Thermodynamics of mixtures with strongly negative deviations from Raoult's Law: Part 4. Application...

Ž .Fluid Phase Equilibria 168 2000 31–58www.elsevier.nlrlocaterfluid

Thermodynamics of mixtures with strongly negative deviations fromRaoult’s Law

Part 4. Application of the DISQUAC model to mixtures of 1-alkanolswith primary or secondary linear amines. Comparison with Dortmund

UNIFAC and ERAS results

Juan Antonio Gonzalez ), Isaies Garcie de la Fuenta, Jose Carlos Cobos´ ´ ´ ´G.E.T.E.F., Dpto. de Termodinamica y Fısica Aplicada, Facultad de Ciencias, UniÕersidad de Valladolid,´ ´

47071 Valladolid, Spain

Received 14 June 1999; accepted 12 November 1999

Abstract

Binary mixtures of 1-alkanols with primary or secondary linear amines have been characterized in theframework of DISQUAC. The interaction parameters for the corresponding OHrNH and OHrNH contacts are2

reported. DISQUAC represents fairly well the thermodynamic properties examined, which are criticallyŽ . Ž E . Ž E .evaluated: vapor–liquid equilibria VLE , molar excess Gibbs energies G and molar excess enthalpies H .

For example, polyazeotropy of the methanolqdiethylamine mixture is well reproduced. The methanolqŽammonia system can be treated similarly to other 1-alkanolsqprimary amine systems i.e., ammonia is

.assumed, as in a previous work, to be a primary amine without C atoms . The results are discussed in terms ofeffective dipole moments. The information derived from the concentration–concentration structure factors isbriefly analyzed. DISQUAC provides better results than the Dortmund version of UNIFAC using the publishedgeometrical and interaction parameters. Particularly, DISQUAC improves results on GE and for systemscontaining methanol. DISQUAC results on H E are also compared to those obtained from the ERAS model. Forsystems containing primary amines, parameters available in literature were used along calculations. In the caseof methanolqdiethylamine and 1-alkanolsqdibutylamine mixtures, new ERAS parameters are reported in thiswork. The mean standard deviations for H E obtained using DISQUAC and ERAS, are 151 and 216 J mol-1,respectively. DISQUAC also improves results on GE, while ERAS describes properly the available excess

Ž E .volume V data. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Theory; Liquids; Associated; Thermodynamics; Group contributions

) Corresponding author.Ž .E-mail address: [email protected] J.A. Gonzalez .´

0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0378-3812 99 00326-X

( )J.A. Gonzalez et al.rFluid Phase Equilibria 168 2000 31–58´32

1. Introduction

Mixtures of alcohols and primary or secondary linear amines are an interesting class of systemsthat exhibits very strong negative deviations from Raoult’s law. As a matter of fact, they show

E w x w xextremely negative H values 1–6 , which can be interpreted in terms of two opposing effects 3–7 :Ž .a In pure state, both the alcohol and the amine are associated by the formation of O-H---O and

E Ž .N-H---N bonds. The disruption of these bonds upon mixing leads to a positive contribution to H ; bStrong intermolecular interactions between the hydroxyl and amine groups contribute negatively toH E. So, H E -0 means that the O-H---N bonds are stronger than the O-H---O and N-H---N bonds in

Ž .the investigated systems, and remarks that amines primary, secondary, tertiary or aromatic are goodproton acceptors because the electrons around the N atoms have a less s and more p character than in

Ž . w xother groups e.g., nitrile or carbonile groups 8,9 . On the other hand, it is possible to findw xpolyazeotropy in the mixture methanolqdiethylamine 10,11 , which shows negative deviation from

Raoult’s law at 298.15 and 348.15 K, and positive and negative deviations at 398.15 K.The purpose of this paper is the characterization of mixtures containing 1-alkanols and primary or

w xsecondary linear amines in terms of DISQUAC 12,13 , a purely physical model based on the rigidw x w xlattice theory developed by Guggenheim 14 . In previous works 15–17 , other binary liquid

mixtures, which show strong negative deviations from Raoult’s law, have been also successfullycharacterized in the framework of this model. In particular, the systems investigated up to now are:

w x w x Ž .methanol or ethanol with propanal 15 ; n-alkanones with CHCl 15 ; oxaalkanes linear or cyclic3w xwith CHCl or CH Cl 16 ; and CHCl or 1-alkanols, 2-alkanols and tert-butanol with triethylamine3 2 2 3

w x17 . It is noteworthy that DISQUAC and different continuous association models yield similar resultsw xfor such systems 15 .

A systematic comparison between DISQUAC calculations and predictions from the Dortmundw x Ž .version of UNIFAC model 18 hereafter, UNIFAC is shown. At this end, the corresponding

w xpublished geometrical and interaction parameters were used without modification 18 .w xIn this work, we have also applied the ERAS model 19 , which combines the real association

w x w xsolution model 20–23 with a physical term, namely the Flory’s equation of state 24 , to characterizemethanolqdiethylamine and 1-alkanolsqdibutylamine systems. The corresponding results together

w xwith those from the ERAS model for 1-alkanolsqprimary amines mixtures 1,2 are compared withDISQUAC values.

2. Theory

2.1. DISQUAC

In the framework of DISQUAC, mixtures of 1-alkanols with primary or secondary linear aminesŽ . Žare regarded as possessing three types of surfaces: i type a, aliphatic: CH , CH in 1-alkanols or3 2

. Ž . Ž . Ž . Žamines ; ii type n NH or NH in primary or secondary amines, respectively ; iii type h hydroxyl,2.OH in 1-alkanols .

2.1.1. Assessment of geometrical parametersWhen DISQUAC is applied, the total relative molecular volumes, r , surfaces, q , and thei i

molecular surface fractions, a , of the compounds present in the mixture are usually calculateds i

( )J.A. Gonzalez et al.rFluid Phase Equilibria 168 2000 31–58´ 33

Table 1Relative group increments for molecular volumes, r s R rR , and areas, q sQ rQ , calculated using Bondi’sG G CH G G CH4 4

w x Ž y6 3 y1 y5 2 y1.method 25 R s17.12=10 m mol ; Q s2.90=10 m molCH CH4 4

Group r q ReferenceG G

w xCH 0.79848 0.73103 263w xCH 0.59755 0.46552 262w xOH 0.46963 0.50345 27w xNH 0.61565 0.60000 312w xNH 0.47196 0.34138 30

w xadditively on the basis of the group volumes R and surfaces Q recommended by Bondi 25 . AsG Gw xvolume and surface units, the volume R and surface Q of methane are taken arbitrarily 26 .CH CH4 4

The geometrical parameters referred to in this work are listed in Table 1.

2.1.2. EquationsE E w x ŽThe equations used to calculate G and H are the same as in other applications 27 see

. E E E ŽAppendix A . The interaction terms in the excess thermodynamic properties G , H , and C excessP.heat capacity at constant pressure contain a DIS and a QUAC contribution, which are calculated

independently by the classical formulas and then simply added. The degree of non-randomness is thusexpressed by the relative amounts of dispersive and quasichemical terms.

F E sF E, COMB qF E, DIS qF E, QUAC 1Ž .int int

E E E E Ž . E, COMB E E Žwhere F sG ; H or C . In Eq. 1 , F is only different to zero for F sG Flory–Hug-pw x.gins combinatorial term 26,28 .

For the QUAC part, as coordination number, the reference value was chosen, that is zs4.The temperature dependence of the interaction parameters g , h and c has been expressed inst st pst

w x DIS QUACterms of the DIS and QUAC interchange coefficients 27 C and C , where s, tsa, h, n andst, l st, lŽ DISrQUAC DISrQUAC Ž . . Ž DISrQUACl s 1 Gibbs energy; C s g T rRT ; l s 2 enthalpy; C sst, 1 st 0 0 st, 2

DISrQUAC Ž . . Ž DISrQUAC DISrQUAC Ž . .h T rRT and ls3 heat capacity; C sc T rR . T s298.15 K is thest 0 0 st, 3 pst 0 0

scaling temperature.

