases without understanding the movement of gas par-ticles Remember from your study of the kinetic-molecular theory in Chapter13 that gas particles behave differently than those of liquids and solids Thekinetic theory provides a model that is used to explain the properties of solidsliquids and gases in terms of particles that are always in motion and the forcesthat exist between them The kinetic theory assumes the following conceptsabout gases are truebull Gas particles do not attract or repel each other Gases are free to move
within their containers without interference from other particlesbull Gas particles are much smaller than the distances between them You
saw in the DISCOVERY LAB that gas has volume However the kinetictheory assumes that gas particles themselves have virtually no volume
More Than Just Hot Air
How does a temperature change affect the air in a balloon
Safety Precautions
Always wear goggles to protect eyes from broken balloons
Procedure
1 Inflate a round balloon and tie it closed
2 Fill the bucket about half full of cold water and add ice
3 Use a string to measure the circumference of the balloon
4 Stir the water in the bucket to equalize the temperature Submergethe balloon in the ice water for 15 minutes
5 Remove the balloon from the water Measure the circumference
Analysis
What happens to the size of the balloon when its temperature is low-ered What might you expect to happen to its size if the temperatureis raised
Materials
5-gal bucketround balloonicestring
null
100413445
420 Chapter 14 Gases
Almost all the volume of a gas is empty space Gases can be com-pressed by moving gas particles closer together because of this lowdensity of particles
bull Gas particles are in constant random motion Gas particles spread out andmix with each other because of this motion The particles move in straightlines until they collide with each other or with the walls of their container
bull No kinetic energy is lost when gas particles collide with each other or withthe walls of their container Such collisions are completely elastic As longas the temperature stays the same the total kinetic energy of the systemremains constant
bull All gases have the same average kinetic energy at a given temperature Astemperature increases the total energy of the gas system increases As tem-perature decreases the total energy of the gas system decreases
The nature of gases Actual gases donrsquot obey all the assumptions made bythe kinetic theory But for many gases their behavior approximates the behav-ior assumed by the kinetic theory You will learn more about real gases andhow they vary from these assumptions in Section 143
Notice how all the assumptions of the kinetic theory are based on the fourfactors previously mentionedmdashthe number of gas particles present and thetemperature the pressure and the volume of the gas sample These four vari-ables all work together to determine the behavior of gases When one vari-able changes it affects the other three Look at the following example of howa change in one variable affects at least one other variable
What happens to the gas in a plastic balloon if you squeeze it decreasingits volume Because the balloon is closed the amount of gas is constantAssume the temperature is held constant Decreasing the volume pushes thegas particles closer together Recall from the kinetic-molecular theory that asgas particles are pushed closer together the number of collisions between par-ticles themselves and between the particles and the walls of their containerincreases As the number of collisions per unit time increases so does theobserved pressure Therefore as the volume of a gas decreases its pressureincreases Similarly if the balloon is no longer squeezed the volume increasesand the pressure decreases You can see another example of this principle inFigure 14-1 The interdependence of the variables of volume pressure tem-perature and amount of gas is the basis for the following gas laws
Figure 14-1
The kinetic theory relates pres-sure and the number of colli-sions per unit time for a gas
When the bicycle pump ispulled out as far as it will gothe pressure of the air insidethe pump equals that of theatmosphere
If the piston is pushed downhalf the length of the pump theair particles are squeezed into aspace half the original sizePressure doubles because thefrequency of collisions betweenthe gas particles and the innerwall of the pump has doubled
b
a
a b
LAB
See page 958 in Appendix E forUnder Pressure
null
15464436
141 The Gas Laws 421
MeteorologistWould you like to be able toplan your days better becauseyou know what the weatherwill be Then consider a careeras a meteorologist
Most weather is caused by theinteraction of energy and airMeteorologists study howthese interactions affect andare affected by changes intemperature and pressure ofthe air For example winds andfronts are direct results of pres-sure changes caused by unevenheating of Earthrsquos atmosphereby the sun
Condition 1
k P1V1k (1 atm)(10 L)k 10 atmbullL
Condition 2
k P2V2k (2 atm)(5 L)k 10 atmbullL
Condition 3
k P3V3k (4 atm)(25 L)k 10 atmbullL
1 atm
10 L
2 atm
4 atm5 L25 L
0
10
8
6
4
2
005
Vo
lum
e (L
)
10 15 20 25 30 35 40
Pressure (atm)
PressurendashVolume Changes
1 (10 atm 10 L)
2 (20 atm 5 L)
(40 atm 25 L)
3
Boylersquos LawRobert Boyle (1627ndash1691) an Irish chemist did experiments like the oneshown in Figure 14-2 to study the relationship between the pressure and thevolume of a gas By taking careful quantitative measurements he showed thatif the temperature is constant doubling the pressure of a fixed amount of gasdecreases its volume by one-half On the other hand reducing the pressureby half results in a doubling of the volume A relationship in which one vari-able increases as the other variable decreases is referred to as an inverselyproportional relationship For help with understanding inverse relationshipssee the Math Handbook page 905
Boylersquos law states that the volume of a given amount of gas held at a con-stant temperature varies inversely with the pressure Look at the graph inFigure 14-2 in which pressure versus volume is plotted for a gas The plotof an inversely proportional relationship results in a downward curve If youchoose any two points along the curve and multiply the pressure times thevolume at each point how do your two answers compare Note that the prod-uct of the pressure and the volume for each of points 1 2 and 3 is 10 atmLFrom the graph what would the volume be if the pressure is 25 atm Whatwould the pressure be if the volume is 2 L
The products of pressure times volume for any two sets of conditions areequal so Boylersquos law can be expressed mathematically as follows
P1 and V1 represent a set of initial conditions for a gas and P2 and V2 rep-resent a set of new conditions If you know any three of these four valuesfor a gas at constant temperature you can solve for the fourth by rearrang-ing the equation For example if P1 V1 and P2 are known dividing bothsides of the equation by P2 will isolate the unknown variable V2
Use the equation for Boylersquos law to calculate the volume that correspondsto a pressure of 25 atm assuming that the amount of gas and temperatureare constant Then find what pressure corresponds to a volume of 20 L Use20 atm for P1 and 5 L for V1 How do these answers compare to those youfound using the graph in Figure 14-2
P1V1 P2V2
Figure 14-2
The gas particles in this cylindertake up a given volume at agiven pressure As pressureincreases volume decreases Thegraph shows that pressure andvolume have an inverse relation-ship which means that as pres-sure increases volumedecreases This relationship isillustrated by a downward curvein the line from condition 1 tocondition 2 to condition 3
null
15265886
EXAMPLE PROBLEM 14-1
Boylersquos LawA sample of helium gas in a balloon is compressed from 40 L to 25 L at aconstant temperature If the pressure of the gas in the 40-L volume is210 kPa what will the pressure be at 25 L
1 Analyze the Problem You are given the initial and final volumes and the initial pressure ofa sample of helium Boylersquos law states that as volume decreases pres-sure increases if temperature remains constant Because the volumein this problem is decreasing the pressure will increase So the initialpressure should be multiplied by a volume ratio greater than one
Known Unknown
V1 40 L P2 kPaV2 25 LP1 210 kPa
2 Solve for the UnknownDivide both sides of the equation for Boylersquos law by V2 to solve for P2
P1V1 P2V2
P2 P1VV
1
2
Substitute the known values into the rearranged equation
P2 210 kPa 4205
LL
Multiply and divide numbers and units to solve for P2
P2 210 kPa 4205
LL
340 kPa
3 Evaluate the Answer When the volume is decreased by almost half the pressure isexpected to almost double The calculated value of 340 kPa is reason-able The unit in the answer is kPa a pressure unit
PRACTICE PROBLEMSAssume that the temperature and the amount of gas present are con-stant in the following problems
1 The volume of a gas at 990 kPa is 3000 mL If the pressure is increasedto 188 kPa what will be the new volume
2 The pressure of a sample of helium in a 100-L container is 0988 atmWhat is the new pressure if the sample is placed in a 200-L container
3 Air trapped in a cylinder fitted with a piston occupies 1457 mL at 108 atm pressure What is the new volume of air when the pressure isincreased to 143 atm by applying force to the piston
4 If it takes 00500 L of oxygen gas kept in a cylinder under pressure tofill an evacuated 400-L reaction vessel in which the pressure is 0980atm what was the initial pressure of the gas in the cylinder
5 A sample of neon gas occupies 0220 L at 0860 atm What will be itsvolume at 292 kPa pressure
422 Chapter 14 Gases
MathHandbookMath
Handbook
Review using inverse relationshipsin the Math Handbook on page905 of your textbook
For more practice withBoylersquos law problemsgo to SupplementalSupplementalPractice ProblemsPractice Problems in
Appendix A
Practice
141 The Gas Laws 423
Charlesrsquos LawHave you ever noticed that on a cold day a tire on a car might look as if itrsquoslow on air However after driving the car for awhile the tire warms up andlooks less flat What made the difference in the tire When canning vegeta-bles at home why are they often packed hot in the jars and then sealed Thesequestions can be answered by applying another of the gas laws Charlesrsquos lawAnother example of how gases are affected by temperature is shown in theproblem-solving LAB If kelvin temperature is doubled so is the volume
