Hindawi Publishing CorporationISRN Physical ChemistryVolume 2013 Article ID 804576 9 pageshttpdxdoiorg1011552013804576

Research ArticleExtension of LIR Equation of State to Alkylamines Using GroupContribution Method

Zahra Kalantar Hossein Nikoofard and Faezeh Javadi

School of Chemistry Shahrood University of Technology PO Box 3619995161 Shahrood Iran

Correspondence should be addressed to Zahra Kalantar zahrakalantaryahoocom

Received 31 December 2012 Accepted 3 February 2013

Academic Editors Y Kimura and H Reis

Copyright copy 2013 Zahra Kalantar et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this work the modified linear isotherm regularity (LIR) equation of state parameter table is extended in order to representvolumetric behaviour of primary alkylamines In addition the isothermal compressibility and thermal expansion coefficient ofthese compounds have been predicted To do so we consider each of primary alkylamine as a hypothetical mixture of methylmethylene and a primary amine functional group in which the interaction potential of each pair is assumed to be the averageeffective pair potential Then the LIR equation of state has been extended to such a hypothetical mixture Furthermore three basiccompounds namely propane 119899-butane and cyclohexane are used to obtain the contribution of methyl and methylene groups inthe EOS parameters and also other appropriate compounds are used to obtain the contribution of the primary amine functionalgroups such as 1-pentylamine for the contribution of minusCH

2NH2and 2-aminopentane for the contribution of ⟩CHNH

2groupsThe

calculated EOS parameters along with the modified EOS are then used to calculate the density and its derivatives for alkylaminesat different pressures and temperatures The obtained results for different properties are compared with the experimental values

1 Introduction

The thermodynamic studies are important for efficient designof chemical processes to develop correlation and predictionmethods applicable over wide temperature and pressureranges Among others volumetric properties such as densityand its derivatives are of great interest not only for industrialapplications but also for fundamental aspects These prop-erties can be obtained either experimentally or by thermo-dynamic modeling based on the equation of state (EOS)Since experimental measurements are lengthy and costly theamount of experimental works can be reduced if efficientthermodynamic models are used to calculate the propertiesat different conditions of pressure and temperature Howeverequations of state which are often used to predict thermody-namic properties require pure fluid parameters as inputsThevalues of such parameters are however not only fluid specificbut also temperature dependent

To develop an EOS which is predictive a group contri-bution method (GCM) can be used This method has strongtheoretical ties to statisticalmechanical theoryThemain ideaof GCM is to reduce all the interactions existing in the system

to those pertaining to the pairs of the functional groupsor segments from which the molecules are built There-fore properties andor EOS parameters of correspondingchemicals may be calculated through formulae accountingfor weighted contributions of the different groups presentin the molecules In the last 3 decades this method hasprovided a practical and powerful tool for predicting as wellas calculating the parameters of equations of state from thechemical composition and state of matter In 1974 Nittaet al published the first group contribution EOS [1] thatis based on the cell model and is only able to deal withsome pure compounds in liquid phase In 1975 the firstsuccessful and widely applied group contribution methodUNIFACmodel was published based on the lattice theory [2]The further development of the group contribution methodsproceeded through the generalization of the lattice theoryto describe the gas and vapor properties and the high-pressure vapor-liquid equilibria as well [3] Skjold-Joslashrgensendeveloped a group contribution equation of state (GC-EOS)by employing a Carnahan-Starling-van der Waals equationto calculate vapor-liquid equilibria of nonideal mixtures withlow to medium molecular weight compounds [4] Then

2 ISRN Physical Chemistry

Espinosa et al [5] extended the application of this modelto low-volatile high-molecular weight compounds using aunique set of parameters a satisfactory correlation andprediction of VLE and LLE in mixtures of supercriticalfluids with natural oils and derivatives could be achieved[6] Majeed and Wagner developed the parameters of themodified Flory-Huggins theory to account for the molecularsize difference [7] Georgeton and Teja developed a GC-EOSusing a modified form for the perturbed hard chain equationof state [8] Pults et al developed chain-of-rotator groupcontribution equation of state [9] Gros et al introduceda group contribution associating term to the original GC-EOS Helmholtz residual energy expression extending theapplication of the model (so-called GC Associating EOS) toalcohols water gases and their mixtures [10] Then GCA-EOS parameters table extended in order to represent phaseequilibria behavior of carboxylic acids alcohols water andgases mixtures [11] and aromatic compounds containing phe-nol aromatic acid and aromatic ether compounds [12] Alsoa few group contribution hole models and their numerousversions have been appeared [13ndash15]

Recently the extension of the linear isotherm regularityequation of state to long chain organic compounds such as 119899-alkanes primary secondary and tertiary alcohols ketonesand 1-carboxylic acids is reported via group contributionmethod [16 20]Thepresent paper is a fresh attempt to extendLIR equation of state to alkylamines and their mixtures andalso predict the parameters of equations of state using thegroup contribution method

2 Theory

21 Linear Isotherm Regularity Equation of State Using theLJ (12 6) potential for the average effective pair potential(AEPP) along with the pairwise additive approximation forthemolecular interactions in the dense fluids and consideringonly the nearest neighbor interactions linear isothermalregularity equation of state (LIR-EOS) have been derivedfrom the exact thermodynamic relations as [21]

(119885 minus 1) V2= 119860 + 119861120588

2 (1)

where119885 = 119901120588119877119879 is the compressibility factor 120588 = 1V is thenumber density and 119860 and 119861 are the temperature dependentparameters AEPP was considered to be the interactionbetween the nearest neighbor molecules to which all of thelonger range interactions are added and also the effect ofthe medium in the charge distributions of two neighboringmolecules was included [22] The temperature dependenciesof the LIR parameters were found as follows

119860 = 1198602minus

1198601

119877119879

119861 = 1198612+

1198611

119877119879

(2)

where 1198601and 119861

1are related to the attraction and repulsion

terms of the average effective pair potential and 1198602is related

to the nonideal thermal pressure

The LIRwas experimentally found to be hold for densitiesgreater than the Boyle density (120588

119861asymp 18120588

119862 where 120588

119862is

the critical density) and temperature less than twice theBoyle temperature the temperature at which the second virialcoefficient is zero According to the one-fluid approximationthe regularity holds for the dense fluid mixtures as well [23]

In our previous works we have showed that such linearityvanished for different organic compounds [16 20] Such abehavior is expected because the mathematical form of theAEPP function is assumed to be the LJ (12 6) and the poten-tial function which is more appropriate for the spherical-symmetrical molecules then nonspherical molecules such aschain organic compounds show deviation from the linearbehavior of the LIR Hence using the group contributionmethod the LIR may be modified for such fluids

22 Modified LIR Equation of State for Long Chain OrganicCompounds Using the GC concept each organic compoundwas considered as a hypothetical mixture of their carbonicgroups in which the interaction potential of each pair isassumed to be the average effective pair potential Thispotential includes both physical and chemical (bond) inter-actions Then according to the Van der Waals one-fluidapproximation the LIR-EOS would be appropriate for sucha mixture but the new EOS parameters depend on the groupcompositions in the mixture (the length of the chain in thiscase) as well as temperature Hence if the molar density ofthe organic compound at temperature119879 is 120588 the total densityfor the hypothetical fluid is equal to 119899120588 where 119899 is numberof carbonic groups of the molecule Therefore the LIR isreduced to

((119901119899120588119877119879) minus 1)

11989921205882

= 119860119898+ 11986111989811989921205882997904rArr

((119885119899) minus 1)

1205882

= 1198601015840+ 11986110158401205882

(3)

which we were referred to it as the modified linear isothermregularity (MLIR) [16 20] Like the LIR theMLIR was foundto be valid for dense fluids only for 120588 gt 120588

119861 119860119898and 119861

119898are

the MLIR parameters per each carbonic group and

1198601015840= 1198601198981198992

1198611015840= 1198611198981198994

(4)

For all studied organic compounds we found a betterlinearity for (119885119899 minus 1)V2 versus 1205882 than (119885 minus 1)V2 versus 1205882for each isotherm especially for the longer chains Also wefound that the values obtained for119860

119898and 119861

119898are linear with

respect to 1119879 just the same as those for the LIR parameters[16 20]

119860119898=

1198861

119877119879

+ 1198862

119861119898=

1198871

119877119879

+ 1198872

(5)

23 Carbonic Group Contributions in119860119898and 119861

119898Parameters

To predict the MLIR parameters (119860119898 119861119898) for the mentioned

ISRN Physical Chemistry 3

Table 1 Values of 1198861119877 1198862 1198871119877 and 119887

2for 8 basic compounds namely Propane 119899-Butane Cyclohexane 1-Pentanol 2-Pentanol 119905-BuOH

2-Pentanone and 1-Pentanoic acid taken from [16]

Basic compound (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 (119886

1119877) L2 molminus2 K 119886

2times 104 L2 molminus2

propane 3330 4677 minus0982 6057119899-butane 2830 1810 minus0911 6570cyclohexane 1006 1323 minus0532 024581-pentanol 3559 1605 minus1139 47592-pentanol 4914 minus3473 minus1582 2124119905-BuOH 3285 5264 minus1098 22892-pentanone 3549 minus0329 minus1207 106241-pentanoic acid 3860 minus00648 minus1191 8182

organic compounds using the group contribution methodeach of these fluids has been considered as a hypotheticalmixture of their carbonic groups namely methyl terminal

methylene middle methylene minusCH2OH ⟩CHOH minus

|

C|

OH

⟩C=O and minusCOOH groupsIf 11986011

and 11986111

are the contributions of methyl groupsin 119860119898and 119861

119898 and 119860

22and 119861

22are those for the terminal

methylene groups respectively the contributions of methyland terminalmethylene groups in119860

119898and119861

119898parameterswill

be obtained from two basic compounds namely propane and119899-butane from the following expressions

(119861119898)propane = (

2

3

radic11986111+

1

3

radic11986122)

2

(119861119898)119899-butane = (

2

4

radic11986111+

2

4

radic11986122)

2

(

119860119898

119861119898

)

propane= (

2

3

radic

11986011

11986111

+

1

3

radic

11986022

11986122

)

2

(

119860119898

119861119898

)

119899-butane= (

2

4

radic

11986011

11986111

+

2

4

radic

11986022

11986122

)

2

(6)

The unlike parameters are taken as the mean geometric ofthe like parameters that is 119861

12= radic119861

1111986122

and 1198601211986112=

radic(1198601111986111)(1198602211986122) Note that the 23 and 13 coefficients

in the former expressions are the fraction of carbonic groups(1) and (2) in propane respectively and 24 in the othersare for 119899-butane The contributions of a middle methylenegroup in 119860

119898and 119861

119898parameters are related to those of CH

2

in cyclohexane If 11986033

and 11986133

are the contributions of themiddle methylene groups to the 119860

119898and 119861

119898 then the values

of 119860119898and 119861

119898for cyclohexane are the same as 119860

33and 119861

33

for linear alkanes [20] Other appropriate compounds werealso used to obtain the contributions of the five functionalgroups to the MLIR-EOS parameters in the same approach1-pentanol for the contribution of minusCH

2OH (119860

44 11986144) 2-

pentanol for ⟩CHOH (11986055 11986155) 2-methyl-2-propanol (119905-

BuOH) for minus|

C|

OH (11986066 11986166) 2-pentanon for ⟩C=O

(11986077 11986177) and 1-pentanoic acid for minusCOOH (119860

88 11986188)

We may use the values for 1198861119877 1198862 1198871119877 and 119887

2for the basic

compounds given in Table 1 along with (5) to obtain values of119860119898and 119861

119898for them at any temperature [16]

Having the contributions of the groups from whichthe molecules are built in the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each of the compounds mentionedwere predicted using the following expressions

(119861119898) = (

8

sum

119894=1

119909119894radic119861119894119894)

2

(

119860119898

119861119898

) = (

8

sum

119894=1

119909119894radic

119860119894119894

119861119894119894

)

2

(7)

where

119909119894=

number of group 119894total number of groups (119899)

(8)

Then using the calculated 119860119898and 119861

119898parameters along with

(3) densities of these compounds and their binary mixturesat different pressures and temperatures were calculated

3 Results and Discussion

31 Extension of MLIR Equation of State to Primary Alky-lamines The main purpose in this section is to investigatethe accuracy of the MLIR-EOS for primary alkylaminesAccording to MLIR-EOS plot of (119885119899 minus 1)V2 must be linearagainst 1205882 for each isotherm of these dense fluids To do sowe may use the experimental 119901V119879 data for these compoundsto plot (119885119899 minus 1)V2 against 1205882 for each isotherm As shownin Figure 1 the linearity holds quite well for each isotherm ofthese fluids with the correlation coefficient 1198772 ge 09994 forall chains

The line for each isotherm given in Figure 1 for differentalkylamines were used to determine 1198601015840 (from the intercept)and 1198611015840 (from the slope) in order to calculate the parameters119860119898and 119861

119898for that isotherm using (4) Then the calculated

values for the parameters were plotted versus 1119879 to obtainthe values for 119886

1119877 119886

2 1198871119877 and 119887

2 These values and

4 ISRN Physical Chemistry

0005

minus0005

minus0010

minus0015

minus0020

60 65 70 75 80 85 90 95

0000

119879 = 29315K 1198772 = 09997119879 = 30315K 1198772 = 09994119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(a) 1-Pentylamine

0005

0000

minus0005

minus0010

minus0015

minus0020

minus0025

48 50 52 54 56 58 60 62 64 66 68 70

119879 = 29315K 1198772 = 09998119879 = 30315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(b) 1-Hexylamine

0005

0000

minus0005

minus0010

minus0015

minus0020

minus0025

minus0030

38 40 42 44 46 48 50 52 54 56

119879 = 29315K 1198772 = 09997119879 = 30315K 1198772 = 09995119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09997119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(c) 1-Heptylamine

0004

0002

0000

80 90 100 110 120 130 140

minus0002

minus0004

minus0006

minus0008

minus0010

minus0012

minus0014

119879 = 29315K 1198772 = 09995119879 = 30315K 1198772 = 09995119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09995

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09996119879 = 35315K 1198772 = 09997

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(d) 2-Aminobutane

65 70 80 85 90

0000

minus0002

minus0004

minus0006

minus0008

minus0010

minus0012

minus0014

minus0016

75

119879 = 29315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 33315K 1198772 = 09992119879 = 35315K 1198772 = 09998

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(e) 2-Aminopentane

36 38 40 42 44 46 48 50 52

0000

minus0005

minus0010

minus0015

minus0020

minus0025

minus0030

119879 = 29315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 33315K 1198772 = 09992119879 = 35315K 1198772 = 09998

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(f) 2-Aminoheptane

Figure 1 Continued

ISRN Physical Chemistry 5

36

001

000

minus001

minus002

minus003

minus004

30 32 34 38 40 42 44 46

119879= 29315K 1198772 = 09996119879= 30315K 1198772 = 09996119879= 31315K 1198772 = 09995119879= 32315K 1198772 = 09996

119879= 33315K 1198772 = 09996119879= 34315K 1198772 = 09995119879 = 35315K 1198772 = 09994

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(g) 2-Aminooctane

Figure 1 Plot of (119885119899 minus 1)V2 versus 1205882 for different alkylamines at given temperature

the correlation coefficients of (5) are given in Table 2 foreach alkylamine Having these values and using (5) thevalues of 119860

119898and 119861

119898for an alkylamine may be calculated

at any temperature Then having the calculated values forthe parameters and using (4) along with (3) density ofthe alkylamine can be calculated at different pressures andtemperatures

32 Prediction of MLIR Parameters for Alkylamines UsingGCM The next step is to predict MLIR parameters for alky-lamines using GCM At first we consider the 1-alkylaminesCompared to an 119899-alkane in a linear 1-alkylamine (H

3C minus

CH2minus (CH

2)119899minus4

minus CH2minus CH

2NH2) one methyl group is

replaced with a minusCH2NH2group Hence in 1-alkylamine

we consider minusCH2NH2as a new functional group and use

the values of 119860119898

and 119861119898

of 1-pentylamine to calculatethe contribution of minusCH

2NH2group (119860

99 11986199) from the

following expressions at temperature of interest

(119861119898)1-pentylamine

= (

1

5

radic11986111+

2

5

radic11986122+

1

5

radic11986133+

1

5

radic11986199)

2

(

119860119898

119861119898

)

1-pentylamine

= (

1

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

11986033

11986133

+

1

5

radic

11986099

11986199

)

2

(9)

where the mole fractions of the methyl terminal methylenemiddle methylene and minusCH

2NH2groups in 1-pentylamine

are 15 25 15 and 15 respectivelySimilarly in the primary alkylamines in which an minusNH

2

group is attached to a secondary carbon atom in alkyl groupwe consider ⟩CHNH

2as a new functional group and use

the values of 119860119898

and 119861119898

of 2-aminopentane to calculate

the contribution of ⟩CHNH2group (119860

1010 1198611010

) in theMLIR parameters at each temperature from the followingexpressions

(119861119898)2-aminopentane = (

2

5

radic11986111+

2

5

radic11986122+

1

5

radic1198611010)

2

(

119860119898

119861119898

)

2-aminopentane= (

2

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

1198601010

1198611010

)

2

(10)

where the mole fractions of the methyl terminal methyleneand ⟩CHNH

2groups in 2-aminopentane are 25 25 and

15 respectivelyWe may use the values for 119886

1119877 1198862 1198871119877 and 119887

2for the

basic compounds given in Table 2 along with (5) to obtainvalues for 119860

119898and 119861

119898at any temperature We calculated the

contributions of three carbonic groups and the alkylaminefunctional groups at different temperatures (30315 32315and 34315 K) Having the contributions of the constituentgroups to the MLIR parameters along with dependenciesof the LIR parameters to system composition the values of119860119898and 119861

119898for each alkylamine may be calculated using the

following expressions

(119861119898)alkylamine = (1199091radic11986111 + 1199092radic11986122 + 1199093radic11986133

+1199099radic11986199+ 11990910radic1198611010)

2

(

119860119898

119861119898

)

alkylamine= (119909

1radic

11986011

11986111

+ 1199092radic

11986022

11986122

+ 1199093radic

11986033

11986133

+1199099radic

11986099

11986199

+ 1199091010radic

1198601010

1198611010

)

2

(11)

6 ISRN Physical Chemistry

Table 2 The calculated values of 1198861119877 1198862 1198871119877 and 119887

2and the correlation coefficients of (5) for studied alkylamines

Fluids (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 R 2

1198861119877 L2 molminus2 K 119886

2times 104 L2 molminus2 R 2 References

1-Pentylamine 5075 0478 09991 minus1488 11992 09994 [17]1-Hexylamine 4307 0237 09989 minus1350 10334 09993 [17]1-Hepyylamine 3811 0077 09980 minus1257 9323 09987 [17]2-Aminobutane 6072 1951 09987 minus1253 16042 09986 [18]2-Aminopentane 4524 1550 09989 minus1346 9116 09991 [19]2-Aminoheptane 3728 0007 09991 minus1201 8808 09993 [19]2-Aminooctane 3357 0297 09995 minus1138 7492 09995 [18]

Table 3 AAD 119863max and bias of the calculated density for some alkylamines at given temperatures and for the given pressure range (Δ119901)using the calculated values of 119860

119898and 119861

119898parameters along with (3)

Fluid 119879 K Δp MPa AAD 119863max bias NP1-Butylamine 29815 01ndash339 0570 0965 0570 10

