experiment 30a1: m...the term precision is used to refer to the closeness of multiple measurements...
TRANSCRIPT
1
EXPERIMENT30A1:MEASUREMENTS
LearningOutcomesUponcompletionofthislab,thestudentwillbeableto:
1) Usevariouscommonlaboratorymeasurementtoolssuchasgraduatedcylinders,volumetricflask,burettes,electronicbalance,andthermometer.
2) Differentiatebetweenprecisionandaccuracy.3) Constructgraphicalrepresentationsofdata.
IntroductionAlllaboratoryworkinvolvessomeformofmeasurement-volume,mass,temperature,pressureetc.Everymeasurementhassomedegreeofuncertaintyduetoinherentlimitationsoftheinstrumentsusedforthemeasurements.Itisthereforeimportanttounderstandthesignificanceofeachdigitinthemeasuredvalue.Multiplemeasurementsareoftennecessaryinordertoimprovethechancesofobtainingaccuratemeasurements.Accuracyreferstotheclosenessofthemeasuredvaluetothetrueoracceptedvalueofthemeasurement.Thetermprecisionisusedtorefertotheclosenessofmultiplemeasurementstoeachother.Thebestsetofdatawillideallybebothaccurateaswellasprecise.Ifthetruevalueofaparticularmeasurementisknown,thenanestimateoftheaccuracyofthedatacanbeobtainedbycalculatingthepercenterrorinthedata.
PercentError=
€
Experimental Value - True ValueTrue Value
⎛
⎝ ⎜
⎞
⎠ ⎟ ×100
Percenterrormaybepositiveornegative.Apositivevalueofpercenterrorimpliesthattheexperimentalvalueislargerthanthetruevalue.Likewise,anegativevalueofpercenterrorimpliesthattheexperimentalvalueissmallerthanthetruevalue.Alternately,itisalsoacceptabletosimplyindicatetheabsolutevalueofpercenterror,inwhichcasethevalueisanindicationofthedeviationfromthetruevalue.Inallcasesasmallerpercenterrorsignifiesamoreaccuratedataset.Acommonexampleofprecisionandaccuracyisgivenbelow:
2
EXAMPLESOFACCURACYANDPRECISION
!!!!!!!!!!!! NOTPRECISEANDNOTACCURATEPRECISEBUTNOTACCURATE ! ! ! !!! !!! ! ! ! ACCURATEBUTNOTEPRECISEPRECISEANDACCURATEErrorsinmeasurementarebroadlyascribedtotwocategories:systematicandrandomerrors.Systematicerroristheresultofimproperhandlingoftheinstrumentoradefectiveinstrument.Randomerrorisaresultofvariedfactorsthataredifficulttoisolate(changesinenvironmentalconditionsinthelaboratory,voltagefluctuations,parallaxetc).Whileitispossibletominimizeoreveneliminatesystematicerrorthroughinstrumentcalibrationandthoroughreviewoftheinstrument’soperationsmanual,itisimpossibletoeliminaterandomerror.
3
Uncertaintyisthetermassociatedwiththemarginoferrorinanymeasurement.Eachinstrument(e.g.,ruler,beaker,thermometer,balance,etc.)usedinthelaboratoryhasaprecisionthatdeterminestheuncertaintyofmeasurements,duetorandomerror,takenwiththatinstrument.Theprecisionofameasuringdeviceisusuallyexpressedintermsofa±valueindicatingthelimitationofthedevice.ThecommoninstrumentsusedinGeneralChemistrycanbedividedintotwotypes:thosethathaveagraduatedscaleandcanmakemeasurementsoverarangeofvalues(e.g.,ruler,thermometer,balance,graduatedcylinder,graduatedpipette,beaker)andthosethatmeasureasingle,fixedvolumeofaliquid(e.g.,volumetricflask,volumetricpipette).Thedistancebetweengraduationmarksonaruler,thermometer,buretteorotherglasswaremaybesubdividedintoones,tenths,hundredsorotherdivisionsdependingontheprecisionofthedevice.A50-mLgraduatedcylinder,forexample,hasgraduationmarksateach1mL.Sincetheexperimentercanestimatebetweenthegraduationmarks,thevolumecanbemeasuredandrecordedtotheone-tenthofamL(0.1mL,Figure1a).Aburette,ontheotherhand,hasgraduationmarksateachone-tenthmL(0.1mL,Figure1b)orthehundredthplace(0.01mL,Figure1c).Therefore,anextradigittotherightisgainedwhentheburetteisused,makingtheburettemoreprecise.Ineachinstance,thelastdigit(underlinedandinitalics)isanestimate.