( )2.2. Modified UNIFAC Dortmund Õersion

w x w xModified UNIFAC 18 differs from the original UNIFAC 29 by the combinatorial term and thetemperature dependence of the group interaction parameters.

The equations used to calculate GE and H E are obtained from the fundamental equation for theactivity coefficient g of component i:i

lng slng COMB q lng RES 2Ž .i i i

where ln g COMB is the combinatorial term and ln g RES is the residual term. Equations are given ini i

Appendix A.

2.2.1. Assessment of parametersIn modified UNIFAC, alcohols are characterized by two main groups, OH and CH OH. The3

Ž . Ž . Ž .former is subdivided in three subgroups: OH p ; OH s and OH t , which represent the hydroxyl


group in primary, secondary and tertiary alcohols. CH OH is a group itself, which characterizes3

methanol. Primary and secondary amines are characterized by two different main groups: CNH and2

CNH, respectively. The first is subdivided in four subgroups CH NH , CH NH CHNH , and3 2 2 2 2

CNH , while the CNH group is subdivided in three subgroups CH NH, CH NH and CHNH. The2 3 2

subgroups have different geometrical parameters, but the subgroups within the same main group areassumed to have identical group energy–interaction parameters.

The geometrical parameters, the relative van der Waals volumes and the relative van der Waalssurfaces of the different subgroups are not calculated from molecular parameters like in the originalUNIFAC but fit together with the interaction parameters to the experimental values of the thermody-

w xnamic properties considered. The geometrical and interaction parameters are taken from literature 18and used without modification.

2.3. The ERAS model

w xThis model combines the real association solution model 20–23 with Flory’s equation of statew x24 . The excess functions are written as:

X E sX E qX E 3Ž .phys chem

E E E E Ž . Ewhere X sG , H , V . In Eq. 3 , X is the chemical contribution, mainly due to associationchem

reactions, and X E represents the physical contribution, consequence of the physical interactionsphys

between molecules. The corresponding expressions are given in Appendix A.The chemical contribution to the excess properties arises from chemical interactions between the

molecules, in particular hydrogen bonding. It is assumed that there is an equilibrium of linear chainŽ . Ž .association of the component A alcohol and B amine :

KA

A qAlA 4Ž .m mq1

K B

B qBlB 5Ž .n nq1

with m or n being the degree of self-association, ranging from 1 to `. The cross-association betweenA and B molecules is represented by:

KAB

A qB lA B . 6Ž .m n m n

The association constants K are assumed to be independent from the chain length. Theiri

temperature dependence is given by:UK sK exp y Dh rR 1rTy1rT 7Ž . Ž . Ž .i 0 i 0

where K is the equilibrium constant at the standard temperature T and DhU is the enthalpy0 0 i

variation for reactions 4–6, which corresponds to the hydrogen bonds energy. Reactions 4–6 are alsocharacterized by the volume change DÕ

U, related to the formation of the linear chains.iE w xX is derived from Flory’s equation of state 24 , which is assumed to be valid not only for purephys

components but also for the mixture:

˜ ˜ ˜ ˜ 1r3 ˜ 1r3 ˜ ˜P V rT sV r V y1 y1r V T 8Ž .ž / ž /i i i i i i i

˜ mol U ˜ U ˜ UŽ . Ž .where isA, B, M mixture . In Eq. 8 , V sV rV ; P sPrP and T sTrT are the reducedi i i i i i i

volume, pressure and temperature, respectively. The pure components reduction parameters V U, PU,i i


U w xT are determined by fitting the Flory equation of state to PVT data of pure components 1,2 . Thei

reduction parameters for the mixture PU and TU are calculated via certain following mixing rulesM MŽ .see Appendix A .

3. Estimation of the adjustable parameters

3.1. DISQUAC interaction parameters

Ž . Ž . Ž .The three types of surface generate three pairs of contacts: a,n , a,h and h,n . The aliphaticramineŽ .a,n interactions are represented by DIS and QUAC coefficients, which are different for mixturescontaining primary or secondary amines. They were calculated on the basis of experimental data for

w x Ž .these systems 30,31 . Similarly, the aliphaticrhydroxyl a,h contacts are also described by both DISw xand QUAC interchange coefficients, obtained from data for 1-alkanolsqn-alkanes systems 27 .

Ž . Ž . Ž .So, because the a,n and a,h parameters are known, only those for the h,n contacts must beobtained. The general procedure applied is as follows. Firstly, the experimental database for thesystems under study is carefully analyzed in order to select those mixtures that will be used in thefitting of the parameters. Secondly, the parameters are fitted to reproduce as well as make possible theconcentration dependence of the experimental GE and H E data of those systems selected for the

Ž w x.adjustment. This is made by means of a Marquardt algorithm see, e.g., Bevington 32 , whichminimizes the objective function:

2 2DISr QUAC DIS r QUAC DIS r QUAC E E E EF C ,C ,C sÝ G yG rN qÝ H yH rN 9Ž .Ž . ž / ž /hn , 1 hn , 2 hn , 3 calc exp G calc exp H

where the sums are taken over N and N experimental points for GE and H E, respectively. Thirdly,G H

when needed data are not available or are considered not reliable, the corresponding interchange

Table 2DIS QUAC ŽInterchange coefficients, dispersive C and C ls1, Gibbs energy; ls2, enthalpy; ls3, heat capacity for contactshn, l hn, l

Ž . Ž .h,n type h, OH in 1-alkanols; type n, NH in primary linear amines2

u in n in CH `CH `OH3 ny1

CH `H `NH 1 2 3 4 5 6 7 8 G93 uy1 2

DISu C y9.5 y9.5 y13.0 y11.4 y11.4 y11.4 y11.4 y11.4 y11.4hn, 1DIS a au C y19.5 y19.5 y40.0 y50.0 y60.0 y64.0 y68.0 y73.0 y80.0hn, 2DISu C 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0hn, 3QUACu C y1.50 y0.95 1.50 1.50 1.50 1.50 1.50 1.50 1.50hn, 1QUAC a a a a a3 C y4.10 y2.85 2.00 4.75 6.50 6.50 6.50 6.50 6.50hn, 2

4 y4.10 y2.85 1.00 3.75 5.50 5.50 5.50 5.50 5.50a a a a a a5 y4.10 y2.85 0.20 2.75 4.75 5.00 5.00 5.00 5.00a a a6 y4.10 y2.85 y0.20 2.00 4.00 4.25 4.25 4.25 4.25a a a a a a a7 y4.10 y2.85 y1.00 1.25 3.50 3.75 3.75 3.75 3.75a a a8 y5.00 y3.75 y1.80 0.50 2.25 3.25 3.25 3.25 3.25a a a a a a aG9 y5.00 y3.75 y3.30 y1.00 0.60 2.00 2.00 2.00 2.00

QUACu C 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0hn, 3

aEstimated value.


Table 3DIS QUAC ŽInterchange coefficients, dispersive C and C ls1, Gibbs energy; ls2, enthalpy; ls3, heat capacity for contactshn, l hn, l

Ž . Ž .h,n type h, OH in 1-alkanols; type n, NH in secondary linear amines

Ž .u,Õ in n in CH `CH `OH3 ny1

CH `CH `NH`CH `CH 1 2 3 4 5 6 G73 uy1 Õy1 3

DIS aŽ .1,G1 C y18.50 y18.00 y18.00 y18.00 y18.00 y18.00 y18.00hn, 1Ž .2,G2 y21.75 y21.00 y24.50 y24.50 y24.50 y24.50 y24.50

aŽ .G3,G3 y20.75 y19.00 y24.50 y24.50 y24.50 y24.50 y24.50DISŽ .u,Õ C y50.00 y50.00 y61.00 y83.00 y104.0 y118.5 y126.0hn, 2DISŽ .u,Õ C 24.00 24.00 24.00 24.00 24.0 24.0 24.0hn, 3QUACŽ .u,Õ C y1.2 y0.6 0.6 0.6 0.6 0.6 0.6hn, 1QUAC aŽ .-4,G4 C y6.75 y3.0 1.0 4.5 8.0 9.5 10.2hn, 2

aŽ .G4,G4 y8.50 y5.5 y1.6 2.3 5.6 8.0 8.5QUACŽ .u,Õ C 12.0 12.0 12.0 12.0 12.0 12.0 12.0hn, 3

aEstimated value.

coefficients are estimated by interpolation or extrapolation of the well-known parameters, taking intoaccount their overall variation with the chain length of the mixture compounds. This procedureincreases markedly the predictive ability of the model. Final interaction parameters are listed inTables 2 and 3.

