Chemistry51 Chapter7

PROPERTIESOFGASES

Gasesaretheleastdenseandmostmobile ofthethreephasesofmatter.

Particlesofmatterinthegasphasearespacedfarapartfromoneanotherandmove
rapidlyandcollidewitheachotheroften.

Gasesoccupymuchgreaterspace thanthesameamountofliquidorsolid.This
isbecausethegasparticlesarespacedapartfromoneanotherandaretherefore
compressible.Solidorliquidparticlesarespacedmuchcloserandcannotbe
compressedfurther.

Gasesarecharacterizedbyfourproperties.Theseare:

1. Pressure(P).
2. Volume(V)
3. Temperature(T)
4. Amount(n)

KineticMolecularTheoryofGases
Scientistsusethekineticmoleculartheory(KMT) todescribethebehaviorofgases.
TheKMTconsistsofseveralpostulates:

1. Gasesconsistof smallparticles(atomsormolecules)thatmoverandomly
with rapidvelocities.

2. Gasparticleshavelittleattractionforoneanother. Therefore,attractive
forcesbetweengasmoleculescanbeignored.

3. Thedistancebetweentheparticlesislargecomparedtotheirsize.Therefore
thevolume occupiedby gasmoleculesissmallcomparedtothevolumeofthe
gas.

4. Gasparticlesmovein straightlinesandcollidewitheachotherandthe
containerfrequently. Theforceof collisionsofthegasparticleswiththe
wallsofthecontainercausespressure.

5. Theaveragekineticenergyofgasmoleculesisdirectlyproportionaltothe
absolutetemperature(Kelvin).

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Chemistry51 Chapter7

PRESSUREANDITSMEASUREMENT

Pressureistheresultof collisionofgasparticleswiththesidesofthe
container.Pressureisdefinedastheforceperunitarea.

Pressureismeasuredin unitsofatmosphere (atm)or mmHg or torr.

1atm =760mmHg
1mmHg=1torr
1atm=101.325kPa

Atmosphericpressurecanbemeasuredwiththeuseofa
barometer. Mercuryisusedinabarometerduetoitshigh
density. Atsealevel,themercurystandsat760mmaboveits
base.

Thepressureofagasisdirectlyproportional tothenumberofparticles(moles)present.

Examples:
1. TheatmosphericpressureatWalnut,CAis740.mmHg.Calculatethispressureintorrand
atm.

1mmHg=1torr therefore, 740.mmHg=

740.mmHgx =atm

2.Thebarometeratalocationreads1.12atm.CalculatethepressureinmmHgandtorr.

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Chemistry51 Chapter7

RELATIONSHIPBETWEENPRESSURE&VOLUME
BOYLESLAW

Atconstanttemperature,thevolumeofafixed
amount ofgasisinverselyproportional toits
pressure.

P1V1 =P2V2

Examples:
1. AsampleofH2 gashasavolumeof5.0Landapressureof1.0atm.Whatisthenew
pressureifthevolumeisdecreasedto2.0Latconstanttemperature?

P1V1 (1.0atm)(5.0L)
P1 =1.0atmP2 =???P2= = =2.5atm
V2 2.0L
V1 =5.0LV2=2.0L

2. Asampleofgashasavolumeof12Landapressureof4500mmHg.Whatisthevolume
ofthegaswhenthepressureisreducedto750mmHg?

P1 =P2=

V1 =V2=???

3. Asampleofhydrogengasoccupies4.0Lat650mmHg.Whatvolumewoulditoccupyat
2.0atm?

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Chemistry51 Chapter7

RELATIONSHIPBETWEENTEMP.&VOLUME
CHARLESSLAW

Atconstantpressure,thevolumeofafixedamount
ofgasisdirectlyproportionaltoitsabsolute
temperature.

V1 V
= 2
T1 T2

Note:TmustbeinunitofK

Examples:
1. A2.0Lsampleofagasiscooledfrom298Kto278K,atconstantpressure.Whatisthe
newvolumeofthegas?

T2 278K
V1 =2.0LV2 =???V2 =V1x =2.0Lx =1.9L
T1 298K
T1 =298KT2=278K

2. Asampleofgashasavolumeof5.0Landatemperatureof20C.Whatisthevolumeof
thegaswhenthetemperatureisincreasedto50C,atconstantpressure?