How are gas temperature and volume related The French physicistJacques Charles (1746ndash1823) studied the relationship between volume andtemperature In his experiments he observed that as temperature increasesso does the volume of a gas sample when the pressure is held constant Thisproperty can be explained by the kinetic-molecular theory at a higher tem-perature gas particles move faster striking each other and the walls of theircontainer more frequently and with greater force For the pressure to stay con-stant volume must increase so that the particles have farther to travel beforestriking the walls Having to travel farther decreases the frequency with whichthe particles strike the walls of the container
Look at Figure 14-3 which includes a graph of volume versus temper-ature for a gas sample kept at a constant pressure Note that the resultingplot is a straight line Note also that you can predict the temperature atwhich the volume will reach a value of zero liters by extrapolating the lineat temperatures below which values were actually measured The temper-ature that corresponds to zero volume is 27315degC or 0 on the kelvin (K)temperature scale This temperature is referred to as absolute zero and itis the lowest possible theoretical temperature Theoretically at absolutezero the kinetic energy of particles is zero so all motion of gas particlesat that point ceases
Examine the relationship between temperature and volume shown by thecylinders in Figure 14-3 In the graph note that 0degC does not correspond tozero volume Although the relationship is linear it is not direct For exam-ple you can see from the graph that increasing the temperature from 25degC to50degC does not double the volume of the gas If the kelvin temperature is plot-ted instead a direct proportion is the result See Figure 14-4 on the next page
HistoryCONNECTION
Jacques Charlesrsquos interest in thebehavior of gases was sparked
by his involvement in ballooningHe built the first balloon thatwas filled with hydrogen insteadof hot air Charlesrsquos investigationsattracted the attention of KingLouis XVI who allowed Charlesto establish a laboratory in theLouvre which is a museum inParis
Figure 14-3
The gas particles in this cylindertake up a given volume at agiven temperature When thecylinder is heated the kineticenergy of the particles increasesThe volume of the gas increasespushing the piston outwardThus the distance that the pistonmoves is a measure of theincrease in volume of the gas asit is heated Note that the graphof volume versus temperatureextrapolates to 27315degC or 0 K
1 atm
1 atm
300 250 200 150 50 0 50100
Vo
lum
e (m
L)
800
600
400
200
0
Temperature (˚C)
Celsius Temperature vs Volume
(75˚C 703 mL)
(0˚C 551 mL)
(75˚ C 400 mL)
null
1565776
Charlesrsquos law states that the volume of a given mass of gasis directly proportional to its kelvin temperature at constantpressure For help with understanding direct relationships seethe Math Handbook page 905 So for any two sets of condi-tions Charlesrsquos law can be expressed as
Here V1 and T1 represent any initial pair of conditionswhile V2 and T2 are any new set of conditions As with Boylersquoslaw if you know any three of the four values you can cal-culate the fourth using the equation
The temperature must be expressed in kelvin units when using the equa-tion for Charlesrsquos law The kelvin scale starts at absolute zero which corre-sponds to ndash27315degC and is 0 K Because a Celsius degree and a kelvin unitare the same size it is easy to convert a temperature in Celsius to kelvin unitsRound 27315 to 273 and add it to the Celsius temperature
TK 273 TC
VT1
1
VT2
2
424 Chapter 14 Gases
problem-solving LAB
How is turbocharging in a carengine maximized Interpreting Scientific Illustrations Aftergasoline and air are burned in the combustionchamber of an automobile the resulting hotgases are exhausted out the tailpipe The horse-power of an automobile engine can be signifi-cantly improved if the energy of these exhaustgases is used to operate a compressor that forcesadditional air into the combustion chamberOutside air is then blown over this compressedair to cool it before it enters the engineIncreasing the power of an engine in this manneris known as turbocharging
AnalysisExamine the illustration of an engine fitted with
a turbocharging system The paths of the exhaustgas entering combustion air and the cooling airare shown
Thinking Critically1 What property of the exhaust gas is being
used to turn the turbine that runs the com-pressor Explain
2 If more power is to be gained from this designwhat must also accompany the extra supply ofoxygen to the combustion chamber
3 What property does the compressor alter sothat more air can be injected into the combus-tion chamber Explain
4 Why does the air in the compressor get hotand why does cooling help to improve thepower of the engine
Charge-air cooler
Turbocharger
Exhaustgas
Turbinewheel
Compressorwheel
Airinlet
Engine cylinder
Oil outlet
Oil inlet
Figure 14-4
This graph illustrates the directlyproportional relationshipbetween the volume and thekelvin temperature of a gas heldat constant pressure When thekelvin temperature doubles thevolume doubles
500 100 150 250 300 350200
Vo
lum
e (m
L)
800
600
400
200
0
Temperature (K)
Kelvin Temperature vs Volume
(348 K 703 mL)
(273 K 551 mL)
(198 K 400 mL)
null
6875468
141 The Gas Laws 425
EXAMPLE PROBLEM 14-2
Charlesrsquos LawA gas sample at 400degC occupies a volume of 232 L If the temperature israised to 750degC what will the volume be assuming the pressure remainsconstant
1 Analyze the ProblemYou are given the initial temperature and volume of a sample of gasCharlesrsquos law states that as the temperature increases so does the vol-ume assuming the pressure is constant Because the temperature inthis problem is increasing the volume will increase So the initial vol-ume should be multiplied by a volume ratio greater than one
Known Unknown
T1 400ordmC V2 LV1 232 LT2 750ordmC
2 Solve for the Unknown Add 273 to the Celsius temperature to obtain the kelvin temperature
TK 273 TC
Substitute the known Celsius temperatures for T1 and T2 to convertthem to kelvin units
T1 273 400degC 313 K
T2 273 750degC 348 K
Multiply both sides of the equation for Charlesrsquos law by T2 to solve for V2
VT1
1
VT2
2
V2 V1TT
2
1
Substitute the known values into the rearranged equation
V2 232 L 334183
KK
Multiply and divide numbers and units to solve for V2
V2 232 L 334183
KK
258 L
3 Evaluate the Answer The increase in kelvin units is relatively small Therefore you expectthe volume to show a small increase which agrees with the answerThe unit of the answer is liters a volume unit
PRACTICE PROBLEMSAssume that the pressure and the amount of gas present remain con-stant in the following problems6 A gas at 89ordmC occupies a volume of 067 L At what Celsius tempera-
ture will the volume increase to 112 L
7 The Celsius temperature of a 300-L sample of gas is lowered from800ordmC to 300ordmC What will be the resulting volume of this gas
8 What is the volume of the air in a balloon that occupies 0620 L at25ordmC if the temperature is lowered to 000ordmC
MathHandbookMath
Handbook
Review using direct relationshipsin the Math Handbook on page905 of this textbook
For more practice withCharlesrsquos law problemsgo to SupplementalSupplementalPractice ProblemsPractice Problems in
Appendix A
Practice
Figure 14-5
Compare the relationshipbetween pressure and kelvintemperature as shown in thisgraph and the relationshipbetween volume and kelvintemperature as shown inFigure 14-4 Notice that bothshow direct relationships
EXAMPLE PROBLEM 14-3
Gay-Lussacrsquos LawThe pressure of a gas in a tank is 320 atm at 220degC If the temperaturerises to 600degC what will be the gas pressure in the tank
1 Analyze the ProblemYou are given the initial pressure and the initial and final tempera-tures of a gas sample Gay-Lussacrsquos law states that if the temperatureof a gas increases so does its pressure Because the temperature inthis problem is increasing the pressure will increase So the initialpressure should be multiplied by a volume ratio greater than one
Known Unknown
P1 320 atm P2 atmT1 220ordmCT2 600ordmC
2 Solve for the Unknown Add 273 to the Celsius temperature to obtain the kelvin temperature
TK 273 TC
Substitute the known Celsius temperatures for T1 and T2 to convertthem to kelvin units
T1 273 220degC 295 K
T2 273 600degC 333 K
Multiply both sides of the equation for Gay-Lussacrsquos law by T2 to solvefor P2
PT
1
1
PT
2
2
P2 P1TT
2
1
426 Chapter 14 Gases
Gay-Lussacrsquos LawBoylersquos law relates pressure and volume of a gas and Charlesrsquos law statesthe relationship between a gasrsquos temperature and volume What is the rela-tionship between pressure and temperature Pressure is a result of collisionsbetween gas particles and the walls of their container An increase in tem-perature increases collision frequency and energy so raising the temperatureshould also raise the pressure if the volume is not changed
How are temperature and pressure of a gas related Joseph Gay-Lussac explored the relationship between temperature and pressure of a con-tained gas at a fixed volume He found that a direct proportion exists betweenthe kelvin temperature and the pressure such as that illustrated in Figure 14-5Gay-Lussacrsquos law states that the pressure of a given mass of gas varies directlywith the kelvin temperature when the volume remains constant It can beexpressed mathematically
As with Boylersquos and Charlesrsquos laws if you know any three of the four vari-ables you can calculate the fourth using this equation Remember that tem-perature must be in kelvin units whenever it is used in a gas law equation
PT1
1
PT2
2
0 100 200 300 500 600400
Pres
sure
(at
m)
4035302520151005
0
Temperature (K)
(450 K 30 atm)
(300 K 20 atm)
(150 K 10 atm)
This cooker is sealed so that thevolume is constant Pressureincreases in the cooker as temper-ature increases
Kelvin Temperature vsPressure
null
7277733
141 The Gas Laws 427
You have seen how the variables of temperature pressure and volumeaffect a gas sample The gas laws covered in this section each relate two ofthese three variables if the other variable remains constant What happenswhen all three of these variables change Yoursquoll investigate this situation inthe next section