Table 4Ž .ERAS parameters of pure compounds at temperature T K

U U U UmolCompound TrK K P r V r V r Dh r DÕ ri iy3 3 y1 3 y1 y1 3 y1J cm cm mol cm mol J mol cm mol

a b b b a,b a,bMethanol 293.15 1172 424.3 40.49 32.06 y25100 y5.6a a a a a,b a,b298.15 986 443.6 40.73 32.13 y25100 y5.6a b b b a,b a,b313.15 607 443.6 40.73 32.13 y25100 y5.6

aa a a a aEthanol 298.15 317 426.4 58.67 47.11 y25100 y5.6aa a a a a1-Propanol 298.15 197 433.9 75.16 61.22 y25100 y5.6aa a a a a1-Butanol 298.15 175 422.7 91.97 75.70 y25100 y5.6

c c c c a,c a,c313.15 108 392.9 92.77 75.70 y25100 y5.6d d d d a,d a,d1-Pentanol 298.15 153 411.0 108.69 89.76 y25100 y5.6b b b b a,b a,b1-Hexanol 298.15 197 433.9 75.16 61.22 y25100 y5.6e e e e a,e a,e1-Heptanol 298.15 101 417.9 141.80 118.90 y25100 y5.6

c c c c c cButylamine 313.15 0.74 351.1 101.62 78.00 y13200 y2.8f c c c c c cDEA 298.15 0.84 511.3 104.57 78.80 y8500 y4.7g e e e e e eDBA 293.15 0.16 283.5 170.00 144.70 y6500 y3.4

e e e e e e298.15 0.16 319.1 171.00 143.00 y6500 y3.4

aw x1 .bw x37 .cw x5 .dw x2 .ew x6 .f Diethylamine.gDibutylamine.


Table 5Ž . Ž .ERAS parameters this work for mixtures at temperature T K

U UMixture TrK K Dh r DÕ r Q r X rAB AB AB AB ABy3 3 y1 y3 y1 y3J cm cm mol J cm K J cm

MethanolqDEA 298.15 3150 y45450 y13.3 0.055 6.0MethanolqDBA 293.15 1050 y42400 y13.3 10.0EthanolqDBA 293.15 395 y37800 y12.0 10.01-PropanolqDBA 298.15 280 y34500 y11.0 10.01-ButanolqDBA 298.15 210 y34500 y11.0 10.01-PentanolqDBA 298.15 185 y34500 y11.0 10.01-HexanolqDBA 298.15 135 y34500 y11.0 10.01-HeptanolqDBA 298.15 95 y34500 y11.0 10.0

a a a a1-butanolqbutylamine 313.15 368 y38600 y10.2 y0.096 5.3

aw x1 .

3.2. ERAS parameters

The parameters adjustable to excess properties are K , K , K , DhU, DhU , DhU , DÕU, DÕ

U,A B AB A B AB A B

DÕU , X U , and Q . X is the energetic interaction parameter characterizing the difference ofAB AB AB AB

dispersive intermolecular interactions between molecules A and B in the solution and in the pureE E w xcomponents, and is the only adjustable parameter of the physical part of H and V 1,2,33 . QAB

appears only in the expression of GE and it characterizes the entropic contribution to the difference ofw xintermolecular interactions 34–38 .

K , K and DhU, DhU are known for all alcohols and amines from H E of alcohol orA B A B

amineqalkane mixtures, respectively. DÕU, DÕ

U are also known, as they are fitted to V E of alcoholA B

or amineqalkane systems. The remaining parameters K , DhU , DÕU and X are usuallyAB AB AB AB

E E w xadjusted to H and V data. More details are given in literature 1,2 . However, for 1-alkanolsqE w x Udibutylamine systems, only V data are available for the solution with 1-propanol 6 , and DÕ wasAB

determined using these measurements, and assumed constant for the longer 1-alkanols. In the case ofmixtures with methanol or ethanol, K , DhU , DÕ

U and X were calculated on the basis of H EAB AB AB AB

data.Q was only obtained for 1-butanolqbutylamine at 313.15 K and for methanol diethylamine atAB

E w x298.15 K using the available G data 10,39 due to the application of the model over a wide range oftemperature is restricted by the necessity of the determination of the reduction parameters over suchrange. This is one of the limitations of the model.

Parameters for pure compounds and those corresponding for the new mixtures analyzed in thiswork are listed in Tables 4 and 5, respectively.

4. Results

4.1. Comparison of DISQUAC with experiment

The comparison between the experimental data and the results obtained using DISQUAC ispresented in Tables 6 and 7, and shown graphically, for selected systems, in Figs. 1–7.


Table 6E Ž .Molar excess Gibbs energies, G , at temperature T K and equimolar composition for 1-alkanolsqamines mixtures.

Ž . Ž .Comparison between experimental results exp and values obtained using DISQUAC DQ with the coefficients fromŽ . w xTables 2 and 3, or UNIFAC UNIF using the interaction parameters from Ref. 18 . A comparison between the respectiveŽ .standard relative deviations, s P , as defined by Eq. 10, is also included . N is the number of data points for each systemr

E y1 Ž .System TrK N G rJ mol s P Referencer

w Ž .xnqu or q u,Õ exp DQ UNIF exp DQa w x3q3 302.95 14 y752 y759 y972 0.0008 0.011 75

w x312.30 14 y668 y698 y917 0.0007 0.013 75w x318.15 16 y556 y661 y884 0.002 0.035 75

bw x343.15 y533 y511 y754 76a bw x1q4 348.15 y799 y727 y489 77

bw x2q4 313.15 10 y692 y819 y704 0.006 0.037 78bw x3q4 318.15 9 y849 y476 y768 0.011 0.12 79bw x328.15 9 y747 y410 y712 0.015 0.11 79bw x338.15 8 y689 y348 y660 0.003 0.10 79

a w x4q4 313.15 8 y384 y385 y862 0.01 0.015 39bw x368.15 y445 y40 y623 80

a bŽ . w x2q 1,1 293.15 y1144 y1119 y1033 81bw x313.15 y972 y909 y900 81bŽ . w x3q 1,1 293.15 y831 y842 y1084 81bw x298.15 y828 y800 y1056 81bw x303.15 y855 y758 y1028 81bw x313.15 y785 y678 y970 81

aŽ . w x1q 2,2 297.97 13 y823 y813 y981 0.002 0.018 10bw x338.15 y298 y370 y597 77

w x348.09 13 y307 y279 y524 0.0006 0.078 10w x398.58 13 77 45 y246 0.0007 0.009 10

aŽ . w x2q 2,2 313.15 9 y529 y522 y395 0.009 0.025 42bw x340.15 y275 y321 y218 82bŽ . w x4q 2,4 386.30 90 97 y21 83

aŽ . w x1q 3,3 351.00 88 83 y385 84Ž . w x2q 3,3 360.00 190 144 69 84

a bŽ . w x3q 3,3 373.15 46 25 11 76Ž . w x4q 4,4 403.15 247 275 137 80

aSystem used in the estimation of the interaction parameters.b w xSee also Ref. 93a,b,c cited therein.