1-Hexylamine30315 01ndash140 0703 105 0703 1532315 01ndash140 0542 0861 0542 1534315 01ndash140 0424 0708 0424 15

1-Heptylamine30315 01ndash140 0636 0993 0636 1532315 01ndash140 0459 0677 0459 1534315 01ndash140 0388 0547 0388 15

2-Aminobutane30315 01ndash140 1452 1672 1452 1532315 01ndash140 1231 1430 1231 1534315 10ndash140 1091 1219 1091 14

2-Aminoheptane 29315 01ndash100 117 148 117 633315 01ndash100 0934 1688 0934 6

2-Aminooctane30315 01ndash140 134 164 134 1532315 01ndash140 117 158 117 1534315 01ndash140 0939 125 0939 15

where 119909119894could be obtained using (8) Then we may use

the values calculated for 119860119898

and 119861119898

parameters at thetemperature of interest along with (3) for a given alkylamineto obtain its density at different pressures Some of thecalculated results are given in Table 3

The statistical parameter namely the absolute averagepercent deviation (AAD) the maximum deviation (119863max)and the average deviation (bias) are defined as

ADD = 100119873

119873

sum

119894=1

1003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

119863Max = Max(1001003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

)

bias = 100119873

Nsum

119894=1

120588exp119894minus 120588

cal119894

120588exp119894

(12)

where 119873 is the number of experimental data and 120588exp119894

and120588cal119894are the experimental density values and those obtained

with (3) for studied fluids respectively Since the values ofAAD can characterize the fact that the calculated values aremore or less close to experimental data it can be claimedthat MLIR EOS can predict the density of these organic

compounds with good accuracy at any temperatures andpressures

33 Extension to Mixture of Alkylamines with PreviouslyStudied Organic Compounds The main purpose in thissection is to investigate the accuracy of the MLIR-EOS formixtures of the alkylamines with previously studied organiccompounds (119899-alkanes alcohols ketones and carboxylicacids) To do so we may use the experimental 119901V119879 datafor binary mixture of 119899-butylamine with 1-alkanols [24]These binary mixtures besides self-association exhibit verystrong cross association due to the strong hydrogen bondingbetween the hydroxyl and the amine groups This strongintermolecular association exhibits relatively large negativeexcess volumes [24] Again we have found that the linearityof (119885119899minus1)V2 against 1205882 for each isothermof a binarymixtureis as good as those for its pure compounds see Figure 2 Notethat the average value of 119899 for a mixture may be definedas

119899mix = sum

number of component119909119894119899119894 (13)

where 119909119894and 119899

119894refer to the mole fraction and number of

carbon atom of component 119894 in the mixture

ISRN Physical Chemistry 7

minus0005

minus0006

minus0007

minus0008

minus0009

minus0010

100 105 110 115 120 125 130

1-Butanol (1) + n-butylamine (2)

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

1199091 = 02011 1198772 = 099991199092 = 03957 1198772 = 099991199093 = 05002 1198772 = 09999

1199094 = 05986 1198772 = 099991199095 = 07975 1198772 = 09999

Figure 2 Plot of (119885119899minus1)V2 versus1205882 for binarymixture of 1-butanol(1) + 119899-butylamine (2) at 29815 K

Wemay use the group contributionmethod to predict theMLIR parameters formixturesThe contributions of differentgroups at the temperature of interest may be calculated fromthe same procedure explained in the previous sections (usingthe values for pure compounds) Having the contributions ofconstituent groups in the MLIR parameters along with thedependencies of the LIR parameters to system compositionthe MLIR parameters for a mixture may be calculated fromthe following expressions

(119861119898)mixture = (

10

sum

119895=1

119883119895radic119861119895119895)

2

(

119860119898

119861119898

)

mixture= (

10

sum

119895=1

119883119895radic

119860119895119895

119861119895119895

)

2

(14)

where 119860119895119895

and 119861119895119895

are the contribution of group 119895 in 119860119898

and 119861119898

and 119883119895is its mole fraction in the hypothetical

mixture Note that 119883119895may be calculated from the following

expression

119883119895=

total number of component

sum

119894=1

119909119894times

119899119895

119899119894

(15)

where 119909119894and 119899

119894are the mole fraction and number of carbon

atoms of component 119894 in the mixture and 119899119895is the number of

group 119895 in component 119894Using the calculated values of 119860

119898and 119861

119898parameters

along with (3) the density of a mixture at any pressuretemperature and mole fraction may be calculated We haveused this approach to calculate the density of binary mixtureof 119899-butylamine with ethanol 1-propanol and 1-butanol atdifferent pressures andmole fractions Some of the results aregiven in Table 4 An ispection of Table 4 indicates that thestrength of the intermolecular hydrogen bonding (between

Table 4 AAD and119863max of the calculated density for binarymixtureof different 1-alkanols (1) + 1-butylamine (2) in a pressure range from01 to 339MPa and different mole fractions using the calculatedvalues of 119860

119898and 119861

119898parameters along with (3) at 29815 K

Binary mixture 1199091

ADD 119863max

(a) Ethanol (1) + 1-butylamine (2)

01973 181 30604013 197 31906102 209 33207996 227 345

(b) 1-Propanol (1) + 1-butylamine (2)

02096 151 20904001 179 22605980 187 25507977 193 27102011 145 179

(c) 1-Butanol (1) + 1-butylamine (2)03957 161 19105986 179 21307975 185 227

the hydroxyl and the amine groups) is an important factorinfluencing the predicted density deviation of thesemixturesThe deviation is remarkable for the mixture with ethanoland decreases as the chain length of the alkanol moleculeincreases This result corresponds to heats of mixing study inthese systems Measured heats of mixing values at 29815 Kare minus2915 minus2870 and minus2705 Jsdotmolminus1 for the mixtures of 119899-butylamine with ethanol 1-propanol and 1-butanol respec-tively [24]

34 Calculation of Other Properties Having an accurate EOSthe MLIR for different chemicals we may expect to makeuse of it to calculate other properties such as isothermalcompressibility compressibility (120581

119879) and thermal expansion

coefficient (120572119875) via the GCM We may use the calculated

values of 119860119898and 119861

119898parameters along with an appropriate

derivative of pressure to obtain these properties at anythermodynamic state For instance the isothermal compress-ibility may be calculated using the following expression

120581119879=

1

119899120588119877 + 311989931205883119877119879119860119898+ 511989951205885119877119879119861119898

(16)

We have calculated 119860119898

and 119861119898

parameters for penty-lamine hexylamine heptylamine 2-aminobutane and 2-aminooctane at different temperatures 30315 32315 and34315 K as explained before along with (16) to calculate 120581

119879

for these compounds at different pressures see Table 5 Theaverage percentage error for 120581

119879was found to be less than 211

4 Conclusions

In this work the MLIR equation of state is extended toprimary alkylamines by group contribution method To doso the linearity of (119885119899 minus 1)V2 against 1205882 was investigated foraliphatic esters Experimental 119901V119879 data for different aliphaticesters were used to check the linearity of (119885119899minus1)V2 against 1205882for different isotherms (Figure 1) As shown in this figure the

8 ISRN Physical Chemistry

Table 5 AADand119863max of the calculated isothermal compressibilityof different alkylamines at given temperatures and in a pressurerange from 01 to 140MPa using the calculated values of 119860

119898and 119861

119898

parameters along with (16)

fluid 119879 K AAD 119863max

1-Hexylaminel30315 195 30232315 189 28634315 171 256

1-Heptylamine30315 187 28232315 166 25834315 159 231

2-Aminooctane30315 211 34532315 198 32634315 189 298

linearity holds quite well with the correlation coefficient1198772 ge09994 for these fluids over a wide range of temperaturesand pressuresThe temperature dependencies of the interceptand slope parameters of MLIR-EOS were also determined forthese fluids

In order to predict the MLIR parameters for primaryalkylamines via the group contribution method we hadto use appropriate compounds to obtain the contributionof primary alkylamine functional groups in the MLIRparameters Three basic compounds namely propane 119899-butane and cyclohexanewere used to obtain the contributionof methyl and methylene groups and 1-pentylamine and2-aminopentane for contribution of minusCH

2NH2 ⟩CHNH

2

groups in the MLIR parameters Having the contributionof constituent groups to the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each compound were calculatedUsing the calculated EOS parameters along with the MLIRthe densities of these series of compounds were calculatedat different pressures and temperatures with the averagepercentage error less less than 154 (Table 3) Furthermorewe have used the group contribution method to predict theMLIR parameters for mixtures (14) Using the calculatedvalues of119860

119898and119861

119898parameters along with (3) the density of

mixtures at any pressure temperature andmole fractionmaybe calculated (Table 4) Thus using the parameters of (5) forthe basic compounds we may calculate the density of pure ormixed fluids even for temperatures for which experimentaldata of basic compounds are not available

We may use the calculated values of 119860119898and 119861

119898parame-

ters along with an appropriate pressure derivative in orderto obtain other properties at any thermodynamic stateThe isothermal compressibility at different pressures wascalculated for different alkylamines and compared with theliterature values (Table 5)

Acknowledgment

Financial support for this work by the research affair ofShahrood University of Technology Shahrood Iran is grate-fully acknowledged

References

[1] T Nitta E A Turek R A Greenkorn and K C Chao ldquoGroupcontribution estimation of activity coefficients in nonidealliquidmixturesrdquoAIChE Journal vol 23 no 2 pp 144ndash160 1977

[2] A Fredenslund R L Jones and J M Prausnitz ldquoGroupcontribution estimation of activity coefficients in nonidealliquid mixturesrdquo AIChE Journal vol 21 no 6 pp 1086ndash10991975

[3] N A Smirnova and A I Victorov ldquoThermodynamic propertiesof pure fluids and solutions from the hole group-contributionmodelrdquo Fluid Phase Equilibria vol 34 no 2-3 pp 235ndash2631987

[4] S Skjold-Joslashrgensen ldquoGas solubility calculations II Applicationof a new group-contribution equation of staterdquo Fluid PhaseEquilibria vol 16 no 3 pp 317ndash351 1984

[5] S Espinosa GM Foco A Bermudez andT Fornari ldquoRevisionand extension of the group contribution equation of state tonew solvent groups and highermolecular weight alkanesrdquo FluidPhase Equilibria vol 172 no 2 pp 129ndash143 2000

[6] S Espinosa T Fornari S B Bottini and E A Brignole ldquoPhaseequilibria in mixtures of fatty oils and derivatives with nearcritical fluids using the GC-EOSmodelrdquo Journal of SupercriticalFluids vol 23 no 2 pp 91ndash102 2002

[7] A I Majeed and J Wagner ldquoParameters from group contri-butions equation and phase equilibria in light hydrocarbonsystemsrdquo Journal of American Chemical Society SymposiumSeries vol 300 pp 452ndash473 1986

[8] G K Georgeton and A S Teja ldquoA simple group contributionequation of state for fluid mixturesrdquo Chemical EngineeringScience vol 44 no 11 pp 2703ndash2710 1989

[9] J D Pults R A Greenkorn and K C Chao ldquoChain-of-rotatorsgroup contribution equation of staterdquo Chemical EngineeringScience vol 44 no 11 pp 2553ndash2564 1989

[10] H P Gros S B Bottini and E A Brignole ldquoHigh pressurephase equilibriummodeling of mixtures containing associatingcompounds and gasesrdquo Fluid Phase Equilibria vol 139 no 1-2pp 75ndash87 1997

[11] O Ferreira T Fornari E A Brignole and S B BottinildquoModeling of association effects in mixtures of carboxylicacids with associating and non-associating componentsrdquo LatinAmerican Applied Research vol 33 no 3 pp 307ndash312 2003

[12] S Espinosa S Dıaz and T Fornari ldquoExtension of the groupcontribution associating equation of state to mixtures contain-ing phenol aromatic acid and aromatic ether compoundsrdquoFluid Phase Equilibria vol 231 no 2 pp 197ndash210 2005

[13] I Ishizuka E Sarashina Y Arai and S Saito ldquoGroup contri-bution model based on the hole theoryrdquo Journal of ChemicalEngineering of Japan vol 13 no 2 pp 90ndash97 1980

[14] K P Yoo and C S Lee ldquoNew lattice-fluid equation of stateand its group contribution applications for predicting phaseequilibria of mixturesrdquo Fluid Phase Equilibria vol 117 no 1 pp48ndash54 1996

[15] W Wang X Liu C Zhong C H Twu and J E CoonldquoGroup contribution simplified hole theory equation of state forliquid polymers and solvents and their solutionsrdquo Fluid PhaseEquilibria vol 144 no 1-2 pp 23ndash36 1998

[16] G A Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain primary secondary and tertiary alco-hols ketones and 1-carboxylic acids by group contributionmethodrdquo Fluid Phase Equilibria vol 234 no 1-2 pp 11ndash21 2005

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

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CatalystsJournal of

ElectrochemistryInternational Journal of

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2 ISRN Physical Chemistry

Espinosa et al [5] extended the application of this modelto low-volatile high-molecular weight compounds using aunique set of parameters a satisfactory correlation andprediction of VLE and LLE in mixtures of supercriticalfluids with natural oils and derivatives could be achieved[6] Majeed and Wagner developed the parameters of themodified Flory-Huggins theory to account for the molecularsize difference [7] Georgeton and Teja developed a GC-EOSusing a modified form for the perturbed hard chain equationof state [8] Pults et al developed chain-of-rotator groupcontribution equation of state [9] Gros et al introduceda group contribution associating term to the original GC-EOS Helmholtz residual energy expression extending theapplication of the model (so-called GC Associating EOS) toalcohols water gases and their mixtures [10] Then GCA-EOS parameters table extended in order to represent phaseequilibria behavior of carboxylic acids alcohols water andgases mixtures [11] and aromatic compounds containing phe-nol aromatic acid and aromatic ether compounds [12] Alsoa few group contribution hole models and their numerousversions have been appeared [13ndash15]

Recently the extension of the linear isotherm regularityequation of state to long chain organic compounds such as 119899-alkanes primary secondary and tertiary alcohols ketonesand 1-carboxylic acids is reported via group contributionmethod [16 20]Thepresent paper is a fresh attempt to extendLIR equation of state to alkylamines and their mixtures andalso predict the parameters of equations of state using thegroup contribution method

2 Theory

21 Linear Isotherm Regularity Equation of State Using theLJ (12 6) potential for the average effective pair potential(AEPP) along with the pairwise additive approximation forthemolecular interactions in the dense fluids and consideringonly the nearest neighbor interactions linear isothermalregularity equation of state (LIR-EOS) have been derivedfrom the exact thermodynamic relations as [21]

(119885 minus 1) V2= 119860 + 119861120588

2 (1)

where119885 = 119901120588119877119879 is the compressibility factor 120588 = 1V is thenumber density and 119860 and 119861 are the temperature dependentparameters AEPP was considered to be the interactionbetween the nearest neighbor molecules to which all of thelonger range interactions are added and also the effect ofthe medium in the charge distributions of two neighboringmolecules was included [22] The temperature dependenciesof the LIR parameters were found as follows

119860 = 1198602minus

1198601

119877119879

119861 = 1198612+

1198611

119877119879

(2)

where 1198601and 119861

1are related to the attraction and repulsion

terms of the average effective pair potential and 1198602is related

to the nonideal thermal pressure

The LIRwas experimentally found to be hold for densitiesgreater than the Boyle density (120588

119861asymp 18120588

119862 where 120588

119862is

the critical density) and temperature less than twice theBoyle temperature the temperature at which the second virialcoefficient is zero According to the one-fluid approximationthe regularity holds for the dense fluid mixtures as well [23]

In our previous works we have showed that such linearityvanished for different organic compounds [16 20] Such abehavior is expected because the mathematical form of theAEPP function is assumed to be the LJ (12 6) and the poten-tial function which is more appropriate for the spherical-symmetrical molecules then nonspherical molecules such aschain organic compounds show deviation from the linearbehavior of the LIR Hence using the group contributionmethod the LIR may be modified for such fluids

22 Modified LIR Equation of State for Long Chain OrganicCompounds Using the GC concept each organic compoundwas considered as a hypothetical mixture of their carbonicgroups in which the interaction potential of each pair isassumed to be the average effective pair potential Thispotential includes both physical and chemical (bond) inter-actions Then according to the Van der Waals one-fluidapproximation the LIR-EOS would be appropriate for sucha mixture but the new EOS parameters depend on the groupcompositions in the mixture (the length of the chain in thiscase) as well as temperature Hence if the molar density ofthe organic compound at temperature119879 is 120588 the total densityfor the hypothetical fluid is equal to 119899120588 where 119899 is numberof carbonic groups of the molecule Therefore the LIR isreduced to

((119901119899120588119877119879) minus 1)

11989921205882

= 119860119898+ 11986111989811989921205882997904rArr

((119885119899) minus 1)

1205882

= 1198601015840+ 11986110158401205882

(3)

which we were referred to it as the modified linear isothermregularity (MLIR) [16 20] Like the LIR theMLIR was foundto be valid for dense fluids only for 120588 gt 120588

119861 119860119898and 119861

119898are

the MLIR parameters per each carbonic group and

1198601015840= 1198601198981198992

1198611015840= 1198611198981198994

(4)

For all studied organic compounds we found a betterlinearity for (119885119899 minus 1)V2 versus 1205882 than (119885 minus 1)V2 versus 1205882for each isotherm especially for the longer chains Also wefound that the values obtained for119860

119898and 119861

119898are linear with

respect to 1119879 just the same as those for the LIR parameters[16 20]

119860119898=

1198861

119877119879

+ 1198862

119861119898=

1198871

119877119879

+ 1198872

(5)

23 Carbonic Group Contributions in119860119898and 119861

119898Parameters

To predict the MLIR parameters (119860119898 119861119898) for the mentioned

ISRN Physical Chemistry 3

Table 1 Values of 1198861119877 1198862 1198871119877 and 119887

2for 8 basic compounds namely Propane 119899-Butane Cyclohexane 1-Pentanol 2-Pentanol 119905-BuOH

2-Pentanone and 1-Pentanoic acid taken from [16]

Basic compound (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 (119886

1119877) L2 molminus2 K 119886

2times 104 L2 molminus2

propane 3330 4677 minus0982 6057119899-butane 2830 1810 minus0911 6570cyclohexane 1006 1323 minus0532 024581-pentanol 3559 1605 minus1139 47592-pentanol 4914 minus3473 minus1582 2124119905-BuOH 3285 5264 minus1098 22892-pentanone 3549 minus0329 minus1207 106241-pentanoic acid 3860 minus00648 minus1191 8182

organic compounds using the group contribution methodeach of these fluids has been considered as a hypotheticalmixture of their carbonic groups namely methyl terminal

methylene middle methylene minusCH2OH ⟩CHOH minus

|

C|

OH

⟩C=O and minusCOOH groupsIf 11986011

and 11986111

are the contributions of methyl groupsin 119860119898and 119861

119898 and 119860

22and 119861

22are those for the terminal

methylene groups respectively the contributions of methyland terminalmethylene groups in119860

119898and119861

119898parameterswill

be obtained from two basic compounds namely propane and119899-butane from the following expressions

(119861119898)propane = (

2

3

radic11986111+

1

3

radic11986122)

2

(119861119898)119899-butane = (

2

4

radic11986111+

2

4

radic11986122)

2

(

119860119898

119861119898

)

propane= (

2

3

radic

11986011

11986111

+

1

3

radic

11986022

11986122

)