PRACTICE PROBLEMSAssume that the volume and the amount of gas are constant in the fol-lowing problems9 A gas in a sealed container has a pressure of 125 kPa at a tempera-
ture of 300ordmC If the pressure in the container is increased to 201 kPawhat is the new temperature
10 The pressure in an automobile tire is 188 atm at 250degC What will bethe pressure if the temperature warms up to 370degC
11 Helium gas in a 200-L cylinder is under 112 atm pressure At 365ordmCthat same gas sample has a pressure of 256 atm What was the initialtemperature of the gas in the cylinder
12 If a gas sample has a pressure of 307 kPa at 000ordmC by how much doesthe temperature have to decrease to lower the pressure to 284 kPa
13 A rigid plastic container holds 100 L methane gas at 660 torr pres-sure when the temperature is 220ordmC How much more pressure willthe gas exert if the temperature is raised to 446ordmC
Substitute the known values into the rearranged equation
P2 320 atm 323935
KK
Multiply and divide numbers and units to solve for P2
P2 320 atm 323935
KK
361 atm
3 Evaluate the AnswerGay-Lussacrsquos law states that pressure and temperature are directly pro-portional Kelvin temperature shows a small increase so you expectthe pressure to show a small increase which agrees with the answercalculated The unit is atm a pressure unit
Section 141 Assessment
14 State Boylersquos Charlesrsquos and Gay-Lussacrsquos lawsusing sentences then equations
15 A weather balloon of known initial volume isreleased The air pressures at its initial and finalaltitudes are known Why canrsquot you find its newvolume by using these known values and Boylersquoslaw
16 Which of the three variables that apply to equalamounts of gases are directly proportional Whichare inversely proportional
17 Thinking Critically Explain why gases such asthe oxygen found in tanks used at hospitals arecompressed Why must care be taken to preventcompressed gases from reaching a hightemperature
18 Concept Mapping Draw a concept map thatshows the relationship among pressure volumeand temperature variables for gases and BoylersquosCharlesrsquos and Gay-Lussacrsquos laws
For more practice withGay-Lussacrsquos lawproblems go toSupplemental Practice
Problems in Appendix A
Practice
chemistrymccomself_check_quiz
null
21629362
428 Chapter 14 Gases
Section 142
The Combined Gas Law andAvogadrorsquos Principle
Objectivesbull State the relationship
among temperature vol-ume and pressure as thecombined gas law
bull Apply the combined gas lawto problems involving thepressure temperature andvolume of a gas
bull Relate numbers of particlesand volumes by usingAvogadrorsquos principle
Vocabulary combined gas lawAvogadrorsquos principle molar volume
In the previous section you applied the three gas laws covered so far to prob-lems in which either pressure volume or temperature of a gas sample washeld constant as the other two changed As illustrated in Figure 14-6 in anumber of applications involving gases all three variables change If all threevariables change can you calculate what their new values will be In this sec-tion you will see that Boylersquos Charlesrsquos and Gay-Lussacrsquos laws can be com-bined into a single equation that can be used for just that purpose
The Combined Gas LawBoylersquos Charlesrsquos and Gay-Lussacrsquos laws can be combined into a single lawThis combined gas law states the relationship among pressure volume andtemperature of a fixed amount of gas All three variables have the same rela-tionship to each other as they have in the other gas laws Pressure is inverselyproportional to volume and directly proportional to temperature and volumeis directly proportional to temperature The equation for the combined gas lawcan be expressed as
As with the other gas laws this equation allows you to use known valuesfor the variables under one set of conditions to find a value for a missing vari-
able under another set of conditions Whenever five of the sixvalues from the two sets of conditions are known the sixthcan be calculated using this expression for the combined gaslaw
This combined law lets you work out problems involvingmore variables that change and it also provides a way for youto remember the other three laws without memorizing eachequation If you can write out the combined gas law equationequations for the other laws can be derived from it by remem-bering which variable is held constant in each case
For example if temperature remains constant as pressureand volume vary then T1 T2 After simplifying the com-bined gas law under these conditions you are left with
P1V1 P2V2
You should recognize this equation as the equation for Boylersquoslaw See whether you can derive Charlesrsquos and Gay-Lussacrsquoslaws from the combined gas law
P
T1V
1
1 =
PT2V
2
2
Figure 14-6
Constructing an apparatus that uses gases must take intoaccount the changes in gas variables such as pressure vol-ume and temperature that can take place As a hot-air bal-loonist ascends in the sky pressure and temperature bothdecrease and the volume of the gas in the balloon isaffected by those changes
null
14199986
null
46341347
142 The Combined Gas Law and Avogadrorsquos Principle 429
EXAMPLE PROBLEM 14-4
The Combined Gas LawA gas at 110 kPa and 300degC fills a flexible container with an initial vol-ume of 200 L If the temperature is raised to 800degC and the pressureincreased to 440 kPa what is the new volume
1 Analyze the ProblemYou are given the initial pressure temperature and volume of a gassample as well as the final pressure and temperature The volume ofa gas is directly proportional to kelvin temperature so volumeincreases as temperature increases Therefore the volume should bemultiplied by a temperature factor greater than one Volume isinversely proportional to pressure so as pressure increases volumedecreases Therefore the volume should be multiplied by a pressurefactor that is less than one
Known Unknown
P1 110 kPa V2 LT1 300ordmCV1 200 LT2 800ordmCP2 440 kPa
2 Solve for the Unknown Add 273 to the Celsius temperature to obtain the kelvin temperature
TK 273 TC
Substitute the known Celsius temperatures for T1 and T2 to convertthem to kelvin units
T1 273 300degC 303 K
T2 273 800degC 353 K
Multiply both sides of the equation for the combined gas law by T2and divide it by P2 to solve for V2
PT1V
1
1
PT2V
2
2
V2 V1PP
1
2
TT
2
1
Substitute the known values into the rearranged equation
V2 200 L 141400
kkPPaa
335033
KK
Multiply and divide numbers and units to solve for V2
V2 200 L 141400
kkPPaa
335033
KK
= 058 L
3 Evaluate the Answer Increasing the temperature causes the volume to increase butincreasing the pressure causes the volume to decrease Because thepressure change is much greater than the temperature change thevolume undergoes a net decrease The calculated answer agrees withthis The unit is L a volume unit
MathHandbookMath
Handbook
Review rearranging algebraicequations in the Math Handbookon page 897 of this textbook
PRACTICE PROBLEMSAssume that the amount of gas is constant in the following problems19 A helium-filled balloon at sea level has a volume of 21 L at 0998 atm
and 36degC If it is released and rises to an elevation at which the pres-sure is 0900 atm and the temperature is 28degC what will be the newvolume of the balloon
20 At 000ordmC and 100 atm pressure a sample of gas occupies 300 mLIf the temperature is increased to 300ordmC and the entire gas sample istransferred to a 200-mL container what will be the gas pressureinside the container
21 A sample of air in a syringe exerts a pressure of 102 atm at a temper-ature of 220ordmC The syringe is placed in a boiling water bath at1000ordmC The pressure of the air is increased to 123 atm by pushingthe plunger in which reduces the volume to 0224 mL What was theoriginal volume of the air
22 An unopened cold 200-L bottle of soda contains 460 mL of gas con-fined at a pressure of 130 atm at a temperature of 50ordmC If the bot-tle is dropped into a lake and sinks to a depth at which the pressureis 152 atm and the temperature is 209ordmC what will be the volume ofgas in the bottle
23 A sample of gas of unknown pressure occupies 0766 L at a tempera-ture of 298 K The same sample of gas is then tested under knownconditions and has a pressure of 326 kPa and occupies 0644 L at303 K What was the original pressure of the gas
430 Chapter 14 Gases
Avogadrorsquos PrincipleThe particles making up different gases can vary greatly in size Howeveraccording to the kinetic-molecular theory the particles in a gas sample are usu-ally far enough apart that size has a negligible influence on the volume occu-pied by a fixed number of particles as shown in Figure 14-7 For example1000 relatively large krypton gas particles occupy the same volume as 1000much smaller helium gas particles at the same temperature and pressure It wasAvogadro who first proposed this idea in 1811 Today it is known asAvogadrorsquos principle which states that equal volumes of gases at the sametemperature and pressure contain equal numbers of particles
For more practice withcombined gas lawproblems go toSupplemental PracticeSupplemental Practice
Problems in Appendix A
Practice
Figure 14-7
Compressed gas tanks of equalvolume that are at the samepressure and temperature con-tain equal numbers of gas parti-cles regardless of which gasthey contain Refer to Table C-1in Appendix C for a key to atomcolor conventions
null
4414701
142 The Combined Gas Law and Avogadrorsquos Principle 431
EXAMPLE PROBLEM 14-5
Avogadrorsquos PrinciplemdashUsing MolesCalculate the volume that 0881 mol of gas at standard temperature andpressure (STP) will occupy
1 Analyze the ProblemYou are given the temperature and pressure of a gas sample and theamount of gas the sample contains According to Avogadrorsquos princi-ple 1 mol of gas occupies 224 L at STP The number of moles of gas should be multiplied by the conversion factor 2
12m4
oLl
to find the volume
Known Unknown
n 0881 moles V LT 000degCP 100 atm
2 Solve for the Unknown Because conditions are already at STP multiply the known number ofmoles by the conversion factor that relates liters to moles to solve forthe unknown volume
V 0881 mol 212m4
oLl
197 L
3 Evaluate the Answer Because the amount of gas present is slightly less than one mole youexpect the answer to be slightly less than 224 L The answer agreeswith that prediction The unit in the answer is L a volume unit
Remember from Chapter 11 that the most convenient unit for countingnumbers of atoms or molecules is the mole One mole contains 602 1023
