WPC0 {fDpk)A;{XAa3톊"U\_8+c%bxz1d&V1Cx%z\k{'R<(5*|X (I wnl`%47 oXhOnVĀ ݽʋ A*,Icڗ陡DG܇e88`_aֲ]LQ\^wNh~/G-SnٽY1,&JK~HͫB.1 n5。a7;תU#71]sKPPW 6~Ob}xƻIod4yeW8h%ct@r(琝ޑ`Hܕ|eI9|5V%Ɉ g!eU^v``#!@U*Na % 0(UNw@+ 4k   m 1u 1 0-c 1 1 0w& 1 1* 1 bD 1V 1 0j 1 1 1 1 10 1 1N 1flanU> 1 1O 1bmd B| 0D AS0(9 Z6Times New Roman RegularX($9 Z6Times New Roman Regular E[PEEE1Pz73|xU##37=CIQYag1.a.i.(1)(a)(i)1)a) CEMU]emu}AutoList1(a)(a)(a)(a)(a)(a)(a)(a)(;3$2#  0  .3  0   CEMU]emu}AutoList2(i)(i)(a)(i)(i)(i)(i)(i)( CEMU]emu}AutoList3(a)(a)(a)(a)(a)(a)(a)(a)(O;$0  2#  a  .3  0` (#(#( CEMU]emu}AutoList4(a)(a)(a)(a)(a)(a)(a)(a)(W CEMU]emu}AutoList9(a)(a)(a)(a)(a)(a)(a)(a)(' CEMU]emu}AutoList6(a)(a)(a)(a)(a)(a)(a)(a)Page - -(7 CEMU]emu}AutoList7(a)(a)(a)(a)(a)(a)(a)(a)(hCEKQW]cioAutoList81.1.1.1.1.1.1.1.(b$0  0` (#(#2#   .3  0 ` (#` (#(wEEGOW_gowAutoList10(a)(a)(a)(a)(a)(a)(a)(a)(EEGOW_gowAutoList11(a)(a)(a)(a)(a)(a)(a)(a)(EEGOW_gowAutoList12(a)(a)(a)(a)(a)(a)(a)(a)(EEGOW_gowAutoList13(a)(a)(a)(a)(a)(a)(a)(a)(EEGOW_gowAutoList14(a)(a)(a)(a)(a)(a)(a)(a)(EEGOW_gowAutoList15(a)(a)(a)(a)(a)(a)(a)(a)(%EGOW_gowAutoList17(a)(a)(a)(a)(a)(a)(a)(a)(%EGOW_gowAutoList18(a)(a)(a)(a)(a)(a)(a)(a)hTABLE A\  `&Times New Roman(EEGOW_gowAutoList16(a)(a)(a)(a)(a)(a)(a)(a)(FEGOW_gowAutoList19(a)(a)(a)(a)(a)(a)(a)(a)(EEGOW_gowAutoList20(a)(a)(a)(a)(a)(a)(a)(a) XCsubpCsubv=[P+({ U}over{ V})subT]({ V}over{ T})subPXX#CpXXXXjCvXX1XX[XXPXXgXX(X-XXCV XXVUXXNG XXGVXXG)TXX]XX(<XeXX{V XXVVXXG XXGTXXi)P d(3$ !  YM -, dc !  _ XXXX8XXdd8R,QXX@ff"CHEMISTRY440/540   @ PHYSICALCHEMISTRY:FALL,2006.#XXQR,#MXXԈ H #XXMJ#XXName:__________________________  SocialSecurityNo.____________   #XX#&%XX#&%%&.#&%%&FINALEXAMINATION   h   November27,2006[6:457:00p.m.8:459:00p.m. ]   Answerallquestionsonthisexaminthespaceprovidedusinganonerasablepen.Inordertoreceivefullcreditforanyquestionyoumuststateallassumptions,showallequations,showallyourworkandsupplythepropersignandunitsforyouranswer.IfIcannotfollowyourlogic,thenIwillnotassignanypartialcredit.PLEASEBENEAT. 򀀀[Notethattheuniversalgasconstant,R,variesaccordingtothe X  unitsonewishestouse] #&%%&#&%%& F  Thisexamis17pageslongandisgradedoutofatotalpossiblescoreof200.[thereisabonusquestion (  onpage17whichstudentsdonothavetoattemptforfullcredit]#&%%&S#&%%&#XX%&F#&%XX   #XX%&#R,QXX #XXQR,#&%XXStudentsareadvisedtoproceeddirectlytoThefirstteeboxandmaybeattemptTheProloguelast.#XX%&R#R,QXX  > #XXQR,#&%XXSomepossiblyusefulconstants. ~ Speedoflight0 ` 0 ` (#` (#0 (# (#2.998x108ms1_(#(# _Planck_sconstant0 0 (# (#6.626x1034Js@(#(# Boltzmannconstant0 0 (# (#1.381x1023JK1!q(#(# Atomicmassunit0 0 (# (#1.6605x1027kgR(#(# AvogadroNumber0 0 (# (#6.022x1023mol13(#(# GasConstant0 ` 0 ` (#` (#0 (# (#0.08206Latmmol1K1;8.314Jmol1K1;0.08314Lbarmol1K1(#(# *w X!ddd Xdd Xdd X(#(#w,dd , dd ,<dd +   g  Number     Act     Score    One  M"  Prologue(Theputtinggreen)  M"!   