V1 =V2=

T1 =T2 =

3. If20.0Lofoxygengasiscooledfrom100 Cto0 C,whatisthenewvolume?

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Chemistry51 Chapter7

RELATIONSHIPBETWEENTEMP.&PRESSURE
GAYLUSSACSLAW

Atconstantvolume,thepressureofafixed
amount ofgasisdirectlyproportionaltoits
absolutetemperature.

P1 P
= 2
T1 T2

Examples:
1. Anaerosolspraycanhasapressureof4.0atmat25C.Whatpressurewillthecanhave
ifitisplacedinafireandreachestemperatureof400C?

T2 673K
P1 =4.0atmP2 =???P2 =P1x =4.0atmx =9.0atm
T1 298K
T1 =298KT2=673K

2. Acylinderofgaswithavolumeof15.0Landapressureof965mmHgisstoredata
temperatureof55C.Towhattemperaturemustthecylinderbecooledtoreacha
pressureof850mmHg?

P1 =P2=
T1 =T2=???

3. Thepressureofacontainerofheliumis650mmHgat25 C.Ifthecontaineriscooledto
0 C,whatwillthepressurebe?

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Chemistry51 Chapter7

VAPORPRESSURE&BOILINGPOINT

Inanopencontainer,liquidmoleculesatthesurfacethatpossesssufficientenergy,can
breakawayfromsurfaceandbecomegasparticlesorvapor.Inaclosedcontainer,these
gasparticlescanaccumulateandcreatepressurecalledvaporpressure.

Vaporpressureisdefinedasthepressureabovealiquidatagiven temperature. Vapor

Aliquidreachesitsboilingpointwhenitsvaporpressurebecomesequaltotheexternal
pressure(atmosphericpressure).Forexample,atsealevel,waterreachesitsboilingpoint
at100Csinceitsvaporpressureis760mmHgatthistemperature.

Athigheraltitudes,whereatmosphericpressureislower,waterreachesboilingpointat
temperatureslowerthan100C.ForexampleinDenver,whereatmosphericpressureis
630mmHg,waterboilsat95C,sinceitsvaporpressureis630mmHgatthistemperature.

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Chemistry51 Chapter7

RELATIONSHIPBETWEENPRESSURE,VOL.&TEMP.
COMBINEDGASLAW

All pressurevolumetemperaturerelationshipscanbecombinedintoasinglerelationship
calledthecombinedgaslaw.Thislawisusefulforstudyingtheeffectof changesintwo
variables.

P1 V1 P V
= 2 2
T1 T2

Theindividualgaslawsstudiedpreviouslyareembodiedinthecombinedgaslaw.

P1 V1 P V
= 2 2 Boyle'sLaw
T1 T2
P1 V1 P V
= 2 2 Charles'sLaw
T1 T2
P1 V1 P V
= 2 2 GayLussac'sLaw
T1 T2

Examples:
1. A25.0mLsampleofgashasapressureof4.00atmatatemperatureof10C.Whatisthe
volumeofthegasatapressureof1.00atmandatemperatureof18C?

P1 T2
P1 = P2 = V2 =V1x x
P2 T1
V1 = V2 =
4.00atm 291K
T1 = T2 = V2=25.0mLx x =103mL
1.00atm 283K

2. Asampleofammoniahasavolumeof20.0mLat5 Cand700mmHg.Whatisthe
volumeofthegasat50Cand850torr?

P1 = P2 =

V1 = V2 =

T1 = T2 =

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Chemistry51 Chapter7

RELATIONSHIPBETWEENVOLUME&MOLES
AVOGADROSLAW

Atconstanttemperatureandpressure,thevolume
ofafixedamount ofgasisdirectlyproportionalto
thenumberofmoles.

AsaresultofAvogadrosLaw,equalvolumes of
differentgasesatthesametemperatureand
pressurecontain equalnumberofmoles
(molecules).

Thisrelationshipalsoallowschemiststorelatevolumesandmolesofagasinachemical
reaction.Forexample:

2H2 (g)+O2 (g) 2H2O(g)

2molecules1molecule2molecules
2moles1mole2moles
2Liters1Liter 2Liters

Examples:
1. Asampleofheliumgaswithamassof18.0g occupies1.6Litersataparticular
temperatureandpressure.Whatmassofoxygenwouldoccupy1.6L atthesame
temperatureandpressure?

