Post on 30-Nov-2021
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.
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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 =
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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)
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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
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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
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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
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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
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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.
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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.
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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
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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
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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
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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
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Theunitprefixesinthetableabovecanalsobethoughtofasconversionfactors:awaytogofromoneunittoanotherunit,basedontheideaofequivalentunits.
1 kilometer = 1×10! meters1. Supposethatduringalaboratoryexperiment,Seanrecordsthemassofasampleofwater
as240.5grams.
i. ExpressSean’smeasurementinmilligrams.
ii. ExpressSean’smeasurementinkilograms.
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3.07
DimensionalAnalysisInchemistrycalculations,dimensionalanalysisisatoolusedtoconvertameasurementintoamoreuseful,orappropriate,form.Indimensionalanalysis,oneormoreconversionfactors,writtenasfractions,areusedtogetfromtheinitialunittosomedesiredunit.
35 minutes × 60 seconds1 minute = 2100 seconds
1. SupposethattheaverageadultmaleintheUnitedStatesweighs200pounds.Usingthefact
that1poundequals453.59grams,convertthisweighttokilograms.
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2. AspaceshuttlelaunchingfromtheLyndonB.JohnsonSpaceCenterinHouston,Texas,mustreachaspeedof28,000kilometersperhourtoescapethegravitationalforceoftheearthandreachorbit.Convertthisspeedintomilespersecond,usingthefactthat1mileisequivalentto1.609kilometers.
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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.
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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.
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