particles The molar volume for a gas is the volume that one mole occupiesat 000degC and 100 atm pressure These conditions of temperature and pres-sure are known as standard temperature and pressure (STP) Avogadroshowed experimentally that one mole of any gas will occupy a volume of224 L at STP The fact that this value is the same for all gases greatly sim-plifies many gas law calculations Because the volume of one mole of a gasat STP is 224 L you can use the following conversion factor to find the num-ber of moles the mass and even the number of particles in a gas sample
Conversion factor 212m4
oLl
Suppose you want to find the number of particles in a sample of gas thathas a volume of 372 L at STP First find the number of moles of gas in thesample
372 L 212m4
oLl
= 0166 mol
A mole of gas contains 602 1023 gas particles Use this definition to convertthe number of moles to the number of particles
0166 mol = 999 1022 particles
The following example problems show you how to use molar volume inother ways
602 1023 particles1 mol
MathHandbookMath
Handbook
Review unit conversion in theMath Handbook on page 901 ofthis textbook
null
9999551
EXAMPLE PROBLEM 14-6
432 Chapter 14 Gases
Avogadrorsquos PrinciplemdashUsing MassCalculate the volume that 20 kg of methane gas (CH4) will occupy at STP
1 Analyze the ProblemYou are given the temperature and pressure of a gas sample and themass of gas the sample contains One mole of a gas occupies 224 L atSTP The number of moles can be calculated by dividing the mass ofthe sample m by its molar mass M
Known Unknown
m 200 kg V LT 000ordmCP 100 atm
2 Solve for the Unknown Use atomic masses and numbers of each type of atom to determinemolecular mass for methane Express that molecular mass in gramsper mole to determine molar mass
M
1201 amu 404 amu 1605 amu 1605 gmol
Multiply the mass of methane by a conversion factor to change itfrom kg to g
200 kg 1010k0gg
200 103 g
Divide the mass in grams of methane by its molar mass to find thenumber of moles
Mm
2160005
g1m03
ogl
125 mol
Because conditions are already at STP multiply the known number ofmoles by the conversion factor of 224 L1 mol to solve for theunknown volume
V 125 mol 212m4
oLl
280 103 L
3 Evaluate the Answer The mass of methane present is much more than 1 mol so you expecta large volume which is in agreement with the answer The units areL a volume unit
4 H atoms 101 amu
H atom1 C atom 1201 amu
C atom
PRACTICE PROBLEMS24 Determine the volume of a container that holds 24 mol of gas at STP
25 What size container do you need to hold 00459 mol N2 gas at STP
26 What volume will 102 mol of carbon monoxide gas occupy at STP
27 How many moles of nitrogen gas will be contained in a 200-L flask atSTP
28 If a balloon will rise off the ground when it contains 00226 mol ofhelium in a volume of 0460 L how many moles of helium areneeded to make the balloon rise when its volume is 0865 L Assumethat temperature and pressure stay constant
For more practice withAvogadrorsquos principleproblems that usemoles go to
Supplemental PracticeProblems in Appendix A
Practice
Avogadrorsquos principle is essentialto manufacturers that use gasesThis factory produces ammonia
142 The Combined Gas Law and Avogadrorsquos Principle 433
PRACTICE PROBLEMS29 How many grams of carbon dioxide gas are in a 10-L balloon at STP
30 What volume in milliliters will 000922 g H2 gas occupy at STP
31 What volume will 0416 g of krypton gas occupy at STP
32 A flexible plastic container contains 0860 g of helium gas in a vol-ume of 192 L If 0205 g of helium is removed without changing thepressure or temperature what will be the new volume
33 Calculate the volume that 45 kg of ethylene gas (C2H4) will occupy atSTP
For more practice withAvogadrorsquos principleproblems that usemass go to
Supplemental PracticeProblems in Appendix A
Practice
Why arenrsquot weather balloonscompletely inflated when theyare released How strong mustthe walls of a scuba tank beLook at the example of the com-bined gas law and Avogadrorsquosprinciple shown in Figure 14-8Using the combined gas law andAvogadrorsquos principle togetherwill help you understand howgases are affected by pressuretemperature and volume
Section 142 Assessment
34 State the combined gas law using a sentence andthen an equation
35 What variable is assumed to be constant whenusing the combined gas law
36 What three laws are used to make the combinedgas law
37 Explain why Avogadrorsquos principle holds true forgases that have large particles and also for gasesthat have small particles
38 Why must conditions of temperature and pressurebe stated to do calculations involving molarvolume
39 Thinking Critically Think about what happenswhen a bottle of carbonated soft drink is shakenbefore being opened Use the gas laws to explainwhether the effect will be greater when the liquidis warm or cold
40 Applying Concepts Imagine that you are goingon an airplane trip in an unpressurized plane Youare bringing aboard an air-filled pillow that youhave inflated fully Predict what will happen whenyou try to use the pillow while the plane is at itscruising altitude
Figure 14-8
The combined gas law andAvogadrorsquos principle have manypractical applications that scien-tists and manufacturers mustconsider
chemistrymccomself_check_quiz
null
25704405
434 Chapter 14 Gases
Section 143 The Ideal Gas Law
Objectivesbull Relate the amount of gas
present to its pressure tem-perature and volume byusing the ideal gas law
bull Compare the properties ofreal and ideal gases
Vocabularyideal gas constant (R)ideal gas law
In the last section you learned that Avogadro noted the importance of beingable to calculate the number of moles of a gas present under a given set ofconditions The laws of Avogadro Boyle Charles and Gay-Lussac can becombined into a single mathematical statement that describes the relationshipamong pressure volume temperature and number of moles of a gas Thisformula is called the ideal gas law because it works best when applied to prob-lems involving gases contained under certain conditions The particles in anideal gas are far enough apart that they exert minimal attractive or repulsiveforces on one another and occupy a negligible volume
The Ideal Gas LawThe number of moles is a fourth variable that can be added to pressure vol-ume and temperature as a way to describe a gas sample Recall that as theother gas laws were presented care was taken to state that the relationshipshold true for a ldquofixed massrdquo or a ldquogiven amountrdquo of a gas sample Changingthe number of gas particles present will affect at least one of the other threevariables
As Figure 14-9 illustrates increasing the number of particles present in asample will raise the pressure if the volume and temperature are kept con-stant If the pressure and temperature are constant and more gas particles areadded the volume will increase
Because pressure volume temperature and the number of moles presentare all interrelated it would be helpful if one equation could describe theirrelationship Remember that the combined gas law relates volume tempera-ture and pressure of a sample of gas
P
T1V
1
1
PT2V
2
2
For a specific sample of gas you can see that this relationship of pressurevolume and temperature is always the same You could say that
PTV k
where k is a constant based on the amount of gas present n Experiments usingknown values of P T V and n show that
k nR
where R represents an experimentally determined constant that is referred toas the ideal gas constant Therefore the ideal gas law
describes the physical behavior of an ideal gas in terms of the pressure vol-ume temperature and number of moles of gas present The ideal gas law isused in the CHEMLAB in this chapter
The ideal gas constant In the ideal gas equation the value of R dependson the units used for pressure Table 14-1 shows the numerical value of R fordifferent units of pressure
PV nRT
Figure 14-9
The volume and temperature ofthis tire stay the same as air isadded However the pressure inthe tire increases as the amountof air present increases
null
16655736
null
64679726
The R value you will probably find most useful is the first one listed inthe table 00821 m
Lo
la
tmK
Use this R in problems in which the unit of volumeis liters the pressure is in atmospheres and the temperature is in kelvins
Real versus ideal gases What does the term ideal gas mean An ideal gasis one whose particles take up no space and have no intermolecular attractiveforces An ideal gas follows the gas laws under all conditions of temperatureand pressure
In the real world no gas is truly ideal All gas particles have some volumehowever small it may be because of the sizes of their atoms and the lengthsof their bonds All gas particles also are subject to intermolecular interactionsDespite that most gases will behave like ideal gases at many temperature andpressure levels Under the right conditions of temperature and pressure cal-culations made using the ideal gas law closely approximate actual experi-mental measurements
When is the ideal gas law not likely to work for a real gas Real gases devi-ate most from ideal gas behavior at extremely high pressures and low tem-peratures As the amount of space between particles and the speed at whichthe particles move decrease the effects of the volume of gas particles andintermolecular attractive forces become increasingly important The gasbehaves as a real gas in Figure 14-10a Lowering the temperature of nitro-gen gas results in less kinetic energy of the gas particles which means theirintermolecular attractive forces are strong enough to bond them more closelytogether When the temperature is low enough this real gas condenses to forma liquid The gas in Figure 14-10b also behaves as a real gas Increasing thepressure on a gas such as propane lowers the volume and forces the gas par-ticles closer together until their volume is no longer negligible compared tothe volume of the tank Real gases such as propane will liquefy if enough pres-sure is applied
143 The Ideal Gas Law 435
Numerical Values of the Gas Constant R
NumericalUnits of R value of R Units of P Units of V Units of T Units of n
mLa
otlmK
00821 atm L K mol
mL
oklPaK
8314 kPa L K mol
L
mm
omlK
Hg 624 mm Hg L K mol
Table 14-1
Figure 14-10
Real gases deviate most fromideal behavior at low tempera-tures and high pressures
Liquid nitrogen is used tostore biological tissue samples atlow temperatures
