Download Experiment 30A1- Measurements

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EXPERIMENT30A1:MEASUREMENTS
LearningOutcomes
Uponcompletionofthislab,thestudentwillbeableto:
1) Usevariouscommonlaboratorymeasurementtoolssuchasgraduated
cylinders,volumetricflask,burettes,electronicbalance,and
thermometer.
2) Differentiatebetweenprecisionandaccuracy.
3) Constructgraphicalrepresentationsofdata.
Introduction
Alllaboratoryworkinvolvessomeformofmeasurement-volume,mass,
temperature,pressureetc.Everymeasurementhassomedegreeofuncertaintydue
toinherentlimitationsoftheinstrumentsusedforthemeasurements.Itistherefore
importanttounderstandthesignificanceofeachdigitinthemeasuredvalue.
Multiplemeasurementsareoftennecessaryinordertoimprovethechancesof
obtainingaccuratemeasurements.
Accuracyreferstotheclosenessofthemeasuredvaluetothetrueoracceptedvalue
ofthemeasurement.Thetermprecisionisusedtorefertotheclosenessofmultiple
measurementstoeachother.Thebestsetofdatawillideallybebothaccurateas
wellasprecise.Ifthetruevalueofaparticularmeasurementisknown,thenan
estimateoftheaccuracyofthedatacanbeobtainedbycalculatingthepercenterror
inthedata.
⎛ Experimental Value - True Value ⎞
PercentError= ⎜
⎟ × 100 ⎝
⎠
True Value
Percenterrormaybepositiveornegative.Apositivevalueofpercenterrorimplies
thattheexperimentalvalueislargerthanthetruevalue.Likewise,anegativevalue
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ofpercenterrorimpliesthattheexperimentalvalueissmallerthanthetruevalue.
Alternately,itisalsoacceptabletosimplyindicatetheabsolutevalueofpercent
error,inwhichcasethevalueisanindicationofthedeviationfromthetruevalue.In
allcasesasmallerpercenterrorsignifiesamoreaccuratedataset.
Acommonexampleofprecisionandaccuracyisgivenbelow:
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EXAMPLESOFACCURACYANDPRECISION
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NOTPRECISEANDNOTACCURATEPRECISEBUTNOTACCURATE
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ACCURATEBUTNOTEPRECISEPRECISEANDACCURATE
Errorsinmeasurementarebroadlyascribedtotwocategories:systematicand
randomerrors.Systematicerroristheresultofimproperhandlingoftheinstrument
oradefectiveinstrument.Randomerrorisaresultofvariedfactorsthataredifficult
toisolate(changesinenvironmentalconditionsinthelaboratory,voltage
fluctuations,parallaxetc).Whileitispossibletominimizeoreveneliminate
systematicerrorthroughinstrumentcalibrationandthoroughreviewofthe
instrument’soperationsmanual,itisimpossibletoeliminaterandomerror.
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Uncertaintyisthetermassociatedwiththemarginoferrorinanymeasurement.
Eachinstrument(e.g.,ruler,beaker,thermometer,balance,etc.)usedinthe
laboratoryhasaprecisionthatdeterminestheuncertaintyofmeasurements,dueto
randomerror,takenwiththatinstrument.Theprecisionofameasuringdeviceis
usuallyexpressedintermsofa±valueindicatingthelimitationofthedevice.The
commoninstrumentsusedinGeneralChemistrycanbedividedintotwotypes:
thosethathaveagraduatedscaleandcanmakemeasurementsoverarangeof
values(e.g.,ruler,thermometer,balance,graduatedcylinder,graduatedpipette,
beaker)andthosethatmeasureasingle,fixedvolumeofaliquid(e.g.,volumetric
flask,volumetricpipette).
Thedistancebetweengraduationmarksonaruler,thermometer,buretteorother
glasswaremaybesubdividedintoones,tenths,hundredsorotherdivisions
dependingontheprecisionofthedevice.A50-mLgraduatedcylinder,forexample,
hasgraduationmarksateach1mL.Sincetheexperimentercanestimatebetween
thegraduationmarks,thevolumecanbemeasuredandrecordedtotheone-tenthof
amL(0.1mL,Figure1a).Aburette,ontheotherhand,hasgraduationmarksateach
one-tenthmL(0.1mL,Figure1b)orthehundredthplace(0.01mL,Figure1c).
Therefore,anextradigittotherightisgainedwhentheburetteisused,makingthe
burettemoreprecise.Ineachinstance,thelastdigit(underlinedandinitalics)isan
estimate.
