Concept Development Studies in Chemistry 2012

By: John S. Hutchinson

Concept Development Studies in Chemistry 2012

By: John S. Hutchinson

Online: < http://cnx.org/content/col11444/1.4/ >

CONNEXIONSRice University, Houston, Texas

This selection and arrangement of content as a collection is copyrighted by John S. Hutchinson. It is licensed under the Creative Commons Attribution 3.0 license (http://creativecommons.org/licenses/by/3.0/). Collection structure revised: August 16, 2012 PDF generated: February 6, 2013 For copyright and attribution information for the modules contained in this collection, see p. 233.

Table of ContentsI refe to gonept hevelopment tudies in ghemistry F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F F I P etomi woleulr heory F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F Q Q etomi wsses nd woleulr pormuls F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F II R truture of n etom F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PQ S iletron hell wodel of n etom F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F QQ T untum iletron inergy vevels in n etom F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F F RI U iletron yritls nd iletron gon(gurtions in etoms F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F RW V govlent fonding nd iletron ir hring F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F TQ W woleulr trutures F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F UQ IH inergy nd olrity of govlent ghemil fonds F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F VU II fonding in wetls nd wetlExonEwetl lts F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F WW IP woleulr qeometry nd iletron homin heory F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F III IQ wesuring inergy ghnges in ghemil etions F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F IPQ IR etion inergy nd fond inergy F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F IQI IS sdel qs vw F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F IRI IT uineti woleulr heory F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F ISQ IU etion tes F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F ITQ IV hse iquilirium nd sntermoleulr sntertions F F F F F F F F F F F F F F F F F F F F F F FF F F F F F F F F F F F F F F F F IVQ IW etion iquilirium in the qs hse F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F IWS PH eidEfse iquilirium F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PHU PI iquilirium nd the eond vw of hermodynmis F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PIW sndex F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PQI ettriutions F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F FPQQ

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Available for free at Connexions

Chapter 1

Preface to Concept Development Studies in Chemistry1

1.1 Why Concept Development Studies?he ody of knowledge lled iene onsists primrily of models nd oneptsD sed on oservtions nd dedued from reful resoningF iewed in this wyD iene is retive humn endevorF he modelsD oneptsD nd theories we use to desrie nture re omplishments equl in retivity to ny rtistiD musilD or literry workF nfortuntelyD textooks in ghemistry trditionlly present these models nd onepts essentilly s estlished ftsD stripped of the lever experiments nd logil nlyses whih give them their humn esseneF es onsequeneD students re typilly trined to memorize nd pply these modelsD rther thn to nlyze nd understnd themF es resultD retiveD nlytil students re inlined to feel tht they nnot 4do4 ghemistryD tht they nnot understnd the oneptsD or tht ghemistry is dull nd uninterestingF his olletion of gonept hevelopment tudies in ghemistry is presented to rediret the fous of lerningF sn eh onept development studyD mjor hemil onept is developed nd re(ned y nlysis of experimentl oservtions nd reful resoningF ih study egins with the de(nition of n initil poundtion of ssumed knowledgeD followed y sttement of questions whih rise from the poundtionF enlysis of these questions is presented s series of oservtions nd logil dedutionsD followed y further questionsF his detiled proess is followed until the oneptul development of model provides resonle nswer to the stted questionsF gonept hevelopment tudies in ghemistry is written with two ene(ts to the reder in mindF pirstD y onstruting eh signi(nt onept through oservtion nd ritil resoningD you will gin muh deeper understnding of tht oneptF sn ddition to knowing how to work with modelD you will hve oth n understnding of why the model is elievle nd n ppreition of the essentil euty of the modelF st will mke sense to you in your own termsF eondD the resoning required to understnd these onept development studies will enhne your development of ritilD nlytil thinkingD skill whih is most importnt to suess in ieneF es noteD these studies re not intended to e historil developmentsD lthough the experiments presented re the ones whih led to the onepts disussedF ynly smll mount of historil informtion hs een inluded for perspetiveF

1.2 How to Study the Concept Development Studiesou should study eh onept development studyD not y memoriztionD ut y refully thinking out the experiments nd the logil development of the onepts nd modelsF ih study is shortD nd is ment1 This content is available online at .Available for free at Connexions

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CHAPTER 1. PREFACE TO CONCEPT DEVELOPMENT STUDIES IN CHEMISTRY

to e red slowly nd metiulouslyF ih sentene ontins sustne to e studied nd understoodF ou shouldD t eh step in the nlysisD hllenge yourself s to whether you n reprodue the resoning leding to the next onlusionF yne good wy to do this is to outline the onept development studyD mking sure you understnd how eh piee of the rgument ontriutes to the development of onept or modelF st is very importnt to understnd tht sienti( models nd theories re lmost never 4provenD4 unlike mthemtil theoremsF therD they re logilly developed nd dedued to provide simple explntions of oserved phenomenonF es suhD you will disover mny times in these onept development studies when onlusion is not logilly required y n oservtion nd line of resoningF snstedD we my rrive t model whih is the simplest explntion of set of oservtionsD even if it is not the only oneF ientists most ommonly ide y the priniple of ym9s rzorD one sttement of whih might e tht the explntion whih requires the lest ssumptions is the est oneF yne very importnt wy to hllenge your understnding is to study in group in whih you tke turns explining the development of the modelF he ility to explin onept is muh stronger inditor of your understnding thn the ility to solve prolem using the oneptF se the questions t the end of the onept development studies to prtie your skill t explining tehnil rguments lerly nd oniselyF

1.3 Updates in the 2012 Editionhe PHIP editions of these gonept hevelopment tudies were ompletely rewritten with two gols in mindF he (rst ws to mke these more redleD less terseD more onverstionlD more pprohleF he seond ws to rek them into shorter segmentsD to e more mngele in individul unitsF foth of these gols were sed on the invlule input of my students nd of the high shool tehers s hve worked with for the pst dedeF s m grteful for their feedkF xot ll of the modules hve een rewritten in the PHIP editionF purther new modules will e dded in the next edition

1.4 Acknowledgmentswy own thinking in writing gonept hevelopment tudies in ghemistry hs een strongly in)uened y three ooksX The Historical Development of Chemical ConceptsD y omn wierzekiY The History of ChemistryD y tohn rudsonY Chemical PrinciplesD y ihrd hikersonD rrry qryD nd qilert rightF s m deeply ppreitive of the ontriutions of tonn pirD uren eini tevensD uevin eusmnD urin rightD nd usn iediger in reviewing nd ritiizing erly drfts of the mnusript for this textF he PHIP editions of these modules were written with signi(nt ssistne from grrie yenlndD ves rnD grolyn xiholD nd uristi uinidF s ppreite the hrd work of te'rey ilvermn nd henver qreene to onvert these douments for use in the gonnexions rojet2 t ie niversity3 F gonept hevelopment tudies in ghemistry would not hve een written were it not for the loving enourgement of my wife ulD who reminded me ontinully over mny yers nd prtiulrly t the most di0ult of times tht writing it ws the right thing to doF s will e forever grtefulF sf this ook is of ny ssistne to you in understnding ghemistryD your thnks must go to ulF tr tuly PHIP Vision Impaired Access: hnks to the trnsltion e'orts of ie niversity9s hisility upport ervies4 D this olletion is now ville in frilleEprintle versionF lese lik here5 to downlod Fzip (le ontining ll the neessry Fdx nd imge (lesF2 http://cnx.org 3 http://www.rice.edu 4 http://www.dss.rice.edu/ 5 See the le at Available for free at Connexions

Chapter 2

Atomic Molecular Theory2.1 Introduction

1

sn this studyD our gol is to develop the onept of the etomi woleulr heoryF his is the theory t the foundtion of everything we understnd out ghemistryD s it sttes tht ll mtter is mde up of individul prtiles lled tomsD whih omine in wys tht re oth simple nd omplex to form lrger prtiles lled moleulesF hen we understnd these toms nd moleulesD it hnges the wy tht we look t the world round usF e n understnd the properties of the sustnes we intert withD we n mke preditions out the hnges nd retions tht these sustnes will undergoD nd we n design mterils with properties tht would e useful to usF he ide tht everything is mde of toms is something we re told t very erly geD nd for mny studentsD it is hrd then to imgine world in whih we don9t know tht everything is mde of tomsF yn the other hndD this prtiulte view of mtter does seem ounter to lmost ll of our own oservtionsF he desks in front of usD the ir we retheD the wter we drinkD nd even our own )esh show no signs of these prtilesF uite the oppositeX they seem to e either very solid or quite )uidD nd ertinly not griny like olletion of prtiles might e expeted to eF sn this onept development studyD thenD we set side our knowledge of these toms nd moleules nd skD quite skeptillyD why do we elieve tht there re toms tht omine to form moleulesc yr sked nother wyD if we elieve tht ll mtter is mde up of tomsD how would we show tht this is truec ht is the evidenec hoes the proof require us to see tomsD or is it possile to prove tht they exist without tully seeing themc

2.2 Foundationghemistry is the study of mtterD so it mkes sense for us to gree on wht we men y mtter nd wht we wnt to know out itF ehnillyD mtter is nything tht hs mssD ut more ommonlyD mtter is wht we regrd s stu'F enything tht hs physil properties nd tkes up speD whether solidD liquidD or gsD is mtterF wtter n e nything from mirosopi to gltiD or from roks nd ir to utter)ies nd humnsF fut we n go further thn this nd fous on spei( type of mtter lled pure sustneF his is mteril tht is ompletely uniform in properties regrdless of the size of the smple we tke or from where we tke the smpleF st is esiest to understnd pure sustne y ompring it to mixtureD whih my or my not e uniform in its properties suh s olorD densityD nd texture nd n vry depending on how we mke the mixture or its originF howing tht sustne is either pure sustne or mixture requires lot of experimenttionD ut we will ssume for our foundtion tht we hve lredy identi(ed whih smples of mtter re pure sustnes nd whih re mixturesF1 This content is available online at .Available for free at Connexions

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CHAPTER 2. ATOMIC MOLECULAR THEORY

es of PHHWD the most omprehensive list of hemil sustnes numered over SH million entriesF his huge numer of mterils seems inomprehensileD fr eyond our understndingF roweverD it turns out tht these SH million sustnes re ll mde up from muh smller set of pure sustnes lled elementsF en element is sustneD whih nnot e roken down into simpler sustnesF here re only out WH ommonly ourring elements on erthF he remining SH million pure sustnes re omintions of these elements lled ompoundsD nd these re distinguishle from the elements in tht ompound n e roken down into the elements from whih it is mdeF por exmpleD metlli iron nd gseous oxygen re oth elementsD whih nnot e redued into simpler sustnesD ut ommon iron rustD ferrous oxideD is ompound mde up from iron nd oxygenF hereforeD rust n e redued to iron nd oxygenD nd rust n e reted y omining iron nd oxygenF fut iron nd oxygen re elementsY they nnot e trnsformed into one nother nd re not omposed of simpler or ommon mterilsF hetermining whether pure sustne is n element or ompound is di0ult nd timeEonsuming proess of experimenttionF e will ssume for our study tht the elements hve ll een identi(edF ine mtter is nything tht n hve mssD we will spend muh of our time in this study nlyzing mssF ithout proving itD we will ssume the vlidity of the vw of gonservtion of wssD n experimentl result tht simply sysD he totl mss of ll produts of hemil retion is equl to the totl mss of ll retnts of the retionF sn other wordsD mtter nnot e reted or destroyed y hemil or physil proessesF his lw mkes it possile for us to mesure msses of mterils during retions knowing tht these msses ren9t vrile or unpreditleF ith these ssumptions in mindD we n proeed diretly to experiments whih led to the development of the etomi woleulr heoryF

