1
EXPERIMENTB1:MOLARVOLUMEOFAGAS
LearningOutcomes
Uponcompletionofthislab,thestudentwillbeableto:
1) Demonstrateasinglereplacementreaction.
2) CalculatethemolarvolumeofagasatSTPusingexperimentaldata.
3) Calculatethemolarmassofametalusingexperimentaldata.
Introduction
Metalsthatareabovehydrogenintheactivityserieswilldisplacehydrogenfroman
acidandproducehydrogengas.Magnesiumisanexampleofametalthatismore
activethanhydrogenintheactivityseries.Thereactionbetweenmagnesiummetal
andaqueoushydrochloricacidisanexampleofasinglereplacementreaction(a
typeofredoxreaction).Thechemicalequationforthisreactionisshownbelow:
Mg(s)+2HCl(aq)!MgCl2(aq)+H2(g) Equation1
Whenthereactionbetweenthemetalandtheacidisconductedinaeudiometer,the
volumeofthehydrogengasproducedcanbeeasilydetermined.Intheexperiment
describedbelowmagnesiummetalwillbereactedwithanexcessofhydrochloric
acidandthevolumeofhydrogengasproducedattheexperimentalconditionswill
bedetermined.
AccordingtoAvogadro’slaw,thevolumeofonemoleofanygasatStandard
TemperatureandPressure(STP=273Kand1atm)is22.4L.
TwoimportantGasLawsarerequiredinordertoconverttheexperimentally
determinedvolumeofhydrogengastothatatSTP.
1. Dalton’slawofpartialpressures.
2. Combinedgaslaw.
Dalton’sLawofPartialPressures
AccordingtoDalton’slawofpartialpressuresinamixtureofnon-reactinggases,the
totalpressureexertedisequaltothesumofthepartialpressuresoftheindividual
gases.
Forinstance,ifthereisamixtureoftwogaseswhoseindividualpartialpressures
areP1andP2,thenthetotalpressureexertedbythetwogases,PTisgivenby:
PT=P1+P2 Equation2
2
Inordertoseehowthislawappliestothecurrentexperiment,itisimportantto
understandtheexperimentalsetup.Asstatedabove,thereactionbetween
magnesiummetalandaqueoushydrochloricacidwillbeconductedinaeudiometer.
SeeFigure1below.
H2(g)+H2O(g)
Patm
HCl(aq)
Mg(s)
Water
FIGURE1:EXPERIMENTALSETUP
Themagnesiummetalisattachedtothestopperoftheeudiometer.Theaqueous
hydrochloricacidisintheeudiometer.Theinvertedeudiometerisplacedinsidea
waterbath.Whenthemetalcomesincontactwiththeacid,thereactionproduces
hydrogengas.Thehydrogengasfillstheeudiometer.Thereactioncontinuesuntilall
themagnesiummetal(whichisthelimitingreagentinthisexperiment)is
completelyconsumed.
AsshowninFigure1,theH2(g)thatisformediscombinedwithwatervapor.The
watervaporisaresultofthevaporpressureofwaterfoundintheaqueousmedium.
Therefore,thetwogases:H2(g)andH2O(g)arebothfoundintheeduiometer.
Assumingthesurfaceofliquidinteeudiometerislevelwiththewateroutside,the
totalpressureofthegasesinsidetheeudiometeristhesameastheatmospheric
pressure.Abarometerthatisfoundinthelaboratoryisusedtodeterminethe
atmosphericpressure.
Therefore,accordingtoDalton’slaw:
3
Patm = PH 2 + PH 2O Equation3
Intheaboveequation, PH 2 isthepartialpressureofthehydrogengasproducedin
PH 2O isthevaporpressureofwateratthetemperatureatwhich
theexperimentand
€
theexperimentedisconducted.
€
Thepressure,volume,andtemperatureoftheH2(g)producedintheexperimentare
€
neededtocalculatethemolarvolumeofthegasatSTP.ThereforeEquation3is
rearrangedasfollows:
PH 2 = Patm − PH 2O Equation4
Thevaporpressureofwatervarieswithtemperature.Thevaporpressureofwater
atthetemperature(T,inKelvin)atwhichtheexperimentisconductedmaybe
€
approximatelydeterminedusingthefollowingformula(theoriginoftheformulais
beyondthescopeofthecurrentdiscussion).