Increased pressure allows alarger mass of propane to fitinto a smaller volume for easiertransport Propane is sold as LP(liquid propane) for this reasonalthough it is actually burnedfor fuel as a gas
b
a
a b
null
12564642
EXAMPLE PROBLEM 14-7
The Ideal Gas LawmdashUsing MolesCalculate the number of moles of gas contained in a 30-L vessel at300 102 K with a pressure of 150 atm
1 Analyze the ProblemYou are given the volume temperature and pressure of a gas sampleWhen using the ideal gas law to solve for n choose the value of R thatcontains the pressure and temperature units given in the problemKnown Unknown
V 30 L n molT 300 102 KP 150 atm
R 00821 mLa
otlmK
The nature of the particles making up a gas also affects how ideally thegas behaves For example polar gas molecules such as water vapor gener-ally have larger attractive forces between their particles than nonpolar mol-ecules such as chlorine gas The oppositely charged ends of polar moleculesare pulled together through electrostatic forces as shown in Figure 14-11Therefore polar gases do not behave as ideal gases Also the particles of gasescomposed of molecules such as butane (C4H10) occupy more actual volumethan an equal number of gas particles of smaller molecules such as helium(He) Therefore larger gas molecules tend to cause a greater departure fromideal behavior than do smaller gas molecules
Applying the Ideal Gas LawLook again at the combined gas law on page 428 Notice that it cannot beused to find n the number of moles of a gas However the ideal gas law canbe used to solve for the value of any one of the four variables P V T or n ifthe values of the other three are known Rearranging the PV nRT equationallows you to also calculate the molar mass and density of a gas sample ifthe mass of the sample is known
To find the molar mass of a gas sample the mass temperature pressureand volume of the gas must be known Remember from Chapter 12 that thenumber of moles of a gas (n) is equal to the mass (m) divided by the molarmass (M) Therefore the n in the equation can be replaced by mM
PV m
MRT or M
mPRVT
436 Chapter 14 Gases
Figure 14-11
In polar gas molecules such aswater vapor oppositely chargedpoles attract each other throughelectrostatic forces A nonpolar gas such as heliumis uncharged Thus nonpolargases are more likely to behavelike ideal gases than are polargases
MathHandbookMath
Handbook
Review fractions in the MathHandbook on page 907 of this textbook
null
10689148
Recall from Chapter 2 that density (D) is defined as mass (m) per unit vol-ume (V) After rearranging the ideal gas equation to solve for molar mass Dcan be substituted for mV
M mPRVT
D
PRT
This equation can be rearranged to solve for the density of a gas
D MRT
P
Why might you need to know the density of a gas Consider what requirementsare necessary to fight a fire One way to put out a fire is to remove its oxygensource by covering it with another gas that will neither burn nor support com-bustion This gas must have a greater density than oxygen so that it will fall tothe level of the fire You can observe applications of density when you do theminiLAB later in this section and read the Chemistry and Technology feature
143 The Ideal Gas Law 437
2 Solve for the UnknownDivide both sides of the ideal gas law equation by RT to solve for n
PV nRT
n PRVT
Substitute the known values into the rearranged equation
n
Multiply and divide numbers and units to solve for n
n 018 mol
3 Evaluate the Answer One mole of a gas at STP occupies 224 L In this problem the volumeis much smaller than 224 L while the temperature and pressure val-ues are not too different from those at STP The answer agrees withthe prediction that the number of moles present will be significantlyless than one mole The unit of the answer is the mole
(150 atm)(30 L)
00821 mLa
otlmK
(300 102 K)
(150 atm)(30 L)
00821 mLa
otlmK
(300 102 K)
PRACTICE PROBLEMS41 If the pressure exerted by a gas at 25degC in a volume of 0044 L is
381 atm how many moles of gas are present
42 Determine the Celsius temperature of 249 moles of gas contained ina 100-L vessel at a pressure of 143 kPa
43 Calculate the volume that a 0323-mol sample of a gas will occupy at265 K and a pressure of 0900 atm
44 What is the pressure in atmospheres of a 0108-mol sample of heliumgas at a temperature of 200ordmC if its volume is 0505 L
45 Determine the kelvin temperature required for 00470 mol of gas tofill a balloon to 120 L under 0988 atm pressure
For more practice withideal gas law problemsthat use moles go toSupplemental PracticeSupplemental Practice
Problems in Appendix A
Practice
null
61858437
EXAMPLE PROBLEM 14-8
PRACTICE PROBLEMS46 How many grams of gas are present in a sample that has a molar mass
of 700 gmol and occupies a 200-L container at 117 kPa and 351ordmC
47 Calculate the grams of N2 gas present in a 0600-L sample kept at 100 atm pressure and a temperature of 220ordmC
48 What is the density of a gas at STP that has a molar mass of 440 gmol
49 What is the molar mass of a sample of gas that has a density of109 gL at 102 atm pressure and 250ordmC
50 Calculate the density a gas will have at STP if its molar mass is399 gmol
438 Chapter 14 Gases
The Ideal Gas LawmdashUsing Molar MassWhat is the molar mass of a pure gas that has a density of 140 gL at STP
1 Analyze the ProblemYou are given the density temperature and pressure of a sample ofgas Because density is known and mass and volume are not use theform of the ideal gas equation that involves density
Known Unknown
D 140 gL
M m
gol
T 000ordmCP 100 atm
R 00821 mLa
otlmK
2 Solve for the UnknownConvert the standard T to kelvin units
TK 273 TC
TK 273 000degC 273 K
Use the form of the ideal gas law that includes density (D) andsolves for M
M D
PRT
Substitute the known values into the equation
M
Multiply and divide numbers and units to solve for M
M 314 gmol
3 Evaluate the Answer You would expect the molar mass of a gas to fall somewherebetween that of one of the lightest gases under normal conditionssuch as 2 gmol for H2 and that of a relatively heavy gas such as 222 gmol for Rn The answer seems reasonable The unit is gmolwhich is the molar mass unit
140 gL
00821 mLa
otlmK
(273 K)
1 atm
140 gL
00821 mLa
otlmK
(273 K)
1 atm
The density of a gas can be usedto identify it This gas is denserthan air and can be poured fromone container to another
For more practice withideal gas law problemsthat use molar massgo to Supplemental
Practice Problems inAppendix A
Practice
143 The Ideal Gas Law 439
The Density of Carbon DioxideHypothesizing Air is a mixture of mostlynitrogen and oxygen Use observations to forma hypothesis about which has greater densityair or carbon dioxide
Materials masking tape aluminum foil metricruler 1-L beaker candle matches thermometerbarometer or weather radio baking soda(NaHCO3) vinegar (5 CH3COOH)
Procedure1 Record the temperature and the barometric
pressure of the air in the classroom
2 Roll a 23-cm 30-cm piece of aluminum foilinto a cylinder that is 6 cm 30 cm Tape theedges with masking tape
3 Use matches to light a candle CAUTION Runwater over the extinguished match beforethrowing it away Keep all hair and looseclothing away from the flame
4 Place 30 g of baking soda in the bottom of alarge beaker Add 40 mL of vinegar
5 Quickly position the foil cylinder at approxi-mately 45deg up and away from the top of thecandle flame
6 While the reaction in the beaker is activelyproducing CO2 gas carefully pour the gas butnot the liquid out of the beaker and into thetop of the foil tube Record your observations
Analysis1 Based on your observations state a hypothesis
about whether CO2 is heavier or lighter than air
2 Use the combined gas law to calculate molarvolume at room temperature and atmosphericpressure
3 Carbon dioxide gas (CO2) has a molar mass of44 gmol The two major components of airwhich are oxygen and nitrogen have molarmasses of 32 gmol and 28 gmol respectivelyCalculate the room-temperature densities ingL of nitrogen (N2) oxygen (O2) and carbondioxide (CO2) gases
4 Do these calculations confirm your hypothesisExplain
miniLAB
Section 143 Assessment
51 Write the equation for the ideal gas law
52 Use the kinetic-molecular theory to analyze andevaluate the ideal gas lawrsquos applicability to realgases
53 List common units for each variable in the idealgas law
54 Thinking Critically Which of the followinggases would you expect to behave most like anideal gas at room temperature and atmosphericpressure water vapor carbon dioxide helium orhydrogen Explain
55 Making and Using Graphs The accompanyingdata show the volume of hydrogen gas collectedat a number of different temperatures Illustratethese data with a graph and use them to determinethe temperature at which the volume will reach avalue of 0 mL What is this temperature calledFor more help refer to Drawing Line Graphs inthe Math Handbook on page 903 of this text
Volume of H2 Collected at Different Temperatures
Trial 1 2 3 4 5 6
T (degC) 300 175 110 0 100 150
V (mL) 48 37 32 22 15 11
chemistrymccomself_check_quiz
440 Chapter 14 Gases
Section 144 Gas Stoichiometry
Objectivesbull Determine volume ratios for
gaseous reactants and prod-ucts by using coefficientsfrom a chemical equation
bull Calculate amounts ofgaseous reactants and prod-ucts in a chemical reactionusing the gas laws
All the laws you have learned so far involving gases can be applied to cal-culate the stoichiometry of reactions in which gases are reactants or productsRecall that the coefficients in chemical equations represent molar amounts ofsubstances taking part in the reaction For example when butane gas burnsthe reaction is represented by the following chemical equation
2C4H10(g) 13O2(g) 0 8CO2(g) 10H2O(g)
From the balanced chemical equation you know that 2 mol of butanereacts with 13 mol of oxygen producing 8 mol of carbon dioxide and 10 molof water vapor By examining this balanced equation you are able to find moleratios of substances in this reaction Avogadrorsquos principle states that equal vol-umes of gases at the same temperature and pressure contain equal numbersof particles Thus when gases are involved the coefficients in a balancedchemical equation represent not only molar amounts but also relative volumesFor example if 2 L of butane reacts the reaction involves 13 L of oxygenand produces 8 L of carbon dioxide and 10 L of water vapor
Calculations Involving Only VolumeTo find the volume of a gaseous reactant or product in a reaction you mustknow the balanced chemical equation for the reaction and the volume of atleast one other gas involved in the reaction Examine the reaction showingthe combustion of methane which takes place every time you light a Bunsenburner
