MOLECULAR THERMODYNAMICS John D. Simon University Science Bouks Sausalito, Califurnid lllrivrrsity Science Books Preface x i 551) (;,11c I:~vcK odd S ,~u \~ l~CtoA. 94965 Acknowledgments x i ii CHAPTER1 / The Energy Levels ot Atorns and M o l e c ~ ~ l c sI Production manager: Susunna Tadlock 1-1. Tllcs Eltactrunic Fnergy of Atoln~ct Iyclrogt.11 is (>LI~IIIIIL(YI 2 Manuscript ed~torA: nn McCuire 1-2. Tlic Al lowcd Energies of d System arc, Ol)t ,~~r~eIreoln 1 tlie Sc lirotlinger L c ( t r , t l t ~ ~ t t 1 , Designer: Robert Ishi 1-3. Atonis Have Translationdl Energy 111 At ld~t ionto F l c ~I r on~cE nergy 7 Illustrator: Johtt Choi 1-4. The Vil~ratlorlaMl ot ion ot a Diatoni~cM oleculc C,rn t)cx hlc~tleledIl y 1' I I.IIIIIIII~II Compositor: Eigent)pe Ov i I l ,~ lor 9 Printer & Binder: Edwards Brothers. Inc 1-5. 1 lit, I Ilcq!,y I (>vtsls( i l ( ]LIJI I~LI I~~-M~~I I IcI~rIlIi~~ I(CO~ ~\~( l~~ cl l ~ ~Atr(t'l r I l l ~ ( t , I ;) \.\.1111 1' = 0. I. 2 . . . . 1 .$ T h ~ sb ook is prlnted on acid-free paper 1-0. I I I ~I, l . t r~~ror iOn j1 il1,itor Accourils for the Infrarc,cl Sptrc Irunl (11 '1 1)1,1toni11. h111lts11 1 1 . 1-1 Copyright 01999 by Un~versityS cience Books 1-7. 1 lit, I ) I \ ~ o I , I I I ~ 1I ~rlc rfiy <~ncthi e Ground-State Election~ct n c r ~ \o i a U ~ ~ i t c ~ l n ~ c I I I I K I I I I I I = I , + I / 1 6 Reproduction or translation of any part o f 1111s work beyond th,~t ~ ~ c r n i ~ thtye d I-I!. 1 1 1 1 . I I I ( , I ~ \ .I (.\.I,I\ 111 ,I K~g i tKl ot,~tc~Arr e c , = ~ ' J ( . tI I ) . l ? I I H Sect~on1 07 or 108 of the 1976 Un~tedS tates Copyr~ghAt ct wlthout the 1.9. Ill(.\ ' 1 1 1 1 . 1 1 1 ~ 1 1 1 ~ 0 1 I'II~~.IIIIIIIII hlo1t.c i~Ic,\A rt, Rcy,reselit(~tl I)y Xr~rni,ilM ot lc> -12 pcrlnissron of thc copyr~ghro wner IS unlawfill. Kequcsts for purn i~ss l~onr 1-10. Ill,. l i h ~ ~ , i l ~ r\I,IIV~ ~ .ItIlI III~01 $1 I ' I I IV~ I I~ I~M~OI II CYiil cl 1)(~11(~111(1\1 10111 11(, MOIII(.III~0 1 further inlornlation should be addresaed to the Perni~sstonsD epa~tmcnt, I I I I I t I I 5 Univers~tyS cience Books. 1-11 . rli(x I o(3rgy0 1 h111lcL~II C1 11 t l ~ tK, ~ g ~ ~ l - l < oI It~~It~oII~I~ I I I<-O1\1( l~it1,1~1\ ~ I I I ~ ~ \ I I ~ I , ~ ~ I ~ I I ( ,In IN' \Vr~tten.I \ t = c ,, ,,,,\ + ~ 5 , < > , - + t \ , l > ~ t2t7, l < L Problems $0 Library of Congress Cataloging-in-Publ~cationD ata MATHCHAPTEAR / Numerical Llethods 30 McoJarr~e,D onald A. (Donald Allen) Problems 4 0 Molecular thermodynamics I Donald A. McQuarr~cJ, ohn D.Simon. p, cm. Includes bibliographical references and index. CHAPTER2 / The Properties of Gases 49 ISHN 1-891389-05-X 2-1. Al l Caws Belidvc Itlrally li They Are Sufficiently Dilute 4') I ' I ' l i ~~ r~~ i~~ t l ynaI .m Simcso n, John D. (John Douglas), 1957- 2-2. Tlirl V J I , der \V~' i lsE q~rdtlona nd the Krtll~c-h-KwongE qir,ition Arc Ex,ln~[~lt,s 1 1 1111<. of Two-f'ardmeter tcluat~onso i St,~tc 54 01) ~ o . I A I \ l i IOO(I 2-3. A TLII>I~E: qu,it~ono t State Call [ksc r ~ l ) cI3 11f t i the c;,~itaous ;ind I I C I L I IS~tl it(,i ill1 \.t 1 \'I+) ,I, .'I 98-48543 2-4. T11c' VJII dcr l'V,>.ils E c l ~ ~ a ~ainotn1 tlit' Kcell~clit i\\.orig Erlu,it~on C)I~tsyt ilt, l .I\\ . CIP of C'orrcxsptrn(lingS t,itc>s 67 ~- .