1
EXPERIMENTB4:CHEMICALEQUILIBRIUM
LearningOutcomes
Uponcompletionofthislab,thestudentwillbeableto:
1) Analyzetheabsorbancespectrumofasample.
2) Calculatetheequilibriumconstantforachemicalreactionusingdata
obtainedbyspectrophotometricmethods.
Introduction
ElectromagneticSpectrum
Awaveisoftendefinedasa“vibratingdisturbancebywhichenergyistransmitted”.
Anelectromagneticwaveisatypeofwavethathasassociatedwithitanelectrical
fieldandamagneticfieldthatareperpendiculartooneanother.Lightthatcanbe
seenbythenakedeye,alsoknownasvisiblelight,isanexampleofan
electromagneticradiation.Wavessuchasradiowaves,microwaves,orx-raysare
alsoexamplesofelectromagneticradiation.
Mathematically,wavessuchaselectromagneticwavesareknownaspropagating
waves,andcanberepresentedbyarepeatingorperiodicfunctionuchassinewave.
Therearethreecharacteristicpropertiesassociatedwiththesekindsofwaves:
1. Wavelength(λ)-thedistancebetweenidenticalpointsonsuccessivewaves
2. Frequency(ν)-thenumberofwavesthatpassthroughaparticularpointina
second
3. Amplitude-theheightofthepeakortroughofawave.
Whatmakesoneelectromagneticwavedifferentfromanotherwaveisthe
wavelengthandfrequencyassociatedwithit.Thesetwoareinverselyrelatedto
eachaccordingtotheformula:
c=νλ,wherecisthespeedoflight=3.00×108m/s
Theelectromagneticspectrum(Figure1)isanarrangementofthedifferentkindsof
wavesintheorderofincreasingwavelengths(ordecreasingfrequencies).
2
Wavelength(nm)
10-2
100
Gamma
X-ray
ray
1020
400nm 1018
102
U
V
1016
104
Infrare
d
1014
106
Micro-
wave
1012
1010
1012
Radiowaves
1010 Frequency(s
108
106 -1)
108
700nm
FIGURE1
Asmentionedabove,electromagneticradiationatcertainwavelengths,isvisibleto
thehumaneye,rangingfromredlightwithlongerwavelengths(~700nm)toviolet
lightwithshorterwavelengths(~400nm).
Asolutioncontainingasubstancethatabsorbslightinthevisibleregionofthe
electromagneticspectrumwillappearcoloredtotheeye.Thecolorthatisobserved
dependsonthewavelengthoftheradiationthatsubstanceabsorbs.Forinstance,if
youlookatasolutionofvitaminB2(alsoknownasriboflavin)underawhitelight,it
appearsyellowincolor.AsolutionofvitaminB2absorbsthemaximumlightata
wavelengthof450nm.FromFigure1,lightwithawavelengthof450nm
correspondstoviolet-bluelight.Themoleculesofriboflavinthereforeareabsorbing
theviolet-bluepartsofthevisiblelight,andalltherestofthevisiblelightwillnotbe
absorbedbutinsteadtransmittedthroughthesolution.Theriboflavinisessentially
removingtheblue-violetlightfromthewhitelightandasaresultthecoloryou
observeforriboflavinisamixtureoftherestofthe“un-absorbed”colors.Ingeneral
thecolorofasolutionthatcanbeobservedbythehumaneyeisthe“complement”of
thecolorofthelightitabsorbs.Thefollowing“color-wheel”isarepresentationof
complementarycolors(Figure2).
3
Violet
400-420nm
Red
630-720nm
Deepblue
420-450nm
Orange
580-630nm
Lightblue
450-490nm
Yellow
545-580nm
Green
Yellow-green
490-530nm 530-545nm
FIGURE2
Inthecaseofriboflavinsincethesolutionabsorbedlightwithawavelengthof450
nmcorrespondingtobluelight,itshouldappeartobeyellowtoyellow-green,which
arethecomplementarycolors.Andindeed,asolutionofriboflavindoesappeartobe
yellowincolor.
Spectrophotometry
Aspectrophotometerisaninstrumentusedtomeasuretheamountoflightthata
sampleabsorbs.Thismethodisknownasspectrophotometry.Theinstrument
operatesbypassingabeamoflightthroughasampleandmeasuringtheintensityof
thetransmittedlightreachingadetector.Themostbasicarrangementofa
spectrophotometerisshowninFigure3.