2

(

119860119898

119861119898

)

119899-butane= (

2

4

radic

11986011

11986111

+

2

4

radic

11986022

11986122

)

2

(6)

The unlike parameters are taken as the mean geometric ofthe like parameters that is 119861

12= radic119861

1111986122

and 1198601211986112=

radic(1198601111986111)(1198602211986122) Note that the 23 and 13 coefficients

in the former expressions are the fraction of carbonic groups(1) and (2) in propane respectively and 24 in the othersare for 119899-butane The contributions of a middle methylenegroup in 119860

119898and 119861

119898parameters are related to those of CH

2

in cyclohexane If 11986033

and 11986133

are the contributions of themiddle methylene groups to the 119860

119898and 119861

119898 then the values

of 119860119898and 119861

119898for cyclohexane are the same as 119860

33and 119861

33

for linear alkanes [20] Other appropriate compounds werealso used to obtain the contributions of the five functionalgroups to the MLIR-EOS parameters in the same approach1-pentanol for the contribution of minusCH

2OH (119860

44 11986144) 2-

pentanol for ⟩CHOH (11986055 11986155) 2-methyl-2-propanol (119905-

BuOH) for minus|

C|

OH (11986066 11986166) 2-pentanon for ⟩C=O

(11986077 11986177) and 1-pentanoic acid for minusCOOH (119860

88 11986188)

We may use the values for 1198861119877 1198862 1198871119877 and 119887

2for the basic

compounds given in Table 1 along with (5) to obtain values of119860119898and 119861

119898for them at any temperature [16]

Having the contributions of the groups from whichthe molecules are built in the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each of the compounds mentionedwere predicted using the following expressions

(119861119898) = (

8

sum

119894=1

119909119894radic119861119894119894)

2

(

119860119898

119861119898

) = (

8

sum

119894=1

119909119894radic

119860119894119894

119861119894119894

)

2

(7)

where

119909119894=

number of group 119894total number of groups (119899)

(8)

Then using the calculated 119860119898and 119861

119898parameters along with

(3) densities of these compounds and their binary mixturesat different pressures and temperatures were calculated

3 Results and Discussion

31 Extension of MLIR Equation of State to Primary Alky-lamines The main purpose in this section is to investigatethe accuracy of the MLIR-EOS for primary alkylaminesAccording to MLIR-EOS plot of (119885119899 minus 1)V2 must be linearagainst 1205882 for each isotherm of these dense fluids To do sowe may use the experimental 119901V119879 data for these compoundsto plot (119885119899 minus 1)V2 against 1205882 for each isotherm As shownin Figure 1 the linearity holds quite well for each isotherm ofthese fluids with the correlation coefficient 1198772 ge 09994 forall chains

The line for each isotherm given in Figure 1 for differentalkylamines were used to determine 1198601015840 (from the intercept)and 1198611015840 (from the slope) in order to calculate the parameters119860119898and 119861

119898for that isotherm using (4) Then the calculated

values for the parameters were plotted versus 1119879 to obtainthe values for 119886

1119877 119886

2 1198871119877 and 119887

2 These values and

4 ISRN Physical Chemistry

0005

minus0005

minus0010

minus0015

minus0020

60 65 70 75 80 85 90 95

0000

119879 = 29315K 1198772 = 09997119879 = 30315K 1198772 = 09994119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(a) 1-Pentylamine

0005

0000

minus0005

minus0010

minus0015

minus0020

minus0025

48 50 52 54 56 58 60 62 64 66 68 70

119879 = 29315K 1198772 = 09998119879 = 30315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(b) 1-Hexylamine

0005

0000

minus0005

minus0010

minus0015

minus0020

minus0025

minus0030

38 40 42 44 46 48 50 52 54 56

119879 = 29315K 1198772 = 09997119879 = 30315K 1198772 = 09995119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09997119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(c) 1-Heptylamine

0004

0002

0000

80 90 100 110 120 130 140

minus0002

minus0004

minus0006

minus0008

minus0010

minus0012

minus0014

119879 = 29315K 1198772 = 09995119879 = 30315K 1198772 = 09995119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09995

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09996119879 = 35315K 1198772 = 09997

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(d) 2-Aminobutane

65 70 80 85 90

0000

minus0002

minus0004

minus0006

minus0008

minus0010

minus0012

minus0014

minus0016

75

119879 = 29315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 33315K 1198772 = 09992119879 = 35315K 1198772 = 09998

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(e) 2-Aminopentane

36 38 40 42 44 46 48 50 52

0000

minus0005

minus0010

minus0015

minus0020

minus0025

minus0030

119879 = 29315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 33315K 1198772 = 09992119879 = 35315K 1198772 = 09998

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(f) 2-Aminoheptane

Figure 1 Continued

ISRN Physical Chemistry 5

36

001

000

minus001

minus002

minus003

minus004

30 32 34 38 40 42 44 46

119879= 29315K 1198772 = 09996119879= 30315K 1198772 = 09996119879= 31315K 1198772 = 09995119879= 32315K 1198772 = 09996

119879= 33315K 1198772 = 09996119879= 34315K 1198772 = 09995119879 = 35315K 1198772 = 09994

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(g) 2-Aminooctane

Figure 1 Plot of (119885119899 minus 1)V2 versus 1205882 for different alkylamines at given temperature

the correlation coefficients of (5) are given in Table 2 foreach alkylamine Having these values and using (5) thevalues of 119860

119898and 119861

119898for an alkylamine may be calculated

at any temperature Then having the calculated values forthe parameters and using (4) along with (3) density ofthe alkylamine can be calculated at different pressures andtemperatures

32 Prediction of MLIR Parameters for Alkylamines UsingGCM The next step is to predict MLIR parameters for alky-lamines using GCM At first we consider the 1-alkylaminesCompared to an 119899-alkane in a linear 1-alkylamine (H

3C minus

CH2minus (CH

2)119899minus4

minus CH2minus CH

2NH2) one methyl group is

replaced with a minusCH2NH2group Hence in 1-alkylamine

we consider minusCH2NH2as a new functional group and use

the values of 119860119898

and 119861119898

of 1-pentylamine to calculatethe contribution of minusCH

2NH2group (119860

99 11986199) from the

following expressions at temperature of interest

(119861119898)1-pentylamine

= (

1

5

radic11986111+

2

5

radic11986122+

1

5

radic11986133+

1

5

radic11986199)

2

(

119860119898

119861119898

)

1-pentylamine

= (

1

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

11986033

11986133

+

1

5

radic

11986099

11986199

)

2

(9)

where the mole fractions of the methyl terminal methylenemiddle methylene and minusCH

2NH2groups in 1-pentylamine

are 15 25 15 and 15 respectivelySimilarly in the primary alkylamines in which an minusNH

2

group is attached to a secondary carbon atom in alkyl groupwe consider ⟩CHNH

2as a new functional group and use

the values of 119860119898

and 119861119898

of 2-aminopentane to calculate

the contribution of ⟩CHNH2group (119860

1010 1198611010

) in theMLIR parameters at each temperature from the followingexpressions

(119861119898)2-aminopentane = (

2

5

radic11986111+

2

5

radic11986122+

1

5

radic1198611010)

2

(

119860119898

119861119898

)

2-aminopentane= (

2

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

1198601010

1198611010

)

2

(10)

where the mole fractions of the methyl terminal methyleneand ⟩CHNH

2groups in 2-aminopentane are 25 25 and

15 respectivelyWe may use the values for 119886

1119877 1198862 1198871119877 and 119887

2for the

basic compounds given in Table 2 along with (5) to obtainvalues for 119860

119898and 119861

119898at any temperature We calculated the

contributions of three carbonic groups and the alkylaminefunctional groups at different temperatures (30315 32315and 34315 K) Having the contributions of the constituentgroups to the MLIR parameters along with dependenciesof the LIR parameters to system composition the values of119860119898and 119861

119898for each alkylamine may be calculated using the

following expressions

(119861119898)alkylamine = (1199091radic11986111 + 1199092radic11986122 + 1199093radic11986133

+1199099radic11986199+ 11990910radic1198611010)

2

(

119860119898

119861119898

)

alkylamine= (119909

1radic

11986011

11986111

+ 1199092radic

11986022

11986122

+ 1199093radic

11986033

11986133

+1199099radic

11986099

11986199

+ 1199091010radic

1198601010

1198611010

)

2

(11)

6 ISRN Physical Chemistry

Table 2 The calculated values of 1198861119877 1198862 1198871119877 and 119887

2and the correlation coefficients of (5) for studied alkylamines

Fluids (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 R 2

1198861119877 L2 molminus2 K 119886

2times 104 L2 molminus2 R 2 References

1-Pentylamine 5075 0478 09991 minus1488 11992 09994 [17]1-Hexylamine 4307 0237 09989 minus1350 10334 09993 [17]1-Hepyylamine 3811 0077 09980 minus1257 9323 09987 [17]2-Aminobutane 6072 1951 09987 minus1253 16042 09986 [18]2-Aminopentane 4524 1550 09989 minus1346 9116 09991 [19]2-Aminoheptane 3728 0007 09991 minus1201 8808 09993 [19]2-Aminooctane 3357 0297 09995 minus1138 7492 09995 [18]

Table 3 AAD 119863max and bias of the calculated density for some alkylamines at given temperatures and for the given pressure range (Δ119901)using the calculated values of 119860

119898and 119861

119898parameters along with (3)

Fluid 119879 K Δp MPa AAD 119863max bias NP1-Butylamine 29815 01ndash339 0570 0965 0570 10

1-Hexylamine30315 01ndash140 0703 105 0703 1532315 01ndash140 0542 0861 0542 1534315 01ndash140 0424 0708 0424 15

1-Heptylamine30315 01ndash140 0636 0993 0636 1532315 01ndash140 0459 0677 0459 1534315 01ndash140 0388 0547 0388 15

2-Aminobutane30315 01ndash140 1452 1672 1452 1532315 01ndash140 1231 1430 1231 1534315 10ndash140 1091 1219 1091 14

2-Aminoheptane 29315 01ndash100 117 148 117 633315 01ndash100 0934 1688 0934 6

2-Aminooctane30315 01ndash140 134 164 134 1532315 01ndash140 117 158 117 1534315 01ndash140 0939 125 0939 15

where 119909119894could be obtained using (8) Then we may use

the values calculated for 119860119898

and 119861119898

parameters at thetemperature of interest along with (3) for a given alkylamineto obtain its density at different pressures Some of thecalculated results are given in Table 3

The statistical parameter namely the absolute averagepercent deviation (AAD) the maximum deviation (119863max)and the average deviation (bias) are defined as

ADD = 100119873

119873

sum

119894=1

1003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

119863Max = Max(1001003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

)

bias = 100119873

Nsum

119894=1

120588exp119894minus 120588

cal119894

120588exp119894

(12)

where 119873 is the number of experimental data and 120588exp119894

and120588cal119894are the experimental density values and those obtained

with (3) for studied fluids respectively Since the values ofAAD can characterize the fact that the calculated values aremore or less close to experimental data it can be claimedthat MLIR EOS can predict the density of these organic

compounds with good accuracy at any temperatures andpressures

33 Extension to Mixture of Alkylamines with PreviouslyStudied Organic Compounds The main purpose in thissection is to investigate the accuracy of the MLIR-EOS formixtures of the alkylamines with previously studied organiccompounds (119899-alkanes alcohols ketones and carboxylicacids) To do so we may use the experimental 119901V119879 datafor binary mixture of 119899-butylamine with 1-alkanols [24]These binary mixtures besides self-association exhibit verystrong cross association due to the strong hydrogen bondingbetween the hydroxyl and the amine groups This strongintermolecular association exhibits relatively large negativeexcess volumes [24] Again we have found that the linearityof (119885119899minus1)V2 against 1205882 for each isothermof a binarymixtureis as good as those for its pure compounds see Figure 2 Notethat the average value of 119899 for a mixture may be definedas

119899mix = sum

number of component119909119894119899119894 (13)

where 119909119894and 119899

119894refer to the mole fraction and number of

carbon atom of component 119894 in the mixture

ISRN Physical Chemistry 7

minus0005

minus0006

minus0007

minus0008

minus0009

minus0010

100 105 110 115 120 125 130

1-Butanol (1) + n-butylamine (2)

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

1199091 = 02011 1198772 = 099991199092 = 03957 1198772 = 099991199093 = 05002 1198772 = 09999

1199094 = 05986 1198772 = 099991199095 = 07975 1198772 = 09999

Figure 2 Plot of (119885119899minus1)V2 versus1205882 for binarymixture of 1-butanol(1) + 119899-butylamine (2) at 29815 K

Wemay use the group contributionmethod to predict theMLIR parameters formixturesThe contributions of differentgroups at the temperature of interest may be calculated fromthe same procedure explained in the previous sections (usingthe values for pure compounds) Having the contributions ofconstituent groups in the MLIR parameters along with thedependencies of the LIR parameters to system compositionthe MLIR parameters for a mixture may be calculated fromthe following expressions

(119861119898)mixture = (

10

sum

119895=1

119883119895radic119861119895119895)

2

(

119860119898

119861119898

)

mixture= (

10

sum

119895=1

119883119895radic

119860119895119895

119861119895119895

)

2

(14)

where 119860119895119895

and 119861119895119895

are the contribution of group 119895 in 119860119898

and 119861119898

and 119883119895is its mole fraction in the hypothetical

mixture Note that 119883119895may be calculated from the following

expression

119883119895=

total number of component

sum

119894=1

119909119894times

119899119895

119899119894

(15)

where 119909119894and 119899

119894are the mole fraction and number of carbon

atoms of component 119894 in the mixture and 119899119895is the number of

group 119895 in component 119894Using the calculated values of 119860

119898and 119861

119898parameters

along with (3) the density of a mixture at any pressuretemperature and mole fraction may be calculated We haveused this approach to calculate the density of binary mixtureof 119899-butylamine with ethanol 1-propanol and 1-butanol atdifferent pressures andmole fractions Some of the results aregiven in Table 4 An ispection of Table 4 indicates that thestrength of the intermolecular hydrogen bonding (between

Table 4 AAD and119863max of the calculated density for binarymixtureof different 1-alkanols (1) + 1-butylamine (2) in a pressure range from01 to 339MPa and different mole fractions using the calculatedvalues of 119860

119898and 119861

119898parameters along with (3) at 29815 K

Binary mixture 1199091

ADD 119863max

(a) Ethanol (1) + 1-butylamine (2)

01973 181 30604013 197 31906102 209 33207996 227 345

(b) 1-Propanol (1) + 1-butylamine (2)

02096 151 20904001 179 22605980 187 25507977 193 27102011 145 179

(c) 1-Butanol (1) + 1-butylamine (2)03957 161 19105986 179 21307975 185 227

the hydroxyl and the amine groups) is an important factorinfluencing the predicted density deviation of thesemixturesThe deviation is remarkable for the mixture with ethanoland decreases as the chain length of the alkanol moleculeincreases This result corresponds to heats of mixing study inthese systems Measured heats of mixing values at 29815 Kare minus2915 minus2870 and minus2705 Jsdotmolminus1 for the mixtures of 119899-butylamine with ethanol 1-propanol and 1-butanol respec-tively [24]

34 Calculation of Other Properties Having an accurate EOSthe MLIR for different chemicals we may expect to makeuse of it to calculate other properties such as isothermalcompressibility compressibility (120581

119879) and thermal expansion

coefficient (120572119875) via the GCM We may use the calculated

values of 119860119898and 119861

119898parameters along with an appropriate

derivative of pressure to obtain these properties at anythermodynamic state For instance the isothermal compress-ibility may be calculated using the following expression

120581119879=

1

119899120588119877 + 311989931205883119877119879119860119898+ 511989951205885119877119879119861119898

(16)

We have calculated 119860119898

and 119861119898

parameters for penty-lamine hexylamine heptylamine 2-aminobutane and 2-aminooctane at different temperatures 30315 32315 and34315 K as explained before along with (16) to calculate 120581

119879

for these compounds at different pressures see Table 5 Theaverage percentage error for 120581

119879was found to be less than 211

4 Conclusions

In this work the MLIR equation of state is extended toprimary alkylamines by group contribution method To doso the linearity of (119885119899 minus 1)V2 against 1205882 was investigated foraliphatic esters Experimental 119901V119879 data for different aliphaticesters were used to check the linearity of (119885119899minus1)V2 against 1205882for different isotherms (Figure 1) As shown in this figure the

8 ISRN Physical Chemistry

Table 5 AADand119863max of the calculated isothermal compressibilityof different alkylamines at given temperatures and in a pressurerange from 01 to 140MPa using the calculated values of 119860

119898and 119861

119898

parameters along with (16)

fluid 119879 K AAD 119863max

1-Hexylaminel30315 195 30232315 189 28634315 171 256

1-Heptylamine30315 187 28232315 166 25834315 159 231

2-Aminooctane30315 211 34532315 198 32634315 189 298

linearity holds quite well with the correlation coefficient1198772 ge09994 for these fluids over a wide range of temperaturesand pressuresThe temperature dependencies of the interceptand slope parameters of MLIR-EOS were also determined forthese fluids

In order to predict the MLIR parameters for primaryalkylamines via the group contribution method we hadto use appropriate compounds to obtain the contributionof primary alkylamine functional groups in the MLIRparameters Three basic compounds namely propane 119899-butane and cyclohexanewere used to obtain the contributionof methyl and methylene groups and 1-pentylamine and2-aminopentane for contribution of minusCH

2NH2 ⟩CHNH

2

groups in the MLIR parameters Having the contributionof constituent groups to the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each compound were calculatedUsing the calculated EOS parameters along with the MLIRthe densities of these series of compounds were calculatedat different pressures and temperatures with the averagepercentage error less less than 154 (Table 3) Furthermorewe have used the group contribution method to predict theMLIR parameters for mixtures (14) Using the calculatedvalues of119860

119898and119861

119898parameters along with (3) the density of

mixtures at any pressure temperature andmole fractionmaybe calculated (Table 4) Thus using the parameters of (5) forthe basic compounds we may calculate the density of pure ormixed fluids even for temperatures for which experimentaldata of basic compounds are not available

We may use the calculated values of 119860119898and 119861

119898parame-

ters along with an appropriate pressure derivative in orderto obtain other properties at any thermodynamic stateThe isothermal compressibility at different pressures wascalculated for different alkylamines and compared with theliterature values (Table 5)

Acknowledgment

Financial support for this work by the research affair ofShahrood University of Technology Shahrood Iran is grate-fully acknowledged

References

[1] T Nitta E A Turek R A Greenkorn and K C Chao ldquoGroupcontribution estimation of activity coefficients in nonidealliquidmixturesrdquoAIChE Journal vol 23 no 2 pp 144ndash160 1977

[2] A Fredenslund R L Jones and J M Prausnitz ldquoGroupcontribution estimation of activity coefficients in nonidealliquid mixturesrdquo AIChE Journal vol 21 no 6 pp 1086ndash10991975

[3] N A Smirnova and A I Victorov ldquoThermodynamic propertiesof pure fluids and solutions from the hole group-contributionmodelrdquo Fluid Phase Equilibria vol 34 no 2-3 pp 235ndash2631987

[4] S Skjold-Joslashrgensen ldquoGas solubility calculations II Applicationof a new group-contribution equation of staterdquo Fluid PhaseEquilibria vol 16 no 3 pp 317ndash351 1984

