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

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1 EXPERIMENT 30A1: MEASUREMENTS Learning Outcomes Upon completion of this lab, the student will be able to: 1) Use various common laboratory measurement tools such as graduated cylinders, volumetric flask, burettes, electronic balance, and thermometer. 2) Differentiate between precision and accuracy. 3) Construct graphical representations of data. Introduction All laboratory work involves some form of measurement- volume, mass, temperature, pressure etc. Every measurement has some degree of uncertainty due to inherent limitations of the instruments used for the measurements. It is therefore important to understand the significance of each digit in the measured value. Multiple measurements are often necessary in order to improve the chances of obtaining accurate measurements. Accuracy refers to the closeness of the measured value to the true or accepted value of the measurement. The term precision is used to refer to the closeness of multiple measurements to each other. The best set of data will ideally be both accurate as well as precise. If the true value of a particular measurement is known, then an estimate of the accuracy of the data can be obtained by calculating the percent error in the data. Percent Error = Experimental Value - True Value True Value × 100 Percent error may be positive or negative. A positive value of percent error implies that the experimental value is larger than the true value. Likewise, a negative value of percent error implies that the experimental value is smaller than the true value. Alternately, it is also acceptable to simply indicate the absolute value of percent error, in which case the value is an indication of the deviation from the true value. In all cases a smaller percent error signifies a more accurate data set. A common example of precision and accuracy is given below:

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Page 1: EXPERIMENT 30A1: M...The term precision is used to refer to the closeness of multiple measurements to each other. The best set of data will ideally be both accurate as well as precise

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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= _________________________________________