2.3 Observation 1: Mass Relationships during Chemical Reactionsine mtter is nything tht hs mssD then the vw of gonservtion of wss suggests tht mtter is lso onserved during hemil retionsX whtever we strt withD we wind up withD t lest in totlF roweverD this does not men tht mtter must e mde up of tomsF st simply sys tht mtter is reorgnized in some wy to produe new sustnes with new properties when retion tkes pleF ine we know tht ll sustnes re mde of elementsD then we n nlyze the msses of the elements tht prtiipte in hemil retionF wost importntlyD we n tke ompoundD rek it into the elements tht it is mde ofD nd then (nd the msses of those elementsF prom the vw of gonservtion of wssD the totl mss of the elements tht mke up the ompound must equl the mss of the strting ompoundF por exmpleD prtiulr ompound lled opper ronte is omposed of the elements opperD ronD nd oxygenF sf we tke IHHFH g smple of opper ronteD we (nd tht it ontins SIFS g of opperD QVFV g of oxygenD nd WFU g of ronF he totl of these three msses is SIFS gCQVFV gCWFU g a IHHFHg nd is the sme s the mss of the opper ronteF his turns out to lwys e trueF st does not mtter wht smple of opper ronte we nlyzeD where it me fromD who gve it to usD or how we mde itF e lwys get these sme msses of the elementF ht if we tke PHHFH g of opper ronte instedc ixperiments show us tht we get IHQFH g of opperD UUFT g of oxygenD nd IWFR g of ronF he totl of these three msses is IHQFH gCUUFT gCIWFR g a PHHFHgD so gin the totl mss is onservedF iven more importntlyD there is something striking out these numers when ompred to the IHHFH g smpleF hen we doule the mss of the opper ronteD we lso doule the mount of opper it ontinsX PHHFH g of opper ronte ontins IHQFH g of opperD nd IHHFH g of opper ronte ontins SIFS gF he sme is true for the mounts of oxygen nd ronF yne wy to look t this is tht the frtion of the opper ronte whih is opper is the sme in oth smplesX SIFS gGIHHFH g is equl to IHQFH gGPHHFH gD whih is equl to SIFS7F his is very importnt resultF efter looking t dt from mny experimentsD we (nd tht regrdless of the spei( smple of opper ronteD regrdless of the mss of tht smpleD nd regrdless of where tht smple me fromD the frtion of the mss of the smple whih is opper is lwys the smeD SIFS7F e get similr results for the oxygen nd ronF he frtions of the mss of every smple of opper ronte re lwys SIFS7 opperD QVFV7 oxygenD nd WFU7 ronFAvailable for free at Connexions

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Figure 2.1: A sample of copper carbonate basic, CuCO

3 Cu(OH)2

illustrating the blue-green color.

Figure

2.2:

A

graph

showing

ratios

of

components

in

copper

http://woelen.homescience.net/science/chem/compounds/index.html ).

2

carbonate

(photograph

from

yther ompounds show similr resultsF por exmpleD every smple of the ompound led sul(de ontins VTFU7 led nd IQFQ7 sulfur y mssF his is true whether we tke IFHH g of led sul(de or IFHH kg of led sul(de or ny other totl mssF e lwys get the sme proportions of the msses of led nd sulfur in the smpleF2 http://woelen.homescience.net/science/chem/compounds/index.html

Available for free at Connexions

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CHAPTER 2. ATOMIC MOLECULAR THEORY

his experimentl oservtion is so onsistent for the vst mjority of ll ompounds tht we regrd it s nturl lwD summry of mnyD mny oservtions tht we therefore lwys expet to oserve in future oservtionsF sn this seD the nturl lw we hve oserved is the vw of he(nite roportionsX vw of he(nite roportionsX hen two or more elements omine to form ompoundD their msses in tht ompound re in (xed nd de(nite rtioF his mens tht if we rek ompound down into its elements nd mesure the msses of the elements tht mke it upD those msses re lwys in the sme rtioF e n illustrte this with set of simple ompounds eh ontining two of the elements of hydrogenD nitrogenD nd oxygenF he de(nite rtios given y the vw of he(nite roportions re show in le PFIX wss eltionships of imple gompounds of rydrogenD xitrogen nd yxygen for IHHFH g of eh ompoundX

wss eltionships of imple gompounds of rydrogenD xitrogen nd yxygengompound ter emmoni xitri yxide otl wss @gA IHHFH IHHFH IHHFH wss of rydrogen @gA IIFP IUFU ETable 2.1

wss of xitrogen @gA E VPFQ RTFU

wss of yxygen @gA VVFV E SQFQ

ho these (xed msses men tht we re omining tiny prtiles of (xed mss together to form these ompoundsc o test this hypothesisD let9s look t these numers more losely to see if we n mke ny sense of themF yne wy to look t these dt is to imgine tking smple of wter tht ontins extly IFHH g of hydrogenD nd lso smple of mmoni tht ontins extly IFHH g of hydrogenF sf we do thisD the dt now look s shown in the (rst two lines of le PFPX wss eltionships of imple gompounds of rydrogenD xitrogen nd yxygenF

wss eltionships of imple gompounds of rydrogenD xitrogen nd yxygengompound ter emmoni xitri yxide otl wss @gA VFWQ SFTS PFIR wss of rydrogen @gA IFHH IFHH ETable 2.2

wss of xitrogen @gA E RFTS IFHH

wss of yxygen @gA UFWQ E IFIR

vooking t the dt this wy llows us to ompre how (xed mount of hydrogen omines with either nitrogen or oxygenF prom the vw of he(nite roportionsD we know we will lwys get the (xed mss rtios shown in le PFPX wss eltionships of imple gompounds of rydrogenD xitrogen nd yxygenF e might imgine tht this mens tht wter is formed from I tom of hydrogen nd I tom of oxygenD nd tht therefore the mss of I tom of oxygen is UFWQ times greter thn the mss of I tom of hydrogenF sf this is trueD then mmoni might lso e formed from I tom of hydrogen nd I tom of nitrogenD in whih se I tom of nitrogen hs mss RFTS times greter thn I tom of hydrogenF his ll seems onsistent with the ide tht these elements re mde up of toms omining in oneEtoEone rtiosF fut now we (nd prolemX if n tom of oxygen is UFWQ times s mssive s n tom of hydrogen nd if n tom of nitrogen is RFTS times s mssive s n tom of hydrogenD then it must e tht n tom of oxygen is more mssive thn n tom of nitrogen y the rtio of UFWQGRFTS a IFUHF hen we now look t the third row of le PFPX wss eltionships of imple gompounds of rydrogenD xitrogen nd yxygenD the dt tell us if nitri oxide is mde up I tom of nitrogen nd I tom of oxygenD n oxygen tom hs Available for free at Connexions

U mss IFIV times greter thn the mss of nitrogenF yur numers nd our onlusion ren9t onsistent with the experimentl dtD so we must hve mde n inorret ssumptionF yne possiility is tht we were wrong when we ssumed tht there re toms of the three elements omining to form these three ompoundsF fut this does not seem likelyD sine it is hrd to understnd the (xed mss proportions without thinking tht we re omining prtiles with (xed mss proportionsF tillD we must hve mde n inorret ssumption sine our onlusions were ontrditoryF ell tht in doing our lultions of the msses of the tomsD we ssumed tht in eh ompound one tom of eh element omined with one tom of the other elementF elthough this is simple ssumptionD there is no reson why only one tom of eh type might omineF erhps the rtios re di'erent thn thisD nd toms omine in rtios of IEtoEPD PEtoEQD or ny other simple omintionF he prolem tht this poses is tht we don9t hve wy to proeed from hereF iven if we ssume tht the vw of he(nite roportions tells us tht the elements re mde up of tomsD we hve no wy to determine nything out these tomsF ithout knowing the rtios of toms in di'erent ompoundsD we nnot determine the msses of the toms of the elementsF end without knowing the msses of the toms of the elementsD we nnot determine the rtios of the toms in di'erent ompoundsF ithout knowing nything out the toms of these elementsD we do not hve sis for elieving tht these elements re mde up of tomsF he etomi woleulr heory is still outside our rehF ithout further oservtionsD we nnot sy for ertin whether mtter is omposed of toms or notF

2.4 Observation 2: Multiple Mass Ratiose disovered ove tht we nnot onlude from the vw of he(nite roportions how mny toms of eh element omine to form prtiulr ompoundD even if we ssume tht this is how ompound is formedF here is dditionl evidene tht the vw of he(nite roportions is not (nl proof of the existene of tomsF st is esy to (nd di'erent ompounds with di'erent hemil nd physil propertiesD whih re formed from the sme two elementsF his mens thtD if there re tomsD they n omine in mny di'erent wysF por exmpleD there re huge numer of simple hydroron ompounds formed just from hydrogen nd ronF le PFQX wss eltionships of imple gompounds of rydrogen nd gron lists the mss perentges of just few of theseX

wss eltionships of imple gompounds of rydrogen nd grongompound wethne ithne fenzene otl wss@gA IHHFH IHHFH IHHFH wss of rydrogen@gA PSFI PHFI UFUTable 2.3

wss of gron@gA URFW UWFW WPFQ

he vw of he(nite roportions sys tht the rtio of the msses of two elements in ompound is (xedF sn le PFQX wss eltionships of imple gompounds of rydrogen nd gron we see severl rtios of the msses of ron nd hydrogenF his is onsistent with the vw of he(nite roportionsD thoughD euse eh (xed rtio gives us di'erent ompound with di'erent hemil nd physil propertiesF hereforeD di'erent proportions of elements re possileD nd depending on the elementsD there my e one or mny possile proportions nd ompoundsF his is referred to s multiple proportionsF ih ompound gives us one de(nite proportion of the elementsD ut euse there n e mny ompoundsD there n e multiple di'erent ut de(nite proportionsF le PFQX wss eltionships of imple gompounds of rydrogen nd gron provides just three exmples of ompounds formed from ron nd hydrogenF he numer of suh ompounds is hugeD eh with di'erent de(nite mss rtio nd eh with its own distint physilAvailable for free at Connexions

