1
EXPERIMENTB8:EFFECTOFTEMPERATUREONEQUILIBRIUMCONSTANT
LearningOutcomes
Uponcompletionofthislab,thestudentwillbeableto:
1) Predicttheeffectoftemperatureontheequilibriumconstant.
2) Designanexperimenttomeasurethethermodynamicparametersforthe
dissolvingofmetalhydroxidesinwater.
Introduction
Whenioniccompoundsaredissolvedinwater,itisgenerallyassumedthat
increasingthetemperaturewillcausemoreofthesolidtodissolve.However,this
assumptionisnotalwaystrue,aswillbedemonstratedinthisexperiment.
Inthisexperiment,calciumhydroxidewillbedissolvedinwaterandtheeffectof
temperatureonthisprocesswillbestudied.Thedatafromtheexperimentwillnot
onlybeusedtodeterminetheeffectoftemperatureontheequilibriumconstant,but
alsotodeterminethermodynamicparameterssuchasΔH,ΔS,andΔGforthe
process.
Severalconceptsdiscussedthroughoutthisclasswillbeexaminedinthis
experiment.Theseinclude:
a. Effectoftemperatureonequilibrium
b. RelationshipbetweenpHandequilibriumconstantforasaturatedsolution
c. DeterminationofthermodynamicparameterssuchasΔHandΔS.
Effectoftemperatureonequilibrium
AccordingtoLeChatelier’sprinciple,“whenasystematequilibriumissubjectedto
changeinconcentration,temperature,volume,orpressure,thenthesystem
readjustsitselfto(partially)counteracttheeffectoftheappliedchangeandanew
equilibriumisestablished”.
Inthissection,theeffectoftemperatureontheequilibriumprocesswillbefurther
examined.
Theeffectoftemperatureontheequilibriumprocessdependsonwhetherthe
reactionisexothermicorendothermic.Exothermicreactionsarethoseinwhichthe
systemgeneratesheatandasaresultheatmaybeconsideredasaproduct(an
output)ofthesereactions.Ontheotherhand,endothermicreactionsarethosein
whichthesystemabsorbsheatandasaresultheatmaybeconsideredasareactant
(aninput)ofthesereactions.
2
ConsidertheexothermictransformationofAtoB.Sinceheatisgeneratedinthis
reaction,theequationcanbewrittenas:
A ⇔ B+heat
Ifheatisaddedtothisreaction,i.e.,ifthetemperatureisincreased,theequilibrium
willshiftleftandproducemoreA.Conversely,ifheatisremovedfromthisreaction,
€
i.e.,ifthetemperatureisdecreased,theequilibriumwillshiftrightandproduce
moreB.
Therefore,ingeneral,increasingthetemperatureofanexothermicreactionshifts
theequilibriuminthedirectionofthereactantsandviceversa.
Now,considertheendothermictransformationofCtoD.Sinceheatisabsorbedin
thisreaction,theequationcanbewrittenas:
C+heat ⇔ D
Ifheatisaddedtothisreaction,i.e.,ifthetemperatureisincreased,theequilibrium
willshiftrightandproducemoreD.Conversely,ifheatisremovedfromthis
€
reaction,i.e.,ifthetemperatureisdecreased,theequilibriumwillshiftleftand
producemoreC.
Therefore,ingeneral,increasingthetemperatureofanendothermicreactionshifts
theequilibriuminthedirectionoftheproductsandviceversa.
RelationshipbetweenpHandequilibriumconstantforasaturatedsolution
Asaturatedsolutionisobtainedwhenthemaximumamountofsolutehasbeen
dissolvedinagivenamountofsolvent.Inasaturatedsolutionofanionicsubstance
inwater,thesoluteisinequilibriumwiththeaqueousions.Forinstance,ina
saturatedsolutionofcalciumhydroxide:
Ca(OH)2(s) ⇔ Ca2+(aq)+2OH−(aq)
Theequilibriumconstantforthisprocessisgivenby:
€
K=[Ca2+][OH−]2
NotetheabsenceofCa(OH)2(s)intheexpressionfortheequilibriumconstant.Since
theamountofasolidisgenerallythoughttobeunchanged,itisexcludedfromthe
equilibriumconstantexpression.
Thefollowingequilibriumtableshowshowtheequilibriumconstantiscalculated
forsuchaprocess.Inthetable,“I”isassumedtobesomeinitialamountofthesolid
3
calciumhydroxide,and“x”istheamountofthesolidthatdissolvesinwatertoform
theaqueousions.
⇔ Ca2+(aq)
Ca(OH)2(s)
+
2OH−(aq)
Initialconcentrations
I
0
~0
Amountthatdissolves
-x € +x
+2x
Equilibriumamount I–x x
2x
Therefore:
K = [Ca 2+ ][OH − ]2
K = x × (2x) 2 = 4 x 3
InordertodeterminetheequilibriumconstantK,“x”mustbeknown.
