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Fluid Phase Equilibria 290 (2010) 15–20

Contents lists available at ScienceDirect

Fluid Phase Equilibria

journa l homepage: www.e lsev ier .com/ locate / f lu id

xcess enthalpies of oxygenated compounds + hydrocarbon mixtures: Binary andernary mixtures containing dibutyl ether (DBE), 1-butanol and,2,4-trimethylpentane at 298.15 K

ernando Aguilara, Fatima E.M. Alaouia, José J. Segoviab,iguel A. Villamanánb, Eduardo A. Monteroa,∗

Departamento de Ingeniería Electromecánica, Escuela Politécnica Superior, Universidad de Burgos, E-09006 Burgos, SpainGrupo de Termodinámica y Calibración TERMOCAL, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, E-47071 Valladolid, Spain

r t i c l e i n f o

rticle history:eceived 22 June 2009

a b s t r a c t

Measurements of excess molar enthalpies at the temperature of 298.15 K and atmospheric pressurein a quasi-isothermal flow calorimeter are reported for the ternary system dibutyl ether (DBE) + 1-

eceived in revised form 4 November 2009ccepted 9 November 2009vailable online 17 November 2009

eywords:xcess enthalpy

butanol + 2,2,4-trimethylpentane (TMP) and the corresponding binary systems. All the binary and theternary systems show endothermic character. The Redlich–Kister equation and the NRTL and UNIQUACmodels have been used to fit the experimental data for the binary and ternary systems.

© 2009 Elsevier B.V. All rights reserved.

xygenated compoundasoline

. Introduction

Presently several oxygenated compounds are added to gaso-ine to enhance the octane number and to reduce air pollution. Forroper design of synthesis and separation processes of these refor-ulated gasolines, which contain ethers and alcohols, the phase

ehaviour and thermodynamic properties of the fluid mixtureseed to be known. As a part of our research work on thermo-ynamic properties of octane boosters [1,2], this paper presentsxperimental excess molar enthalpies of the ternary systemBE + 1-butanol + 2,2,4-trimethylpentane and the correspondinginary systems at T = 298.15 K and atmospheric pressure. DBE issed as blending agent in reformulated gasoline and 1-butanol

s a basic component in the synthesis of the ether, and there-ore is always contained as an impurity. 2,2,4-Trimethylpentanes an essential component in gasoline. Excess molar enthalpiesave been measured with a quasi-isothermal flow calorimeter. Thexperimental data have been fitted using polynomial equationsnd group contribution models. The values of the standard devi-tion indicate good agreement between the experimental results

nd those calculated from the equations. Data are also used toescribe the structural effects and interactions that occur betweenolecules in the solutions.

∗ Corresponding author. Tel.: +34 947 258 916; fax: +34 947 259 088.E-mail address: emontero@ubu.es (E.A. Montero).

378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2009.11.010

2. Experimental

All the chemicals used here were purchased from Fluka ChemieAG and were of the highest purity available, chromatography qual-ity reagents (of the series puriss p.a.) with a stated purity >99.5%.The purity of all reagents was checked by gas chromatography,and the values of purity obtained were >99.6% for DBE, >99.8% forTMP and >99.8% for 1-butanol. The water content of 1-butanol waschecked to be less than 0.009%.

Excess molar enthalpies have been measured with a quasi-isothermal flow calorimeter previously described [1]. Twoprecision positive displacement pumps deliver the liquids at pro-grammable constant flow rates into the mixing coil sitting in theflow cell, which is included in the measure unit immersed in a waterbath. In case of binary systems, the two liquids are the pure com-ponents and, in case of ternary systems, one of them is a purecomponent and the other the corresponding binary mixture inwhich the excess molar enthalpy value is known. The calorime-ter is thermostated at T = 298.15 ± 0.01 K. To achieve this condition,a Peltier cooler and a controlled heater actuate simultaneously tomaintain the flow cell temperature constant. The calibration of themeasurement system is made by simulating an exothermic mix-

ing process by a calibration resistor. The change of heating powerof the control-heater before, during and after measurements is anindirect measure for the excess enthalpy HE. The HE is calculatedfrom differences in the heating power control, once the calibrationprocedure has been performed.

