Research Article Extension of LIR Equation of State to Alkylamines Using Group Contribution Method

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1 ISRN Physcal Chemstry Volume 013, Artcle ID , 9 pages Research Artcle Extenson of LIR Equaton of State to Alkylamnes Usng Group Contrbuton Method Zahra Kalantar, Hossen Nkoofard, and Faezeh Javad School of Chemstry, Shahrood Unversty of Technology, P.O. Box , Shahrood, Iran Correspondence should be addressed to Zahra Kalantar; zahrakalantar@yahoo.com Receved 31 December 01; Accepted 3 February 013 Academc Edtors: Y. Kmura and H. Res Copyrght 013 Zahra Kalantar et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. In ths work, the modfed lnear sotherm regularty (LIR) equaton of state parameter table s extended n order to represent volumetrc behavour of prmary alkylamnes. In addton, the sothermal compressblty and thermal expanson coeffcent of these compounds have been predcted. To do so, we consder each of prmary alkylamne as a hypothetcal mxture of methyl, methylene and a prmary amne functonal group, n whch the nteracton potental of each par s assumed to be the average effectve par potental. Then, the LIR equaton of state has been extended to such a hypothetcal mxture. Furthermore, three basc compounds, namely, propane, n-butane, and cyclohexane are used to obtan the contrbuton of methyl and methylene groups n the EOS parameters, and also other approprate compounds are used to obtan the contrbuton of the prmary amne functonal groups, such as 1-pentylamne for the contrbuton of CH NH and -amnopentane for the contrbuton of CHNH groups. The calculated EOS parameters along wth the modfed EOS are then used to calculate the densty and ts dervatves for alkylamnes at dfferent pressures and temperatures. The obtaned results for dfferent propertes are compared wth the expermental values. 1. Introducton The thermodynamc studes are mportant for effcent desgn of chemcal processes, to develop correlaton and predcton methods applcable over wde temperature and pressure ranges. Among others, volumetrc propertes such as densty and ts dervatves are of great nterest not only for ndustral applcatons but also for fundamental aspects. These propertes can be obtaned ether expermentally or by thermodynamc modelng based on the equaton of state (EOS). Snce expermental measurements are lengthy and costly, the amount of expermental works can be reduced f effcent thermodynamc models are used to calculate the propertes at dfferent condtons of pressure and temperature. However, equatons of state whch are often used to predct thermodynamc propertes requre pure flud parameters as nputs. The values of such parameters are, however, not only flud specfc but also temperature dependent. To develop an EOS whch s predctve, a group contrbuton method (GCM) can be used. Ths method has strong theoretcal tes to statstcal mechancal theory. The man dea of GCM s to reduce all the nteractons exstng n the system to those pertanng to the pars of the functonal groups or segments from whch the molecules are bult. Therefore, propertes and/or EOS parameters of correspondng chemcals may be calculated through formulae accountng for weghted contrbutons of the dfferent groups present n the molecules. In the last 3 decades, ths method has provded a practcal and powerful tool for predctng as well as calculatng the parameters of equatons of state from the chemcal composton and state of matter. In 1974, Ntta et al. publshed the frst group contrbuton EOS [1] that s based on the cell model and s only able to deal wth some pure compounds n lqud phase. In 1975, the frst successful and wdely appled group contrbuton method, UNIFAC model was publshed based on the lattce theory []. The further development of the group contrbuton methods proceeded through the generalzaton of the lattce theory to descrbe the gas and vapor propertes and the hghpressure vapor-lqud equlbra as well [3]. Skjold-Jørgensen developed a group contrbuton equaton of state (GC-EOS) by employng a Carnahan-Starlng-van der Waals equaton to calculate vapor-lqud equlbra of nondeal mxtures wth low to medum molecular weght compounds [4]. Then,

