Chapter 1 - Copy

MATTER, MEASUREMENT,AND PROBLEM SOLVING

The most ;l1fOlI1prcI1C11sib/c Ihil1g about the lmil'ersc is Ilwl i/ iscomprl'lrcrrsibk

-.'lnERT Fl"'~TfI'" (lM~\I"""19~~l

VVH AT DO YOU TH I NK is the most important idea in all of human knowkdgc1

Thl'fl' arc, of cours..., many possibll' answers to this question-sollle practical, some

philosophical, and som", scientific. If we limit oursch'cs only to sdcntif'k answers, mine would

be this: the properli~of mailer are determined by the properties of mol~ulesand atoms.

Atoms and rnolcrules determine how matter behavc,s-if they were different, matter would be

different. Thl" properties of waler molecules, for example. determine 11o,,' ",..Ier behaws; Ih('

properties of sugar moll"<ulcs determine how sugar behaves; and the molc.:u1cs thaI colllpose

our bodies dctnmine how our bodies behave. The understanding or mailer at the molecular

level gives us unprcredented control ov<.'r that matter. For example, the r<.'volution chat has

occurred in biology over the last 50 rears can be largely attributed to understanding the details

or the lIIolcculcs that compose living organisms.

~ Hemoglobin. the orygen-carrying protein Inblood (depiCled schematocally here). canalso bind carbon monoXide molecules (1helinked red and blaCk spheres)

2

1.1 AlomS and MoIe<:lIles

1.2 The Scientific Approachto Knowledge

1.3 The Classifi<;ation 01 Mattllt"

1.4 Ph~ical and ChemicalChanges and Ph~lcal

and Chemical Propll<tles

1.5 Ene<gy: A Fundam&nlal Part 01Ph~icallll1d Chemical Change

1.6 The Units of Measuremenl

1.1 The ReHab4lity01 a Measurement

1.8 SoIvmg Chemical Problems

1.1 Atoms and MoleculesThe ~ir O"er mOSl u.s. cilies. illduding my own. c<)nl~ins ~l IUSI rome poliUlion. A sisnifi.c~nl compom·nl of lh~l pollulion is carbon mon<)xide, a colorless sas emiu,-d in lhe eX­hausl of cars and lrucks. Carbon monoxide gas is COmPOSl-d of carbon monoxidcmolecules, each o( which com~ins a c~rbon alvm ~nd ~ll oX)"gell mom held loselher by ~

chemic~1 bond. AIOniS ~re lhe submicroscopic particles lhal cQnSlilule lhe fundamenlalbuilding blocks of ordinary mal1er. The)' are mQSl often found in mol«ulu, IWQ or more~l<)ms joined in ~ specific geomelrical arr~ngemerl1.

The propulies of lhe subSl~nCCS around us dq'end on lhe aloms and mol«uk'$ lhalcoml>Osc lhem. .so lhe properlies Qf carbon monoxide gas depend on the properlies of car­bon monoxide malcrula, urbon monoxide mohxulcs h~ppen 10 be iusl rhe righl si~e andshapc,~nd happen 10 haw jUSllhe righl chemical properties., to lit neally inlo cavilles with­in hemQglobin-lhe ox)'g"n-carryil1g mol«ule in blood-lhal arc normalll' rescrH-d foroxygen mol«uks (Figure 1.1"). ConscquemJl', carbon monoxide diminishes lhe oxygen­carrying cap.acilY of blood. Bre~lhing air CQnuinillg 100 much carbon monoxide (grealerlhan 0.04% by "olume) can lead 10 unconsciousness and ""en dealh because nOl enoughoxygen reaches the brain. urbon monoxide de~lhs ha"e occurrt'<.l, (or eumpk as a resul!of running an aUlomQbik ill a closed garage Or using a propane burner in an cndo~d

4 Chapler I Maller. Mnluremenl. and Problem Solv,ng

Hemoglobin, the oxygen-calf)'ingmoItcUle in rtd blood cells

Carbon mono~idt molecule

... FIGURE 1.1 Binding 01 O~ygetl and Carbon Mono~ide 10 Hemoglobin Hemoglobin,.l'Ile prolein mol...:ule, is theoX)Vn (-urier in red blood cell •. Ea<h subunit ofrM hemoslobin mol­<cule com.ins.n iron .lOm to ,,'hich 0trs.n bind.. Corbon monoxid< mol.cul., Con t.ke th. pt.ceof oX)1l.... thu. reducing lh••moun! ofoxysen re.chinllthe body'. r;..u.,.

Carbon dio~ide molecule

lIydmgtnatoms

spa'e for 100 long. 10 smaller amounts, ",roon monoxide caukS th. hurt .nd lungs 10

work h.rdu .nd nn r.sull in h.adache, di1.Z;ness., weakness. and confused lhinking.C.rs .nd lrucks emil .nolher closel), rdated mol«uk, called caroon dioxide, in far

greolerquartlities lhan carbon monoxide, Th. onl}' diffcrence belween uroon dioxide andurbon monoxid.. is that urbon dioxide mol«ule. contain two OX)'gen atom. instead ofjust one. Ilowe'·cr. this e~tra oxrgen atom dram.tiullr .ff«u Ih. prope,,;'s of Ihe gas. W..br..alhe much more carlx," dioxide-which is nalUr;ll1y O,03,*, of air. and. prodUCl ofourown r.spiration as well-than carbon monoxide, )'el it does not kill us. Wh)'! Be<aose th.presence of lhe $t'Cond oxrg.n alOm prewnls carbon dioxide from binding to lhe ox)'Sen·carrying sire in hemoglobin, making il far less toxic. Although high I"'ds or ,.rbon dioxide(gr.ater than 10% of air) nn be toxic for Olh.r reasons. lowcr 1.\'(ls nn .nter th. blood­stre.m with no ad"erse effeCls. Such is the molecular world. Any changes in molecules-­su,h:u Ihe .ddilion of.n oxrgen 310m 10 carbon monoxide-..elikdy to result in largechanges in Ihe prop<'rties of the substanceslhel' compose.

As another example, consider IWO other clost'll' rd3led molecules, wal~r and h)'drogenperoxide:

W~lf' moluule

Oxygen.,~

Oxys...otOm

Ic.rbon

.1Om

c.rbon.tum

O~Yl;<'n

.1001

In !he IMy or c/'IemIslry, .1OttlS n o!IellPOrtrayed as Gdored SIlhms. wrth each Gdorrepresenll"lllllrtlefen1 kmd or atom f« a·ample, • blad< $llI1erl1 re;Jre$enIS I ea1lonIbn. a recI sphere~1s an oxrgen110m. and I while $Ilhete~ a~ogen alom. Fer a cc:rnl*le Gdor coxlloIl!oms, see Appenlb M..

Tlw:~ IItlOXde used as ., Illbst\lllCor bleacllulil agen111 aJtlSIlImbly diluIed

A water molecule is composed of one oxrgtn alom .nd IWO hrdrogcn aloms. A brdrogtnperoxide mol«u1e is cnmposed of "'" oxygen aloms and twtJ hrdrogen .toms. This seem­ingl)' small mol~cular difference resulls in a huge differ.nce belw..,n water and h)'drogenperoxide. Waler is Ihe familiar .nd slableliquid we all drink .nd balhe in, ~l)'drogen perox·ide, in comuS!, is an unSl3b1e liquid lh.t. in ils pure form, burns Ihe skin on COnla(\ and isu~d in rf,ICkl't fuel. When rou poor water onto )'our hair, rour hair simlily becomes Wd.Ilowe\"(r, ifrou pUI h)'drogen peroxide in )'Our hair-which rou m.)' ha"c done if )'Ou hawblu,hed rour hair-a cbemkal rUClion occurs thallurns )'tJur hair blonde.

1.2 The SClenllfic Approach to Knowledge 5

The decailsofhow sp«ific aloms bond 10 form a nlOkcuk-in a slr~ighlline, al a par­liwlar angle, in a ring. or in somc olher paltern_s wdl aslhe lype of aloms in Ihe mole­cule, delnmine ewrylhing al:>uul Ihe SUbSlanCe lhal lhe mulecule composes. If we wan110undersland che subSlances around us. we musc undersland lhe acoms and molecules lhalcompoSt lhem-this is the cenl ...1 gO'll of chemistry. A good simple ddinition ofchemistry is, therefore,

ChemiSlry-lhe science that $Ceks 10 underSland the behavior "f maUer bystud)'ing Ihe behavior"f al"ms and molecules.

1.2 The Scientific Approach to KnowledgeScientific ....nowledge is empirical-Ihat is, il is based 00 o"savrl/io/l and cxprr;mCIII. Scien­lislS obS<'rve and perform experiments on the ph)'sical world to learn aboul it Some obS<'r­"acions and experiments are qualiuti'·e (noling or de.scribing how a process happens), butmany arc quaolilati"e (measuring or quanlifying something aboullhe pmces:s). For exam­ple.Amoine ul\"oisier (1743-179~),a I'rench chemist who sludied combustion. made care­ful measuremems of the mass of obt«ts before and after burniog Ihem ill closedcontainers. He noticed thac Ihere was no change in the cotal mass of malerial wichin checonlainer during combustion. lamisier made an important ObSf'rnllir'" about the phrsicalworld.

Observalions ofcen kad scienli51S co formulace a hYp"thesis. a tencati'·e inlerpretalinnor Cllplanation of the observations. For Cllample.la,'Oisin explained his obserl'ations oncombustion by hypothesizing chac when a substance combusts, it combines with a rompo­nenl of air. A good hYP"thesis isfnbifinblc. which means Ihat il ma....cs predictions lhac canbe confirmed ur refuled by further observalions. Hypotheses arc tested by experiments,highly conlrolled procedures designed to generate such observations. The results of an ex­perimenl mal· suppon a hypochesis or pm'"C ic wrong_in which case Ihe hypochesis mustbe modified or discarded.

In some ca~. a series of similar observations can lead to Ihe development of aKientific law. a brief Slacemenl Ihat summarizes p;ut obsenlltions and predicts fUlUreones. For example. lavoisier summarized his obS<'rllIlions on cnmbuJlion with Ihe law ofconKrllltion of mass, which states. kin a chemical reaclion, maHer is neither crealed nord"5tl"Oyed.k This 51Jcemenc summarized lavt);sier's obKn"alions on chemicJI reaClions andpredicled Ihe outcome of future ob,.,n·ations on reactions. laws.li....e hypotheS<'s. are alsosubjeci to experiments, which call add supl't)rt to them or prow Ihem wrong.

Scienlific laws arc not I",~s ;nlhe same sense asci,-il or gm·ernmenlall;Iws. Nature dOC'Snot follow laws in Ihe way Ihal "·e obey Ihe l;Iws against sp«ding or running a SlOp sign.Rather, scientific laws desu;w how nature hehal·es--Ihe}' ar" generalizations aboul whalnalure docs. For that rcason, some pcopk find ic more appropriale CO rder 10 them asprinriples ralher than 111"'5.

On" or mOre well-cslablished h)·pothe,.,s may form the basis for a scientific theory. Ascienlific cheory is a model for Ihe way nature is and cries 10 explain nOl merel)' what naturedoes bUI wh),. As surh. well-established theories arc the pinnacle of scientific .... nowledge.ofun predicling behavior far beyond lhe obKrnlions or laws from which the}' were dewl·oped. A good eumple of a cheory is che atom;r theory propoS<'d by English chemisl lohnDalton (1766-18~~). Dalton explain.x1 the law of conscTl'alion of mass, as well as othcrlaws and obsen·alions of the time. by proposing IhJC maner is composed of smJl1. inde­struclible panicles caned Jtoms. Since these parlic!d are merely rearrJnged in chemicalchangcs (and nOI crealcd or destroy.x1), lhe total amount of mass remains the sam.·. Dal­lon's lhror}' is a model for Ihe physical world-it gh'es us insighl intu how nature works.and cherefore expldins our laws and observations.

Finally. Ih.· Kientific approach returns 10 obserl'ation to tesltheories. Theories are I'al­idaled by cxptrimems, though Ihey can nel·cr be conelusi,·e1~· pro'·ed-Ihere is always chepossibilily chal a new observation or experimenl will re'"Cal a flaw. For e~ampk, the alomicIheory can be tested by Irying 10 isolate single atoms. or by lq'ing to imagc thcm (bolh ofwhich, b)' the way, hal"( already been accomplished). Notice chat chc scienlific approach 10

• Ap.int;ngofthe French rhemist An·coine bmi!w' w;ch hi! wife. !>brie. whohell'C'l him in hIS wu,k hy iIIumatinghIS "pcrlmenlS and lran!lollng leWntif.ic art;cl" from fngli!h. l.avoi.;"r. whoalso made .ignlflCanl runtribUliun! 1<>

agTicullu'•. indu,try, educalion. andg...vernm.nl adminislracion, "'UexCCul·ed dunng Ihe French fl..w)ucion.("" loW! n.vid (F"""'. t7... t,»).

•...."" ·I...'""l.._{17.J-I~)~ lb,",f< {M ;O'A1l...·Pi........ P....... 17lo'-l&l/il:liN. o~ "" <am"U, H. I~·V. i•. W. 70·%,;n.

(l;;'.7" I"... coo). T1>< M"""P"Ii",. ~lu""",

oJ ArL f\.o..:hok••\1,...... M a..rIn W""",.

..... G;~. In _ oJ [ , f.hr. 1977.

(19n.HI) I.....~I On.. ~I<t"'lool;"'.

~1"lnOmoJ""'L)

In Oaltcn·S ~rre. atoms wm \IIoI.I¢I1o b9IndestrueWe, Today, because 01 nuclearreacbOnS, we know IIlat aloms WI be brokenapart Into their SIIIaIer COIllIXIfl8Il\S.

6 Chapler t Maller, Measuremenl. and Problem Solv,ng

The Scientific Method

conr.... .I IIypolMl.iIj Conr.... I ,,~"]

r 101 ,"Ill! I\ypolhrsiIl

J r(01 _Ihf<lryl

'"'[ ObsenllioftsJ I hp.'im.nlS.... - I E.p"'....ntl

'"'I '"' 1,....

101 rnMlIwj I ~]

A FIGURE 1,2 The SCientifIc Melhod

knowledge begins Wilh obsen'~lion ~nd ends Wilh obsen'alion, because ~n cxpt'riment issimply ~ highly controlled procedure for generating crilical obset\'ations designed to lest athrory or h}'pothesis, Each new set of obse"'ations allows rd"inemem ofthe original model.This apprNch, oflen called the scientific method, is summarized in Figu... 1.2A. Scientif·ic laws, hypolh..ses. and thwries are all Subtul to col11inued experim.nlation. If a law. hy·pothesis, or theory is proved wrong by an cxpcrimem, it musth<: revised and tested withnew experim.nlS. Owr lim.., fM>Or lheories and 1310'S are eliminated or c"rrecl<'d ~nd guo<!theories and laws-lh"sc consist.nt wilh .xflt'rim.nlal resulls-remain.

E.stablished throriC$ with strong experimental support are the most powerful pi«c:s ofscienlific knm"kdge. ruu mar ha,'. heard the phrase. MThal is JUSl a lheorl"~ as if lheoriesWere u5ily di5missible. lIowe\'(r, such a 5talem.nl ...·'·.als a deep misunderstanding of lhenalUre of a SCienlific thwry, W.II-eslablished lheories are as close 10 lrUlh as we gel in sei.ena. The idea lhat ~II mall"r is m~de of atomS is "just a thwry.~bul il has m'e' 200 year5 ofexpcrimenlale"idenc. to supporl it II is a powuful pi...:e ()fsci.ntific knuwl.dge on whichmany olhu seiemific ideas have been buill.

On. last word aboUlthe sci.mific method: some pwple wrongly im~gine sci.nc"ll) hi'a stricl SCI of rules and proco:dure5 that automalically lead to inarguable. obj...:,j,'e faets..This i5 nOlthe casc. E"en our di~gram of lhe scientific method i5 onl}'an ideali7.alion of realKience. useful 10 hdp us s« th" ke}' diSlinctions of scienCe. Doing real science requir~

hard work, care, crutil'itr, and eWn a bit of luck. $ci..nlific thwric:s do not just fall out ofdata-ther are crafted b)' men and WOmen of great geniu5 and crealil-ity. A great thror}' isnot unlike a m~Ster painting and many s« a similar kind of beaut)' in both.

::Conceptual Connection 1.1 Laws and Theories

Which of th~ fnllowing beSI explains the difference between a law and a th~ory?

(a) ,\ 13I~ is truth whereas a theory is ntere sl....-<ulation.

(b) A law summaril.CS a series of related observations.. while a th""ry gil'es the underlringreaSOn5 for them.

(c) A lheory describe, II'ltIll nalure docs; a law describes why nalUre don iI,

Answer: (b) A bow simplr 5umn,.rius a SUItS of ....bled obs¢rvdllons, while. throry gW¢$ lh. und~r·lying r~aso"s (or t!>em.