16 F. Aguilar et al. / Fluid Phase Equilibria 290 (2010) 15–20

Table 1Experimental excess molar enthalpies of binary systems DBE + 2,2,4-trimethylpentane, DBE + 1-butanol and 2,2,4-trimethylpentane + 1-butanol at T = 298.15 K.

x HE/J mol−1 x HE/J mol−1 x HE/J mol−1 x HE/J mol−1

xDBE + (1 − x)2,2,4-trimethylpentane0.0497 26.88 0.2995 109.48 0.5494 120.48 0.7996 73.970.0997 51.00 0.3500 117.17 0.5996 115.38 0.8495 57.430.1497 71.17 0.3997 121.05 0.6499 107.85 0.8995 39.330.1998 86.08 0.4494 123.47 0.6993 99.00 0.9497 19.550.2501 99.90 0.4994 122.95 0.7499 87.66

xDBE + (1 − x)1-butanola

0.0501 119.4 0.3004 624.6 0.5506 879.8 0.8000 772.80.1002 236.0 0.3498 698.4 0.5998 892.4 0.8501 679.10.1497 344.5 0.4006 762.1 0.6505 890.6 0.8994 543.10.2003 447.6 0.4507 814.0 0.7000 872.6 0.9493 330.10.2503 540.2 0.4997 853.2 0.7509 833.2

x2,2,4-trimethylpentane + (1 − x)1-butanol0.0502 67.15 0.3000 395.64 0.5500 605.64 0.7995 579.930.1001 140.02 0.3502 449.14 0.5997 623.63 0.8501 536.220.1504 210.84 0.4000 497.67 0.6497 630.88 0.9000 473.31

atmcbtpaT[tft

3

wTm

eitu

H

B[e

H

wop

s

0.2002 276.46 0.4498 540.400.2504 338.99 0.5006 578.91

a Data taken from Ref. [1].

Knowing the volumetric flow rates delivered, the molar massesnd the densities of the pure compounds, the mole fractions ofhe mixtures obtained in the mixing coil can be calculated. The

aximum absolute uncertainty of mole fraction at equimolaromposition is ±0.0008. Densities of pure liquids are determinedy interpolating density data obtained from Riddick et al. [3] athe measured temperature of flow delivery of the displacementumps. Estimated densities at T = 298.15 K, were 764.10, 687.80nd 805.75 kg m−3 for the DBE, TMP and 1-butanol, respectively.hese results agree within <0.1% with values found in the literature4–7]. Mixtures of different compositions are studied by changinghe ratio of flow rates and in this way the dependence of HE on moleraction can be determined. The estimated relative uncertainty ofhe determined HE/J mol−1 is ±0.01HE.

. Results and discussion

The experimental excess molar enthalpies obtained in thisork for the binary mixtures DBE + TMP and TMP + 1-butanol at= 298.15 K are listed in Table 1. Experimental data for the binaryixture DBE + 1-butanol were previously reported [1].For binary systems, there are several models and empirical

quations proposed to fit the HE measurements. The smooth-ng Redlich–Kister function [8], given by Eq. (1), was fitted tohe results, in which the Ai coefficients are determined by thenweighted least-squares method.

E = x(1 − x)n∑

i=1

Ai(2x − 1)i−1 (1)

inary systems have also been correlated using the UNIQUAC model9], which expression for the excess molar enthalpy is given by thequation:

E =n∑

i=1

qixi

∑nj=1ϑj �uji�ji∑n

j=1ϑj�ij

(2)

∑

here ϑi = qixi/ jqjxj and qi is the molecular surface area,

btained as the sum of the contributions of the functional groupsresent in the compound.

The NRTL model [10] has also been used to correlate the binaryystems. In the NRTL model, the expression for the excess molar

0.6998 624.75 0.9506 373.880.7498 608.68

enthalpy is given by the equation:

HE = −RT

n∑i=1

xi�i (3)

where xi is the mole fraction of the component i and �i is given by

�i =∑p

k=1xk�kiGki

[˛

(�ki −

(∑pn=1xn�niGni/

∑nl=1xlGli

))− 1

]∑p

l=1xlGli

(4)

Gji = exp(−˛�ij) (5)

The NRTL theory assumes that the excess molar enthalpy of a multi-component mixture depends only on the binary parameters. In thiswork, the non-randomness parameter ˛ is an adjustable parameterfor the three-parameter NRTL model.