Sourceof
light
Sample
FIGURE3
Light
detector
However,asdiscussedbeforedifferentsamplesabsorblightofdifferent
wavelengths.Theamountoflightabsorbedbythesamplewilldependonthe
wavelengthofthelight.Inordertoselectlightofaparticularwavelengthtoshineon
thesample,thelightmustpassthroughamonochromator,whichisessentiallya
filterthatallowsaselectedwavelengthoflighttopassthroughthesample.
Whenanalyzingasampleforthefirsttime,itisunlikelythatonewillknowthe
wavelengthatwhichthesampleabsorbsmaximumlight.Thereforethecomplete
absorbancespectrumofthesamplemustfirstbedetermined.Theabsorbance
spectrumshowshowtheabsorbanceoflightdependsuponthewavelengthofthe
light.Thespectrumisaplotofabsorbance(y-axis)versuswavelength(x-axis).The
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wavelengthatwhichtheabsorbanceisthehighestisoftendenotedasλmax.Theλmax
ischaracteristicofeachcompoundandprovidesinformationontheelectronic
structureoftheanalyte.
Theabsorbanceofaparticularsolutiondependsonanotherimportantparameter:
theamountoftheanalytepresentinthesolution.
Beer’slawstatesthattheabsorbanceisdirectlyproportionaltothenumberof
moleculesperunitvolumeoflight-absorbingcompoundthroughwhichthelight
passes.ThemathematicalformcorrespondingtoBeer’slawisgivenby:
A=ε×c×l
Thevariablesintheaboveequationare:
• A=absorbanceofthesample(thisisaunit-lessquantity)
• c=concentrationoftheanalyte(typicallyinunitsofMolarityormoles/liter)
• ε=molarextinctioncoefficient(unitsofMolarity-1cm-1)
• l=pathlengththroughwhichlighttravels
Thepathlengthdependsonthespectrophotometerandthesampleholderor
cuvettebeingusedandistypically1.00cmformostinstruments.Theextinction
coefficientεthatisusedintheaboveequationisaconstantforaparticularsample
ataparticularwavelength.Theextinctioncoefficientforseveralsubstanceshas
beenexperimentallydetermined.
ChemicalEquilibrium
Inthisexperiment,theanalyticalmethodofspectrophotometrydescribedinthe
precedingsectionwillbeusedtoexaminethechemicalequilibriumofaparticular
reaction.Asshouldbeevidentfromtheearlierdiscussion,inordertousethis
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analyticalmethod,thechemicalsubstancesstudiedmustabsorblightinthevisible
regionoftheelectromagneticspectrum.
Thereactionthatwillbestudiedisbetweenaqueoussolutionsoftheiron(III)ion
(Fe3+)andthiocyanateion(SCN−).Theionicequationforthereactionandthe
expressionfortheequilibriumconstantaregivenbelow.
3+
−
Feaq
+ SCN aq
⇔ Fe(SCN) 2+
aq
[Fe(SCN) 2+ ]eq
KC =
3+
−
[Fe ]eq [SCN ]eq
Atthewavelengthofmaximumabsorbance,λmax,themolarextinctioncoefficient,ε,
fortheproduct,Fe(SCN)2+,is6120M-1cm-1.Sincetheinitialconcentrationsofthe
€
reactantsareknownandtheproductconcentrationisrelatedtoitsabsorbance,the
methodofspectophotometrycanbeusedtodeterminetheequilibriumconstantfor
thisreaction.
AssumethattheinitialconcentrationofFe3+isAandthatofCNS−isB.Thefollowing
tabledescribeshowtheconcentrationsofallionsatequilibriumcanbedetermined.
Sincetheionsareallina1:1stoichiometricrelationshipwitheachother,the
amountofoneoftheionsconsumedintermsofconcentration(-x)willbethe
sameamountastheotherionconsumedandwillresultinanequalamountof
productbeingformed(+x).
Fe3+ +
SCN− ⇔ Fe(SCN)2+
Initialconcentrations
A
B
0
€ -x
Amountreactedtoreachequilibrium
-x
+x
Equilibriumconcentrations
A-x B-x x
x
KC =
(A − x)(B − x)
Since“A”and“B”areknownquantities,inordertodeterminetheequilibrium
constantKC,itisnecessarytodeterminethechangeinconcentration“x”.Fortuntely,
€
thechangeinconcentrationisequaltotheequilibriumconcentrationofthe
complex,Fe(SCN)2+.