FIGURE1A FIGURE1B FIGURE1CReading:44.5units 4.45units 4.045units
4.05.0
4050
4.04.1
4
Ascanbeseenfromfigures1a,1b,and1c,uncertaintyinthedataisrelatedtothenumberofsignificantdigitsinthedata.Thenumberofsignificantdigitsdependsontheinstrumentusedformeasurement.Theinstrumentprovidingthemostnumberofsignificantdigits(figure1c)isalsotheinstrumentwiththesmallestuncertainty.Twootherdevicesarecommonlyusedinthelaboratory:digitalthermometerandelectronicbalance.Inbothofthesecases,allthedigitsdisplayedaretoberecordedandtheuncertaintyisassumedtobeinthelastdigitofthedisplay.DigitalThermometer
Reading:91.9°F
ElectronicBalance
Reading:31.8116g
5
StatisticalToolsThemostcommonstatisticaltoolsneededfordataanalysisaremeanandstandarddeviation.Themeanoraveragevalueiscalculatedusingthefollowingformula:
€
Mean = x =
xii=1
n
∑n
Intheaboveformula:
€
x isthemean,xiisadatapoint,andnisthenumberofdatapoints.Instatisticsameasureofthedeviationofeachvalueinadatasetfromthemeanvalueofthatdatasetisgivenbythestandarddeviation.Thestandarddeviation(S.D.)iscalculatedusingthefollowingformula:
€
S.D. =σ =
(xi − x)2
i=1
n
∑n −1
Intheaboveformula:σ isthestandarddeviation,xiisadatapoint,
€
x isthemean,andnisthenumberofdatapoints.Thesestatisticalvaluescanalsobecomputedbyenteringthedatainaspreadsheetandusinganappropriateformula.Forinstance,whenusingMicrosoftExcel,theformulatocalculatethemeanis:“=AVERAGE(selectdata)”andtheformulatocalculatethestandarddeviationis:“=STDEV(selectdata)”.GraphicalRepresentationofDataOftentimesonemightencounteradatasetwherethemeasuredquantitiesmaybedirectlyproportionaltoeachother.Forinstance,inthisexperiment,thetwomeasuredquantities-massandvolumearedirectlyproportionaltoeachotherandtheratioofmasstovolumeisdefinedasthedensityofthatsubstance.Ifdata“x”isproportionaltodata“y”,thenwecansaythat:
yαx
ory=mxory=mx+b
Insuchinstances,thevalueoftheslope,m,providesusefulinformation.Intheexampleofthemass-volumerelationship,theslopewouldbethedensityofthe
6
substancewhenmassisplottedonthey-axisandvolumeisplottedonthex-axis.Asimplemethodtoobtaintheslopeistoplotofagraphofvolumevs.mass.Onceagain,variousspreadsheetprogramssuchasMicrosoftExcelcanbeusedtoplotagraphofthedatasetandobtainthebest-fitlinearregressionequationtofindtheslope.
7
ExperimentalDesignInordertounderstandthedifferencesbetweenthevariouscommonlaboratorytools,inthisexperiment,youwillmeasurethedensityofwater.Densityisdefinedasthemassofasubstanceperunitvolume.Densityiscalculatedusingtheformula:
€
Density =MassVolume
Densityofliquidsiscommonlyexpressedinunitsofgrams/ml.Thetruevalueortheacceptedvalueforthedensityofwateratroomtemperatureis1.00gram/ml.ReagentsandSupplies10-mland100-mlgraduatedcylinders,burette,25-mlvolumetricflask,andwater
8
ProcedurePART1:MEASURETHEDENSITYOFWATERUSINGA10-MLGRADUATEDCYLINDER
1. Measurethemassofanempty10-mlgraduatedcylinder.
2. Addsometapwaterintothegraduatedcylindertoanywherebelowthe10-mlmark.
3. Recordthevolumeofthewater.
4. Measureofthemassofthegraduatedcylinderwithwater.
5. Emptythewaterinthesink.
6. Repeatthestepstwomoretimes.
7. Calculatethedensityofwaterforeachtrial,theaveragedensity,thestandard
deviation,andthepercenterror.PART2:MEASURETHEDENSITYOFWATERUSINGA100-MLGRADUATEDCYLINDER
1. Measurethemassofanempty100-mlgraduatedcylinder.
2. Addsometapwaterintothegraduatedcylindertoanywherebelowthe100-mlmark.
3. Recordthevolumeofthewater.
4. Measureofthemassofthegraduatedcylinderwithwater.
5. Emptythewaterinthesink.
6. Repeatthestepstwomoretimes.
7. Calculatethedensityofwaterforeachtrial,theaveragedensity,thestandard
deviation,andthepercenterror.PART3:MEASURETHEDENSITYOFWATERUSINGAVOLUMETRICFLASK
1. Measurethemassofanempty25-mlvolumetricflask.
2. Fillthevolumetricflaskwithwatertillthemark.
3. Recordthevolumeofthewater.
9
4. Measureofthemassofthevolumetricflaskwithwater.
5. Emptythewaterinthesink.
6. Repeatthestepstwomoretimes.
7. Calculatethedensityofwaterforeachtrial,theaveragedensity,thestandard
deviation,andthepercenterror.
