Section 3: Measurements - Study Edge

Section3:MeasurementsThefollowingmapsthevideosinthissectiontotheTexasEssentialKnowledgeandSkillsforScienceTAC§112.35(c).3.01MathSkills

• Chemistry(2)(G)3.02GraphInterpretation

• Chemistry(2)(H)3.03RecordingMeasurements

• Chemistry(2)(F)3.04Temperature

• Thisvideocontainsinformationabouttemperaturescalesthatisnecessaryfortheunderstandingofheattransfer,gaslaws,andcalorimetryinlatersections.

3.05ScientificNotationandSignificantFigures

• Chemistry(2)(G)3.06DecimalPrefixesandEqualities

• Chemistry(2)(G)3.07DimensionalAnalysis

• Chemistry(2)(G)3.08LabReports

• Chemistry(2)(I)• Chemistry(2)(H)

Note:Unlessstatedotherwise,anysampledataisfictitiousandusedsolelyforthepurposeofinstruction.

Copyright 2017 Licensed and Authorized for Use Only by Texas Education Agency 1

3.01

MathSkillsManyproblemsinchemistryinvolvenumericalcalculations,soitisimportanttobecomfortablewithsomebasicmathskills.PlaceValuesInthenumberbelow,eachnumeralhasacorrespondingplacevalue(asshowninthefollowingtable)thatsignifieswhatmultipleof10thatnumeralrepresents.Theplacevaluestotherightofthedecimalpointarecalleddecimalplaces.

2,134.382

Numeral 2 1 3 4 3 8 2

PlaceValue thousands hundreds tens ones tenths hundredths thousandthsPositiveandNegativeNumbersArithmeticwithpositiveandnegativenumberscanbetricky,sorememberthefollowingrules:

• Theadditionoftwopositivenumbersyieldsapositivenumber.

• Theadditionoftwonegativenumbersyieldsanegativenumber.

• Theadditionofapositivenumberandanegativenumbermayyieldapositiveornegativeresult,dependingonthevaluesofthenumbers.

2+ −4 =

5+ −3 =

• Themultiplicationordivisionoftwopositivenumbersyieldsapositivenumber.

• Themultiplicationordivisionoftwonegativenumbersyieldsapositivenumber.

• Themultiplicationordivisionofanegativenumberandapositivenumberyieldsanegativenumber.

−20÷ 5 =


PercentagesApercentagerepresentsaportionofatotalvalue.Apercentagecanbeexpressedasanequivalentdecimalnumberifyoumovethedecimalpointtwospacestotheleft.Forexample,25%canalsobewrittenas0.25.

Percentage = the partsthe total

×100

1. Supposethata25-gramcandybarcontains12gramsofsugar,3gramsofprotein,and10

gramsoffat.Whatpercentageofthecandybarisfat?

A. 25%B. 40%C. 15%D. 60%

2. Solvethefollowingexpressionfor𝑥:

𝐻 = −𝑘!𝑇(1𝑥−1𝑧)


3.02

GraphInterpretationAgraphisavisualrepresentationoftherelationshipbetweentwovariables,whichareplottedonthehorizontalaxis(𝒙-axis)andtheverticalaxis(𝒚-axis).Thepointsonthegraphshowthecorrelationofthetwovariablesasindividualorderedpairs.Thevariablescanbedescribedashavingadirectrelationshipifbothvariablesfollowthesamebehavior(i.e.,theybothincreaseortheybothdecrease).Thevariablescanbedescribedashavinganindirectrelationshipifthevariablesbehaveinoppositemanners(i.e.,whenoneincreases,theotherdecreases).

Percentage change =final − initial

initial ×100


1. Inalaboratoryexperiment,ironreadilyreactswithpureoxygentoformanoxideofiron.Thegraphbelowshowsthemassofiron(inkilograms)remaininginthesample,plottedagainsttheamountoftimeelapsed(inseconds).

i. Classifytherelationshipaboveaseitherdirectorindirect.ii. Provideapossibleexplanationfortherelationshipshowninthegraphabove.iii. Approximatelyhowmanymorekilogramsofironarepresentat20secondsthanat40

seconds?