[5] S Espinosa GM Foco A Bermudez andT Fornari ldquoRevisionand extension of the group contribution equation of state tonew solvent groups and highermolecular weight alkanesrdquo FluidPhase Equilibria vol 172 no 2 pp 129ndash143 2000

[6] S Espinosa T Fornari S B Bottini and E A Brignole ldquoPhaseequilibria in mixtures of fatty oils and derivatives with nearcritical fluids using the GC-EOSmodelrdquo Journal of SupercriticalFluids vol 23 no 2 pp 91ndash102 2002

[7] A I Majeed and J Wagner ldquoParameters from group contri-butions equation and phase equilibria in light hydrocarbonsystemsrdquo Journal of American Chemical Society SymposiumSeries vol 300 pp 452ndash473 1986

[8] G K Georgeton and A S Teja ldquoA simple group contributionequation of state for fluid mixturesrdquo Chemical EngineeringScience vol 44 no 11 pp 2703ndash2710 1989

[9] J D Pults R A Greenkorn and K C Chao ldquoChain-of-rotatorsgroup contribution equation of staterdquo Chemical EngineeringScience vol 44 no 11 pp 2553ndash2564 1989

[10] H P Gros S B Bottini and E A Brignole ldquoHigh pressurephase equilibriummodeling of mixtures containing associatingcompounds and gasesrdquo Fluid Phase Equilibria vol 139 no 1-2pp 75ndash87 1997

[11] O Ferreira T Fornari E A Brignole and S B BottinildquoModeling of association effects in mixtures of carboxylicacids with associating and non-associating componentsrdquo LatinAmerican Applied Research vol 33 no 3 pp 307ndash312 2003

[12] S Espinosa S Dıaz and T Fornari ldquoExtension of the groupcontribution associating equation of state to mixtures contain-ing phenol aromatic acid and aromatic ether compoundsrdquoFluid Phase Equilibria vol 231 no 2 pp 197ndash210 2005

[13] I Ishizuka E Sarashina Y Arai and S Saito ldquoGroup contri-bution model based on the hole theoryrdquo Journal of ChemicalEngineering of Japan vol 13 no 2 pp 90ndash97 1980

[14] K P Yoo and C S Lee ldquoNew lattice-fluid equation of stateand its group contribution applications for predicting phaseequilibria of mixturesrdquo Fluid Phase Equilibria vol 117 no 1 pp48ndash54 1996

[15] W Wang X Liu C Zhong C H Twu and J E CoonldquoGroup contribution simplified hole theory equation of state forliquid polymers and solvents and their solutionsrdquo Fluid PhaseEquilibria vol 144 no 1-2 pp 23ndash36 1998

[16] G A Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain primary secondary and tertiary alco-hols ketones and 1-carboxylic acids by group contributionmethodrdquo Fluid Phase Equilibria vol 234 no 1-2 pp 11ndash21 2005

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CatalystsJournal of

ElectrochemistryInternational Journal of

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ISRN Physical Chemistry 3

Table 1 Values of 1198861119877 1198862 1198871119877 and 119887

2for 8 basic compounds namely Propane 119899-Butane Cyclohexane 1-Pentanol 2-Pentanol 119905-BuOH

2-Pentanone and 1-Pentanoic acid taken from [16]

Basic compound (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 (119886

1119877) L2 molminus2 K 119886

2times 104 L2 molminus2

propane 3330 4677 minus0982 6057119899-butane 2830 1810 minus0911 6570cyclohexane 1006 1323 minus0532 024581-pentanol 3559 1605 minus1139 47592-pentanol 4914 minus3473 minus1582 2124119905-BuOH 3285 5264 minus1098 22892-pentanone 3549 minus0329 minus1207 106241-pentanoic acid 3860 minus00648 minus1191 8182

organic compounds using the group contribution methodeach of these fluids has been considered as a hypotheticalmixture of their carbonic groups namely methyl terminal

methylene middle methylene minusCH2OH ⟩CHOH minus

|

C|

OH

⟩C=O and minusCOOH groupsIf 11986011

and 11986111

are the contributions of methyl groupsin 119860119898and 119861

119898 and 119860

22and 119861

22are those for the terminal

methylene groups respectively the contributions of methyland terminalmethylene groups in119860

119898and119861

119898parameterswill

be obtained from two basic compounds namely propane and119899-butane from the following expressions

(119861119898)propane = (

2

3

radic11986111+

1

3

radic11986122)

2

(119861119898)119899-butane = (

2

4

radic11986111+

2

4

radic11986122)

2

(

119860119898

119861119898

)

propane= (

2

3

radic

11986011

11986111

+

1

3

radic

11986022

11986122

)

2

(

119860119898

119861119898

)

119899-butane= (

2

4

radic

11986011

11986111

+

2

4

radic

11986022

11986122

)

2

(6)

The unlike parameters are taken as the mean geometric ofthe like parameters that is 119861

12= radic119861

1111986122

and 1198601211986112=

radic(1198601111986111)(1198602211986122) Note that the 23 and 13 coefficients

in the former expressions are the fraction of carbonic groups(1) and (2) in propane respectively and 24 in the othersare for 119899-butane The contributions of a middle methylenegroup in 119860

119898and 119861

119898parameters are related to those of CH

2

in cyclohexane If 11986033

and 11986133

are the contributions of themiddle methylene groups to the 119860

119898and 119861

119898 then the values

of 119860119898and 119861

119898for cyclohexane are the same as 119860

33and 119861

33

for linear alkanes [20] Other appropriate compounds werealso used to obtain the contributions of the five functionalgroups to the MLIR-EOS parameters in the same approach1-pentanol for the contribution of minusCH

2OH (119860

44 11986144) 2-

pentanol for ⟩CHOH (11986055 11986155) 2-methyl-2-propanol (119905-

BuOH) for minus|

C|

OH (11986066 11986166) 2-pentanon for ⟩C=O

(11986077 11986177) and 1-pentanoic acid for minusCOOH (119860

88 11986188)

We may use the values for 1198861119877 1198862 1198871119877 and 119887

2for the basic

compounds given in Table 1 along with (5) to obtain values of119860119898and 119861

119898for them at any temperature [16]

Having the contributions of the groups from whichthe molecules are built in the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each of the compounds mentionedwere predicted using the following expressions

(119861119898) = (

8

sum

119894=1

119909119894radic119861119894119894)

2

(

119860119898

119861119898

) = (

8

sum

119894=1

119909119894radic

119860119894119894

119861119894119894

)

2

(7)

where

119909119894=

number of group 119894total number of groups (119899)

(8)

Then using the calculated 119860119898and 119861

119898parameters along with

(3) densities of these compounds and their binary mixturesat different pressures and temperatures were calculated

3 Results and Discussion

31 Extension of MLIR Equation of State to Primary Alky-lamines The main purpose in this section is to investigatethe accuracy of the MLIR-EOS for primary alkylaminesAccording to MLIR-EOS plot of (119885119899 minus 1)V2 must be linearagainst 1205882 for each isotherm of these dense fluids To do sowe may use the experimental 119901V119879 data for these compoundsto plot (119885119899 minus 1)V2 against 1205882 for each isotherm As shownin Figure 1 the linearity holds quite well for each isotherm ofthese fluids with the correlation coefficient 1198772 ge 09994 forall chains

The line for each isotherm given in Figure 1 for differentalkylamines were used to determine 1198601015840 (from the intercept)and 1198611015840 (from the slope) in order to calculate the parameters119860119898and 119861

119898for that isotherm using (4) Then the calculated

values for the parameters were plotted versus 1119879 to obtainthe values for 119886

1119877 119886

2 1198871119877 and 119887

2 These values and

4 ISRN Physical Chemistry

0005

minus0005

minus0010

minus0015

minus0020

60 65 70 75 80 85 90 95

0000

119879 = 29315K 1198772 = 09997119879 = 30315K 1198772 = 09994119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(a) 1-Pentylamine

0005

0000

minus0005

minus0010

minus0015

minus0020

minus0025

48 50 52 54 56 58 60 62 64 66 68 70

119879 = 29315K 1198772 = 09998119879 = 30315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(b) 1-Hexylamine

0005

0000

minus0005

minus0010

minus0015

minus0020

minus0025

minus0030

38 40 42 44 46 48 50 52 54 56

119879 = 29315K 1198772 = 09997119879 = 30315K 1198772 = 09995119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09997119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(c) 1-Heptylamine

0004

0002

0000

80 90 100 110 120 130 140

minus0002

minus0004

minus0006

minus0008

minus0010

minus0012

minus0014

119879 = 29315K 1198772 = 09995119879 = 30315K 1198772 = 09995119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09995

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09996119879 = 35315K 1198772 = 09997

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(d) 2-Aminobutane

65 70 80 85 90

0000

minus0002

minus0004

minus0006

minus0008

minus0010

minus0012

minus0014

minus0016

75

119879 = 29315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 33315K 1198772 = 09992119879 = 35315K 1198772 = 09998

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(e) 2-Aminopentane

36 38 40 42 44 46 48 50 52

0000

minus0005

minus0010

minus0015

minus0020

minus0025

minus0030

119879 = 29315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 33315K 1198772 = 09992119879 = 35315K 1198772 = 09998

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(f) 2-Aminoheptane

Figure 1 Continued

ISRN Physical Chemistry 5

36

001

000

minus001

minus002

minus003

minus004

30 32 34 38 40 42 44 46

119879= 29315K 1198772 = 09996119879= 30315K 1198772 = 09996119879= 31315K 1198772 = 09995119879= 32315K 1198772 = 09996

119879= 33315K 1198772 = 09996119879= 34315K 1198772 = 09995119879 = 35315K 1198772 = 09994

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(g) 2-Aminooctane

Figure 1 Plot of (119885119899 minus 1)V2 versus 1205882 for different alkylamines at given temperature

the correlation coefficients of (5) are given in Table 2 foreach alkylamine Having these values and using (5) thevalues of 119860

119898and 119861

119898for an alkylamine may be calculated

at any temperature Then having the calculated values forthe parameters and using (4) along with (3) density ofthe alkylamine can be calculated at different pressures andtemperatures

32 Prediction of MLIR Parameters for Alkylamines UsingGCM The next step is to predict MLIR parameters for alky-lamines using GCM At first we consider the 1-alkylaminesCompared to an 119899-alkane in a linear 1-alkylamine (H

3C minus

CH2minus (CH

2)119899minus4

minus CH2minus CH

2NH2) one methyl group is

replaced with a minusCH2NH2group Hence in 1-alkylamine

we consider minusCH2NH2as a new functional group and use

the values of 119860119898

and 119861119898

of 1-pentylamine to calculatethe contribution of minusCH

2NH2group (119860

99 11986199) from the

following expressions at temperature of interest

(119861119898)1-pentylamine

= (

1

5

radic11986111+

2

5

radic11986122+

1

5

radic11986133+

1

5

radic11986199)

2

(

119860119898

119861119898

)

1-pentylamine

= (

1

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

11986033

11986133

+

1

5

radic

11986099

11986199

)

2

(9)

where the mole fractions of the methyl terminal methylenemiddle methylene and minusCH

2NH2groups in 1-pentylamine

are 15 25 15 and 15 respectivelySimilarly in the primary alkylamines in which an minusNH

2

group is attached to a secondary carbon atom in alkyl groupwe consider ⟩CHNH

2as a new functional group and use

the values of 119860119898

and 119861119898

of 2-aminopentane to calculate

the contribution of ⟩CHNH2group (119860

1010 1198611010

) in theMLIR parameters at each temperature from the followingexpressions

(119861119898)2-aminopentane = (

2

5

radic11986111+

2

5

radic11986122+

1

5

radic1198611010)

2

(

119860119898

119861119898

)

2-aminopentane= (

2

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

1198601010

1198611010

)

2

(10)

where the mole fractions of the methyl terminal methyleneand ⟩CHNH

2groups in 2-aminopentane are 25 25 and

15 respectivelyWe may use the values for 119886

1119877 1198862 1198871119877 and 119887

2for the

basic compounds given in Table 2 along with (5) to obtainvalues for 119860

119898and 119861

119898at any temperature We calculated the

contributions of three carbonic groups and the alkylaminefunctional groups at different temperatures (30315 32315and 34315 K) Having the contributions of the constituentgroups to the MLIR parameters along with dependenciesof the LIR parameters to system composition the values of119860119898and 119861

119898for each alkylamine may be calculated using the

following expressions

(119861119898)alkylamine = (1199091radic11986111 + 1199092radic11986122 + 1199093radic11986133

+1199099radic11986199+ 11990910radic1198611010)

2

(

119860119898

119861119898

)

alkylamine= (119909

1radic

11986011

11986111

+ 1199092radic

11986022

11986122

+ 1199093radic

11986033

11986133

+1199099radic

11986099

11986199

+ 1199091010radic

1198601010

1198611010

)

2

(11)

6 ISRN Physical Chemistry

Table 2 The calculated values of 1198861119877 1198862 1198871119877 and 119887

2and the correlation coefficients of (5) for studied alkylamines

Fluids (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 R 2

1198861119877 L2 molminus2 K 119886

2times 104 L2 molminus2 R 2 References

1-Pentylamine 5075 0478 09991 minus1488 11992 09994 [17]1-Hexylamine 4307 0237 09989 minus1350 10334 09993 [17]1-Hepyylamine 3811 0077 09980 minus1257 9323 09987 [17]2-Aminobutane 6072 1951 09987 minus1253 16042 09986 [18]2-Aminopentane 4524 1550 09989 minus1346 9116 09991 [19]2-Aminoheptane 3728 0007 09991 minus1201 8808 09993 [19]2-Aminooctane 3357 0297 09995 minus1138 7492 09995 [18]

Table 3 AAD 119863max and bias of the calculated density for some alkylamines at given temperatures and for the given pressure range (Δ119901)using the calculated values of 119860

119898and 119861

119898parameters along with (3)

Fluid 119879 K Δp MPa AAD 119863max bias NP1-Butylamine 29815 01ndash339 0570 0965 0570 10

1-Hexylamine30315 01ndash140 0703 105 0703 1532315 01ndash140 0542 0861 0542 1534315 01ndash140 0424 0708 0424 15

1-Heptylamine30315 01ndash140 0636 0993 0636 1532315 01ndash140 0459 0677 0459 1534315 01ndash140 0388 0547 0388 15

2-Aminobutane30315 01ndash140 1452 1672 1452 1532315 01ndash140 1231 1430 1231 1534315 10ndash140 1091 1219 1091 14

2-Aminoheptane 29315 01ndash100 117 148 117 633315 01ndash100 0934 1688 0934 6

2-Aminooctane30315 01ndash140 134 164 134 1532315 01ndash140 117 158 117 1534315 01ndash140 0939 125 0939 15

where 119909119894could be obtained using (8) Then we may use

the values calculated for 119860119898

and 119861119898

parameters at thetemperature of interest along with (3) for a given alkylamineto obtain its density at different pressures Some of thecalculated results are given in Table 3

The statistical parameter namely the absolute averagepercent deviation (AAD) the maximum deviation (119863max)and the average deviation (bias) are defined as

ADD = 100119873

119873

sum

119894=1

1003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

119863Max = Max(1001003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

)

bias = 100119873

Nsum

119894=1

120588exp119894minus 120588

cal119894

120588exp119894

(12)

where 119873 is the number of experimental data and 120588exp119894

and120588cal119894are the experimental density values and those obtained

with (3) for studied fluids respectively Since the values ofAAD can characterize the fact that the calculated values aremore or less close to experimental data it can be claimedthat MLIR EOS can predict the density of these organic

compounds with good accuracy at any temperatures andpressures

33 Extension to Mixture of Alkylamines with PreviouslyStudied Organic Compounds The main purpose in thissection is to investigate the accuracy of the MLIR-EOS formixtures of the alkylamines with previously studied organiccompounds (119899-alkanes alcohols ketones and carboxylicacids) To do so we may use the experimental 119901V119879 datafor binary mixture of 119899-butylamine with 1-alkanols [24]These binary mixtures besides self-association exhibit verystrong cross association due to the strong hydrogen bondingbetween the hydroxyl and the amine groups This strongintermolecular association exhibits relatively large negativeexcess volumes [24] Again we have found that the linearityof (119885119899minus1)V2 against 1205882 for each isothermof a binarymixtureis as good as those for its pure compounds see Figure 2 Notethat the average value of 119899 for a mixture may be definedas

119899mix = sum

number of component119909119894119899119894 (13)

where 119909119894and 119899

119894refer to the mole fraction and number of

carbon atom of component 119894 in the mixture

ISRN Physical Chemistry 7

minus0005

minus0006

minus0007

minus0008

minus0009

minus0010

100 105 110 115 120 125 130

1-Butanol (1) + n-butylamine (2)

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

1199091 = 02011 1198772 = 099991199092 = 03957 1198772 = 099991199093 = 05002 1198772 = 09999

1199094 = 05986 1198772 = 099991199095 = 07975 1198772 = 09999

Figure 2 Plot of (119885119899minus1)V2 versus1205882 for binarymixture of 1-butanol(1) + 119899-butylamine (2) at 29815 K

Wemay use the group contributionmethod to predict theMLIR parameters formixturesThe contributions of differentgroups at the temperature of interest may be calculated fromthe same procedure explained in the previous sections (usingthe values for pure compounds) Having the contributions ofconstituent groups in the MLIR parameters along with thedependencies of the LIR parameters to system compositionthe MLIR parameters for a mixture may be calculated fromthe following expressions

(119861119898)mixture = (

10

sum

119895=1

119883119895radic119861119895119895)

2

(

119860119898

119861119898

)

mixture= (

10

sum

119895=1

119883119895radic

119860119895119895

119861119895119895

)

2

(14)

where 119860119895119895

and 119861119895119895

are the contribution of group 119895 in 119860119898

and 119861119898

and 119883119895is its mole fraction in the hypothetical

mixture Note that 119883119895may be calculated from the following

expression

119883119895=

total number of component

sum

119894=1

119909119894times

119899119895

119899119894

(15)

where 119909119894and 119899

119894are the mole fraction and number of carbon

atoms of component 119894 in the mixture and 119899119895is the number of

group 119895 in component 119894Using the calculated values of 119860

119898and 119861

119898parameters

along with (3) the density of a mixture at any pressuretemperature and mole fraction may be calculated We haveused this approach to calculate the density of binary mixtureof 119899-butylamine with ethanol 1-propanol and 1-butanol atdifferent pressures andmole fractions Some of the results aregiven in Table 4 An ispection of Table 4 indicates that thestrength of the intermolecular hydrogen bonding (between

Table 4 AAD and119863max of the calculated density for binarymixtureof different 1-alkanols (1) + 1-butylamine (2) in a pressure range from01 to 339MPa and different mole fractions using the calculatedvalues of 119860

119898and 119861

119898parameters along with (3) at 29815 K

Binary mixture 1199091

ADD 119863max

(a) Ethanol (1) + 1-butylamine (2)

01973 181 30604013 197 31906102 209 33207996 227 345

(b) 1-Propanol (1) + 1-butylamine (2)

02096 151 20904001 179 22605980 187 25507977 193 27102011 145 179

(c) 1-Butanol (1) + 1-butylamine (2)03957 161 19105986 179 21307975 185 227

the hydroxyl and the amine groups) is an important factorinfluencing the predicted density deviation of thesemixturesThe deviation is remarkable for the mixture with ethanoland decreases as the chain length of the alkanol moleculeincreases This result corresponds to heats of mixing study inthese systems Measured heats of mixing values at 29815 Kare minus2915 minus2870 and minus2705 Jsdotmolminus1 for the mixtures of 119899-butylamine with ethanol 1-propanol and 1-butanol respec-tively [24]