For the sake of clarity, Table 6 includes standard relative deviations for pressure defined as:1r22

s P s 1rNÝ P yP rP 10Ž . Ž .Ž .½ 5r exp calc exp

Table 7 lists the standard deviation for H E:1r22E y1 E Es H rJ mol s 1rNÝ H yH 11Ž . Ž .ž /exp calc

Ž . Ž .In Eqs. 10 and 11 , N is the number of data points of each system. In Tables 6 and 7, experimentalŽ . Ž E.values for s P and s H are also reported. These quantities were calculated assuming ar

Redlich–Kister expansion for GE and H E. The respective coefficients were taken from literature or


Table 7E Ž .Molar excess enthalpies, H , at temperature T K and equimolar composition for 1-alkanolsqamines mixtures. Compari-

Ž . Ž .son between experimental results exp and values obtained using DISQUAC DQ with the coefficients from Tables 2 andŽ . w x w x3; UNIFAC UNIF using the interaction parameters from Ref. 18 and ERAS using parameters from Refs. 1,2 or from

Ž E.Tables 4 and 5. It also includes a comparison between the respective standard deviations, s H , as defined by Eq. 11. N isthe number of data points for each system

E y1 E y1Ž .System TrK N H rJ mol s H rJ mol Referencew Ž .xnqu or q u,Õ exp DQ UNIF exp DQ UNIF ERAS

( ) ( )CH ` CH OHqCH ` CH NH3 2 ny 1 3 2 uy 1 2w x1q3 298.15 26 y2330 y3793 y3240 34 1100 770 43

a,b w x19 y3794 25 110 334 174 1w x1q4 293.15 18 y3918 y3655 y3264 22 140 337 85w x298.15 24 y3730 y3588 y3240 46 270 352 380 43

a,b w x19 y3767 17 120 322 232 1w x14 y3867 83 190 356 289 86w x12 y3850 33 160 397 278 87w x11 y3754 68 130 333 215 88w x313.15 9 y3746 y3384 y3166 61 230 339 245 89w x318.15 9 y3658 y3314 y3143 71 210 317 88

b w x1q6 298.15 22 y3200 y3227 y3187 18 77 21 159 2w x1q8 298.15 26 y3135 y3192 y3099 14 92 53 178 2w x1q10 298.15 27 y3128 y2956 y2996 11 90 153 116 2

a,b w x2q3 298.15 19 y2889 y2931 y3079 19 90 212 122 1w x2q4 293.15 16 y3095 y2873 y3085 31 110 82 85w x298.15 13 y2970 y2814 y3022 41 130 113 87

a,b w x19 y2890 17 66 177 116 1w x313.15 12 y2887 y2629 y2827 32 220 68 89

a,b w x3q3 298.15 19 y2849 y2811 y2856 16 92 151 153 1w x3q4 293.15 16 y3003 y2823 y2899 30 110 133 85w x298.15 15 y3066 y2784 y2840 51 190 169 204 90

a,b w x19 y2844 15 65 118 175 1w x313.15 12 y2849 y2655 y2666 50 130 122 328 89w x3q5 288.15 10 y2935 y2812 y2936 – 100 156 91w x308.15 10 y2731 y2627 y2673 – 92 80 91


a,b w x4q3 298.15 19 y2669 y2652 y2635 10 120 137 238 1a,b w x4q4 298.15 19 y2681 y2637 y2652 18 59 118 211 1b w x4q5 288.15 10 y2827 y2690 y2773 – 90 134 91b w x308.15 10 y2662 y2552 y2522 – 77 97 91

w x5q4 298.15 27 y2413 y2633 y2473 10 210 135 165 2w x5q6 298.15 37 y2567 y2542 y2481 13 51 75 64 2w x5q8 298.15 26 y2730 y2503 y2428 18 190 187 100 2w x5q10 298.15 32 y2539 y2469 y2347 12 180 130 208 2w x7q4 293.15 12 y2777 y2494 y2209 36 240 400 85

b w x8q6 298.15 30 y2456 y2462 y2112 12 100 238 203 2

( )continued on next page


Ž .Table 7 continuedE y1 E y1Ž .System TrK N H rJ mol s H rJ mol Reference

w Ž .xnqu or q u,Õ exp DQ UNIF exp DQ UNIF ERAS

( ) ( )CH ` CH OHqCH ` CH NH3 2 ny 1 3 2 uy 1 2w x8q8 298.15 42 y2836 y2390 y2134 14 330 485 97 2w x8q10 298.15 31 y2666 y2355 y2118 11 230 409 162 2w x10q4 298.15 33 y2045 y2316 y1755 6 510 215 107 2


( ) ( ) ( )CH ` CH OHqCH ` CH NH` CH `CH3 2 ny 1 3 2 uy 1 2 Õy 1 3bŽ . w x1q 2,2 298.15 14 y4581 y4535 y4447 130 270 238 295 88

w x318.15 7 y4351 y4079 y3784 24 190 361 88Ž . w x1q 4,4 293.15 14 y3646 y3665 y3947 140 280 274 340 41Ž . w x2q 2,2 293.15 8 y2036 y3478 y2658 79 910 361 42Ž . w x2q 4,4 293.15 13 y2973 y2875 y2467 87 120 283 141 41Ž . w x3q 4,4 293.15 10 y2917 y2287 y2446 67 380 287 41

w x298.15 14 y2232 y2200 y2421 13 32 159 99 3Ž . w x4q 1,4 298.15 15 y2658 y2677 y2764 19 41 212 92

bŽ . w x4q 3,3 298.15 24 y2432 y2389 y2468 12 40 63 4Ž . w x4q 4,4 293.15 16 y2771 y2320 y2443 74 260 176 41

b w x298.15 17 y2268 y2249 y2407 12 48 128 87 3Ž . w x5q 1,4 298.15 18 y2577 y2625 y2666 13 34 205 92

bŽ . w x5q 3,3 298.15 24 y2438 y2425 y2422 15 44 62 4Ž . w x5q 4,4 298.15 17 y2321 y2300 y2382 15 53 79 92 3Ž . w x6q 1,4 298.15 17 y2515 y2603 y2575 24 72 169 92

bŽ . w x6q 3,3 298.15 23 y2346 y2467 y2377 18 84 56 4bŽ . w x6q 4,4 298.15 18 y2281 y2255 y2355 15 40 108 90 3bŽ . w x7q 3,3 298.15 22 y2298 y2386 y2334 14 79 42 4

Ž . w x7q 4,4 293.15 10 y2826 y2279 y2349 26 400 313 41b w x298.15 15 y2228 y2225 y2327 10 28 105 81 3

Ž . w x8q 3,3 298.15 23 y2213 y2195 y2294 18 80 106 4

a Ž .Direct experimental data not available; values from a Redlich–Kister equation using rounded x x increments0.05 .1 1bSystem used in the estimation of the interaction parameters.

determined by minimization of the sum of deviations in P or in H E, all points being weightedequally. In the case of VLE, vapour phase imperfection was accounted for in terms of the second

w xvirial coefficients, calculated by the Hayden–O’Connell method 40 .DISQUAC represents fairly well the thermodynamic properties of the systems investigated. The

larger discrepancies can be attributed to experimental inaccuracies. For example, it is clear that theE w xmeasured H values for ethanolqdiethylamine, or 1-propanolqdibutylamine at 293.15 K 41,42

Ž .do no fit in the general scheme of mixtures involving 1-alkanols and secondary amines Table 7 .w xSimilarly, it occurs for data of the methanolqpropylamine system from 43 .

On the other hand, it is noticeable that the shape of the curves of the excess functions is usuallywell represented. Here, we remark the good results obtained for GE of the methanolqdiethylamine

Ž .system Table 6; Figs. 1 and 2 .


E Ž . Ž . w x Ž . Ž . w xFig. 1. G of the 1-butanol 1 qbutylamine 2 at 313.15 K 39 and methanol 1 qdiethylamine 2 at 298. K 10Ž . Ž . Ž . Ž . Ž . Ž .mixtures. Points, experimental values: v 1-butanol 1 qbutylamine 2 ; B methanol 1 qdiethylamine 2 . Solid lines,

Ž .DISQUAC calculations; dashed lines, ERAS or UNIFAC results. The latter are only shown for methanol 1 qdiethylamineŽ .2 .

