Chapter 1 Chemistry as a Quantitative Science and

Chapter1ChemistryasaQuantitativeScienceandaScienceofMatter1.1IntroductionEveryobjectintheworldaroundyoucanbedescribedintermsofchemistry.Manyeventsthatyoucanseeoccurringinnatureinvolvechemicalchanges:thechangingcoloroftheleavesinthefall,thetransformationofapondintoaswamp,therustingofiron.Curiosityaboutwhatcanbeobservedintheworldhasledtothestudyofchemistry.Let'sdescribewhatisseeninonespecificchemicalchange.Twosubstancesareinvolved.Oneisablackpowderysolid.Theotherisacolorlessliquidthatcausesirritation,ifspilledontheskin.Ifsomeoftheblacksolidisplacedinacontainerandtheliquidslowlyadded,thingshappen.Theblacksolidbeginstodissolve.Thesolutionthatisformedisnotblack,butverypalegreen.Atthesametime,agasbeginstobubbleoutofthesolution.Andtheairisfilledwithaterriblesmell,likethatofrotteneggs.Whatamultitudeofquestionscanbeaskedhere.Whatarethesesubstances?Whydidtheblacksoliddissolve?Whatwasformedinitsplace?Howmuchoftheliquiddoesittaketodissolvealloftheblacksolid?Howmuchofthegascanbeproduced?Howlongdidthechangetake?Willeventsspeedupifweheatthemixture?Ifso,byhowmuchperdegreeoftemperature?1Noticehowmanyofthequestionsarequantitativeones.Observationandmeasurementbothplayvitalrolesinansweringthequestionsofchemistry.Achemicalchangeisnotcompletelyunderstooduntilitisunderstoodquantitatively--intermsofmeasurementsandnumbers.Ourunderstandingofchemistryistestedbymakingmeasurements.Ifapredictionismadebasedonwhatwethinkweunderstand,andifthepredictionisshowntobecorrectbyobtainingthepredictednumbersinaquantitativetest,wehavegreaterconfidenceinourunderstanding.Instudyingchemistryyouwillbepresentedwithfactsaccumulatedduringhundredsofyearsofobservationandmeasurement.Youwillalsolearnhowtheprinciplesofchemistryareusedtoexplainwhathasbeenobserved.Totestyourunderstandingofchemicalprinciples,youwillsolveproblems,frequentlyproblemsthatutilizetheresultsofmeasurementsofphysicalproperties.1.2NumbersinPhysicalQuantities1.MeasurementandSignificantFigures(1)Theresultofmeasuringaphysicalpropertyisexpressedbyanumericalvaluetogetherwithaunitofmeasurement,forexample,180pounds91kilograms(2)Exactnumbersarenumberswithnouncertainty;theyarisebydirectlycountingwholeitemsorbydefinition.Numbersthatresultfrommeasurementsareneverexact.Thereisalwayssomedegreeof2uncertaintyduetoexperimentalerrors:limitationsofthemeasuringinstrument,variationsinhoweachindividualmakesmeasurements,orotherconditionsoftheexperiment.(3)Significantfiguresinanumberincludeallofthedigitsthatareknownwithcertainty,plusthefirstdigittotherightthathasanuncertainvalue.Forexample,theuncertaintyinthemassofapowdersample,i.e.3.1267g.asreadfromananalyticalbalance''is±0.0001g.(4)Errorsinmeasurement:(i)Randomerrorswhichresultfromuncontrolledvariablesinanexperimentandaffectprecision--thereproducibilityoftheresultsofameasurement;(ii)Systematicerrorswhichcanbeassignedtodefinitecausesandaffectaccuracy---theclosenesstothetrueresultofameasurementoranexperiment.2.FindingtheNumberofSignificantFigures(1)Thenumberofsignificantfiguresisfoundbycountingfromlefttoright,beginningwiththefirstnonzerodigitandendingwiththedigitthathastheuncertainvalue,e.g.,454(3)0.296(3)7.31(3)0.00846(3)10.7(3)1520(3)1520.(4)N.B.[(Lat.)(notabene)]Zerosattheendofanumbergivenwithoutadecimalpointpresentaproblembecausetheyareambiguous.3Ingeneral,werecommendthatsuchterminalzerosbeassumedtobenotsignificant.Theambiguityisremovedifadecimalpointisgiven;thenallthezerosprecedingthedecimalpointaresignificant.(2)Ex.（Example）Howmanysignificantfiguresareinthenumbers(a)57,(b)82.9,(c)340,(d)700.,(e)10.000,(f)0.000002,(g)0.0402,and(h)0.04020？3.ArithmeticUsingSignificantFigures(1)Additionandsubtraction:Roundtheanswertotheplace(beforeorafterthedecimalpoint)withthegreatestuncertainty,e.g.,23.253536.052600600．139.4168168168.652821821(±1)168.7(±0.1)800(±100)(2)Multiplicationanddivision:Roundtheanswertothesamenumberofsignificantfiguresasinthenumberwiththefewestsignificantfigures,e.g.(23.2)(0.1257)=[2.91624]=2.92(6)×(6.35g)=38.1g(3)Ex.Performthefollowingcalculationandexpresstheanswertothepropernumberofsignificantfigures.x=⎟⎠⎞⎜⎝⎛−30812981)987.1)(303.2()316.95(=2.2693789541/298=0.003361/308=0.003251/298-1/308=0.000114x=2.34.ScientificNotation(ExponentialNotation)(1)Instandardscientificnotationthesignificantfiguresofanumberareretainedinafactorbetween1and10andthelocationofthedecimalpointisindicatedbyapowerof10,e.g.0.0063=6.3×10-3900,000,000=9×108(2)ArithmeticUsingScientificNotation99+1.23×103or0.099×1031.23×1031.329×1031.33×10321.0101.21001.2103.4112=×=××−−−4.3×10-2(6.022×1023)(4.2×103)=25×1026=2.5×10271.3UnitsofMeasurement1.SystemsofMeasurement(1)TheweightofanEnglishman=14stone(14pounds)(89kilograms)anAmerican=180pounds(82kilograms)aCanadian=91kilograms(2)Metricsystem:devisedbytheFrenchNationalAcademyofSciencesin1793.(3)SIsystemn.(forSystemeInternational):adoptedbytheInternationalBureauofWeightsandMeasuresin1960,itisarevisionandextensionofthemetricsystem.Scientistsandengineersthroughout5theworldinalldisciplinesarenowbeingurgedtouseonlytheSIsystemofunits.SIBasePhysicalQuan