- 2-5. Sccoriti t'irial ( .oc~i i ic~e~C~dtn, Bc Ilsccl III Dctc~r l~ i i rIlnr~l ( ~ r l i i r~1l1i1~~ 1r1 I ' I I~ I , I I I I . I~~1 ~ I - ( , . I ( I ~ I ~ I I I I~ II \~ , 1~,111 ,4.Ih CI \ ~ uI*)~(~ II,~II 111 1, I . ~ ~ c i *( \it~ t ! l r~ I )~~tot iIo~nI rC " ~T t>rriii r i lhr! CHAPTE5R / The First Law of Thermodynamics 185 I f ~ r l l l , l l ( l l #11!1, \ ~ ~ ~ l t ~ ~ l l l' ?l . b l 2 I I i I I I I I I ~r l I T I of o r r i r H2 5-1. I? Con~n~oTnyp e of LVrjrk I S P~~SSIIT- VPo I~nie\,V Rrk 1 95 f'rol)lth1n> l l 4 8 5-2. iVmk anrl Hrmt Arr Not Slal(. Funr-t~on1~)1,1 t Ent'lg) I< a Stat(. Ft~nctl cm I tli< 5-3. I hr. kirst L.IW of Tli~~rr~iodyti,>+ rS~~lirp 5th r! trlrlrgy Is Clotr! Fuuc l i r ) ~ ~1 ' ) L 5-4. Ari .Arli~ti.lticP: roc-th\s Ic A Pror thcsi ll l.L'liir h hrj Encbrgv ,is t - lc~It$ Tr,>r>dvrrr.d 1 \ I I M A THCHAPTEBR / I'ruI7ahility and Stal is l ics 9; 5-5. Ih e Icmljc~rdtl~rltf. A Gas Ilvr rr.,i\t-+ in ,i Kt>vt,rsit>lrh- tli,~l).itir.t xp,~n\ior~ IYh Prrrtdr~ms lIll 5-6. iVrirk anrl H tw Haw. ,>S ilriplt. n-lol(.c-ul,~rI ~~tt:rlir~.l.>titjr1>9 8 5-7. -1l1r.E rltllalpy Chr l r )~I~$ .E tjudI 1 0 tllf Erlergy Trar>sierrcrla s t leal In ;l Corlstzrll-t'rcs~:~-r I'rorcss Irivrllving Only !'-\I Wt>rk 20 0 CHAPTER3 / Tho Roltzrndnn Factor and Partition Functivns I 05 5-0. Heat Capacity 1s a l'ath tunr-tion 1112 3-1. Tlw Bollzlnann Factor Is Cjne of tht- Mo+tI rriport,~ntQ udntilies in the Phvslcal 5-9. Relatlve Cnthall~lesC -an I anrl Ht..)f< 5r iences 106 o i T ransillon 205 3-2. T t ~Pr rotwbililv Tlwt a System In an tnst,mk>lr. Is i n thr. Stdtr! wilh Energy E , ( ! V . V ) 5-111. Ert~hatpyC hdrlgcs tot Cl~e11~1cEaqI ~lati~tAisre Addltive 207 5-1 1. tivats o i Rt.dctir>ri!,C arl Br C,lr ulalftl (rotn T,d)ul~lcdI -lmls of Fortndllon L 111 IC I ~ ~ , ~ ~ ~ ~ >1I0I( ,~ CI I I'wlY~' 'nIr " 106 3 4 . i.2.t-I 'r~,irtisr l Prorllfr ts 21 7 111 ,I 5yl>j 1 I 0 3.1. I l ~ eH t ~Ct.q ).~ri rv ,it Ct>rl+r;lr)Vl olulne Is ihe lbnlperat~lreL lerivativr nf thr Problems 220 Avel ace Ener~t 1 14 '1-5. i'r:r- ( ' . i r i Fxprrqr lhr Prrswrr In Tellns of a Partition Fun(-tirlri I 1 h MATHCHAPTEER / The Binomial Distribution and Stirling's 3.6. rI.r, l',)~ti llon I - ~ l l ~ r t n~fo ,I n5 ystrrii of Ir~rlc*l>mtDlt~i~~tinjlj,i uisl)ahleM olecules Approxim a t 'r on 229 I\ i t i t , Prrlrlucr ni hlolecular Partition IKunctiuns 1: 19 3-7. 1114. !',~rtitiori Funr tior) rlf a Syslenl of Indepe~tdent,ln dlstinguishable Atorr~sr lr .kl<~lecule(s:3 n 1Jsu;ljly Rt: LZ.'ritfcrl AS Iq(V.. I ' ) ] ? ' ! N ! 120 3-0. ,A Mnlerul~rP altition Function Carl H t - Dr.tr>rnposcrli nlo Partitior) runctlons irrr r,3rli I ~ P ~ni PfrwPrln m 12 i CHAPTER6 / Entropy and the Second Law of Therrnorlynamics ;I I - Problelns l ?n 6-1. The Change ol C n e ~ pA lone Is Not Skrffiritwt tn I ) ~ t ~ r ~ nth~rr>iI )c~*r tvr-tir>l~ of a Sllorltarleotrs Process 2 3 7 MATHCHAPTECR / Series and I-irnits 135 6-2. hlr>r)rqrril~briurIns olated 5vsten)s Evolve In a IJlrection T h ~Itn crease< I huir Ui!,orrlcr L 39 Problems 13U 6-3. Irrllikt- ryw% , Er>trrjpyI s ,I St~fcF ur,t.litin 241 6-4. 