M"" Two  ## Thefirstteebox(lickingoneschops)  $%   #& vThree  &h!' Thesignaturehole  &h!(  &h!) v Four  '"* Theturn(theBackNine)  '"+   '", Five  )S$- StrokeIndexOne  )S$.   )S$/ Six  x*%0 Replaceyourdivot!  x*%1   x*%2   d Epilogue/BonusPoints(Sand saves)#XX%&W#&%XX#&%%&o#&%%&  E   d Hole#19  K TotalScorecard(intheClubhouse)  j  j  #XX%&##XXXX# &%XX Question1;ThePrologue. 0  [ 40points ]\ (#(# L  (# L  3   "&%%& 32 (  a  )3  0    Prove,fromtheconceptchemicalpotential,freeenergies,andmolefractionsthatthemixingof J   twoidealgassesisalwaysaspontaneousprocess.#&%%"&##XX%&# p [20points]  3݌+ { (#(# Ќ  &%XX   `   % u     3    3"2 (  b  )3  0    Acontainerisdividedintotwoequalcompartmentsofsamevolume.Onecontains1.0mol  Argonandtheothercontains1.0molNeon;bothat250C.CalculatetheGibbsenergyofmixing  whenthepartitionisremovedandoneassumesidealbehavior.     x [10points]  3"M݌r(#(# Ќ     `     h     3    32 (  c  )3  0    CalculatetheentropychangewhenNeon,at250Cand1.225barpressureinacontainerof  volume3.50dm3isallowedtoexpandto4.25dm3andsimultaneouslyheatedto2180C.Assume  Neonisanidealgas.   h      p      x [10points]  3݌r(#(# Ќ  #XX%&# &%XX  :   3    3g2 (  d  )3  0    Calculatetheworkdonewhen200gofCaCO3(s)isdissolvedinexcesshydrochloricacidat  298.15Kandanexternalpressureof1.678bar.   p     [10points]  3g݌(#(# Ќ    Note:CaCO3(s)#XX%&0#&%XXԀ+2HCl(aq)CaCl2(aq)+2H2O(l)+CO2(g)    `  Question2;Thefirstteebox. 0 h [40points,4each] h(#h(# Provideshortdefinitionsordescriptionsand,whereneeded,theappropriateequationsaswellforthefollowing:L  (( L ;   ;0  2 (  a  )3  0` (#(#  _zeroth_Ԁlawofthermodynamics;2݌5` (#` (# Ќ   ;   ;'0  2 (  b  )3  0` (#(#  compressibilityfactor;'R݌n ` (#` (# Ќ   ;   ;!0  2 (  c  )3  0` (#(#  _Trouton_srule;!L݌W` (#` (# Ќ   ;   ;7 0  2 (  d  )3  0` (#(#  Fugacity;7 b ݌ ! ` (#` (# Ќ   !!  ;   ;P!0  2 (  e  )3  0` (#(#  Firstorder_Ehrenfest_Ԁtransition;P!{!݌` (#` (# Ќ   ;   ;v"0  2 (  f  )3  0` (#(#  Henrysand_Raoult_sLaws;v""݌ H ` (#` (# Ќ   ;   ;#0  2 (  g  )3  0` (#(#  Differencebetweenanidealgaseousmixtureandanidealsolutionmixture;##݌h` (#` (# Ќ   ;   ;$0  2 (  h  )3  0` (#(#  Excessenthalpyfunctionofmixing,HE#XT'X%&Iaw#&Ia%XXT';$$݌`!"` (#` (# Ќ   +&. Ї ;   ;6&0  2 (  i  )3  0` (#(#  Chemicalpotential;6&a&݌` (#` (# Ќ   ;   ;,'0  2 (  j  )3  0` (#(#  TheGibbs_Duhem_Ԁequation#XT'X%&Ia%#&Ia%XXT';,'W'݌H  ` (#` (# Ќ  Question3;AmenCorner.0  [20points] X(#(#  L %E(( L  3    3O)2E(  a  )3  0    DescribevanderWaalsloops.Underwhatconditionsaretheyobserved?Describetheuseof 0 theMaxwellConstruction.. h      p      x [10points]  3O)z)݌(#(# Ќ     `     h        (L$+ L wE((%L  3    3+2wE(  b  )3  0    GivetheVanderWaalsequationintermsofmolarvolumes.Analyzetheequationandexamine  regions(oftemperatureandpressure)wheretheequationapproachestheidealgasbehavior#XT'X%&Ia&(#&Ia%XXT'. @L"  @L"  @L"  @L"  @L"  @L"  @L"  @L"   Ѐ `     h      p      x [10_points]#XT'X%&IaZ-#&Ia%XXT' #XT'X%&Ia.