It is interesting to note that the methanolqammonia mixture can be studied similarly to otherw x Ž .alcoholsqamines systems. In a previous paper 31 , NH was treated as a primary amine H`NH3 2

with no C atom. This approach was successful in order to predict liquid–liquid equilibria of NH with3QUAC Ž .n-alkanes. Here, we proceeded similarly. Using the C ls1, 2, 3 of methanolqhn, l

E Ž . Ž .Fig. 2. G of the methanol 1 qdiethylamine 2 mixture at temperatures ranging from 363.8 to 369.9 K. Points,w xexperimental values 11 . Solid line, DISQUAC calculations; dashed line, UNIFAC results.


E Ž . Ž . w xFig. 3. H of the methanol 1 q n-propylamine 2 system at 298.15 K. Points, experimental results 1 . Solid line:DISQUAC values; dashed lines: calculations from the UNIFAC or ERAS models.

Ž . Ž . DIS DISCH ` CH `NH us1, 2, 3, 4, 5 , and C sy2.5, C s13.0, we can reproduce the3 2 uy1 2 hn, 1 hn, 2w x Ž .available VLE data 44 Fig. 8 .

4.2. Comparison between the DISQUAC and the UNIFAC models

Ž .This comparison is presented in detail along Tables 6 and 7 see also Figs. 1–6 . DISQUACprovides better results. For example, the mean deviation for GE at equimolar composition of systems

E Ž . Ž . w xFig. 4. H of the methanol 1 q n-decylamine 2 system at 298.15 K. Points, experimental results 2 . Solid line:DISQUAC values; dashed lines: calculations from the UNIFAC or ERAS models.


E Ž . Ž . w xFig. 5. H of the 1-butanol 1 q n-butylamine 2 system at 298.15 K. Points, experimental results 1 . Solid line:DISQUAC values; dashed lines: calculations from the UNIFAC or ERAS models.

containing primary amines is 26% and 35.5% for the DISQUAC and UNIFAC models, respectively.In the case of mixtures with secondary amines, these values are 14.6% and 99%. Regarding H E, the

E EŽ . Ž . .mean standard deviation s H , defined as Ýs H rnumber of systems , for 1-alkanolsqprimaryŽ . Ž . y1amines is 173 DISQUAC and 200 UNIFAC J mol ; and for solutions with secondary amines, the

values are 167 and 186 J moly1. These close results are due in part to the large deviations obtainedusing DISQUAC for systems in which experimental H E values are in error as ethanolqdiethylamine,

Ž w x .and 1-propanol or 1-butanolqdibutylamine at 293.15 K Refs. 41,42 ; Table 7 . DISQUACŽ .improves clearly results for mixtures with methanol Tables 6 and 7; Figs. 1 and 2 .

E Ž . Ž . w xFig. 6. H of the 1-decanol 1 q n-hexylamine 2 system at 298.15 K. Points, experimental results 2 . Solid line:DISQUAC values; dashed lines: calculations from the UNIFAC or ERAS models.


E Ž . Ž .Fig. 7. H of 1-alkanols 1 qsecondary amines 2 mixtures at 298.15 K. Solid lines: DISQUAC calculations; dashed line:Ž . Ž . Ž . Ž . Ž .ERAS results for methanol 1 qdiethylamine 2 ; points, experimental measurements: v , methanol 1 qdiethylamine 2

w x Ž . Ž . Ž . w x Ž . Ž . Ž . w x Ž . Ž .88 ; % 1-butanol 1 qmethylbutylamine 2 92 ; B 1-pentanol 1 qdipropylamine 2 4 ; ' 1-heptanol 1 qŽ . w xdibutylamine 2 3 .

4.3. ERAS results and comparison with DISQUAC

H E results for methanolqdiethylamine and 1-alkanolsqdibutylamine mixtures are listed in TableE y1Ž . Ž . Ž . Ž7 see also Fig. 7 . For this type of systems eight mixtures , s H rJ mol s153 DISQUAC

. E w x w xvalue, 94 . V data at 298.15 K for methanolqdiethylamine 45 and 1-propanolqdibutylamine 6Ž .are well represented Fig. 9 .

Ž . Ž .Fig. 8. VLE phase diagrams of the methanol 1 qammonia 2 mixtures at different temperatures. Points, experimentalw x Ž . Ž . Ž .results 44 : v , 313.15 K; B 333.15 K; lines DISQUAC calculations.


E Ž . Ž . Ž . Ž . Ž .Fig. 9. V at 298.15 K for methanol 1 qdiethylamine 2 and 1-propanol 2 qdibutylamine 2 . solid lines ERASŽ . Ž . Ž . w x Ž . Ž . Ž .calculations; points, experimental results: B methanol 1 qdiethylamine 2 45 ; v 1-propanol 1 qdibutylamine 2

w x6 .

w xFor solutions of alcohols and primary amines, ERAS parameters from literature 1,2 were used andE Ž .H results compared with DISQUAC values Table 7; Figs. 3–6 . For a total of 32 systems,

E y1Ž . Ž . Ž .s H rJ mol s232 ERAS and 165 DISQUAC . It is remarkable that DISQUAC yields muchbetter results for those mixtures containing the lower alcohols, and particularly methanol. Inexchange, ERAS describes better systems with 1-octanol or 1-decanol, whose experimental data seem

Ž .to be not reliable see below .E Ž .ERAS results on G of 1-butanolqbutylamine and methanolqdiethylamine are poorer Fig. 1 .

The difficulty of the model to represent simultaneously VLE, H E and V E has been already pointedw xout 34–38 .

Of course, the main advantage of ERAS is its ability to represent V E. DISQUAC is a rigid latticeE Ž .theory and hence V s0. However, one should keep in mind that physical theories as DISQUAC

w x Žcan be applied to any type of binary mixture 15–17,27,28,46–53 , while ERAS or any association.model can be only used for those systems where association is expected.

5. Discussion

Thermodynamic properties of mixtures can be examined taking into account differences inmolecular size and shape, anisotropy, dispersion forces and so forth. To investigate the impact of

w x Ž .polarity on bulk properties the effective dipole moment, m can be used 16,53–57 see Appendix B .A large m does not always mean strong interactions between unlike molecules because the strength of

w xthese interactions depend on those between molecules in pure liquids 16 , what can be analyzed interms of the differences between the standard enthalpy of vaporization of a given compound with a

w xcharacteristic group Z and that of the homomorphic alkane 16,53,58 .


5.1. The effect of increasing chain length of the amine for a giÕen alcohol

Ž .In this case, m of the amine decreases Table 8 indicating that amine–amine interactions in thecondensed phase decrease in the sequence propylamine)butylamine)hexylamine . . . ; or dieth-ylamine)dipropylamine)dibutylamine.

