QuantitativeAnalysis

定量分析Chapter24

IntroductiontoSpectrochemicalMethods

Measurementsbasedonlightandotherformsofelectromagneticradiationarewidelyusedthroughoutanalyticalchemistry.Theinteractionsofradiationandmatterarethesubjectofthesciencecalledspectroscopy.Spectroscopicanalyticalmethodsarebasedonmeasuringtheamountofradiationproducedorabsorbedbymolecularoratomicspeciesofinterest.Classification

Wecanclassifyspectroscopicmethodsaccordingtotheregionoftheelectromagneticspectruminvolvedinthemeasurement.Theregionsinclude–ray,X-ray,ultraviolet(UV),visible,infrared(IR),microwave,andradiofrequency(RF).

Spectrochemicalmethodshaveprovidedthemostwidelyusedtoolsfortheelucidationofmolecularstructureaswellasthequantitativeandqualitativedeterminationofbothinorganicandorganiccompounds.PropertiesofElectromagneticRadiation

Electromagneticradiationisaformofenergythatistransmittedthroughspaceatenormousvelocities.Electromagneticradiationcanbedescribedasawavewithpropertiesofwavelength,frequency,velocity,andamplitude.Incontrasttosoundwaves,lightrequiresnosupportingmediumforitstransmission;thus,itreadilypassesthroughavacuum. Electromagneticradiationcanbetreatedasdiscretepacketsofenergyorparticlescalledphotonsorquanta.Thesedualviewsofradiationasparticlesandwavesarenotmutuallyexclusivebutcomplementary.

TheSpeedofLight

Inavacuum,thevelocity(c)oflightis2.99792x108ms-1andthevelocityoflightinairisabout0.03%less.Thus,foravacuum,orforair,thevelocityoflight: c==3.00x108ms-1=3.00x1010cms-1 Inamediumcontainingmatter,lighttravelswithavelocitylessthancbecauseofinteractionbetweentheelectromagneticfieldandelectronsintheatomsormoleculesofthemedium.Sincethefrequencyoftheradiationisconstant,thewavelengthmustdecreaseasthelightpassesfromavacuumtoamediumcontainingmatter. Thewavenumberisanotherwaytodescribeelectromagneticradiation.Itisdefinedasthenumberofwavespercentimeterandisequalto1/.Thehastheunitsofreciprocalcentimeters(cm-1)-TheparticleNatureofLight:Photons

Inmanyradiation/matterinteractions,itisusefultoconsiderlightasconsistingofphotonsorquanta.Wecanrelatetheenergyofphotontoitswavelength,frequency,andwavenumberby E=h=hc/=hc where,hisPlanck’sconstant(6.63x10-34Js).Thewavenumberandfrequency,incontrasttothewavelength,aredirectlyproportionaltothephotonenergyE.Theradiantpowerofabeamofradiationisdirectlyproportionaltothenumberofphotonspersecond.TheElectromagneticSpectrum Theelectromagneticspectrumcoversanenormousrangeofenergies(frequencies)andthuswavelengths.Usefulfrequenciesvaryfrom>1019Hz(-ray)to103Hz(radiowaves).AnX-rayphoton(3x1018Hz,

10-10m),forexample,isapproximately10,000timesasenergeticasaphotonemittedbyanordinarylightbulb(3x1014Hz,

10-6m)and1015timesasenergeticasaradio-frequencyphoton(3x103Hz,

105m).SpectroscopicMeasurements Spectroscopistsusetheinteractionsofradiationwithmatertoobtaininformationaboutasample.Thesampleisstimulatedbyapplyingenergyintheformofheat,electricalenergy,light,particles,orachemicalreaction.Theanalyteispredominatelyinitslowest-energyorgroundstate.Thestimulusthencausessomeanalytespeciestoundergoatransitiontoahigher-energyorexcitedstate.Weobtaininformationabouttheanalytebymeasuringtheelectromagneticradiationemittedasitreturnstothegroundstateorbymeasuringtheamountofelectromagneticradiationabsorbedasaresultofexcitation.…continued…

Inemissiontheanalyteisstimulatedbytheapplicationofheat,electricalenergy,orachemicalreaction.Emissionspectroscopyusuallyreferstomethodsinwhichthestimulusisheatorelectricalenergy,whereaschemiluminescencespectroscopyreferstoexcitationoftheanalytebyachemicalreaction.Measurementoftheradiantpoweremittedastheanalytereturnstothegroundstatecangiveinformationaboutitsidentityandconcentration.Theresultsofsuchameasurementareoftenexpressedgraphicallybyaspectrum,whichisaplotoftheemittedradiationasafunctionoffrequencyorwavelength.…continued…

Whenthesampleisstimulatedbyapplicationofanexternalelectromagneticradiationsource,severalprocessesarepossible.Someoftheincidentradiationcanbeabsorbedandpromotesomeoftheanalytespeciestoanexcitedstate.Inabsorptionspectroscopy,theamountoflightabsorbedasafunctionofwavelengthismeasured,whichcangivequalitativeandquantitativeinformationaboutthesample.Inphotoluminescencespectroscopytheemissionofphotonsismeasuredfollowingabsorption.Themostimportantformsofphotoluminescenceforanalyticalpurposesarefluorescenceandphosphorescencespectroscopy.TheAbsorptionProcess