2 ISRN Physcal Chemstry Espnosa et al. [5] extended the applcaton of ths model to low-volatle hgh-molecular weght compounds usng a unque set of parameters; a satsfactory correlaton and predcton of VLE and LLE n mxtures of supercrtcal fluds wth natural ols and dervatves could be acheved [6]. Majeed and Wagner developed the parameters of the modfed Flory-Huggns theory to account for the molecular sze dfference [7]. Georgeton and Teja developed a GC-EOS usng a modfed form for the perturbed hard chan equaton of state [8]. Pults et al. developed chan-of-rotator group contrbuton equaton of state [9]. Gros et al. ntroduced a group contrbuton assocatng term to the orgnal GC- EOS Helmholtz resdual energy expresson, extendng the applcaton of the model (so-called GC Assocatng EOS) to alcohols, water, gases, and ther mxtures [10]. Then, GCA- EOS parameters table extended n order to represent phase equlbra behavor of carboxylc acds, alcohols, water, and gases mxtures[11] and aromatc compounds contanng phenol, aromatc acd, and aromatc ether compounds [1]. Also, a few group contrbuton hole models and ther numerous versons have been appeared [13 15]. Recently, the extenson of the lnear sotherm regularty equaton of state to long chan organc compounds such as nalkanes, prmary, secondary, and tertary alcohols, ketones, and 1-carboxylc acds s reported va group contrbuton method [16, 0]. The present paper s a fresh attempt to extend LIR equaton of state to alkylamnes and ther mxtures and also predct the parameters of equatons of state usng the group contrbuton method.. Theory.1. Lnear Isotherm Regularty Equaton of State. Usng the LJ (1, 6) potental for the average effectve par potental (AEPP) along wth the parwse addtve approxmaton for the molecular nteractons n the dense fluds and consderng only the nearest neghbor nteractons, lnear sothermal regularty equaton of state (LIR-EOS) have been derved from the exact thermodynamc relatons as [1] (Z 1) V =A+Bρ, (1) where Z=p/ρRTs the compressblty factor, ρ=1/v s the number densty, and A and B are the temperature dependent parameters. AEPP was consdered to be the nteracton between the nearest neghbor molecules, to whch all of the longer range nteractons are added, and also the effect of themedumnthechargedstrbutonsoftwoneghborng molecules was ncluded []. The temperature dependences of the LIR parameters were found as follows: A=A A 1 RT, B=B + B 1 RT, where A 1 and B 1 are related to the attracton and repulson terms of the average effectve par potental and A s related to the nondeal thermal pressure. () The LIR was expermentally found to be hold for denstes greater than the Boyle densty (ρ B 1.8ρ C,whereρ C s the crtcal densty) and temperature less than twce the Boyletemperature,thetemperatureatwhchthesecondvral coeffcent s zero. Accordng to the one-flud approxmaton, the regularty holds for the dense flud mxtures as well [3]. In our prevous works, we have showed that such lnearty vanshed for dfferent organc compounds [16, 0]. Such a behavor s expected, because the mathematcal form of the AEPP functon s assumed to be the LJ (1, 6), and the potental functon whch s more approprate for the sphercalsymmetrcal molecules then nonsphercal molecules, such as chan organc compounds, show devaton from the lnear behavor of the LIR. Hence, usng the group contrbuton method,thelirmaybemodfedforsuchfluds... Modfed LIR Equaton of State for Long Chan Organc Compounds. Usng the GC concept, each organc compound was consdered as a hypothetcal mxture of ther carbonc groups, n whch the nteracton potental of each par s assumed to be the average