1 IJP S~rur ldI aw of I htbrrnotlyn~rrlir+ 5t~tc.sT h ~!th t. Er11roi)y r i l r l r > Icr>lr~lvStly ~l(~r11 CHAPTER4 1 Partition Functions and Ideal Cases I 43 Irlcreases AS a Result of a Spont~neuusl' rur-e- 2.15 6-5. The Mosl ralnuus Equation of Statistic-a1 Therrnndrnam~c-sI+ S = L,,1 11 11' 2-4(? 4.1. Tlrc Tra~~sl;ll~onPaalr titlnn runtt~uno f an /\tom in ;l Monatrmir Itir!dl <;a!, Is 6-6. !Ve MI AS^ Alw~ysU evise J Revers1b le t'ruc-es5 trj (-; ltr ulatv tntropy (-.han~r.s 25 < ~2 , - r~~~k l ,1 / l~ ' j134"3V 6-7. Thermodyiian~icsG ives Us Insight into the Conversion of tleat into i,ilr>rk '58 4-2. XZost Aiorrlc Arc i r > tl1r Ground Eleclrunlc State at Room Temperature 1,15 6-8. Fr~frol>Tv,I ~I R r Exl)rcssctl in Tcrnls nf ,I Parlillon Function 2GO 3-3. 1 hr 1-ner);r. uf ,I n i . ~ f r > r r ~hi rlr ilvr ulr?L i r > R r h Al)llroxin)d~cda s a Suln 6-9. The Molecular Furmula S = k, In W Is Analrycll~stn thtl 1 ttc~rmrldyridrnirF orrlil~l.~ rd 5t.pardrr Tcrnls 1 4Cl d S = S q t c h ; l 263 4.1. Mo+IM olc~cult!A~r c i t ) lhc Ground Vit>ral~oi>aSlt ate at Room Ternperatur~ 1 5 2 Prt~filcms L h4 4-5, hh~sht lr,lr>c ult.+ hrr . in Exr i t t h t l Rot;lfinr>,>lS 1;Hcs dl Ordinary Telnperati~res 155 4-6. Kot,ttional I'arlltlriri I unctions Conhin J Syrrlnlrtry Numt~rr 158 4-7. -1 t i t > L'ihr,itirjri,ll I',irlilion Ful)clifir) of a Polvatornjc Molecule Is a t'roduct uf H~rmonic CHAPTE7R / Entropy and the Third Law of.Thermodynarnics 2 71 ClsrlI1~tort 'art~t~oFnu nr tion5 for fat-h Nrlrrrl;il Corlrdirlate 160 4-U. The iorln oi tlie Kot~tionaIl' artitiun Fun~tionn i a Prilyatt)rrlir Mt>iucu!c Dcpcr)ds upon 7-1. Entropv Increases with Increasing leml~erature 273 ! l ~ r ?5 h,lpe of the Molecule 163 7-2. The Thlrd L a w of Therlnodynaln~csS ~ v Ts h at tlie Entropb ui a Perfect (. ryst,il 4-9.( . - r ~ l c u ~ l 1 3 t rM~ rol lr>rI tr.nl C;ll);lc III(!F Arc 111 Very C ~ o Adg reement wlth Is Zero ,lt 0 K 275 l-xl~rrinient,jbI I=IIAI Oh 7-3. Al,,~~Arisirs.c~r ts Th,it I' , . 0 ,>5 I , 0 I - ' r < w 7-5. I'rx tic-,11A l>\t)lulc tritropics C,rn Bc Dc~t!rrr~ir~Ccadl orirnt,tr~,r1 1 1 ~ .) 7-6. rJrLllti e a1 Al~srjlu~Een lropies ot C ,~seCs an Be C,llcul~tcdt i c Ilrl 1'.u 1111 ,r t ~I ~ I I 1I1 4~ 111 % ':>I 7-7. TIrc* V,iluc$ th 5tdr)ddrd EoIropic~D.F PCI! L I ~ O I > ,%lr>l -1 ( ,tkrrirnt.lric Enfropit<< 28H 7-9. 51.1rlddr(l Entropics Can R? Used trl Calculate Entropy Changes oi Chcnucal 11-1 . L%kI I >[,< I Ur~ok~IIl'\O 5iI,1~rltl~ lrrSl I ~ ~ Ih~rr. tlrv Siil\tbnt , ~ r l t lGI t lt,!lry'+ 1 .I!% ~ I , L I I < I Kt,ns 289 tor lhr Solutr. ior \r>lul~onso f S(111rls [)h+srllvr>rinl I icl~uds 4 Problems 29CI 11-2. 1 he Ar-tivity of n Nr,nvol.itllc Soluttb (-an Ht. I ~ l > t , ~ l r ~ ri r~trrl~ r tih t' Vdl)trr l'rc>++clr,(,,I ! Solvent 443 11-3. Colligativr. Prof)crt~~Asre Sr,lrrtir,n Prr>pc.rtirhcT hat Dcpthnri (.h~lyI lprln tllc NI.,I , s . Den5ily ui Sol~~Ptca rticles 448 11-4. Osrntjt~cP rcssurc C J B~e Used to Detr.r~ninth~hMeu ler uldr M;tssc-+o t l ' t ) l y~n<~:, ~. CHAPTER8 / H e l m h o l t z and Gibbs Energies 301 11- 5. Solutions of E1e~trolytr.sA re Nonltleal dt Rel~livelyL obv Cunt r-~~lralions4; 1 8-1 . 