Theabsorptionlaw,alsoknownastheBeer-LambertlaworjustBeer’slaw,tellsusquantitativelyhowtheamountofattenuationdependsontheconcentrationoftheabsorbingmoleculesandthepathlengthoverwhichabsorptionoccurs.Aslighttraversesamediumcontaininganabsorbinganalyte,decreasesinintensityoccurastheanalytebecomesexcited.Forananalytesolutionofagivenconcentration,thelongerthelengthofthemediumthroughwhichthelightpasses(pathlengthoflight),themoreabsorbersareinthepathandthegreatertheattenuation.Alsoforagivenpathlengthoflight,thehighertheconcentrationofabsorbers,thestrongertheattenuation.TheAbsorptionProcess

Theattenuationofaparallelbeamofmonochromaticradiationasitpassesthroughanabsorbingsolutionofthicknessbcmandconcentrationcmolesperliter.Becauseofinteractionsbetweenthephotonsandabsorbingparticles,theradiantpowerofthebeamdecreasesfromP0toP.ThetransmittanceTofthesolutionisthefractionofincidentradiationtransmittedbythesolution.Transmittanceisoftenexpressedasapercentageandcalledthepercenttransmittance. T=P/P0 TheabsorbanceAofasolutionisrelatedtothetransmittanceinalogarithmicmanner. A=-logT=log(P0/P)

MeasuringTransmittanceandAbsorbance Ordinarily,transmittanceandabsorbance,cannotbemeasuredasshownbecausethesolutiontobestudiedmustbeheldinsomesortofcontainer(cellorcuvette).Reflectionandscatteringlossescanoccuratthecellwalls.Theselossescanbesubstantial.Lightcanalsobescatteredinalldirectionsfromthesurfaceoflargemoleculesorparticles,suchasdust,inthesolvent,andthiscanalsocausefurtherattenuationofthebeamasitpassesthroughthesolution.…continued… Tocompensatefortheseeffects,thepowerofthebeamtransmittedthroughacellcontainingtheanalytesolutioniscomparedwithonethattraversesanidenticalcellcontainingonlythesolventorareagentblank.Anexperimentalabsorbancethatcloselyapproximatesthetrueabsorbanceforthesolutionisthusobtained;thatis A=logP0/PlogPsolvent/Psolution

Beer’sLaw AccordingtoBeer’slaw,absorbanceAisdirectlyproportionaltotheconcentrationoftheabsorbingspeciescandthepathlengthboftheabsorbingmedium A=logP0/P=abc Here,aisaproportionalityconstantcalledtheabsorptivity.Becauseabsorbanceisaunitlessquantity,theabsorptivitymusthaveunitsthatcanceltheunitsofbandc.If,forexample,chastheunitsofgramsperliter(gL-1)andbhastheunitsofcentimeters(cm),absorptivityhastheunitsofliterspergramcentimeter(Lg-1cm-1).

…continued…

Whenweexpresstheconcentrationinmolesperliterandbincentimeters,theproportionalityconstant,calledthemolarabsorptivity,isgiventhespecialsymbol.Thus, A=bc where,hastheunitsofliterspermolecentimeter(Lmol-1cm-1).

ApplyingBeer’sLawtoMixture Beer’slawalsoappliestosolutionscontainingmorethanonekindofabsorbingsubstance.Providedthattherearenointeractionsamongthevariousspecies,thetotalabsorbanceforamulticomponentsystemisthesumoftheindividualabsorbances.Inotherwords, Atotal=A1+A2+…An

=1bc1+2bc2+…+nbcn

wherethesubscriptsrefertoabsorbingcomponets1,2,…,n. LimitstoBeer’sLaw Therearefewexceptiontothelinearrelationshipbetweenabsorbanceandpathlengthatafixedconcentration.Wefrequentlyobservedeviationsfromthedirectproportionalitybetweenabsorbanceandconcentrationwherebisaconstant.Someofthesedeviations,calledrealdeviations,arefundamentalandrepresentreallimitationstothelaw.Othersoccurasaconsequenceofthemannerinwhichtheabsorbancemeasurementsaremadeorasaresultofchemicalchangesassociatedwithconcentrationchanges.Thesedeviationsarecalledinstrumentaldeviationsandchemicaldeviationrespectively.