1.3 The Classification of MatterMatte, is anrthing that occupies 5paCe and has mass. F()r crample, this book. ~'our de5k,your chair, and evcn }'our bod)' arc all COIllPOsro of mailer. l.ess Obl';ousl~', lhe air aroundyou is also mattu-;t 100 occupies sp.>cc and has mass. We nften call a specific instance ()fmatter-5uch as air. water, or 5Snd-a subllance. We can c1assif)' mailer according to itsstat(----solid, liquid. or gaS-and according 10 its composition,

[ Solid mall<1" ) ( G~slnan<1" )

'.3 The Class,llCat'On ot Malte, 7

<II tn a oolhl,lhe aloms or molccul.. af<'fixr<1 in place and can only "ibralr. In aliquid, ahltough Ihe >loml .... mulrcul..are clouly pukrd, lhey can 1n0V< IUSIone anolher, allowing 1M liqUId 10 flowand ...umrlhr .hapr o(itoronla",,,.lna ga"lhr or",... or molccukJ arc wlddyIpaced. making P-'" rolnp,wibk aswrn as nuid.

The States of Matter: Solid, liquid, and GasL\lall~r can nist in three diff..renl states: solid, liquid, and gas. In IOlid 1IIIl1t...., atoms ormolecules pad: dOM: to ~ach other in fixed locations. Although the atoms and molecules ina 501id "ibrate, lhcy do nOi mm'C around or Palt each other. C.onse<juently, a solid hu afixed ,"Ulume and rigid shapc.lee, aluminum. and diamond arc good namplrs or solids.Solid mailer mal' be crySlallinc, in which cas<: its atoms or molecules are arranged in pat·lerns "'ith long-unge. repeating order (Figure 1.3(a)"'), or it mal' be amorphous, in whichcaM: its atoms or molecules do nOl haw an)" long-range order {Figure 1.3(b)"'). Examples

The stale g/ mall« C'*"l/eS from soMIlO! Ilqud to llII W11h lIlCl!85lll\l1e<T1peralure

CrySlalline:RcguJ.r 3·dimcnsional

panern

DiamondC (I, di.mond)

Amorpho""No ..gul.r p.ttem

CharcoalC (.,amorpl>ous)

'4 FIGURE 1.3 Crystalline andAmOrph0l.l5 SolIds Diamund if a<ryJtal!inc ~lhl <umpuJtd of carbonalums arungrd in a ..-gular, "pealingpa1tcrn. Charcual is an amo'phoUJ ",l'd<ompoJtd of carbon atoml WIth n"Iong,nns< urder.

8 Chaple, I Malle" Measu'emenl. and P,oblem Solv,ng

SoIid-nol cOll19fffiiblt

of crY'/lIl/ine .solid. illc1ude lable J;ll! and dianlOnd; Ihe well·ordem.lgt(,melri, shape. of ,$;;lit and diamond (rJ'$lals rcnccllhe ,,'e1I·orderedgwmdric arrangemenl of Iheir alOms. Exam"I". of amorphl/tll solidsinclude glass, plUlic, and charcoaL In li'/lUd n,,"'", alOms or mole·cule. pack aboul as closely as ,hey do in solid maUer, bUI Ihey are free10 mOl'e relal've 10 each olher, giving liquids a fixed "olume bUI nOI afixed shape. Liquids assume Ihe .hal" of Iheir comainer, Waler, alco·hoI. and gasoline arc all good eXample. of sulmanC"'lhal arc liqoidsal room I"mperalurc.

In gll"'ous mm,er, aloms or molecules h.,'e a 101 of 51'ace b<:lweenIhem and arc fr.... '0 mo"e rcblil'e 10 one anOlher, making gase5comprrs.siblc (Figure I A 4), When you squeeu a balloon or sil down011 an air nlallress, )'Ou force Ihe alom. and mol«ules into a .mallersp.ce, so lhallhey arc closer IOgClher, G;I.$d ;l.lway. a.sume Ihe shape1I",! \'Illume of Iheir conlainer, Subslances Ihal ate gases al room lem·peralure include helium, nilrogen (Ihe main componCnl of air), andcarbon dimidc,

'" FIGURE 1,4 The Compressibili.ty of Gases Gaso Clln t... romprffitd­5qu«1,cU ;nlo a SIllol"', volum.-b«a~,neR II .jQ muen emp'Y .pace bttw...naloms 0' molC'<ul.. m ,n. ga~s sl.le.

Classifying Matter According to Its Composition:Elements, Compounds, and MixturesIn addilion 10 c1assifring mailer according 10 ilS Slale, we can classify il according 10 ilscomposilion, i.e" lhe kinds and amounlS of subslances Ihal cumpoSf it The followingchari shows how 10 c1a:ssifr malle, according 10 ilS compo.ilion:

• -. .- . . "CO I• • 'f"~b"lL&..s.- *9" .~ ...•• • ~.," ...... .iJ• •• • '0 ... ., • <

• • • .-~g .\:>.-• • • ~ ~I:l'e~ .:s-• • ,.. lL.

Helium PIIr~ wale!

..... .. ......, ..', ...... (~'

.... ., ~. f...... ~I" ..... _r·

" -w.,..., '~awi1ltwgill

The firSI di,';sion in Ihe cl~!>Sificalion of mailer depends on ",helher or nOl ils compo.silion can "ar)' from one sample 10 anolher. For example, lhe Composilion of dislilled (orpure) waler newr varies-il i. alwars ll>ll% waler and is lhereFore a pur~ subSlanc~, one

1.~ PhySIcal and Chemical Changes and PhysIcal and ChemIcal P'ope'lies 9

COnlPOS<"d of ollly a single lrpe of atOnl or nlokcuk. In COluraSl, lh~ cOnll'Ositioll of sw~el­encd I~"- call "arr subsl,,-nlial1y from on~ ",-mple 10 all<>lh~r, depelldillg. for inSl,,-nce, on Ih~

slrength of the lea or how much sugar has b«n added. Swcel..ncd Ica is an nampl.. of anli.rlu~. a substallcc composed of lWO or morc differClll Iypes of atoms or mokculn Ihalcan be combined in conlinuously \'ariabk pr'Jp<Htiolls.

Pure subslances can be divided into two t}'pe_lemenls and compounds­depending on wh~theror nOI they call be brok~n dO,,"Il into simpkr subslanceS. The hdi­urn in a blimp or pari), ballooll is a good eramp1cof an dCnlent. a substance thai ",nnOI bechemically broken down inlo simpler subslances. Waler is a good example of a compound,a substallce cOlllprlS<'d of two or nwre cl~nlcnlS (hydrogen and o~n;ell) in fi~ed, d~finite

proporliolls. On bnh. coml'OUllds are more common Ihan pure elemenu because mostdemenlS combine ...·ilh olher clements 10 form compt)unds.

Mixtures can be divided into IWO I)'~s--hetcrogenwus and homogelleous-­depending on how uniformly the substallces within lhem mix. Wei "'-Ild is a good erampkof a hetfrogeneous mixture, One in which Ihe composition "aries from one region to an­olher. Swrtlened lea is a good exampk of a homogeneous nlixlu~. one wilh Ihe "'-mecompusition Ihmughoul. HomugenCtJus miXIUr,:S ha"e uniform compositions b«"ausc lhealoms or molecules that compoS<' Ihem mix uniformly. Ilderogeneous mixtures are madeup of distill" rcgiolls becaus<: Ihe atOnlS or molC'i:ules that comllOS<' Ihem separale. ]-Iereagain we sec Ihal the prO~rlies of m"-ller are determined b)' lhe aloms or molecules Ihalcompose it

1.4 Physical and Chemical Changes and Physicaland Chemical Properties

E"cry day we wilnt'SS changes in mailer: ice mells. iron rusI$.Kasoline burns, fruit ripens.,and ...·ater ""poralt-s. Whal happens to the molecules Ihat compose tht-SC samples of mal­ICr during such changes! The ans ....er depends on the Iype of change. Changes Ihal alleronly sUle or appearance. but not composition, are calk..! physical changes. The atoms ormoleculn Ihal compose a subslance do 1101 rhallge Iheir idenlil)' during a physical change.For eumple.....hen ....alerOOils. il change-s its Slal~ from a liquid loa gu, bUllhe gas r~mainscompoS<"d of waler molecules. $0 Ihis is a physical chanK" (Figure 15.).

In conlraSI. changtos lhal alter Ih~ composilion of mall..r ar.: called chemical changes.During a chemical change. aloms rearrange. lransforming lite original substallce, iOlO dif­fereOl subSlances. For exampk Ih.. rUSling of iron is a ch.-mical change. The alom.! Ihal

<II FIGURE 1.5 Boiting, a PhysicalChange Wh.n "'Ol.r boils. it lu'nSinl.. a gos bul does ""1 alr.T;1$ (ltemicalid.nll1y-IM "'·al.. molecules are lh.S.me III both th. liquid and g.....us11.10. Boiling i5lhus. physical (hange,and the boiling point of "'al.. is. phys·i••1propeny.

10 Chaple, 1 Malle'. Mnsu'emenl. and P,oblem Solv,ng

Iron alUm!

... FIGURE 1.6 Rusting, a Chemi.cal Change Wh.n iron ,">11.,lh. Itonaloml combln. wi,h ox)'!;.n alom! 1ofo,m I diff.,em ,h.rnkll >Ublll""'.lh.compound ,ron oxide. RUlIing is lbe,.­fo,. I chemicllehlng., Ind Ibe l.ndon­cy or iron Iu ,ull i•• chemi..1properly.

In Chaptlll' 19we W111llsl11um abool~~ wfloc/l CIIII '""OIve .1CWIlS or ona ele­men! c/IInlliOlIllIlo attnlS oll diTleren1

"""'"A~ thatlQI rlISli1s In I dlllerem torrnat IhIII $arne $l.IbStanCe, whilel chenUcalcharIglI moJIs ilia ~tetyd<Tlttelll......

Answm 10 For Pfactlce and For MIn Prac­bI:e pml:ilem$ CIIIIIle t(JJnd lnAwenOO: IV,

compos.: iron (irOll llOnlS) combi"e wilh oxygen 11101«ules from air 10 form iron oxide,lhe orange subslance we normally call rIISI (Figure 1.6"). Some OIher examples of ph)'sicaland chemical changes are shown in Figur. 1.7"_

Vhrsical and chemical changes art: manifeslalions of physical and chemiCllI properties.A physical property i, one Ihal a subSlance displays WilhoUl changing il$ comf>l»ilion,whereas a chemical property is one lhal a subslance displays onl)' by changing ilS compo­Silioll ,-ia a ,hemical change. For example, lhe smell of gasoline is a ph)'sical pmpert)'­gasoline docs rlOl change ils composilion ,,'hell il exhibitS ilS odor. The J1"",mnltility ofgasoline, howe... r, is a chemical propertr-gasoline do<:s chang.. ilS COmposilion when itburns, lurning il1lo compleldy new subSlances (primaril)' carbon dioxide and waler}.Ph)'sical properties indude odor, lasle. color. appeuance, meiling poi"l. boiling point. andd..nsil)·. Chemical properties indud.. corrosi'·eness. flammabilily, acidily, loxicily, andother such charaCleriSlics.

The differences belween physil'aland chemil'al changes arc nOl always apparenl. Onlychemtcalenminalion can confirm whdher an)' particular change is physical or ch..mica!'In ,nanr CIS<:S, howe"er, we can id..mify chemical and physical changes bas.:d on what "'eknow aboul lh~ changes. Changeli in the slale of maller, such a~ mehing or boiling. orchanges in lh~ physical condilion of malt~r.suchas lho",", lhal resull fT<)m CUlling orcrush­ing, ar.. I)·pically physical changes. Changes in\'oh'ing chemical rt:aetions--ofl~n ~"idenc«l

by heal exchange or colQr changes-arc chemical changes.

-EXAMPLE 1.1 Physical and Chemical Changes and PropertiesDelermine ",helher each of lhe following changes i~ physical or chemical. Whal kind ofproperly (chemical Or physical) is being demonstraled in nch cud

(al lhe ..1'Iporalion of rubbing alcohol

(b) Ihe burning o(lamp oil

(c) lhe bleaching of hair with hl'drog..n peroxide

(d) lhe forming of frusl on a cold nighl

Solution(a) When rubbing aloohol e....porales. il changel from liquid 10 ga~, bUI il remains

alcohol-Ihis is a phy~ical change. The volalililY (or abilily 10 ..vaporale casily) ofalcohol is lhrefore a ph)'si",1 propert),.

(b) Lamp oil burns b«aus.: il reaClS wilh oxysen in air 10 form carbon dioxidt' andwater-lhis is a chemical change. The Rammabilily of lamp oil is Ihercf(jre achemical prop'·rly.

(c) Appl)'ing hrdrogen peroxide 10 hair changes pigmenl molecules in hair Ihal gi'·e ilC()lor-lhis is a ch..mical chang... Th.. susceplibilily of hair 10 bleaching is lhereforea chemical properly.

(d) FroJl forms on a cold night becau",", wal..r "apor in air changes its state 10 fonn solidiC~lhis is a ph)'sical change. The lemperalure at "'hich waler fr«les is lh.refore aphysical properly.

For Practice 1.1O<'lermine whether ..ach of the following is a physical or chemical change. Whal kind ofproperly (chemical or ph)'sical) is bt:ing demonslraled in each case!

(al A copper wire is hammered Bal.

(b) ,\ nickd dissokt'S in add 10 form a blut··gn...·n Solulion.

(e) Or}' icc sublimes (change~ imo a gas) ",ilhoUl mdling.

(d) A mateh igniles "'hen struck un a flint.

1.~ PhySIcal and Chemical Changes and Physical and Chemical Properlies 11

Physical Change and Chemical Change,,1)'1' ice subliming;

COI(S) --> COlI:)

ChemicoJ composi""n unalinedPbysical cbange

co.(s)

Solid carbon diox~

(dry kt)

'.J

Sugardissol~inll:

CUlilPlIls) --> C,III l10,,( ..,,1

Clltmi,al compositiun unali...edPhysical change

CIlHnO,,(s)Solid $llgill

CIIHllO,l( ..q)

Dis~wgar

"""'""(hI

I'rupanegll5 burning:

C,H1(g) + 5 OIl:) -->3COl (:1 + ~ HIO(:)

Chrmical composition all.redChemical chanll"

,,,4..

COl(S).lI l0(S)

CilIbcn dioxide andWill!!" mole<:ul!1

'<I• FIGURE 1.7 Physical and Chemical Changes (a) Tilt sublimati"n "r dry icc ' ....1id COl) is a physi·cal change. (b) The dlW>luli"" uf sUII"" is a phpkal change. (e) The burning ufpropanc is,. chemic-al ,hange.

12 Chapler I Maller. Mnsuremenl. and Problem Solv,ng

g. Conceptual Connection 1.2 Chemical and Physical Changes

The diallr~m 10 lhe lefl repr«l'nlS liquid w~ll'T moll'cul.-s in 3 pan.Which of Ihl' following diagrams m,SI repr''SI'nIS lh,' wal~r mol«uk., afll'r lh~~' haw

ocen 'llporil.cd by Ihe boiling of liquid "'lIlcr?

•~

1.1 Ibl 1<1

Answer: Vi.... (a) ~t "'p~nt, thl' ""'I" afl" vapori,alion. Vapori,alion i,. phpic.1 change....thl' n....l...,uJl'$ must remain tl>c J;lmel>cfore.nd .fier Ihe change.

[ F",,,,, 0<1. through di,tance; ""Urk ;.oone. )

High potenlialentrqy (unstablt)

low potentialenerlN (sLlble)

.... FIGURE 1.8 Energy ConversionsGr;lVl101ional potenH~l enerl;)' ;. COn·'"I'"ed into ktne!tc energy when rhc"'eight i, rek;ucd. The kineric eneTj;Y i,convened m",tly to therm.) energy,,'hen Ihe "-e;ghr mike. the gruund.

1.5 Energy: AFundamental Partof Physical and Chemical Change

The physiclllllnd chemical changes lhal IH ha\"I' jusl discuSSI'dare usually accompanin! by I'nersy changl'S. For I'xample. whenwaler e"aPOf3t~s from rour skin (a physical change), lh. walermol«ules absorb enerllY from )'Qur body, mal:ing ~'Qu fedcooler. When rou burn natural gas on Ih. SIO,'. (a chemicalchange), enerllY is released, healing the food ~'Ou arc cool:ing.UnderSlanding Ihe physic;al and chemical changcs of mallcr­that is, understandinll chemistry-r"'luires lhal we alS(l under·stand enerll}' chanllfi and energr flow.

The scienlific definilion of energy is /11( '''f''l.iI}' /0 ,10n·o:>rk. Worl: is ddined as lhe aClion of a fora through a di$lance. For inSlance, whl'nruu push a box across the floor ur pedal ruur biq-c1e down lhe Slreet, yuu ha"e doneworl:.

The IOral e"erg)' of an object i, a sum of ilS kinetic energy, Ihl' energy aSS(>Cialn! wilhilS mOliun, and ils potenlial energy, Ihe encrgr associaled wilh ils position ur composi·tion. For example, a weight held lit $C"cral mete~ from lhe ground has polenlial energy due10 ilS po.ilion within Earth's gra,'il~lional field (Figure I.S<I). If the Wl'illht is dropped. ilaccelerales, and the POll'nliall'nerllr is con"erted 10 kinel;C I'ncrgy. When the weighl hi,sthe ground, ilS kinl'lic energy is conwrll'd primarily 10 Ihermal energy, the I'nergy associ·atn! with the lemperalU,," of an obj«l. Thermall'nl'rgy is a(luaHy a type of kinl'tic enl'rg)'m,cauk il ariks from the mOlion uflhe indi,-idual aloms or mol«ules lhal make up an ob­i~ct. In other words. when the weighl hilS lhe ground its kin~tic energy is esscnliall)' trans·ferred to the atoms and mokcuks Ihal COmpok thl' ground, raising the lemperalure of theground e'-eT so slighll~'.