34 Calculation of Other Properties Having an accurate EOSthe MLIR for different chemicals we may expect to makeuse of it to calculate other properties such as isothermalcompressibility compressibility (120581

119879) and thermal expansion

coefficient (120572119875) via the GCM We may use the calculated

values of 119860119898and 119861

119898parameters along with an appropriate

derivative of pressure to obtain these properties at anythermodynamic state For instance the isothermal compress-ibility may be calculated using the following expression

120581119879=

1

119899120588119877 + 311989931205883119877119879119860119898+ 511989951205885119877119879119861119898

(16)

We have calculated 119860119898

and 119861119898

parameters for penty-lamine hexylamine heptylamine 2-aminobutane and 2-aminooctane at different temperatures 30315 32315 and34315 K as explained before along with (16) to calculate 120581

119879

for these compounds at different pressures see Table 5 Theaverage percentage error for 120581

119879was found to be less than 211

4 Conclusions

In this work the MLIR equation of state is extended toprimary alkylamines by group contribution method To doso the linearity of (119885119899 minus 1)V2 against 1205882 was investigated foraliphatic esters Experimental 119901V119879 data for different aliphaticesters were used to check the linearity of (119885119899minus1)V2 against 1205882for different isotherms (Figure 1) As shown in this figure the

8 ISRN Physical Chemistry

Table 5 AADand119863max of the calculated isothermal compressibilityof different alkylamines at given temperatures and in a pressurerange from 01 to 140MPa using the calculated values of 119860

119898and 119861

119898

parameters along with (16)

fluid 119879 K AAD 119863max

1-Hexylaminel30315 195 30232315 189 28634315 171 256

1-Heptylamine30315 187 28232315 166 25834315 159 231

2-Aminooctane30315 211 34532315 198 32634315 189 298

linearity holds quite well with the correlation coefficient1198772 ge09994 for these fluids over a wide range of temperaturesand pressuresThe temperature dependencies of the interceptand slope parameters of MLIR-EOS were also determined forthese fluids

In order to predict the MLIR parameters for primaryalkylamines via the group contribution method we hadto use appropriate compounds to obtain the contributionof primary alkylamine functional groups in the MLIRparameters Three basic compounds namely propane 119899-butane and cyclohexanewere used to obtain the contributionof methyl and methylene groups and 1-pentylamine and2-aminopentane for contribution of minusCH

2NH2 ⟩CHNH

2

groups in the MLIR parameters Having the contributionof constituent groups to the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each compound were calculatedUsing the calculated EOS parameters along with the MLIRthe densities of these series of compounds were calculatedat different pressures and temperatures with the averagepercentage error less less than 154 (Table 3) Furthermorewe have used the group contribution method to predict theMLIR parameters for mixtures (14) Using the calculatedvalues of119860

119898and119861

119898parameters along with (3) the density of

mixtures at any pressure temperature andmole fractionmaybe calculated (Table 4) Thus using the parameters of (5) forthe basic compounds we may calculate the density of pure ormixed fluids even for temperatures for which experimentaldata of basic compounds are not available

We may use the calculated values of 119860119898and 119861

119898parame-

ters along with an appropriate pressure derivative in orderto obtain other properties at any thermodynamic stateThe isothermal compressibility at different pressures wascalculated for different alkylamines and compared with theliterature values (Table 5)

Acknowledgment

Financial support for this work by the research affair ofShahrood University of Technology Shahrood Iran is grate-fully acknowledged

References

[1] T Nitta E A Turek R A Greenkorn and K C Chao ldquoGroupcontribution estimation of activity coefficients in nonidealliquidmixturesrdquoAIChE Journal vol 23 no 2 pp 144ndash160 1977

[2] A Fredenslund R L Jones and J M Prausnitz ldquoGroupcontribution estimation of activity coefficients in nonidealliquid mixturesrdquo AIChE Journal vol 21 no 6 pp 1086ndash10991975

[3] N A Smirnova and A I Victorov ldquoThermodynamic propertiesof pure fluids and solutions from the hole group-contributionmodelrdquo Fluid Phase Equilibria vol 34 no 2-3 pp 235ndash2631987

[4] S Skjold-Joslashrgensen ldquoGas solubility calculations II Applicationof a new group-contribution equation of staterdquo Fluid PhaseEquilibria vol 16 no 3 pp 317ndash351 1984

[5] S Espinosa GM Foco A Bermudez andT Fornari ldquoRevisionand extension of the group contribution equation of state tonew solvent groups and highermolecular weight alkanesrdquo FluidPhase Equilibria vol 172 no 2 pp 129ndash143 2000

[6] S Espinosa T Fornari S B Bottini and E A Brignole ldquoPhaseequilibria in mixtures of fatty oils and derivatives with nearcritical fluids using the GC-EOSmodelrdquo Journal of SupercriticalFluids vol 23 no 2 pp 91ndash102 2002

[7] A I Majeed and J Wagner ldquoParameters from group contri-butions equation and phase equilibria in light hydrocarbonsystemsrdquo Journal of American Chemical Society SymposiumSeries vol 300 pp 452ndash473 1986

[8] G K Georgeton and A S Teja ldquoA simple group contributionequation of state for fluid mixturesrdquo Chemical EngineeringScience vol 44 no 11 pp 2703ndash2710 1989

[9] J D Pults R A Greenkorn and K C Chao ldquoChain-of-rotatorsgroup contribution equation of staterdquo Chemical EngineeringScience vol 44 no 11 pp 2553ndash2564 1989

[10] H P Gros S B Bottini and E A Brignole ldquoHigh pressurephase equilibriummodeling of mixtures containing associatingcompounds and gasesrdquo Fluid Phase Equilibria vol 139 no 1-2pp 75ndash87 1997

[11] O Ferreira T Fornari E A Brignole and S B BottinildquoModeling of association effects in mixtures of carboxylicacids with associating and non-associating componentsrdquo LatinAmerican Applied Research vol 33 no 3 pp 307ndash312 2003

[12] S Espinosa S Dıaz and T Fornari ldquoExtension of the groupcontribution associating equation of state to mixtures contain-ing phenol aromatic acid and aromatic ether compoundsrdquoFluid Phase Equilibria vol 231 no 2 pp 197ndash210 2005

[13] I Ishizuka E Sarashina Y Arai and S Saito ldquoGroup contri-bution model based on the hole theoryrdquo Journal of ChemicalEngineering of Japan vol 13 no 2 pp 90ndash97 1980

[14] K P Yoo and C S Lee ldquoNew lattice-fluid equation of stateand its group contribution applications for predicting phaseequilibria of mixturesrdquo Fluid Phase Equilibria vol 117 no 1 pp48ndash54 1996

[15] W Wang X Liu C Zhong C H Twu and J E CoonldquoGroup contribution simplified hole theory equation of state forliquid polymers and solvents and their solutionsrdquo Fluid PhaseEquilibria vol 144 no 1-2 pp 23ndash36 1998

[16] G A Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain primary secondary and tertiary alco-hols ketones and 1-carboxylic acids by group contributionmethodrdquo Fluid Phase Equilibria vol 234 no 1-2 pp 11ndash21 2005

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

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CatalystsJournal of

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

4 ISRN Physical Chemistry

0005

minus0005

minus0010

minus0015

minus0020

60 65 70 75 80 85 90 95

0000

119879 = 29315K 1198772 = 09997119879 = 30315K 1198772 = 09994119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(a) 1-Pentylamine

0005

0000

minus0005

minus0010

minus0015

minus0020

minus0025

48 50 52 54 56 58 60 62 64 66 68 70

119879 = 29315K 1198772 = 09998119879 = 30315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(b) 1-Hexylamine

0005

0000

minus0005

minus0010

minus0015

minus0020

minus0025

minus0030

38 40 42 44 46 48 50 52 54 56

119879 = 29315K 1198772 = 09997119879 = 30315K 1198772 = 09995119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09997

119879 = 33315K 1198772 = 09997119879 = 34315K 1198772 = 09995119879 = 35315K 1198772 = 09996

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(c) 1-Heptylamine

0004

0002

0000

80 90 100 110 120 130 140

minus0002

minus0004

minus0006

minus0008

minus0010

minus0012

minus0014

119879 = 29315K 1198772 = 09995119879 = 30315K 1198772 = 09995119879 = 31315K 1198772 = 09996119879 = 32315K 1198772 = 09995

119879 = 33315K 1198772 = 09996119879 = 34315K 1198772 = 09996119879 = 35315K 1198772 = 09997

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(d) 2-Aminobutane

65 70 80 85 90

0000

minus0002

minus0004

minus0006

minus0008

minus0010

minus0012

minus0014

minus0016

75

119879 = 29315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 33315K 1198772 = 09992119879 = 35315K 1198772 = 09998

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(e) 2-Aminopentane

36 38 40 42 44 46 48 50 52

0000

minus0005

minus0010

minus0015

minus0020

minus0025

minus0030

119879 = 29315K 1198772 = 09996119879 = 31315K 1198772 = 09997119879 = 33315K 1198772 = 09992119879 = 35315K 1198772 = 09998

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(f) 2-Aminoheptane

Figure 1 Continued

ISRN Physical Chemistry 5

36

001

000

minus001

minus002

minus003

minus004

30 32 34 38 40 42 44 46

119879= 29315K 1198772 = 09996119879= 30315K 1198772 = 09996119879= 31315K 1198772 = 09995119879= 32315K 1198772 = 09996

119879= 33315K 1198772 = 09996119879= 34315K 1198772 = 09995119879 = 35315K 1198772 = 09994

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(g) 2-Aminooctane

Figure 1 Plot of (119885119899 minus 1)V2 versus 1205882 for different alkylamines at given temperature

the correlation coefficients of (5) are given in Table 2 foreach alkylamine Having these values and using (5) thevalues of 119860

119898and 119861

119898for an alkylamine may be calculated

at any temperature Then having the calculated values forthe parameters and using (4) along with (3) density ofthe alkylamine can be calculated at different pressures andtemperatures

32 Prediction of MLIR Parameters for Alkylamines UsingGCM The next step is to predict MLIR parameters for alky-lamines using GCM At first we consider the 1-alkylaminesCompared to an 119899-alkane in a linear 1-alkylamine (H

3C minus

CH2minus (CH

2)119899minus4

minus CH2minus CH

2NH2) one methyl group is

replaced with a minusCH2NH2group Hence in 1-alkylamine

we consider minusCH2NH2as a new functional group and use

the values of 119860119898

and 119861119898

of 1-pentylamine to calculatethe contribution of minusCH

2NH2group (119860

99 11986199) from the

following expressions at temperature of interest

(119861119898)1-pentylamine

= (

1

5

radic11986111+

2

5

radic11986122+

1

5

radic11986133+

1

5

radic11986199)

2

(

119860119898

119861119898

)

1-pentylamine

= (

1

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

11986033

11986133

+

1

5

radic

11986099

11986199

)

2

(9)

where the mole fractions of the methyl terminal methylenemiddle methylene and minusCH

2NH2groups in 1-pentylamine

are 15 25 15 and 15 respectivelySimilarly in the primary alkylamines in which an minusNH

2

group is attached to a secondary carbon atom in alkyl groupwe consider ⟩CHNH

2as a new functional group and use

the values of 119860119898

and 119861119898

of 2-aminopentane to calculate

the contribution of ⟩CHNH2group (119860

1010 1198611010

) in theMLIR parameters at each temperature from the followingexpressions

(119861119898)2-aminopentane = (

2

5

radic11986111+

2

5

radic11986122+

1

5

radic1198611010)

2

(

119860119898

119861119898

)

2-aminopentane= (

2

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

1198601010

1198611010

)

2

(10)

where the mole fractions of the methyl terminal methyleneand ⟩CHNH

2groups in 2-aminopentane are 25 25 and

15 respectivelyWe may use the values for 119886

1119877 1198862 1198871119877 and 119887

2for the

basic compounds given in Table 2 along with (5) to obtainvalues for 119860

119898and 119861

119898at any temperature We calculated the

contributions of three carbonic groups and the alkylaminefunctional groups at different temperatures (30315 32315and 34315 K) Having the contributions of the constituentgroups to the MLIR parameters along with dependenciesof the LIR parameters to system composition the values of119860119898and 119861

119898for each alkylamine may be calculated using the

following expressions

(119861119898)alkylamine = (1199091radic11986111 + 1199092radic11986122 + 1199093radic11986133

+1199099radic11986199+ 11990910radic1198611010)

2

(

119860119898

119861119898

)

alkylamine= (119909

1radic

11986011

11986111

+ 1199092radic

11986022

11986122

+ 1199093radic

11986033

11986133

+1199099radic

11986099

11986199

+ 1199091010radic

1198601010

1198611010

)

2

(11)

6 ISRN Physical Chemistry

Table 2 The calculated values of 1198861119877 1198862 1198871119877 and 119887

2and the correlation coefficients of (5) for studied alkylamines

Fluids (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 R 2

1198861119877 L2 molminus2 K 119886

2times 104 L2 molminus2 R 2 References

1-Pentylamine 5075 0478 09991 minus1488 11992 09994 [17]1-Hexylamine 4307 0237 09989 minus1350 10334 09993 [17]1-Hepyylamine 3811 0077 09980 minus1257 9323 09987 [17]2-Aminobutane 6072 1951 09987 minus1253 16042 09986 [18]2-Aminopentane 4524 1550 09989 minus1346 9116 09991 [19]2-Aminoheptane 3728 0007 09991 minus1201 8808 09993 [19]2-Aminooctane 3357 0297 09995 minus1138 7492 09995 [18]

Table 3 AAD 119863max and bias of the calculated density for some alkylamines at given temperatures and for the given pressure range (Δ119901)using the calculated values of 119860

119898and 119861

119898parameters along with (3)

Fluid 119879 K Δp MPa AAD 119863max bias NP1-Butylamine 29815 01ndash339 0570 0965 0570 10

1-Hexylamine30315 01ndash140 0703 105 0703 1532315 01ndash140 0542 0861 0542 1534315 01ndash140 0424 0708 0424 15

1-Heptylamine30315 01ndash140 0636 0993 0636 1532315 01ndash140 0459 0677 0459 1534315 01ndash140 0388 0547 0388 15

2-Aminobutane30315 01ndash140 1452 1672 1452 1532315 01ndash140 1231 1430 1231 1534315 10ndash140 1091 1219 1091 14

2-Aminoheptane 29315 01ndash100 117 148 117 633315 01ndash100 0934 1688 0934 6

2-Aminooctane30315 01ndash140 134 164 134 1532315 01ndash140 117 158 117 1534315 01ndash140 0939 125 0939 15

where 119909119894could be obtained using (8) Then we may use

the values calculated for 119860119898

and 119861119898

parameters at thetemperature of interest along with (3) for a given alkylamineto obtain its density at different pressures Some of thecalculated results are given in Table 3

The statistical parameter namely the absolute averagepercent deviation (AAD) the maximum deviation (119863max)and the average deviation (bias) are defined as

ADD = 100119873

119873

sum

119894=1

1003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

119863Max = Max(1001003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

)

bias = 100119873

Nsum

119894=1

120588exp119894minus 120588

cal119894

120588exp119894

(12)

where 119873 is the number of experimental data and 120588exp119894

and120588cal119894are the experimental density values and those obtained

with (3) for studied fluids respectively Since the values ofAAD can characterize the fact that the calculated values aremore or less close to experimental data it can be claimedthat MLIR EOS can predict the density of these organic

compounds with good accuracy at any temperatures andpressures

33 Extension to Mixture of Alkylamines with PreviouslyStudied Organic Compounds The main purpose in thissection is to investigate the accuracy of the MLIR-EOS formixtures of the alkylamines with previously studied organiccompounds (119899-alkanes alcohols ketones and carboxylicacids) To do so we may use the experimental 119901V119879 datafor binary mixture of 119899-butylamine with 1-alkanols [24]These binary mixtures besides self-association exhibit verystrong cross association due to the strong hydrogen bondingbetween the hydroxyl and the amine groups This strongintermolecular association exhibits relatively large negativeexcess volumes [24] Again we have found that the linearityof (119885119899minus1)V2 against 1205882 for each isothermof a binarymixtureis as good as those for its pure compounds see Figure 2 Notethat the average value of 119899 for a mixture may be definedas

119899mix = sum

number of component119909119894119899119894 (13)

where 119909119894and 119899

119894refer to the mole fraction and number of

carbon atom of component 119894 in the mixture

ISRN Physical Chemistry 7

minus0005

minus0006

minus0007

minus0008

minus0009

minus0010

100 105 110 115 120 125 130

1-Butanol (1) + n-butylamine (2)

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

1199091 = 02011 1198772 = 099991199092 = 03957 1198772 = 099991199093 = 05002 1198772 = 09999

1199094 = 05986 1198772 = 099991199095 = 07975 1198772 = 09999

Figure 2 Plot of (119885119899minus1)V2 versus1205882 for binarymixture of 1-butanol(1) + 119899-butylamine (2) at 29815 K

Wemay use the group contributionmethod to predict theMLIR parameters formixturesThe contributions of differentgroups at the temperature of interest may be calculated fromthe same procedure explained in the previous sections (usingthe values for pure compounds) Having the contributions ofconstituent groups in the MLIR parameters along with thedependencies of the LIR parameters to system compositionthe MLIR parameters for a mixture may be calculated fromthe following expressions

(119861119898)mixture = (

10

sum

119895=1

119883119895radic119861119895119895)

2

(

119860119898

119861119898

)

mixture= (

10

sum

119895=1

119883119895radic

119860119895119895

119861119895119895

)

2

(14)

where 119860119895119895

and 119861119895119895

are the contribution of group 119895 in 119860119898

and 119861119898

and 119883119895is its mole fraction in the hypothetical

mixture Note that 119883119895may be calculated from the following

expression

119883119895=

total number of component

sum

119894=1

119909119894times

119899119895

119899119894

(15)

where 119909119894and 119899

119894are the mole fraction and number of carbon

atoms of component 119894 in the mixture and 119899119895is the number of

group 119895 in component 119894Using the calculated values of 119860

119898and 119861

119898parameters

along with (3) the density of a mixture at any pressuretemperature and mole fraction may be calculated We haveused this approach to calculate the density of binary mixtureof 119899-butylamine with ethanol 1-propanol and 1-butanol atdifferent pressures andmole fractions Some of the results aregiven in Table 4 An ispection of Table 4 indicates that thestrength of the intermolecular hydrogen bonding (between

Table 4 AAD and119863max of the calculated density for binarymixtureof different 1-alkanols (1) + 1-butylamine (2) in a pressure range from01 to 339MPa and different mole fractions using the calculatedvalues of 119860

119898and 119861

119898parameters along with (3) at 29815 K

Binary mixture 1199091

ADD 119863max

(a) Ethanol (1) + 1-butylamine (2)

01973 181 30604013 197 31906102 209 33207996 227 345

(b) 1-Propanol (1) + 1-butylamine (2)

02096 151 20904001 179 22605980 187 25507977 193 27102011 145 179

(c) 1-Butanol (1) + 1-butylamine (2)03957 161 19105986 179 21307975 185 227

the hydroxyl and the amine groups) is an important factorinfluencing the predicted density deviation of thesemixturesThe deviation is remarkable for the mixture with ethanoland decreases as the chain length of the alkanol moleculeincreases This result corresponds to heats of mixing study inthese systems Measured heats of mixing values at 29815 Kare minus2915 minus2870 and minus2705 Jsdotmolminus1 for the mixtures of 119899-butylamine with ethanol 1-propanol and 1-butanol respec-tively [24]