effectve par potental. Ths potental ncludes both physcal and chemcal (bond) nteractons. Then, accordng to the Van der Waals one-flud approxmaton, the LIR-EOS would be approprate for such a mxture, but the new EOS parameters depend on the group compostons n the mxture (the length of the chan, n ths case) as well as temperature. Hence, f the molar densty of the organc compound at temperature T s ρ, the total densty for the hypothetcal flud s equal to nρ, wheren s number of carbonc groups of the molecule. Therefore, the LIR s reduced to ((p/nρrt) 1) n ρ =A m +B m n ρ ((Z/n) 1) ρ (3) =A +B ρ whch we were referred to t as the modfed lnear sotherm regularty (MLIR) [16, 0]. Lke the LIR, the MLIR was found to be vald for dense fluds only for ρ>ρ B. A m and B m are the MLIR parameters per each carbonc group and A =A m n, B =B m n 4. For all studed organc compounds, we found a better lnearty for (Z/n 1)V versus ρ than (Z 1)V versus ρ for each sotherm, especally for the longer chans. Also we found that the values obtaned for A m and B m are lnear wth respect to 1/T, just the same as those for the LIR parameters [16, 0], A m = a 1 RT +a, B m = b 1 RT +b..3. Carbonc Group Contrbutons n A m and B m Parameters. To predct the MLIR parameters (A m, B m ) for the mentoned (4) (5)

3 ISRN Physcal Chemstry 3 Table 1: Values of a 1 /R, a, b 1 /R,andb for 8 basc compounds, namely, Propane, n-butane, Cyclohexane, 1-Pentanol, -Pentanol, t-buoh, -Pentanone, and 1-Pentanoc acd taken from [16]. Basc compound (b 1 /R) 10 4,L 4 mol 4 K b 10 7,L 4 mol 4 (a 1 /R),L mol K a 10 4,L mol propane n-butane cyclohexane pentanol pentanol t-buoh pentanone pentanoc acd organc compounds usng the group contrbuton method, each of these fluds has been consdered as a hypothetcal mxture of ther carbonc groups, namely, methyl, termnal methylene, mddle methylene, CH OH, CHOH, C OH, C=O, and COOH groups. If A 11 and B 11 are the contrbutons of methyl groups n A m and B m,anda and B are those for the termnal methylene groups, respectvely, the contrbutons of methyl and termnal methylene groups n A m and B m parameters wll be obtaned from two basc compounds, namely, propane and n-butane, from the followng expressons: (B m ) propane =( 3 B B ), (B m ) n-butane =( 4 B B ), =( B m )propane 3 A B 11 3 A ) B =( B m )n-butane 4 A 11 + B 11 4 A ) B The unlke parameters are taken as the mean geometrc of the lke parameters; that s, B 1 = B 11 B and A 1 /B 1 = (A 11 /B 11 )(A /B ).Notethatthe/3and1/3coeffcents n the former expressons are the fracton of carbonc groups (1) and () n propane, respectvely, and /4 n the others are for n-butane. The contrbutons of a mddle methylene group n A m and B m parameters are related to those of CH n cyclohexane. If A 33 and B 33 are the contrbutons of the mddle methylene groups to the A m and B m, then the values of A m and B m for cyclohexane are the same as A 33 and B 33 forlnearalkanes[0]. Other approprate compounds were also used to obtan the contrbutons of the fve functonal groups to the MLIR-EOS parameters n the same approach: 1-pentanol for the contrbuton of CH OH (A 44,B 44 ), - pentanol for CHOH (A 55,B 55 ), -methyl--propanol (t- BuOH) for C OH (A 66,B 66 ), -pentanon for C=O (A 77,B 77 ), and 1-pentanoc acd for COOH (A 88,B 88 ).,. (6) We may use the values for a 1 /R, a, b 1 /R,andb for the basc compounds gven n Table 1 along wth (5)toobtanvaluesof A m and B m for them at any temperature [16]. Havng the contrbutons of the groups from whch the molecules are bult n the EOS parameters, along wth dependences of the LIR parameters to system composton, themlirparametersforeachofthecompoundsmentoned were predcted usng the followng expressons: where x = (B m )=( 8 =1 8 =1 x B ), )=( x B A ), m B (7) number of group total number of groups (n). (8) Then usng the calculated A m and B m parameters along wth (3), denstes of these compounds and ther bnary mxtures at dfferent pressures and temperatures were calculated. 