The first principII' 10 nOlI' aboUI lhe war Ihaten~rgych~ngfi liS the weighl faUs 10 lheground is thal"""rgy '5 n..irh..r.rcated nordeSlro)'~d.The poll'nliall'nl'rgy of Ihl' weight be·comes kindic energy as lhe weighl accelerates toward lhe ground. The kinelie energr lhenbecomes thermal energy when lhe weighl hits Ih... ground. The IOtal amount of lhermal en·erg~'lhal 15 reieased Ihrough thl' proce5S is I'uctly equal to thl' dif(l'.enu \)et""I'en the ini·I;al and filial polelltialellNIlY of Ihe weight. The obkr.'alion thalenergl' is neilher crealn!nor dcslro~'n! is known as lhl' law of conservation of energy. Although elle.g)' can changefrom one kind to anOlher, and although it can flow from onl' objl'ct 10 another, the ro/"I'/Il"",il}'of I'llergl' dOl'S 1101 change-it Temains consun!.

1.6 The Untts of Measurement 13

Molecules ingasoline (unstable)

Molecules inexhaust (stable)

1

Th~ ~cond prin iple to not~ i systems wit/r /rig// potenlial energy /rm'e a tendenc)' 10c/range 1/1 a wa)' 1//tII lowers l/reir pOlell/ial energy. For this reason, obje tors)' terns \"ithhigh pot~ntial ~n~rg)·tend to be "nsMb/e. The weight lifted scveral meters from the groundi un table because it contains a ignificant amount oflocalized potential energy. nle re­trained, the weight will naturally fall, lowering it potential energ)'. ome f the rai ed

weight' p tential cncrg)' can be harne cd to do work. For e ample, the weight can beatta hed to a rope that turn. a paddle \ heel or pin. a drill a the weight fall. fter it fallto the ground, Ihe weight contain Ie potential energy-it has become more sMb/e.

ome chemical ubstan es are like the raiscd weight 'u t de ribed. For example, themol~cul~. that ompo ga~olin~ have a relatively high potential ~nerg)'-~nergyi on ~n­

trated in them ju t as energ)' i oncentrated in the rai ed weight. The molecules in Ih~

ga line there~ re tend t undergo hemi alhange ( p~ ifically ombustion) that will lower

their potential energy. the energy of the mole­cule i. released, some of it can be harne sed todo w rk, u h as moving a ar down the treet(Figure 1.9~). The molecule that re ull fromthe hemi al hange h ve I potential energ)'than the original mole ule in ga.oline and retherefore more table.

Chemi al potential energ', uch J thatontained in lhe molecule Ihat ompo ega 0­

line, ari e primarily from the force betweenth electri ally harged panicle (proton andde Iron) lhat ompo e atom and mole ule . We will learn more about tho e pani le ,as well a the propertie of electrical charge, in -hapter 2, but for now, know lhat m le­cule contain specifi. metimes c mplex, arrangements of the e charged pani Ie .

ome of these arrangements- uch a the one within the mole ule that ompo ega aline-haw a much higher potential energ)' than other. When gasoline undergoe

mbustion the arrangement of the e pani Ie hange, creating molecule with mu hlo\"er potential energy and tran ferring a great deal of energ)' (mostl)' in the ~ rm ofheat) to the surroundings.

IIl11l11nrizillg:

~ Energy is always onserved in a phl'si al or chemi al hange; it is neither reated norde troyed.

~ )'stem with high potential energy lend to hange in a direction of lower potentialenergy, releasing energy into the urroundings.

1.6 The Units of Measurement

Chapter 1 Page 12

We WIll 'lOd 10 Chapter 19 IIlat energy con­servalJon Is actually pan of a more enerallaw IIlat allows for the Inlerconven'bohty ofmass and energy

r move fon'ard

... FIGURE 1.9 Using ChemicalEnergy to 00 Work The compoundprodu ed wh n ga oline burn have Iehemical pUlential energy Ihan Ihe gaso-

line mole ul .

... The 125 million Mars Climate Or­/1I1N' wa I t in the Marlian atm pherein 1999 because two group of engineersfailed to communicale 10 each other theunits that they use<! in their calcuJatio'h,

14 Chapter 1 Maller. Measurement. and Problem Solving

TABLE 1.1 51 Base Units The Standard Units

Ouantity

Lenglh

~Ias

Time

Tem peralU re

Amounl of substance

Elect ric cu rrenl

Luminous imensily

Un~

Meier

Kilogram

~ond

Kelvin

~Iole

Ampere

Candela

Symbol

m

kg

K

mol

A

cd

The standard I base unit are shown in Table 1.1. For now, we , illfocus on the first four of Ihe e units including the lIIeler as Ihe tan­dard unit of lenglh, the kilogram a Ihe slandard unil of ma ,Ihsecolld a Ihe standard unil of lime, and the kelvill as the slandard unitof lemperature.

The Meter: AMeasure of LengthThe meter (01) i lightly longer Ihan a l'ard (1 yard i 36 inche whilI meter is 39.37 inche ).

YardslickThe abbrevlabon 51 comes trom the French.5ysleme InlernatlOnal d'Umles

2m

---"->:<,._lA baskelball player stand aboul2 meters tall.

A Anickel (5 enl ) weigh about5gram.

Meier Ii k

Thu ,a 100-yard football field mea ure only 91..1 meter. The meIer wa originally defineda 1/10,000,000 of the distance from the equator 10 Ihe north pole (through Pari ).It i nowdefined more precisely as Ihe dislance lightlravel Ihrough a va uum in a certain period oftime, 1/299,792,-158 econd.

The Kilogram: A Measure of MassThe kilogram (kg) i. defined as the ma s of a metal cylinder kept at Ihe Internalional Bu­reau of Weights and Measures at hres, France. The kilogram is a measure of IIInss, a quan­tity differem from weighr. The ma fan objecl i a measure of the quanlity of mailerwithin iI, while the weighI of an object is a measure of the gravilntiollnl pI/II on the mailerwithin it. If you weigh yourself on Ihe moon, for example, its weaker gravily pulls on youwith Ie for ethan d e. Earth' gravity, re ulting in a lower weight. 130-pound (Ib) per­son on arth weighs 21.5 Ib on the moon. However, Ihe person' ma Ihe quanlity ofmailer in his or her body-remains the ame. One kilogram of mass is Ihe equivalent of2.2051b f weight on Earth, 0 if we expre mass in kilograms, a 130-lb per on ha a maof approximately 59 kg and this book has a ma S of about 2.0 kg. A se ond common unil ofmass is the gram (g). One gram is 1/1000 kg. A nickel (5¢) has a rna S of about 5 g.

o Conceptual Connection 1.3 The Mass of aGas

A drop of water i PUI inlo a container and the container i sealed. The drop of water thenvaporizes (turns from a liquid inlO a gas). Does the mass of the sealed conlainer and itscoment change upon vapori7.3tion?

Answer: '0. The water vaporize and be omes a gas, bUI the 'valer molecules are till pre..,nl wilhinthe flask and have the same rna .

The Second: AMeasure of TimeFor Ihose of us who live in the nited tates, the econd ( ) is perhaps the rno t familiar 51unit. The second wa originally defined in terms of the day and Ihe year, but it i nowdefined m re precisely a the duralion of 9,192,631,770 period of the radialion emittedfrom a certain Iransition in a cesium-133 alom.

The Kelvin: AMeasure of TemperatureThe kelvin (K) is lhe I unil of temperature. The lemperalure of a sample of matter i amea ure of the amount of average kinetic energy-the energy due to motion-of Ihealom or molecule Ihat ompose the mailer. For example, the mole ule in a hOI gla of

Chapter 1 Page 13

Temperature Scales

180Fdhrenheitdegree

)00

100C.cbiudegree

373 K --- Water boils

)00kelvin

1.6 The Untts of Measurement 15

.... FIGURE 1.10 Comparison ofthe Fahrenheit, Celsius, and KelvinTemperature Scales The Fahrenheitdegree IS five-ninths the ize of the e1­IU degree and the kelvin. The zero

point of the Kelvin .Ie i absolute zerolthe 100,'e t po ible temperature)."""erea the lero point of the Cel iu

ale i the fremng point of ''''dter.

32 F---- 0.00 273 K--- Water freezes

-459 of -- - 27 ° -- 0 K--- Absolute zero

Fahrenheit Celsius Kelvin

w~ter are, on average, moving fa ter than the mole ule in a cold gla" of water. Tempera­ture i a mea ure of thi mole ular motion.

The three common temperature ale are h wn in Figure 1.10•. The mo t familiarin the United late i the Fahre.nheit (OF) cale., ho' non the. left. On the Fahrenheit ale.waler freeze at 32 of and boil at 212 of at sea level. Room temperature i appr ximately72 oF. TIle ale mo t often u ed by s ienti t and by mo I countries other than the niled

lales i the Cel iu (0C) calc, hown in the middle. n lhi ale, pure waler freeze at 0°C and boil al 100 0' (at ea level). Room lemperature i approximatel)' 22 ° . Therahrenheil cale and lhe 'e1 iu ale differ both in the ize their re pe li"e degree andthe temperature each design~les a "zero." Both the Fahrenheil and -e1 iu ales allow fornegative temperatures.

The I unit for temperalure, as we have seen, i the kelvin, hown on the right in Figure1.10. The Kelvin calc (sometime al 0 ailed the absolu/e sen/e) avoid negative tempera­ture by a igning 0 K to the olde t temper ture po ible, ab olute zero. b olute zero(-273 0' or --159 OF) i lhe lemperature al whi h mole ular motion virtually stop. Lowertemperature do not e i t. The ize of the kelvin i identi at to that of th Celsius degree-

The Celsius Temperature Scale

ecular mo on does not completely stop atabsolute zero because 01 the uncertainlypnnc,ple '" QuantlJm mechanICS, whICh weWIll diSCUSS In Chapter 7

o°C - Water freezes 10 ·C - Brisk rail day

Chapter 1 Page 14

22 °C - Room temperature 40 ·C - Summer day in Death Valley

16 Chapter t Maller. Mnsuremenl. and Problem Solv,ng

lhe onl)' difference is the lerllP<'nllun: th~t each designares as zero. You un con"ert b<tw«nIhe temperature $(~les with the following formubs:

~ 1ha1 we lI"'lI KeIvm ~petilllIt!lS rnkeIwIs lllOl-6egrees KelvIn 01 KlllOf oK),

,-",--',,-;,,-"oc'·C -- 1.8

K .. "C + 213.15

Throughoulthis book )'Ou will s,:e <·xamples worked our in formars that are design<'<!10 help )'OU de,-dop problcm-soh'ing skills. The most eommon format usc:s two columns toguide YQU through the worked ex~mple. The left column de$Crilxs the thooght pro<:eS:le$and steps uS<!d in soh'ing the I'robkm while tit,· right column shows the implementation.The first example in this tw"-column format follows.

EXAMPLE 1.2 Converting between Temperature SCalesA sick child has a temperaton: of 40.00·C. What is the child's temperatore in (a) K and {b) OF!

Solution

(a) !legin by finding the equation lhal rdates the qoamity that isgi"en (OC) and the quamil)' )'Ou are t'l'ing to find (K).

Since this rqU3tion gi,'cs the temperature in Kdirectlr. simpl)'substitute in the correct '1Ilue for lhe temperature in·C andcompute the anS"'er.

(b) To con"ert from"C to OF. first find the <oquation that rdatesthese two quantities.

Since this eqU;llion expre».:s"C in terms "foF, }'Ou must snh'ethe equatiQn fQt°E

Now sobstitute·C intQ lhe equ~tion and compote the ~nSWer.

NOle: The n"mller ofl/igils re['<'Tled in Ilris onsh'Ufollowslignifilalll figure (om'enlionl, (OI'Cn:d rn Melion '.7.

K - "C + 273.15

K .. "C + 273.15

K - 40.00 + 273.15 00 313.15 K

0(; ", ,-",-',,-,,',,2)I.,

"C 00 (OF - 32)

1.8

l.8(°C) 00 {OF - 32)

OF 00 1.8("C) + 32

OF 00 1.ll{"C) ... 32

OF 00 1.8{40.00°C) + 31 _ I04.00°F

For Practice 1.2Gallium isa solid metal at room t<·mperature, but it will mdttoa liquid in )'Our hand. The melting point Qfgallium is 85.6 OF. Whatis this temperature on (a) the Celsius scale and (b) the Kelvin scale!

Prefix Multipliers

While scientific nQtatiQn allQws uS to express wry l3rge or "ery small quantities in ~ com­pact manm·r. it l'l.'quir<'S us to lISt: '<er}'large posit;'<e or negative exponents to do so. For ex­3mple. the diameter of ~ h~'drogen atom can Ix wril1en as 1,06 X 10-ro m. TheInternatiQnal Sj'stem of Units U§d the prt'fix multiplius shown in T3ble 1.2 with lhe $tan­dard units. The$(' multipliers change the valucof the unit b)' poweC!l of 10. For example, thekilometer h3s the prefix ~kilo~ me~ning 1000 or 103. Therefore,

1 kilometer - 1000 meters 00 10' meten

Similnly, the millimeter has the prefix ·m;ni~ meaning 0.001 or 10-'.

I millimetrr 00 0.001 meters _ LO-s meters

t.6 The UMs or Measurement 17

TABLE 1.2 51 Prefix Multipliers

".f' """ ""-'"

, 1.000.000.000.000.000.000 (10'1)

p'" P 1.000.000.000.000.000 (lo's)

'''', 1.000.000.000.000 (lOll)... , 1.000.000.000 (IO~

m", " 1.000.000 (Ilf)

kilo • ,.. (Ht')

d,,, d .., (10 ')

colll' 0.01 (10 I)

milh m 0.001 (10 1)

m~ • O.llOOOOl (10 ")

~OO 0.000ll00001 (10-")

r~ r O.lJOOOOXllXXIl)1 (10 Il)

ffmlO , O.OOOOOOOOOlllXiO1 (10 ,s)

". O.OOOIXXlOOOOOOOlI (10 ")

When repo>rting a musu~menl. choose a prdix muhiplier close 10 lhe size of lhequamil)' being measured. For nampk. lO stale lhe d;ameler of ~ hydrogen alOnt, which is1.06 X 10-'0 m, usc picometers (106 pm) or nanometers (0.106 nm) r~lher than microm­eters or millimcters. Choose lh.. prdix muhiplier thaI is most conwnient for a particularnumber.

Derived Units: Volume and Density

A duiv<'d unit is a comhination of olh..r unils. For example, the Sl unil for spe.-d is metersper second (m/s}, a deri"ed unit. Nmiee thaI this unil is formed from IWO mher SI units­meters and .seconds-pul logelher. We arc probahly more familiar Wilh speed inmiles/hour or kilometers/hour-Ihese ar.. also examples of deri"ed unils. Two other com­mon dcri,'ed units are those for mlume (SI base unil is ml ) and density (Sl 1J<I.<c unit iskg/m1). We will look al each of these individually.

Volume Volu111e is a measure of span'. Any unit of lenglh, when cubed (raised to lheIhird power), becomes a unit of ,~,Iumc. Thus. the cubic meter (m)). cubic cemimeler(COl)), and cubic millimeter (mOll) arc all units of volume. The cubic nature of \'Olume isnot alw~ys intuitive, and slUdi<:s have shown that our brains arc nO! nalurally wired tothink abSlraetly, as required to lhink aboUI ,'olume. For example, consider lhe fullowingquestion: How many small cubes measuring I cm un each side are required to construct alarge cube measuring 10 Cm (or I dOl) on a side?

The answer hI this qUC$tion, ~s you can sec b)' carefully enmining lhe unil cube inFigure 1.11 ~,is 1000 small cubes. Wh{'n )'OU go from a linl'ar, one-dimensional distance 10

thrCl'-dimensional volume, )'Ou must raiS<' both the linear diml'nsion lind its unit to lhethird power (nOl multiply by 3}, Thus lhe "olume of a cube is equal 10 the lenglh of itsedg..cubed:

"olume ofcube - (edge length))

A cube with a IO-cm edge lenglh has a ,'Olume of(IO cm)l or 1000 cml, and a cube with al00-cm cdg~ l(nglh has a "olume of (100 cm)) = 1,000.000 cml.

Olher common unit.s <If ,'Olume in chemislry arc lhe lilrr (L) and the milliliter (OIL).One millilit..r (10-) L) is equal 10 1eml. A gallon <If gasoline contains 3.785 L Tab[.. l.3lists SOme common unils-for ,'Olume and other quantities-and lheir equivalenls.

Relationship between lengthand Volume

r-- IOcm--J

I (1n

M..A lO-Cm cubuonuin~

1000 1-em tubes.