0

100

200

300

400

500

0 10 20 30 40 50 60

Mass(kg)

Time(s)

MassofIronversusTime


2. Thegraphbelowshowstheinternalpressureofacylinder(inatmospheres)plottedagainstthetemperatureofthecylinder(indegreesCelsius).

i. Classifytherelationshipaboveaseitherdirectorindirect.

ii. Whatistheapproximatepercentagechangeinthepressureofthecylinderwhenthetemperatureisincreasedfrom30°Cto60°C?

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60 70 80 90 100

Pressure(atm

)

Temperature(°C)

PressureofaCylinderversusTemperature


3.03

RecordingMeasurements

Inorderformembersofthescientificcommunitytocommunicateclearlyacrossdifferentlanguages,astandardsetofmeasurementsisneeded.Inthe19thcentury,aGermanmathematiciannamedCarlFriedrichGaussadvocatedforsuchasystem.

Hiswork,andtheworkofothers,ledtowhatwouldeventuallybecalledtheInternationalSystemofUnits(SI):asetofunitsrecognizedastheworldwidestandardformeasuringspecificpropertiesanddimensions.TheseSIunitsprovideabaseforallexperimentalmeasurements.

SIBaseUnits

Quantity(Dimension) UnitName Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature kelvin K

Amountofsubstance mole mol

Luminousintensity candela cd

Electriccurrent ampere A

Whendescribingmeasurementsrecordedinanexperiment,weusethefollowingterms:

• Precision–Ameasureofhowcloseyourrecordedvaluesaretoeachother(or,alternatively,ameasureofhoweasilytheresultscanbereproduced)

• Accuracy–Ameasureofhowcloseyourrecordedvaluesaretotheactualvalue


1. SupposeKelseyandherdadgotowatchastockcarraceatTexasMotorSpeedway,anoval-shapedracetrackinFortWorth,Texas.Aftertherace,sheusesameasuringwheeltodeterminethelengthofthetrack.Kelseyrecordedthefollowingfivemeasurements,inmiles,forthelengthofthetrack:

1.21,1.23,1.22,1.21,1.20

i. Iftheknownlengthofthetrackis1.50miles,describetheaccuracyandprecisionofKelsey’smeasurements.

ii. Provideapossibleexplanationfortheresultsabove.


3.04

TemperatureTemperatureisameasureoftheaverageamountofenergyoftheparticleswithinasubstance.Weusetemperaturetopredictthedirectionofheattransfer.Thereareanumberofdifferentscalescommonlyusedtoexpresstemperature.

• Fahrenheit(°F)−ThescalewearemostfamiliarwithintheUnitedStates,althoughitisrarelyusedinthescientificcommunity

• Celsius(°C)−Ascalebasedonthefreezingpointandboilingpointofwater

• Kelvin(K)−Anabsolutetemperaturescale,basedontheideathatzerokelvinisthepointwherenothermalenergyinasubstanceremains.Thispointisreferredtoasabsolutezero.

ToconvertbetweentheKelvin,Celsius,andFahrenheitscales,usethefollowingformulas:

𝑇 𝑖𝑛 𝐾 = 𝑇 𝑖𝑛 ˚𝐶 + 273.15

𝑇 𝑖𝑛 ˚𝐶 =59

× (𝑇 𝑖𝑛 ˚𝐹 − 32)1. SupposethatwhilewatchingaHoustonAstrosgame,Aaronnoticesthatthescoreboardin

rightfielddisplaysthetemperatureas95°F.

i. ConvertthistemperatureintodegreesCelsius.

ii. ConvertthetemperaturefromdegreesCelsiusintokelvin.


3.05

ScientificNotationandSignificantFiguresScientificnotationisawaytoexpressverylargeorverysmallnumbersinmanageableterms.Therearethreecomponentsinscientificnotation:acoefficient,apowerof10,andaunitofmeasurement.