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CHAPTER 2. ATOMIC MOLECULAR THEORY

nd hemil propertiesF por exmpleD methne gs is ommonly urned in gs stoves nd liquid otne is ommonly used in rsY yet oth re ompounds of ron nd hydrogen onlyF e will now look in gret detil t few ompounds formed just from nitrogen nd oxygenD simply lled nitrogen oxidesF ine we don9t know nything out these ompoundsD for now we9ll just ll them yxide eD yxide fD nd yxide gF hese three ompounds re very di'erent from one notherF wo of these re quite toxiD ut one is used s n nesthetiD prtiulrly y dentistsF wo of these re olorlessD ut one is drk rown olorF vet9s look t the mss rtios for these three ompounds in le PFRX wss eltionships of imple gompounds of xitrogen nd yxygenF

wss eltionships of imple gompounds of xitrogen nd yxygengompound yxide e yxide f yxide g otl wss@gA IHHFH IHHFH IHHFH wss of xitrogen@gA QHFS RTFU TQFUTable 2.4

wss of yxygen@gA TWFS SQFQ QTFQ

et (rst glneD there is nothing speil out these numersF here re no ovious ptterns or reltionE ships mongst the msses or mss rtiosF fut let9s look t this dt in the sme wy s we did in le PFPX wss eltionships of imple gompounds of rydrogenD xitrogen nd yxygen y (nding the mss of oxygen tht omines with IFHH g of nitrogenF his is in le PFSX wss eltionships of imple gompounds of xitrogen nd yxygenF

wss eltionships of imple gompounds of xitrogen nd yxygengompound yxide e yxide f yxide g otl wss@gA QFPV PFIR IFSU wss of xitrogen@gA IFHH IFHH IFHHTable 2.5

wss of yxygen@gA PFPV IFIR HFSU

ou might hve to look t these dt very hrd to see itD ut there is pttern tht is ovious one you see itF sn the olumn for the wss of yxygenD the three vlues listed hve simple reltionshipX eh one is multiple of HFSUF e n see this most lerly if we divide eh of the msses for the three oxides y HFSUF his shows us tht the rtio PFPV X IFIR X HFSU is equl to the rtio R X P X IF ht does this tell usc st mens tht if we hve (xed mss of nitrogenD the mss of oxygen whih will omine with it nnot e simply ny mountF sn ftD the opposite is trueF here re few spei( msses of oxygen whih will omine with the (xed nitrogenD nd those spei( msses re integer multiples of (xed unit of mssF st is prtiulrly interesting tht the msses of oxygen re in integer rtiosF sntegers re speil set of numers used for one primry purposeD whih is to ount ojetsF sn this seD the ojet must e (xed unit of mss of oxygenF he dt in le PFSX wss eltionships of imple gompounds of xitrogen nd yxygen tell us tht when we hve (xed mount of nitrogenD it n e omined only with some integer numer of (xed unit of mss of oxygenF hy would there e (xed unit of mss of oxygenc he simplest nd est explntion is tht oxygen exists s (xed units of mssD or prtilesD nd we ll these prtiles toms of oxygenF husD the dt in le PFSX wss eltionships of imple gompounds of xitrogen nd yxygen led us to onlusion tht the element oxygen is omposed of individul toms with identil mssF e hve shown tht mtter is mde up of prtiles nd tht elements onsist of identil prtiles or tomsFAvailable for free at Connexions

W e n see these simple integer rtios in other ompoundsD s wellF vet9s look k t le PFQX wss eltionships of imple gompounds of rydrogen nd gronD whih shows ompounds of ron nd hydrogenF he rtios of the msses don9t pper to e interesting until we do the sme type of nlysis tht we did on the nitrogen oxidesF vet9s (x the mss of hydrogen in eh of these ompounds nd (nd out the msses of ronF he results re in le PFTX wss eltionships of imple gompounds of rydrogen nd gronF

wss eltionships of imple gompounds of rydrogen nd grongompound wethne ithne fenzene otl wss@gA QFWV RFWU IPFWW wss of rydrogen@gA IFHH IFHH IFHHTable 2.6

wss of gron@gA PFWV QFWU IIFWW

he rtio PFWV X QFWU X IIFWW is the sme s the rtio Q X R X IPF yne gin for (xed mount of hydrogenD the mss of ron tht n omine is multiple of (xed mss unitF hereforeD ron n only ret in smll (xed units of mssD so ron is mde up of tomsF hese dt lso show the sme onlusion for hydrogenF ell we hve to do is (x the ron mss nd ompre the msses of hydrogen tht will omine with tht mount of ronF he oservtions we hve mde for ron nd hydrogen ompounds nd nitrogen nd oxygen ompounds re generlF hey pply to ll simple ompoundsF husD we stte new nturl lw whih summrizes these oservtionsD the vw of wultiple roportionsX vw of wultiple roportionsX hen two elements omine to form more thn one ompoundD the msses of one element tht omine with (xed mss of the other element re in simple integer rtioF he vw of wultiple roportions is rther wordy nd di0ult to stteD ut the dt in le PFSX wss eltionships of imple gompounds of xitrogen nd yxygen nd le PFTX wss eltionships of imple gompounds of rydrogen nd gron illustrte it lerlyF sf we (x the mss of one elementD the msses of the other element in the three ompounds re lwys in simple integer rtioF ine these oservtions re generlD then the onlusions tht follow re lso generlX ll elements re mde up of (xed units of mssD nd we ll these prtiles tomsF hese onlusions point to other very importnt onlusionsD s wellF ine ompounds re formed from the elementsD then ompounds onsist of toms of the elements in vrious omintionsF ery importntlyD the integer rtios of the msses of the toms re lwys simpleD tht isD smll integersF hereforeD the toms of the di'erent elements omine in simple rtiosD tooF his mens tht the smll prtiles lled toms re omining in simple wys to form smll prtiles of the ompoundF e ll these prtiles moleulesD nd ompounds onsist of identil moleules mde up of toms in simple integer rtiosF he etomi woleulr heoryX e hve now oserved experimentl dt whih revel to us severl importnt onlusionsF e ll these onlusions postultesD nd tken together these postultes form the etomi woleulr heoryX IF ih element is omposed of very smllD identil prtiles lled tomsF PF ell toms of single element hve the sme hrteristi mssF QF he numer nd msses of these toms do not hnge during hemil trnsformtionF RF ih ompound onsists of identil moleulesD whih re smllD identil prtiles formed of toms omined in simple whole numer rtiosF et this pointD we know very little out these tomsD other thn tht they existD hve (xed mss for eh elementD nd omine to form moleulesF e don9t know wht the tomi msses reD even in omprison to eh otherD nd we don9t know the simple integer rtios y whih they omine to form moleules nd ompoundsF e hve mde mjor step forwrd in proving tht mtter is mde up of toms nd moleulesD ut we hve long wy to go to mke this theory usefulFAvailable for free at Connexions

IH

CHAPTER 2. ATOMIC MOLECULAR THEORY

2.5 Review and Discussion QuestionsIF essume tht mtter does not onsist of tomsF how y exmple how this ssumption leds to hypoE thetil preditions whih ontrdit the vw of wultiple roportionsF ho these hypothetil exmples ontrdit the vw of he(nite roportionsc ere oth oservtions required for on(rmtion of the tomi theoryc PF wo ompoundsD e nd fD re formed entirely from hydrogen nd ronF gompound e is VHFH7 ron y mssD nd PHFH7 hydrogenD wheres gompound f is VQFQ7 ron y mss nd ITFU7 hydrogenF hemonstrte tht these two ompounds oey the vw of wultiple roportionsF ixplin why these results strongly indite tht the elements ron nd hydrogen re omposed of tomsF QF sn mny hemil retionsD mss does not pper to e onserved quntityF por exmpleD when tin n rustsD the resultnt rusty tin n hs greter mss thn efore rustingF hen ndle urnsD the remining ndle hs invrily less mss thn efore it ws urnedF rovide n explntion of these oservtionsD nd desrie n experiment whih would demonstrte tht mss is tully onserved in these hemil retionsF RF he following question ws posed on n exmX An unknown non-metal element (Q) forms two gaseousuorides of unknown molecular formula. A 3.2 g sample of Q reacts with uorine to form 10.8 g of the unknown uoride A. A 6.4 g sample of Q reacts with uorine to form 29.2 g of unknown uoride B. Using these data only, demonstrate by calculation and explanation that these unknown compounds obey the Law of Multiple Proportions.

e student responded with the following nswerX

essess the ury of the students nswerF sn your ssessmentD you must determine wht informtion is orret or inorretD provide the orret informtion where neededD explin whether the resoning is logil or notD nd provide logil resoning where neededF fy tohn F ruthinsonD ie niversityD PHII

The Law of Multiple Proportions states that when two elements form two or more compounds, the ratios of the masses of the elements between the two compounds are in a simple whole number ratio. So, looking at the data above, we see that the ratio of the mass of element Q in compound A to the mass of element Q in compound B is 3.2:6.4 = 1:2, which is a simple whole number ratio. This demonstrates that these compounds obey the Law of Multiple Proportions.

Available for free at Connexions

Chapter 3

Atomic Masses and Molecular Formulas3.1 Introduction

1

sn this studyD our gols re to determine the msses of the toms of eh element nd to (nd the rtios of the toms tht omine to form the moleules of di'erent ompoundsF e will (nd tht we determine the tomi msses reltive to one notherF sn other wordsD we will (nd tht the toms of one element my e IFP times s mssive s the toms of nother elementF e will not tully determine the mss of n tom reltive toD syD lrge smple of mtter like r of metl or glss of wterF por lmost ll purposes in ghemistryD it turns out tht we only need these reltive mssesF e will lso (nd the formuls of individul moleules for di'erent ompoundsF he moleulr formul tells us how mny toms of eh type there re in moleule of ompoundF por exmpleD mny people know tht wter is r2 yD mening tht moleule of wter ontins two hydrogen toms nd one oxygen tomF elthough we hven9t shown it yetD the moleulr formul of wter is r2 yF he postultes of the etomi woleulr heory provide us gret del of understnding of pure suE stnes nd hemil retionsF por exmpleD the theory revels the distintion etween n element nd ompoundF sn n elementD ll toms re identilF sn ompoundD there re toms of two or more elements omined into smll identil moleules in smll integer rtiosF he theory lso revels to us wht hppens during hemil retionF hen two elements retD their toms omine to form moleules in (xed rE tiosD mking new ompoundF hen two ompounds retD the toms in the moleules of these retnt ompounds reomine into new moleules of new produt ompoundsF es good s this isD it is out s fr s we n go without further oservtions nd nlysisF e don9t know the reltive msses of the tomsD nd we don9t know the moleulr formul for ny ompoundF st turns out tht to know one of these things we need to know the other oneF o see thisD let9s tke nother look t the dt in the gonept hevelopment tudy on etomi woleulr heory @le PFSX wss eltionships of imple gompounds of xitrogen nd yxygenAF rere it is gin s le QFIX wss eltionships of imple gompounds of xitrogen nd yxygenX