CH4(g) 2O2(g) 0 CO2(g) 2H2O(g)
Because the coefficients represent volume ratios for gases taking part inthe reaction you can determine that it takes 2 L of oxygen to react completelywith 1 L of methane The complete combustion of 1 L of methane will pro-duce 1 L of carbon dioxide and 2 L of water vapor as shown in Figure 14-12
What volume of methane is needed to produce 26 L of water vaporBecause the volume ratio of methane and water vapor is 12 the volume ofmethane needed is half that of the water vapor Thus 13 L of methane isneeded to produce 26 L of water vapor What volume of oxygen is needed toproduce 60 L of carbon dioxide
Note that no conditions of temperature and pressure are listed They arenot needed as part of the calculation because after mixing each gas is at thesame temperature and pressure The same temperature and pressure affect allgases in the same way so these conditions donrsquot need to be considered
Figure 14-12
The coefficients in a balancedequation show the relationshipsamong numbers of moles of allreactants and products Thecoefficients also show the rela-tionships among volumes of anygaseous reactants or productsFrom these coefficients volumeratios can be set up for any pairof gases in the reaction
2 moles2 volumes
2 moles2 volumes
1 mole1 volume
1 mole1 volume
0
0
Methane gasCH4 (g)
Oxygen gas2O2 (g)
Carbon dioxide gasCO2 (g)
Water vapor 2H2O(g)
null
17444711
null
1488446
144 Gas Stoichiometry 441
EXAMPLE PROBLEM 14-9
Volume-Volume ProblemsWhat volume of oxygen gas is needed for the complete combustion of400 L of propane gas (C3H8) Assume constant pressure and temperature
1 Analyze the ProblemYou are given the volume of a gaseous reactant in a chemical reaction Remember that the coefficients in a balanced chemicalequation provide the volume relationships of gaseous reactants and products
Known Unknown
VC3H8 400 L VO2
L
2 Solve for the UnknownWrite the balanced equation for the combustion of C3H8
C3H8(g) 5O2(g) 0 3CO2(g) 4H2O(g)
Use the balanced equation to find the volume ratio for O2 and C3H8
15
vvoolluumm
ees
C3
OH
2
8
Multiply the known volume of C3H8 by the volume ratio to find thevolume of O2
(400 L C3H8) 200 L O2
3 Evaluate the Answer The coefficients in the combustion equation show that a much largervolume of O2 than C3H8 is used up in the reaction which is in agree-ment with the calculated answer The unit of the answer is L a unitof volume
5 volumes O21 volume C3H8
PRACTICE PROBLEMS56 What volume of oxygen is needed to react with solid sulfur to form
35 L SO2
57 Determine the volume of hydrogen gas needed to react completelywith 500 L of oxygen gas to form water
58 How many liters of propane gas (C3H8) will undergo complete com-bustion with 340 L of oxygen gas
59 What volume of oxygen is needed to completely combust 236 L ofmethane gas (CH4)
For more practice withvolume-volume prob-lems go toSupplemental PracticeSupplemental Practice
Problems in Appendix A
Practice
Calculations Involving Volume and MassTo do stoichiometric calculations that involve both gas volumes and massesyou must know the balanced equation for the reaction involved at least onemass or volume value for a reactant or product and the conditions underwhich the gas volumes have been measured Then the ideal gas law can beused along with volume or mole ratios to complete the calculation
In doing this type of problem remember that the balanced chemical equa-tion allows you to find ratios for moles and gas volumes onlymdashnot for massesAll masses given must be converted to moles or volumes before being usedas part of a ratio Also remember that the temperature units used must be kelvin
Correct proportions of gases areneeded for many chemical reac-tions The combustion of propaneheats the air that inflates the balloon
null
4508744
442 Chapter 14 Gases
EXAMPLE PROBLEM 14-10
Volume-Mass ProblemsAmmonia is synthesized from hydrogen and nitrogen gases
N2(g) 3H2(g) 0 2NH3(g)
If 500 L of nitrogen reacts completely by this reaction at a constant pres-sure and temperature of 300 atm and 298 K how many grams of ammo-nia are produced
1 Analyze the ProblemYou are given the volume pressure and temperature of a gas sam-ple The mole and volume ratios of gaseous reactants and productsare given by the coefficients in the balanced chemical equationVolume can be converted to moles and thus related to mass by usingmolar mass and the ideal gas law
Known Unknown
VN2 500 L mNH3
gP 300 atmT 298 K
2 Solve for the UnknownDetermine volume ratios from the balanced chemical equation
21vovolulummees N
NH2
3
Use this ratio to determine how many liters of gaseous ammonia willbe made from 500 L of nitrogen gas
500 L N2 21vovolulummees N
NH
2
3 100 L NH3
Rearrange the equation for the ideal gas law to solve for n
PV nRT
n PRVT
Substitute the known values into the rearranged equation using thevolume of NH3 for V Multiply and divide numbers and units to solvefor the number of moles of NH3
n 123 mol NH3
Find the molar mass M of NH3 by finding the molecular mass andexpressing it in units of gmol
M 1704 amu
M 1704 m
gol
Convert moles of ammonia to grams of ammonia using molar mass ofammonia as a conversion factor
123 mol NH3 1704 m
gol 210 g NH3
3 Evaluate the Answer To check your answer calculate the volume of reactant nitrogen atSTP Then use molar volume and the mole ratio between N2 and NH3to determine how many moles of NH3 were produced You can con-vert the answer to grams using the molar mass of NH3 All data wasgiven in three significant digits as is the answer
3 H atoms 101 amu
H atom1 N atom 1401 amu
N atom
(300 atm)(100 L)
00821 mLa
otlmK
(298 K)
Ammonia is essential in the pro-duction of chemical fertilizers
144 Gas Stoichiometry 443
Section 144 Assessment
65 How do mole ratios compare to volume ratios forgaseous reactants and products in a balancedchemical equation
66 Is the volume of a gas directly or inversely pro-portional to the number of moles of a gas at con-stant temperature and pressure Explain
67 Determine the volume ratio of ammonia to nitro-gen in the reaction shown
3H2 N2 0 2NH3
Which will occupy a larger volume at a giventemperature and pressure one mole of H2 or onemole of NH3
68 Thinking Critically One mole of a gas occupiesa volume of 224 L at STP Calculate the tempera-ture and pressure conditions needed to fit twomoles of a gas into a volume of 224 L
69 Predicting Using what you have learned aboutgases predict what will happen to the size of thereaction vessel you need to carry out a reactioninvolving gases if the temperature is doubled andthe pressure is held constant
Stoichiometric problems such as these are considered in industrialprocesses that involve gases How much of a reactant should be purchasedHow much of a product will be produced What conditions of temperatureand presssure are necessary Answers to these questions are essential to effec-tive production of a product
PRACTICE PROBLEMS60 Ammonium nitrate is a common ingredient in chemical fertilizers Use
the reaction shown to calculate the mass of solid ammonium nitratethat must be used to obtain 0100 L of dinitrogen oxide gas at STP
NH4NO3(s) 0 N2O(g) 2H2O(g)
61 Calcium carbonate forms limestone one of the most common rockson Earth It also forms stalactites stalagmites and many other typesof formations found in caves When calcium carbonate is heated itdecomposes to form solid calcium oxide and carbon dioxide gas
CaCO3(s) 0 CaO(s) CO2(g)
How many liters of carbon dioxide will be produced at STP if 238 kgof calcium carbonate reacts completely
62 Determine how many moles of water vapor will be produced at 100atm and 200degC by the complete combustion of 105 L of methane gas(CH4)
63 When iron rusts it undergoes a reaction with oxygen to form iron(III)oxide
4 Fe(s) 3O2(g) 0 2Fe2O3(s)
Calculate the volume of oxygen gas at STP that is required to com-pletely react with 520 g of iron
64 Solid potassium metal will react with Cl2 gas to form ionic potassiumchloride How many liters of Cl2 gas are needed to completely reactwith 0204 g of potassium at STP
For more practice withvolume-mass problemsgo to SupplementalPractice Problems in
Appendix A
Practice
chemistrymccomself_check_quiz
Topic GasesTo learn more about gasesvisit the Chemistry Web siteat chemistrymccomActivity Research how thegas laws are important to fishand scuba divers Explainyour answers using equationswhen possible
null
21368141
444 Chapter 14 Gases
Pre-Lab
1 Read the entire CHEMLAB
2 Prepare all written materials that you will take intothe laboratory Be sure to include safety precau-tions procedure notes and a data table
3 Because you will collect the aerosol gas overwater the beaker contains both the aerosol gas andwater vapor Form a hypothesis about how thepresence of water vapor will affect the calculatedvalue of the molar mass of the gas Explain
4 The following gases are or have been used inaerosol cans some as propellants Use the gasesrsquomolecular formulas to calculate their molar massesa propane C3H8b butane C4H10c dichlorodifluoromethane CCl2F2d tetrafluoroethane C2H2F4
5 Given the following data for a gas use the equa-tion for the ideal gas law to calculate the molarmassa mass 0810 gb pressure 0954 atmc volume 0461 Ld temperature 291 K
Procedure
1 Place the bucket in the sink and fill it with water
2 Submerge the beaker in the water Then invert itin the bucket being careful to keep it completelyfilled with water
3 Measure the mass of an aerosol can of officeequipment duster Record the mass in the datatable
Safety Precautions
bull Read and observe all cautions listed on the aerosol can of office equip-ment duster
bull Do not have any open flames in the room
ProblemHow can the equation for theideal gas law be used to cal-culate the molar mass of agas
Objectivesbull Measure the mass volume
temperature and pressureof an insoluble gas col-lected over water
bull Calculate the molar mass ofan unknown gas using theideal gas equation
Materialsaerosol can of
duster600-mL graduated
beakerbucket or bowl thermometer (degC)barometer or
weather radio
plastic microtippipette
latex tubing glass tubing scissorselectrical or duct
tapebalance
Using the Ideal Gas LawThe ideal gas law is a powerful tool that the chemistmdashand now
youmdashcan use to determine the molar mass of an unknown gasBy measuring the temperature pressure volume and mass of a gassample you can calculate the molar mass of the gas