• Fornumberslargerthan10:

o Thecoefficientisobtainedbymovingthedecimalplacetotheleftuntilyoureachanumbergreaterthan1butlessthan10.

o Thepowerof10isthenumberofdecimalplacesyoumovedandwillbeapositivevalue.

4,200ft

• Fornumberssmallerthan1:

o Thecoefficientisobtainedbymovingthedecimalplacetotherightuntilyoureachanumbergreaterthan1butlessthan10.

o Thepowerof10isthenumberofdecimalplacesyoumovedandwillbeanegativevalue.

0.00039g

1. Expressthenumbersbelowinscientificnotation.

i. 35,413

ii. 0.0453

iii. 34.7268


Ameasurednumberisanumberobtainedwhenyoumeasureaquantityusingameasuringtool(e.g.,thelengthofapieceofpaperortheweightofapenny).Thesignificantfiguresinameasurementareallthedigitsinthereportedvaluethatareknown,includingoneestimateddigit.Significantfiguresallowustoexpressareportedvaluewithaspecifieddegreeofcertainty.Thereareafewrulesfordeterminingsignificantfiguresinareportedvalue:

• Allnonzerodigitsaresignificant.

7.185inches

• Zerosbetweentwononzerodigitsaresignificant.

204.2pounds

• Thezero(s)totheleftofthefirstnonzerodigitis/arenotsignificant.

0034.12seconds

• Zerostotherightofthelastnonzerodigitaresignificantifthereisadecimalplacepresent.

6.300liters

• Zerostotherightofthelastnonzerodigitarenotsignificantifthereisnodecimalplacepresent.

2040gramsExactnumbersarethenumbersyouobtainfromcountingorthenumbersinaknownconversionfactor.Exactnumbersdonotaffectthenumberofsignificantfiguresinacalculatedanswer.Forexample,thereare60secondsin1minute.Inthiscase,boththe60andthe1areexactnumbers.2. Howmanysignificantfiguresdoeseachofthevaluesreportedbelowhave?

i. 203.10inches

ii. 003.430seconds

iii. 250.0grams


Whendeterminingthenumberofsignificantfiguresintheresultofanarithmeticoperation,wemustusethefollowingrules:

• Formultiplicationanddivision,thereportedanswermustcontainasmanysignificantfiguresasthegivenvaluewiththefewestsignificantfigures.

1.39×2.7 =

• Foradditionandsubtraction,thereportedanswermustcontainasmanydecimalplacesasthegivenvaluewiththefewestdecimalplaces.

2.42+ 14.2 =Whendoinglongcalculationswithseveralsteps,donotroundtheansweraftereachstep.Ingeneral,youshouldleaveextrasignificantfiguresinyourintermediatevalues,foraccuracy,untilyouarereadytoreportthefinalanswer.3. Whatistheresultofthefollowingcalculation,reportedwiththecorrectnumberof

significantfigures?

137.8 𝑔 + 32.23 𝑔1.23 𝑐𝑚!

A. 138.24g/cm3B. 138.2g/cm3C. 138g/cm3D. 140g/cm3


3.06

DecimalPrefixesandEqualitiesWhendealingwithquantitiesthataremuchsmallerorlargerthanthecommonSIunits,weuseprefixestoexpresstheunitsinmanageableterms.Thetablebelowshowsasetofstandardizedprefixes,basedonpowersoften.