In alcoholic solutions with secondary amines, we note that, for the symmetrical ones, H E is nearlyŽ .constant when m decreases Table 7 , due to the decrease of the amine–amine interactions is balanced

E Žby the weakening of the interactions between unlike molecules. On the other hand, H methyl-. E Ž .butylamine -H dipropylamine , as the N atom in the asymmetrical amine is less hindered than in

dipropylamine and the alcohol–amine interactions become stronger.In systems containing 1-alkanols and primary amines, one could expect a similar behaviour. H E

data for mixtures with methanol or propanol do not depend on the amine for propylamine or

Table 8Ž . Ž . Ž mol. Ž .Critical temperatures T , pressures P , molar volumes V , dipole moments in vapor phase m , effective dipolec c

XUŽ . ŽŽ . .moments m, Eq. B4 , and reduced dipole moments m , Eq. B3 in liquid phase for some of the compounds consideredin this work

XUmol, a 3 y1 Ž .Compound T rK P rbars V rcm mol mrD m mc c

a a b cMethanol 512.64 80.92 40.48 1.7 1.023 0.216a a b cEthanol 513.92 61.32 58.37 1.7 0.852 0.188a a b c1-Propanol 536.78 51.68 74.80 1.7 0.752 0.165a a b a1-Butanol 563.05 44.23 91.53 1.66 0.664 0.142a a b c1-Pentanol 588.15 39.09 108.24 1.7 0.625 0.131a a b d1-Hexanol 610.70 34.70 125.59 1.7 0.580 0.119a a b c1-Heptanol 632.54 31.35 141.38 1.7 0.547 0.109a a e d1-Octanol 652.54 28.60 157.63 1.6 0.488 0.095a a b d1-Nonanol 671.50 26.30 174.37 1.6 0.464 0.088

a a b f1-Decanol 689. 24.10 190.77 1.6 0.443 0.083a a e cMethylamine 430.70 76.14 47.35 1.3 0.723 0.191

a a e cEthylamine 456. 56.20 66.59 1.3 0.610 0.155a a b cPropylamine 497. 47.20 82.41 1.3 0.548 0.130

a a b cButylamine 531.9 42.50 98.65 1.3 0.500 0.115g g b dHexylamine 613.6 38.5 132.10 1.3 0.433 0.095

g g b dOctylamine 716. 32.5 165.15 1.2 0.357 0.069g g b dDecylamine 780. 27.8 198.20 1.3 0.353 0.064

a a b cDimethylamine 437.2 53.4 66.26 1.0 0.470 0.121a a b cDiethylamine 499.99 37.58 103.66 1.1 0.413 0.098

a a b cDipropylamine 555.8 36.3 136.74 1.0 0.327 0.079a a b cDibutylamine 607.5 31.1 168.51 1.1 0.324 0.073a a b cTriethylamine 535.6 30.32 139.10 0.9 0.292 0.067

aw x95 .bData at 208C.cw x96 .dw x97 .eData at 258C.f Estimated value.g w xFrom Joback’s method 96 .


E w xFig. 10. H at 298.15 K and equimolar composition 1,2 for 1-alkanolsqprimary amines systems vs. u, the number ofcarbon atoms in the amine.

butylamine, while a rather steep transition is observed for hexylamine. We note that for systems withpentanol, octanol or decanol, H E results are probably in error, as the erratic change of H E with the

Ž .chain length of amine shows Table 7; Fig. 10 . The same occurs for mixtures with the longer aminesŽ .octylamine or decylamine . So, the above trend should be confirmed through new measurements.

5.2. The effect of passing from a primary amine to an isomeric secondary amine

w x ŽIt is known that such replacement decreases the affinity for protons of the adjacent atoms 59 N. Ein this case . It leads to a decrease of H of systems containing amines and n-alkanes in the sequence

Ž .primary)N, N-dialkylamine)N, N, N-trialkylamine. Note that m Table 8 and D H decreases in theÕ

Ž . Ž . y1 Ž .same order. For example, H butylamine yH n-pentane s9.1 kJ mol ; and H diethylamineÕ Õ Õ

Ž . y1 Ž w x.yH n-pentane s4.7 kJ mol data at 298.2 K from Ref. 60 . In solutions containing alcohols,Õ

the behaviour should be the opposite. Nevertheless, results depend strongly on steric factors, whichplay a role of the major importance in secondary and tertiary amines. We remark the very exothermicH E for systems containing methylbutylamine, similar to those of mixtures with primary amines of

Ž .same size Table 7 .

5.3. The effect of increasing the chain length of the alcohol for a giÕen amine

Ž .The m of alcohols decreases Table 8 and, consequently, the same goes with the alcohol–alcoholinteractions in the condensed phase in the sequence methanol)ethanol) . . . )decanol.

EIn systems of 1-alkanols with a given primary amine, H seems to increase when m of the alcoholdecreases. This occurs for mixtures of methanol, ethanol, propanol or butanol with propyl or

Ž .butylamine Table 7; Fig. 10 . We note that the transition from methanol to ethanol is much steepercompared to the transition from ethanol to butanol. Excess volume measurements confirm this point


w x61,62 . It is remarkable that a similar behaviour is also found in other type of mixtures, e.g.,w x1-alkanolsqpolyethers 63 . So interactions between methanol and amines are much stronger than

w xwith other alcohols. Similar results are found for 1-alkanolsqpyridines 64,65,94 , or qtriethylaminew x E17 mixtures. The poor H results for systems with the longer amines have been already pointed out.

Ž .For 1-alkanolsqsecondary amines Table 7 , we also find the steep transition from methanol tothe remainder alcohols. For the latter, H E is nearly constant, indicating that the decrease ofalcohol–alcohol interactions is balanced by weaker alcohol–amine interactions.

5.4. Concentration–concentration structure factors

w xRecently, Cobos 66 has presented, in terms of the quasichemical approximation of the latticew xtheory developed by Guggenheim 14 , a rigorous and comprehensible treatment of excess heat

capacities at constant volume and pressure and of their relationships with the concentration–con-Ž .centration structure factor, S 0 , showing that these physical magnitudes are useful in order tocc

analyze the mixture structure. From this point of view, we will refer here merely to the main featuresŽ . w x w xof S 0 66 . This quantity may be written as 67–69 :cc

S 0 sRTr E2DGrEx 2 sx x rD 12Ž . Ž .Ž .cc 1 1 2P ,T

with

Ds x x rRT E2DGrEx 2 s1q x x rRT E2GErEx 2 13Ž . Ž . Ž .Ž . Ž .1 2 1 1 2 1P ,T P ,T

where R is the gas constant, T the system temperature, and DG is the molar Gibbs energy of mixing.w x Ž .Therefore, D is a function closely related to the thermodynamic stability 8,67,69–71 see below .

E, id id idŽ .For ideal mixtures, G s0, D s1 and S 0 sx x .cc 1 2Ž . w x Ž .As stability conditions require, S 0 )0 68 and if the system is close to phase separation, S 0cc cc

Ž .must be very large and positive `, in the limit, when the mixture presents a miscibility gap . InŽ . Žexchange, if compound formation between components appears, S 0 must be very low 0, in thecc

. Ž . idŽ .limit . So, if S 0 )x x sS 0 , i.e., D-1, the dominant trend in the system is the separation ofcc 1 2 ccŽ .the components homocoordination and the mixture is less stable than the ideal. On the contrary,

Ž . idŽ .when 0-S 0 -x x sS 0 , i.e., D)1, the fluctuations in the system have been removed andcc 1 2 ccŽ .the dominant trend in the solution is the compound formation heterocoordination . The system is

more stable than ideal. Fig. 11 shows that heterocoordination is the main feature in the studiedŽ Ž . .mixtures S 0 -x x .cc 1 2

As it is known, H E curves are slightly shifted to lower mole fractions of the amine for alcoholicsolutions with, e.g., secondary amines. This has been explained assuming formation of 1–1 com-

w x Ž . Ž .plexes between both components 3,4 . However, S 0 results for methanolqdiethylamine Fig. 11cc

suggest that several alcohol molecules are associated to one amine. A similar conclusion has beenw xreported elsewhere 11 .

5.5. Structure dependence of the interaction parameters

Ž .For 1-alkanolsqprimary amines mixtures, we note Table 2 the following.DIS DIS QUACŽ .i C and C are independent of the amine. C decreases when m of the alcohol alsohn, 1 hn, 2 hn, 2

decreases. C DIS remains constant from 1-butanol.hn, 1


Ž . Ž . Ž . Ž . Ž . Ž .Fig. 11. S 0 for amines 1 q1-alkanols 2 mixtures. Points, experimental results: B n-propylamine 1 q1-propanol 2ccw x Ž . Ž . Ž . w xat 302.95 K 75 ; v diethylamine 1 qmethanol 2 at 297.97 K 10 . Solid lines: DISQUAC results; dashed line: ideal

mixture.