1mol
molofHe=18.0 g x =4.50molHe
4.00 g
molofO 2=molHe=4.50mol(sinceatsameT&P)
32.0g
massofO 2=4.50 mol x =144g
1 mol

2. HowmanyLitersofNH3 canbeproducedfromreactionof1.8LofH2 withexcessN2,as

N2 (g)+3H2 (g) 2NH3 (g)

2LNH3
1.8 LH2 x =1.2LNH 3
3 LH2

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Chemistry51 Chapter7

STP&MOLARVOLUME

Tobetterunderstandthefactorsthataffectgasbehavior,asetof standardconditionshave
beenchosenforuse,andarereferredtoasStandardTemperatureandPressure(STP).

STP:0C(273K)and1atm(760mmHg)

AtSTPconditions,onemoleofanygasisobservedtooccupyavolumeof22.4L.This
quantityisreferredtoasMolarVolume.

MolarVolumeofagasatSTP=22.4L

Examples:
1.If2.00LofagasatSTPhasamassof3.23g,whatisthemolarmassofthegas?

1mol
molofgas=2.00 L x =0.0893mol
22.4 L
g 3.23g
molarmass= = =36.2g/mol
mol 0.0893mol

2. Asampleofgashasavolumeof2.50Lat730mmHgand20C.Whatisthevolumeof
thisgasatSTP?

P1 = P2 =

V1 = V2 =

T1 = T2 =

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Chemistry51 Chapter7

IDEALGASLAW

Combiningallthelawsthatdescribethebehaviorofgases,onecan obtainauseful
relationshipthatrelatesthevolumeofagastothetemperature,pressureandnumberof
moles.

nRT
V=
P
Latm
R=UniversalGasConstant=0.0821
molK

ThisrelationshipiscalledtheIdealGasLaw,andcommonlywrittenas:

P V = nR T
- - - -
atm L mol K

Examples:
1. AsampleofH2 gashasavolumeof8.56Latatemperatureof0Candpressureof1.5atm.
Calculatethemolesofgaspresent.
PV
P=1.5atm n=??? n=
RT
(1.5atm)(8.56L)
V=8.56L T=273K n= =0.57mol
(0.0821Latm/molK)(273K)

2. Whatvolumedoes40.0gofN2 gasoccupyat10Cand750mmHg?

P= n=

nRT
V=??? T= V= =
P

3. A23.8Lcylinderofcontainsoxygenat20.0 Cand732mmHg.Howmanymolesof
oxygendoesitcontain?

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 Chemistry51 Chapter7

PARTIALPRESSURES
DALTONSLAW

Manygassamplesaremixtureofgases.Forexample,theairwebreatheisamixtureof
mostlyoxygenandnitrogen gases.

Sincegasparticleshavenoattractionstowardsoneanother,eachgasinamixturebehaves
asifitispresentbyitself,andisnotaffectedbytheothergasespresentinthemixture.

Inamixture,eachgasexertsapressureasifitwastheonly gaspresentinthecontainer.
Thispressureiscalledpartialpressureofthegas.

Inamixture,thesumofallthepartialpressuresofgasesinthemixtureisequaltothetotal
pressureofthegasmixture.ThisiscalledDaltonslawofpartialpressures.

Ptotal =P1 +P2 +P3 +

Thepartialpressureofeachgasinamixtureisproportionaltotheamount(mol)ofgas
presentinthemixture.Forexample,inamixtureofgasesconsistingof1moleofnitrogen
and1molofhydrogengas,thepartialpressureofeachgasisonehalfofthetotalpressure
inthecontainer.

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Chemistry51 Chapter7

PARTIALPRESSURES

Examples:
1. Two10Ltanks,onecontainingpropanegasat300torrandtheothercontainingmethaneat
500torr,arecombinedina10Ltankatthesametemperature.Whatisthetotalpressureof
thegasmixture?

Ptotal=P1 +P2 =300torr+500torr=800torr

2. Ascubatankcontainsamixtureofoxygenandheliumgaseswithtotalpressureof7.00atm.
Ifthepartialpressureofoxygeninthetankis1140mmHg,whatisthepartialpressureof
heliuminthetank?

Poxygen (inatm)=1140mmHgx =

Ptotal =Poxygen +Phelium

Phelium =

3. Amixtureofgasescontains2.0molofO2 gasand4.0molofN2 gaswithtotalpressureof

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