Prefix Abbreviation Meaning Example

peta- P 1015 1m=1×10-15Pm

Or

1Pm=1×1015m

tera- T 1012 1g=1×10-12Tg 1Tg=1×1012g

giga- G 109 1s=1×10-9Gs 1Gs=1×109s

mega- M 106 1L=1×10-6ML 1ML=1×106L

kilo- k 103 1m=1×10-3km 1km=1×103m

hecto- h 102 1g=1×10-2hg 1hg=1×102g

deca- da 101 1s=1×10-1das 1das=1×101s

BaseUnit m,g,s,L,etc. 100 1m,1g,1s,1L

deci- d 10-1 1dL=1×10-1L

Or

1L=1×101dL

centi- c 10-2 1cm=1×10-2m 1m=1×102cm

milli- m 10-3 1mg=1×10-3g 1g=1×103mg

micro- µ 10-6 1µs=1×10-6s 1s=1×106µs

nano- n 10-9 1nL=1×10-9L 1L=1×109nL

pico- p 10-12 1pm=1×10-12m 1m=1×1012pm

femto- f 10-15 1fg=1×10-15g 1g=1×1015fg


Theunitprefixesinthetableabovecanalsobethoughtofasconversionfactors:awaytogofromoneunittoanotherunit,basedontheideaofequivalentunits.

1 kilometer = 1×10! meters1. Supposethatduringalaboratoryexperiment,Seanrecordsthemassofasampleofwater

as240.5grams.

i. ExpressSean’smeasurementinmilligrams.

ii. ExpressSean’smeasurementinkilograms.


3.07

DimensionalAnalysisInchemistrycalculations,dimensionalanalysisisatoolusedtoconvertameasurementintoamoreuseful,orappropriate,form.Indimensionalanalysis,oneormoreconversionfactors,writtenasfractions,areusedtogetfromtheinitialunittosomedesiredunit.

35 minutes × 60 seconds1 minute = 2100 seconds

1. SupposethattheaverageadultmaleintheUnitedStatesweighs200pounds.Usingthefact

that1poundequals453.59grams,convertthisweighttokilograms.


2. AspaceshuttlelaunchingfromtheLyndonB.JohnsonSpaceCenterinHouston,Texas,mustreachaspeedof28,000kilometersperhourtoescapethegravitationalforceoftheearthandreachorbit.Convertthisspeedintomilespersecond,usingthefactthat1mileisequivalentto1.609kilometers.


3.08

LabReportsAccuratelyandclearlyreportingthefindingsofalaboratoryexperimentisoneofthemostimportantstepsofascientificinvestigation.Whethertheresultssupportyourhypothesisornotisimmaterial.

Alabreportisasummaryofalabexperiment,anditisusedtocommunicateallthenecessarydetailsofthatexperiment.Atypicallabreporthasmanydifferentparts,whichmayincludethefollowing:

• Purpose−Describestheproblemstatementoftheexperimentandthequestionthattheexperimentistryingtoanswer

• Materials−Liststheequipmentandsubstancesneededtocarryouttheexperiment

• Procedure−Outlinesthenecessarystepstocompletetheexperiment

• Results−Presentsthedatacollectedandobservationsmadeduringtheexperiment

• Conclusion−Summarizesthefindingsoftheexperimentandofferspotentialexplanationsortheoriesabouttheresults

1. SupposeChris,Omar,Gabby,andMorganareperformingalabexperimenttoanalyzethe

flowofwater.Intheexperiment,OmarandGabbypour100litersofwaterintoa120-litertankthathasapluggedholeatthebottom.Thetankhasmarkingsdownthesideat10-literintervals.

i. Sketchandlabeladiagramtoshowthesetupforthisexperiment.


ii. Chrisremovestheplug,andMorganusesherstopwatchtorecordtheamountoftimethatpassesuntilthewaterlevelreacheseachofthemarkingsdowntheside.Shestopstakingmeasurementsoncethewaterlevelreaches10liters.Thedataisshowninthechartbelow.

WaterLevel(liters) TimeElapsed(seconds)

100 0

90 1.40

80 3.36

70 6.10

60 9.95

50 15.32

40 22.85

30 33.39

20 48.15

10 68.81

iii. Createalinegraphthatreflectsthedatafromthetableabove.


iv. Summarizethedataandproposeapossibleexplanationfortheobservedbehavior.


Section 3: Measurements - Study Edge

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