problems and solutions2

Chapter66.1.Carbondioxideisdiffusingthroughnitrogeninonedirectionatatmosphericpressureand0°C.ThemolefractionofCO2atpointAis0.2;atpointB,3maway,inthedirectionofdiffusion,itis0.02.DiffusivityDis0.144cm2/s.Thegasphaseasawholeisstationary;thatis,nitrogenisdiffusingatthesamerateasthecarbondioxide,butintheoppositedirection.(a)WhatisthemolalfluxofCO2,inkilogrammolespersquaremeterperhour?(b)Whatisthenetmassflux,inkilogramspersquaremeterperhour?(c)Atwhatspeed,inmeterspersecond,wouldanobserverhavetomovefromonepointtotheothersothatthenetmassflux,relativetohimorher,wouldbezero?(d)Atwhatspeedwouldtheobserverhavetomovesothat,relativetohimorher,thenitrogenisstationary?(e)Whatwouldbethemolalfluxofcarbondioxiderelativetotheobserverundercondition(d)?solution:(a)from(6.1-8)27308206.01RTPcccMBAfromequation(6.1-19)hmkmolyyzDcJNAAiMAA244/10388.102.02.027308206.03360010144.0(b)netmassfluxforcarbondioxide(molecularweight=44)massfluxofCO2=44×1.388×10-4kg/m2hfornitrogen(molecularweight=28)massfluxofN2=28×1.388×10-4kg/m2hsothenetmassfluxinthedirectionofCO2diffusionm=(44-28)×1.388×10-4=2.221×10-3kg/m2h(c)HereJA=NA=NB,sincethediffusionisequimolal.Theconcentrationatanypointdependsonpositionduetotheconcentrationprofileoftheequimolaldiffusion,sodoesvelocitybasedonequations(6.1-3a)and(6.1-3b).Toselecttwopoints,yA=0.2and0.02,respectively,tocalculatethepositionsofobserverforyA=0.2,CA=Cm×yA=00893.027308206.02.0fromequation(6.1-3a)410388.1AAAAuCNJthediffusingvelocityofA:01555.000893.010388.14AuforB:CB=Cm×(1-yA)=03571.027308206.02.01thediffusingvelocityofB:003887.003571.010388.14BABCJuletuoisthevelocityoftheobservermovinginthedirectionofCO2diffusion,thennetvelocity(uA-uo)givesamasstransferratemAequaltothatinoppositedirectionmBcorrespondingto(uB+uo)fromequations(6.1-4)and(6.1-5))(44oAAAAAuuCJMm)(28oBBABBuuCJMmformA=mB,andrearrangingtwoequationsabovegiveshmCCNCCCuuCuBAABABBAAo/00159.099988.039292.00022208.003571.02800893.0441610388.12844)2844(284428444atyA=0.2,ItissimilartocalculatinguoatthepointofyA=0.02(d)Whenthevelocityofobservermovingisequaltothatofnitrogendiffusing,thenitrogenisstationaryuo=m/h003887.003571.010388.14BABCJu(e)Whenthevelocityofobservermovingisequaltothatofnitrogendiffusing,themolalfluxofcarbondioxidediffusingisindicatedbyhkmoluuCuuCJAAoAAA/10736.1)003887.001555.0(00893.0)()(4BChapter77.1solution:ThedatafromthirdcolumninthetableareusedascalculatingMolefractionxofammoniainwater:01048.018100170.1170.1xmolarratioofammoniatowaterXinliquid01059.001048.0101048.01xxXmolarratioofammoniatoinertgas00796.08.03.1018.0pPpYtheresultsofcalculationarelistinthetablep/kPa00.40.81.21.62.02.433.324.236.679.28x00.005270.010480.015630.020740.02580.030790.040630.050280.073570.09574X00.005300.010590.015880.021180.02650.031770.042350.052940.079400.1059Y00.003960.007960.011980.016000.02010.024530.033870.043530.070400.1008ThedatainthetableareusedtoplotthemolefractionxversuspartialpressurepdiagramandmolarratioX-Ydiagram0.000.020.040.060.080.100246810p/kPax/molefractionB0.000.020.040.060.080.100.120.000.020.040.060.080.10Y/molarratioX/molarratioB7.3Vapor-pressuredataforamixtureofpentane(C5H12)andhexane(C6H14)aregivenbythetable.Calculatethevaporandliquidcompositioninequilibriumforthepentane-hexaneat13.3kpapressureonassumingthatthevaporofmixture虚线范围表示符合Herry’slaw虚线范围表示符合Herry’slawapproachesidealbehaviorandliquidfollowsRaoult’slow.t,K260.6265270275280285289PA,kPa13.317.321.926.534.542.548.9PB,kPa2.833.54.265.08.5311.213.3Solution:FromRaoult’slow（equations(7.1-4)and(7.1-5)）Andthetotalpressureofsystemisequaltosumofthepartialpressuresoftwosubstances)1(ABAABBAABAxPxPxPxPppPrearrangingequationaboveBABAPPPPx1andAAAAxPpyprearrangingequationabovegivesPxPyAAA2substitutingthedataforthetableintotheequations1and2givestheresultsinthefollowingtablet,K260.6265270275280285289PA,kPa13.317.321.926.534.542.548.9PB,kPa,2.833.54.265.08.5311.213.3x1.00.7100.5130.3860.1840.0670y1.00.9240.8450.7690.4770.21407.4Usingtheconditionsintheproblem7.3forthepentane-hexanemixture,doasfollows:(a)Calculatetherelativevolatility.(b)Usetherelativevolatilitytocalculatethevaporandliquidcompositioninequilibriumandcomparewiththeresultgivenbytheproblem7.3.Solution:(a)calculatethevalueofbyBAPPTheresultsaregiveninthetable:t,K260.6265270275280285289PA,kPa13.317.321.926.534.542.548.9PB,kPa,2.833.54.265.08.5311.213.3α4.704.945.145.34.043.793.68Averagerelativevolatility1(4.704.945.145.304.043.793.68)4.517mandequilibriumrelationwithrelativevolatilityforamixtureofpentane(C5H12)andhexane(C6H14)isexpressedbyxxxxy51.3151.4)1(1(b)Usingtheequationabovetocalculatethevaporandliquidcompositioninequilibriumandcomparewiththeresultgivenbytheproblem7.3.T,KαxyTheresultsofproblem7.3Thecalculatingresultbyusingmx260.62652702752802852894.511.00.7100.5130.3860.1840.06701.00.9240.8450.7690.4770.21401.00.9170.8260.7390.5040.24507.5BoilingPointandRaoult'sLaw.Forthesystembenzene–toluene,doasfollows,usingthedataf