1 hv 51gn0 1 Ih e Hr.lmholt7 Energy Ch,~nge[ >c.lerrn~ncsth e Direction of d 5prjrllane01ls 11-6. The ilc:byr-tliikr.l Theory Gives an Exat I txpress~onu t In y+ Lor Vt.rp D~lute 1'rotr.s~I n a Systcm a1 Cnristhnt Volume ~ n rTie rnp~ralure 301 Soltrtions 459 8-2. 1 tic C~t>t>Esn ergy I3eterrnincs the Ilircction o i a Sporjtan~!usP rocr!ss for a System 11-7. The Mean Spherical Approxinlatir>[lI s An Extcns~oroi i thc Urhye-Hucktd Tht~o~t l;j at Constdn! Presslire 2nd rclrnperature 304 klighrr Concentrdtion~ 36 1 8-3. Mdxwell Hih c CHAPTE9R / Phase Equilibria -44s rjirer-tion in whlr:h a Kc;lct~c>Wrl ill Prncced 488 9-1. A Ph3w Diagrdnl S~rnrn~~ritzhecs S ol~d-Liq~l~d-GdDse h~v~ofr a Substance 350 22-6. lhc Sign oi A,G And Not T h ~ot f A < G ' Determin4.s the D~recti nn r r f Redctiorl 9-2. I hr C~bbsE nergy t j i a 5ut,stancr Has a Close Connrbction to Its Phase Diagram ,157 5finntant:ily 490 9-3. The Chemical Pott~ntialso f a Pure Sul)slan~t?in Two Phases in Equilibrium 12-7. The Variation u i an Equilillri~lmC .onsl,lnt with rr!rnprhraturr! Is Given 1). th~. Are Erlual 159 Vdn't tiofi Equation 491 9-4. The Cldus~usXlal~evrcmEy trdtic~nL ives the Vdpor Prrswre ui a Substdrlce As a 12-0. We Cdr l C-alculdtr Equilibrium Crlnstarits In 1. ( , I l'ortit~orii uoclion., 4') i F~rnct~oirT~c nlper~turt: 365 12-9, hlnlec-ular I'art~tionF uriclions ~ n Rdel dtcd -1 hcrmrjdy~urnict ldta Are 9-5. ( Iir'llric .il Po t i ~ r l ~Cia~r)~ 1l 3 r~va ludlerl 1ri)ln ,I P,rrtit~r>nF urlct~on 369 txtun+ivcly rL~t>uldlecl4 99 Problems 373 12-10, Eq~~i i~t l rCluonrrls tant+ lor Hcdl C;dses Are kxljres5r!rl in Tc~m!, ui l ' l~ ( t~d l Fugar ities 50h 12-11 . Tlit~r~nurlynarnttcq u~lihriuqnC onstants ,%re txpreswrl in Terms of Ac r~vit~cs) r l < q 12-12. The Use of Activities Makc5 a Sig~~ifirdnltf frrtlrice in 5mlubiiity C~lr.ul;rtrrin\ CHAPTER1 0 / Solutions 1: Liquid-Liquid Solutions 387 Involving lunic Sllecic~ 5 12 Prohlerns 51 5 10-1. Pa~tldMl olar Quantiti~sA re lnlportarrt Thermcldynamic Properties of Solutions 387 10-2. I h r Lihbl-Duhtam Equation Rdalr!s lhe Chnnge In the Chvm~caPl otentidl of Onr Crmrponent of a 5olution to the Change in thc Chemir dl Poteriiial of lhe 0thr.r 390 CHAPTER1 3 / Thermodynamics of Electrochemical Ce l l s i:') 1U-3. At Fr~l~iiibrlurlnh.e Chcmical I'r,lcnt~al r ) i Each Cornpunt-nt Has the Sdr r~V~a lur in Each I ' h ~ cIn Which the Colnponr.n~r \ppcars 393 13-1. An Elpt ~rochcnl i~Cdel ll Prurluces dn Elcctrir. Uurrcnt a< (he Result o i d I-I~V;!II<. 10-4. Thc Cornprmc.nts of an ideal Sol~rtionO bey Rauult's Law fur All Cunt cntraticlrlr J9.1 Kedcllori 524 10-5. hlo5t Solutron5 are Nut Irleal 4 ~ 1 13-2. Hali (Yells Tan Be Cla~sitiedin to Varirlus iypes 53 1 10-6. The Gibt)s-Cl\~h(.rEr qtlation Reldtthst he Vdpor Prthssureso f the l w n Components oi a 13-3. A Cell D~agranIls Used to Ktlprestlnt ~ r Eilec :trocht!