34 Calculation of Other Properties Having an accurate EOSthe MLIR for different chemicals we may expect to makeuse of it to calculate other properties such as isothermalcompressibility compressibility (120581

119879) and thermal expansion

coefficient (120572119875) via the GCM We may use the calculated

values of 119860119898and 119861

119898parameters along with an appropriate

derivative of pressure to obtain these properties at anythermodynamic state For instance the isothermal compress-ibility may be calculated using the following expression

120581119879=

1

119899120588119877 + 311989931205883119877119879119860119898+ 511989951205885119877119879119861119898

(16)

We have calculated 119860119898

and 119861119898

parameters for penty-lamine hexylamine heptylamine 2-aminobutane and 2-aminooctane at different temperatures 30315 32315 and34315 K as explained before along with (16) to calculate 120581

119879

for these compounds at different pressures see Table 5 Theaverage percentage error for 120581

119879was found to be less than 211

4 Conclusions

In this work the MLIR equation of state is extended toprimary alkylamines by group contribution method To doso the linearity of (119885119899 minus 1)V2 against 1205882 was investigated foraliphatic esters Experimental 119901V119879 data for different aliphaticesters were used to check the linearity of (119885119899minus1)V2 against 1205882for different isotherms (Figure 1) As shown in this figure the

8 ISRN Physical Chemistry

Table 5 AADand119863max of the calculated isothermal compressibilityof different alkylamines at given temperatures and in a pressurerange from 01 to 140MPa using the calculated values of 119860

119898and 119861

119898

parameters along with (16)

fluid 119879 K AAD 119863max

1-Hexylaminel30315 195 30232315 189 28634315 171 256

1-Heptylamine30315 187 28232315 166 25834315 159 231

2-Aminooctane30315 211 34532315 198 32634315 189 298

linearity holds quite well with the correlation coefficient1198772 ge09994 for these fluids over a wide range of temperaturesand pressuresThe temperature dependencies of the interceptand slope parameters of MLIR-EOS were also determined forthese fluids

In order to predict the MLIR parameters for primaryalkylamines via the group contribution method we hadto use appropriate compounds to obtain the contributionof primary alkylamine functional groups in the MLIRparameters Three basic compounds namely propane 119899-butane and cyclohexanewere used to obtain the contributionof methyl and methylene groups and 1-pentylamine and2-aminopentane for contribution of minusCH

2NH2 ⟩CHNH

2

groups in the MLIR parameters Having the contributionof constituent groups to the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each compound were calculatedUsing the calculated EOS parameters along with the MLIRthe densities of these series of compounds were calculatedat different pressures and temperatures with the averagepercentage error less less than 154 (Table 3) Furthermorewe have used the group contribution method to predict theMLIR parameters for mixtures (14) Using the calculatedvalues of119860

119898and119861

119898parameters along with (3) the density of

mixtures at any pressure temperature andmole fractionmaybe calculated (Table 4) Thus using the parameters of (5) forthe basic compounds we may calculate the density of pure ormixed fluids even for temperatures for which experimentaldata of basic compounds are not available

We may use the calculated values of 119860119898and 119861

119898parame-

ters along with an appropriate pressure derivative in orderto obtain other properties at any thermodynamic stateThe isothermal compressibility at different pressures wascalculated for different alkylamines and compared with theliterature values (Table 5)

Acknowledgment

Financial support for this work by the research affair ofShahrood University of Technology Shahrood Iran is grate-fully acknowledged

References

[1] T Nitta E A Turek R A Greenkorn and K C Chao ldquoGroupcontribution estimation of activity coefficients in nonidealliquidmixturesrdquoAIChE Journal vol 23 no 2 pp 144ndash160 1977

[2] A Fredenslund R L Jones and J M Prausnitz ldquoGroupcontribution estimation of activity coefficients in nonidealliquid mixturesrdquo AIChE Journal vol 21 no 6 pp 1086ndash10991975

[3] N A Smirnova and A I Victorov ldquoThermodynamic propertiesof pure fluids and solutions from the hole group-contributionmodelrdquo Fluid Phase Equilibria vol 34 no 2-3 pp 235ndash2631987

[4] S Skjold-Joslashrgensen ldquoGas solubility calculations II Applicationof a new group-contribution equation of staterdquo Fluid PhaseEquilibria vol 16 no 3 pp 317ndash351 1984

[5] S Espinosa GM Foco A Bermudez andT Fornari ldquoRevisionand extension of the group contribution equation of state tonew solvent groups and highermolecular weight alkanesrdquo FluidPhase Equilibria vol 172 no 2 pp 129ndash143 2000

[6] S Espinosa T Fornari S B Bottini and E A Brignole ldquoPhaseequilibria in mixtures of fatty oils and derivatives with nearcritical fluids using the GC-EOSmodelrdquo Journal of SupercriticalFluids vol 23 no 2 pp 91ndash102 2002

[7] A I Majeed and J Wagner ldquoParameters from group contri-butions equation and phase equilibria in light hydrocarbonsystemsrdquo Journal of American Chemical Society SymposiumSeries vol 300 pp 452ndash473 1986

[8] G K Georgeton and A S Teja ldquoA simple group contributionequation of state for fluid mixturesrdquo Chemical EngineeringScience vol 44 no 11 pp 2703ndash2710 1989

[9] J D Pults R A Greenkorn and K C Chao ldquoChain-of-rotatorsgroup contribution equation of staterdquo Chemical EngineeringScience vol 44 no 11 pp 2553ndash2564 1989

[10] H P Gros S B Bottini and E A Brignole ldquoHigh pressurephase equilibriummodeling of mixtures containing associatingcompounds and gasesrdquo Fluid Phase Equilibria vol 139 no 1-2pp 75ndash87 1997

[11] O Ferreira T Fornari E A Brignole and S B BottinildquoModeling of association effects in mixtures of carboxylicacids with associating and non-associating componentsrdquo LatinAmerican Applied Research vol 33 no 3 pp 307ndash312 2003

[12] S Espinosa S Dıaz and T Fornari ldquoExtension of the groupcontribution associating equation of state to mixtures contain-ing phenol aromatic acid and aromatic ether compoundsrdquoFluid Phase Equilibria vol 231 no 2 pp 197ndash210 2005

[13] I Ishizuka E Sarashina Y Arai and S Saito ldquoGroup contri-bution model based on the hole theoryrdquo Journal of ChemicalEngineering of Japan vol 13 no 2 pp 90ndash97 1980

[14] K P Yoo and C S Lee ldquoNew lattice-fluid equation of stateand its group contribution applications for predicting phaseequilibria of mixturesrdquo Fluid Phase Equilibria vol 117 no 1 pp48ndash54 1996

[15] W Wang X Liu C Zhong C H Twu and J E CoonldquoGroup contribution simplified hole theory equation of state forliquid polymers and solvents and their solutionsrdquo Fluid PhaseEquilibria vol 144 no 1-2 pp 23ndash36 1998

[16] G A Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain primary secondary and tertiary alco-hols ketones and 1-carboxylic acids by group contributionmethodrdquo Fluid Phase Equilibria vol 234 no 1-2 pp 11ndash21 2005

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Medicinal ChemistryInternational Journal of

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Applied ChemistryJournal of

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CatalystsJournal of

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

ISRN Physical Chemistry 5

36

001

000

minus001

minus002

minus003

minus004

30 32 34 38 40 42 44 46

119879= 29315K 1198772 = 09996119879= 30315K 1198772 = 09996119879= 31315K 1198772 = 09995119879= 32315K 1198772 = 09996

119879= 33315K 1198772 = 09996119879= 34315K 1198772 = 09995119879 = 35315K 1198772 = 09994

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

(g) 2-Aminooctane

Figure 1 Plot of (119885119899 minus 1)V2 versus 1205882 for different alkylamines at given temperature

the correlation coefficients of (5) are given in Table 2 foreach alkylamine Having these values and using (5) thevalues of 119860

119898and 119861

119898for an alkylamine may be calculated

at any temperature Then having the calculated values forthe parameters and using (4) along with (3) density ofthe alkylamine can be calculated at different pressures andtemperatures

32 Prediction of MLIR Parameters for Alkylamines UsingGCM The next step is to predict MLIR parameters for alky-lamines using GCM At first we consider the 1-alkylaminesCompared to an 119899-alkane in a linear 1-alkylamine (H

3C minus

CH2minus (CH

2)119899minus4

minus CH2minus CH

2NH2) one methyl group is

replaced with a minusCH2NH2group Hence in 1-alkylamine

we consider minusCH2NH2as a new functional group and use

the values of 119860119898

and 119861119898

of 1-pentylamine to calculatethe contribution of minusCH

2NH2group (119860

99 11986199) from the

following expressions at temperature of interest

(119861119898)1-pentylamine

= (

1

5

radic11986111+

2

5

radic11986122+

1

5

radic11986133+

1

5

radic11986199)

2

(

119860119898

119861119898

)

1-pentylamine

= (

1

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

11986033

11986133

+

1

5

radic

11986099

11986199

)

2

(9)

where the mole fractions of the methyl terminal methylenemiddle methylene and minusCH

2NH2groups in 1-pentylamine

are 15 25 15 and 15 respectivelySimilarly in the primary alkylamines in which an minusNH

2

group is attached to a secondary carbon atom in alkyl groupwe consider ⟩CHNH

2as a new functional group and use

the values of 119860119898

and 119861119898

of 2-aminopentane to calculate

the contribution of ⟩CHNH2group (119860

1010 1198611010

) in theMLIR parameters at each temperature from the followingexpressions

(119861119898)2-aminopentane = (

2

5

radic11986111+

2

5

radic11986122+

1

5

radic1198611010)

2

(

119860119898

119861119898

)

2-aminopentane= (

2

5

radic

11986011

11986111

+

2

5

radic

11986022

11986122

+

1

5

radic

1198601010

1198611010

)

2

(10)

where the mole fractions of the methyl terminal methyleneand ⟩CHNH

2groups in 2-aminopentane are 25 25 and

15 respectivelyWe may use the values for 119886

1119877 1198862 1198871119877 and 119887

2for the

basic compounds given in Table 2 along with (5) to obtainvalues for 119860

119898and 119861

119898at any temperature We calculated the

contributions of three carbonic groups and the alkylaminefunctional groups at different temperatures (30315 32315and 34315 K) Having the contributions of the constituentgroups to the MLIR parameters along with dependenciesof the LIR parameters to system composition the values of119860119898and 119861

119898for each alkylamine may be calculated using the

following expressions

(119861119898)alkylamine = (1199091radic11986111 + 1199092radic11986122 + 1199093radic11986133

+1199099radic11986199+ 11990910radic1198611010)

2

(

119860119898

119861119898

)

alkylamine= (119909

1radic

11986011

11986111

+ 1199092radic

11986022

11986122

+ 1199093radic

11986033

11986133

+1199099radic

11986099

11986199

+ 1199091010radic

1198601010

1198611010

)

2

(11)

6 ISRN Physical Chemistry

Table 2 The calculated values of 1198861119877 1198862 1198871119877 and 119887

2and the correlation coefficients of (5) for studied alkylamines

Fluids (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 R 2

1198861119877 L2 molminus2 K 119886

2times 104 L2 molminus2 R 2 References

1-Pentylamine 5075 0478 09991 minus1488 11992 09994 [17]1-Hexylamine 4307 0237 09989 minus1350 10334 09993 [17]1-Hepyylamine 3811 0077 09980 minus1257 9323 09987 [17]2-Aminobutane 6072 1951 09987 minus1253 16042 09986 [18]2-Aminopentane 4524 1550 09989 minus1346 9116 09991 [19]2-Aminoheptane 3728 0007 09991 minus1201 8808 09993 [19]2-Aminooctane 3357 0297 09995 minus1138 7492 09995 [18]

Table 3 AAD 119863max and bias of the calculated density for some alkylamines at given temperatures and for the given pressure range (Δ119901)using the calculated values of 119860

119898and 119861

119898parameters along with (3)

Fluid 119879 K Δp MPa AAD 119863max bias NP1-Butylamine 29815 01ndash339 0570 0965 0570 10

1-Hexylamine30315 01ndash140 0703 105 0703 1532315 01ndash140 0542 0861 0542 1534315 01ndash140 0424 0708 0424 15

1-Heptylamine30315 01ndash140 0636 0993 0636 1532315 01ndash140 0459 0677 0459 1534315 01ndash140 0388 0547 0388 15

2-Aminobutane30315 01ndash140 1452 1672 1452 1532315 01ndash140 1231 1430 1231 1534315 10ndash140 1091 1219 1091 14

2-Aminoheptane 29315 01ndash100 117 148 117 633315 01ndash100 0934 1688 0934 6

2-Aminooctane30315 01ndash140 134 164 134 1532315 01ndash140 117 158 117 1534315 01ndash140 0939 125 0939 15

where 119909119894could be obtained using (8) Then we may use

the values calculated for 119860119898

and 119861119898

parameters at thetemperature of interest along with (3) for a given alkylamineto obtain its density at different pressures Some of thecalculated results are given in Table 3

The statistical parameter namely the absolute averagepercent deviation (AAD) the maximum deviation (119863max)and the average deviation (bias) are defined as

ADD = 100119873

119873

sum

119894=1

1003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

119863Max = Max(1001003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

)

bias = 100119873

Nsum

119894=1

120588exp119894minus 120588

cal119894

120588exp119894

(12)

where 119873 is the number of experimental data and 120588exp119894

and120588cal119894are the experimental density values and those obtained

with (3) for studied fluids respectively Since the values ofAAD can characterize the fact that the calculated values aremore or less close to experimental data it can be claimedthat MLIR EOS can predict the density of these organic

compounds with good accuracy at any temperatures andpressures

33 Extension to Mixture of Alkylamines with PreviouslyStudied Organic Compounds The main purpose in thissection is to investigate the accuracy of the MLIR-EOS formixtures of the alkylamines with previously studied organiccompounds (119899-alkanes alcohols ketones and carboxylicacids) To do so we may use the experimental 119901V119879 datafor binary mixture of 119899-butylamine with 1-alkanols [24]These binary mixtures besides self-association exhibit verystrong cross association due to the strong hydrogen bondingbetween the hydroxyl and the amine groups This strongintermolecular association exhibits relatively large negativeexcess volumes [24] Again we have found that the linearityof (119885119899minus1)V2 against 1205882 for each isothermof a binarymixtureis as good as those for its pure compounds see Figure 2 Notethat the average value of 119899 for a mixture may be definedas

119899mix = sum

number of component119909119894119899119894 (13)

where 119909119894and 119899

119894refer to the mole fraction and number of

carbon atom of component 119894 in the mixture

ISRN Physical Chemistry 7

minus0005

minus0006

minus0007

minus0008

minus0009

minus0010

100 105 110 115 120 125 130

1-Butanol (1) + n-butylamine (2)

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

1199091 = 02011 1198772 = 099991199092 = 03957 1198772 = 099991199093 = 05002 1198772 = 09999

1199094 = 05986 1198772 = 099991199095 = 07975 1198772 = 09999

Figure 2 Plot of (119885119899minus1)V2 versus1205882 for binarymixture of 1-butanol(1) + 119899-butylamine (2) at 29815 K

Wemay use the group contributionmethod to predict theMLIR parameters formixturesThe contributions of differentgroups at the temperature of interest may be calculated fromthe same procedure explained in the previous sections (usingthe values for pure compounds) Having the contributions ofconstituent groups in the MLIR parameters along with thedependencies of the LIR parameters to system compositionthe MLIR parameters for a mixture may be calculated fromthe following expressions

(119861119898)mixture = (

10

sum

119895=1

119883119895radic119861119895119895)

2

(

119860119898

119861119898

)

mixture= (

10

sum

119895=1

119883119895radic

119860119895119895

119861119895119895

)

2

(14)

where 119860119895119895

and 119861119895119895

are the contribution of group 119895 in 119860119898

and 119861119898

and 119883119895is its mole fraction in the hypothetical

mixture Note that 119883119895may be calculated from the following

expression

119883119895=

total number of component

sum

119894=1

119909119894times

119899119895

119899119894

(15)

where 119909119894and 119899

119894are the mole fraction and number of carbon

atoms of component 119894 in the mixture and 119899119895is the number of

group 119895 in component 119894Using the calculated values of 119860

119898and 119861

119898parameters

along with (3) the density of a mixture at any pressuretemperature and mole fraction may be calculated We haveused this approach to calculate the density of binary mixtureof 119899-butylamine with ethanol 1-propanol and 1-butanol atdifferent pressures andmole fractions Some of the results aregiven in Table 4 An ispection of Table 4 indicates that thestrength of the intermolecular hydrogen bonding (between

Table 4 AAD and119863max of the calculated density for binarymixtureof different 1-alkanols (1) + 1-butylamine (2) in a pressure range from01 to 339MPa and different mole fractions using the calculatedvalues of 119860

119898and 119861

119898parameters along with (3) at 29815 K

Binary mixture 1199091

ADD 119863max

(a) Ethanol (1) + 1-butylamine (2)

01973 181 30604013 197 31906102 209 33207996 227 345

(b) 1-Propanol (1) + 1-butylamine (2)

02096 151 20904001 179 22605980 187 25507977 193 27102011 145 179

(c) 1-Butanol (1) + 1-butylamine (2)03957 161 19105986 179 21307975 185 227

the hydroxyl and the amine groups) is an important factorinfluencing the predicted density deviation of thesemixturesThe deviation is remarkable for the mixture with ethanoland decreases as the chain length of the alkanol moleculeincreases This result corresponds to heats of mixing study inthese systems Measured heats of mixing values at 29815 Kare minus2915 minus2870 and minus2705 Jsdotmolminus1 for the mixtures of 119899-butylamine with ethanol 1-propanol and 1-butanol respec-tively [24]

34 Calculation of Other Properties Having an accurate EOSthe MLIR for different chemicals we may expect to makeuse of it to calculate other properties such as isothermalcompressibility compressibility (120581

119879) and thermal expansion

coefficient (120572119875) via the GCM We may use the calculated

values of 119860119898and 119861

119898parameters along with an appropriate

derivative of pressure to obtain these properties at anythermodynamic state For instance the isothermal compress-ibility may be calculated using the following expression

120581119879=

1

119899120588119877 + 311989931205883119877119879119860119898+ 511989951205885119877119879119861119898

(16)

We have calculated 119860119898

and 119861119898

parameters for penty-lamine hexylamine heptylamine 2-aminobutane and 2-aminooctane at different temperatures 30315 32315 and34315 K as explained before along with (16) to calculate 120581

119879

for these compounds at different pressures see Table 5 Theaverage percentage error for 120581

119879was found to be less than 211

4 Conclusions

In this work the MLIR equation of state is extended toprimary alkylamines by group contribution method To doso the linearity of (119885119899 minus 1)V2 against 1205882 was investigated foraliphatic esters Experimental 119901V119879 data for different aliphaticesters were used to check the linearity of (119885119899minus1)V2 against 1205882for different isotherms (Figure 1) As shown in this figure the

8 ISRN Physical Chemistry

Table 5 AADand119863max of the calculated isothermal compressibilityof different alkylamines at given temperatures and in a pressurerange from 01 to 140MPa using the calculated values of 119860

