ECRE Sol Man Title-FM 5e(2016)

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Access Full Complete Solution Manual enclature AlwaysassignedI InfrequentlyassignedAA AlwaysassignonefromthegroupofS SeldomassignedalternatesG GraduatelevelO OftenassignedE.g.,AAP1- roblem AAP1- ‐2willalwaysbeassignedaswill AAP1- olvetheproblem. AAP1- isanexcellentproblem. AAP1- dtobeagreatmotivationforthismaterial. AAP1- tryinmolebalance.SP1- cessedfromtheWebHomePage(www.umich.edu/ erydayexample.Itisoftenassignedasanin- suallyomitted.AAP1- xample1- eactorsinchapter4.AAP1- forchemicalreactionengineeringproblems.IP1- s.AAP1- ems.S1- ‐1

nts-of-chemical-reaction-engineering-fogler/

onsforChapter1–MoleBalancesQ1- ‐1Individualizedsolution.Q1- ‐2Individualizedsolution.Q1- ‐3Individualizedsolution.Q1- ‐4(a)Individualizedsolution.Q1- rticularcompound.Q1- onofabatchreactorare:- ystem.- Wellmixed,nospatialvariationinsystemproperties- ConstantVolumeorconstantpressure.Q1- onofCSTR,are:- Steadystate.- actionratethroughoutthevessel.Q1- onofPFRare:- Steadystate.- Noradialvariationinpropertiesofthesystem.Q1- onofPBRare:- Steadystate.- Noradialvariationinpropertiesofthesystem.Q1- ‐5(e)Forareaction,A B - runittimeperunitvolume[ ]moles/(dm3.s). - ass(orarea)ofcatalyst[ ]moles/(time.massofcatalyst). unitmass(orarea)ofcatalyst[ ]moles/(time.masscatalyst).1- ‐1

nts-of-chemical-reaction-engineering-fogler/ - ssense,- ‐rAisindependentofthe‘extent’ofthesystem.Q1- ume.Applyinggeneralmolebalanceweget:dN jdt F j 0 F j r j dVNoaccumulationandnospatialvariationimplies0 Fj0 Fj rjVAlsorj ρbrj andW Vρbwhereρbisthebulkdensityofthebed. 0 (Fj0 Fj ) rj"ρbVHencetheaboveequationbecomesW Fj 0 Fj rj'WecanalsojustapplythegeneralmolebalanceasdN jdt ( Fj 0 Fj ) rj' (dW ,wegetthesameformasabove:W V rj'P1- ‐1(a)IndividualizedSolutionP1- ‐1(b)ThegeneralequationforaCSTRis:Fj 0 FjFA0 FA rA1- ‐2

istherateofafirstorderreactiongivenby:rA - ‐kCAGiven:CA 0.1CA0,k 0.23min- ‐1,v0 10dm3min- ‐1Substitutingintheaboveequationweget:V C A0 v 0 C A v 0kC A C A0 v 0 (1 0.1) (10dm3 / min)(0.9) 0.1kC A0(0.23min 1 )(0.1)V 391.3m3P1- ‐1(c)k 0.23min- ‐1Frommolebalance:Ratelaw:dN Adt rA rAk rA Vk CANAVCombine:dNAdt k NAatt 0 ,NAO 100molandt t ,NA (0.01)NAO t 1 N A0 ln k N A 1ln(100) min0.23t 20minP1- ‐2Individualizedsolution.1- ‐3

nts-of-chemical-reaction-engineering-fogler/P1- ‐3P1- ‐4GivenA 2*1010 ft 2TSTP 491.69RH 2000 ftV 4*1013 ft 3T 534.7 RPO 1atmR 0.7302atm ft 3lbmol RyA 0.02C 4*105carsFS COinSantaAnawindsv A 3000C S 2.04*10 10FA COemissionfromautosft 3percaratSTPhrP1- ‐4(a)Totalnumberoflbmolesgasinthesystem:PVN 0RTN 1atm (4 1013 ft 3 ) 1.025x1011lbmol"%3 0.73 atm. ft ' 534.69R lbmol.R '&#P1- ‐4(b)MolarflowrateofCOintoL.A.Basinbycars.FA y AFT y A v A CTFT %no.%of%carsSTP3000 ft 3 1lbmol 400000 carshr car 359 ft 3(SeeappendixB)FA 6.685x104lbmol/hrP1- ‐4(c)WindspeedthroughcorridorisU 15mphW 20milesThevolumetricflowrateinthecorridorisvO U.W.H (15x5280)(20x5280)(2000)ft3/hr 1.673x1013ft3/hr1- ‐4lbmolft 3