#
5132 &
Equation5
PH 2O = exp%20.386 −
(mmHg $
T '
CombinedGasLaw
€
Asdiscussedintheprevioussection,theexperimentallowsforthedeterminationof
pressure,volume,andtemperatureofH2(g).Avogadro’slawspecifiesthatthevolume
ofonemoleofanygasatSTPis22.4L.
Thereforetwocalculationsarenecessarytodeterminethemolarvolumeofagasat
STPusingtheexperimentalresults.
1. ThevolumeofthegasatSTPiscalculatedusingthecombinedgaslaw.
2. Thestoichiometryofthereaction(Equation1)isusedtodeterminethe
numberofmolesofthegasproduced.
Themathematicalformofthecombinedgaslawisgivenbelow:
P1V1 P2V2
Equation6
=
T1
T2
InEquation6,assumethatthevaluesofpressure,volume,andtemperature(in
Kelvin),obtainedfromtheexperimentarerespectively,P1,V1,andT1.Then,V2
€
wouldbethevolumeatSTP,P2is1atmandT2is273K.Thesevaluesshouldbe
substitutedinEquation6tosolveforV2.
4
Finally,themolesofH2(g)producedintheexperimentmustbedeterminedinorder
toobtainthevolumeofonemoleofthegas.Theexperimentisdesignedsuchthat
themagnesiummetalisthelimitingreagent.Therefore,ifthemassofthe
magnesiummetalisknown,themolesofH2(g)producedcaneasilybedetermined
usingthereactionstoichiometery(Equation1).
SampleDataandCalculation
Inacertainexperiment,0.0369gramsofmagnesiumwasreactedwithexcessHCl.
Thereactionresultedin38.2mLofH2(g)at22°C.Thebarometricpressurewas
recordedas749.2mmofHg.CalculatethemolarvolumeofthegasatSTP.
Massofmagnesiummetal=0.0369grams
Atomicmassofmagnesiummetal=24grams/mol
Molesofmagnesiummetal=0.00154moles
Mg(s)+2HCl(aq)!MgCl2(aq)+H2(g)
1 mole H 2
MolesofH2(g)=MolesofMg×
=0.00154moles
1 mole Mg
TemperatureofH2(g)=22°C=295K=T1
€
#
5132 &
CalculatethePH2Ousingequation5: PH 2O = exp%20.386 −
(mmHg
$
T '
PH2O=19.89mmofHg
€
Barometricpressure=749.2mmofHg
PH2=749.2–19.89=729.31mmofHg=P1
VolumeofH2(g)=38.2mL=0.0382L=V1
AtSTP:
Pressure=760mmofHg=P2
Temperature=273K=T2
UseEquation6tosolveforV2:
5
V2 =
€
P1V1 T2 729.31mmHg × 0.0382L × 273K
×
=
= 0.0339L
T1
P2
295K × 760mmHg
MolesofH2=0.00154moles
0.0339L
L
= 22.0
mol Thereforemolarvolume= 0.00154moles
€
ExperimentalDesign
Asmallpieceofmagnesiummetalwillbetiedtothestopperofaeudiometer.The
eudiometerisfilledwithaqueoushydrochloricacid.Theeudiometerwillbe
invertedandsuspendedintoawaterbath.Thevolumeandtemperatureofthegas
shouldberecorded.Also,theatmosphericpressureshouldberecordedfromthe
barometerinthelaboratory.
ReagentsandSupplies
Magnesiummetal,6Mhydrochloricacid
50-mLeudiometer,600-mLbeaker,thermometer,copperwire,sandpaper
(SeepostedMaterialSafetyDataSheets)
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7
Procedure
1. Obtaina50-mLeudiometerandathermometerfromthestockroom.Alsoobtain
aburetstandandclampfromthelaboratory.
2. Placea100-mLgraduatedcylinderinanempty600-mLbeaker.Clampthe
graduatedcylinderinplaceandfillthegraduatedcylinderwithwatertotherim.