~n~c,C~le ll 5 < 3 Volatile Binary 5olution 1115 13-4. Th(: Ciblls Cncrgy Changr. of a Cell Reaction Is Dirtlclly Kclatr-rl to ihe t i r , ~1 1 , . , . . 10-7. The Ghntral Thermorlynamir quantity ior Nonldedl Solutions is the Activity 410 Fort e uf the Ccl l 5 16 10-8. Activrties Must Be Cdlc u1att:ci rv~thK cspect to Slandarrl States 413 13-5. The Stand~rdfr rrf of an E1t.c-lroc.ticmii,d Ccll Cdn Be: F~~urtl~r l vE \ttl~jlollI~( l 10-9. We Can C-rjrl\truc~a M o l u~ldr Mrjrlcl r l i Non-idtldl Solution5 414 13-4. lt'e Carl .4ssign Values td E' lo Sirlgle Electrodes 541 Problems 426 13-7. Clec.tror he~nicaCl tllls CAI] Be User1 10 Ilrrerrrrine Actrvity Cr)r.ii ir h rmr l t \ . , 1 { - H . 1I1.rir o , t i ~ ~ ~.II r Mi ~t>t. lwrtbinr>r~(:atr?t+r > iL i c ~ Ak rhk (-dn He Iletermined with Efectrochenlical Cells 556 13-11. W e Can Assign Tht.rn~udynamicV alues to lndiv~duaIlo ns in Solution 554 13-12. Rattcries ant1 Furl C(!lls Art, I l ~v i resTh at Use Cl~emicaRl eactiorm to Pror1ut:r. Elrrtrir rurrcrlt., i h 5 Prr~hlcms 5h8 CHAPTER1 4 / Nonequilibrium Thermodynamics 581 14-1. Entropy Is A lw~psP rodutc~din a Spontdneous Process 582 14-2. Eritroy iv Always ln~reasesW hen There I s a Iblalcrial Flow from a Region uf Higher ( hcm~caPl otrrl~ialo 2 Rt.~ir>onf I .~~wCchr ernical Potential 505 This book has cvolved from ou~.physiuacl hemistry tcxt, Pl i~sicuCl hrrnirtry, A MoIt~r,- 14-3. h\;lrly Flux-Fort-(*K clat~onsA re Linear 5RD u h r Approach. I n (hat book, we emphasize a molecular approach to the l cach i~~01-g 14-4. l~hr,C)ns~jieRr eciprocal Kclalior>S~a y Thnl I.,= 1. 591 physical chcmistry. Consequently, unlike most other physical chcmistry books, ours 14-5. Various El~c~rokinrtQicu-d ntities Are Kelated hv th;0nsagcr Reciprocal Krldtions 593 discusses the principles of quantum nlechar~icsf irst and thert uses these ideas i r l thc 14-6. The Clnsager Rec~procaRl rlatir>r~Asr t. RA+CY(I In thp Principle of Detailed subscqucnt clevelopment o f thermodyrtamics. We l'ollr,w that same approach i n this lext. U~lance 597 Mo1err~lu1I-l rcr~noriyna~rlicMs.a rly of thc chaplers irt this b~lclka re siniilar to those i n 14-7. Elccfroclwrr~ira l I'rittwtials Play the Role of the Chernicdl PotcnfidI for Charged our physical chenii\trjr book. hut we have added new material to sevclal chapters attd Skstr!rr~r i r i r l i f i t-r~nPt hases 602 have three cn~ i re lyIl ew chnpters. l 'he first chapter, The kncrgy Levclx of A t o m and 14-I<. The hlagnilurh r > i t hv I ir l l~idlu nrt~onP otential Depends Upc~rT) rdn\lir>rt Numbers 6 U i Molecules, is new and presents resulls of quantum mechanics that arc needed i t ) Inter 14-9. The Liqtrid Jut~ctionP oic>ritidlI s i,Vt,ll Approximated by the I fendersorl Equdtion 6TO chapters. Only a fcw quantu~n-mechanicarle sults are rcally needed Students learn to 14-10. Thp Flux-Force Rchtiorls Ir)r C(>ntinunusS ystems Involve Cradienls of lhink in tcrnm ol' discrete clcctn)nic energy lcvels i n general c h c m i s t ~a nd organic Thcrrnr>tlynarr!ir Qu~nt i t~eRsa ther Than Differerlccs 61 7 chemistp. We begin our discussion o f thermodynamics ill Chapter 2, where we discuss 14-1 1. :I Slt*,~rlvS tate 15 a State of Minimum Entropy Produt.tir)n 622 the properties o f gases. We introduce the Boltzmann factc~ra nd partition functiuns i r i 14-12. TIw Cl,~n$rjnrff-Pr~guginInee quality Applies to Systfms That 110 Not Necessarily t l.avt? I inr,.