nts-of-chemical-reaction-engineering-fogler/P1- S : v0 C S 1.673x1013ft3/hr 2.04 10 10lbmol/ft3 3.412x103lbmol/hrP1- ‐4(e)RateofemissionofCObycars RateofCOinWind- ‐RateofremovalofCO dNCOdtdCFA FS voCco V co(V constant, Nco CcoV )dtP1- ‐4(f)t 0,Cco CcoOt dt V0t Cco CcoOdCcoFA FS voCcoV " FA FS voCcoO %'lnvo # FA FS voCco '&P1- ‐4(g)Timeforconcentrationtoreach8ppm.CCO0 2.04 10 8lbmol3,CCO lbmol2.04 10 84ft 3ftFrom(f),%V " F F v .Ct ln A S O CO0 ''vo # FA FS vO .CCO &" 6.7 104 lbmol 3.4 103 lbmol 1.673 10133 hrhr4 ftln ft 3 lbmollbmol1.673 10136.7 104 3.4 103 1.673 1013 hr #hrhr%ft 3lbmol ' 2.04 10 8hrft 3 ''ft 3 8 lbmol ' 0.51 10'hrft 3 &t 6.92hrP1- ‐4(h)(1)to 0tf 72hrsCco 2.00E- ‐10lbmol/ft3a 3.50E 04lbmol/hrv o 1.67E 12ft3/hrb 3.00E 04lbmol/hrFs 341.23lbmol/hrV 4.0E 13ft3! t dCa bsin# π & Fs voCco V codt" eenCcovs.t1- ‐5

nts-of-chemical-reaction-engineering-fogler/P1- ‐4(h)continuedSeePolymathprogramP1- ‐4- ‐h- riablesVariable initial value minimal valueT00C2.0E-102.0E-10v01.67E 121.67E 12a3.5E 043.5E 04b3.0E 043.0E 04F341.23341.23V4.0E 134.0E 13maximal value722.134E-081.67E 123.5E 043.0E 04341.234.0E 13final value721.877E-081.67E 123.5E 043.0E 04341.234.0E theuser[1]d(C)/d(t) (a b*sin(3.14*t/6) F- ‐v0*C)/VExplicitequationsasenteredbytheuser[1]v0 1.67*10 12[2]a 35000[3]b 30000[4]F 341.23[5]V 4*10 13! t dC(2)tf 48hrsFs 0a bsin# π & voCco V codt" eenCcovstSeePolymathprogramP1- ‐4- ‐h- riablesVariable initial value minimal valueT00C2.0E-102.0E-10v01.67E 121.67E 12a3.5E 043.5E 04b3.0E 043.0E 04F341.23341.23V4.0E 134.0E 13maximal value722.134E-081.67E 123.5E 043.0E 04341.234.0E 131- ‐6final value721.877E-081.67E 123.5E 043.0E 04341.234.0E 13

nts-of-chemical-reaction-engineering-fogler/P1- onsasenteredbytheuser[1]d(C)/d(t) (a b*sin(3.14*t/6)- ‐v0*C)/VExplicitequationsasenteredbytheuser[1]v0 1.67*10 12[2]a 35000[3]b 30000[4]V 4*10 13(3)Changinga ebaseline.Changingb ooth.Changingv0 tedsin- hincreasingcurve.P1- ‐5(a)–rA kwithk 0.05mol/hdm3CSTR:ThegeneralequationisF FV A0 A rAHereCA 0.01CA0,v0 10dm3/min,FA 5.0mol/hrAlsoweknowthatFA CAv0andFA0 CA0v0,CA0 FA0/v0 eget,C v C v(0.5)10 0.01(0.5)10V A0 0 A 0 k0.05 V 99dm3PFR:ThegeneralequationisdFAdV rA k ,NowFA CAv0andFA0 CA0v0 1- ‐7dC Av0dV k