119898and 119861

119898

parameters along with (16)

fluid 119879 K AAD 119863max

1-Hexylaminel30315 195 30232315 189 28634315 171 256

1-Heptylamine30315 187 28232315 166 25834315 159 231

2-Aminooctane30315 211 34532315 198 32634315 189 298

linearity holds quite well with the correlation coefficient1198772 ge09994 for these fluids over a wide range of temperaturesand pressuresThe temperature dependencies of the interceptand slope parameters of MLIR-EOS were also determined forthese fluids

In order to predict the MLIR parameters for primaryalkylamines via the group contribution method we hadto use appropriate compounds to obtain the contributionof primary alkylamine functional groups in the MLIRparameters Three basic compounds namely propane 119899-butane and cyclohexanewere used to obtain the contributionof methyl and methylene groups and 1-pentylamine and2-aminopentane for contribution of minusCH

2NH2 ⟩CHNH

2

groups in the MLIR parameters Having the contributionof constituent groups to the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each compound were calculatedUsing the calculated EOS parameters along with the MLIRthe densities of these series of compounds were calculatedat different pressures and temperatures with the averagepercentage error less less than 154 (Table 3) Furthermorewe have used the group contribution method to predict theMLIR parameters for mixtures (14) Using the calculatedvalues of119860

119898and119861

119898parameters along with (3) the density of

mixtures at any pressure temperature andmole fractionmaybe calculated (Table 4) Thus using the parameters of (5) forthe basic compounds we may calculate the density of pure ormixed fluids even for temperatures for which experimentaldata of basic compounds are not available

We may use the calculated values of 119860119898and 119861

119898parame-

ters along with an appropriate pressure derivative in orderto obtain other properties at any thermodynamic stateThe isothermal compressibility at different pressures wascalculated for different alkylamines and compared with theliterature values (Table 5)

Acknowledgment

Financial support for this work by the research affair ofShahrood University of Technology Shahrood Iran is grate-fully acknowledged

References

[1] T Nitta E A Turek R A Greenkorn and K C Chao ldquoGroupcontribution estimation of activity coefficients in nonidealliquidmixturesrdquoAIChE Journal vol 23 no 2 pp 144ndash160 1977

[2] A Fredenslund R L Jones and J M Prausnitz ldquoGroupcontribution estimation of activity coefficients in nonidealliquid mixturesrdquo AIChE Journal vol 21 no 6 pp 1086ndash10991975

[3] N A Smirnova and A I Victorov ldquoThermodynamic propertiesof pure fluids and solutions from the hole group-contributionmodelrdquo Fluid Phase Equilibria vol 34 no 2-3 pp 235ndash2631987

[4] S Skjold-Joslashrgensen ldquoGas solubility calculations II Applicationof a new group-contribution equation of staterdquo Fluid PhaseEquilibria vol 16 no 3 pp 317ndash351 1984

[5] S Espinosa GM Foco A Bermudez andT Fornari ldquoRevisionand extension of the group contribution equation of state tonew solvent groups and highermolecular weight alkanesrdquo FluidPhase Equilibria vol 172 no 2 pp 129ndash143 2000

[6] S Espinosa T Fornari S B Bottini and E A Brignole ldquoPhaseequilibria in mixtures of fatty oils and derivatives with nearcritical fluids using the GC-EOSmodelrdquo Journal of SupercriticalFluids vol 23 no 2 pp 91ndash102 2002

[7] A I Majeed and J Wagner ldquoParameters from group contri-butions equation and phase equilibria in light hydrocarbonsystemsrdquo Journal of American Chemical Society SymposiumSeries vol 300 pp 452ndash473 1986

[8] G K Georgeton and A S Teja ldquoA simple group contributionequation of state for fluid mixturesrdquo Chemical EngineeringScience vol 44 no 11 pp 2703ndash2710 1989

[9] J D Pults R A Greenkorn and K C Chao ldquoChain-of-rotatorsgroup contribution equation of staterdquo Chemical EngineeringScience vol 44 no 11 pp 2553ndash2564 1989

[10] H P Gros S B Bottini and E A Brignole ldquoHigh pressurephase equilibriummodeling of mixtures containing associatingcompounds and gasesrdquo Fluid Phase Equilibria vol 139 no 1-2pp 75ndash87 1997

[11] O Ferreira T Fornari E A Brignole and S B BottinildquoModeling of association effects in mixtures of carboxylicacids with associating and non-associating componentsrdquo LatinAmerican Applied Research vol 33 no 3 pp 307ndash312 2003

[12] S Espinosa S Dıaz and T Fornari ldquoExtension of the groupcontribution associating equation of state to mixtures contain-ing phenol aromatic acid and aromatic ether compoundsrdquoFluid Phase Equilibria vol 231 no 2 pp 197ndash210 2005

[13] I Ishizuka E Sarashina Y Arai and S Saito ldquoGroup contri-bution model based on the hole theoryrdquo Journal of ChemicalEngineering of Japan vol 13 no 2 pp 90ndash97 1980

[14] K P Yoo and C S Lee ldquoNew lattice-fluid equation of stateand its group contribution applications for predicting phaseequilibria of mixturesrdquo Fluid Phase Equilibria vol 117 no 1 pp48ndash54 1996

[15] W Wang X Liu C Zhong C H Twu and J E CoonldquoGroup contribution simplified hole theory equation of state forliquid polymers and solvents and their solutionsrdquo Fluid PhaseEquilibria vol 144 no 1-2 pp 23ndash36 1998

[16] G A Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain primary secondary and tertiary alco-hols ketones and 1-carboxylic acids by group contributionmethodrdquo Fluid Phase Equilibria vol 234 no 1-2 pp 11ndash21 2005

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

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Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Hindawi Publishing Corporationhttpwwwhindawicom

International Journal of

Analytical ChemistryVolume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

6 ISRN Physical Chemistry

Table 2 The calculated values of 1198861119877 1198862 1198871119877 and 119887

2and the correlation coefficients of (5) for studied alkylamines

Fluids (1198871119877) times 10

4 L4 molminus4 K 1198872times 107 L4 molminus4 R 2

1198861119877 L2 molminus2 K 119886

2times 104 L2 molminus2 R 2 References

1-Pentylamine 5075 0478 09991 minus1488 11992 09994 [17]1-Hexylamine 4307 0237 09989 minus1350 10334 09993 [17]1-Hepyylamine 3811 0077 09980 minus1257 9323 09987 [17]2-Aminobutane 6072 1951 09987 minus1253 16042 09986 [18]2-Aminopentane 4524 1550 09989 minus1346 9116 09991 [19]2-Aminoheptane 3728 0007 09991 minus1201 8808 09993 [19]2-Aminooctane 3357 0297 09995 minus1138 7492 09995 [18]

Table 3 AAD 119863max and bias of the calculated density for some alkylamines at given temperatures and for the given pressure range (Δ119901)using the calculated values of 119860

119898and 119861

119898parameters along with (3)

Fluid 119879 K Δp MPa AAD 119863max bias NP1-Butylamine 29815 01ndash339 0570 0965 0570 10

1-Hexylamine30315 01ndash140 0703 105 0703 1532315 01ndash140 0542 0861 0542 1534315 01ndash140 0424 0708 0424 15

1-Heptylamine30315 01ndash140 0636 0993 0636 1532315 01ndash140 0459 0677 0459 1534315 01ndash140 0388 0547 0388 15

2-Aminobutane30315 01ndash140 1452 1672 1452 1532315 01ndash140 1231 1430 1231 1534315 10ndash140 1091 1219 1091 14

2-Aminoheptane 29315 01ndash100 117 148 117 633315 01ndash100 0934 1688 0934 6

2-Aminooctane30315 01ndash140 134 164 134 1532315 01ndash140 117 158 117 1534315 01ndash140 0939 125 0939 15

where 119909119894could be obtained using (8) Then we may use

the values calculated for 119860119898

and 119861119898

parameters at thetemperature of interest along with (3) for a given alkylamineto obtain its density at different pressures Some of thecalculated results are given in Table 3

The statistical parameter namely the absolute averagepercent deviation (AAD) the maximum deviation (119863max)and the average deviation (bias) are defined as

ADD = 100119873

119873

sum

119894=1

1003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

119863Max = Max(1001003816100381610038161003816100381610038161003816100381610038161003816

120588exp119894minus 120588

cal119894

120588exp119894

1003816100381610038161003816100381610038161003816100381610038161003816

)

bias = 100119873

Nsum

119894=1

120588exp119894minus 120588

cal119894

120588exp119894

(12)

where 119873 is the number of experimental data and 120588exp119894

and120588cal119894are the experimental density values and those obtained

with (3) for studied fluids respectively Since the values ofAAD can characterize the fact that the calculated values aremore or less close to experimental data it can be claimedthat MLIR EOS can predict the density of these organic

compounds with good accuracy at any temperatures andpressures

33 Extension to Mixture of Alkylamines with PreviouslyStudied Organic Compounds The main purpose in thissection is to investigate the accuracy of the MLIR-EOS formixtures of the alkylamines with previously studied organiccompounds (119899-alkanes alcohols ketones and carboxylicacids) To do so we may use the experimental 119901V119879 datafor binary mixture of 119899-butylamine with 1-alkanols [24]These binary mixtures besides self-association exhibit verystrong cross association due to the strong hydrogen bondingbetween the hydroxyl and the amine groups This strongintermolecular association exhibits relatively large negativeexcess volumes [24] Again we have found that the linearityof (119885119899minus1)V2 against 1205882 for each isothermof a binarymixtureis as good as those for its pure compounds see Figure 2 Notethat the average value of 119899 for a mixture may be definedas

119899mix = sum

number of component119909119894119899119894 (13)

where 119909119894and 119899

119894refer to the mole fraction and number of

carbon atom of component 119894 in the mixture

ISRN Physical Chemistry 7

minus0005

minus0006

minus0007

minus0008

minus0009

minus0010

100 105 110 115 120 125 130

1-Butanol (1) + n-butylamine (2)

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

1199091 = 02011 1198772 = 099991199092 = 03957 1198772 = 099991199093 = 05002 1198772 = 09999

1199094 = 05986 1198772 = 099991199095 = 07975 1198772 = 09999

Figure 2 Plot of (119885119899minus1)V2 versus1205882 for binarymixture of 1-butanol(1) + 119899-butylamine (2) at 29815 K

Wemay use the group contributionmethod to predict theMLIR parameters formixturesThe contributions of differentgroups at the temperature of interest may be calculated fromthe same procedure explained in the previous sections (usingthe values for pure compounds) Having the contributions ofconstituent groups in the MLIR parameters along with thedependencies of the LIR parameters to system compositionthe MLIR parameters for a mixture may be calculated fromthe following expressions

(119861119898)mixture = (

10

sum

119895=1

119883119895radic119861119895119895)

2

(

119860119898

119861119898

)

mixture= (

10

sum

119895=1

119883119895radic

119860119895119895

119861119895119895

)

2

(14)

where 119860119895119895

and 119861119895119895

are the contribution of group 119895 in 119860119898

and 119861119898

and 119883119895is its mole fraction in the hypothetical

mixture Note that 119883119895may be calculated from the following

expression

119883119895=

total number of component

sum

119894=1

119909119894times

119899119895

119899119894

(15)

where 119909119894and 119899

119894are the mole fraction and number of carbon

atoms of component 119894 in the mixture and 119899119895is the number of

group 119895 in component 119894Using the calculated values of 119860

119898and 119861

119898parameters

along with (3) the density of a mixture at any pressuretemperature and mole fraction may be calculated We haveused this approach to calculate the density of binary mixtureof 119899-butylamine with ethanol 1-propanol and 1-butanol atdifferent pressures andmole fractions Some of the results aregiven in Table 4 An ispection of Table 4 indicates that thestrength of the intermolecular hydrogen bonding (between

Table 4 AAD and119863max of the calculated density for binarymixtureof different 1-alkanols (1) + 1-butylamine (2) in a pressure range from01 to 339MPa and different mole fractions using the calculatedvalues of 119860

119898and 119861

119898parameters along with (3) at 29815 K

Binary mixture 1199091

ADD 119863max

(a) Ethanol (1) + 1-butylamine (2)

01973 181 30604013 197 31906102 209 33207996 227 345

(b) 1-Propanol (1) + 1-butylamine (2)

02096 151 20904001 179 22605980 187 25507977 193 27102011 145 179

(c) 1-Butanol (1) + 1-butylamine (2)03957 161 19105986 179 21307975 185 227

the hydroxyl and the amine groups) is an important factorinfluencing the predicted density deviation of thesemixturesThe deviation is remarkable for the mixture with ethanoland decreases as the chain length of the alkanol moleculeincreases This result corresponds to heats of mixing study inthese systems Measured heats of mixing values at 29815 Kare minus2915 minus2870 and minus2705 Jsdotmolminus1 for the mixtures of 119899-butylamine with ethanol 1-propanol and 1-butanol respec-tively [24]

34 Calculation of Other Properties Having an accurate EOSthe MLIR for different chemicals we may expect to makeuse of it to calculate other properties such as isothermalcompressibility compressibility (120581

119879) and thermal expansion

coefficient (120572119875) via the GCM We may use the calculated

values of 119860119898and 119861

119898parameters along with an appropriate

derivative of pressure to obtain these properties at anythermodynamic state For instance the isothermal compress-ibility may be calculated using the following expression

120581119879=

1

119899120588119877 + 311989931205883119877119879119860119898+ 511989951205885119877119879119861119898

(16)

We have calculated 119860119898

and 119861119898

parameters for penty-lamine hexylamine heptylamine 2-aminobutane and 2-aminooctane at different temperatures 30315 32315 and34315 K as explained before along with (16) to calculate 120581

119879

for these compounds at different pressures see Table 5 Theaverage percentage error for 120581

119879was found to be less than 211

4 Conclusions

In this work the MLIR equation of state is extended toprimary alkylamines by group contribution method To doso the linearity of (119885119899 minus 1)V2 against 1205882 was investigated foraliphatic esters Experimental 119901V119879 data for different aliphaticesters were used to check the linearity of (119885119899minus1)V2 against 1205882for different isotherms (Figure 1) As shown in this figure the

8 ISRN Physical Chemistry

Table 5 AADand119863max of the calculated isothermal compressibilityof different alkylamines at given temperatures and in a pressurerange from 01 to 140MPa using the calculated values of 119860

119898and 119861

119898

parameters along with (16)

fluid 119879 K AAD 119863max

1-Hexylaminel30315 195 30232315 189 28634315 171 256

1-Heptylamine30315 187 28232315 166 25834315 159 231

2-Aminooctane30315 211 34532315 198 32634315 189 298

linearity holds quite well with the correlation coefficient1198772 ge09994 for these fluids over a wide range of temperaturesand pressuresThe temperature dependencies of the interceptand slope parameters of MLIR-EOS were also determined forthese fluids

In order to predict the MLIR parameters for primaryalkylamines via the group contribution method we hadto use appropriate compounds to obtain the contributionof primary alkylamine functional groups in the MLIRparameters Three basic compounds namely propane 119899-butane and cyclohexanewere used to obtain the contributionof methyl and methylene groups and 1-pentylamine and2-aminopentane for contribution of minusCH

2NH2 ⟩CHNH

2

groups in the MLIR parameters Having the contributionof constituent groups to the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each compound were calculatedUsing the calculated EOS parameters along with the MLIRthe densities of these series of compounds were calculatedat different pressures and temperatures with the averagepercentage error less less than 154 (Table 3) Furthermorewe have used the group contribution method to predict theMLIR parameters for mixtures (14) Using the calculatedvalues of119860

119898and119861

119898parameters along with (3) the density of

mixtures at any pressure temperature andmole fractionmaybe calculated (Table 4) Thus using the parameters of (5) forthe basic compounds we may calculate the density of pure ormixed fluids even for temperatures for which experimentaldata of basic compounds are not available

We may use the calculated values of 119860119898and 119861

119898parame-

ters along with an appropriate pressure derivative in orderto obtain other properties at any thermodynamic stateThe isothermal compressibility at different pressures wascalculated for different alkylamines and compared with theliterature values (Table 5)

Acknowledgment

Financial support for this work by the research affair ofShahrood University of Technology Shahrood Iran is grate-fully acknowledged

References

[1] T Nitta E A Turek R A Greenkorn and K C Chao ldquoGroupcontribution estimation of activity coefficients in nonidealliquidmixturesrdquoAIChE Journal vol 23 no 2 pp 144ndash160 1977

[2] A Fredenslund R L Jones and J M Prausnitz ldquoGroupcontribution estimation of activity coefficients in nonidealliquid mixturesrdquo AIChE Journal vol 21 no 6 pp 1086ndash10991975

[3] N A Smirnova and A I Victorov ldquoThermodynamic propertiesof pure fluids and solutions from the hole group-contributionmodelrdquo Fluid Phase Equilibria vol 34 no 2-3 pp 235ndash2631987

[4] S Skjold-Joslashrgensen ldquoGas solubility calculations II Applicationof a new group-contribution equation of staterdquo Fluid PhaseEquilibria vol 16 no 3 pp 317ndash351 1984

[5] S Espinosa GM Foco A Bermudez andT Fornari ldquoRevisionand extension of the group contribution equation of state tonew solvent groups and highermolecular weight alkanesrdquo FluidPhase Equilibria vol 172 no 2 pp 129ndash143 2000

[6] S Espinosa T Fornari S B Bottini and E A Brignole ldquoPhaseequilibria in mixtures of fatty oils and derivatives with nearcritical fluids using the GC-EOSmodelrdquo Journal of SupercriticalFluids vol 23 no 2 pp 91ndash102 2002

[7] A I Majeed and J Wagner ldquoParameters from group contri-butions equation and phase equilibria in light hydrocarbonsystemsrdquo Journal of American Chemical Society SymposiumSeries vol 300 pp 452ndash473 1986

[8] G K Georgeton and A S Teja ldquoA simple group contributionequation of state for fluid mixturesrdquo Chemical EngineeringScience vol 44 no 11 pp 2703ndash2710 1989

[9] J D Pults R A Greenkorn and K C Chao ldquoChain-of-rotatorsgroup contribution equation of staterdquo Chemical EngineeringScience vol 44 no 11 pp 2553ndash2564 1989

[10] H P Gros S B Bottini and E A Brignole ldquoHigh pressurephase equilibriummodeling of mixtures containing associatingcompounds and gasesrdquo Fluid Phase Equilibria vol 139 no 1-2pp 75ndash87 1997

[11] O Ferreira T Fornari E A Brignole and S B BottinildquoModeling of association effects in mixtures of carboxylicacids with associating and non-associating componentsrdquo LatinAmerican Applied Research vol 33 no 3 pp 307ndash312 2003

[12] S Espinosa S Dıaz and T Fornari ldquoExtension of the groupcontribution associating equation of state to mixtures contain-ing phenol aromatic acid and aromatic ether compoundsrdquoFluid Phase Equilibria vol 231 no 2 pp 197ndash210 2005

[13] I Ishizuka E Sarashina Y Arai and S Saito ldquoGroup contri-bution model based on the hole theoryrdquo Journal of ChemicalEngineering of Japan vol 13 no 2 pp 90ndash97 1980

[14] K P Yoo and C S Lee ldquoNew lattice-fluid equation of stateand its group contribution applications for predicting phaseequilibria of mixturesrdquo Fluid Phase Equilibria vol 117 no 1 pp48ndash54 1996