wss eltionships of imple gompounds of xitrogen nd yxygengompound yxide e yxide f yxide g otl wss @gA QFPV PFIR IFSU wss of xitrogen @gA IFHH IFHH IFHHTable 3.1

wss of yxygen @gA PFPV IFIR HFSU

1 This content is available online at .Available for free at Connexions

II

IP

CHAPTER 3. ATOMIC MASSES AND MOLECULAR FORMULAS

e now know tht (xed mss of nitrogen mens (xed numer of nitrogen tomsD sine eh tom hs the sme mssF end if we doule the mss of oxygenD we hve douled the numer of oxygen tomsF oD ompring yxide e to yxide fD for the sme numer of nitrogen tomsD yxide e hs twie s mny oxygen toms s yxide fD whih hs twie s mny oxygen toms s yxide gF here re mny possile moleulr formuls whih re onsistent with these rtiosF o see thisD we n show tht ny one of the oxides eD fD or g ould hve the moleulr formul xyF sf yxide g hs the moleulr formul xyD then yxide f hs the formul xy2 D nd yxide e hs the formul xy4 F sf yxide f hs moleulr formul xyD then yxide e hs formul xy2 D nd yxide g hs formul x2 yF st might not e ler tht yxide g would e x2 yF he mss dt tell us tht yxide f hs twie s mny oxygen toms per nitrogen atom s yxide gF o if yxide f nd yxide g hve the sme numer of oxygen tomsD then yxide g hs twie s mny nitrogen toms s yxide fF es similr exmpleD if yxide e hs formul xyD then yxide f hs formul x2 y nd yxide g hs formul x4 yF hese three possiilities re listed in le QFPX ossile woleulr pormule for xitrogen yxidesF

ossile woleulr pormule for xitrogen yxidesyxide g is xy xy4 xy2 xy yxide f is xy xy2 xy x2 y

essuming thtX yxide e is yxide f is yxide g is

yxide e is xy xy x2 y x4 y

Table 3.2

e don9t hve wy to know whih of these sets of moleulr formuls re rightD sine ll three sets re onsistent with the dt we hveF row n we pik the right onec sf we hd some wy to ount the numers of toms in smple of eh ompoundsD then we would knowF his sounds quite di0ultD thoughF yn the other hndD if we knew tht the rtio of the mss of n nitrogen tom to n oxygen tom is PFPVXIFHHD whih is the mss rtio in yxide eD then we ould know tht yxide e is xyF fut we don9t hve wy to tke the mss of n individul tomD even on reltive sisF ht we hve lerned is thtD if we know the reltive msses of the tomsD we n determine moleulr formulsF end if we know the moleulr formulsD we n determine reltive tomi mssesF e need one or the other to move forwrdF

3.2 Foundatione re ssuming tht we know the postultes of the etomi woleulr heoryD s developed in the (rst gonept hevelopment tudyF hese reX @IA the elements re omprised of identil tomsY @PA ll toms of single element hve the sme hrteristi mssY @QA the numer nd msses of these toms do not hnge during hemil trnsformtionY nd @RA ompounds onsist of identil moleules formed of toms omined in simple whole numer rtiosF e will se muh of our work on the oserved nturl lws on whih our theory is sedX the vw of gonservtion of wssD the vw of he(nite roportionsD nd the vw of wultiple roportionsF e will e mking oservtions out the physil properties of gs smplesD prtiulrly the volumes of gses mesured under onditions with (xed temperture nd (xed pressureF e will not need muh tehnil informtion out temperture nd pressureF por nowD we will simply stik with the ommon understnding tht temperture is mesure of how hot or old smple of sustne isF emperture n e mesured y thermometerD whih is ny kind of gdget whih gives us the sme vlue for two ojets tht re in ontt with eh other so tht they hve the sme tempertureF ressure is mesure of wht is sometimes lled the spring of irD whih is the fore with whih gs resists ompressionF here re numer of wys to mesure pressureD ut we will only need to know tht we hve wy to tke mesurements on gs smples suh tht they hve the sme pressureFAvailable for free at Connexions

IQ

3.3 Observation 1: Volumes of Gases during Chemical Reactionshuring hemil retionsD some hemil nd physil properties suh s the totl mss of the mterils remin unhngedD ut most properties do hngeF e ommonly oserve hnges in properties when new mterils re mdeF por exmpleD produts of retions in omprison to the retnts my pper hrder or softerD more or less olorfulD more or less rittleD nd more or less denseF por gses tht retD volume is one of those properties tht is not lwys onservedF e fmous explosive retion of gses involves the urning of hydrogen gs in oxygen gs to form wter vporD s shown in pigures I nd PF sf I liter of oxygen gs rets with P liters of hydrogen gsD the produt wter vpor will oupy P liters with no hydrogen or oxygen gs left overF @his is true if the volumes re mesured with ll gses t the sme temperture nd pressureFA xotie tht the totl volume of gses is not onservedX the omined volume of the retnts is Q litersD ut the volume of the produt is P litersF

Figure 3.1:

Demonstration of an exploding balloon containing hydrogen and oxygen done at Rice

University by Dr. Mary McHale (http://chemistry.rice.edu/ ).

2

2 http://chemistry.rice.edu/

Available for free at Connexions

IR

CHAPTER 3. ATOMIC MASSES AND MOLECULAR FORMULAS

Figure

3.2:

The

Hindenburg,

(http://www.nlhs.com/tragedy.htm ).

3

a

German

passenger

airship,

bursting

into

ames

in

1937

here isD howeverD something striking out the dt just given for retion of hydrogen nd oxygen tht should use us to tke loser look the property of volumeX the volumes of the gses re in simple integer rtiosF his might look like simple onsequene of our hoosing to ret I liter of oxygen with P liters of hydrogenF fut we n tke ny volumes we wntD not just integer numer of litersF e n ret IFRP liters of oxygen with PFVR liters of hydrogenD nd ll of the hydrogen nd oxygen will e onsume to form PFVR liters of wter vporF xotie tht the rtio of volumes is oxygenXhydrogenXwter vpor a IXPXPD simple integer rtioF sf we try to ret di'erent rtioD like IFRP liters of oxygen with QFHH liters of hydrogenD there will e leftover hydrogen when the retion is ompleteF his is one wy of oserving the vw of he(nite roportionsF e nnot hoose to ret ritrry mounts of hydrogen nd oxygenD sine they omine in (xed rtio y mssF e thus oserve tht the volumes of hydrogen nd oxygen tht retD s well s the volume of wter vpor produtD re in simple integer rtioF he only requirement for this to e true is tht ll of the gs volumes re mesured with the sme temperture nd pressureF his result is quite generl when we oserve hemil retions involving gsesF he volume of hydrogen tht will ret with IFH v @litersA of nitrogen is QFH vD nd the produt of the retion mmoni gs hs volume PFH vF he rtio of volumes is simple set of integersF rydrogen hloride gs is formed from reting hydrogen gs with hlorine gsD nd ginD IFH v of hlorine will only ret with IFH v of hydrogen gsD with no hydrogen or hlorine left over nd with PFH v of hydrogen hloride gs produedF wnyD mny suh oservtions n e mde leding us to generl lw of nture lled the vw of gomining olumesX vw of gomining olumesX hen gses omine during hemil retion t (xed temperture nd pressureD the volumes of the reting gses nd produts re in simple integer rtiosF3 http://www.nlhs.com/tragedy.htm

Available for free at Connexions

IS

3.4 Avogadro's Law Counting Particleshe integer rtios in the vw of gomining olumes re very strikingF here re few quntities in nture whih re mesured in integersD so it is lwys surprising nd reveling to disover integers in mesurementsF sntegers re generlly mesured only when we re ounting prtiles or tking rtios of prtilesF yserving volumes in simple integer rtios should e very revelingF vooking k t the dt for hydrogen nd oxygenD we see tht the volumes re in simple PXI rtioF yne of our mjor onlusions expressed in the etomi woleulr heory is tht toms nd moleules ret in simple integer rtiosF e possile explntion of the integer volume rtios is tht these re the sme integer rtios s the prtiles ret inF sn the hydrogenEoxygen seD this mens tht the rtio of hydrogen toms to oxygen toms reting is PXID sine the volume rtio is PXIF sf the volumes re in PXI rtio nd the prtiles re in PXI rtioD then powerful onlusion emergesX equl volumes of the two gses must ontin equl numers of prtilesD regrdless of whether they re hydrogen or oxygenF his seems like quite lep to mkeD sine we re onluding something out the numers of prtiles without ever hving ounted themF ht is the sis for this lep of logic he most importnt prt of the resoning is the uniqueness of the integersF st is hrd to ome up with simple explntion for why gs volumes should only ret in integer rtiosF he only simple onlusion is the one we hve ome to nd tht ws (rst stted y evogdroX evogdro9s vwX iqul volumes of gs ontin equl numers of prtilesD if the volumes re mesured t the sme temperture nd pressureF yne wy to ome to this onlusion is to imgine tht it is not trueF essume tht equl volumes of gses do not ontin equl numers of prtiles nd insted ontin unrelted numers of prtilesF vet9s ssume for exmple tht I v of gs e ontins QFIR times s mny prtiles s I v of gs fF hen to tke equl numers of e nd f prtilesD we would need QFIR v of gs f for every I v of gs eF por the gs prtiles of e nd f to ret in simple integer rtio of prtilesD we would then need nonEinteger rtio of volumesF fut this is not wht is oserved in the vw of gomining olumesX the volume of e nd f tht ret re lwys oserved to e simple integer rtioF yur ssumption tht equl volumes ontin unrelted numers of prtiles leds us to onlusion tht is ontrdited y experimentsD so our ssumption must e wrongF hereforeD equl volumes of gses ontin equl numers of prtilesF e n onlude tht evogdro9s vw follows logilly from the vw of gomining olumesF here is prolem tht we hve to work outF vooking k t one piee of evidene tht led us to the vw of gomining olumesD we found tht I v of hydrogen plus I v of hlorine yields P v of hydrogen hlorideF sing the onlusion of evogdro9s vwD the volume rtio nd the prtile rtio must e the smeF his seems to sy tht I hydrogen tom plus I hlorine tom mkes P hydrogen hloride moleulesF fut this n9t e3 row ould we mke P identil moleules of hydrogen hloride from single hlorine tom nd single hydrogen tomc his would require us to divide eh hydrogen nd hlorine tomD violting the postultes of the etomi woleulr heoryF here is one solution to this prolemD s ws reognized y evogdroF e hve to e le to divide hydrogen gs prtile into two identil pieesF his mens tht hydrogen gs prtile must ontin n even numer of hydrogen tomsD most simplyD twoF his sys tht hydrogen gs exists s hydrogen moleulesD nd eh hydrogen moleule ontins two hydrogen tomsF he sme onlusions pply to hlorineX hlorine gs moleule must ontin two hlorine tomsF sf these onlusions re orretD then one hydrogen moleuleD r2 D n ret with one hlorine moleuleD gl2 D to form two hydrogen hloride moleulesD rglF he rtio of the retnt prtiles nd the produt prtiles is then the sme s the rtio of the retnt gs volumes nd the produt gs volumesF his is wonderful result euse we hve now determined the moleulr formul of hydrogen hlorideD rglF e hve found wy to ount the numers of toms in the retionD t lest in rtioD y mesuring the volumes of the gses tht ret nd tht re produedF his gives us hemil retion showing the toms nd moleules tht prtiipte in the retion in the orret rtioX I r2 moleule C I gl2 moleule P rgl moleules his hemil eqution is onsistent with ll of our known oservtions nd the postultes of the etomi woleulr heoryFAvailable for free at Connexions