Ž . DIS QUACii C and C do not depend on the compounds present in the system. As the availablehn, 3 hn, 3

database on H E at T/298.15 K is rather limited and not reliable, these interaction parameters shouldbe taken with caution. Nevertheless, we remark that the temperature dependence of H E is correctlypredicted, as this magnitude increases with T.

QUACŽ .iii C is independent of the amine, and increases when m of the alcohol decreases. Fromhn, 1

1-propanol, it is constant.QUACŽ .iv C depends on both components of the mixture. For a fixed amine, it increases when m ofhn, 2

Ž .the alcohol decreases, and remains constant from 1-hexanol Fig. 12 . For a given alcohol, m

decreases with the size of the amine, being constant for the longer amines.In the case of 1-alkanolqsecondary amine mixtures, the structure dependence of the interaction

QUAC Ž .parameters is similar. Nevertheless, some differences for C ls1,2 are found. When the aminehn, l

is fixed, C QUAC varies with the alcohol as in solutions with primary amines. For a given alkanol, onlyhn, 2Ž .two groups of amines are distinguished Table 3 . The more complex behaviour found in systems with

primary amines may be attributed, at least in part, to the mentioned experimental inaccuracies. Fromthe point of view of the ERAS model, it leads to K values, which vary in an unrealistic way.AB

w xTherefore, K is 2900 for methanolqhexylamine, and 2125 for methanolqpropylamine 1,2 . ForAB

systems of 1-pentanol with hexylamine or octylamine, K is 125 and 145, respectively. The sameABw xoccurs for mixtures with 1-octanol, or 1-decanol 2 . Note the rather correct relative variation of KAB

Ž .in 1-alkanolsqdibutylamine systems Table 5 as the corresponding values were obtained fromreliable data.

When the present interaction parameters are compared with those derived in previous works forother alcoholic solutions, we note that the QUAC coefficients are usually independent of the alkanol

w xfor ls1,2,3 15,17,47–52 . Only some different values of such coefficients have been obtained formethanol or ethanol, what may be explained by their different character when compared to the longer

Ž w x.ones higher dielectric constant, stronger self-association 72 . This is the case of 1-alcoholsqCCl4


QUAC Ž . Ž w x. Ž .Fig. 12. C full symbols; this work or K r100 open symbols 1,2 vs. the effective dipole moment Eq. B4 forhn, 2 ABŽ . Ž . Ž . Ž . Ž . X Žseveral 1-alkanols 1 qamines 2 mixtures: v n-propylamine, B n-butylamine; ' N, N -dialkylamines N-4,

X . Ž . Ž .N F4 ; ` , n-butylamine; I n-decylamine.

w x w x48 , or qaromatic compounds 47 . A similar trend has been obtained when treating such mixtures inw xterms of Barker’s theory 73,74 .

QUAC Ž .In the present mixtures, we also found somewhat different C ls1,2 coefficients forhn, l

methanol or ethanol. Their negative value remarks that for such alcohols the negative deviations fromw xRaoult’s law are stronger. Similarly, it occurs in 1-alkanolsq triethylamine mixtures 17 . In terms of

the ERAS model, this is supported by more negative values of DhU for those solutions withABŽ w x.methanol or ethanol Table 5; Refs. 1,17 .

6. Conclusions

The DISQUAC model has been extended to binary mixtures of 1-alkanols with primary andsecondary amines. New ERAS parameters have also been reported for solutions of 1-alkanols andsome secondary amines. Experimental results have been carefully analyzed and compared withDISQUAC, UNIFAC and ERAS calculations. DISQUAC properly describes the investigated mix-

Ž w x.tures. So, the main conclusion of this and previous studies see, e.g., Refs. 15–17,27,28,46–53 isthat DISQUAC can be applied successfully to any type of binary mixtures. ERAS model improvesDISQUAC as it can provide information on V E, but, of course, can only be used when association isexpected.

List of symbolsa, b, c UNIFAC group interaction parametersc interchange heat capacity at constant pressure parameterp

C interchange coefficient in DISQUAC


g interchange Gibbs energy parameterG molar Gibbs energyh interchange enthalpy parameterH molar enthalpyDhU, DhU self-association enthalpies of components A and BA B

DhU association enthalpies of component A with component BAB

K , K self-association constants of components A and BA B

K association constant of component A with component BAB

P pressureP reduced pressurePU reduction parameter for pressureq relative molecular area of component in DISQUACr relative molecular volume of component in DISQUACS surface-to-volume fractionS concentration–concentration structure factorcc

T absolute temperatureT reduced temperatureTU reduction parameter for temperatureDÕ

U, DÕU self-association volumes of components A and BA B

DÕU association volumes of component A with component BAB

V mol molar volumeV reduced volumeV U reduction parameter for volumex mole fraction in the liquid phaseX physical adjustable parameter in ERAS modelAB

y mole fraction in the vapor phasez coordination number

Greek lettersa molecular surface fractiong activity coefficientF hard core volume fraction of component i in the mixture in ERAS or volumei

molar fraction in DISQUAC and UNIFACm dipole moment

U Ž U.m , m , or m reduced dipole momentsˆm effective dipole moments standard deviations standard relative deviationr

u surface fraction in ERAS model of component ii

SuperscriptsCOMB combinatorial partDIS dispersive termE excess property


QUAC quasichemical termRES residual part

Subscriptsa, h type of contact surface: a, CH , CH ; h, OH in DISQUAC3 2

chem chemical contribution to excess functions in ERAS modelŽ . Ž . Ž .i type of molecule; in ERAS model isA alcohol ; B amine ; M mixture

l order of interchange coefficient: ls1, Gibbs energy; ls2, enthalpy; ls3, heatcapacity

Žm, n type of subgroup in UNIFAC, or contact surface in DISQUAC n, NH or NH in2.primary or secondary amines, respectively

phys physical contribution to excess functions in ERAS modelŽ .s, t type of contact surface in DISQUAC s/ t

Acknowledgements

This work was supported by the Programa Sectorial de Promocion General del Conocimiento de la´Ž .S.E.U.I. y D. del M.E.C. Spain , Project no. PB97-0488 and by the Consejerıa de Educacion y´ ´

Ž .Cultura de la Junta de Castilla y Leon Spain , under Project VA54r98.´

Appendix A

A.1. DISQUAC equations

Ž . EIn Eq. 1 , we have for G :

GE, COMBrRTsx ln F rx qx ln F rx A1Ž . Ž . Ž .1 1 1 2 2 2

Ž .which represents the Flory–Huggins combinatorial term. Here, F sx r r x r qx r is the volumei i i 1 1 2 2Ž .fraction, x , the mole fraction and r the total relative molecular volume of component i is1,2 .i i

The dispersive contribution is given by:

F E, DIS s q x qq x j j f DIS A2Ž . Ž .int 1 1 2 2 1 2 12

Žwhere q stands for the total relative molecular area of a molecule of type i and j sx q r q x qi i i i 1 1. Ž . E Eq x is the surface fraction of component i in the mixture is1,2 . Moreover, if F sG , then2 2

f DIS sg DIS; if F E sH E, then f DIS shDIS, and if F E sC E, then f DIS scDIS. f DIS is represented by12 12 12 12 p 12 p12 12

the equation:

f DIS sy1r2 S S a ya a a f DIS A3Ž . Ž . Ž .12 s t s1 s2 t t st1 2

being a is the molecular surface fraction of surface type s on a molecule of type i.s i

For the QUAC part:

GE, QUAC sx mE, QUAC qx mQUAC A4Ž .int 1 int , 1 2 int , 2


where

mE, QUAC szq S a ln x a rx a , is1,2 A5Ž . Ž .int ,i i s s i s s i s i s

andE, QUAC QUACH s1r2 x q qx q S S x x y j x x qj x x h h A6Ž . Ž . Ž .int 1 1 2 2 s t s t 1 s1 t1 2 s2 t2 st st

being

h sexp yg QUACrzRT A7Ž .Ž .st st

and z the lattice coordination number.Accordingly,

C E, QUAC sd H E, QUACrdT . A8Ž .pint int

ŽThe quantities x and x are obtained by solving the system of l equations l is the number ofs t.contact surfaces :

x x qS x h sa A9Ž . Ž .s s t t st s

Ž . Ž . Ž . Ž .x and x is1,2 are the solutions of Eq. A9 for x s1 pure component i . Eq. A2 fors i t i iE E E E E E Ž . Ž .F sG , F sH , or F sC is obtained from the quasichemical Eqs. A4 – A9 when z™`,p