€
Howcan“x”bedeterminedexperimentally?
Inapreviousexperiment(ExperimentB4),“x”wasdetermined
spectrophotometrically.Inthatcase,theproductwascoloredandsucha
determinationwasthereforepossible.
Inthissituationhowever,spectrophotometricdeterminationisnotasimpleoption.
Acloseexaminationoftheequilibriumtableaboveshowsthat:
2x=[OH−]
[OH − ]
Therefore: x =
2
Theconcentrationofhydroxide,[OH−],isrelatedtothehydrogenionconcentration,
[H+],andthereforetothepHofthesolution,bytheionicproductofwater.
€
KW=1.0×10-14=[H+]×[OH−]
pH=-log[H+]
Insummary,ifthepHofthesaturatedsolutionisdetermined,the[H+]canbe
ascertained.Usingtheionicproductofwater,onecanthendeterminethe[OH−].
Knowingthe[OH−]onecancalculate“x”andthereforeK.
4
DeterminationofthermodynamicparameterssuchasΔH,ΔS,andΔG
Asdiscussedearlier,chemicalequilibriumisimpactedbychangesintemperature.
Therelationshipbetweentheabsolutetemperature,T,andtheequilibrium
constant,K,forareactionisgiveninEquation1below:
ΔG°=-RTlnK Equation1
InEquation1,ΔG°isthestandardfreeenergychangeandRistheuniversalgas
constant(8.314J/mol-K).
Bydefinition,thestandardfreeenergychange,ΔG°isalsorelatedtothestandard
enthalpychange,ΔH°andthestandardentropychange,ΔS°accordingtoEquation2.
ΔG°=ΔH°-TΔS° Equation2
Inthermodynamics,thevaluesofΔH°andΔS°maygenerallybeconsideredtobe
invariablewhenthetemperatureischangedandthevalueofΔG°ontheotherhand
changeswithtemperature.
Therefore,Equations1and2maybecombinedasfollows:
−RTlnK=ΔH°−TΔS°
Equation3
Equation3canfurtherbemanipulatedtoisolatethedependentvariablesandthe
constants.Dividingbothsidesoftheequationby“-RT”resultsinEquation4.
ΔH ! ⎛ 1 ⎞ ΔS !
lnK = −
⎜ ⎟+
Equation4
R ⎝T ⎠ R
InEquation4,ΔH°,ΔS°,andRareconstantsandKandTarevariables.
€
AcomparisonofEquation4withtheequationofastraightline,y=mx+b,indicates
thefollowing:
lnKisanalogoustoy
1
isanalogoustox
T
ΔH !
−
isanalogoustom
R
ΔS !
€
isanalogoustob
R
€
€
5
1
shouldresultinastraightline
T
ΔH !
ΔS !
whoseslopewillbe −
andwhosey-interceptwillbe
.SinceRisthe
R
R
universalgasconstant,thevaluesofΔH°andΔS°canbedeterminedfromtheslope
€
andtheintercept,respectivelyofthebestfitline.
€
€
ThereforealinearregressionofaplotoflnKvs.
ExperimentalDesign
6
Asaturatedsolutionofcalciumhydroxidewillbeprovidedforthisexperiment.This
solutionwillbeheatedtoabout70°CandthepHofthesolutionwillbedetermined
usingapHmeter.Thesolutionshouldthenbecooledinabout5°Cintervalsdownto
about5°CandthepHdeterminedateachintermediatetemperature.ThepHofthe
solutionwillbeusedtodeterminethe[H+]ateachtemperature.Thiswillthenbe
convertedto[OH−]andthenKateachtemperature.AplotoflnKvs.1/Twillbeused
todeterminethevariousthermodynamicparameters.
ReagentsandSupplies
SaturatedsolutionofCa(OH)2,pHmeter,hotplate,thermometer
(SeepostedMaterialSafetyDataSheets)
Procedure
7
1. ReadthecompleteinstructionmanualfortheoperationofapHmeter.
2. ObtainapHmeter,thermometer,andahotplatefromthestockroom.
3. TheinstructorwilldemonstratetheproperuseandcalibrationofthepHmeter.
Theinstructorwillalsodemonstratehowtoadjustthetemperaturesettingof
thepHmeter.Thissettingmustbeadjustedforeachtemperatureatwhichthe
pHwillbemeasured.
4. Setupahotwaterbath.Inordertodothis,halffillalargebeakerwithtapwater
andplaceonahotplate.Heatthewatertoabout70-75°C.Monitorthe
temperaturewithathermometer.