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4.0
50
5.0
FIGURE1A
FIGURE1B FIGURE1C
Reading:44.5units 4.45units 4.045units
4.0
4.1
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Ascanbeseenfromfigures1a,1b,and1c,uncertaintyinthedataisrelatedtothe
numberofsignificantdigitsinthedata.Thenumberofsignificantdigitsdependson
theinstrumentusedformeasurement.Theinstrumentprovidingthemostnumber
ofsignificantdigits(figure1c)isalsotheinstrumentwiththesmallestuncertainty.
Twootherdevicesarecommonlyusedinthelaboratory:digitalthermometerand
electronicbalance.Inbothofthesecases,allthedigitsdisplayedaretoberecorded
andtheuncertaintyisassumedtobeinthelastdigitofthedisplay.
DigitalThermometer
ElectronicBalance
Reading:91.9°F
Reading:31.8116g
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StatisticalTools
Themostcommonstatisticaltoolsneededfordataanalysisaremeanandstandard
deviation.
Themeanoraveragevalueiscalculatedusingthefollowingformula:
n
∑x
Mean = x =
i
i=1
n
Intheaboveformula: x isthemean,xiisadatapoint,andnisthenumberofdata
points.
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Instatisticsameasureofthedeviationofeachvalueinadatasetfromthemean
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valueofthatdatasetisgivenbythestandarddeviation.Thestandarddeviation
(S.D.)iscalculatedusingthefollowingformula:
n
∑ (x
S.D. = σ =
i
− x) 2
i=1
n −1
Intheaboveformula:σ isthestandarddeviation,xiisadatapoint, x isthemean,
andnisthenumberofdatapoints.
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Thesestatisticalvaluescanalsobecomputedbyenteringthedatainaspreadsheet
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andusinganappropriateformula.Forinstance,whenusingMicrosoftExcel,the
formulatocalculatethemeanis:“=AVERAGE(selectdata)”andtheformulato
calculatethestandarddeviationis:“=STDEV(selectdata)”.
GraphicalRepresentationofData
Oftentimesonemightencounteradatasetwherethemeasuredquantitiesmaybe
directlyproportionaltoeachother.Forinstance,inthisexperiment,thetwo
measuredquantities-massandvolumearedirectlyproportionaltoeachotherand
theratioofmasstovolumeisdefinedasthedensityofthatsubstance.Ifdata“x”is
proportionaltodata“y”,thenwecansaythat:
yαx
ory=mxory=mx+b
Insuchinstances,thevalueoftheslope,m,providesusefulinformation.Inthe
exampleofthemass-volumerelationship,theslopewouldbethedensityofthe
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substancewhenmassisplottedonthey-axisandvolumeisplottedonthex-axis.A
simplemethodtoobtaintheslopeistoplotofagraphofvolumevs.mass.Once
again,variousspreadsheetprogramssuchasMicrosoftExcelcanbeusedtoplota
graphofthedatasetandobtainthebest-fitlinearregressionequationtofindthe
slope.
ExperimentalDesign
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Inordertounderstandthedifferencesbetweenthevariouscommonlaboratory
tools,inthisexperiment,youwillmeasurethedensityofwater.Densityisdefinedas
themassofasubstanceperunitvolume.Densityiscalculatedusingtheformula:
Mass
Density =
Volume
Densityofliquidsiscommonlyexpressedinunitsofgrams/ml.Thetruevalueorthe
acceptedvalueforthedensityofwateratroomtemperatureis1.00gram/ml.
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ReagentsandSupplies
10-mland100-mlgraduatedcylinders,burette,25-mlvolumetricflask,andwater
Procedure
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PART1:MEASURETHEDENSITYOFWATERUSINGA10-MLGRADUATEDCYLINDER
1. Measurethemassofanempty10-mlgraduatedcylinder.
2. Addsometapwaterintothegraduatedcylindertoanywherebelowthe10mlmark.
3. Recordthevolumeofthewater.
4. Measureofthemassofthegraduatedcylinderwithwater.
5. Emptythewaterinthesink.
6. Repeatthestepstwomoretimes.
7. Calculatethedensityofwaterforeachtrial,theaveragedensity,thestandard
deviation,andthepercenterror.
PART2:MEASURETHEDENSITYOFWATERUSINGA100-MLGRADUATEDCYLINDER
1. Measurethemassofanempty100-mlgraduatedcylinder.
2. Addsometapwaterintothegraduatedcylindertoanywherebelowthe100mlmark.
3. Recordthevolumeofthewater.
4. Measureofthemassofthegraduatedcylinderwithwater.
5. Emptythewaterinthesink.
6. Repeatthestepstwomoretimes.
7. Calculatethedensityofwaterforeachtrial,theaveragedensity,thestandard
deviation,andthepercenterror.