CHEMLAB 14
Data and Calculations
Mass of can before release of gas (g)
Mass of can after release of gas (g)
Mass of gas released (g)
Air temperature (degC)
Air temperature (K)
Air pressure (list what unit was used)
Air pressure (atm)
Volume of gas collected (L)
CHEMLAB 445
4 Use scissors to cut the stem from a plasticmicrotip pipette
5 Fit the pipette stem over the long plastic spray tipthat comes with the aerosol can to extend thelength of the tip and enlarge the diameter
6 Connect one end of 30 cm of latex tubing to glasstubing that is 8 cm long
7 Connect the other end to the pipette stem that isattached to the aerosol can If necessary tape anyconnections so that they donrsquot leak
8 Place the end of the glass tubing under the pourspout of the inverted beaker as shown in the photo
9 Hold the beaker down while you slowly releasethe gas from the aerosol can Collect between 400and 500 mL of the gas by water displacement
10 To equalize the air pressure lift the beaker so thatthe water level inside and outside the beaker isthe same
11 Carefully read the volume of the gas collectedusing the graduations on the beaker
12 Record this volume of the gas collected in thedata table
13 Remove the tubing from the aerosol can
14 Measure the mass of the can and record it in thedata table
15 Using a barometer or weather radio record theatmospheric pressure in the data table
16 Using a thermometer determine air temperatureRecord it in the data table
Cleanup and Disposal
1 Dispose of the empty can according to the instruc-tions on its label
2 Pour the water down the drain
3 Discard any tape and the pipettes in the trash can
4 Return all lab equipment to its proper place
Analyze and Conclude
1 Using Numbers Fill in the remainder of the datatable by calculating the mass of the gas that wasreleased from the aerosol can converting theatmospheric pressure from the units measured intoatmospheres and converting the air temperatureinto kelvins Substitute your data from the tableinto the form of the ideal gas equation that solvesfor M Calculate the molar mass of the gas in thecan using the appropriate value for R
2 Using Numbers Read the contents of the can anddetermine which of the gases from step 4 in thePre-Lab is the most likely propellant
3 Remember that you are collect-ing the gas after it has bubbled through waterWhat might happen to some of the gas as it goesthrough the water What might be present in thegas in the beaker in addition to the gas from thecan Calculate the percent error using your calcu-lated molar mass compared to the molar mass ofthe gas in the aerosol can
4 Interpreting Data Were your data consistentwith the ideal gas law Evaluate the pressure andtemperature at which your experiment was doneand the polarity of the gas Would you expect thegas in your experiment to behave as an ideal gas ora real gas
Real-World Chemistry
1 Explain why the label on an aerosol can warnsagainst exposing the can to high heat
2 Use the ideal gas law to explain why the windblows
Error Analysis
CHAPTER 14 CHEMLAB
CHEMISTRY and
TechnologyHave you ever been caught in a traffic jam causedby a truck carrying an oversized piece of industrialequipment The need to transport heavy loads moreefficiently is one factor leading to the revival of atechnology that most people considered to bedeadmdashthe airship sometimes called a dirigible orzeppelin The burning of the zeppelin Hindenburgin May 1937 followed closely by World War IIended nearly all commercial use of these ldquolighter-than-airrdquo ships But by the 1990s chemists andengineers had developed strong lightweight alloysand tough fiber-reinforced composite plasticsThese materials along with computerized controland satellite navigation systems are making com-mercial airships practical again
Modern airshipsModern airships use helium to provide lift TheHindenburg used hydrogen gas which providesabout twice the lift of helium but is no longer usedbecause it is extremely flammable The helium iscontained in bags made of a space-age leakprooffabric called Tedlar a type of plastic The bags areloosely inflated so that the helium pressure is aboutthe same as atmospheric pressure The quantity ofhelium determines the lifting ability of the ship
Airships and Boylersquos lawAs the airship rises atmospheric pressure decreasesand the helium expands as Boylersquos law predictsAs the ship reaches the desired altitude air ispumped into another bag called a ballonet Thepressure of the ballonet prevents the helium bagsfrom expanding further thus keeping the ship atthat altitude To descend more air is pumped intothe ballonet This added pressure squeezes thehelium bags causing the volume to decrease andthe density of the helium to increase Also the com-pressed air adds weight to the ship The liftingpower of the helium is reduced and the airshipmoves downward
Uses for modern airshipsThe old airships of 1900 to 1940 were used mostlyfor luxury passenger service Among modern air-ships the German Zeppelin-NT and a ship being
developed by the Hamilton Airship Company inSouth Africa are designed to carry passengers
Probably the most interesting new airship is thehuge CargoLifter from a German-American com-pany Its length is slightly less than the length ofthree football fields CargoLifterrsquos skeleton is con-structed of a strong carbon fiber composite mate-rial that is much less dense than metals At themooring mast it is as tall as a 27-story building andcontains 450 000 m3 of helium It is designed tocarry loads up to 160 metric tons (352 000 pounds)It can pick up and deliver objects such as large tur-bines and entire locomotives Because modernroads are not needed equipment can be deliveredto locations in developing countries that would oth-erwise be impossible to reach
1 Thinking Critically No plastics fabrics ormetals that are ldquolighter-than-airrdquo existYetthese materials are used to make airshipsWhy is it possible to describe an airship as alighter-than-air craft
Investigating the Technology
Giving a Lift to Cargo
446 Chapter 14 Gases
Visit the Chemistry Web site atchemistrymccom to find links to moreinformation about airships
Study Guide 447
CHAPTER STUDY GUIDE14
Vocabulary
Key Equations and Relationships
Summary141 The Gas Lawsbull Boylersquos law states that the pressure and volume of a
contained gas are inversely proportional if tempera-ture is constant
bull Charlesrsquos law states that the volume and kelvin tem-perature of a contained gas are directly proportionalif pressure is constant
bull Gay-Lussacrsquos law states that the pressure and kelvintemperature of a contained gas are directly propor-tional if volume is constant
142 The Combined Gas Law and AvogadrorsquosPrinciple
bull Boylersquos Charlesrsquos and Gay-Lussacrsquos laws arebrought together in the combined gas law whichpermits calculations involving changes in the threegas variables of pressure volume and temperature
bull Avogadrorsquos principle states that equal volumes ofgases at the same temperature and pressure containequal numbers of particles The volume of one moleof a gas at STP is 224 L
143 The Ideal Gas Lawbull The combined gas law and Avogadrorsquos principle
are used together to form the ideal gas law In theequation for the ideal gas law R is the ideal gasconstant
bull The ideal gas law allows you to determine the num-ber of moles of a gas when its pressure tempera-ture and volume are known
bull Real gases deviate from behavior predicted for idealgases because the particles of a real gas occupy vol-ume and are subject to intermolecular forces
bull The ideal gas law can be used to find molar mass ifthe mass of the gas is known or the density of thegas if its molar mass is known
144 Gas Stoichiometrybull The coefficients in a balanced chemical equation
specify volume ratios for gaseous reactants andproducts
bull The gas laws can be used along with balancedchemical equations to calculate the amount of agaseous reactant or product in a reaction
bull Boylersquos law P1V1 P2V2 constant temperature(p 421)
bull Charlesrsquos law VT1
1
VT2
2 constant pressure
(p 424)
bull Gay-Lussacrsquos law PT
1
1
PT
2
2 constant volume
(p 426)
bull Combined gas law PT1V
1
1
PT2V
2
2 (p 428)
bull Ideal gas law PV nRT (p 434)
bull Finding molar mass M mPRVT
(p 437)
bull Finding density D MRT
P (p 437)
bull Avogadrorsquos principle (p 430)bull Boylersquos law (p 421)bull Charlesrsquos law (p 424)
bull combined gas law (p 428)bull Gay-Lussacrsquos law (p 426)bull ideal gas constant (R) (p 434)
bull ideal gas law (p 434)bull molar volume (p 431)
chemistrymccomvocabulary_puzzlemaker
448 Chapter 14 Gases
Go to the Glencoe Chemistry Web site atchemistrymccom for additionalChapter 14 Assessment
Concept Mapping70 Complete the following concept map that shows how
Boylersquos law Charlesrsquos law and Gay-Lussacrsquos law arederived from the combined gas law
Mastering Concepts71 State the laws of Boyle Charles and Gay-Lussac as
equations (141)
72 What will happen to the pressure of a contained gas ifits temperature is lowered (141)
73 Why is it important not to puncture an aerosol can(141)
74 Explain why an unopened bag of potato chips left in ahot car appears to become larger (141)
75 If two variables have an inverse relationship whathappens to the value of one as the value of the otherincreases (141)
76 If two variables have a direct relationship what hap-pens to the value of one as the value of the other isincreased (141)
77 Label the following examples as being generally rep-resentative of direct or inverse relationship (141)
a popularity of a musical group versus how hard it isto get tickets for its concert
b number of carats a diamond weighs versus its costc number of people helping versus how long it takes
to clean up after a party
78 Label the following examples as being representativeof a direct or inverse relationship (141)
a pressure versus volume of a gasb volume versus temperature of a gasc pressure versus temperature of a gas
79 What four variables are used to describe gases (141)
80 List the standard conditions for gas measurements(142)
81 Write the equation for the combined gas law Identifythe units most commonly used with each variable(142)
82 State Avogadrorsquos principle (142)
83 What volume is occupied by one mole of a gas atSTP What volume do two moles occupy at STP(142)
84 What units must be used to express the temperature inthe equation for the ideal gas law Explain (143)
85 List two conditions under which a gas is least likely tobehave ideally (143)