atingtheaboveequationwegetCAv0k C A0dC A Vv dV V k0 (C A0 C A )0HenceV ateisconstantandindependentofconcentration.P1- ‐5(b)- ‐rA kCAwithk 0.0001s- ‐1CSTR:WehavealreadyderivedthatC v C vv C (1 0.01)V A0 0 A 0 0 A0kC A rAk 0.0001s- ‐1 0.0001x3600hr- ‐1 0.36hr- ‐1 V (10dm3 / hr)(0.5mol / dm3 )(0.99)3 1(0.36hr )(0.01*0.5mol / dm ) V 2750dm3PFR:FromabovewealreadyknowthatforaPFRdC Av0v0dVIntegratingkCA C A0 rA kC AdC ACAV dV 0v0Cln A0 Vk CAAgaink 0.0001s- ‐1 0.0001x3600hr- ‐1 0.36hr- ‐1SubstitutingthevaluesinaboveequationwegetV 127.9dm3P1- ‐5(c)- ‐rA kCA2withk 300dm3/mol.hrCSTR:v C (1 0.01)C v C vV A0 0 A 0 0 A0 rAkC 2ASubstitutingallthevalueswegetV (10dm3 / hr)(0.5mol / dm3 )(0.99)332(300dm / mol.hr)(0.01*0.5mol / dm ) V 660dm3PFR:dC Av0dV rA kC 2A1- ‐8

atingv0kCA C A0 V Vv 11) V dV 0 ( 2k C A C A0CA0dC A 10dm3 / hr11 ) 6.6dm330.01CC300dm / mol.hrA0A0(P1- ‐5(d)CA .001CA0t NA0 NAdN rAVConstantVolumeV V0t C A0 dC A CA rAZeroorder:.999C Ao1t "#C A0 0.001C A0 % 9.99h0.05kFirstorder:! 1 1 !C 1t ln## A0 && ln#& 69078s 19.19hk " C A % 0.0001 " .001 %Secondorder:11" 11 % 1 "1 %' t ' 6.66hk # C A C A0 '& 300 # 0.5 0.001 0.5 &P1- ‐6(a)Initialnumberofrabbits,x(0) 500Initialnumberoffoxes,y(0) 200Numberofdays 500dx k x k2 xy .(1)dt 1dy k3 xy k4 y .(2)dtGiven,k1 0.02day 1k2 0.00004 / (day foxes)k3 0.0004 / (day rabbits)k4 0.04day 1SeePolymathprogramP1- ‐6- ‐a.pol.1- ‐9

THResultsCalculatedvaluesoftheDEQvariablesVariable initial value minimal value maximal entialequationsasenteredbytheuser[1]d(x)/d(t) (k1*x)- ‐(k2*x*y)[2]d(y)/d(t) (k3*x*y)- ‐(k4*y)Explicitequationsasenteredbytheuser[1]k1 0.02[2]k2 0.00004[3]k3 0.0004[4]k4 0.04When,tfinal 800andk3 0.00004 /(day rabbits)1- ‐10final value5004.2199691117.629280.024.0E-054.0E-040.04

ngrabbitsvs.foxesP1- ‐6(b)P1- ‐7EnricoFermiProblemP1- ‐7(a)PopulationofChicago 4,000,000SizeofHouseholds 4NumberofHouseholds 1,000,000FractionofHouseholdsthatownapiano 1/5NumberofPianos 200,0001- ‐11

ofTunes/yearperPiano 1NumberofTunesNeededPerYear 200,000Tunesperday 2Tunesperyearpertuner 250!days 2 500/yr/tuneryrday200,000!tunes1 400Tunersyr500!tunes / yr / tunerP1- ce,theareaof1sliceofpizza 19.242inch2 hs,eats20000*2slices*4months*4weeks/month 4m2 7945m2ofpizzainthefallsemester.P1- 5days/year 27375days1L/day*27375days 27375LdrankinlifeBathtubdimensions:1m*0.7m*0.5m 0.35m3 350L/tubBathtubsdrunk 27375L*1tub/350L 78tubsP1- ‐7(d)JeanValjean,LesMisérables.P1- ‐8MoleBalance:F "FV" " A0 A rARateLaw: rA kC 2ACombine:F "FV" " A0 AkC 2AFA0 v0C A 3FA v0C A 3dm3 2molA 6molA. ssdm3dm3 0.1molA 0.3molA. ssdm3molsV" " 1900dm33dmmol tconcentration.(6 0.3)1- ‐12

1"1# SolutionsforChapter1–MoleBalances) Q171)Individualizedsolution.# Q172)Individualizedsolution. Q173)Individualizedsolution. Q174(a)Individualizedsolution. e# r