Theequilibriumconcentrationofthecomplex,Fe(SCN)2+,canbedeterminedby
measuringitsabsorbanceatλmaxandemployingBeer’slaw:
6
A
ε×l
ε = 6120M −1cm −1 l = 1cm
Thevalueof“l”(thepathlength)isspecifictothespectrophotometer.The
spectrophotometersusedinthislaboratoryhaveapathlengthof1.00cm.
€
C=x=
ExperimentalDesign
7
0.00200MaqueoussolutionsofFe3+andSCN−areprovided.Thesesolutionsare
preparedin0.50MHNO3.Differentinitialconcentrationsofthesetwosolutionswill
becombinedtoformtheFe(SCN)2+complex.Theabsorbanceoftheequilibrium
mixturewillbemeasuredatλmaxusingaspectrophotometer.
Theλmaxforthecomplex,Fe(SCN)2+,mustfirstbedetermined.Inordertodothis,
thecompleteabsorbancespectrumofthecomplex(from370nmto700nm)must
beobtained.
ReagentsandSupplies
0.00200MFe3+,0.00200MSCN−,0.50MHNO3
Spectrophotometer,cuvettes
(SeepostedMaterialSafetyDataSheets)
Procedure
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PART1:DETERMINATIONOFλMAXFORFe(SCN)2+
1. Obtaintwocuvettesandaspectrophotometer.Powerupthespectrophotometer
andallowtheinstrumenttowarmupfor10minutes.Theinstructorwill
demonstratetheproperuseofthespectrophotometer.
2. Inalargetesttubecombine4.00mlofFe3+and3.00mlofSCN−.Thoroughlymix
thecontentsandallowthemixturetoequilibrate(~5minutes).
3. Fillonecuvettewith0.50MHNO3(thiswillbethe“blank”)andthesecond
cuvettewiththeFe(SCN)2+complexpreparedinstep2(thiswillbethe
“sample”).
4. Wipethesidesofthecuvetteswithkimwipesandmakesurethereareno
smudgesorfingerprints.
5. Setthewavelengthofthespectrophotometerto370nm.
6. Ensurethatthereisnosampleinthesamplecompartmentandthatthelidtothe
compartmentisclosed.Setthespectrophotometertotransmittancemode.Using
theappropriatecontrols,adjustthetransmittancetozero.
7. Placethecuvettecontainingthe“blank”insidethesamplecompartment,align
theguidemarkonthecuvettewiththeguidemarkatthefrontofthesample
compartment,andclosethelid.Setthespectrophotometertoabsorbancemode.
Usingtheappropriatecontrolsadjusttheabsorbancereadingtozero.
8. Nowplacethecuvettecontainingthe“sample”insidethesamplecompartment,
aligntheguidemarkonthecuvettewiththeguidemarkatthefrontofthe
samplecompartment,closethelidandrecordtheabsorbance.
9. Changethewavelengthto380nmandthenrepeatSteps6through8.Continue
thisprocessin10nmincrementsofthewavelength,untilabsorbancevalues
havebeenrecordedat700nm.
10. Emptythecontentsofthecuvettesintoalargebeakerlabeledas“Waste”.Rinse
andcleanthecuvettes.Disposeallthereagentsinanappropriatelabeledwaste
containerprovidedbytheinstructor
11. Plotagraphofabsorbance(y-axis)vs.wavelength(x-axis).Fromtheplot
determinethewavelengthatwhichtheabsorbancemaximumisfound.This
wavelengthwillbeusedforallsubsequentmeasurements.
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PART2:DETERMINATIONOFKCFORTHEREACTIONBETWEENFe3+ANDSCN−
1. Obtainaspectrophotometerandturnthepoweronandallowtheinstrumentto
warmupforatleast10minutes.
2. Obtainninelargetesttubesandnumberthemfrom1to9.
3. CombineFe3+andSCN−ineachofthetesttubesaccordingtothefollowingtable.
Thesewillbethe“sample”testtubes.Thoroughlymixthecontentsafter
combiningthetwosolutionsandallowtheresultingmixturetoequilibrateforat
leastfiveminutes.
SolutionNumber Fe3+(mL),SolutionA SCN−(mL),SolutionB
1
0.50
3.00
2
1.00
2.50
3
1.25
2.25
4
1.50
2.00
5
1.75
1.75
6
2.00
1.50
7
2.25
1.25
8
2.50
1.00
9
3.00
0.50
4. Measurethetemperatureoftheequilibriummixture.Thetemperatureisnot
usedinanyofthecalculations.Butequilibriumconstantvaluesarealways
reportedataparticulartemperatureasthevaluechangeswithtemperature.