PART4:MEASURETHEDENSITYOFWATERUSINGABURETTE
1. Measurethemassofanemptybeaker(anysmallbeakerisacceptable).
2. Obtainaburettestand,aburetteclamp,andaburette,andclamptheburettetothestand(youmayuseamicro-buretteora25-mlburetteasperthediscretionofyourinstructor).
3. Filltheburettewithwatertosomelevellessthanthemaximumpossible.
4. Recordthe“InitialBuretteReading”.
5. Dispenseasmallvolumeofwaterintothebeaker(fromstep1);
approximately0.2mlifyouareusingamicroburetteor2mlifyouareusingalargerburette.
6. Recordthe“FinalBuretteReading”.
7. Measurethemassofthebeakercontainingthewater.
8. Dispenseanadditionalamountofwaterintothebeaker(approximatelythe
samevolumeasbefore).
9. Recordthenew“FinalBuretteReading”.
10. Measurethemassofthebeakercontainingtheadditionalwater.
11. Repeatsteps8-10fourmoretimes.
12. Plotofgraphofthisdataandobtainthedensityofwaterfromtheslopeofthebest-fitlinearregressionline.Calculatethepercenterrorinthedensityofwater.
10
INSTRUCTIONSFORPLOTTINGAGRAPHANDOBTAININGTHEREGRESSIONEQUATION
1. Enterthedataintwocolumns,thex-datafirstandthenthey-data.
2. Selectthedataset(xandy).
3. Clickthe“Gallery”tabor“InsertChart”.
4. SelecttheXY-scatterplot.
5. Choosetheplottypewherethedatapointsarenotalreadyconnected.
6. Thegraphwillnowbedisplayed.
7. Clickonanyofthedatapointsonthegraph.
8. Clickonthe“ChartLayout”tabandselect“Addtrendline”underanalysis.
9. Clickonthetrendlineoptions.
10. Checktheboxes:“Displayequation”and“Displayr-squaredvalue”(maybeunderoptions).
11. Iftheinterceptissupposedtobezero,besuretoalsochecktheboxthatsays:
“setintercept=0”.
12. ClickOK.Theequationoftheline,andthecorrelationcoefficientwillbedisplayedonthegraph.
11
DataTablePART1:MEASURETHEDENSITYOFWATERUSINGA10-MLGRADUATEDCYLINDER
Trial1
Trial2
Trial3
Massofemptygraduatedcylinder(grams)
Volumeofwater(ml)
Massofgraduatedcylinder+water(grams)
Massofwater(grams)
Densityofwater(grams/ml)
Averagedensityofwater= _________________________________StandardDeviationofdensityofwater= _________________________________Percenterrorindensityofwater= _________________________________
12
PART2:MEASURETHEDENSITYOFWATERUSINGA100-MLGRADUATEDCYLINDER
Trial1
Trial2
Trial3
Massofemptygraduatedcylinder(grams)
Volumeofwater(ml)
Massofgraduatedcylinder+water(grams)
Massofwater(grams)
Densityofwater(grams/ml)
Averagedensityofwater= _________________________________StandardDeviationofdensityofwater= _________________________________Percenterrorindensityofwater= _________________________________
13
PART3:MEASURETHEDENSITYOFWATERUSINGAVOLUMETRICFLASK
Trial1
Trial2
Trial3
Massofvolumetricflask(grams)
Volumeofwater(ml)
Massofvolumetricflask+water(grams)
Massofwater(grams)
Densityofwater(grams/ml)
Averagedensityofwater= _________________________________StandardDeviationofdensityofwater= _________________________________Percenterrorindensityofwater= _________________________________
14
PART4:MEASURETHEDENSITYOFWATERUSINGABURETTEMASSMassofEmptyBeaker(grams)
1.Massofbeaker+water(grams)
1.Massofwater(grams)
2.Massofbeaker+water(grams)
2.Massofwater(grams)
3.Massofbeaker+water(grams)
3.Massofwater(grams)
4.Massofbeaker+water(grams)
4.Massofwater(grams)
5.Massofbeaker+water(grams)
5.Massofwater(grams)
VOLUMEInitialBuretteReading(ml)
1.FinalBuretteReading(ml)
1.Volumeofwater(ml)
2.FinalBuretteReading(ml)
2.Volumeofwater(ml)
3.FinalBuretteReading(ml)
3.Volumeofwater(ml)
4.FinalBuretteReading(ml)
4.Volumeofwater(ml)
5.FinalBuretteReading(ml)
5.Volumeofwater(ml)
15
Volume(x-axis)vs.Mass(y-axis)
Volume(ml)
Mass(grams)
Equationofregressionline: _________________________________________Densityofwater= _________________________________________PercentErrorinDensity= _________________________________________