#&Ia%XXT'_ 3+,݌d(#(# Ќ  #XT'X%&Ia /#&Ia%XXT'   Question4;StartoftheBackNine.  h [40points]   L 7 ((L  3    3027 (  a  )3  0    Theenthalpychangeforthefollowingreactionisdifficulttoexperimentallydeterminefrom  calorimetrictechniques: 300݌ (#(# Ќ     `  C(graphite)+2H2(g)CH4(g).0 p 0p(#p(#H0rxn=?8(#(# 0  Itcanbedetermined,however,indirectly,byusingtheenthalpiesofcombustionofC(graphite), ` H2(g)andCH4(g)whosevaluesarerespectively(inkJmol1):393.51,285.84and890.35. 8 Usingthesedata,determineH0rxn.   [20points]  (#(# L E((L     3    342E(  b  )3  0    Byasuitablediagramandrelevantequation(s),explainwhytheadditionofanonvolatilesolute  intoasolventwillresultwiththesolventboilingatahighertemperatureandmeltingatalowertemperature.Assumethesoluteisinsolubleinthesolid,frozensolvent.    x   [10points]  344݌`(#(# Ќ  #XT'X%&Ia/#&Ia%XXT'  3    3H72E(  c  )3  0    AssumeapuresolventboilsatT*andwithdissolvedsoluteB,itboilsatT.Provethat l approximately_/B_=_Hvap_/R[1/T*󀄀1/T];where_/B_ismolefractionofsolute. x [10points]  3H7s7݌ D(#(# Ќ  Question5;StrokeIndexOne.0 h [20points] h(#h(# L #E((L  3    3P:2E(  a  )3  0    Supposethat10.0molofC2H6(g)isconfinedto4.860dm3at270C.Predictthepressureexerted  bythisgasfromthe(a)perfectgasand(b)vanderWaalsequationofstate.Calculatethecompressionfactorsinboth(a)and(b). 3P:{:݌ (#(# Ќ    Forethane:a=5.562L2atmmol2;b=6.380x102Lmol1.#XT'X%&Ia7#&Ia%XXT' `   8 L E((#L #XT'X%&Ia<#&Ia%XXT'Question6;Replaceyourdivot!0 h [40points] h(#h(# L E((L #XT'X%&Ia`=#&Ia%XXT' #XT'X%&Iau>#L %((L  3   &Ia%XXT' 3?2%(  a  )3  0    Forrealgases,therelationshipbetweenCpand_Cv_isgivenby: 3?Q?݌`(#(# Ќ     `    `  W_()! `E  W0  Provethatthisrelationshipgivesyouasimpleandfamiliarrelationshipwhenappliedtoidealgases. `     h      p      x [10points] (#(#  #XT'X%&Ia2?#  L    3    3GB2%(  b  )3  0    &Ia%XXT'SupposeagasobeysthevanderWaalsequation,provethat 3GBrB݌(#(# Ќ     ` (_ U_/_ Vm_)T=a/Vm20 h 0h(#h(#0(#(#0p(#(#0p(#p(#0 (#(#0x (# (# [10points]#XT'X%&IaB# x(#x(#   d   3    3D2%(  c  )3  0    &Ia%XXT'AgasobeyingthevanderWaalsequationofstateundergoesareversibleisothermalchangeof  volumefromV1toV2.Obtaintheexpressionforwork,w.Bysubstitutinga=b=0;provethat  theexpressionsimplifiestoafamiliarone.   p      x [10points] 3DE݌t(#(# Ќ  #XT'X%&IaaE# 0   (#(#   <   3    3G2%(  d  )3  0    &Ia%XXT'Thedensityofwatervaporat327.6atmand776.4Kis133.2gdm3.Determinethemolar  volumeofwaterandthecompressionfactor,Z,fromthesedata.CalculateZfromthevanderWaalsequationwitha=5.536L2atmmol2;b=3.049x102Lmol1.   x [10points] #XT'X%&IaH# 3GG݌t(#(# Ќ   P  &Ia%XXT'BonusQuestion(neednotbeattemptedforfullcredit)0 p 0p(#p(#0 (#(#0x (# (#[10points]x(#x(#  L $F((L  3    36K2F(  a  )3  0    Twomolesofagasarecompressedisothermallyandreversiblyat300Kfromaninitialvolume  of10dm3toafinalvolumeof1dm3.IftheequationofstateofthegasisP(_Vm_󀄀b)=RT;withb ` =0.03dm3mol1.Calculatetheworkdoneonthesystem,_U_,_H_.