~r Flu,: Force Relations 025 Chaptcr 3 and the11 use the results of that chapter i n Chapter 4 to ualculate energies P r o t ~ l ~ l lt~, , !\i { and heat capacities of ideal gases. Note that we do this beforc we introduce the First 1,aw c~Tf hermodynamics i n Chaptcr 5. This approach works perfectly wcll heci~use / \ r > \ t ~ t l r ct rr thc Nunierical Problems 639 we treat only rneuhat~icapl roperties (pressure, cnerpy, and heat capacity) that 5tndcnt.s havc encountered i n previoux chetriistry and physics courscs. This approach all(~wsu s to immediately givc a mnlecular intcrpretalion to the three laws of thermodynt~rnics and l o nlnrty thermodynamic relations. The molecular interpretation of entropy is an obvious example, but eve11 thc vr:ncepts o f work and heat it1 the First Law of 'I'her~ttn- dynamic'; have a nice, physical. molecular interpretation i n tcrlns c~efn ergy levcls and their populaiions. In Chapters 5 through 8. we in~roduceth e principal Ihermndynamic state func~iuns,g iving them a molecolar interpreti i t io~th~r oughoul. I t ) Chaptcr 9. we examine nnc-component phase equilibria artd introduce chemical potential. The next two chapters concern solutionx: C'hnptcr 10 discusses solutions of lwo liquids and Chap1t.r II , solutions oi'sulids dissnlvcd i n liquids. Following Chapter 12. on chen~icii l equil ihriu~nw, e present a new ch;~p~oznr electmchemiciil cells. 'I'hc finill chitptr~'sctvc.s as an itltroduction 10 notlequilihrium lherrrlodynamica, or irreve~'siblctI icnnodyr~;i[nic~ This chapter is a unique feature of our book hcvau.se Sew pedagopical i n ~ r t d u c t i n na~re available to this topic, itlthnugh it finds exletlsive application i n biopl1ysic.c and hiology. As in our physical chemistry book, we have included a nutnher 01-so-called Math- Chapten, uhich arc short reviews of the mathematical topics used i r ~su hsequcnt chupcr . 'l'hc tivc Mirthl'haptcrb AI-cN UIIIC~ILM'IeItIh od\. I'rohahili~y and Stilt iatlcs, Scrics und I.imira. Partial Uiffcwntiation, a11d Thc Binomral Distributiotl and Stirling's Appronirn;liio;~.I n cach one, thc discussions art: brief, elementary, and self'contained. At'tcr reading cach MathChapler and doing the problems, a student will be able to focus 1111 lhc subsequent physical chemical lnatcrial rather than having to cope simultanc- t)usly with the physical che~rlistrya nd the mathema~ics.W e believe this fcature greatly enhances the pedagogy of our text. An important feature of the text ih the inclusion of about I 0 to 12 wclrkctl example.