... FIGURE 1.11 The Relationshipbetween Length and VolUme

18 Chapler 1 Maller, Mnsuremenl. and Problem Solv,ng

TABLE 1.3 Some Common Units and Their Equivalents

Ililomtt... (bn) .. O,621~ milt(mi)

I m<1r«m)· 39,l7inrn.. (in)" I.094J"1nls(yJ)

I~ (fr) '"' )0.48 cmllmC'l<rs (em)

I indl(in)" !'s4CtflUm<1<rs(cmj(naet)

....I kilogram (keJ .. nos pounds (Ib)

I pound (Ib) .. ~53.S9V"m.(g)

loonr. (0)) • 28.35g",m.(g)

lln.. (l)" IOOOml .. lO00cmJ

I hl.. (l)" I.057quam(<p)

I u.s. pilon (pll .. 3.785 lilr.. (l)

Density An old riddl.. asks, ~Which w.. ighs more, a ton of bricks or a Ion of fealhus?·Th.. answer, of COUrK, is neilher-Ihey both weigh lh. same (I Ion). If rou answerrdbricks, rOU confu.s.-d weighl Wilh drnsitr. Thr d..nsity (tI) of a subslanc.. is the ralio of iumass (m) 10 its \'olume (I'):

III 22.5g ,II - - - --- - 9.45 g/cm

V 2.3gcm'

massIXnsil}" - --­

,"olume

In lhis case. lh.. densit)' r~\'cals that Ihe nuggd is nol pure gold.

The drnsil)' of a substance is calculaled b~' di"iding the mass of a gi"en amount ofthe subSlance by its ,·olume. For eumple, suppose a small nuggel suspected 10 begold has a mass of 22.5 g and a ,'olum~ of 2.38 em). To find i15 d~nsilr, w. dividelhe mass br the "olume:

Calculating Density

IXnsil}" is a charaCleristlc ph}'si",1 propt'rl}" of malerials and differs from one subslance 10

anolher, as ~'(Ju can s.-e in Table IA. The densit}'of a substanc.. also d'p<'nds on ilS lemper­atur<·. Dt:nsit), is an uample of an inlcnsh'c prop.rly, om.' Ihal is illlf..pendent of theamounl uf Ihe subSlance. Th. densit)' of alumillum, fur "",ample, is lhe same whelher you

ha,'" an oullce Or a Ion. Intensi .... prop"Tli~'S are oflcn uSN! 10 idelltify subslancesbecause lh.-sc propt'rti~"Sdel'end unl}' un the tl'pt' ofsubslance, not onlhe amounlof ;1. For uampl~, one w~}' to det~rmine whether ~ ~ubsl~nce is pure gold i~ 10

m~asur~ ils densily and compar~ il 10 Ihe densily of gold. 19.3gJcm'. Mass, incuntrasl, is an ulerls;ve properly, one lhal depends on the amounl of lhesubstance.

The unilS of d..nsity Ue Ihoseof mass divided by ,·olume.Ahhough the Sl de·riwd unit for densily is klllm', the densit}' of liquids and solids is mOSI oftenupressrd ill g/cmJ or g/mL. (Remember that em' and mL are equi"aklll unils.)Aluminum is one oflhe le~sl dense struclural mel~ls wilh a densily of 2.70 g/cmJ,

while 1,lalinum is une of the densesl mel~ls with a densit}' of 21.4 g/cm'.

0.57,,~

0.917(aI0"C)

1.00 (a14 "C)

,."U6

"Lro~.Sl,...•."

11.4

U..sS

'"21.~

Alum,uom

TilOn'um

ChartMI (from ook)

."'"k,

"';11...

s..glr(ou<Nlot)

T~hIt uk ls«hum d1londf)

""

M......ry,..,Plannum

TABLE 1.4 The Density of SomeCommon Substances at 2O·C....~

~e IhaIIhlI In l'l1h:s!QUIllon IS In rtIhl;

type, mearong lllal ~ s1llllds lot mass ra1hetthan tor meIers.1n gennI,lhlI symbols Itr00115 such as melers (ml, secon;ls lSi, Ofketms fIQ aooear on~ lype whole IlIoseIOf Yanables such lIII mass (~. VIlllme (Ij,n lime (~.wear In otaIocs

IEXAMPLE 1.3 CalCUlating DensityA man r«.ives a platinum ring from his fiand•. Before the wedding. he notic~s that lh~

ring feds a lillIe lighl for ils size alld dceid..s lu mcaSur.. its dellsit),. lie plae.., Ihe ring 011a balance and finds lhal it has a mass of 3.15 grams. lie then finds thaI the ring displaces0.233 em J of "..t~r, Is the ring made of plalinum! {Nole: The mlum. of irregularlyshaped objects is oflen measurnl by Ihe displacem~1Il of "..l~r. To use this mrlhod, theobject is placed in waler and Ih~ chang.. in volume of th~ water is mcasurnl. This increasrin Ih~ 10iai volum~ represenls Ihe \'(Jlomc of water illsplllwl by lh~ object, and is ~qualloIh~ ,'(Jlume of Ihe object.)

Set up the problem by wriling lhe impomnt inforn'alion that is giv.." as well a$lhe information lhat roo arc asked tofind. In this uS<', We ar.. 1lI find the denS;lyof the ring and comp<ln: ilto that of plJlinum.

Note: This s,,,,,<1I1,d '''''y "/s.>lti"K "I' problems;s diK'mt'd in ,I""il i" 5«/i"" 1.7.

1.7 The Reliability or a MeilSuremem 19

Given m = 3.15g

V - 0.233 cm J

Non, write down the equation thai defincs density.

Soh-e the problem bl' SUbslituling the com'ct values of mass and "olume intolhe expR'$Sion for density.

Equation

Solution

"'ii--V

Th.... densilr "fthe ring is much too low ," be platinum (platinum density is 21,4 g/cm'),and ,he ring is therefore a fah.

~or Practice 1.3

The ""Oman in the abo"e example is sllOCkcd thallhe ri"g is fake and re\Urns it She bursa new ring Ihal has a mass of 4,53 g and a ,"Olume of 0,212 cmJ , Is Ihis ring genuine!

For More Practice 1,3A metal cube has an edge length of 11,4 mm and a mass of 6.67 g. Calculale the densit), oflhe melal and usc Table 1,4 to delermine the likely identity of the n!Clal.

:= Conceptual Connection 1.4 Density

Th, densily of copper decrea~with increasing t,mperature (as docs lhe density of mOSIsubslanccs). Which of the following will be true upon changing lhe temperature of a sam­ple of copper from room lemperalUre to 95 "C!

(I) the copper sample "'ill bcrome lighter

(b) the copper sample will become hea"il'r

(e) the copper sample will <'llpand

(d) the copper sample will romracl

1.7 The Reliability of a MeasurementRecall from our opening example (5«tion 1.1) lhal carbon monoxide is a colorkss gasemined by motor "ehieksand found in polluted air. The labk below shnwscarbnn monox_ide concentrations in los Angeles Counly as ",paned by the U.S. Environmental I'rotec·lion Agency (EI'A) onr lhc period 1997-2007:

eartxJn Moooxicle

"'" Concenlr.ltion (ppm)"

'"' t5.0

'''' 11.1

"" 7.2

,." ",." H

,." •••·s..:-l ..._I_........ "..-,..,.,.., ......ddonl ••l,......,.._.lol...

20 Chapler t Maller. Mnsuremenl. and Problem Solv,ng

The first Ih;ng )'ou should nOl;ce aboul lheK ''lllucs is lhat they arc dee~asing O"ertimt. For this de<rtasc. ,,'e can lhank the Cltan Air Act and ils amendmenlS. "'hich ha,.... reosuhrti in mure dr.cient engines. in specially blended fuels. and consequenllr in deaner airin all major U.S. cilies O"er Ihe lasl 30 rurs. The second lhing you mighl nOliee is Ihe num·~r of digilS 10 ,,'hich lhe nlC3suremenlS are reported. The numlxr of digils in a reponedmusurement indicates the certainly aS5l)Cialed with lhal measurement. For example. a lesscertain measurement of carbon monoxide 1e",1s nligtu b;: reported as follows:

'"""-... CO:lcentraliln (ppm)

'''' "'''' "1001 ,1003 ,lOOS •""

,

Estimation in Weighing

{.)

M.rk;nSH'~ry l SF~I;mOlN ~ad;ng 1.2g

{b)

Markings <v..y 0.1 8F.sl;m.ltd rt~dins 1,27 8

Nmice lhallhe firsl set of dala is reported to the nearest 0.1 ppm while lhc second selis reported 10 lhe nearest I ppm. &ienlists agr..... on a standard way of reporting measuredquanlilies in which lhe number of reporled digits refleclS lhe certainly in the me~sure·

mem: more digin.. more cenaimr; fewer digil.. less ccnaimy. Numbers arc usually wrillenso lhal lhe uncertainly;s in the last reporled digit (ThaI uncerlainty is assumed to be ::l: Iin the last digil unlen olherwise indiutro.) For example. by reporling the 1997 carbonmOR<lxide concenlralion as 15.0 ppm. Ihe scicmisl.< mean l5.0 ± 0.1 ppm. The carbonmonoxide concentralion is between 14.9 and 15.l ppm-il might be 15.1 ppm. fOI nam·pic, but it could not be 16.0 ppm.ln comraSl, if the reported "alue "'as 15 ppm {w;lhoUlthc .o}.lhiswnuld mun 15 ± 1 ppm. or betw.....n 14 and 16 ppm. In general.

&ienlific mcasuremcnlS arc reported solhat "'cry digil isccrtain CJrceptlhe lasl.which is estimated.

For exampk consider the (ollo"'ing reported number:

5.213! \

«nun ...-...1

The first lhr~~ digits arc certain; the last digit is estimated.The number o( digits reported in a measurement depends on lhe RlCJsuring de\·ice.

For example. consider weighing a pistachio nul On two diffcrent balances (Figure l.l24).The bal~nceon lhe lOp has marks e\'err I gram, whilc the balance on the bonom has markse\'ery 0.1 gram, For Ihe balance on the top., we menIally divide lhe space bet"'"n Ihe 1- and2·gram marks im" 10 equal sp....es and estimate thai thc poimer is at about 1.2 grams.We then write the measurement as 1.2 grams indicating that we are sure ofthe~l" but ha\'eeslimaled lhe~.2."The bal~n,e on the bonom, with marks e\'ery umllt o( a g!1lm. requires usto writc the resuh with more digits. The pointer is betw....,n the 1.2·gram mark and lhe1.3-gr~rn mark. We again di"ide the slIJU belween the two marks into 10 equal spaces andeSlimate the third digit.l'or lhe figure shown. we report 1.27 g.

4 FIGURE 1.12 Estimation in Weighing (_I This S(;Ile h~smark·ing.< lOWry 1 g.so we estlm.te!l' 1M tenthl place by menially dividingthe space into 10"lual s~<$ to ..timal< the Lost digit. Th,s reading il1.2 g. (bl Ikcou<e lhi! bolan.e hOI tn.,klllg.< e\'try 0.1 g...~ ellimal< t<>the hundredlhl pla.ce. Thil read,ng is 1.27 8.

t.7 The Reliability 01 a MeilSurement 21

EXAMPLE 1.4 Reporting the Correct Number of DigitsTh.. gr~du~l..d c)'lind.. r shown at right has m~rkings ..,....y 0.1 mL. It..port th.. I·olum..(which is rud ~t tht Ixmom of the meniscus) 10 th.. correct numlltrof digits. {Note: Themeniscus is tht cro:scenl·sha~dsurface allht lOp of a column ofliquid.}

Solution

Sinc.. th.. bollom of th.. meniscus is between th .. 4.5 and 4.6 ml markings. menl~lIy

di"idt the spact Ilttween tht markings inlU 10 <'<Iu~1 spaces and <'Slimatt lht nut digit.In Ihis usc:, you should report the result as 4.57 ml.

Whal if )1lU ..stimated a lillie diff..r..nlly and wrole 4.56 ml! In general. On.. unildifferenc.. in tht last digit is acc..plablt IltcauSC' the lasl digit is eSlimat(d and differentprople mighl estimale il slightly differtntly. Ilowever, if )"OU wrott 4.63 ml, l"u wouWhal'e misreport"'! the measurement.

For Practice 1.4Record tht temperaturt on lht thennomtler shown ~t right to the corr«t numlltr ofdigits.

,Counting Significant FiguresTit .. prtcision of a m(aSUrem..nt-which dep.mds on the instrument used to make 111<'mU5urtment-is key. not only wll ..n r"C<)rIling tht m..asurem..nt, but alS<) when perform­ing "'akulalion5 that us.. the musur..ment. The prC$Crl'ation of this pr..cision is ronW­nkntly accomplished by using signifimll1 figures. In any reporlN measurement, lit ..non-placc-holdingdigits--th05e' that are not simpl)' marking the d«in'al plac<:-are ulledsignificanl figures (or significanl digits)_ Tlr.. gmu..r II,e ""'lIbrr ofligrrifimlll fig"rrJ. liltgm'lrr IS I/Ie (trlmrrl}' of lilt IlWIJlIrrrrreru. For example, th,' numlltr 23.5 has three signifi­cant figuT<'S while Ihe number 2356 has four. To delermine the number of significam fig­UrtS in a numberrontaining z..r<X5, IW must distinguish betWten zeroes that art signifiuntand those thatsimpll' mark the decimal plact. For example, in the numbcr 0.0008, the lead­ing urocs mark the d«imal plaCt but do nOI add lU the certaint)' of the measuro:ment andarc therefore not signifinnt; this numbcr has only one $ignifi .....m figure. In contrast, th,·trdiling l(rOCS in the numbcr 0.000800 do add to the certainl), of the mNsurcment and ~rc

therefore counle<! as significant; lhis number has tlt.."( signifiC"dm figura.

To dettrmine Ihe number of significant figures in a number, follol<' these ruleJ("'ilh examples shol<'lI 0" Ihe right).

Examples

0.0540

7.0301

~

\ !.... ~p'''''''''''

28.0)<0,@32

Significant Figure R"les

I. All nonzero digits ue significant.

2. Inl"rior urocs (zeroes bcll<'een tl<'O digits) ue significant.

). leading zeroes (zeroes 10 the lefl of lhe firSI nonuro digit) arcnot significant. They only ~T\'e to locate the de<::imal point.

4. Trailing zerocs (lcr<xS al the tnd of a number) arc categorized asfollo.....s:

Trailing 1.Cr<>es after a decimal point arc ~I .....a)·s significant.

Trailing 1.erocS before a d,..:imal point (and after a nomeronumber) arc al .....a)'s significant.

Trailing 1.cT<leS bef"re an intl'li.'<I decimal point are ambiguous;ll1d should bc a"oided by using scientific nOlation.

Some textbooks put a decimal poinl afteT one or more trdilingzerocs if the zerocs uc to be considcred significant. We "'oidthat practice in this book, but roo should be aw.. rc of it.

45.000

140.00

12001.2 X 10'1.20 X 10)1.200 X 10'

1200.

'.5<0025.0505

omb,s"",,·1 "J,,,Jk.n' liS" ....

} ~n,flGln' f'l"'"

~ ''lInirlGlntlisu""

~ ..gn,flGln' iiI" .....(cam""," ,n "'m.. ,n,bookol

22 Chapter 1 Maller. Measurement. and Problem Solving

Exact NumbersExact number have no uncertainty. and thus do not limit the number of significantfigure in any calculation. In other words, we can regard an exact number as having anunlimited number of ignificant figures. Exact numbers originate from three urce:

• From the accurate counting of di crete objects. For example, 3 atom means3.00000 ... atoms.

• From defined quantities. su h a the number of centimeters in I m. Be ause 100 em idefined as 1 m,

100 m = I m means 100.00000 ... em = 1.0000000 ... m

• From integral numbers that are part of an equation. For example, in the equation.diameter

radills = --2--' the number 2 i exact and therefore has an unlimited number of

significant figures.

1EXAMPLE 1.5 Determining the Number of Significant Figures in aNumberHow many ignificant figure are in each of the following?

(a) 0.04450 m (b) 5.0003 km

(c) 10 dm = I m (d) 1.000 x 105

(el 0.00002 mm (f) 10,000 m

Solution

(a) 0.04450 m

(b) 5.0003 km

(c) 10dm - 1m

(d) 1.000 X lOS s

(el 0.00002 mm

(f) 10,000 m

FOllr sigllificant figllres. The two 4' and the 5 are significant (rule I). The trailing zero is after a decimalpoint and i therefore ignificant (rule 4). The leading zeroes only mark the decimal place and are thereforenot ignifi ant (rule 3).

Five sigllificmrt figllres. The 5 and 3 are ignificant (rule I) as are the three interior 7.eroe (rule 2).

Ulllimited sigllificnnt figllres. Defined quantities have an unlimited number of significant figure.

FOllr sigllificnm figllres. The I i significant (rule I). The trailing zeroes are after a decimal point and there­fore ignificant (rule 4).

Qlle sigllificalll figllre. The 2 is significant (rule I). The leading zeroes only mark the decimal place and aretherefore not significant (rule 3).

Ambigllolls. The I i ignificant (rule 1) butlhe trailing zeroes 0 cur before an implied decimal point andare therefore ambiguou (rule 4). Without more information, we would a sume I ignificant figure. It isbener to write thi a I X 105 t indicate one ignificant figure or as 1.0000 X lOS to indicate five (rule 4).

For Practice 1.5How many significant figure

(a) 554 km

(c) 1.01 X 105 m

~ 1.4500km

are in each of the following numbers?

(b) 7 pennies

(d) 0.00099

(f) 21,000 m

Significant Figures in CalculationsWhen you use measured quantirie in calculations. the results of the calculation must re­ne tthe preci i n fthe mea ured quantitie . You should not lose or gain preci ion duringmathematical operation. Follo\ these rule when carrying ignificant figures throughcalculations.