3. Results and Dscusson 3.1. Extenson of MLIR Equaton of State to Prmary Alkylamnes. The man purpose n ths secton s to nvestgate the accuracy of the MLIR-EOS for prmary alkylamnes. Accordng to MLIR-EOS, plot of (Z/n 1)V must be lnear aganst ρ for each sotherm of these dense fluds. To do so, we may use the expermental pvt data for these compounds to plot (Z/n 1)V aganst ρ for each sotherm. As shown n Fgure 1 the lnearty holds qute well for each sotherm of these fluds wth the correlaton coeffcent, R , for all chans. The lne for each sotherm gven n Fgure 1 for dfferent alkylamnes were used to determne A (from the ntercept) and B (from the slope) n order to calculate the parameters A m and B m for that sotherm usng (4). Then the calculated values for the parameters were plotted versus 1/T to obtan the values for a 1 /R, a, b 1 /R, and b. These values and

4 4 ISRN Physcal Chemstry (Z/n 1)v (L mol ) (Z/n 1)v (L mol ) (Z/n 1)v (L mol ) T=93.15K, R = T = K, R = T = K, R = T = K, R = ρ (mol L ) (a) 1-Pentylamne T = K, R = T = K, R = T = K, R = (Z/n 1)v (L mol ) T=93.15K, R = T = K, R = T = K, R = T = K, R = ρ (mol L ) (c) 1-Heptylamne T = K, R = T = K, R = T = K, R = ρ (mol L ) T = K, R = T = K, R = T = K, R = T = K, R = (e) -Amnopentane (Z/n 1)v (L mol ) (Z/n 1)v (L mol ) T=93.15K, R = T = K, R = T = K, R = T = K, R = ρ (mol L ) (b) 1-Hexylamne T = K, R = T = K, R = T = K, R = T = K, R = T = K, R = T = K, R = T = K, R = ρ (mol L ) (d) -Amnobutane T = K, R = T = K, R = T = K, R = ρ (mol L ) T = K, R = T = K, R = T = K, R = T = K, R = (f) -Amnoheptane Fgure 1: Contnued.

5 ISRN Physcal Chemstry (Z/n 1)v (L mol ) T= K, R = T= K, R = T= K, R = T= K, R = ρ (mol L ) (g) -Amnooctane T= K, R = T= K, R = T = K, R = Fgure 1: Plot of (Z/n 1)V versus ρ for dfferent alkylamnes at gven temperature. the correlaton coeffcents of (5) are gven n Table for each alkylamne. Havng these values and usng (5), the values of A m and B m for an alkylamne may be calculated at any temperature. Then havng the calculated values for the parameters and usng (4) along wth(3), densty of the alkylamne can be calculated at dfferent pressures and temperatures. 3.. Predcton of MLIR Parameters for Alkylamnes Usng GCM. The next step s to predct MLIR parameters for alkylamnes usng GCM. At frst, we consder the 1-alkylamnes. Compared to an n-alkane, n a lnear 1-alkylamne (H 3 C CH (CH ) n 4 CH CH NH ) one methyl group s replaced wth a CH NH group. Hence, n 1-alkylamne, we consder CH NH as a new functonal group and use the values of A m and B m of 1-pentylamne, to calculate the contrbuton of CH NH group (A 99,B 99 )fromthe followng expressons at temperature of nterest: (B m ) 1-pentylamne =( 1 5 B B B B 99), B m )1-pentylamne =( 1 5 A 11 B A B A 33 B A 99 B 99 ), (9) the contrbuton of CHNH group (A 1010,B 1010 ) n the MLIR parameters at each temperature from the followng expressons: (B m ) -amnopentane =( 5 B B B 1010), =( B m )-amnopentane 5 A 11 + B 11 5 A + 1 B 5 A 1010 ), B 1010 (10) where the mole fractons of the methyl, termnal methylene, and CHNH groups n -amnopentane are /5, /5, and 1/5,respectvely. We may use the values for a 1 /R, a, b 1 /R, andb for the basc compounds gven n Table along wth (5) toobtan values for A m and B m at any temperature. We calculated the contrbutons of three carbonc groups and the alkylamne functonal groups at dfferent temperatures (303.15, 33.15, and343.15k).havngthecontrbutonsoftheconsttuent groups to the MLIR parameters along wth dependences of the LIR parameters to system composton, the values of A m and B m for each alkylamne may be calculated usng the followng expressons: (B m ) alkylamne = (x 1 B 11 +x B +x 3 B 33 +x 9 B 99 +x 10 B 1010 ), where the mole fractons of the methyl, termnal methylene, mddle methylene, and CH NH groups n 1-pentylamne are 1/5, /5, 1/5, and 1/5, respectvely. Smlarly, n the prmary alkylamnes n whch an NH groupsattachedtoasecondarycarbonatomnalkylgroup, we consder CHNH as a new functonal group and use the values of A m and B m of -amnopentane to calculate = (x B 1 A 11 +x m )alkylamne B A +x 11 B 3 A 33 B 33 +x 9 A 99 B 99 +x 1010 A 1010 B 1010 ), (11)