86 Write the value and units for the gas constant R in twocommon forms (143)
87 What information is needed to solve a volume-massproblem that involves gases (144)
Mastering ProblemsThe Gas Laws (141)88 Use Boylersquos Charlesrsquos or Gay-Lussacrsquos law to calcu-
late the missing value in each of the following
a V1 20 L P1 082 atm V2 10 L P2 b V1 250 mL T1 V2 400 mL T2 298 Kc V1 055 L P1 740 mm Hg V2 080 L P2 d T1 25degC P1 T2 37degC P2 10 atm
89 What is the pressure of a fixed volume of a gas at300degC if it has a pressure of 111 atm at 150degC
90 A fixed amount of oxygen gas is held in a 100-L tankat a pressure of 350 atm The tank is connected to anempty 200-L tank by a tube with a valve After thisvalve has been opened and the oxygen is allowed toflow freely between the two tanks at a constant tem-perature what is the final pressure in the system
91 Hot-air balloons rise because the hot air inside the bal-loon is less dense than the cooler air outside Calculatethe volume an air sample will occupy inside a balloonat 430degC if it occupies 250 L at the outside air tem-perature of 220degC assuming the pressure is the sameat both locations
CHAPTER ASSESSMENTCHAPTER ASSESSMENT14
remains constant
combined gas law
temperaturepressure volume
results in
21 3
chemistrymccomchapter_test
Assessment 449
CHAPTER 14 ASSESSMENT
The Combined Gas Law (142)92 A sample of nitrogen gas is stored in a 5000-mL
flask at 108 kPa and 100degC The gas is transferred toa 7500-mL flask at 210degC What is the pressure ofnitrogen in the second flask
93 The air in a dry sealed 2-L soda bottle has a pressureof 0998 atm at sea level at a temperature of 340degCWhat will be its pressure if it is brought to a higheraltitude where the temperature is only 230degC
94 A weather balloon is filled with helium that occupiesa volume of 500 104 L at 0995 atm and 320degCAfter it is released it rises to a location where thepressure is 0720 atm and the temperature is120degC What is the volume of the balloon at thatnew location
Avogadrorsquos Principle (142)95 Propane C3H8 is a gas commonly used as a home
fuel for cooking and heating
a Calculate the volume that 0540 mol of propaneoccupies at STP
b Think about the size of this volume compared tothe amount of propane that it contains Why doyou think propane is usually liquefied before it istransported
96 Carbon monoxide CO is a product of incompletecombustion of fuels Find the volume that 42 g ofcarbon monoxide gas occupies at STP
The Ideal Gas Law (143)97 The lowest pressure achieved in a laboratory is about
10 1015 mm Hg How many molecules of gasare present in a 100-L sample at that pressure and atemperature of 220ordmC
98 Determine the density of chlorine gas at 220degC and100 atm pressure
99 Geraniol is a compound found in rose oil that is usedin perfumes What is the molar mass of geraniol if itsvapor has a density of 0480
Lg
at a temperature of2600degC and a pressure of 0140 atm
100 A 200-L flask is filled with propane gas (C3H8) at100 atm and 150degC What is the mass of thepropane in the flask
Gas Stoichiometry (144)101 Ammonia is formed industrially by reacting nitrogen
and hydrogen gases How many liters of ammoniagas can be formed from 137 L of hydrogen gas at930degC and a pressure of 400 kPa
102 When 300 L of propane gas is completely com-busted to form water vapor and carbon dioxide at atemperature of 350degC and a pressure of 0990 atmwhat mass of water vapor will result
103 When heated solid potassium chlorate (KClO3)decomposes to form solid potassium chloride andoxygen gas If 208 g of potassium chlorate decom-poses how many liters of oxygen gas will form atSTP
104 Use the reaction shown below to answer these ques-tions
CO(g) NO(g) 0 N2(g) CO2(g)
a Balance the equationb What is the volume ratio of carbon monoxide to
carbon dioxide in the balanced equationc If 427 g CO is reacted completely at STP what
volume of N2 gas will be produced
Mixed ReviewSharpen your problem-solving skills by answering thefollowing
105 Gaseous methane (CH4) undergoes complete com-bustion by reacting with oxygen gas to form carbondioxide and water vapor
a Write a balanced equation for this reactionb What is the volume ratio of methane to water inthis reaction
106 If 233 L of propane at 24degC and 672 kPa is com-pletely burned in excess oxygen how many moles ofcarbon dioxide will be produced
107 Use Boylersquos Charlesrsquos or Gay-Lussacrsquos law to cal-culate the missing value in each of the following
a V1 14 L P1 V2 30 L P2 12 atmb V1 705 mL T1 273 K V2 T2 323 Kc V1 0540 L P1 V2 0990 L
P2 775 mm Hgd T1 37degC P1 50 atm P2 25 atm T2
108 Determine the pressure inside a television picturetube with a volume of 350 L that contains200 105 g of nitrogen gas at 220degC
109 Determine how many liters 880 g of carbon dioxidegas would occupy at
a STP c 288 K and 118 kPab 160degC and 300 atm
110 If 500 L of hydrogen gas measured at 200ordmC and801 kPa is burned in excess oxygen to form waterwhat mass of oxygen (measured at the same temper-ature and pressure) will be consumed
450 Chapter 14 Gases
Thinking Critically111 Making and Using Graphs Automobile tires
become underinflated as temperatures drop during thewinter months if no additional air is added to the tiresat the start of the cold season For every 10degF drop in temperature the air pressure in a carrsquos tiresgoes down by about 1 psi (147 psi equals 100 atm)Complete the following table Then make a graphillustrating how the air pressure in a tire changes overthe temperature range from 40degF to 10degF assumingyou start with a pressure of 300 psi at 40degF
112 Applying Concepts When nitroglycerin(C3H5N3O9) explodes it decomposes into the follow-ing gases CO2 N2 NO and H2O If 239 g of nitro-glycerin explodes what volume will the mixture ofgaseous products occupy at 100 atm pressure and2678degC
113 Analyze and Conclude What is the numericalvalue of the ideal gas constant (R) in
cKmm
3Poal
114 Applying Concepts Calculate the pressure of amixture of two gases that contains 467 1022 mole-cules CO and 287 1024 molecules of N2 in a 600-L container at 348degC
Writing in Chemistry115 It was the dream of many early balloonists to com-
plete a trip around the world in a hot-air balloon agoal not achieved until 1999 Write about what youimagine a trip in a balloon would be like including adescription of how manipulating air temperaturewould allow you to control altitude
116 Investigate and explain the function of the regulatorson the air tanks used by scuba divers
Cumulative ReviewRefresh your understanding of previous chapters byanswering the following
117 Convert each of the following mass measurements toits equivalent in kilograms (Chapter 2)
a 247 gb 53 Mgc 723 gd 975 mg
118 How many atoms of each element are present in fiveformula units of calcium permanganate (Chapter 8)
119 Terephthalic acid is an organic compound used in theformation of polyesters It contains 578 percent C364 percent H and 385 percent O The molar massis known to be approximately 166 gmol What is themolecular formula of terephthalic acid (Chapter 11)
120 The particles of which of the following gases havethe highest average speed The lowest averagespeed (Chapter 13)
a carbon monoxide at 90degCb nitrogen trifluoride at 30degCc methane at 90degCd carbon monoxide at 30degC
CHAPTER ASSESSMENT14
Tire Inflation Based on Temperature
Temperature (degF) Pressure (psi)
40
30
20
10
0
10
Standardized Test Practice 451
Use these questions and the test-taking tip to preparefor your standardized test
1 The kinetic-molecular theory describes the micro-scopic behavior of gases One main point of the theoryis that within a sample of gas the frequency of colli-sions between individual gas particles and between theparticles and the walls of their container increases ifthe sample is compressed The gas law that states thisrelationship in mathematical terms is
a Gay-Lussacrsquos Lawb Charlesrsquos Lawc Boylersquos Lawd Avogadrorsquos Law
2 Three 20-L containers are placed in a 50ordmC roomSamples of 05 mol N2 05 mol Xe and 05 molethene (C2H4) are pumped into Containers 1 2 and 3respectively Inside which container will the pressurebe greatest
a Container 2b Container 3c Containers 2 and 3 have the same higher pressured Containers 1 2 and 3 have equal pressures
Interpreting Graphs Use the graph to answerquestions 3ndash5
3 It can be seen from the graph that
a as temperature increases pressure decreasesb as pressure increases volume decreasesc as temperature decreases moles decreased as pressure decreases temperature decreases
4 Which of these gases is an ideal gasa Gas A c Gas Cb Gas B d none of the above
5 What is the predicted pressure of Gas B at 310 K
a 260 kPa c 1000 kPab 620 kPa d 1200 kPa
6 What volume will 0875 moles of SF4 occupy at STP
a 196 L c 224 Lb 214 L d 327 L
7 While it is on the ground a blimp is filled with566 106 L of He gas The pressure inside thegrounded blimp where the temperature is 25ordmC is110 atm Modern blimps are non-rigid which meansthat their volume is changeable If the pressure insidethe blimp remains the same what will be the volumeof the blimp at a height of 2300 m where the tempera-ture is 12ordmC
a 566 106 L c 54 106 Lb 272 106 L d 592 106 L
8 The reaction that provides blowtorches with theirintense flame is the combustion of acetylene (C2H2) toform carbon dioxide and water vapor Assuming thatthe pressure and temperature of the reactants are thesame what volume of oxygen gas is required to com-pletely burn 560 L of acetylene
a 224 L c 112 Lb 560 L d 140 L
9 A sample of argon gas is compressed into a volume of0712 L by a piston exerting 392 atm of pressure Thepiston is slowly released until the pressure of the gasis 150 atm What is the new volume of the gas
a 0272 L c 186 Lb 367 L d 419L
10 Assuming ideal behavior how much pressure will00468 g of ammonia (NH3) gas exert on the walls ofa 400-L container at 350ordmC
a 00174 atm c 000198 atmb 0296 atm d 0278 atm
STANDARDIZED TEST PRACTICECHAPTER 14
Ask Questions If yoursquove got a question aboutwhat will be on the test the way the test is scoredthe time limits placed on each section or anythingelse by all means ask Will you be required toknow the specific names of the gas laws such asBoylersquos law and Charlesrsquos law
250 260 270 280 290 300
Pres
sure
(kP
a)
1200
1000
800
600
400
200
0
Gas C
Gas A
Gas B
Temperature (K)
Pressures of Three Gasesat Different Temperatures
chemistrymccomstandardized_test