+ in each chapter. In addition. cacl~c hapter provides sotne 60 problems, and soluticlns to he numerical l~rnhlcmsa re given in the back of the book. Some prohlemc exlend the material in the chapters and introduce tiew topics that are somewhat more advanced. They have becn written in such a way as to leiid the student step hy step hrough the material. Many peuple have contributed to the writing and prtxluction of this book. Wc thank Tuday's sludents are comfortablc with compulers. In the past few yeal,s, we have our ccrlleagucs Paul Barbara, James T. Hynes, Veronica Vaida, Juhn Crowell, Andy seen homework assignmcnts turned in for which students used programs such as Math- Kurn~nel,R obert Continetti, Amit Sinhn. Juhn Wearc, John Whcclcr. Ki1r1 3;iltlrirlpv. Cad and Marhcmatica to solve problems. rather than pcncil and paper. Data oblained in Jack Kyte. Sill Trtjgler. and Jim Ely for slirnulating discussions on thc topics th;lt laboratory courses rtrz now gri~pheda nd fit to functions using programs such as Excel, sh(luld be included in a rntldenl physical chcmistry cuurqe. and our students B;trry L o ~ u s1 23, and Kalciciagraph. Almost all sluderits have access to prsonal compulers, Holding. Peij~tnC ong, Ruben Dunn, Scott Fcller. Susan krzut , Jcff Grei~thuu yr hc I'r>~-liult l,:,i 'l'his field i~ called .rmristic,rrlt ~~ern~uciyr~nhmccirasu se it relates avcr;iges of ~nuleclllar --2.17864 x 10 '",'II'. whcrc ttlc qrj;ullurlr p rop t i e s l o ~nrtcroscnpicr tlermodyriamic pruperties such as temperature or pFCshUE. nulrlbcr n - 1. 2. 7 , . . .. Notc thnr the vc~tical The tnatrnill ill Chiipters 3 and 4 i r actually an elementary treatment uf statistical axis i~l abel hy sm/lO-lhJ . Thi\ nt,pafir>r~II ic.arl5 that the tlirnencionlcc:, nurllbcrs on that :lxis :,rc thcrmody~~a~niMusa.n y of thc resul~5o f slatistical tl~ermodynaniicsd epend upotl thc cnrrgicv divided hy l0-ld J . We will u\e [ h ~ c mr~lecu!nrr l~odelsu sed. so these rcsl~llsa re not as solidly based ~5 are those c~cfl ns.cical -2.00 notation to label colunins in tablcs and axc? in rhcl-mcdynnmics. Ncvcrlheless, the intuitive advantage of having a ~nulecularp iuh~rc - , -2 . 8,1 '.- figures bccause of its unambiguous nature and of certain quantities or processes is very convenient. Consequently, irl ou~~deuelopnient algebraic ccr~menience. of thermodynamics in this bonk, we will use a mixture of classical and statistical thermodyi~n~niues,v cn though this approach will cost u< some of the rigor of thc 1-ccult5. For 11s to use a statistical ther~nudyna~niacp proach, we must use n few qtrantilrtl Notc that F , e , - P , . . . hecause of (he ncgativc sign in Eqr~ation1 .1. The stilte of ~ncchanicalr esults f(lr alorns and tnolccules. It is not at all necessary to be an e x p r t i n 7 ~ r oer lergy occul-v when 1 1 -+ w in Equation 1.1. In this state, the prototi and thc quiintum mechanics to w e these results. In this chapter, we will discuss the quantum electroll arc so far apart that they do not attract cacli other at all. so wc take their rllcchanicnl energies 01-a~omas nd nlolccules and relate them to atomic and rn(llecu1ar intrraction energy to he zero. At cloacr distances (snlnller values 01' I ! ) , the proton \ ~ ~ w t n ) x o pEyve ry collcge general chetnistry course treais thc energy lcvels of atonilc and the clccrron atlract each othcr heciu~seo f their opposite charses. i\ statc that has Ilytll,clpcn and it< associated spzclrun~i n sornc detail, so we begin with a discussion of negative energy i s Inore stable rhan nnc thal has Leru energy. thl\ lopic in the first section. We then discuss niultielectron aloms, the vibrational and The a l l o ~ e del lcrgy states yiven by ['quation I . 