Chapter 1 Page 21

1.7 The Reliability of a Measurement 23

Example

1.052 X 12.054 X 0.53 - 6 7J.(4 .g. ligun- ) (S Ig. ligurrs) (2 ig. figur..)

Rules for alculation

I. In multipli tion or divi ion, the re ult arrie thesame number of ignificant figure a Ihe fa torwith the fewesl ignifi am figure.

2. In addilion or ubtra lion, the re ult arries Ihesame number of de imal pia es as Ihe quanlitywith the fewe t de imal pia e .

2.0035(S .g. ligur< )

4·3

0.0

2.9 5- 5.4\

3.20(3 'g. figur

=W.

-0. 1- 5.7

0.626(3 ig. ligun- )

6.7(2 'g. figurc )

In .dd'l/on .nd ubtr.C1Ion. It is hdpfulto dr.w. bnc n t to ,hc numbtr with ,hc f.,. td«,m.1 pl. . This linc dCltrmlnts ,hc numbtr of dc im.1 pl.c< In thc.n ·cr.

3. \ hen rounding 10 the corre t number of ignifi antfigure, round down if the la I (or leflmo I) digitdropped is four or I ; round up if the la t (orleftmost) digil dropped i five or more.

To two signifi ant figure:

5.372 r und

5.342 round

5.352 round

5.349 r und

lO 5.4

105.3

105.4

.3'o'i« ,hot only thc UISI (or It{rmost) digit btlllgtitopprd drtcrm,nes In which dorecl/on to

round-Ignol"t" all digit.. (0 thr right of It.

4. To avoid rounding error in mullistep al ulalionround only the final answer-do not roundintermediale tep .If you write down intermediatean wer ,keep Ira k f ignifi ant figure byunderlining the lea I significant digit.

6.78 X 5.903 X (5.489 - 5.01)= 6.78 X 5.903 X 0.479

= 19undt'r1lnC' k.ut1l1g1\1(iunldl II

Afew books recommend asllghUVdifferent roundmg procedure forcases where the last d,grt IS 5However. the procedure presentedhere IS conSistent IVlth electrontCcalculators and IVlII be usedthroughout this book

oti e that for multiplication or division, the quantity wilh the fewest sigttificatlt fig·tires determine the number of sigtlificlIlII figures in Ihe answer, but r. r addition and ub­tra lion, the quantit)· with the fewe t decitltlll plllces delermine the number f decrtltlllpillces in the an wer. In multipli ation and divi ion, we fo u on ignifi ant figure, but inaddition and ublTa lion we focu on decimal placc . When a problem in\'oh'cs addition orublTa lion, the an ,ver ma have a different number of ignifi ant figure than the initial

quantitie . Keep thi in mind in pr blems that invoh'e bOlh addition or ubIT3 tion andmultiplication or divi- ion. For example,

1.002 - 0.999 0.003=--

3.754 3.754J

= 8 X 10 4

The an wer has only one ignificanl figure, even though the initial number had threeor four.

EXAMPLE 1.6 Significant Figures in CalculationsPaform the following al ulations 10 the orre t number of ignifi ant figure.

(a) 1.\0 X 0.5120 X 4.00\5 + 3.4555

(b) 0.355

+105.1

-100.5820

(c) 4.562 X 3.99 70 + (452.67 5 - 4 2.33)

(d) (14.84 X 0.55) - 8.02

Chapter 1 Page 22

24 Chapter I Malter. Measurement, and Problem Solving

Solution

(a) Round the interm diale re ull (in blue) 10 Ihree ignifi ant figureto rene I the three ignifiCilnt figures in Ihe lea t preci ely knOI nquantit)' (1.10).

(b) Round Ihe intermediale an wer (in blue) to one decimal pia e torenect the quanlily wilh Ihe felve I de imal pia e' (105.1). oli ethaI 105.1 i 1101 the quanlily wilh the felve t ignifi ant figure.bUI il h Ihe fewe I de imal places and Iherefore determine Ihenumber of de imal pia e in Ihe answer.

(c) lark Ihe intermediale re ull 10 111'0 decimal pia e to rene I Ihenumber of de imal place in Ih.. quanlil)' within the par..nlhe eshaving Ihe fewe I number f de imal pia e (452.33). Round thefinal an I er I two igni Icant figure to ren.. I the IW ignifi antfigure in the lea I pr..ci dy known quanlily (0.3i55).

(d) Mark Ihe intermediale re ull I IWO signifi ani figure to rene Ithe number of significanl figure in Ihe quanlity wilhin theparenlhese having th fewe I number of ignifi ant figure {0.5-}.Round Ihe fin Ian wer to one de imal pia e 10 rene I Ihe onedecimal place in Ihe lea I preci ely known quantit)' (8..!. 62).

1.10 X 0.5120 X 4.0015 -;. 3.4555

= 1

= 0.652

= 4.9

4.562 X 3.99870 -;. (452.6755 - 452.33)

= 4.562 X 3.99870 -;. 0.3155

= 53

(14.84 X 0.55) - 8.02

= 8.162 - .02

- 1

- 0.1

For Practice 1.6Per~ rm Ihe following al ulati n 10lhe orre I number of ignifi ani figure.

{a} 3.10007 X 9,441 X 0.0301 + 2.31

(b) O. 1

+132.1

- 12.02

{c} 2.5110 X 21.20 + (44.11 + 1.223)

(d) (12.01 X 0.3) + 4. II-Precision and Accuracy

ienlifi measurement are orten repealed several times 10 in rease nfiden e in Iheresuh. We an distingui h bel",e..n IWO diff..renl kind of erlainl)' alkd a cura y , ndpre i ion-as iated Ivith uch mea ur..m..nl. ccuracy rd..rs I how clo e the mea uredvalue is 10 Ihe a lual value. Preci ion ref..r to how lose a ri.. of mea urem..nl are toone anolher or how reproducible Ihq are. seri.. of mea uremenl an be pre ise ( loseto one anolher in value and r 'produ ible) bUI not a curate (n I I e to the Irue I'alue). Forexample. on ider Ihe resuh of Ihree students who repealedly I\eighed a lead blo k knownto have a Irue ma of 10.00 g (indi aled b)' Ihe solid hori70ntal blue line on Ihe graph ).

StudenlA Student B S1udeniC

Trial I 10.49g 9.7 g 10.03g

Trial 2 9.79g 9.2g 9.99g

Trial) 9.92g 9.75g 10.03g

Trial 4 10JI g 9.80g 9.9 g

A,..,ragc 10.l3g 9.79g 10.01 g

Chapter 1 Page 23

1.8 SolVing Chemical Problems 25

• Th~ r~ ult of lud~nt ar~ both inaccurate (not clo ~ to lh~ tru~ value) and impreci I'(not con i lent with one anolher). The incon i. ten y is the r~ ult of random error.error Ihal ha equal probabilir' fbeing too high or 100 low. Jmo t all mea urementshave some degree of random error. Random error can, , ith enough trial., averageitself out.

( Inaccurale. precise ) ccurale. precise )

Student B Student C

2 ~

Trial number

-Avera .. 10.011:

10.03 9.99 10.03 9.98-- ....

-

9

II

10

9.5

10.5

2 3Tnal number

\(r.I·,9.7'1 '

9.78 9.82 975 9.80.... -- .... ---,;:.;;--- .... -

I

II II

Hra '< 10.1' '

10.510,49

10.5....10.31....

B --------- - 1ru<'" 10 9.92- I- rna 10" 9.79 ....::< ....

9.5 9.5

9 92

I3

I

Tnal number

Student A

... 1ea urement are said 10 be pre i elf Ihey are consistent wnh one another, but they are a curateonly.f they are close to the actual value.

• The result of tudenl Bare precise ( I se to one another in value) but ina curale. Theinac ura )' i the result of y lemalic error. crror thaI tend toward being dther I 0

hi 'h or too low. .stemali crrordoentavera.eoulwithrepealedlrial.Foream­ple. if a balance i nOI properly calibraled. it may y temati ally read too high ortoo low.

• The re ult of tudent - di play lillie ystemati error or random error-the)' are botha curale and pre ise.

1.8 Solving Chemical ProblemsLearning I solve problem is one of the 010 t imp rtant kill rou will acquire in Ihiour e. 'oonc u ceed in hemi Iry r in life. really-without Ihe ability to solve prob­

lem. Ithough no simple formula pplic I e"cry problem. you an learn problem- Ivingtralegie and begin 10 devel p some hemical intuilion. Many f the pr blem )' u will

soh'e in this our • an be Ihought of a /Illi/ ollversioll problems, , here you are gi"en Ol1eor more quanlities dnd a kcd t onvert Ihcm inlO different unit. Olher problems requirethe use of spCClfic equatiolls 10 get to the inC< rmalion you are tf)'ing to lind. In thc ti nthat follo'v. you will lind tralegie t help Y u h'c both of the e type of pr blem. foursc. man)' pr blem onlain both conver ion and equation. requirin Ihe combina-

tion of Ihe e tralegie. and ome problem ma require an altogelher differenl approa h,

Converting from One Unit to AnotherIn e tion 1.6. we learned th I unil y tem, the preliKnowing how to work with and manipulate Ihese unit in calculalion i central t solvinghemi al problems. In al ulation • unil help to determine orre tnI'. ing unit a a

guide to h'ing problem is orten ailed dimen ional anaJy i. nilS hould alway be in­cluded in calculation; they are multiplied. divided. and canceled like any olher algebraiquantily.

Chapter 1 Page 24

26 Chapter I Maller. Measurement, and Problem Solving

cm

Con ider con erting 12.5 inche. (in) to centimeter (cm). \ e know fTOm Table 1.3 IhatI in = 2.54 cm (exa t), so ,ve an use thi~ quantity in the calculalion as ~ )lIow :

12. in X 2.54 m = 31.I in

31.

The unit, in, cancel and we arc left with m a our final unit. The quantity z~,~m ironver ion factor-a fraclional quantilY with Ihe unit we are cOllverllllg!rolll on the bot­tom and the unit we are cOllverrillg 10 on the lOp. 'onver ion faclor are constru led romany 1\"0 equivalent quantilie . In thi e ample,2.54 m = I in, so we con tru I the conver-ion factor by dividing both ides of Ihe equality b)' I in and an e1ing the units

2.54 m = 1 in

2.54 em I in---=-I in I in

2.54cm

I in

The quantity 1 II~m i equivalenl to I, 0 multipl)'ing by the onver ion factor i malh­emati all equivalent to multipl)'ing by I. To nverl the ther, a)', fr m enlimeter tin he we must-using unit as a guide-use a differenl form of the conver ion fa tor. If)'OU accidenlally u e the same form. )'OU will gel Ihe wrong result. indi ated bl' erroneouunit. For example, uppo e that )'OU want to om'ert 31. m 10 in he .

2.54 m O. cm!mX---=---

1 in in

The unit in the above an , er ( m!/in), a. well a, the "alue of the answer. arc obviou 1)/

wrong. \ hen you solve a problem, always look at the final unit. Are the the de ired unit?"va)' 10 k atlhe magnitude of the numerical an wer a well. Doe it make sense? In this

ca e, ur mi take' 3l the ~ rm of the e m'er ion fa t r.1I hould ha,'e been inverled 0 thatthe unit cancel a follow:

31.I in

m X --- - 12.5 in2.54 m

'om'ersion fa lor an be inverted be ause Ihe 'are equal 10 I and the im'er e of I i I.Therefore,

2.54 m I in---1---

I in 2.54 m

ught

= desired unitXGiv~'l1 unit

Mo I unit onver ion problem take the following form:

Information given X c nver-i n fa tort ) = inf, rmation

de ired unit

given unit

In this b ok" e diagram a problem IUlion using a cOllceplllnl plnn. A nceplualplan is a visual outline that help )'ou to see the general now of the problem. For unit on­versions, the conceptual plan focuse- on unit and the com'er ion from one unil to anoth­er. The on eptual plan for converting in to m i a follow:

in em

Z.~cm

lin

The on eplual plan for om'erting the other wa)', from m to in. is jusl the reverse,with the recipro I om'er i n fa tor:

em in

1m

Lcm

Chapter 1 Page 25

1.8 $olvlOg Chemical Problems 27

Each arrow in a con eptual plan for a unit com'er ion ha an a. 0 iated com'er ion fa ­tor with the unit of the previou. tep in the denominator and the units of the followingtep in the numerator. In lhe foil wing tion, we in orp rate the idea of a on eptual

plan into an o\'erall approach 10 solving numerical chemi al problem,

General Problem-Solving StrategyIn thi book, we use a tandard problem-soh'ing pro edure that an be adapted 10 man)' ofthe problem en ountered in 'eneral hemi tr), and be)'ond. Iving any problem e en­tially require ),ou to a se the informalion given in the problem and devi e a way to get tothe information asked for. In other word, you mu t

• Identify the tarting point (the givel/ information).

• Identify the end point (whal you mu tfil/d).• Devi e a way to get from the tarting point to the end point using what i given as well

a what)'ou alreadl' know or can look up. (We allthi guide lhe cOl/ceptual plal/.)

In graphi ~ rm, we can represent thi pro're ion a

iven onceptual Plan --+ Find

One of lhe main dim ullie beginning. tudent have when trying to solve problem ingeneral chemi try i imply not kn wing where to tart. \ hile n probl m- Iving pro e­dure i applicable to all problems, the following four- tep procedure n be helpful inworking through man)' of the numeri al pr blems you will encounter in this book.

I. rt. Begin b 'sorting the information in Ihe problem. Gi""n information i the basidata provided bl' the problem-often one or more number wilh their a socialedunit. Find indi ate what information u will need for your an wer.

2. trategize. This i u ualll' the harde t part of solving a problem. In thi proce ,)'oumu t develop a conce("fllli pllln-a eric of tep that will get ),ou from the given in­formation to the informalion ),ou are tr),ing to find. You ha\'e alread), een on eptualplan for imple unit om'er ion problem. a h arro\ in a on eptual plan reprcsenta mputational tep. n the left idc of the arrow i the quantitl' l u had before thetepi on the right side of thc , rrow i the quantit)' ),ou will have afler the lepi and

belm the arrow is the information ou need to get from one to the olher-the rela­tion hip between the quantitie .

Often uch relation hip will take the form of onver ion fa tor or equation.. The emaybegiveninthepr blem,inwhi h a )' uwillhavewrillenlhemd wnunder"Given"in tep 1. uall)', h '''ever, you \ ill need other informalion-whi h rna)' in lude phy i alcon tant , formula, or com'ersion factors-to help get l'oU from what ),ou are given towhat ),ou must find. You mu t re all this in~ rmati n from what you have learned or lookit up in the hapter or in table within the bo k.

In some ca.e ,)'ou rna)' get tuck at the Irategize step. If )'ou annol figure out how 10

get rom the given informati n to the information you are asked 10 find, )'ou might Iryworking ba kward . For e ample, ),ou may want to look at the unit of the quantit)' 'ou aretrying to find and try to find om'er ion fa tor to get to the units of the given quantity. Youma)' even try a ombination of trategiesi work forward, ba kward, or me of both. If youpersist, you will de\'e1op a strategy to olve Ihe problem.

3. olve. Thi is the ea i~t parI of Iving a problem. n e 'ou d up the problem prop­er! ' and devise a on eptual plan,)' u simply f< 1I0w the plan 10 h'e the problem.'arry out anl' mathematical operation (paying attenlion 10 the rule for ignifi ant

figure in al ulation ) and an eI unit a' needed.

4. Check. Thi i the step most often over! okcd by beginning student. Experien cdpr blem olver alway go one tep further and ask, doc thi an wer make ph i aJsen e? re Ihe units orre t1 (s the number I' ignificanl figures corre t! Whcn solvingmulti tep problem, errors easily creep into the olulion. You can cat h most of the eerror by imply che king the answer. For example. uppose l'oU are cal ulating thenumber of atom in a gold oin and end up \ ilh an answer of 1.I X 10-0 atom .Could the gold oin really be composed of one-millionlh of one atom!

Chapter 1 Page 26

ost probl ms can be solved In fllOle thanone way The solubons we denve In thIS bookw" tend to be the most stralg/ltlorward bulcertllnly not the only way to solve theproblem.

28 Chapler 1 Maller. Mnsuremenl. and Problem Solv,ng

»dow "'... apply lhis probkln-soh'ing proc...dure 10 unil conversion proble,"s. Thepr<X...dure is summariz d in th... lcfl c"lumn and two umples of applying th... procedur...ar... shown in th... middl and righl columns. This lhr -column formal will be used in S(.kCled ...umpl...s throughout this le~l. II allows ~'ou 10 se ... how a parlicular procedure canbe applied 10 lWO diff.......nt problcms. Work through one problem firsl (from top 10 bt>!·10m) and lhen 5<'e how the s.amc proccdure is appticd to lhc ...lh .... problem. B...ing able 10S(e thc commonalities and differences between problems is a key pari of d...vdopingproblem,solving skills.

Procedure for Solving UnitConversion Problems

IEXAMPLE 1.7 Unit ConversionCon"erl 1.76 yards to cenlimctcn.

EXAMPLE 1.8 Unit ConversionCOn'·... rt 1.8 quarts to cubic ecnlimeters.

Sort lkgin by sorting thc information inth... problem into Gi....n and Find.

Given 1.76 ~'d

And Cm

Given 1.8 ql

And cml

•Strateglze IXvisc a "maplllni pi"" for theproblem. B<:gin with lhe glVl''' quanlity andsymboli1.c each com'enion slep wilh anarrow. &10'" ea,h arrow, write the appr...•priate nversion faclor for that slep. focuson lh units. The c...nccplUal plan shouldend al th fiml quantilY and ilS unilS.In lh ...sc xampl.-s, lhe other informationneeded consists of rdationships betweenth... various units as shown.