5. Inanothercuvetteobtainabout3.50mLofnitricacid.Thiswillserveasthe
“blank”.
6. SetthewavelengthofthespectrophotometertothevaluedeterminedfromPart
1oftheexperiment.Calibratethespectrophotometerusingthemethod
describedinPart1:Steps6&7.
7. Recordtheabsorbancevaluesofeachoftheninesamples(usethemethod
describedinPart1(Step8).
8. Disposeallthereagentsinanappropriatelabeledwastecontainerprovidedby
theinstructor.
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DataTable
PART1:DETERMINATIONOFλMAXFORFe(SCN)2+
Wavelength(nm)
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
Absorbance
11
PART2:DETERMINATIONOFKCFORTHEREACTIONBETWEENFe3+ANDSCN−
Solution Absorbance
1
2
3
4
5
6
7
8
9
Temperatureoftheequilibriummixture=
DataAnalysis
12
PART1:DETERMINATIONOFλMAXFORFe(SCN)2+
1. Drawagraphofabsorbance(y-axis)vs.wavelength(nm).
2. Fromtheplot,identifythewavelengthatwhichthemaximumabsorbance
occurs.Therewillbetwoabsorbancemaximainthisspectrum.Usethelargerof
thetwowavelengthsforallsubsequentmeasurements.
GRAPH
Theλ maxforFe(SCN)2+wasfoundtobe=
13
PART2:DETERMINATIONOFKCFORTHEREACTIONBETWEENFe3+ANDSCN−
Thenetionicequationandtheexpressionfortheequilibriumconstantforthe
reactionbetweenFe3+andSCN−isgivenby:
3+
−
Feaq
+ SCN aq
⇔ Fe(CNS) 2+
aq
[Fe(CNS) 2+ ]eq
KC =
[Fe 3+ ]eq [CNS − ]eq
Asmentionedbefore,iftheinitialconcentrationofFe3+isAandthatofCNS−isB,
€
thenthefollowingtabledescribestheequilibriumprocess.
Fe3+ +
SCN− ⇔ Fe(SCN)2+
Initialconcentrations
A
B
0
€ -x
Amountreactedtoreachequilibrium
-x
+x
Equilibriumconcentrations
A-x B-x x
x
KC =
(A − x)(B − x)
Theequilibriumconcentrationofthecomplex,Fe(SCN)2+,canbedeterminedfrom
itsabsorbanceatλmaxandemployingBeer’slaw.
€
A
C=x=
ε×l
ε = 6120M −1cm −1 l = 1cm
€
1. FirsttheinitialconcentrationsofFe3+andSCN−mustbedeterminedforeachof
thesixreactionconditions.
Forinstance,insample1(0.50mLofFe3++3.00mLofSCN−):
0.50mL × 0.00200M
= 0.000286M ConcentrationofFe3+inthemixture=
3.50mL
3.00mL × 0.00200M
= 0.00171M ConcentrationofSCN−inthemixture=
3.50mL
€
€
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DeterminetheconcentrationsofFe3+andSCN−inallthesamplesinthesame
manner.
SolutionNumber Fe3+(mL) [Fe3+],M=A SCN−(mL) [SCN−],M=B
1
0.50
0.000286
3.00
0.00171
2
1.00
2.50
3
1.25
2.25
4
1.50
2.00
5
1.75
1.75
6
2.00
1.50
7
2.25
1.25
8
2.50
1.00
9
3.00
0.50
2. Determinetheconcentrationofthecomplex,Fe(SCN)2+,foreachofthesix
solutionsfromtheabsorbancevalue.
A
Solution Absorbance
= x =
[Fe(SCN)2+],M=
6120
1
2
3
4
5
6
7
8
9
€
15
3. CalculatetheequilibriumconstantKCforeachreactionusingtheformula:
x
KC =
(A − x)(B − x)
Solution
KC
€
1
2
3
4
5
6
7
8
9
AVERAGE
STANDARDDEVIATION
NOTE:Equilibriumconstantvaluesaretemperaturedependent.Besuretomeasure
thetemperatureofthesolutionandreporttheaveragevalueoftheequilibrium
constantatthespecifictemperatureatwhichtheexperimentwasconducted.
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Result
Theequilibriumconstant,KC,forthereactionbetweenaqueoussolutionsofFe3+and
SCN−,whichresultedinthecomplexFe(SCN)2+,wasfoundtobe(specifythe
temperature):