IT

CHAPTER 3. ATOMIC MASSES AND MOLECULAR FORMULAS

ine the vw of gomining olumes is generl resultD we n look t mny hemil retions with the sme nlysisF vet9s pply this to the hydrogen nd oxygen retion disussed erlierF ememer tht P v of hydrogen ret with I v of oxygen to form P v of wter vporF his mens tht two prtiles of hydrogen @whih we know to e r2 A ret with one prtile of oxygen to form two prtiles of wterF yne ginD we hve the prolem tht one tom of oxygen nnot mke two moleules of wterF hereforeD n oxygen gs prtile nnot e n oxygen tomD so oxygen gs exists s oxygen moleulesD y2 F ine two r2 moleules ret with one y2 moleule to form two wter moleulesD eh wter moleule must e r2 yF e n write the hemil equtionX P r2 moleules C I y2 moleule P r2 y moleules e n use these oservtions to (nlly solve the riddle whih is posed in le QFPX ossile woleulr pormule for xitrogen yxidesF e need to oserve the volumes of oxygen nd nitrogen whih ret to form yxides eD fD nd gF sn seprte experimentsD we (ndX I v x2 C P v y2 P v yxide e I v x2 C I v y2 P v yxide f P v x2 C I v y2 P v yxide g @et this pointD it is pretty ler from the dt nd using our previous resoning tht nitrogen gs must onsist of nitrogen moleulesD x2 D sine I v of nitrogen gs n mke P v of yxide fFA prom these dtD we n onlude tht yxide f hs moleulr formul xyD sine I v of oxygen plus I v of nitrogen produes P v of yxide f with nothing left overF imilrly nd with the use of le QFPX ossile woleulr pormule for xitrogen yxidesD we n sy tht yxide e is xy2 nd yxide g is x2 yF

3.5 Observation 2: Relative Atomic Massessn the sntrodutionD we presented dilemm in developing the etomi woleulr heoryF o (nd the moleulr formul of ompoundD we needed to (nd the reltive tomi mssesF end to (nd the reltive tomi mssesD we needed to (nd the moleulr formul of ompoundF sing evogdro9s vwD we hve found wy to rek out of this dilemmF fy mesuring gs volumes during retionsD we n essentilly ount the numers of toms in moleuleD giving us the moleulr formulF yur tsk now is to use this informtion to (nd tomi mssesF e n egin y looking t the dt in le QFIX wss eltionships of imple gompounds of xitrogen nd yxygen nd fousing on yxide f t (rstF e know now tht yxide f hs moleulr formul xyF es suhD it is given the nme xitri wonoxideD or more ommonly xitri yxideF e lso know from le QFIX wss eltionships of imple gompounds of xitrogen nd yxygen tht the mss rtio of oxygen to nitrogen in xy is IFIR to IFHHF ine there re equl numers of nitrogen toms nd oxygen toms in ny smple of xyD then the mss rtio of n oxygen tom to nitrogen tom is lso IFIR to IFHHF tted di'erentlyD n oxygen tom hs mss IFIR times greter thn nitrogen tomF his is good strtD ut now we need more elementsF o ring in hydrogenD we n nlyze the dt from le QFPX ossile woleulr pormule for xitrogen yxides in the (rst gonept hevelopment tudy whih gives the mss rtio of oxygen nd hydrogen in wterF ht dt shows tht the mss rtio of oxygen to hydrogen is UFWQ to IFHHF fut we found in the previous setion tht the moleulr formul of wter is r2 yF his mens tht in smple of wter there re twie s mny hydrogen toms s there re oxygen tomsF hereforeD the rtio of the mss of one oxygen tom to one hydrogen tom must e UFWQ to HFSHD or ISFVT to IFHHF hese tomi mss rtios need to e onsistent with eh otherD sine the msses of the toms of n element re lwys the smeF o if the rtio of one hydrogen to one oxygen is IFHH to ISFVTD nd the rtio of one nitrogen to one oxygen is IFHH to IFIRD then the rtio of one hydrogen to one nitrogen must e IFHH to IQFWIF e should e le to hek this y looking t the hydrogenEnitrogen ompound mmoniD lso listed in le QFPX ossile woleulr pormule for xitrogen yxides of the previous gonept hevelopment tudyF here we (nd tht the mss rtio of nitrogen to hydrogen is RFTS to IFHHF glerlyD mmoni is not xrF o (nd the moleulr formul of mmoniD we need dt from the vw of gomining olumesF ixperimentl dt revel tht I v of x2 rets with Q v of r2 to produe P v of mmoniF prom thisD we should e leAvailable for free at Connexions

IU to onlude tht n mmoni moleule hs the moleulr formul xr3 F hereforeD in smple of mmoniD there re three times s mny hydrogen toms s there re nitrogen tomsF his mens tht the rtio of the mss of nitrogen tom to hydrogen tom is QBRFTS to IFHHD or IQFWS to IFHHF e now hve enough dt to sy tht hydrogenD nitrogenD nd oxygen toms hve mss rtio of IFHHXIQFWSXISFVTF

3.6 Observation 3: Atomic Masses for Non-Gaseous Elementshe next element we would ertinly like to hve n tomi mss for would e ronD nd we would ertinly like to e le to determine moleulr formuls for ron ontining ompoundsF e hve dt from le QFQX wss eltionships of imple gompounds of gron nd yxygen in the previous gh on ompounds of hydrogen nd ronF fut our nlysis is not going to work this timeF he vw of gomining olumes nd evogdro9s vw in omintion llow us to ount toms nd (nd moleulr formulsD ut only for elements nd ompounds whih re gsesF gron is not gsF st exists in severl di'erent elementl formsD ut ll re solid t norml tempertures nd even t very high temperturesF his mens tht we need to work hrder nd dd some dditionl oservtions to our workF vet9s strt with the two most ommon oxides of ronD whih for now we will give the nmes yxide e nd yxide fF @heir rel nmesD ron monoxide nd ron dioxideD re sed on ssuming tht we lredy know their moleulr formulsF fut we don9t know theseD so we9ll stik with these ode nmes for nowFA rere re the dt for the mss reltionships from the vw of wultiple roportionsX

wss eltionships of imple gompounds of gron nd yxygengompound otl wss @gA wss of gron @gA wss of yxygen @gA yxide e PFQQ IFHH IFQQ yxide f QFTT IFHH PFTTTable 3.3

st is ler to see the vw of wultiple roportions here sine yxide f hs extly twie the mss of yxide e for the sme mss of ronF xow we would like to oserve the vw of gomining olumes nd pply evogdro9s vwD ut ron is not gsF fut we n t lest look t the rtios of the volume of oxygen nd the volume of the oxides produedF por yxide eD I v of oxygen will produe P v of yxide eF por yxide fD I v of oxygen will produe I v of yxide fF prom these dtD we n see tht n yxide e moleule ontins one oxygen tomD sine single y2 moleule mkes two yxide e moleulesF e n lso see tht n yxide f moleule ontins two oxygen tomsD sine single y2 moleule produes single yxide f moleuleF xow we know prt of the moleulr formuls eh of the oxidesD ut we don9t know the numer of ron toms in ehF yxide e ould e gyD g2 yD g3 yD etFD nd yxide f ould e gy2 D g2 y2 D etF yur only wy to proeed is with evogdro9s vwF e n use this to determine the reltive mss of eh oxide moleuleD even if we n9t determine the reltive mss of the ron tomsF he mss of I v of yxide e is less thn the mss of I v of oxygenF his is euseD even though equl volumes ontin the sme numer of prtilesD the prtiles themselves hve di'erent mssesF sn ftD sine I v of eh gs ontins the sme numer of prtilesD then the mss rtio of I v of yxide e to oxygen is extly the sme s the mss rtio of one yxide e moleule to one oxygen moleuleF en experimentl mesurement shows tht the mss of I v of yxide e is VUFS7 of the mss of I v of oxygenF o the mss of one prtile of yxide e must e VUFS7 of the mss of n y2 moleuleF yn the reltive sle found in the previous setionD the mss of one oxygen moleule is ISFVTBP a QIFUPF o prtile of yxide e must hve reltive mss HFVUSBQIFUP a PUFUTF ememer though tht n yxide e ontins just one oxygen tomF oD of this reltive mssD ISFVT elongs to the oxygen tomD leving IIFWH for the ronF ss this the reltive mss of ron tomc e don9t know euse we don9t know whether moleule of yxide e ontins ID PD or Q toms of ron @or for tht mtterD ny numerAF ht we n sy is thtAvailable for free at Connexions

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CHAPTER 3. ATOMIC MASSES AND MOLECULAR FORMULAS

the mss of ron tom is either IIFWD oneEhlf of thtD oneEthird of thtD or some integer frtion of tht depending on how mny ron toms re in yxide eF row n we determine the right numerc he nswer is found from persisteneF e n repet this sme mesurement nd lultion for yxide fF he mss of I v of yxide f is IFQUS times greter thn the mss of I v of oxygenF hereforeD one prtile of yxide f hs reltive mss RQFSWF fut yxide f moleules ontin two oxygen tomsD so the prt of this mss whih is ron is RQFSW minus the reltive mss of the two oxygen tomsF his gives the mss of ron in yxide f s IIFWF his is the sme mss of ron tht we found in yxide eF hereforeD yxide e nd yxide f hve extly the sme numer of ron tomsF erhpsD the numer of ron toms in eh is just oneD ut we n9t e sure from this dtF o onvine ourselvesD we should repet this proess for mny gseous ompounds of ronD inluding ones tht ontin hydrogen nd oxygen othF sn every experimentD we (nd tht the reltive mss of ron in eh moleule is either IIFW or simple multiple of IIFWF st is never less thn IIFWF e n onlude tht the reltive mss of ron tom on the sme sle we hve een using is IIFWF e n lso onlude tht yxide e nd yxide f eh ontin one ron tomD so the moleulr formuls of yxide e nd yxide f re gy nd gy2 F his proedure n e used to (nd moleulr formuls of ompounds ontining other nonEgseous elementsF his is the tul proedure tht ws used round IVSH to provide the (rst set of reltive tomi msses nd the (rst de(nite moleulr formuls for ommon ompoundsF his is mjor stride forwrd from the postultes of the etomi woleulr heoryF es one lst stepD we note tht the stndrd greed on y hemists for the reltive tomi msses does not tke hydrogen to hve mss IFHHF therD on the greed upon sleD the reltive tomi mss of hydrogen is IFHHVD tht of ron is IPFHID tht of nitrogen is IRFHID nd tht of oxygen is ISFWWWF hese rtios re the sme s the ones we oserved in our lultionsF