[15] W Wang X Liu C Zhong C H Twu and J E CoonldquoGroup contribution simplified hole theory equation of state forliquid polymers and solvents and their solutionsrdquo Fluid PhaseEquilibria vol 144 no 1-2 pp 23ndash36 1998

[16] G A Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain primary secondary and tertiary alco-hols ketones and 1-carboxylic acids by group contributionmethodrdquo Fluid Phase Equilibria vol 234 no 1-2 pp 11ndash21 2005

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Hindawi Publishing Corporationhttpwwwhindawicom

International Journal of

Analytical ChemistryVolume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

ISRN Physical Chemistry 7

minus0005

minus0006

minus0007

minus0008

minus0009

minus0010

100 105 110 115 120 125 130

1-Butanol (1) + n-butylamine (2)

1205882 (mol2 Lminus2)

(119885119899minus1)1199072

(L2m

olminus2)

1199091 = 02011 1198772 = 099991199092 = 03957 1198772 = 099991199093 = 05002 1198772 = 09999

1199094 = 05986 1198772 = 099991199095 = 07975 1198772 = 09999

Figure 2 Plot of (119885119899minus1)V2 versus1205882 for binarymixture of 1-butanol(1) + 119899-butylamine (2) at 29815 K

Wemay use the group contributionmethod to predict theMLIR parameters formixturesThe contributions of differentgroups at the temperature of interest may be calculated fromthe same procedure explained in the previous sections (usingthe values for pure compounds) Having the contributions ofconstituent groups in the MLIR parameters along with thedependencies of the LIR parameters to system compositionthe MLIR parameters for a mixture may be calculated fromthe following expressions

(119861119898)mixture = (

10

sum

119895=1

119883119895radic119861119895119895)

2

(

119860119898

119861119898

)

mixture= (

10

sum

119895=1

119883119895radic

119860119895119895

119861119895119895

)

2

(14)

where 119860119895119895

and 119861119895119895

are the contribution of group 119895 in 119860119898

and 119861119898

and 119883119895is its mole fraction in the hypothetical

mixture Note that 119883119895may be calculated from the following

expression

119883119895=

total number of component

sum

119894=1

119909119894times

119899119895

119899119894

(15)

where 119909119894and 119899

119894are the mole fraction and number of carbon

atoms of component 119894 in the mixture and 119899119895is the number of

group 119895 in component 119894Using the calculated values of 119860

119898and 119861

119898parameters

along with (3) the density of a mixture at any pressuretemperature and mole fraction may be calculated We haveused this approach to calculate the density of binary mixtureof 119899-butylamine with ethanol 1-propanol and 1-butanol atdifferent pressures andmole fractions Some of the results aregiven in Table 4 An ispection of Table 4 indicates that thestrength of the intermolecular hydrogen bonding (between

Table 4 AAD and119863max of the calculated density for binarymixtureof different 1-alkanols (1) + 1-butylamine (2) in a pressure range from01 to 339MPa and different mole fractions using the calculatedvalues of 119860

119898and 119861

119898parameters along with (3) at 29815 K

Binary mixture 1199091

ADD 119863max

(a) Ethanol (1) + 1-butylamine (2)

01973 181 30604013 197 31906102 209 33207996 227 345

(b) 1-Propanol (1) + 1-butylamine (2)

02096 151 20904001 179 22605980 187 25507977 193 27102011 145 179

(c) 1-Butanol (1) + 1-butylamine (2)03957 161 19105986 179 21307975 185 227

the hydroxyl and the amine groups) is an important factorinfluencing the predicted density deviation of thesemixturesThe deviation is remarkable for the mixture with ethanoland decreases as the chain length of the alkanol moleculeincreases This result corresponds to heats of mixing study inthese systems Measured heats of mixing values at 29815 Kare minus2915 minus2870 and minus2705 Jsdotmolminus1 for the mixtures of 119899-butylamine with ethanol 1-propanol and 1-butanol respec-tively [24]

34 Calculation of Other Properties Having an accurate EOSthe MLIR for different chemicals we may expect to makeuse of it to calculate other properties such as isothermalcompressibility compressibility (120581

119879) and thermal expansion

coefficient (120572119875) via the GCM We may use the calculated

values of 119860119898and 119861

119898parameters along with an appropriate

derivative of pressure to obtain these properties at anythermodynamic state For instance the isothermal compress-ibility may be calculated using the following expression

120581119879=

1

119899120588119877 + 311989931205883119877119879119860119898+ 511989951205885119877119879119861119898

(16)

We have calculated 119860119898

and 119861119898

parameters for penty-lamine hexylamine heptylamine 2-aminobutane and 2-aminooctane at different temperatures 30315 32315 and34315 K as explained before along with (16) to calculate 120581

119879

for these compounds at different pressures see Table 5 Theaverage percentage error for 120581

119879was found to be less than 211

4 Conclusions

In this work the MLIR equation of state is extended toprimary alkylamines by group contribution method To doso the linearity of (119885119899 minus 1)V2 against 1205882 was investigated foraliphatic esters Experimental 119901V119879 data for different aliphaticesters were used to check the linearity of (119885119899minus1)V2 against 1205882for different isotherms (Figure 1) As shown in this figure the

8 ISRN Physical Chemistry

Table 5 AADand119863max of the calculated isothermal compressibilityof different alkylamines at given temperatures and in a pressurerange from 01 to 140MPa using the calculated values of 119860

119898and 119861

119898

parameters along with (16)

fluid 119879 K AAD 119863max

1-Hexylaminel30315 195 30232315 189 28634315 171 256

1-Heptylamine30315 187 28232315 166 25834315 159 231

2-Aminooctane30315 211 34532315 198 32634315 189 298

linearity holds quite well with the correlation coefficient1198772 ge09994 for these fluids over a wide range of temperaturesand pressuresThe temperature dependencies of the interceptand slope parameters of MLIR-EOS were also determined forthese fluids

In order to predict the MLIR parameters for primaryalkylamines via the group contribution method we hadto use appropriate compounds to obtain the contributionof primary alkylamine functional groups in the MLIRparameters Three basic compounds namely propane 119899-butane and cyclohexanewere used to obtain the contributionof methyl and methylene groups and 1-pentylamine and2-aminopentane for contribution of minusCH

2NH2 ⟩CHNH

2

groups in the MLIR parameters Having the contributionof constituent groups to the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each compound were calculatedUsing the calculated EOS parameters along with the MLIRthe densities of these series of compounds were calculatedat different pressures and temperatures with the averagepercentage error less less than 154 (Table 3) Furthermorewe have used the group contribution method to predict theMLIR parameters for mixtures (14) Using the calculatedvalues of119860

119898and119861

119898parameters along with (3) the density of

mixtures at any pressure temperature andmole fractionmaybe calculated (Table 4) Thus using the parameters of (5) forthe basic compounds we may calculate the density of pure ormixed fluids even for temperatures for which experimentaldata of basic compounds are not available

We may use the calculated values of 119860119898and 119861

119898parame-

ters along with an appropriate pressure derivative in orderto obtain other properties at any thermodynamic stateThe isothermal compressibility at different pressures wascalculated for different alkylamines and compared with theliterature values (Table 5)

Acknowledgment

Financial support for this work by the research affair ofShahrood University of Technology Shahrood Iran is grate-fully acknowledged

References

[1] T Nitta E A Turek R A Greenkorn and K C Chao ldquoGroupcontribution estimation of activity coefficients in nonidealliquidmixturesrdquoAIChE Journal vol 23 no 2 pp 144ndash160 1977

[2] A Fredenslund R L Jones and J M Prausnitz ldquoGroupcontribution estimation of activity coefficients in nonidealliquid mixturesrdquo AIChE Journal vol 21 no 6 pp 1086ndash10991975

[3] N A Smirnova and A I Victorov ldquoThermodynamic propertiesof pure fluids and solutions from the hole group-contributionmodelrdquo Fluid Phase Equilibria vol 34 no 2-3 pp 235ndash2631987

[4] S Skjold-Joslashrgensen ldquoGas solubility calculations II Applicationof a new group-contribution equation of staterdquo Fluid PhaseEquilibria vol 16 no 3 pp 317ndash351 1984

[5] S Espinosa GM Foco A Bermudez andT Fornari ldquoRevisionand extension of the group contribution equation of state tonew solvent groups and highermolecular weight alkanesrdquo FluidPhase Equilibria vol 172 no 2 pp 129ndash143 2000

[6] S Espinosa T Fornari S B Bottini and E A Brignole ldquoPhaseequilibria in mixtures of fatty oils and derivatives with nearcritical fluids using the GC-EOSmodelrdquo Journal of SupercriticalFluids vol 23 no 2 pp 91ndash102 2002

[7] A I Majeed and J Wagner ldquoParameters from group contri-butions equation and phase equilibria in light hydrocarbonsystemsrdquo Journal of American Chemical Society SymposiumSeries vol 300 pp 452ndash473 1986

[8] G K Georgeton and A S Teja ldquoA simple group contributionequation of state for fluid mixturesrdquo Chemical EngineeringScience vol 44 no 11 pp 2703ndash2710 1989

[9] J D Pults R A Greenkorn and K C Chao ldquoChain-of-rotatorsgroup contribution equation of staterdquo Chemical EngineeringScience vol 44 no 11 pp 2553ndash2564 1989

[10] H P Gros S B Bottini and E A Brignole ldquoHigh pressurephase equilibriummodeling of mixtures containing associatingcompounds and gasesrdquo Fluid Phase Equilibria vol 139 no 1-2pp 75ndash87 1997

[11] O Ferreira T Fornari E A Brignole and S B BottinildquoModeling of association effects in mixtures of carboxylicacids with associating and non-associating componentsrdquo LatinAmerican Applied Research vol 33 no 3 pp 307ndash312 2003

[12] S Espinosa S Dıaz and T Fornari ldquoExtension of the groupcontribution associating equation of state to mixtures contain-ing phenol aromatic acid and aromatic ether compoundsrdquoFluid Phase Equilibria vol 231 no 2 pp 197ndash210 2005

[13] I Ishizuka E Sarashina Y Arai and S Saito ldquoGroup contri-bution model based on the hole theoryrdquo Journal of ChemicalEngineering of Japan vol 13 no 2 pp 90ndash97 1980

[14] K P Yoo and C S Lee ldquoNew lattice-fluid equation of stateand its group contribution applications for predicting phaseequilibria of mixturesrdquo Fluid Phase Equilibria vol 117 no 1 pp48ndash54 1996

[15] W Wang X Liu C Zhong C H Twu and J E CoonldquoGroup contribution simplified hole theory equation of state forliquid polymers and solvents and their solutionsrdquo Fluid PhaseEquilibria vol 144 no 1-2 pp 23ndash36 1998

[16] G A Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain primary secondary and tertiary alco-hols ketones and 1-carboxylic acids by group contributionmethodrdquo Fluid Phase Equilibria vol 234 no 1-2 pp 11ndash21 2005

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Hindawi Publishing Corporationhttpwwwhindawicom

International Journal of

Analytical ChemistryVolume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

8 ISRN Physical Chemistry

Table 5 AADand119863max of the calculated isothermal compressibilityof different alkylamines at given temperatures and in a pressurerange from 01 to 140MPa using the calculated values of 119860

119898and 119861

119898

parameters along with (16)

fluid 119879 K AAD 119863max

1-Hexylaminel30315 195 30232315 189 28634315 171 256

1-Heptylamine30315 187 28232315 166 25834315 159 231

2-Aminooctane30315 211 34532315 198 32634315 189 298

linearity holds quite well with the correlation coefficient1198772 ge09994 for these fluids over a wide range of temperaturesand pressuresThe temperature dependencies of the interceptand slope parameters of MLIR-EOS were also determined forthese fluids

In order to predict the MLIR parameters for primaryalkylamines via the group contribution method we hadto use appropriate compounds to obtain the contributionof primary alkylamine functional groups in the MLIRparameters Three basic compounds namely propane 119899-butane and cyclohexanewere used to obtain the contributionof methyl and methylene groups and 1-pentylamine and2-aminopentane for contribution of minusCH

2NH2 ⟩CHNH

2

groups in the MLIR parameters Having the contributionof constituent groups to the EOS parameters along withdependencies of the LIR parameters to system compositionthe MLIR parameters for each compound were calculatedUsing the calculated EOS parameters along with the MLIRthe densities of these series of compounds were calculatedat different pressures and temperatures with the averagepercentage error less less than 154 (Table 3) Furthermorewe have used the group contribution method to predict theMLIR parameters for mixtures (14) Using the calculatedvalues of119860

119898and119861

119898parameters along with (3) the density of

mixtures at any pressure temperature andmole fractionmaybe calculated (Table 4) Thus using the parameters of (5) forthe basic compounds we may calculate the density of pure ormixed fluids even for temperatures for which experimentaldata of basic compounds are not available

We may use the calculated values of 119860119898and 119861

119898parame-

ters along with an appropriate pressure derivative in orderto obtain other properties at any thermodynamic stateThe isothermal compressibility at different pressures wascalculated for different alkylamines and compared with theliterature values (Table 5)

Acknowledgment

Financial support for this work by the research affair ofShahrood University of Technology Shahrood Iran is grate-fully acknowledged

References

[1] T Nitta E A Turek R A Greenkorn and K C Chao ldquoGroupcontribution estimation of activity coefficients in nonidealliquidmixturesrdquoAIChE Journal vol 23 no 2 pp 144ndash160 1977

[2] A Fredenslund R L Jones and J M Prausnitz ldquoGroupcontribution estimation of activity coefficients in nonidealliquid mixturesrdquo AIChE Journal vol 21 no 6 pp 1086ndash10991975

[3] N A Smirnova and A I Victorov ldquoThermodynamic propertiesof pure fluids and solutions from the hole group-contributionmodelrdquo Fluid Phase Equilibria vol 34 no 2-3 pp 235ndash2631987

[4] S Skjold-Joslashrgensen ldquoGas solubility calculations II Applicationof a new group-contribution equation of staterdquo Fluid PhaseEquilibria vol 16 no 3 pp 317ndash351 1984

[5] S Espinosa GM Foco A Bermudez andT Fornari ldquoRevisionand extension of the group contribution equation of state tonew solvent groups and highermolecular weight alkanesrdquo FluidPhase Equilibria vol 172 no 2 pp 129ndash143 2000

[6] S Espinosa T Fornari S B Bottini and E A Brignole ldquoPhaseequilibria in mixtures of fatty oils and derivatives with nearcritical fluids using the GC-EOSmodelrdquo Journal of SupercriticalFluids vol 23 no 2 pp 91ndash102 2002

[7] A I Majeed and J Wagner ldquoParameters from group contri-butions equation and phase equilibria in light hydrocarbonsystemsrdquo Journal of American Chemical Society SymposiumSeries vol 300 pp 452ndash473 1986

[8] G K Georgeton and A S Teja ldquoA simple group contributionequation of state for fluid mixturesrdquo Chemical EngineeringScience vol 44 no 11 pp 2703ndash2710 1989

[9] J D Pults R A Greenkorn and K C Chao ldquoChain-of-rotatorsgroup contribution equation of staterdquo Chemical EngineeringScience vol 44 no 11 pp 2553ndash2564 1989

[10] H P Gros S B Bottini and E A Brignole ldquoHigh pressurephase equilibriummodeling of mixtures containing associatingcompounds and gasesrdquo Fluid Phase Equilibria vol 139 no 1-2pp 75ndash87 1997

[11] O Ferreira T Fornari E A Brignole and S B BottinildquoModeling of association effects in mixtures of carboxylicacids with associating and non-associating componentsrdquo LatinAmerican Applied Research vol 33 no 3 pp 307ndash312 2003

[12] S Espinosa S Dıaz and T Fornari ldquoExtension of the groupcontribution associating equation of state to mixtures contain-ing phenol aromatic acid and aromatic ether compoundsrdquoFluid Phase Equilibria vol 231 no 2 pp 197ndash210 2005

[13] I Ishizuka E Sarashina Y Arai and S Saito ldquoGroup contri-bution model based on the hole theoryrdquo Journal of ChemicalEngineering of Japan vol 13 no 2 pp 90ndash97 1980

[14] K P Yoo and C S Lee ldquoNew lattice-fluid equation of stateand its group contribution applications for predicting phaseequilibria of mixturesrdquo Fluid Phase Equilibria vol 117 no 1 pp48ndash54 1996

[15] W Wang X Liu C Zhong C H Twu and J E CoonldquoGroup contribution simplified hole theory equation of state forliquid polymers and solvents and their solutionsrdquo Fluid PhaseEquilibria vol 144 no 1-2 pp 23ndash36 1998

[16] G A Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain primary secondary and tertiary alco-hols ketones and 1-carboxylic acids by group contributionmethodrdquo Fluid Phase Equilibria vol 234 no 1-2 pp 11ndash21 2005

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Hindawi Publishing Corporationhttpwwwhindawicom

International Journal of

Analytical ChemistryVolume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

ISRN Physical Chemistry 9

[17] Y Miyake A Baylaucq F Plantier D Bessieres H Ushikiand C Boned ldquoHigh-pressure (up to 140MPa) density andderivative properties of some (pentyl- hexyl- and heptyl-)amines between (29315 and 35315) Krdquo Journal of ChemicalThermodynamics vol 40 no 5 pp 836ndash845 2008

[18] MYoshimuraA Baylaucq J P BazileHUshiki andC BonedldquoVolumetric properties of 2-alkylamines (2-aminobutane and2-aminooctane) at pressures up to 140MPa and temperaturesbetween (29315 and 40315) Krdquo Journal of Chemical andEngineering Data vol 54 no 6 pp 1702ndash1709 2009

[19] M Yoshimura C Boned G Galliero J P Bazile A Baylaucqand H Ushiki ldquoInfluence of the chain length on the dynamicviscosity at high pressure of some 2-alkylaminesmeasurementsand comparative study of some modelsrdquo Chemical Physics vol369 no 2-3 pp 126ndash137 2010

[20] G Parsafar and Z Kalantar ldquoExtension of linear isothermregularity to long chain alkanesrdquo Iranian Journal of Chemistryand Chemical Engineering vol 22 no 2 pp 1ndash8 2003

[21] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsa new regularityrdquo Journal of Physical Chemistry vol 97 no 35pp 9048ndash9053 1993

[22] G Parsafar F Kermanpour and B Najafi ldquoPrediction of thetemperature and density dependencies of the parameters of theaverage effective pair potential using only the LIR equation ofstaterdquo Journal of Physical Chemistry B vol 103 no 34 pp 7287ndash7292 1999

[23] G Parsafar and E AMason ldquoLinear isotherms for dense fluidsextension tomixturesrdquo Journal of Physical Chemistry vol 98 no7 pp 1962ndash1967 1994

[24] D Papaioannou M Bridakis and C G Panayiotou ldquoExcessdynamic viscosity and excess volume of n-butylamine + 1-alkanol mixtures at moderately high pressuresrdquo Journal ofChemical and Engineering Data vol 38 no 3 pp 370ndash378 1993

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Hindawi Publishing Corporationhttpwwwhindawicom

International Journal of

Analytical ChemistryVolume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Carbohydrate Chemistry

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chromatography Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Theoretical ChemistryJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Spectroscopy

Hindawi Publishing Corporationhttpwwwhindawicom

International Journal of

Analytical ChemistryVolume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Quantum Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Organic Chemistry International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CatalystsJournal of

ElectrochemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014