6 6 ISRN Physcal Chemstry Table : The calculated values of a 1 /R, a, b 1 /R,andb and the correlaton coeffcents of (5) for studed alkylamnes. Fluds (b 1 /R) 10 4,L 4 mol 4 K b 10 7,L 4 mol 4 R a 1 /R,L mol K a 10 4,L mol R References 1-Pentylamne [17] 1-Hexylamne [17] 1-Hepyylamne [17] -Amnobutane [18] -Amnopentane [19] -Amnoheptane [19] -Amnooctane [18] Table 3: AAD, D max, and bas of the calculated densty for some alkylamnes at gven temperatures and for the gven pressure range (Δp) usng the calculated values of A m and B m parameters along wth (3). Flud T, K Δp, MPa AAD D max bas NP 1-Butylamne Hexylamne Heptylamne Amnobutane Amnoheptane Amnooctane where x couldbeobtanedusng(8). Then we may use the values calculated for A m and B m parameters at the temperature of nterest along wth (3)foragvenalkylamne to obtan ts densty at dfferent pressures. Some of the calculated results are gven n Table 3. The statstcal parameter, namely, the absolute average percent devaton (AAD), the maxmum devaton (D max ), and the average devaton (bas) are defned as ADD = 100 N N =1 ρ exp ρ cal ρ exp ρ exp ρ cal D Max = Max (100 ρ exp ), bas = 100 N N ρ exp =1 ρ cal ρ exp,, (1) where N s the number of expermental data, and ρ exp and ρ cal are the expermental densty values and those obtaned wth (3) for studed fluds, respectvely. Snce the values of AAD can characterze the fact that the calculated values are more or less close to expermental data, t can be clamed that MLIR EOS can predct the densty of these organc compounds wth good accuracy at any temperatures and pressures Extenson to Mxture of Alkylamnes wth Prevously Studed Organc Compounds. The man purpose n ths secton s to nvestgate the accuracy of the MLIR-EOS for mxtures of the alkylamnes wth prevously studed organc compounds (n-alkanes, alcohols, ketones, and carboxylc acds). To do so, we may use the expermental pvt data for bnary mxture of n-butylamne wth 1-alkanols [4]. These bnary mxtures, besdes self-assocaton, exhbt very strong cross assocaton due to the strong hydrogen bondng between the hydroxyl and the amne groups. Ths strong ntermolecular assocaton exhbts relatvely large negatve excess volumes [4]. Agan, we have found that the lnearty of (Z/n 1)V aganst ρ for each sotherm of a bnary mxture s as good as those for ts pure compounds, see Fgure.Note that, the average value of n for a mxture may be defned as n mx = x n, number of component (13) where x and n refer to the mole fracton and number of carbon atom of component n the mxture.

7 ISRN Physcal Chemstry 7 (Z/n 1)v (L mol ) Butanol (1) + n-butylamne () x 1 = 0.011, R = x = , R = x 3 = 0.500, R = ρ (mol L ) x 4 = , R = x 5 = , R = Fgure : Plot of (Z/n 1)V versus ρ for bnary mxture of 1-butanol (1)+ n-butylamne () at K. We may use the group contrbuton method to predct the MLIR parameters for mxtures. The contrbutons of dfferent groups at the temperature of nterest may be calculated from the same procedure explaned n the prevous sectons (usng the values for pure compounds). Havng the contrbutons of consttuent groups n the MLIR parameters along wth the dependences of the LIR parameters to system composton, the MLIR parameters for a mxture may be calculated from the followng expressons: 10 (B m ) mxture =( B m )mxture j=1 10 =( j=1 X j B jj ), X j A jj ), B jj (14) where A jj and B jj are the contrbuton of group j n A m and B m and X j s ts mole fracton, n the hypothetcal mxture. Note that X j maybecalculatedfromthefollowng expresson: X j = total number of component =1 x n j n, (15) where x and n are the mole