Molecular Thermodynamics

338 Pages·1999·150.64 MB·English

by  John D. Simon

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
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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
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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
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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<e Ut,tern,ined from Hcat (.al~.it itv I),lf,> 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~<lrll,llcI h,~itl i r - Abr.r.~gr,E nrrrnth- tr)crgy I\ Cqual to the Ohserved Energy 5-12. The Tenlperature Dependence of A, I I Is Liven in lerrn+ r i l t h*. Hth.~t
Capxities rjf the R r~c f~ r>,irtisr l Prorllfr ts 21 7
111 ,I 5y<lr>l>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,<S -- Alp H ; 7iP at Ph,isr Tr~nsilirjrl 277
f'roht~ms I h(j 7-4. [ 1 hirrt I.,iw th Thrrrriot~yr>,~~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<bc t r l . . I h1.1-r . I ~ I l+ h ll l l c ' l 111.11
Strur tllrrh 285
7-8. Iht. 511t" 1"l5( 1)1)1( t ~ l t r [ ~ i )o~f !as tc!w Sutlsr.lnces 110 Not Agrthc w ~ l hth e
CHAPTE1R1 / 5 i ~ I u t i r ) n sI I: 5r)li(l - I . ic l i~ i t iS olutlol~> -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,<at.lir>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 H<!lat~onPs rovide Several llseful Ttu~rmodynamirF ornmulas 308 Problems 4415
8-4. The Eillhalpy o i an Icir.dl L a s Is 1ndepr:ndent uf Pressurc 313
8-5. The Vdr~rjusT hcrrnodyn~rnicI 'unr,!ions Have Ndtural Independent Variables 31h
8-6. Vhn Standard Statc. ior a (;AS at Any Telnp~rdfureI s the I lypott~eticaIld eal Gas
CHAPTER1 2 1 Chemical Equilibrium 477
at One Bar 319
8-7. The Citlt)s-Helrntloltz Erlual~onr lcscr~ljccth e limperaturt. Depvndencr ot the 12-1. Chenllcal Eqtlilibrium Results when tkrc Cit)bs Frrcrgy Is a Mllunium with Itc.qrt , '
Cit)ks Lnergy 3 2 1 to the Extent of Kthdctiorl 477
12-2. An Equilibrium Constant IFa Functiol~o i Temp~.raturrO nly 481
8-8. I(~gacityIr d hleasurt. of the rVolridrdlilVo f a Gas 325
Problems 130 12-3. Standard Gibbs Energies nf Fornidt~orCi an Be Chcd to Calr date Equ~l ibr~ur~~
Conslants 484
12-4. A Plot t ) i the Cil~kxE nergy of d Kcldctiurl hlixture Against the Extent of Kt~dcticIi
Is a M~nimurnat Equiltbrium 106
12-5. The Rdt~oo f tlie Reaction Quotit-nt to the t q u ~ l ~ b r Ci ~on~smt;ln t K)ctern~ine>ih 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~(:at<n Iic Uscd to Deternlirlc Valu~.so f A r H , ~ r ~ Ar lr X of
( t.11 Kr..~tl ion5 557
1 J-9. Soluhrli ty Prtirluc-t!, C.I Hv Ilt!tt!rmintd with Flectrorhem~caCl ells 553
1 J-10. Thc Cljssoc~atiotCl urlsf,>r?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<cK. crty
and a mudern course it1 the phyhical scicnces should encourage students to take ad- llilnsor~B, ulnng Li. and Sunney Xie [or reading purliotls of the lnarruscripl and 1n:1h111g
vantage of thesc trcmcndous resources. As a result, wc have written i1 number of our Inany helpful suggestions. We are espec~allyi ndcbted to our superb rcviewzrs Mcrv
pmblelns with the use of computers in mind. For example, the hrst MnthChaptcr intro- Hi~nson,J ohn Frederick. Anne fvfeyers. Gcnrgz Shields, and I'ercr Rook; to Heaththr
duces the Newton-Raphson melhod for sulvirlg higher-ordcr algchr~ice quatiuns and Cnx, who also r e d the entire manuscript, rnitde nulncruus il~sightfuls uggcstiuns, ; I I I L I