Conceptual Plan

,~.

RelationslllpS Used

1.09~ ~'d - I m

Im""loocm

(Th...5<" conwrsion faCIO.S arc fromTables 1.2 and 1.3.)

Conceptual Plan

RelatJonships Used

1.0S7qt - tl

Il- l000ml

Iml= lem l

(Th<"5<' eOn\'euion factors arc fromTables 1.2 and 1.3.)

Solution1m loocm

1.76 yd X --- X --1.094 yd 1m

10' cmJ1 em)

X --. 1702'13, mL

1 702'1.1

SolutionIl l000ml

1.8ql X --- X ---LOS7 qf 1 l

Solve Follow lh... conc...plual plan. Soli·...lh... equation($} for lhe Jiml quamily (if it isnOl already). Gath.... cach Oflhc quantilicslhal mUSl go into lhc cqualion in lhc oor·rect un;U. (COn,'erll0 the correet unils ifneec»ary.) Subslilutc th... numcriul ''31uesand lhcir unilS inl0 Ih ... cquat;on(s) andoomput"'lhe answ...r.

Round Ihe ans", r to thccorreet numbcrof 160.8;"-, cm - 161 cmsignificant figur s.

Check Check J....ur answ..... Are th... unitsconcet! Does thc answer mak... physicalsense!

The UnilS (em) ~re correct. Th... mag"i·lud~ of lh~ ~n5Wer (161) makes phrsi·cal senS( ~cauS( a ct'mimcler is amuch smaller unit than a y~rd.

Th.· units (em') art· corr",cl. The mag·nilude of the ans"'...r (1700) makesph)'sical scnsc bC'Cau$( ~ cubic , ...mime·I". is a much smalle. unil th~n a quart.

For Practice 1.7Conl'erl 21\8 cm 10 yards.

-For Practice 1.8Con\'(rt 9255 em'lO gallons.

18 SolYlng Chemical Problems 29

Units Raised to a Power

When building convusioll faclors ror UnilS raised 10 a power, rememlxr 10 T:liS(' bolh Ihenumlxr and Ihe unillo Ihe pl)\>'er. Foreumpl... ,to conver! frnm in2 10 cm2• \,'e conSlruclIh conversion faclor as follows:

2.54 cm - 1 in(2.54 COl)! ... (I in)!

(2.54)2 cm2", 12 in2

6.45 cm2 '= 1 in!

6.45 COl!l""i,;"l ...

The following uarnple shows how 10 uS(' conwrsion faclon in'·oh·ing unils raised loa power.

-EXAMPLE 1.9 Unit Conversions Involving Units Raised to a PowerCalculale Ihe displaumcnI (the Intal volume of Ihe C)'linders Ihrough which Ihe piSIOllSmm'C) of a 5.70·1. automobile engine in cubic inches.

Sort Sortlhe informalion ill Ihe problem inln Given and Fin,l.

Stralegize Wrile a conc...ptual plan.lkgin wilh Ihe giwninformalion and deviS(' a palh 10 the informalion Ihal)'Ou aT<'asked 10 find. NOlie... Ihal for cubic unilS, Ih... con'"<"niunfaclors mOll I>... cub..-d.

Given 5.701.

Rnd inJ

Conceptual Plan

C~::}-{::0-+(~I ",t I ....' I' "'J'

10 't I .. l Il.S"'.. I'

Relationships Used

lmL_IO-J I.

lml"'lcmJ

2.Hcm'" I ill

(ThCSt' con"ersion factors arc from Tables 1.2 and 1.3.)

Solve FoUow Ihe conceplual plan 10 sol"e the problem.Round Ihe 3nl""<"r 10 Ihree significant figur~:s 10 ren«llheIhree significant figures in Ihe leul prcciso:ly known quan! ity(5.70 I.). Thes<: com'er,ion faclors arc all exaC1 and Ih...rdoredo nOllimillhe numb..-r of significanl figures.

Solution

lOll lema5.701. X --,- X -- X

10- l. 1 011.

{lin)l _ •. JJ - H,.8~~m

(2.S4 cm)

- 348 in l

Check Thc units of Ih," ans"'Cr arc currrci and Ihe magnilude makes Iil:nlil:. The unilcubic inchd is small... r Ihan liters. SQ Ih... ,'Olume in cubic inches should b..-Iarger Ihan Ihe,'olume in lilers.

I~.or Practice 1.9~o,," many cubic centimeters arc Ihere in 2.11 pi'!

For More Practice 1.9

llivincrard has 145 acres of Chardonnar grapes. A p;trlicular SQil supplemenl r<-quircsS.S(} grams for "'ery square nICler or ,·inerard. How m~ny kilograms of Ihe soil supple·menl arc requirexl for Ihe enlire "iner~rd?{I kml - 247 acres}

30 Chapter 1 Malle'. Musuremenl. and Problem Solv,n..

EXAMPLE 1.10 Density as a Conversion FactorTh~ mass of fud in a j~1 muS! b<' cakulat~d b<'fo .... ~ach nighl to tnsur~ that th~ jtt is nottOO heavy to fly. A 747 is fude<! wilh 173,231 I. of ~t fud. If th" d"nsil~' of th" fud is0,768 g/cm J , what is lh~ mass of lh" fud in kilograms?

Sort &gin by SlJrli"S th~ information in th~

probkm into G;''e'' and Fi"d.

Strategize Draw thc conccptual pl.", by beginningI>'ilh th~ gi,..,n quantit)·, in lhis case lh" volum~ inlittrs (l). Th~ o\'~rall goal of lhis problem is to findth" mass. \'ou can com'cn b<'lween n,lume and m;ususing d"nsity (g/cm J ). Ilow"wr, you must firsl con·"ert Ihe \'olumc to em'. Once rou ha"" convert"d the"olumc to cm' , use thc dcn~itr to com'crl to g,l'inallrwnwrl g to kg.

Solve Follow Ih" ronc"ptuall'lan to soh'" th" prob­lem. Round thc answcr to three significant figures 10rdlr(t Iht lhr"'" significant figures in th~ density.

Given fudmlume - 173,231 l

densit), of fud .. 0.768 g/cm'

Rnd maSS in kg

Conceptual Plan

Relationships UsedI ml _ IO-Jl

Iml"'lcnl'

d .. 0.768 g/cmJ

lOOOg-lkg

(These com..,uion faClors arc from Tabl.." 1.2 and 1.3.)

SoItrlionI mt 1 cm' 0.768& I kg

173,231l X -_- X -- X-- X --. = 1.33 X IOSkgIO'l Iml lem) 1000&

Check The units of lh answer (kg) ar" eorr«l. The magnitudc makes sens<: b«ause th"mass (1.33 X 101kg) is simibr in magnitudc to thc gi""n "l)lum~ (173,231 lor1.73231 X lOS l), as lXp«led for a d~nsity dose 10 on" (0.768 g/cm!).

For Practice 1.10

Backpack"rs often use canisters of white gas to fud a cooking StO"c's burner. Ifon" canis­tercontains 1,451. of white gas, and thc dcnsit~· of thc gas isO,710 g/cmJ • what is thc massof lh" fuel in kilograms?

For More Practice 1.10A drop of gasolinc has a mas.< of 22 mg and a dcnsil}' of 0.754 glCnl'. What is ilS volum"in cubic c~nlim~ters?

Problems Involving an Equation

Problems inw,lving equations can b<' soh'ed in much Ih~ sam" way as probl<'ms involvingron'·ersions. Usually, in problems in\'(lh'ing equalions, ~'ou must find one of the '"ariabksin the equ~tion, gi,'~n lh~ others. Thc (o"upwal pi"" concepl outlined ~bo,·~ c~n b<' usedfor probl<'ms im'(}h'ing equalions. For cxample. suppose )'(}u arc gi"'n th" mass (m) ~nd

nllumc (V) of a sample and asked to c~kuLlt~ ilS densit),. Th" conceptual plan shows howthc ('1,ml;on takes )'OU from thc gi...." qu~nti';es to lhefin,1 quanlily.

~- ~,H~rt:, instead of a cot,..crsion factor under thc arrow, this ronc"ptual plan has ~n equal ion.Thc equation shows th~ rclniiolllhip between thc quantities on th~ left of th~ am,w and th~

1.8 SolYlng Chemical Problems 31

EXAMPLE 1.12Problems with EquationsFind Ihe density (in gJ(m'J of a melalC}'lind(r wilh a mass of 8.3 g, a Ienglh(/) of 1.94 (m, and a r.ldius (r) <jfo.sS (m. For a c)'linder, V - ll',.1/.

Find the radius (r), in cenlimelers, or aspherical wal(r dropkl wilh a \ulum((V) (,f 0.058 cmJ . For a sphere.V - (~/)}ll',J.

Procedure for Solving ProblemsInvolving Equations

quanlitieson 11,( right NOl( lhal al Ihis poinl, 11,( equalioo need nol b<: 5Ohl:d for 11,( quan­lity"o th( right (ahhough in this parti(ular ".ISO: il is). The pm<:edure Ihl folio"'$, as well asIhe two examples, will guide )'Ou in de,'doping a slratq;y to soll'e problems in,'Oh'ing eqlU­lions. We agaio use th( thr«-column format h(tl:. Work lhrough ooe problem from top tobottom and then see ho--' the same g<>nt'T:ll pnxedu'e is applied t" Ihe $l'(ond problem,

~

EXAMPLE 1.11Problems with Equations

Sort !kgin by sorting the informal;on inthe problem into Gi'...n and Find.

Given V - O.OSS (mJ

Rnd rin(m

Given m'" 8.3 gl-l.94cmr - 0.55 em

Rod II in gJcm'

Strategize Write a ronupulIIl pl"n for lheprobl..m. Focus on the equation(s). Th..conuptual plan shows how Ihe equationtakes )'ou from Ihe gi"en quamity (orquantitie$) 10 the fiml quantity. Th.. con'ceptual plan may ha'l: SO:"eral parts,imul\oing oth(, equalions or requiredcom·ersions.ln these examples.. you muSIuse the geomelrical relationships given inthe problem Slalemenl5 as well as the deli­nition of densit}'. d '" m/II, which )'()ulurned in lhis chapter.

Conceptual Plan

Relationships Used

V'" ~ll',.J3

Conceptual Plan

Relationships Used V - ll"!/

d - t.!!-v

Solve Follow Ihe conceptual plan. Beginwilh the gil...n quantity and ilS units,Multiply b}' the appropriate con.-ersionfaclOr(s), canuling units, to arr;"e at thefind quantily.

Solution

II '" ~ll'rJ3

,J = 2.... 11..( 3 )'",'" -V,.( 3 )'"~ ~ll' 0.058 cmJ 0.14013 cm

SolutIonII _ ll',l/

'" ll'(0.55 cm}I(I.94 cm)

- 1.8436(m'

d '" t.!!-\'

8.3g _ 4,;j)1ObgJcm'1.8436 cm'

Kound the answer to lhe (orren numlxrof significant figures by following therules in Section 1.7. Ketl1embcr that exact(oml:rsion factors do nnt limit significanlfigures.

O.1401.l em = o.Z~ (m 4501% gfemJ _ 4.5 gjcmJ

Cf1eck Ched: you' anll\>l:r. Are Ihe unihcorrect? Docs Ihe answer make physicalscnse!

The units (cm) are correct and Ihemagnitude ~em~ right.

The unils (gfemJ) are WITecl. The mag­nilude or the answcr Sl.'<:'ns correcl forone of Ihe lighler metah (s« Table 1.4).

For Practice 1.11Find the radius (r) of an aluminumqlinder that i~ Z.OO (m long and has amass of IZ.4 g. For a cylinder, V ... ll',.1/.-

For Practice 1.12

Find the densily. in gf(m'. of a melalculx with a mass of SO.3 g and an edgeIenglh (I) of Z.65 cm.l'orHube, II - I'.-

32 Chapter 1 Malle'. Musuremenl. and Problem Sol",n..

CHAPTER IN REVIEW

Key Terms

Section 1.1

Section 1.2hypothesis (~)

apedment (~)

.lCicmiflC Low IS)I.w ofconservation or moSS (5)th<'Ory (5)

.tomic th<'Ory (5)

JCicnliflC method (6)

Section 1,3mOltCT (6)

Jubst.nce (6)

Jtate (7)

...Iid (7)liquid (7)

Key Concepts

j\a> (7)e'Y't.lline (7)

.mo'1'oouo (7)

romp<>Jition (8)

I'u~ $Ubsunce (8)mixture ('I)

elemem ('I)

compound (9)heterogeneous mi:<lu~ (9)homogetlCOuo ml~lurc (9)

Section 1.4phrsical chonge (9)

chemical chonge (9)

phrsical property (10)

chemical property (10)

Section 1,5energylll)""tIrk (II)kinetic energy (12)

polenti.1 ene'1\Y (II),hermal energy (11)I.... ofc<mscrvation

of energy (12)

Section 1.6units(ll)English SYSlem ( I J)mmicoystem(ll)l"tern.'i,,,,.1 Syslem ofUnilJ

(51) (Il)

meter 1m) (14)kilogram Ikg) (14)mOSJ(l4)second(s)(l.)kclvin(K)(14)lCmper.lurc I14)Fahrenhei, ("F) scale ( I 5)

ulsiuo ("C) scale (IS)Kelvin Kale ( I 5)

prefIX mul,iplim (16)

derived uni, (17)

voIumdl7)liter (l) (17)

millililer (ml) (17)

Lknsily (d) llll)

inlensi"" PfOl>C"Y (18)

e~l,nsiveprupe"y ( 18)

Section 1.7signif""nl figure. (significant

digilsl\ll)(1'<1 numbers (21)

",cur",y «24)

precisiun (24)

random error (IS)system.,i, error (IS)

Section 1.8dimell$i<)"al a"alysis (IS)ronvcrsion faclor (26)

Atoms and Molecules (1.1)All m.lter is compos«! of atums and m...kcuks. Chemistry io the .lCi.en" that inW;JtigalCithe properties and beh.viur uf m.tter by e,,"min.ing the "ulnJ and molecules th>! cumJ"'K II.

The Scientific Method (1.2)Science begin. with the observ->tion uf the pllYSlcal world. A numher ofrelate<! obscrv.t1ons can oftcn he subsume<! in a summary Jtatcmcntor generoliutiun caUe<!a scientific 1.w. Obscrvatiuns may SUl!llcst a hy.pothC$is. a tcnt.tin int,cpretatiun ur uplanatiun ufthe observed phe·numen;>. One ur mure "·ell·e,l.bhJhe<! hypothcK$ m.y pr"mpt th,development uf a .lCicnllfic theory.• model for nature that ",plains tileunderlying re'SOnS (or observations .nd I....J. La..·S, hypothcK$, ondtheories on give rise 'u prediC1ions ,hot c'n he le,le<!by uperiments,carefully c'>III,..,IIe<! procedures d,signe<!lu produce crilical new 00·serv.tiuns.lf rio, p«dietionJ are nul ronfirme<!, th,Io".. hypo'hesis, or'heory mw' be modified Or replaced.

The Classification of Malter (1.3)Matter can be classifie<! "'cording 1o itt J'a« (solid, hquid, or gos) or• ccording ,,, iu cump<>Jirion (pure subs"n" or mix'ure). A pure sub·J"n« can either he an clement, which is nOl decomposable into Jim'pIer Jubstonces, or a compound, which is composed of 1"'0 or moreelemenu in file<! proportiuns. A milture c.n he ei,hCT humogeneouS,wi,h the ",me compo,i,ion Ihroughuu', .... heterogeneou.. wilh differ·en, compositIons in diffCTenl regions.

The Properties of Matter (1.4)The propertiCi of nlalter can be divided inl'" 110'0 kind" physical andchemic-a!. Maner displ.ys ils physical pfOl>Crties Wilh.....1 ,hanging itsrom('OSillon. M.ner displays ilJ chemical I'roperries only throughch.nging iu comp<>Jllion. Ch.nges in m.ner in which ils romposiliondocs n(>1 ,lIange 're c.lled physic.1 changes. Ch.nges in m.ner inwhich iu composilion docs ch.ngr arc rallc<l cllemical ch.nges.

Energy (1.5)In chemical.nd physical change.. m.ller oflen (I,hang" ene'lY wi,hils surl'Q<lndings. In these exch.ngeo. Ih, lUI.I energy is alW':lYS ron·scrved; energy is neilher crealed nor dC$lroycd. SyslCm. wilh high po'lCnli.lenergylCnd toeh.nge in ,he direcliun ...f1......er polenli.1 mergy.releuing ene'lY IIltu ,he lurruundlngs.

The Units of Measurement and Significant Figures(1.6, 1.7)ScientislS use primarily 51 uniu. whicllare bucd on I'" melric lyslCm.The 511..." unil$ include Ihe meIer (m} fur Ienglh, the kilogr.m (kg.)for m'S5.lhe s«ond h) for "mr. and the kelvin (K) for lempe,,'ure.Derived Unill 'rc those formed from a combin.r;"n of olher uniU,Common Lk"vrd unilS include ""Iume (cmJ or ",J) .nd Lknsity(lIcmJ ), Meuured 'luantitlC$.re reporle<! SO Ih.t Ihe numher of dig.ils rellc,U Ihe uncerl.inly in Ihe mcOSU'emenl. The non·place·hold",/;digil. in a reporle<! number are c.lIed signifi'an, figures.