fracton and number of carbon atoms of component n the mxture and n j s the number of group j n component. Usng the calculated values of A m and B m parameters along wth (3), the densty of a mxture at any pressure, temperature,andmolefractonmaybecalculated.wehave used ths approach to calculate the densty of bnary mxture of n-butylamne wth ethanol, 1-propanol, and 1-butanol at dfferent pressures and mole fractons. Some of the results are gven n Table 4. An specton of Table 4 ndcates that the strength of the ntermolecular hydrogen bondng (between Table 4: AAD and D max of the calculated densty for bnary mxture of dfferent 1-alkanols (1) + 1-butylamne (), n a pressure range from 0.1 to 33.9 MPa and dfferent mole fractons usng the calculated values of A m and B m parameters along wth (3) at K. Bnary mxture x 1 ADD D max (a) Ethanol (1) + 1-butylamne () (b) 1-Propanol (1) + 1-butylamne () (c) 1-Butanol (1) + 1-butylamne () the hydroxyl and the amne groups) s an mportant factor nfluencng the predcted densty devaton of these mxtures. The devaton s remarkable for the mxture wth ethanol and decreases, as the chan length of the alkanol molecule ncreases. Ths result corresponds to heats of mxng study n these systems. Measured heats of mxng values at K are 915, 870, and 705 J mol 1 for the mxtures of nbutylamne wth ethanol, 1-propanol, and 1-butanol, respectvely [4] Calculaton of Other Propertes. Havng an accurate EOS, the MLIR for dfferent chemcals, we may expect to make useofttocalculateotherpropertessuchassothermal compressblty compressblty (κ T ) and thermal expanson coeffcent (α P )vathegcm.wemayusethecalculated values of A m and B m parameters along wth an approprate dervatve of pressure to obtan these propertes at any thermodynamc state. For nstance, the sothermal compressblty may be calculated usng the followng expresson: κ T = 1 nρr + 3n 3 ρ 3 RTA m +5n 5 ρ 5 RTB m. (16) We have calculated A m and B m parameters for pentylamne, hexylamne, heptylamne, -amnobutane and - amnooctane, at dfferent temperatures: , 33.15, and Kasexplanedbeforealongwth(16) tocalculateκ T for these compounds at dfferent pressures, see Table 5. The average percentage error for κ T was found to be less than Conclusons In ths work the MLIR equaton of state s extended to prmary alkylamnes by group contrbuton method. To do so, the lnearty of (Z/n 1)V aganst ρ was nvestgated for alphatc esters. Expermental pvt data for dfferent alphatc esters were used to check the lnearty of (Z/n 1)V aganst ρ for dfferent sotherms (Fgure 1).As shown n ths fgure,the

8 8 ISRN Physcal Chemstry Table 5: AAD and D max of the calculated sothermal compressblty of dfferent alkylamnes at gven temperatures and n a pressure range from 0.1 to 140 MPa usng the calculated values of A m and B m parameters along wth (16). flud T, K AAD D max Hexylamnel Heptylamne Amnooctane lnearty holds qute well wth the correlaton coeffcent, R , for these fluds over a wde range of temperatures and pressures. The temperature dependences of the ntercept and slope parameters of MLIR-EOS were also determned for these fluds. In order to predct the MLIR parameters for prmary alkylamnes va the group contrbuton method, we had to use approprate compounds to obtan the contrbuton of prmary alkylamne functonal groups n the MLIR parameters. Three basc compounds, namely, propane, nbutane, and cyclohexane were used to obtan the contrbuton of methyl and methylene groups and 1-pentylamne and -amnopentane for contrbuton of CH NH, CHNH groups n the MLIR parameters. Havng the contrbuton of consttuent groups to the EOS parameters along wth dependences of the LIR parameters to system composton, the MLIR parameters for each compound were calculated. Usng the calculated EOS parameters along wth the MLIR, the denstes of these seres of compounds were calculated at dfferent pressures and temperatures, wth the average percentage