experiment 30a1: m...the term precision is used to refer to the closeness of multiple measurements...

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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:

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EXAMPLESOFACCURACYANDPRECISION

!!!!!!!!!!!! NOTPRECISEANDNOTACCURATEPRECISEBUTNOTACCURATE ! ! ! !!! !!! ! ! ! ACCURATEBUTNOTEPRECISEPRECISEANDACCURATEErrorsinmeasurementarebroadlyascribedtotwocategories:systematicandrandomerrors.Systematicerroristheresultofimproperhandlingoftheinstrumentoradefectiveinstrument.Randomerrorisaresultofvariedfactorsthataredifficulttoisolate(changesinenvironmentalconditionsinthelaboratory,voltagefluctuations,parallaxetc).Whileitispossibletominimizeoreveneliminatesystematicerrorthroughinstrumentcalibrationandthoroughreviewoftheinstrument’soperationsmanual,itisimpossibletoeliminaterandomerror.

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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

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Ascanbeseenfromfigures1a,1b,and1c,uncertaintyinthedataisrelatedtothenumberofsignificantdigitsinthedata.Thenumberofsignificantdigitsdependsontheinstrumentusedformeasurement.Theinstrumentprovidingthemostnumberofsignificantdigits(figure1c)isalsotheinstrumentwiththesmallestuncertainty.Twootherdevicesarecommonlyusedinthelaboratory:digitalthermometerandelectronicbalance.Inbothofthesecases,allthedigitsdisplayedaretoberecordedandtheuncertaintyisassumedtobeinthelastdigitofthedisplay.DigitalThermometer

Reading:91.9°F

ElectronicBalance

Reading:31.8116g

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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

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substancewhenmassisplottedonthey-axisandvolumeisplottedonthex-axis.Asimplemethodtoobtaintheslopeistoplotofagraphofvolumevs.mass.Onceagain,variousspreadsheetprogramssuchasMicrosoftExcelcanbeusedtoplotagraphofthedatasetandobtainthebest-fitlinearregressionequationtofindtheslope.

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ExperimentalDesignInordertounderstandthedifferencesbetweenthevariouscommonlaboratorytools,inthisexperiment,youwillmeasurethedensityofwater.Densityisdefinedasthemassofasubstanceperunitvolume.Densityiscalculatedusingtheformula:

€

Density =MassVolume

Densityofliquidsiscommonlyexpressedinunitsofgrams/ml.Thetruevalueortheacceptedvalueforthedensityofwateratroomtemperatureis1.00gram/ml.ReagentsandSupplies10-mland100-mlgraduatedcylinders,burette,25-mlvolumetricflask,andwater

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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.

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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,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.

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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”(maybeunderoptions).

11. Iftheinterceptissupposedtobezero,besuretoalsochecktheboxthatsays:

“setintercept=0”.

12. ClickOK.Theequationoftheline,andthecorrelationcoefficientwillbedisplayedonthegraph.

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DataTablePART1:MEASURETHEDENSITYOFWATERUSINGA10-MLGRADUATEDCYLINDER

Trial1

Trial2

Trial3

Massofemptygraduatedcylinder(grams)

Volumeofwater(ml)

Massofgraduatedcylinder+water(grams)

Massofwater(grams)

Densityofwater(grams/ml)

Averagedensityofwater= _________________________________StandardDeviationofdensityofwater= _________________________________Percenterrorindensityofwater= _________________________________

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PART2:MEASURETHEDENSITYOFWATERUSINGA100-MLGRADUATEDCYLINDER

Trial1

Trial2

Trial3

Massofemptygraduatedcylinder(grams)

Volumeofwater(ml)

Massofgraduatedcylinder+water(grams)

Massofwater(grams)

Densityofwater(grams/ml)

Averagedensityofwater= _________________________________StandardDeviationofdensityofwater= _________________________________Percenterrorindensityofwater= _________________________________

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PART3:MEASURETHEDENSITYOFWATERUSINGAVOLUMETRICFLASK

Trial1

Trial2

Trial3

Massofvolumetricflask(grams)

Volumeofwater(ml)

Massofvolumetricflask+water(grams)

Massofwater(grams)

Densityofwater(grams/ml)

Averagedensityofwater= _________________________________StandardDeviationofdensityofwater= _________________________________Percenterrorindensityofwater= _________________________________

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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)

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Volume(x-axis)vs.Mass(y-axis)

Volume(ml)

Mass(grams)

Equationofregressionline: _________________________________________Densityofwater= _________________________________________PercentErrorinDensity= _________________________________________