3.7 Chemical Algebra: Stoichiometrysn the sntrodution @etion QFIX sntrodutionAD we deided tht we ould determine moleulr formuls if we knew the reltive tomi mssesF et tht pointD we didn9t hve the reltive tomi mssesD ut now we doF yne we know ll the reltive tomi mssesD we no longer need the vw of gomining olumes nd evogdro9s vw to determine moleulr formulsF vet9s show this y n exmpleD with ompound whih ontins only ronD oxygenD nd hydrogenF en nlysis from the vw of he(nite roportions gives us tht the ompound is RHFH7 ronD SQFQ7 oxygenD nd TFU7 hydrogen y mssF sn other wordsD if we hve IHHFH g smple of the ompoundD it onsists of RHFH g of ronD SQFQ g of oxygen nd TFU g of hydrogenF fut we lso know tht the reltive msses of ronD oxygenD nd hydrogen re IPFHIXIFHHVXISFWWF his will llow us to determine the reltive numers of toms of eh type in the ompoundF o do thisD we rete method of hemil lgerF vet9s strt y ssuming tht we hve extly x toms of ronD x toms of hydrogenD nd x toms of oxygenF x is some very lrge numerD nd it doesn9t mtter wht it isD s long s we hve tken the sme x for ll three elementsF he reltive mss of I ron tom to I hydrogen tom is IPFHI to IFHHVF herefore the reltive mss of x ron toms to x hydrogen toms is lso IPFHI to IFHHVF vet9s pik very spei( xX let9s mke x e whtever numer it is suh tht tht smple of x ron toms hs mss IPFHIgF snterestinglyD we don9t need to know wht x is ! we just need to (nd smple of ron whih hs mss of IPFHI gF ht is the mss of x hydrogen toms @for the ext sme xAc st must e IFHHV gD sine eh hydrogen tom hs mss rtio to eh ron tom IFHHV to IPFHIF hereforeD if we weigh out smple of ron with mss IPFHI g nd smple of hydrogen with mss IFHHV gD we know tht we hve extly the sme numer of toms of eh typeF ine this seems like useful numer of tomsD we will give it nmeF x is lled mole of tomsF e don9t need to know wht x is to know tht we n (nd mole of toms simply y (nding the mss of smpleX IPFHI g of ronD IFHHV g of hydrogenD ISFWW g of oxygenD nd so onF @por historil resonsD the vlue of x whih is mole of toms is lled evogdro9s numerD in his honor ut not euse he disoveredAvailable for free at Connexions

IW the numerF evogdro9s numer is given the symol xA F he numer of prtiles in mole is pproximtely TFHPPIH23 D lthough we will lmost never need this numer when doing hemil lultionsFA ine we know the mss of one mole of sustneD we n (nd the numer of moles in smple of tht sustne just y (nding the mssF gonsider smple of ron with mss PRFHP gF his is twie the mss of one moleD so it must ontin twie the numer of prtiles s one moleF his must e two moles of prtilesF ht exmple ws esyD ut wht if we hve QHFHP g of ronc ine one mole hs mss IPFHI gD then QHFHP g must ontin QHFHPGIPFHI moles a PFS molesF iven more generllyD thenD if we hve smple of n element hs mss m nd the tomi mss of the element is wD the numer of moles of tomsD nD is ine one mole ontins (xed numer of prtilesD regrdless of the type of prtileD lulting the numer of moles n is wy of ounting the numer of prtiles in smple with mss mF por exmpleD in the IHHFH g smple of the ompound oveD we hve RHFH g of ronD SQFQ g of oxygenD nd TFU g of hydrogenF e n lulte the numer of moles of toms of eh element using the eqution oveX 0g nC = 12.40. 0g/mol =3FQQmoles 3g nO = 16.53. 0g/mol =3FQQmoles .7g nH = 1.06 g/mol =6FTUmoles e mole is (xed numer of prtilesF hereforeD the rtio of the numers of moles is lso the sme s the rtio of the numers of tomsF sn the dt oveD this mens tht the rtio of the numer of moles of ronD oxygenD nd hydrogen is IXIXPD nd therefore the rtio of the three types of toms in the ompound is lso IXIXPF his suggests tht the ompound hs moleulr formul gyr2 F roweverD this is just the rtio of the toms of eh typeD nd does not give the numer of toms of eh typeF hus the moleulr formul ould just s esily e g2 y2 r4 or g3 y3 r6 F ine the formul gyr2 is sed on empiril mss rtio dtD we refer to this s the empiril formul of the ompoundF o determine the moleulr formulD we need to determine the reltive mss of moleule of the ompoundD iFeF the moleulr mssF yne wy to do so is sed on the vw of gomining olumesD evogdro9s rypothesisD nd the sdel qs vwF o illustrteD howeverD if we were to (nd tht the reltive mss of one moleule of the ompound is THFHD we ould onlude tht the moleulr formul is g2 y2 r4 F gounting the reltive numer of prtiles in smple of sustne y mesuring the mss nd lulting the numer of moles llows us to do hemil lgerD lultions of the msses of mterils tht ret nd re produed during hemil retionsF his is esiest to see with n exmpleF ome of the most ommon hemil retions re those in whih ompounds of hydrogen nd ronD lled hydroronsD re urned in oxygen gs to form ron dioxide nd wterF he simplest hydroron is methneD nd using the methods of this studyD we n (nd tht methne hs the moleulr formulD gr4 F he hemil eqution whih represents the urning of methne isX I gr4 moleule C P y2 moleules I gy2 moleule C P r2 y moleules st is importnt to note tht the numer of toms of eh type is onserved during the hemil retionF he retnts nd produts oth ontin I ron tomD R hydrogen tomsD nd P oxygen tomsF his is lled lned hemil equtionD nd it expresses the postulte of the etomi woleulr heory tht the numers of toms of eh element does not hnge during hemil retionF sn hemil lgerD we n sk nd nswer questions suh sD sf we urn IFH kg of methneD wht is the mss of ron dioxide whih is produedc uh question would lerly e of importne in understnding the prodution of greenhouse gses like gy2 F he hemil eqution ove expresses reltionship etween the numer of moleules of methne whih re urned nd the numer of moleules of gy2 produedF prom the equtionD eh moleule of gr4 produes one moleule of gy2 F hereforeD if we knew how mny moleules of gr4 we hve in smpleD we know how mny moleules of gy2 we will produeF he hemil eqution works for ny numer of moleulesF sf we urn x moleules of gr4 D we produe x moleules of gy2 F his will work no mtter wht x isF hereforeD we n sy tht I mole of gr4 moleules will produe I mole of gy2 moleulesF he hemil eqution works just s well for moles s it does for moleulesD sine I mole is just (xed numer of moleulesF end we know how to lulte the numer of moles from mesurement of the mss of the smpleFAvailable for free at Connexions m n= M

PH

CHAPTER 3. ATOMIC MASSES AND MOLECULAR FORMULAS

ell tht we re interested in wht hppens when we urn IFHH kg a IHHH g of methneF e just need to know the mss of mole of methneF ine one moleule of methne hs reltive mss ITFHD then one mole of methne hs mss ITFH gGmolF hen the numer of moles in IHHH g of methne n e lulted y dividing y the mss of IFH mole of methneX 1000g nCH = 16. 0g/mol =TPF5moles his mens we hve ounted the numer of prtiles of gr4 in our smpleF end we know tht the numer of prtiles of gy2 produed must e the sme s thisD euse the hemil eqution shows us the IXI rtio of gr4 to gy2 F oD TPFS moles of gy2 re produed y this retion nd this IFH kg smpleF e re usully more interested in the mss of the produtD nd we n lulte thisD tooF he mss of one mole of gy2 is found from the mss of one mole of g nd two moles of yD nd is therefore RRFH gF his is the mss for one moleF he mss for TPFS moles will e mCO =nCO MCO (TPF5moles) (RRF0g/mol) =PUSHg =2FUSkg hereforeD for every I kg of methne urnedD we produe PFUS kg of gy2 F he importnt onlusion from this exmple of hemil lger is tht it is possile to lulte msses of produts from msses of retntsF e do so y using lned hemil eqution nd y understnding tht the eqution gives us the rtio of moles of reting mterils just s it gives us the rtio of moleules of reting mterilsF his is euse numers of moles nd numers of moleules re simply di'erent wys of ounting the numer of prtilesF ghemil lger is usully referred to s stoihiometryD somewht intimidting term tht mkes the lultions seem hrder nd more strt thn they reF e relly only need to rememer two thingsF pirstD from the etomi woleulr heoryD hemil retion n e represented y lned hemil eqution whih onserves the numers of toms of eh elementF eondD the lned eqution provides the rtio of the numer of produt moleules to the numer of retnt moleulesD either in numers of moleules or numers of molesF husD we n solve prolems e0iently y lulting the numer of molesF e (nl interesting note out evogdro9s numer is helpful in understnding wht I mole isF e question often sked isD where did the numer TFHPPIH23 ome fromc sf we wnted to pik very lrge numer for the numer of prtiles in moleD why didn9t we pik something esier to rememerD like TIH23 D or even IIH23 c he vlue of evogdro9s numer omes from the ft tht we hose I mole to e the numer of ron toms in IPFHIg of ronF ine I ron tom hs mss IPFHI muD then the mss of xA ron toms is xA IPFHI muF fut I mole of ron toms hs mss IPFHI gD so IPFHI g must equl xA IPFHI muX IPFHI g a xA IPFHI mu his mens tht I g a xA mu his shows tht evogdro9s numer is just the onversion ftor for mss etween grms nd muF e didn9t rndomly pik evogdro9s numerF therD we piked the unit of mss muD nd it turns out tht there re evogdro9s numer of mu in one grmF4 2 2 2

3.8 Review and Discussion QuestionsIF tte the vw of gomining olumes nd provide n exmple of your own onstrution whih demonE strtes this lwF PF ixplin how the vw of gomining olumesD omined with the etomi woleulr heoryD leds diretly to evogdro9s hypothesis tht equl volumes of gs t equl tempertures nd pressure ontin equl numers of prtilesF QF se evogdro9s hypothesis to demonstrte tht oxygen gs moleules nnot e montomiF RF he density of wter vpor t room temperture nd tmospheri pressure is HFUQU gGvF gompound e is VHFH7 ron y mssD nd PHFH7 hydrogenF gompound f is VQFQ7 ron y mss nd ITFU7 hydrogenF he density of gseous gompound e is IFPPU gGvD nd the density of gompound f is PFWRV gGvF how how these dt n e used to determine the molr msses of gompounds e nd fD ssuming tht wter hs moleulr mss IVFAvailable for free at Connexions