1 are called srarir?nay stittcr. I'hc ic>t ;~t~t l i i : icln crgief nf diatomic mt~leculcsa, nd pdyatornlc rnulectllcs. statc of lowesl energy (n = 1 ) is called the gmtmtl srutu. The othcr states itre called rxr,ii td .rrarcs; the state with n = 2 is called thcjirar excited stntr. that with n = 3 is ci11Ie~thl e .rrr-o~~de.~rit~.dedatn~dt tseo, o n. When an electron makes a transition from one sti~tic)rlnrys tntc to another, i t emits or abhurhs electrntnagnetiu rildii~tior~W. c piclure 1 - 1 . I lit. 1Ir.c ito~licE nergy of Atomic Hydrogen Is Quantized clectrurnagnctic radiatiurl as consisting 01- packets of cnergy called phoronr. wht~se cncrgy is equal to hv . where v is the ftequcncy of- the radiation and h is the I'lnnck ' I ~ III~I ~ I:I ;II \V~ . lc..i~nc.d III pcncral cl~emistrya nd organic chemistry that the energies of constant ~h = 6.6261 x 10." J.s). Consider a transitinn frtlrn the state rt = 1 tn n = 2 I I I ( . c.lci-trrlr~\1 11 ;ilr~ln..; jnd molecules arc quantized; that is, they are rcstricred to only (see Figure 1.1 ). Because e? > F , . cncrgy in the lor111 of a photon must he sbsnrhcd. L crl;l~rtlh rc Ic+lr v :~ l~ct\i )r L ~ K ; L I T I t~h~c~ e, nergy of an electron in a hydrogen atom is and we kave e, = F , -t h v, .+: by cotlscrvation ot ene1,gy. or h 11, &, = e, - e l . For thc c1\1-110 ) t h h~rt lr~ul;~ 2 4 I transition, conservation c~fe nergy gives F~ = xI + hvz +,o.r Iru141 = s,- - E I ' Notice thal hvI+Z= kvI , , ; the freque~~cdye pends unly upon the magnitude of the difference between the energies of the two states. The general result W I I C I V 1111. c~11:11111111111 ~1111l1 1t.. 1I \. I I + \ I I 11 I C 1~0t i ll: integer values 1, 2 , 3, . . .. The units of rnergy 111 kl~cI tlrctrl;~l~rlS~!\~lr,.~lll~ (11 I! I I I ~;\~ l \hr~vi; iStIe)d f ronl tlie French Systkrne 1nter11ation:llc 11' l l ~ l i t c;I~T \I.I I ~ I ~ L -~~l.r \ipll:~tvfi>Iy I. Clnc ,jt111lci s equal to the kinetic where Afi j~ tlie (positive) d i f fc ic~~icne rhe energy nf the two slates invnlvcd in tl:e encl-gy of a mahs 01 lwr~k ilcrp~;lrnI\ lnr\111gw ith ;I qwcd 01-one nlcter per second. If you tmnsitiori, is billcd the BoI!~-jrr~qrtt~nmro:ytd itior~. remember that kinet~ce ncyy IS ] r r r r*'. lllcrr y t r ~c; lrl %cct h;if I J = 1 kg.m2.s- The Figure 1.2 shows tllc oh.cerved emission spectrum of atotnic hydrogrn irl the clcctrunic cnergy of a hydrorct~;1 111111 p1vi.11 I1y ~ : ~ I ~ I : 1I II I iIq IpIl~c~ ttcdi ll Figure 1.1. vihihle i111tln ear ul~raviolert egion of the elcctrornagnetic spcctru~nN. ote that the lincs

Molecular Thermodynamics

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