tra~~scedenteaql uatiuns numerically. We scc n o reason any Iclnger 10 limit calculations did every problem in the coursc of preparing lhe accnlnpangi~igS olurion Manual; to
in a physical chemistry coursc to solving quadra~ice quations and orhcr artitic-ial ex- Carole McQl~arrie,w ho spcnt many hours in the library aitd using h e intcmet lwkillg
amples. Students should graph data, explore expressions that fit experimental dala, and up expt i~nentadl ata and biographical data to write all the bic~graphiciils ketches: iind
plot fu~lctionsth at describe physlcal khavior. The understanding of physiral concepts to Kenneth Pitzer and Jm Hubbard for supplying 11s with sollie critical biographic~hl
i s greatly enhanced by exploring the propenits of real data. Such exercises remove data. We also thartk Susanna Tadlock for coordinating the entirc project, Bob Ist11
the abstractness of many theories and enable students to appreciate the mahematics for designing what wc think is a beautiful-looking book, Iane Ellis tor co~npctcntl!
of physical chcmistry so thal (hey can describe nnd predict the physical behavior of dealing with matiy of the production detaila, Jotin Choi Cor crcati~elyh a~tdlinga ll
chemical systems. he artwork, Anrl McGuire for a very helpful copyrtliting of thc rni~nuscripta. nd otrr
Keeping in mind that our purpose is io teach the next gerlcritlon 01. chemists, publisher, Bruce Armbrurter, for encouraging us to wtitc our owrl hrlu\ and for Ibci~lg
the qua~lrities,u nits, and symhols used in this text are those presented in (he 1993 an exemplary publishcr and a good friend. Last, we thank o i ~wr ive\, Canlie atld D~aliz,
lntcrnational tJnion o l P ure and Applied Chcrnistry (IUPAC) publication, Qltunririps. both of whom are chcrnists, for being great collt.iigucs as well a< greal wivcs.
I/nir.~,u nd Sj~mbolsi n Phy~irzr/C hemi,l-rq. by Ian Mills et al. (Blackwell Scientitic
Puhlrcatiotjs, Oxforti). Our decirion to follow the 1UPAC' recornmendation5 means
t h ~s~olm e of thc syrnhols, units, and standdd slates presented in this h w k may differ
frt~mt hose used in the liieraturc and oldcr tcxthooks and may Lw utlfa~niliart o some
instrt~ctors.i n Fnmc irl\tances, we look some time ourselves to comc to grips with the
new nutalion and ullils. but ~hcreis . indccd, an underlying lugic 10 their use, and we
f o ~ ~tth~e def fort worthwl~ile.
MOLECULAR
THERMODYNAMICS
ertil rc\nh\ 111 thcrn~utlyr~;~n~icnsr )l h:lscd on ony atornlc or m~)lecul;~thre ory: thry
; I I ~i r l dcp~~du(Ir! l ~;i trl~l~3i1c1 dt ~lolecular~ nrjdelsT. he development of thermndynanl-
i c b ;~l{tngtl lcse lincs is cnllcd rloaricnl th~rmotlynnmirsT. his character oT classical
thcr~nodynamicsi s hoth a strength and a weakness. We can bc assured that classical
tl~crrnrdyr~atnrices ults will never need to be modified as our knowlcdge of atomic and
molccul;~r \ll.ucture itnprnves, hut classical thermodynatnics gives us o~llya limited
incight at thc n~ulr!cul;~lerv el. F I G U R E 1.1
With the develnpnient of atonlic and muiecular theorics in the late 1800s and early 1-he :~llrnvede lrclrt~riicc ncrglcs trl I: hyd~a~f:i,n
1900s. tlic~n~udynamicwsn s given a molecular interpretation, or a tnolecular has~s. nroul. 'l'heenergirsarc ~ I V C III> 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