5. Obtainabout10mLofsaturatedCa(OH)2solutioninalargetesttube.Adda
smallamountofsolidCa(OH)2tothetesttubetoensurethatthesolutionis
indeedsaturated.
6. Obtainaringstandandaclampandsuspendthetesttubecontainingthe
Ca(OH)2intothewaterbathensuringthatthesolutioniscompletelysubmerged
insidethewater.
7. MeasureandrecordthetemperatureoftheCa(OH)2solution.Aimtostart
measurementsataround70°C.
8. MeasureandrecordthepHoftheCa(OH)2solution.
9. Coolthewaterbathbyabout5°Cusingroomtemperaturewateratfirstandthen
coldwaterorice.Repeatsteps7and8andobtainmeasurementsinabout5°C
intervalsuntilthetemperaturehasreached5°C.
10. DiscardtheCa(OH)2solutioninanappropriatewastecontainerprovidedbythe
instructor.
8
DataTable
Temperature,°C
pH
9
DataAnalysis
1. Calculatethe[H+]fromthepHmeasuredateachtemperature.
[H + ] = 10 − pH 2. Calculatethe[OH−]
€
1.0 × 10 −14
[OH − ] =
[H + ]
3. Calculate“x”.
€
[OH − ]
x=
2
4. CalculateK.
€
K = 4 x 3
5. CalculatelnK(naturallogarithmofK)
€
1
6. ConvertalltemperaturestotheKelvinscaleandcalculate T
1
7. PlotagraphoflnK(y-axis)vs. (x-axis).
T
€
8. Useregressionanalysestofindtheequationofthebestfitlinearequationforthe
dataandobtaintheslope(m)andthey-intercept(b).
€
9. Usingtheslope,calculatethevalueofΔH°.
ΔH !
slope(m) = −
R !
ΔH = −( slope × R)
10. Usingthey-intercept,calculatethevalueofΔS°.
€
ΔS !
y − intercept =
R
!
ΔS = R × (y − intercept)
€
10
NOTE:Steps1through7ofthedataanalysismaybecompletedusingaspreadsheet
programsuchasMicrosoftExcel.
A
Temperature,T
°C
B
C
D
E
F
G
H
I
pH
[H+]
[OH−]
x
K
T,Kelvin
1/T
ln(K)
2
70
pH1
=10^(-B2)
=(1.0E-14)/C2
=D2/2
=4*((E2)^3)
=A2+273.15
=1/G2
=LN(F2)
3
65
pH2
4
60
pH3
5
55
pH4
6
50
pH5
7
45
pH6
8
40
pH7
9
35
pH8
10
30
pH9
11
25
pH10 12
20
pH11 13
15
pH12 14
10
pH13 5
pH14 1
15
1. Enterthedata(temperaturein°CandpH)incolumnsAandB.UseRow1for
columnheadings.
2. EnterformulasinRow2foreachcalculation,asshowninthetableabove.
3. Ineachcolumn,pointthecursortothebottomrightcornerofacell(sayC2)and
dragdown(tillRow15)theplussigntocopytheformulatotheothercells.
RepeatthisforallthecolumnsDthroughI.
4. Todrawagraph,selectthexandydata,whichwouldbedatainfieldsH:2-15
andI:2-15.
5. Click“Insert”andthen“Chart”.Choose“XY”scatterandselect“MarkedScatter”
6. Whenthegraphisdisplayed,clickonanydatapointonthechartandfromthe
toolbar,select“Chart”andthen“InsertTrendline”.
7. Fromthepop-upbox,selectthe“Options”tabandchecktheboxes:1)Display
equationand2)DisplayR-squaredvalueandclickOK.
Results
11
1. Whathappenstotheequilibriumconstantfortheprocessofdissolving
Ca(OH)2(s)inwater,whenthetemperatureisincreased?
2. Basedontheobservationreportedinquestion1,commentontheeffectof
temperatureonthesolubilityofcalciumhydroxide.
3. Theexperimentalvaluesofthethermodynamicparametersforthedissolvingof
Ca(OH)2(s)inwaterare:
ΔH°=_______________________kJ/mol
ΔS°=______________________J/mol-K
4. Aretheresultsconsistentwiththeobservations?
5. Usethermodynamictablestodeterminethetheoreticalvaluesofthe
thermodynamicparameters.Thetheoreticalvaluesofthethermodynamic
parametersfordissolvingofCa(OH)2(s)inwaterare(showeachcalculation):
ΔH°=_______________________kJ/mol
ΔS°=______________________J/mol-K
6. Thepercentageerrorintheexperimentalresultsare:
ΔH°=_______________________
ΔS°=_______________________
7. Whatarethesourcesoferrorinthisexperiment?
12