PART3:MEASURETHEDENSITYOFWATERUSINGAVOLUMETRICFLASK
1. Measurethemassofanempty25-mlvolumetricflask.
2. Fillthevolumetricflaskwithwatertillthemark.
3. Recordthevolumeofthewater.
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4. Measureofthemassofthevolumetricflaskwithwater.
5. Emptythewaterinthesink.
6. Repeatthestepstwomoretimes.
7. Calculatethedensityofwaterforeachtrial,theaveragedensity,thestandard
deviation,andthepercenterror.
PART4:MEASURETHEDENSITYOFWATERUSINGABURETTE
1. Measurethemassofanemptybeaker(anysmallbeakerisacceptable).
2. Obtainaburettestand,aburetteclamp,andaburette,andclamptheburette
tothestand(youmayuseamicro-buretteora25-mlburetteasperthe
discretionofyourinstructor).
3. Filltheburettewithwatertosomelevellessthanthemaximumpossible.
4. Recordthe“InitialBuretteReading”.
5. Dispenseasmallvolumeofwaterintothebeaker(fromstep1);
approximately0.2mlifyouareusingamicroburetteor2mlifyouareusing
alargerburette.
6. Recordthe“FinalBuretteReading”.
7. Measurethemassofthebeakercontainingthewater.
8. Dispenseanadditionalamountofwaterintothebeaker(approximatelythe
samevolumeasbefore).
9. Recordthenew“FinalBuretteReading”.
10. Measurethemassofthebeakercontainingtheadditionalwater.
11. Repeatsteps8-10fourmoretimes.
12. Plotofgraphofthisdataandobtainthedensityofwaterfromtheslopeof
thebest-fitlinearregressionline.Calculatethepercenterrorinthedensityof
water.
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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”(maybe
underoptions).
11. Iftheinterceptissupposedtobezero,besuretoalsochecktheboxthatsays:
“setintercept=0”.
12. ClickOK.Theequationoftheline,andthecorrelationcoefficientwillbe
displayedonthegraph.
DataTable
PART1:MEASURETHEDENSITYOFWATERUSINGA10-MLGRADUATEDCYLINDER
Trial1
Trial2
Massofemptygraduatedcylinder(grams)
Volumeofwater(ml)
Massofgraduatedcylinder+water(grams)
Massofwater(grams)
Densityofwater(grams/ml)
Averagedensityofwater=
_________________________________
StandardDeviationofdensityofwater=
_________________________________
Percenterrorindensityofwater= _________________________________
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Trial3
PART2:MEASURETHEDENSITYOFWATERUSINGA100-MLGRADUATEDCYLINDER
Trial1
Trial2
Massofemptygraduatedcylinder(grams)
Volumeofwater(ml)
Massofgraduatedcylinder+water(grams)
Massofwater(grams)
Densityofwater(grams/ml)
Averagedensityofwater=
_________________________________
StandardDeviationofdensityofwater=
_________________________________
Percenterrorindensityofwater= _________________________________
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Trial3
PART3:MEASURETHEDENSITYOFWATERUSINGAVOLUMETRICFLASK
Trial1
Trial2
Massofvolumetricflask(grams)
Volumeofwater(ml)
Massofvolumetricflask+water(grams)
Massofwater(grams)
Densityofwater(grams/ml)
Averagedensityofwater=
_________________________________
StandardDeviationofdensityofwater=
_________________________________
Percenterrorindensityofwater= _________________________________
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Trial3
PART4:MEASURETHEDENSITYOFWATERUSINGABURETTE
MASS
MassofEmpty
Beaker(grams)
1.Massofbeaker+ 1.Massofwater
water(grams)
(grams)
2.Massofbeaker+ 2.Massofwater
water(grams)
(grams)
3.Massofbeaker+ 3.Massofwater
water(grams)
(grams)
4.Massofbeaker+ 4.Massofwater
water(grams)
(grams)
5.Massofbeaker+ 5.Massofwater
water(grams)
(grams)
VOLUME
InitialBurette
Reading(ml)
1.FinalBurette
1.Volumeofwater
Reading(ml)
(ml)
2.FinalBurette
2.Volumeofwater
Reading(ml)
(ml)
3.FinalBurette
3.Volumeofwater
Reading(ml)
(ml)
4.FinalBurette
4.Volumeofwater
Reading(ml)
(ml)
5.FinalBurette
5.Volumeofwater
Reading(ml)
(ml)
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Volume(x-axis)vs.Mass(y-axis)
Volume(ml) Mass(grams)
Equationofregressionline:
_________________________________________
Densityofwater= _________________________________________
PercentErrorinDensity= _________________________________________
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