3. Cuta2-cmstripofmagnesiummetalandscrapethemetalwithsandpaperto
removeanydarkoxides.
4. Measurethemassofthemagnesiummetal.[NOTE:Themagnesiumisthe
limitingreagentinthisexperiment]
5. Coilthemagnesiumstrip.Usingthecopperwire,attachthemagnesiummetalto
theinsideofthestopperfortheeudiometer,byformingawirecagearoundthe
magnesiummetal.
6. Add10mLof6MHClintotheeudiometer.
7. Filltheremainderoftheeudiometerwithdeionizedwaterslowly,attempting
thedisturbtheHClaslittleaspossible.[NOTE:Normally,concentratedacidis
addedtowaterfordilutionpurpose.Inthisstep,thereverseprocessisbeing
recommended.Caremustbetakentoavoidspillsorsplashing.]
8. Sealtheeudiometerwiththestopper.Placethestopperedeudiometerabovethe
100-mLgraduatedcylindercontainingwaterandturnitupsidedown.Immerse
thestopperendoftheeudiometercompletelyunderwater.
9. Clamptheeudiometertotheburetstand.Thereactionbetweenthemagnesium
metalandtheHClwillstartmomentarilyandhydrogengaswillcollectinthe
eudiometer.Theaqueoussolutionwillbepushedoutthroughthestopperinto
the100-mLgraduatedcylinder,whichwilloverflowintothe600-mLbeakerthat
thegraduatedcylinderisplacedin.
10. Whenthereactioniscomplete,movetheeudiometersothatthelevelofthe
waterintheeudiometerisequalwiththewaterinside.Ifthisisnotpossible,
recordthedifferenceinheightbetweentheeudiometerandthegraduated
cylinder.
11. Measureandrecordthevolumeofthehydrogengas.
12. Recordthetemperatureofthewaterandassumethistobethetemperatureof
thehydrogengas.
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13. Recordthebarometricpressure.
14. Emptythecontentsoftheeudiometerintothe600-mLbeakerandthecontents
ofthe600-mLbeakerintothewastecontainerprovidedbytheinstructor.Rinse
theeudiometerwithdeionizedwater.
15. Repeatsteps3-14.
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DataTable
Massofmagnesium
(grams)
VolumeofH2(g),L
TemperatureofH2(g),K
Barometricpressure,
mmofHg
Heightdifference
betweeneudiometer
andgraduatedcylinder
Trial1
Trial2
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Calculations
€
€
MOLARVOLUMEOFAGASATSTP
Trial1
Massofmagnesium,
grams
Atomicmassof
magnesium(grams/mol)
MolesofMagnesium
MolesofH2(g)
(usestoichiometry)
TemperatureofH2(g)
(T1inKelvin)
VolumeofH2(g)
(V1inL)
Barometricpressure
(PTinmmofHg)
PH 2O(g ) (mmofHg)
(useEquation5)
PH 2 (g ) (sameasP1)(mmof
Hg)(useEquation4)
VolumeofH2(g)atSTP
(V2inL)(useEquation6)
MolarvolumeofH2(g)at
STP(L/mol)
Percenterror
Trial2
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ATOMICMASSOFAMETAL
Assumethattheidentityofthemetalusedintheexperiment(i.e.,magnesium)is
unknown.Assumealsothatthestoichiometryofthereactionbetweentheunknown
metalMandHClisasfollows:
M(s)+2HCl(aq)!MCl2(aq)+H2(g)
Usingthedatacollected,calculatetheatomicmassofthemetalM
Trial1
Trial2
TemperatureofH2(g)
(T1inKelvin)
VolumeofH2(g)
(VinL)
Barometricpressure
(PTinmmofHg)
PH 2O(g ) (mmofHg)
(useEquation5)
PH 2 (g ) (mmofHg)(use
Equation4)
MolesofH2(g)produced
(HINT:PV=nRT)
Molesofmetal(use
stoichiometry)
Massofmetalingrams
(fromthedatatable)
Atomicmassofmetal
" grams %
$
'
# moles &
AveragevalueofAtomic " grams %
mass $
'
# moles &
€
€
€
€