RealLimitationstoBeer’sLaw Beer’slawdescribestheabsorptionbehaviorofdilutesolutionsonlyandisalimitinglaw.Atconcentrationsexceedingabout0.01M,theaveragedistancesbetweenionsormoleculesarediminishedtothepointwhereeachparticleaffectsthechargedistribution,andthustheextentofabsorptionofitsneighbors.Theoccurrenceofthisphenomenoncausesdeviationsfromthelinearrelationshipbetweenabsorbanceandconcentration.Whenionsareincloseproximity,themolarabsorptivityoftheanalytecanbealteredbecauseofelectrostaticinteractions,whichcanleadtodeparturesfromBeer’slaw.ChemicalDeviations DeviationsfromBeer’slawappearwhentheabsorbingspeciesundergoesassociation,dissociation,orreactionwiththesolventtogiveproductsthatabsorbdifferentlyfromtheanalyte.Theextentofsuchdeparturescanbepredictedfromthemolarabsorptivitiesoftheabsorbingspeciesandtheequilibriumconstantsfortheequilibriainvolved.Unfortunately,weareusuallyunawarethatsuchprocessesareaffectingtheanalyte,socompensationisoftenimpossible.Typicalequilibriathatgiverisetothiseffectincludemonomerdimerequilibria,metalcomplexationequilibriawheremorethanonecomplexispresent,acid/baseequilibria,andsolvent-analyteassociationequilibria. InstrumentalDeviations TheneedformonochromaticradiationandtheabsenceofstrayradiationarepracticalfactorsthatlimittheapplicabilityofBeer’slaw.Beer’slawstrictlyappliesonlywhenmeasurementsaremadewithmonochromaticsourceradiation.Ifthebandselectedcorrespondstoaregioninwhichtheabsorptivityoftheanalyteisessentiallyconstant,departuresfromBeer’slawwillbeminimal.ManymolecularbandsintheUV/visibleregionfitthisdescription.Toavoiddeviation,itisadvisabletoselectawavelengthbandnearthewavelengthofmaximumabsorptionwheretheanalyteabsorptivitychangeslittlewithwavelength.…continued… Strayradiation,commonlycalledstraylight,isdefinedasradiationfromtheinstrumentthatisoutsidethenominalwavelengthbandchosenforthedetermination.Thisstrayradiationisoftentheresultofscatteringandreflectionoffthesurfacesofgratings,lensesormirrors,filters,andwindows.Whenmeasurementsaremadeinthepresenceofstraylight,theobservedabsorbanceisgivenby

A`=

wherePsistheradiantpowerofthestraylight.…continued… Straylightalwayscausestheapparentabsorbancetobelowerthanthetrueabsorbance.Thedeviationsduetostraylightaremostsignificantathighabsorbancevalues.Becausestrayradiationlevelscanbeashighas0.5%inmoderninstruments,absorbancelevelsabove2.0arerarelymeasuredunlessspecialprecautionsaretakenorspecialinstrumentswithextremelylowstraylightlevelsareused. Anotherdeviationiscausedbymismatchedcells.Ifthecellsholdingtheanalyteandblanksolutionsarenotofequalpathlengthandequivalentinopticalcharacteristics,andinterceptwilloccurinthecalibrationcurve.Thiserrorcanbeavoidedeitherbyusingmatchedcellsorbyusingalinearregressionproceduretocalculateboththeslopeandinterceptofthecalibrationcurve.

Absorptionspectra Anabsorptionspectrumisaplotofabsorbanceversuswavelength.Absorbancecouldalsobeplottedagainstwavenumberorfrequency.Mostmodernscanninginstrumentscanproducesuchanabsorptionspectrumdirectly.Olderinstrumentsoftendisplaytransmittanceandproduceplotsof%Tversuswavelength.Occasionally,plotswithlogAastheordinateareused.Aplotofmolarabsorptivityasafunctionofwavelengthisindependentofconcentration.AtomicAbsorption

Whenabeamofpolychromaticuv/visibleradiationpassesthroughamediumcontainingatoms,onlyafewfrequenciesareattenuatedbyabsorption.Thespectrumconsistsofanumberofverynarrowabsorptionlines.Transitionbetweentwodifferentorbitalsaretermedelectronictransitions.Atomicabsorptionismeasuredatasinglewavelengthusingaverynarrowmonochromaticsource. MolecularAbsorption Threetypesofenergychangesoccurwhenmoleculesareexcitedbyultraviolet,visible,andinfraredradiation.ForUV/visibleradiation,whenweexciteamolecule,anelectronresidinginalow-energymolecularoratomicorbitalispromotedtoahigher-energyorbital.Thechangeinenergylevelsiscalledatransition.Wecanonlygetsuchatransitionwhentheenergyhofthephotonisexactlythesameastheenergydifferencebetweenthetwoorbitalenergies.Thetransitionofanelectronbetweendifferentenergylevelsiscalledanelectronictransition,andtheabsorptionprocessiscalledelectronicabsorption.…continued… Moleculesexhibittwoadditionaltypesofradiation-inducedtransitions:vibrationaltransitionsandrotationaltransitions.Thevibrationalenergyofamoleculeisassociatedwiththebondsthatholdthemoleculetogether.Thevibrationalenergyofamoleculeisquantizedandcanonlyassumecertaindiscretelevels.Transitionsbetweenvibrationallevelsarevibrationaltransitions. TheoverallenergyEassociatedwi