error less less than 1.54 (Table 3). Furthermore, we have used the group contrbuton method to predct the MLIR parameters for mxtures (14). Usng the calculated values of A m and B m parameters along wth (3), the densty of mxtures at any pressure, temperature, and mole fracton may be calculated (Table 4). Thus, usng the parameters of (5)for the basc compounds, we may calculate the densty of pure or mxed fluds even for temperatures for whch expermental data of basc compounds are not avalable. We may use the calculated values of A m and B m parameters along wth an approprate pressure dervatve, n order to obtan other propertes at any thermodynamc state. The sothermal compressblty at dfferent pressures was calculated for dfferent alkylamnes and compared wth the lterature values (Table 5). Acknowledgment Fnancal support for ths work by the research affar of Shahrood Unversty of Technology, Shahrood, Iran, s gratefully acknowledged. References [1] T. Ntta, E. A. Turek, R. A. Greenkorn, and K. C. Chao, Group contrbuton estmaton of actvty coeffcents n nondeal lqud mxtures, AIChE Journal,vol.3,no.,pp ,1977. [] A. Fredenslund, R. L. Jones, and J. M. Prausntz, Group contrbuton estmaton of actvty coeffcents n nondeal lqud mxtures, AIChE Journal, vol.1,no.6,pp , [3] N. A. Smrnova and A. I. Vctorov, Thermodynamc propertes of pure fluds and solutons from the hole group-contrbuton model, Flud Phase Equlbra, vol. 34, no. -3, pp , [4] S. Skjold-Jørgensen, Gas solublty calculatons. II. Applcaton of a new group-contrbuton equaton of state, Flud Phase Equlbra,vol.16,no.3,pp ,1984. [5] S.Espnosa,G.M.Foco,A.Bermúdez,andT.Fornar, Revson and extenson of the group contrbuton equaton of state to new solvent groups and hgher molecular weght alkanes, Flud Phase Equlbra,vol.17,no.,pp ,000. [6] S. Espnosa, T. Fornar, S. B. Bottn, and E. A. Brgnole, Phase equlbra n mxtures of fatty ols and dervatves wth near crtcal fluds usng the GC-EOS model, Supercrtcal Fluds,vol.3,no.,pp.91 10,00. [7] A. I. Majeed and J. Wagner, Parameters from group contrbutons equaton and phase equlbra n lght hydrocarbon systems, Amercan Chemcal Socety Symposum Seres,vol.300,pp ,1986. 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9 ISRN Physcal Chemstry 9 [17] Y. Myake, A. Baylaucq, F. Planter, D. Bessères, H. Ushk, and C. Boned, Hgh-pressure (up to 140 MPa) densty and dervatve propertes of some (pentyl-, hexyl-, and heptyl-) amnes between (93.15 and ) K, Chemcal Thermodynamcs,vol.40,no.5,pp ,008. [18] M.Yoshmura,A.Baylaucq,J.P.Bazle,H.Ushk,andC.Boned, Volumetrc propertes of -alkylamnes (-amnobutane and -amnooctane) at pressures up to 140 MPa and temperatures between (93.15 and ) K, Chemcal and Engneerng Data,vol.54,no.6,pp ,009. [19] M. Yoshmura, C. Boned, G. Galléro, J. P. Bazle, A. Baylaucq, and H. Ushk, Influence of the chan length on the dynamc vscosty at hgh pressure of some -alkylamnes: measurements and comparatve study of some models, Chemcal Physcs,vol. 369, no. -3, pp , 010. [0] G. Parsafar and Z. Kalantar, Extenson of lnear sotherm regularty to long chan alkanes, Iranan Chemstry and Chemcal Engneerng,vol.,no.,pp.1 8,003. [1] G. Parsafar and E. A. Mason, Lnear sotherms for dense fluds: anewregularty, JournalofPhyscalChemstry,vol.97,no.35, pp , [] G. Parsafar, F. Kermanpour, and B. Najaf, Predcton of the temperature and densty dependences of the parameters of the average effectve par potental usng only the LIR equaton of state, JournalofPhyscalChemstryB, vol. 103, no. 34, pp , [3] G. Parsafar and E. A. Mason, Lnear sotherms for dense fluds: extenson to mxtures, JournalofPhyscalChemstry,vol.98,no. 7,pp ,1994. [4] D. Papaoannou, M. Brdaks, and C. G. Panayotou, Excess dynamc vscosty and excess volume of n-butylamne + 1- alkanol mxtures at moderately hgh pressures, Chemcal and Engneerng Data,vol.38,no.3,pp ,1993.

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