PHYSICALANDCHEMICALPROPERTIES1.17
TABLE1.3GroupContributionstoIdeal-GasHeatCapacity(Continued)
Coef?cients
Symbol
a
b×102
c×104
d×106
Copyrighted Material ?1.4572?1.3883
1.91471.5159
?0.1233?0.1069
0.0029850.002659
0.1219
1.2170
?0.0855
0.002122
Oxygen-containinggroups6.5128
?0.1347
2.8461
?0.0100
OHO
0.0414
?0.001623
0.0454
?0.002728
3.5184
0.9437
0.0614
?0.006978
1.0016
2.0763
?0.1636
0.004494
1.4055
3.4632
?0.2557
0.006886
2.7350
1.0751
0.0667
?0.009230
?3.7344
1.3727
?0.1265
0.003789
Nitrogen-containinggroups
4.5104
0.5461
CN0.0269
?0.003790
NCNH2
5.0860
0.3492
0.0259
?0.002436
4.1783
0.7378
0.0679
?0.007310
?1.2530?3.4677
2.19322.9433
?0.1604?0.2673
0.0042370.007828
2.44581.0898
0.34362.6401
0.0171
?0.0027190.004750
NO2
?0.1871
Aromatichydrocarbongroups
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1.18SECTIONONE
TABLE1.3GroupContributionstoIdeal-GasHeatCapacity(Continued)
Coef?cients
Symbola
b×102c×104d×106
CalculationProcedure
Copyrighted Material SHS
2.5597
1.3347
?0.1189
0.003820
4.2256
0.1127
?0.0026
?0.000072
4.0824
?0.03012.4735
0.0731
?0.006081
SO3H
6.9218
0.1776
?0.022445
Halogen-containinggroups1.43823.06602.76053.2651
0.34520.21220.47310.4901
FClBrI
?0.0106?0.0128?0.0455?0.0539
?0.0000340.0002760.0014200.001782
Contributionsduetoringformation(forcyclicsonly)
?3.5320?8.6550
?0.03001.07801.86090.7818
Three-memberedringFour-memberedringFive-memberedring:c-Pentanec-Pentene
Six-memberedring:c-Hexanec-Hexene
0.07470.0425
?0.005514?0.0002500.0021450.000591
?12.2850?6.8813
?0.1037?0.0345
?13.3923?8.0238
2.13922.2239
?0.0429?0.1915
?0.0018650.005473
ReprintedwithpermissionfromD.N.RihaniandL.K.Doraiswamy,Ind.Eng.Chem.Fund.4:17,1965.Copyright1965AmericanChemicalSociety.
Sulfur-containinggroups
1.Obtainthemolecularstructurefromahandbook,andlistthenumberandtypeofgroups.For2-methyl-1,3-butadiene,thestructureis
H2CCHCCH2
CH3
andthegroupsare
CH3and
Forn-methyl-2-pyrrolidone,thestructureis
Copyright ? 2004 The McGraw-Hill Companies Retrieved from: www.knovel.com
PHYSICALANDCHEMICALPROPERTIES1.19
andthegroupsare
Copyrighted Material anda5-membered(pentene)ring.
N
a
b×102
c×104
d×106
2-Methyl-1,3-butadiene:
CH3
111
0.60870.2773
2.14333.45803.8857
?0.0852?0.1918?0.2783
0.01135
?0.4173
??(N)(groupparameter)
0.4687
9.48700.7818
?0.5553?0.0345
0.02284
n-Methyl-2-pyrrolidone:
5-membered(pentene)ring
CH3CH2
1
?6.88130.60870.39451.0016
1311
2.14332.13632.07632.9433
?0.0852?0.1197?0.1636?0.2673
0.01135
?3.4677
??(N)(groupparameter)
?7.5552
14.3536
?0.9097
2.Sumupthegroupcontributionsforeachcompound.Obtainthevaluesofa,b,c,anddfromTable1.3,andsetoutthecalculationsinamartix:
0.0041300.007364
0.000591
0.0025960.0044940.007828
0.026859
3.Computetheideal-gasheatcapacityforeachcompound.Refertotheequationinthestatementoftheproblem.Now,T=527+273=800K.Then,for2-methyl-1,3-butadiene,
?2?42?63
C?p=0.4687+(9.4870×10)(800)+(?0.5553×10)(800)+(0.02284×10)(800)
=52.52cal/(g·mol)(K)[52.52Btu/(lb·mol)(?F)]
Andforn-methyl-2-pyrrolidone,
?2?42?63C?p=?7.5552+(14.3536×10)(800)+(?0.9097×10)(800)+(0.02686×10)(800)
=62.81cal/(g·mol)(K)[62.81Btu/(lb·mol)(?F)]
RelatedCalculations.TheRihani-Doraiswamymethodisapplicabletoalargevarietyofcom-pounds,includingheterocyclics;however,itisnotapplicabletoacetylenics.Itpredictstowithin2to3percentaccuracy.Accuracylevelsaresomewhatlesswhenpredictingattemperaturesbe-lowabout300K(80?F).GoodaccuracyisobtainableusingthemethodsofBenson[25]andofThinh[26].
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1.20SECTIONONE
1.9HEATCAPACITYOFREALGASES
CalculationProcedure
Copyrighted Material FIGURE1.4Isothermalpressurecorrectiontothemolarheatcapacityofgases.(PerryandChilton—ChemicalEngineers’Handbook,McGraw-Hill,1973.)
?3?62
C?p=2.247+(38.201×10)T?(11.049×10)T
CalculatetheheatcapacityCpofethanevaporat400K(260?F)and50atm(5065kPa).Also
estimatetheheat-capacityratioCp/Cvattheseconditions.Theideal-gasheatcapacityforethaneisgivenby
whereC?pisincal/(g·mol)(K),andTisinkelvins.Forethane,criticaltemperatureTc=305.4KandcriticalpressurePc=48.2atm.
1.ComputereducedtemperatureTrandreducedpressurePr.ThusTr=T/Tc=400/305.4=1.310,andPr=P/Pc=50/48.2=1.04.
2.Obtain?CpfromFig.1.4.Thus??Cp=Cp?C?p=3cal/(g·mol)(K)atTr=1.31andPr=1.04.
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