Exercises 33

Key Equations and Relationships

Relationship between Kelvin (I() and Celsius rCl TemperatureSca~s (1.6)

K '"' "C + 213.15

Relationship betweet'1 Celsius rCl and Fah'ertheit ('F)Temperature Scales (1.6)

(OF - 32)

"

Key Skills

l)t!ermirting Physiul.nd Chemiul Ch~ng($and Properliu (1.4)

• Example 1.1 • ForPrdcticel.l • Exerci~$11-18

Relationship between Density (11), Mass (m). and Volume (V)(1.6)

'"d' -I'

Com'erting bet ....«11 the TcmperatureSCllln: Fahrertheit. Cdsiu$, and KeI"in (1.6)

• Example 1.2 • For I'r.actice 1.2 • Excrci~$ 19-22

Calculating the Den$ity of 3 Sub$tallu (1.6)

• Example 1.3 • For Practice 1.3 • For More PractKe 1.3 • Exerc'$($ 29-32

Reporting Scientific MU$oremcnts to the Correct Digit of Uncertainty (1.7)

• Example 1.4 • For Practice 1.4 • Ex.',cisn3S,36

Workirtg .... ith Significam Figu'es (1.7)

• Examples 1.5, 1.6 • For Practic.. 1.5, 1.6 • En'rcises 39, 40, 42, 45-50

Using Con"ersion Factor$ (1.8)

• Examples 1.7, 1.8, 1.9, 1.10 For Practice 1.7, 1.8. 1.9, 1.10 • For More Practice 1.9. 1.10 • Exnci$(s 51. 52, 56-59. 61, 62

Solving Problems In"oll'ing Equatiol1$ (1.8)

• Examples 1.11, 1.12 • For Practice 1.11, I 12 • Exercises 75, 76

EXERCISES

Problems by Topic

b. If d,ments are listed in order of inc'euing mISS of theiral"ms, th..r ch",""cal "'OCliv,ty (oil""" a ""pUling pattern.

C. N....n is.n in..t lor ",,",eoct,ve) g>$.

d. Th.c 'ea,,'ivity ,,( clemcn'J d'f'CndJ on Ih, ....ngem.nt oflh'i' d«troM.

3. It ChOm';1 decomposes "'veral SImples "f ",oon m"rw,id, inro"arbon and orygcn and weIghs th' 'Hult.", ,I.m,nu. The ,u"ttsarc sh""'n below:

Nair. Anl"'"ll<> all ",/<I.a"m!'<n'd "",,*rn~ ~um"""M i" 1JIur. 0'" "..

/O,,"'! i~ Ap/",ndu: III. f..<'Jriln ,n IIIf' """*,,,s by Topir S«tio" " .... f'," ....d.witl, N1rh Otld·n"n,,,..,td problem fi>/lDwrd by" simi"', e,",,·nurnbrrrt/

probkm. f~lln '" ,1",Cu",,,"",,'" Probknu S<'(flQ" " .... "Iso f"'"n!. bu'so.......~'m ",orr I~,: (O"lknge Prl>bkml "nd 0"'((1',,,,,1 Probkms.b«",,~ ll{ /1",,, ""'ufr. "IT un/",irrd.}

The Scientific Approach to KnowledgeI. Cla.»ifye>ch o(th, follQWing ~an OOstrvatoon. alaw.<), a lhw,y.

a. All m.n.. OJ m.d, of tiny. ,n~trllClibl, partl"ks calledalom•.

b. When ,ron IUSU ,n a d<>$Cd conl",ne" lhe ml<!l uf lh, ronll;n­er .nd itJeunlent< d"", n"t chonge.

e.. In ,hemic.l "",,'ions. m.tler i. nnth..,. """,ed nu, dC$troycd.d. When a m>tch burnJ. he'l is rv<>lved.

2. Cla.\$lfy 'ach of the folluwing u.n ob",rvatlon. a law. 0' a lhw,y.a. Chlo,in, i.a highly 'eaetive gu.

Mass or Catbon (g)

•""

Mass or Oxygen (II)

•""

34 Cheple, 1 Melte'. Menutement, end P,oblem Solv,ng

Nn,. ,,.. d.nnljt d«omP'H" ~~ra1 IoImpko of "rdfUlC'np<'!'UU<,k Itll" hydror;rn and 0XJIm. Tho mul,••.., """""......

... Clullfy nell of 'M followml molrcullr d......m. lIS 0 p"rt lUb.""rK~ 01'. mmu..,. If II p"rt SUt.srlnu. do...l'y II .. an ~It.

......., I compound. I'" mIX!U"',~lulofyII IS~... ...-.,

b. 00 JOU noI~ • "milurty bfrwftn lhew "",,h. Ind I"""," fOrarbon__In p.on ~

(.. CuI,.... fOnnw.lt. '- from 1M obsnvl'OO<U '" I.nd b!'d.. Con,.... lO,m..LlI~ Iitypothnis ,h,,, "' ...., upU;n J'O'I' t.w

me!

-,oJ

,I,

I,

10. CLul.ify...ch of ,h~ followml mul«uLl, d""flm••• 0 pu.., ...1>­llance 0" miJ:IUrt. If il is 0 p"rr subsunu. cLl...fy il .. on ~k·

mml .... rompound. If .. is. m1"U"" clul,fy II Ii holTlO&mtOw

OT hcT~rusrnmu"

,»

'" '"'" '"1')(,)

(.,

+ ......................'- Cbwfy ....h ohl><~ IS 0 p"rt ...........,. <It. mlllurt.lf

if II • p"'" wbsl,""". cbss.tl'y il .. on drmml or • rompound.lf 11is. "'ISIUrt.dISf>fy il ..~ <IthcT~

a. ....... b. brcfJ,l~

c. 110ft d. arbon IIlOnfm<It

4. I......n .>t'u......"'m~d~lnl pJ.:ucs. IIwy ",n '.Q Ih.,ml>ll "fll><", u. rtM>'I'inK .w.y from ........... lw;'.ln .dJ,lIon,lh.m",. d'lllnl lite pl.u:in, II>< mo.., rap,dly Ih.y.rr likly '" brmov,nl ."-.y from .ach olh~,. C.n )\OU drv;~ a hypu!hr... 10",pllin Ih.5<' ob......."on.~

The Classification and Properties 01 Malters. CLIS..fy~a(hm'M foI""'~nl.S.purr subs/'n« or. mo;lu..,. If

.. i•• p"'" ...bs/.n«, Nmfy;1 .. an rlrmml or 0compound. If II

IS • ml.'U"'. cbss.tl'y 11 as hom,,,,,n.o... Or hcTnolmmu..a. ,"""1 b. arbon d_Mkc. aluminum d.. ~.tlk .....p

_. T..

.-.

12. Srvn3l prop.TUn ofo l. poll","'t ,n II><~ .,..-phrrt.bul pon of 0 prot«, sborld O&o,mt UV II..,. In II>< UppC1'

(d)

b. tbm....bkd. <Im",y ~ O.79l1ml.

(,)

II. XV.fll proptT'oNnfiooprollfl okuhol (alw k"",wn ."ubtlln"I·whol) • .., hllN I><k>w. CLlssify...ch u(,br proprfl,n .. pl>)'SICllor ,hnnlool... rolorkuc. liquid., room InnprnlUrt•. mu.H "'nl> ....,<1'

1"'"

......

-I. Cumpklc Ihc folluw;ngllbl•.

Ill. Ikosrd on 'M mol«ul.or d........... cI.ulJfrue" eh...... a. physiaJ0' cMmiCilll.

a,"""'f'hcrc) arc fulnllX'k>w. \\1"eh afr phywc;al and wh;,;:h arc,lormlClll?L blulJh color I>. J'U'llt'nl odor Co W1'J ructm'

d. dKompoKS on aposu~ 10 ulTr.niolrt liplIt. IoU a, room kmpnalUrc

I J. OaMofr ~,",h 01 1M l'oIIowtnt proprnl(S u p/lyJocal or dormial.L IIor tmdmcy01ffiI,.t alcolooIlO burnI>. lhr sIl..... 01"""""Co lhr odor oIlY'nl llunnrrd.. lMlbmmabililJoIprnp.onorpt

14. a-.frrach 01 1M ':IIJowuo1 proprnors u~ 01 donmc:aLL 1M boib", poonl of rdryI.dcoholto. .... lmlper.lU'UI whICh dry ic~ ~aln

Co 1M tmdmcy of iron 10 r1I$t

d. 'M color vi PdI. o.w.fr ~...:h of lhr folIowlnl ","nl'"" iU phyl.oc-.ol 01 d>nnlC"aL

L N.lurallti bIIm. m a Jll>'T.

I>. 1M liquid pro~"" ,n a .... I.iO tv"'pu"'''' lX'c-auK 11K usrrleft ,lor ..-al"" open.

Co 1M liquMl pro~"" in.pt I'UJ bu,n,;n a n.mr.d. "bic)'l:l~ fr.m~ ru~, on rrpra,rt! rJ[posu~ '0 a,. aad \Q,....

16. Cl.",ifr r...:h of,hr (oUo...,ng ,h."gn.s phy.".l u,eMmicalL Sugar burns wIKn hc.,rt! 0'" skil1r1.II. Sugar dissolvu in ",.'rr.It. "pLlllnum ,ing I>«"m.., dull brou"," o( ronnnurt! abraSIon.d. " ..""r ou.(ocr b«omc:s la.n,"hrd .flr. tlll"'"urr '" air for.

IonS prl"lod of l,mc.

U. Il&Kd on 'IK mol«ular dug,.m. cI.o...fr 'aeh changr as phr.....1orchrm""l.

(.,

«,

Ib'

Units in MeasurementI'. i><1form rado of'M ............S''''''pnall1.~COf1YrnIOnl.

L 12 "1' 10"C C"""pnaIU",.1 whodI ....1<T l'rttuo)

b. 71 K 10 "1' lboibn, pouII oIliquid nil....,)C. -109"1' 10 "CIMIblunooon poOn' 01dl1;e.,)d.. "'6 OF 10 " lbody lmlperal"",)

~ ""*'"" rado oil"'" folIowmll.....pnallm~L 211 "1' IO"C Clmlperal"", oIboiIins _I... al""" Iowftlb. 22"C 10 I: lappnmmau. mom Im1pnallm)Co 0.00 I: 10 "f 1<:oldnI ImIpnalUt~ pos6lblr. abo k-.. U

abtoI"le ""'"d.. 2.n~" 10 'C (•....-. l<mpo""llIn oi'M un"""" iU _

um! from bKk.......rid bbck body radiat_)

!l. 1M roIdr,l l""'pera,u~ C\'C1 measured m lhe VnilN SUI" OJ

-1lO"F on janlLlllJ' 23.1')11. ".1'rosp«1 Cr«k, "Wb. ('".on>T"

,h.. ''''''po''l1u.r I,,"C and 1:. (Assume ,hal 80°F OJ ",cur.lc 10,wo ".,nlkanl fiIU'a.)

22. Tht .....mc:s, "mpo"'II" ~r mea,"red ,n ,he Un;lrt! S'..e, it13~ OF on luly 10. 1913. in [><..11 \'.lley. ('"...I,(orni<l. Cnn"." lha''<mper.lur< ,o'C arid K.

13. UK lhe p"fi~ muh;pheu 'oup...... <"'" of 1M follOWing n"alll_"m<nU wllhoul any "'po""n".LI.2)(100m I>. 22X 10 I),

C. I.S X 100g d. 3.S X IIfL

24. U" 10"",f" ",,'aUon '0 ClIp,"" eac" of 'M foIlowurS'l".nllll"Wllh o"'r the hue IInlill "" prcflll mulupl.....l•L~.Slll b.llIftCo IUpm d..3Sp;.m

(.,

~

, ..•• • • -(bJ

Sl ~

• ~

•«)

36 Cheple, 1 Melte'. Menutement, end P,oblem Solv,ng

15, Cumpklt'M ful!<.I<l'ln' •.,Ie:a. IHH, 1.2H)( 10", 1.20 x 10'm,b. 51Skm dm .:Tn

c. 11U55 a "" Qd. ).~5 kJ I ml

26. F.lJPffl" 'M 'l""n',.y ~.998m UI udo of 'M~a. km b. Mm c. ttl... d. .:Tn

17. How ..",. l-cm J<IIliI'ft -Jd II W:c '0_"'" a tq...... liu,'" monndt....drl

1L How ......,. 1·.:Tn cubn -Jd 11 W:c ... COftUnxI a cube- 'N' il~ em on nlIII'

.......u ,ho corrn:. numhorof """rlClo'"fig..... for .ha. parlleu·Iar balance.

I>)

1,1

J6.. Ikad •..:h of.ho fullowmS'o 'M COtf«, n..mbtl of "P'ficl,...fi",'"- SoI('; ...."'.ory~ should alwaY' ho ...ad from,ho bullOJJ1 of'M mmlSClll. Dip,a1 balancn .........wJy dlSplay

The Reliability of a Measurementand SignifICant Figuresl' Ikad •..:h of ,h¢ folIowtn& 10 ,''' COfnC'l numbtt <Ji OIJ'I,ficanI

lip..... Lobora....,. gLusWilft' tbouId alw-ars br ..ad liom lIwbOllom of!lv mnuscus..

b. JI2,lIOlhd. lJ.12i'J

b. O.OO7md.. I.56JJOO x 10" m

1'1

li'. Fur .ad. u( Ihc f"Uow"'I m••su•• mcnts. underl,ne .he rerun,h.. 0 .. wgniflC".nl and dr..". an. Ihro.."'" ,h. reruci .h•• • rc no.:L I.OSO.SOI km h.0.0020 ...c. 0.OOOOOOOOOOOOOO2a d.O.OOI09Ocm

J.I. Fur cach uflhc folluw'n, numbcn. undcrl",e.hc.<ron lha....signlflClontand draw on ••Ivou",.h¢.cn>n .ha. arc not:L lAO.mt m, b. O.OOIO+Omc. 0.l1057tOkm d.. 90,201 m

J,. How ....",. "gn,ClCIon, r'l"'" art' in each of ,h¢ roo..w""numbcn!L O.ooo)Umc. ).12)( 10' km.""

40. How many Jlll'tOOtnl r.,.uo arc ... cadi of !Iv k>llowulc..uJnbtn·L 0.1111.c. 1000i'tlO km.JO.OOO

al. Which <Ji ,he fOllow,n, numbcn Me OX! n..mbcn and lhe~haw a.. unbmllN numbtt of "'Indican. Ii......!L .. -J.I~b. 12,llChn. I IOu!c. EPA ps milrasc r.lIns of 26milcs pc!" pilond.IV_·'~~

41. IndICat••h. number o(!Isn,flC.n.figUfCS In neh urlM rullow,"Z..umbers. If ,h. n..mber is an cuc' number. ",d,cu. on unhm...cd number o(lig",fkan, figu ....

L 280%.887 (2001 U.S. popula.ion)b. 2.5~cm. lin

c. IIAI/cmJldcnmy"rlcad}d. 12. I do'..n

H. Round e..:h of 'M fol.....'n. numben 10 f<lllr ",,,,f...n. fi,"r....L 156.85~ b. I56.U2 c. 156..8-19 d.. 156.899

44. Round.ach.o ,h......""fica.., filU'"-L i"9,1-f5.82 b. 15-189)7)( 107

c. 1.J.499999995 d. O.llOOlH5J19

-I _"n..I. -=

(bl101

Density.!t. A"",, pm",. tw a ...... of 1.~9, and. mI..",., of0.J.49 cmJ...

'Mpm",.m.odcofpu..~

.Ml. A lIla",..m tncy.:1r fno..... du~ OJI~ l of .....« .no! tw •ma"of I.~I k5- W}\;l, iI'M dmsny ..f,M m.n,um ,n &!.:Tn~

JL. Glycnul if a .yrupy liquid ofte.. wnl i.. cOimellO and _I"- A

J.25-lumplr of pu.. glycerol h.., a m;w of ~.IO x 119 .. Wh.,if ,hedenmyof glyctnol i.. ';cm~

)2. A '"pJ'O'<'dly SOld nul1St' i. 'COlt<! lu <k'c,n"nc lu d.n.I1Y. I, isf""nd 10 di~lK. 19.J ml u(w.'or "nd tw a "'0'" "f J71s,.m..Could .h. nugg.' he ",.d. ufSold1

H. E.hyk... ,lyelll (anllf,..... ) hu. <kn"'yuf 1.1 I &!cm',L What "'M mOSS in Sllf~17 mluflhia loq..ld!b. Wh.t lS'M vulum. in Lof ~.I ksof,hlSliquod!