Ž .and represents the so-called random mixing or zero approximation of the model.The temperature dependence of the DIS or QUAC g parameters is expressed by a three-constantst

equation of the type:DISr QUAC DIS r QUAC DIS r QUACg T rRTsC qC T rT y1Ž . Ž .st st , 1 st , 2 0

DISr QUACqC ln T rT y T rT q1 A10Ž . Ž . Ž .st , 3 0 0

where T is the system temperature. Accordingly:DISr QUAC DIS r QUAC DIS r QUACh T rRTsC T rT yC T rT y1 A11Ž . Ž . Ž . Ž .st st , 2 0 st , 3 0

and

cDISr QUAC T rRsC DISr QUAC . A12Ž . Ž .pst st , 3

A.2. UNIFAC equations

Ž .The combinatorial part for the activity coefficients in Eq. 2 is:X XCOMBlng s1yF q lnF y5q 1y F rj qln F rj A13Ž . Ž . Ž .i i i i i i i i

where F and j are defined as above andi i

FX sr 3r4r x r 3r4qx r 3r4 A14Ž .Ž .i i 1 1 2 2

is an empirical term.Parameters r and q are calculated as the sum of the group volume and area parameters, R andi i K

Q , which are fitted together with the interaction parameters a , b , c , a , b , and c .K nm nm nm mn mn mn


The residual term for activity coefficients is given by:

lng RES sS N i ln G yln G i A15Ž .Ž .i K K K K

where N i is the number of group K for the molecule i. On the other hand:K

ln G sQ 1yln S Q C yS Q C rS Q C A16Ž . Ž . Ž .K K m m mK m m mK n n nK

Q are the surface fractions defined as:m

Q sQ X rS Q X A17Ž .m m m n n n

with X , the mole fraction of group m in the mixture written as:m

X sS x N irS S x N i A18Ž .m i i m i K i K

and2C sexp y a qb Tqc T rT A19Ž .Ž .nm nm nm nm

E E 2 Ž E .so G sRT S x ln g and H syRT E G rRT rET. Particularly:i i

U iE iH sS x S N H yH A20Ž .Ž .i i K K K K

where H represents the excess enthalpy of group K and HU i represents the excess enthalpy of groupK K

K in a solution containing only component i. H can be written as:K

X2H sRT Q C rC qD yE A21Ž . Ž .K K K K K K

being:

C sS Q C ; CX sS Q CX

K m m mK K m m mK

D sS Q CX rC E sS Q C CX rC 2 A22Ž . Ž .Ž .K m m mK m K m m mK m m

The prime indicates a derivative with respect to temperature.

A.3. ERAS equations

E Ž .The chemical contribution to H in Eq. 3 is given by:

H E sx DhU K w yw 0 qx DhU K w yw 0Ž . Ž .chem A A A 1A 1A B B B 1B 1B

U mol molqx Dh K w 1yK w r V rV 1yK w qK wŽ . Ž .Ž .A AB AB 1B A 1A B A B 1B AB 1B

U E ˜ 2yP V rV A23Ž .M chem M

where w and w are the solutions of the following equations:1A 1B

2 mol molF sw r 1yK w 1q V K w r V 1yK w A24Ž . Ž . Ž .Ž .½ 5A 1A A 1A A AB 1B B B 1B

2F sw r 1yK w 1q K w r 1yK w A25� 4Ž . Ž . Ž . Ž .B 1B B 1B AB 1A A 1A

where F and F are the hard-core volume fractions:A B

F sx V Ur x V U qx V U isA,B . A26Ž . Ž . Ž .i i i A A B B

In Eqs. A23 and A24, w sw 0 if f s1.1i 1i i


The chemical contribution to V E is expressed by:E ˜ U 0 U 0V sV x DÕ K w yw qx DÕ K w ywŽ . Ž .½chem M A A A 1A 1A B B B 1B 1B

U mol molqx DÕ K w 1yK w r V rV 1yK w qK w A27Ž . Ž . Ž .Ž . 5A AB AB 1B A 1A B A B 1B AB 1B

The physical contributions to H E and V E are written as:U U U U UE ˜ ˜ ˜H s x V qx V F P rV q F P rV y P rV A28Ž . Ž .ž / ž / ž /phys A A B B A A A B B B M M

and

U UE ˜ ˜ ˜V s x V qx V V yF V yF V A29Ž . Ž .phys A A B B M A A B B

For the mixture, the reduction parameters are calculated using the following mixing rules:

PU sF PU qF PU yF u X A30Ž .M A A B B A B AB

U U U U U UT sP r P F rT q P F rT A31Ž . Ž . Ž .M M A A A B B B

V U sx V U qx V U A32Ž .M A A B B

Ž .In Eq. A31 ,

u s1yu s S rS F r F q S rS F A33Ž . Ž . Ž .B A B A B A B A B

is the surface fraction of the component B in the mixture, and S and S are the surface-to-volumeA Bw xratios of molecules A and B, which are calculated using Bondi’s method 25 of molecular group

contributions.For GE, the expressions of the chemical and physical contributions are:

E 0 0 mol 0 mol 0G sRT x ln w rx w qx ln w rx w yV rVqx V rV qx V rVŽ . Ž .chem A 1A A 1A B 1B B 1B M A A A B B B

A34Ž .U U U UE 1r3 1r3˜ ˜�G syT x V qx V u F Q y 3F P rT ln V y1 r V y1Ž . Ž . ž / ž /phys A A B B B A AB A A A A M

U U 1r3 1r3 E˜ ˜y 3F P rT ln V y1 r V y1 qH A35Ž . Ž .ž / ž /B B B B M phys

Ž .in Eq. A34 ,mol mol1rVsw r V 1yK w qw r V 1yK wŽ . Ž .1A A A 1A 1B B B 1B

molqK w w r V 1yK w 1yK w A36Ž . Ž . Ž .AB 1A 1B B A 1A B 1B

and 1rV 0 and 1rV 0 are the values of 1rV if F s1 and F s0, respectively.A B A B

Appendix B

For the purpose of characterizing the effective polarity of a molecule with dipole moment ingas-phase m, and to examine the impact of the polarity on thermodynamic properties of pure liquids

w xand liquid mixtures, one may define a reduced dipole moment according to Refs. 54–56 :1r22 3ms m r4p´ s ´ B1Ž .ˆ 0


where ´ is the permittivity of the vacuum, s an appropriate molecular size parameter and ´ the0

corresponding interaction energy parameter. This expression may advantageously be transformed byvirtue of the corresponding states principle to:

1r2U 2m s m N r4p´ V k T B2Ž .A 0 c B c

or equivalently to:1r2XU 2 2 2m s m P r4p´ k T B3Ž . Ž .c 0 B c

where V , T and P are the critical molar volume, critical temperature and critical pressure,c c cw x Urespectively. N is the Avogadro’s constant, and k is the Boltzmann’s constant 55,56 . m, m andˆA B

Ž U.Xm refer to a single, isolated molecule. However, if the focus is on the impact of polarity on bulkw xproperties, the appropriate quantity to be used is 56 :

1r22 molms m N r4p´ V k T , B4Ž .A 0 B

which may be called as the effective dipole moment.While for a given series, say 1-alkanols, m varies only slightly with the chain length, by necessity

Uthe reduced dipole moments m or m show much greater variation. For a given temperature, themagnitude of m evidently depends on, if one discusses, e.g., a low-density gaseous system or a denseliquid phase.

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Thermodynamics of mixtures with strongly negative deviations from Raoult's Law: Part 4. Application...

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