PI SF prom the results in rolem RD determine the mss of ron in moleule of gompound e nd in moleule of gompound fF ixplin how these results indite tht ron tom hs tomi mss IPF TF ixplin the utility of lulting the numer of moles in smple of sustneF UF ixplin how we n onlude tht PVg of nitrogen gs @x2 A ontins extly s mny moleules s QPg of oxygen gs @y2 AD even though we nnot possily ount this numerF fy tohn F ruthinsonD ie niversityD PHII

Available for free at Connexions

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CHAPTER 3. ATOMIC MASSES AND MOLECULAR FORMULAS

Available for free at Connexions

Chapter 4

Structure of an Atom4.1 Introduction

1

he etomi woleulr heory is very powerful in helping us understnd mtterF e n esily understnd the di'erenes etween the elements nd ll other ompounds y thinking out the prtiles whih mke them upF ilements ontin ll identil tomsD nd ompounds ontin identil moleulesD eh omposed of de(nite smll numers of toms of the elements tht mke up the ompoundF e n lso do hemil lger lultionsD whih llow us to mke preditions out the msses of mterils tht re involved in hemil retionsF ithout further oservtionsD thoughD this is out s fr s we n go euse our knowledge out the properties of toms is very limitedF e only know tht toms of di'erent elements hve di'erent mssesD nd we know the reltive tomi msses of the elementsF fut this does not give us ny insight into why the toms of di'erent elements hve suh di'ering hemil propertiesF por exmpleD ron nd nitrogen hve very similr tomi mssesF roweverD ron in one of its formsD dimondD is very hrdD unretive solid nd in nother of its solid formsD olD ron will urn in oxygenF xitrogenD thoughD is gs nd is firly unretive with oxygen exept t very high temperturesF glerlyD ron toms intert with eh other very di'erently thn nitrogen toms intert with eh otherF ithout knowing nything else out tomsD we might imgine them s tiny hrd spheresF fut this ide will not help us understnd their hemistryD suh s why they form the ompounds tht they doF ht does it men for hydrogen nd ron to form the ompound methnec e know tht methne9s moleulr formul is gr4 D ut how do these (ve toms hold together in moleulec st seems resonle to imgine tht the ttrtions re due to mgneti fores or eletril fores etween the tomsF roweverD toms of hydrogen nd ron must e eletrilly neutrlD sine ulk smples of hydrogen nd ron re eletrilly neutrlF hey re lso nonEmgnetiF row do neutrlD nonEmgneti toms intert with eh otherc enother riddle is why they form in the prtiulr rtios tht they doF gr4 is ompound ut there isn9t ompound with moleulr formul gr5 F nderstnding these di'ering elementl nd moleulr properties requires us to hve deeper underE stnding of the properties of individul tomsF ine we nnot understnd these properties y thinking of the toms s individul hrd spheresD we need to investigte the struture of the tomF

4.2 Foundationsn this studyD we will ssume tht we know the postultes of the etomi woleulr heory nd our mesureE ments of reltive tomi mssesF e know tht n element is omposed of individul toms with identil mssesD nd we know tht the toms of di'erent elements hve di'erent mssesD whih hve een mesuredF1 This content is available online at .Available for free at Connexions

PQ

PR

CHAPTER 4. STRUCTURE OF AN ATOM

e will lso ssume our understnding from previous study tht eletriity onsists of individul hrged prtiles lled eletronsD whih re ssigned negtive hrgeF he mss of the eletron is quite smll reltive to the mss of n tomF etoms ontin eletronsD nd eletrons n e dded to or removed from toms y pplying n eletril urrentF e noted in the introdution tht toms in elementl form re neutrlD or without hrgeF ine toms ontin negtively hrged eletronsD eh tom must lso ontin positive hrge whih extly equls the totl hrge on the eletrons in the tomF ine eletrons re prtilesD there hs to e n integer numer of negtive hrgesD so there lso hs to e n integer numer of positive hrges in eh tomF hese sttements re importnt to keep in mindD ut they don9t help us very muh without more dtF e don9t know how mny eletrons re in eh tomD nd therefore we don9t know how mny positive hrges re in eh tomF e do not even know whether tht numer of eletrons is the sme or di'erent for di'erent toms of di'erent elementsF sn dditionD we don9t know how these positive nd negtive hrges re rrnged in eh tomF hey might e lustered together in some sort of llD they might e pired o' togetherD they might e rndomly rrngedD or there my e some other rrngement tht we don9t expetF sn this onept development studyD we will determine the rrngement of the hrged prtiles in n tomD nd we will determine the numers of hrged prtiles in the toms of eh elementF

4.3 Observation 1: Scattering of particles by atomso (nd out wht the inside of n tom looks likeD we perform sttering experimentF his involves shooting hrged prtiles t toms nd wthing wht hppensF hepending on how the hrged prtiles re rrnged inside the tomD these hrges should stter the prtiles we shootF sf we look t the pttern of the stteringD we should e le to infer wht the rrngement of the hrges inside the tom looks likeF st would seem very hrd to shoot prtiles t individul tomsD thoughD sine these re very smllD impossile to seeD nd possily even elusiveF yne wy to do this is to tke very thin sheet of metlD so thin tht the thikness of the metl will not e very mny toms rossF qold is good hoie of metlD sine it is esy to hmmer out to very thin sheet nd it is very unretiveD so it is possile to mke it quite pureF sn this experimentD the thikness of the gold foil will e only out IH-4 mD sometimes lled I mironF his is less thn oneEtwentieth of the thikness of one humn hirD so this is very thin indeedF e need prtiles to shoot t this thin foilD preferly hrged prtiles whih will intert with the positive nd negtive hrges in the gold tomsF e good hoie is the prtileD whih is positively hrged nd muh more mssive thn n eletronF sn the experimentD we will (re em of prtiles diretly t the gold foilD nd then we will oserve where the prtiles go fter interting with the gold tomsF hey might pss through the foilD they might e de)eted somewht s they pss throughD or they might even reound in vrious ngles k to the soure of the emF

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Figure 4.1: Diagram of Rutherford's gold foil experiment showing the results of shooting

A

particles

at a very thin sheet of gold foil.

he experimentl dt for the sttering of the prtiles shows three primry resultsD s depited in pigure RFIF pirstD nd perhps most surprisinglyD the gretest numer of the prtiles pss diretly through the gold foil without ny de)etion in their pthsF eondD muh smller numer of the prtiles experiene smll de)etions in their pthsF end thirdD very smll frtion of the prtiles @perhps I in SHDHHH or moreA re de)eted k in the diretion of the em they me fromF por nowD we9ll fous on the (rst nd third oservtionsF st is surprising tht the lrgest numer of the prtiles pss through the gold foil s if it is not thereF sn ftD it is just s if the gold foil onsisted mostly of empty speD nd most of the prtiles seem to pss through tht empty speF his seems strngeD sine the gold foil is ertinly solid nd doesn9t pper to e empty speF he third result gives striking ontrst to this resultF e tiny frtion of the prtiles must enounter something other thn empty speF o reoundD n prtile must hit something muh more mssive thn itselfF e might think tht this is gold tomD whih is muh hevier thn n prtileD ut to e onsistent with the (rst oservtionD most of the gold tom must e empty speF hinking out these two oservtions leds us to simple model for the tomF ih gold tom must e mostly empty spe nd most of the mss of the gold tom must e onentrted into very smll frtion of the volume of the tomF e will ll this onentrted mss the nuleusF e reful lultion sed on the frtion of prtiles whih pss through nd the frtion whih reound tells us tht the dimeter of the nuleus is out IHHDHHH times smller thn the dimeter of the tom itselfF his is n mzing result3 elthough n tom is very smllD the nuleus is very muh smller thn thtD s nlogously depited in the digrm in pigure RFPF

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CHAPTER 4. STRUCTURE OF AN ATOM

Figure 4.2: This map illustrates the size of an atom if the nucleus were a standard-sized basketball at

Lovett Hall on the Rice University campus. The atom is 100,000 times large than the nucleus, so on this map this model of an atom has a radius of 11.9 km.

his is n interesting model tht seems to ount for two of our three oservtionsD ut it is puzzling model tooF sf the mss of the tom is onentrted in suh smll speD wht oupies the rest of the volume of the tomc he seond oservtion from the experiment helps us understnd thisF ine smll numer of the positively hrged prtiles re de)eted in their pthsD this suggests tht they ome lose to ut do not run into something positive in the tomF ine these prtiles re de)etedD whtever they ome lose to must e more mssive thn they reF his mens tht they re oming lose to the nuleus nd the nuleus must e positively hrgedF his gives us lue out wht oupies the vst empty spe of the tomF sf the positive hrges of the tom re onentrted in the nuleusD the negtive hrges in the tomD the eletronsD must e in the muh lrger spe of the tom outside of the nuleusF his nuler model of the tom then ounts for ll three oservtions in the prtiles gold foil sttering experimentF wost of the volume of the tom is empty spe in whih negtively hrged eletrons move outF wost of the mss nd ll of the positive hrge of the tom is onentrted in nuleusD whih is tiny in omprison to the tomF

4.4 Observation 2: X-ray emissions from atomsst is interesting to know tht eh tom hs nuler strutureD prtiulrly sine we now know tht the positive nd negtive hrges in the tom re seprted into di'erent prts of the tomF he intertion of these positive nd negtive hrges must e wht determines the properties of eh type of tomD inluding the types of moleules tht they tend to formF iven though eh tom is neutrlD it might e possile for the positive hrges on one tom to intert with the negtive hrges on nother tomD nd vie versF o show thisD we would need to know how mny positive nd negtive hrges there re in eh tomF st seems resonle to ssume tht these numers re di'erent for toms of di'erent elementsD ut we don9t know tht without mking more oservtionsF et this pointD we know tht toms ontin eletronsD nd tht there re n integer numer of theseF e lso know tht eh tom ontins n equl numer of positive hrgesD ll of whih re in the nuleusF st mkes sense thtD sine the positive hrge is n integerD there must e prtiles of positive hrge in the nuleusD nd we will now ll these prtiles protonsF his doesn9t mke our life ny esierD ut it does lrify our lngugeF yur prolem now oils down to (nding out how mny protons nd how mny eletrons there re in eh tom of eh typeF hese integers re the sme numer for eh tomD of ourseD sine eh tom is neutrlFAvailable for free at Connexions