.M. AMon<' (N~ pol.... 1't'rtIO\'t1'} twa dm.uyofO.i857&!cm'.a. \\,ha. lS ,he mua. ,.. "of18.56 ml. ofKtI0~b. Wh.a. lS ,h¢mI.._. ,.....l..of6..5-lsofacflQnrl

Significant Figures in Calculations45. !'aform IIw folkrw'n, c.k..loh"". 10 IIw (0'1'«1 n..mOO of

..,nofl(llnl fi,um.L 9.IS + 4.970b. I.S~ )( O.OXhlO )( 0.69~ 27.S)( Ul 100.0..d. 12.290)( 10") (6.7)( 10')

46. I'nfonn llw followul& calrubo,ounl 10 ,Iw corTffi n..mbn of..",ofl(lllllli,..rn.L ".) )( n.o )( 0.08b. (5.01 )( t~) + 11.1 )( lol)~ UM)( U lC 0.007do. ~SJ l.oJI

4:'. Pwrform lhor followlllfj cakIlbllonl 10 lhor CWrKt lMImbn of..",of1C'~1I1 fipun..L n.1 - lJ.41... 11.6 + 1.UI .. lJ .. 1I0.nc- 19.6" Sl.JJ ~9H

d. 5.99 5.512

4&.~ lhor foIuwl", c.olnlw...... 10 lhor corrKt IIUmbn of"'I"ofnnl lip.m.L ll..OlH .. lUl9lI7t... 1m,) + 9.n .. U2c- U l.mdo. 5ll + 7,) 4.523

.... I'nform ,hor rolk>wmfi c....."o... 10 m., corrn1 numbn oiO<pUfl(llnl fipm.L UU681 )( 2.38) + n2.53... liS,) - 21.4") ~ 0Jl0S9~ IS12 ~ 911&.7) + 5.44do. !128.7)( 10') 48.5n: + 1"'.99

so. Pnfonn the tOllowtn& cakIlb"ons 10 lhor corrn1 numbn of"fjlll£1(ll1l1 fipm.L [f1.7 )( 10") IUJ)( 100)J + 7.ll... (S68.99 2ll.l1 5J~ (9~4j + 45 9.9) lC 1.1 lC 10"d. (j.l~ )( 2.H61l 2.J~

Cumulative Problems

6J. Tl'M.•••'" n~(Ily 60 ...:ond. ,n ~ m,nUl•• 100. ~'" onelly 60m",.. 'd in an ........ Ioo~ .'" nX11y 24 Iou ;n • ""'... w/;ot day.•nd 1M••••• J6S.l4 JOl•• d.Y' In ........ )"' F,nd Ih" n..mOOof_"nd1 ,n ....I~. )"'ar. Ik ...", 1<11''''' l""" alllW'" w'lh Ih. CO"••n numOO "f.i,n,r...nl fi,..",...

6-4. UJr npontnll..1 nOl~lIon 10 lnd"~I" Ih" numbe. of ..,n,r....nlfigu.,,' ,n Ih. following l1Orrm.nu:L Fifly million F••n,hm.n ClIn'l be Wrtll,,"

b. "F".....ry '.n jol.c... I"".. ha'l g"l.n hundred ,n,m;'" (1.... u·",nuSl"rn.,171.\-l7(1).

~ Tl'M. d,am.l". "r. C. alom i. 1.1 "n, h"ndfN milllonlhs "f.(tnUm"".

d. Slcny lho....nd d"I1... i•• k>l "f m0rItY 10 lUl' f<>.1 Car.

•. TIw dtnlUyof "Lllln.. ,n (Toblt 1.41.

65. Cla$lify Ihr follow,nl U ;II'tnl"" or ""n"", rroprrlln.L YUlu"" ... Iouilong PO"'1~ Itmptr~lu", do. dr<mc~1 (ond...lIyny~ e",,'JY

E.e.c:II.. 37

Unit Conversions51. Pnform .acb ohM follow"" ,0n"""l(>n"

L 1>1,mlo,n b. ).14kfjlOI~ ).5Lloql d.I09mml<>in

52. Pnform ~ach ohM folkow"'l (<>n""..",n"L 1.4'nlomm b. 116ti.o,m~ 11454101> d. BISydlokln

5). A runrw, lIrs 10 rull 10.0 kin. SM knowi IhalOO runn"'l pa<~is 7.5 mil.. hour.llow null)' m"'Ulff mull Jhr run!

S4. A qduo ridn "' .n ......... >pftd of H m,1n pc-r 10010,_ If she­~,"S 10 bLk 195 km.1oow Ionfj fon 10010...) mUll Jhr ndrl

S5. A Ew-optan ~ulorn<JDik hal "Ao" milnFof 14 kmiL \\'h~1 If 1Mpi mik~1" '" milrt pc-r pilon!

S6. A pi an boIdl 5.0 pilon. of ......... Wloal is Ilns quo,"uy",mo~

5-:' A~........ I\ow.r hu ~n.mof 195 .1. \\"'" io ,.. am III:

L kIIll b. dIIlJ C. onJ

sa. A bftlroom hu. O'Olunwof liS m' \\""1 '" .tHollIIM 111:L .....

... dm'L ~•

j9. no......,... U.s. form o«IIpon U5 x..,... How many........., miln1S1lus! (I ""'" - ~J,560 ti', I milt - 5210 til

60. Toul u.s. brmlmd 0«11",", 9>1 .iIloon .an. t'- 1IWIY"'I1lMC'miln io 11m! U ...... _ ~)S60fil, 1m__ S2IOtil. Toul U.s.

bJld • ..,., IS J.5J7 milbon "'l0WlY ..ild. \\"", pommUJl' of U.s.Ia.rwl io f~rmbnd!

,I. All ",f..nl l«'I.mmophm ......- conwns ao mlll0.JO ml~ Tl'M. rKofIlfMndtd doN If IS mJlk& body wntj/I'.How ""'''1 ml of ,hlS ...1P'"1""'" >ho<dd M 'M'II lo.n ",r..ntomfjh'''I141b! IAlNl"" IWO "'InofiCllIII fifjum.)

62. An ",f;lllt ibuprofm MISf)mJMl conl.. ,n. 100 m1ll5.0 mL 0Ul>pm•

POn. Tl'M. m:om........Jnl doN IS 10 ml/kl body om,hl. lIownunr ml oflhlf JWPC'IlSI<Nl Jhoold be 1M'll 10 an ,nr..nl om...•,nfj IIIb! IAssunK'lo'O"'I"ofK.m fifju"",,)

66. Al wha' l~m .....~, ..1U WIll 1M ",.d,np on ."" F~h",n""'l andCc-lJ,uJ Ih"momrl." be Ih. um.!

67 S""1'ill" fU" ha", ,Jc",n.d. _'h~'mum.I,,(..Ik,J 'M X Ih...·mom.,,,. On lhe X lClIol.I'" boihn, poinl of Wal... is 130 OX a"d11K 1Tttling po,nl ofw'lt, is 10"X. AI wh.1 I.m~nlu,~ wililh..ud,nglon the hh"'nhril and XIh.rnlOm"... bo ,"'um~

68. On. n..... l.kyll ••m~•• lU'. 1C.1t.....ler f'««'IOI 17 "'and boilJal 97 "I. O"a"",h., n.......m~.a,u'"....1•. 1M lIyd.....It. ,,'.1«fro.m ., 0"11 .nd bo,l, .1 120'11. If m<lhyi a!cohol b"il, .1I~ 'II, "'hal " ill bo'lrnlt po,nl on Ih. kkyll ....I.!

1>9. 1)0 each of Ih< follow'n, calcu!io'i"n, w,'hou, 01;"1 )'Ou. n!culo·10. and 1''''' ,h, "'~W(1'J 10 Ih, cor''':1 pumbor of IlgnifiCllmfigu"",

L 1.16)( 10 '/1.0 x lol

b.1.l7xl0 1 +2lCIO' ).OlCIO J

(. [(l.J6)( loS)(0.OOO)W/0.0I2: ll29.21

38 Chapter 1 Maller. Measuremen!. and P,oblem SolYlng

70. Th. "'Iu....r ,h. Fouro "'" K«n,ly 51.S1 U.S.•nd th. pric. ofI li,OT of I\<'wlin. in fT.",. i, 1.35 Fouro. Wh., ;, ,h. pri« ofI pilon of I_liM in U.S.dolillrs in Fr'nct!

11. AIhi.fusn. can of ..nd U) rtpl.«" .IOIH! gold cyIind.r ,h., ,il$on. ",.igh'·""'llivt••I..mtd ~~,.1.Th. nn of sand .nd ,h.gold cyIillllor h.vt .""""Iy ,h...m. d,mtn,io... (l.ng,h - 22 em.nd I'••lius - l.8 em).•• C.lcul.,e ,h......... of ••<h cylinder ligno.. ,h< m... of ,h.

can i,..lf). (d<n,i'yofgold" 1'I.lslems, d.nsi.y of ..nd- l.OO sI<m})

b. Did ,h< thi.f stI o[(th< .l...m! F.xp!oin.

12. TM proton h... radius of.pproltim01.ly 1.0 X 10 lJ <m.nd •m.'S of 1.7 X 10 1. g. Dtt..mi.... 'M dtn,"y of. pro'on. F<:>r.spht.. V _ (~I')"..-'.

n. Tho d.n,ity \If "!Onium i, ~.51 sI"nJ • Wh., is ,he "",lum. (in<uh,c in<h.s) of 3.S lb \If ti,.nium!

74. TM dtnsny of iron is 7.86 sleml. Wh., i, ilS dtn,i,y in p<>undspOT <ubi< i"'h (lb/inJ )!

75. A I cyIirtd•• hOI .Iong,h of 2.16 in.• ndiu, of 0.22 in.•nd •m of., g. Whal i,'ht d.nsi'yof ,ht " ..I in g/.mJ!

76. A solid .luminum sph.re hal. m.... of IS g. U.. ,h. dtmi'y of.Iuminum'u find rht r.diusuf tht sph... in i",hO$.

Challenge Problems

8.1. In 1m. Kitn.isrs discQYfred ......... elalS of bl..k holO$ ",nhm....... 100 '0 10.000 rin,O$ rM m.'S of (Ill' ,un. bu' u"upyllllIt.. 'po.t rh.n our moon. SUPP<JS(' ,hor On. of ,h... bl"",k holtsh... m.ll of 1 X 10" sun••nd a ..diu.ftlu.1 ro on••h.lfrh. ra·d,u, uf uu' mOOn. Wh.r i, rho d.ll.\ityof'ht bl,.k hoi. III gfcmJ!The .,diu. uf "ur son " 7.0 X Io'km .nd il has an .....rog.demuyof IA X 10"kgfmJ • Th. d"m.'.. uf rho moon"~.16 X 10' milt...

M. Sterion 1.7 shu"'ed ,h., in 1""7 Lu. Angol., Cuumy .ir h.d ....bon mo"".idt (CO) I.v.u of 15.0 ppm. An .v...g. hum.n in·h.l.s .buu' 0.50 l uf .i. pcr br.01h .nd !Ok•••buut ~o b...,hs pcrminu'•. lIow m.ny miUigram. of ea,bun monu:cidt doo.,h••v·tng' per$<1Il inh.l. in.n g·hour period (0. thi.I.....1of carb<ln",u"".ide pollution! A..um. thOi 'M ... rbun mo"".ide h...den.iry of 1.2 gfl. (~tim: IS.O ppm CO mean. IS.O l. CO pt.Io"l.a".)

77. A body..d .wlmming pool hold. IS5 'uhi' y..d. (yd l ) oflo·.....Whal is Iht mall of 1M Io'oret in pounds!

78. An icd..-rg hOI. ""hlm~ of 7655 cubic f«l. Wh.1 is 'h~ m......f,h. i.. (in kg) ,0mpo'lIIg 'M i(d)<~!

19. Th.ToyolO I'riu.... hybrid .I«trie ""h,cl•. h...n EPA go< m,l.ag.roring o( S2 mi{gol in rM ci'y. II"", m.ny kilonltltrs "'n thc I'riUllr.vtl On IS III.nofpIOlln.!

SO. Th~ Hond. In,ighl•• h~'brid ~leclri, ...hid•. I... ~n FoPA 11"'mil••g...ling of 57 miJpl in Ih. oily. H",,' m.ny kilom...n "ntht Inslgh, rravel on ,h• • 1II0U'" of p",lin. ,h., would fir in asod. pop con? Th. vulom. ofa .lOci. pop "In is l55 m!"

81. Th. singl. pro'on rh., forn" ,h. nudtus of ,h. hydrog.n .1OmI.... radios of .ppro.imJloly 1.0 X 10 IJ cm. Th. hydrog.nOIom iudf h••• tadiu< of .pprmi",.rtly S2.'I pm. Wh01 f"""lionofth.sp... withIn rht ~Ium is ooeupled by ,h. nu,lous!

S2. A ..mpl. of g.stuu. nCOn .,um, .1 .'mosph~,ic pr...ur~ .ndO-C 'un";ns 2.69 X lOll ~,om, PC' 111<•. Th. ",umi, n.d,u. ofn<U" i, 69 pm. Wh., f.a"ion uf ,he 'PO'~ i. oo,upi~d by ,h•..om"h~m.. l....s! Whar do.. lhi. rev••I.oo"llh...pa,.. ion bt·,w«n ",om, in rho "'stu". ph...!

SS. Nanur"hnology. rM fi.1d of'rylng 10 build ull,..m~lI SltueturO$ont .'om ~I' ',m~. hal progrelstd in ,..c.nr ~.rs. On. po'.nri.l~pplka'ion of nanor«hnology i, rho conmuetion of 3tllf"ial'elu. Th. Sllnpkl1 «Us would p'ob.bly n"m,e red hlood «11... tlocbody'. oxyg.n ITan.vo".n. For .nmple. n.nOCUnl"ncrS, ptr·h.", ,onSlru<'c<! of corbon. 'ould be pom~ full o( o'Yl;....ndi"J<"c<!III'u. ptnon's hIuodSlK.m. If th. ptr.lOn ncoded .ddi.,ionil o"ys,n-du. '0. h~'rl ,".,k perhaps. o. for 1M purpo..uf spo," Ira....l-rh<><: ,unroin~ .. 'ouWskowly ,du.. u'Yl;.n in'o,h. blood••1I01o'lIIg rissues ,h., lo'Ould olh ,.. .Ii. 10 Km.i".11.... Sopposo th., the n.""'o",.i"m " 'ubie .nd h.d 'n.dg~ l.ng'h of ~5 ".nUm...n .•. \"'har i.,h. ,'Olum. of oM nanOCU"'.III.r? (ISIlO.. 'M ,hick·

nnsoflh. n.nocon..ind. ",.11.)b. Suppose II....a,h n.nocon,.iner (ould 'onTain pur. ollyg.n

pr.lluri7,N 10. tknsity o( S5 gft. II",,· many g..m. o( o"y'g.n 'ould be e""'ai,,ed broa'h n."",on1Oln..!

c. Norm.l.ir <omai....bou' O.~S g of oxyg.n per lI ..r. An ",..r·.g. hum.n inh.les .bout 0.50 l o( .ir pcr b....h .nd tJ""s.bou' ~O brea,h. pcr mi"ut•. Huw m.nygr.m.ofo.rgen .I....• hum.n inhale per hour! (Aow",. tlo'O oign'fi nt figu )

d. \"'har i. ,h. minimum number of nanoconl.i" ,ha'. per·Jon would ncod in ,h.,. bloodm••m '0 providt I hour's"'tlnh of o_'<}'1l.n!

•. \"'har i. ,h. minimum volum. occupied by ,h. numbe. ofn.nooon1OIII." compurtd in pa .. .I! 1< such ~ volum. (.,,,,bl•.glvtn IhalMa! blood volum. in ... adulT is: ~bout S lilt"'!

Exercises 39

Conceptual Problems86. A voI.1He liquid (one Ih.t ....Iily ev-'p"nl...j iSl'ul int" a for anil

Ih'}:It is Ihen s.,.lod. llvos lhe mass of lho ,.,lod}:l' and i15 eon_l.n15 ch.ng. upun Ih. vapori'A1lion of 11>0 liquid!

81, Th. foll",..ing di.g",m "'p..StnIS solid ,.,oon dioxid•• alsoknown as dry ic•.

90. For .ad. hux bdo\.', ...,uni"" lh. bloch a""hod,,, lhe bobnc....Il• .«d on Ihti, posilionsand si~.... del.rmine which block is mo"d.nSt flh. dark bluck o,'h.liSh,.r-colurod block>, ur if Ih. rtl..­uv. d.nsili.. O"nOl 1>< d,'trmonod. (Thi"k ca..fully .oou, Ih.inform. lion MinS slKtwn.l

Which of lh. following d,agrams btll rtp..StnlS Ih. dry it•• ft..,.,I h:15 5uhhmw inlO a g>.s!

1"

•

,.,•

''I

••-.--,.,

-,••'.I"~

II&. A cub< has a" odS. 1'''Slh of 7 Cm. If It is dividod up i"to I-emcub«. h.".. m."y I·em cub.-. ""'ltlld lh...~

8'#. S"b51.ncc A has a denSl,y"f 1.7 s1cml . SubSlanccll h.,a d.",nyof 1.7 kslm l, Wilhoul doong ."y ..kul""'n$, dtttrmi"" whichsub.l.nu is m<>s1 delll<:.

I"~

'#1. ld<ll1ify ...eh of ,h. f<lIlO"·ing .. Ming mOSI Uk••n ~rVillion,.

I"w, or a Ihwry.•. All <0"11,,1 ....s .'ptrie",. lwo h'gh lid", .nd lwo low lid..

•I<h d.y.b. Th. lidn ,n F.arlh·. oc••n. a.. ",uK<! In.,nly by Ih. g",v,I.·

1I0n"lan","ion Oflhe moo".e. "..Iwby.high IIde in S:ln I:.....doco Ilayoc<urrtd al 2:H A.~I.

.nd 3:07 P.~1.

d.. TId.,.r. higfM,r allh. full In<lUn .nd new ml>(Jn th." al "til..li",.,softh. monlh.