PU pinding this integer for eh element seems quite di0ultD nd the experiment whih revels the numer to us is strnge one whih doesn9t seem relted to the question t llF hen mterils re pled in n eletril dishrgeD they ommonly emit light or eletromgneti rditionF xot ll of this light is visileF ome of this light is highEenergy light lled ultrviolet rditionD nd some of it is even higher energy rdition lled xErysF e n tell the di'erene etween di'erent types of rdition y the frequeny of the rditionD property tht tells us how rpidly the eletromgneti (eld of the rdition osilltesF hi'erent frequenies of rdition n e seprted y pssing the rdition through di'erent mterilsF his is how prism worksD for exmpleF e n lso seprte the di'erent frequenies with something lled di'rtion grtingD whih n e either solid with prllel grooves or trnsprent solid with losely sped linesF es ommon exmples of simple di'rtion grtingsD ompt diss nd hhs hve grooves in prllel to eh other nd n e used to produe visile rinowF e white light soure will revel the di'erent olors of lightD eh with its own frequenyD when the light is re)eted o' of the surfe of the disF his seprtion of light into di'erent frequenies is very useful in type of experiment lled speE trosopyF here re mny types of spetrosopyD ut in most sesD smple of mteril is energized in some wyD often in n eletril dishrgeD nd the smple emits lightF his is n everydy oservtionF por exmpleD heted ojets tend to glowD whih mens tht they re emitting lightF sn spetrosopyD the light whih the smple emits is seprted y prism or grting nd wonderful result oursF ih di'erent element or ompound hs its own hrteristi set of frequenies of light whih re emittedF sn other wordsD only ertin frequenies of light re emitted y eh sustneD nd the set of frequenies for eh sustne is unique to tht sustneF petrosopy hs gret vlue in sieneD euse we n identify tht smple ontins prtiulr ompound or element just y looking t the frequenies of light tht the smple emitsF his is how we know the omposition of distnt strsD for exmpleF e need to fous on tomsD so we9ll look only t the spetrosopy of pure elementsF ih element hs hrteristi spetrum of frequeniesF e will fous on the light frequenies whih re xErys ndD even more refullyD for eh element we will fous on the lowest frequeny xEry whih eh tom emitsF hese re given for mny of the elements in le RFIX Ery prequenies of etomsF he ordering of the elements in le RFIX Ery prequenies of etoms is importntF e ould hve listed them lphetilly y nmeF snstedD we hve listed them in their order of inresing reltive mssF sn the set of elements given hereD lithium is the lest mssive element so it is t the topD then erylliumD nd so forthF xote tht the xEry frequeny emitted y eh tom inreses s the msses of the toms inrese moving down le RFIX Ery prequenies of etomsF @here is one exeption to our order in le RFIX Ery prequenies of etomsX ergon is slightly more mssive thn otssiumD ut we hve put ergon efore otssium for resons tht we will disuss lterFA

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CHAPTER 4. STRUCTURE OF AN ATOM

Ery prequenies of etoms etomi xumer ilement xme Ery frequeny @IH 16 s-1AQ R S T U V W IH II IP IQ IR IS IT IU IV IW PH PI PP PQ PR PS PT PU PV PW QH QI QP vithium feryllium foron gron xitrogen yxygen pluorine xeon odium wgnesium eluminum ilion hosphorous ulfur ghlorine ergon otssium glium ndium itnium ndium ghromium wngnese sron golt xikel gopper in qllium qermnium IFQISV PFTQIT RFRQUW TFUIIR WFRWQU IPFUHI ITFQUT PHFSQR PSFIVW QHFQQR QSFWUI RPFHHV RVFUHI SSFVIR TQFRIT UIFSIV VHFIIV VWFPRP WVFVUQ IHWFHI IIWFTS IQHFVH IRPFRU ISRFTS ITUFQQ IVHFSQ IWRFPS PHVFRV PPQFPI PQVFRU

Table 4.1

e hve lso dded something interesting in le RFIX Ery prequenies of etomsD the tomi numerF his numer is just the rnking of the elements in order of inresing mssF he tomi numer then is just nother nme we hve given to eh element with no more signi(ne thn the nmes we hve givenF @xoteAvailable for free at Connexions

PW gin tht ergon is pled efore otssiumF here re other resons for thisD ut this lso mkes sense in the dtD sine this wyD the frequenies of the xErys inreseFA yther thn the ft tht the xEry frequenies onsistently inreseD there doesn9t seem to e ny other ovious pttern in the dtF e ould look for pttern y plotting the xEry frequeny versus the msses of the tomsD ut this doesn9t show nything dditionlF urprisinglyD thoughD if we plot the xEry frequeny versus the tomi numerD ler pttern emergesD s we see in pigure RFQF

Figure 4.3: X-ray frequency vs. atomic number for the elements lithium to germanium.

he frequenies don9t just inrese with tomi numerD they inrese with very smooth funtionF his type of grph might look fmilir to youF st looks similr to grph of y a x2 D lled prolF ss the grph in pigure RFI prolc o (nd outD we need to know whether the xEry frequeny is funtion of the tomi numer squredF yne wy to do this is to plot the squre root of the xEry frequeny versus the tomi numerF his would e like plotting the squre root of y versus x to see if y a x2 F his new grph is shown in pigure RFRF

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QH

CHAPTER 4. STRUCTURE OF AN ATOM

Figure 4.4:

The square root of x-ray frequencies vs.

atomic number for the elements lithium to

germanium.

he grph in pigure RFP is very signi(ntF st shows tht there is simple reltionship etween the xEry frequeny emitted y eh tom nd the tomi numer of the tomF fut this is strnge resultF he xEry frequeny is physil property of eh tomF he tomi numer is just n integer tht we ssigned to eh element sed on its mss rnkingF his is surprise3 hy would physil property mth up so strongly with nonEphysil property like n integer in the mss rnkingsc here is only one possiilityX the tomi numer must lso e physil property of the tomF st is not n ritrry numerD even though we ssigned it tht wy initillyF st is property of the tomF he tomi numer is lso speil property of the tom euse it is n integerD nd integers re used to ount ojets or prtilesF his mens tht the tomi numer must e ounting some integer numer of ojets or prtiles in eh tomD nd tht numer must e unique for eh tomF fut we know tht there is n integer tht desries eh tomX the numer of protons nd eletrons tht eh tom hsF yur onlusion is therefore tht the tomi numer is property of eh tom whih is equl to the numer of protons in eh tom nd is lso equl to the numer of eletrons in eh tomF e hve found wy to ount the numer of hrges in eh tom3 here re two remrkle results to mention hereF he (rst is tht eh tom hs its own hrteristi numer of protons nd eletronsF his is not shred with ny other tomF his suggests tht these numers must e importnt in determining the hemil nd physil properties of the tomF he seond is tht every integer numer of protons nd eletrons is ounted forF here re no gps or reks in le RFIX Ery prequenies of etoms or in pigure RFI or pigure RFPF e hve them llF here re no missing elements in the rnge from Q to QPD nor for tht mtter from I to IIRF his is why there re only smll numer of elements @out WH nturlly ourring onesAF e now know wht is unique out the toms of di'erent elementsF st does mke sense tht toms with di'erent numers of hrged prtiles would intert di'erentlyD forming ompounds with di'erent hemil nd physil propertiesF fut we might imgine tht toms with similr @ut not equlA numers of hrged prtiles would hve firly similr hemil nd physil propertiesF es we will explore in muh more detil lterD this is not t ll the seF sn ftD it is possile to ompre two elements with very similr tomi numersD sy xeon nd odiumD nd (nd tht their hemil properties re ompletely di'erentF xeon is gsD even t extremely low temperturesD nd is so unretive tht it does not form ompounds with ny other elementsF odium is solid whih is so retive tht its retions with other elements re often violent nd energetiF st seems ler tht just knowing how mny eletrons n tom hs is not su0ient to mkeAvailable for free at Connexions

QI preditions out how tht tom might ehveF e will need to re(ne our model with further oservtionsF

4.5 Review and Discussion QuestionsIF ixplin how the sttering of prtiles from gold foil revels tht n tom ontins mssiveD positively hrged nuleus whose size is muh smller thn tht of n tomF PF ixplin the signi(ne of the reltionship etween the frequeny of xEry emission from eh tom nd the tomi rnking of tht tom in the periodi tleF fy tohn F ruthinsonD ie niversityD PHII

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CHAPTER 4. STRUCTURE OF AN ATOM

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Chapter 5

Electron Shell Model of an Atom5.1 Introduction

1

ht more ould we wnt to know out the struture of n tomc e know tht toms ontin positively nd negtively hrged prtilesD nd tht the numer of these hrges in eh tom is di'erent for eh elementF e lso know tht the positive hrges re onentrted in tiny nuleusD nd tht the eletrons move round the nuleus in spe tht is muhD muh lrger thn the nuleusF roweverD some of the most importnt questions we sked in the previous gonept hevelopment tudy re still unnsweredF ememer tht we sw tht ron nd nitrogen hve very similr tomi mssesF xow we n dd tht these elements hve very similr tomi numersD so their toms hve similr numers of protons nd eletronsF fut ron nd nitrogen reD in most hemil nd physil wysD very di'erentF imilrlyD some elements like sodium nd potssium hve very di'erent tomi numers ut hve quite similr hemil nd physil propertiesF st seems tht ompring the properties of two di'erent toms is not very esy to understnd just from ompring the numers of protons nd eletrons the toms ontinF o ontinue to understnd the nswers to these questionsD we need even more detil out the struture of eh type of tomF

5.2 Foundationsn this studyD we will ssume tht we know the postultes of the etomi woleulr heory nd our mesureE ments of reltive tomi mssesF e know tht n element is omposed of individul toms with identil mssesD nd we know tht the toms of di'erent elements hve di'erent mssesD whih hve een mesuredF e will lso ssume tht we know tht struture of n tomD with tinyD mssiveD positively hrged nuleus surrounded y muh lrger empty spe in whih eletrons moveF he positive hrge on the nuleus is equl to the numer of protons in the nuleus ndD in neutrl tomD is lso equl to the numer of eletrons moving out the nuleusF he numerD lled the tomi numerD is unique for eh type of tomF xo two elements hve the sme tomi numerD nd mongst the nturlly ourring elementsD no tomi numer is skippedX for every integer up to IIV we know n element with tht tomi numerF sn this studyD we will need very importnt oservtion orrowed from the study of hysisF e will use goulom9s vw to desrie the intertion of hrged prtilesF goulom9s vw is n lgeri expression whih reltes the strength of the intertion etween two hrged prtiles to the sizes of the hrges on the prtiles nd the distne etween themF e n think of the strength of the intertion etween prtiles s either the fore tht one prtile exerts on the other prtile or the potentil energy whih exists when the two prtiles intert with eh otherF e will fous on the potentil energyD whih we will ll VF vet9s think of two prtilesD one with hrge q1 nd the other with hrge q2 F hese hrges n e either positive1 This content is available online at .Available for free at Connexions

QQ

QR

CHAPTER 5. ELECTRON SHELL MODEL OF AN ATOM

or negtiveD depending on the properties of the prtilesF vet9s ple the two prtiles distne r wy from eh otherF hen the potentil energy of intertion etween these two hrged prtiles isX his is goulom9s vwF e will very rrely do ny lultions with this equtionF snstedD we will pply it to understnd when V is expeted to e lrge numer or smll numerD positive or negtiveF hen V is lrge negtive numerD the potentil energy is very low nd the two hrges re strongly ttrted to one notherF o see thisD