Results of data correlation for the binary systems are summa-rized in Table 2 together with root mean square deviation, rms,given by

rms =[∑ndat

i (zexp − zcalc)2

ndat − npar

]1/2

(6)

where zexp, zcalc, ndat and npar are the values of the experimentaland calculated property, the number of experimental data and thenumber of parameters of the model respectively. The degree of thepolynomic expansion of Eq. (1) was optimized using the F-test [11].A plot of the experimental and correlated data is shown in Fig. 1a–c.

The excess molar enthalpy of the system DBE + TMP atT = 298.15 K shows endothermic behaviour (HE > 0) in the wholerange of composition. The best fit of the experimental data at thetemperature of 298.15 K is obtained with the Redlich–Kister equa-tion with a root mean square deviation, rms �HE, of 0.5 J mol−1

and a maximum value of the absolute deviation, max|�HE|, of1.0 J mol−1. Deviations obtained with the NRTL and UNIQUAC mod-els are almost the same. The maximum value of the excess molarenthalpy is 124 J mol−1, obtained at a mole fraction of DBE about0.45. Comparison with data for the same system and temperaturereported by Peng et al. [7], shows that our data agree to within 10.2%in the range of composition 0.3 ≤ x ≤ 0.7, being the experimental

data of this work higher than those of the reference [7].

The binary system DBE + 1-butanol measured at a tempera-ture of 298.15 K is also endothermic. The maximum value of HE

is 892 J mol−1, at a mole fraction of DBE about 0.60. Redlich–Kisterequation gives the best fit with a root mean square deviation, rms

F. Aguilar et al. / Fluid Phase Equilibria 290 (2010) 15–20 17

Table 2Summary of parameters for the representation of HE by Redlich–Kister,NRTL (3 parameters) and UNIQUAC models, for binary systems DBE + 2,2,4-trimethylpentane, DBE + 1-butanol and 2,2,4-trimethylpentane + 1-butanol atT = 298.15 K.

Binary systemsa Correlation

Redlich–Kister NRTL (3p) UNIQUAC

DBE (1) + 2,2,4-trimethylpentane (2)A0 492.8 0.0772 −174.7A1 −58.0 0.1745 270.5A2 18.2A3 −35.7˛12 1.47rms �HE/J mol−1 0.5 0.7 0.8max|�HE|/J mol−1 1.0 1.7 1.5max(|�HE|/HE) 5.0% 8.6% 6.9%

DBE (1) + 1-butanol (3)A0 3414.8 2.4081 2160.1A1 1259.1 0.8333 −629.7A2 741.4A3 1310.7A4 1021.7˛13 0.31rms �HE/J mol−1 2.9 11.9 43.2max|�HE|/J mol−1 4.9 21.8 84.5max(|�HE|/HE) 3.5% 9.7% 23.1%

2,2,4-Trimethylpentane (2) + 1-butanol (3)A0 2337.5 2.4838 2159.1A1 1457.5 0.7237 −765.0A2 −134.1A3 −1489.6A4 3080.2A5 4761.2˛23 0.40rms �HE/J mol−1 13.3 31.0 59.7max|�HE|/J mol−1 30.4 93.0 171.7

A

�lsra

tbmfbQrmNp

Toi0mto

H

T

H

Fig. 1. Excess molar enthalpy HE at T = 298.15 K. (a) Experimental results forDBE + 2,2,4-trimethylpentane; this work (�); DBE + cyclohexane, data from Ref. [1](�); DBE + benzene, data from Ref. [2] (©); (—) calculated values for DBE + 2,2,4-trimethylpentane at T = 298.15 K with Eq. (1) using parameters of Table 2. (b)Experimental results for DBE + 1-butanol, data from Ref. [1] (�); (—) calculated val-ues at T = 298.15 K with Eq. (1) using parameters of Table 2. (c) Experimental resultsfor 2,2,4-trimethylpentane + 1-butanol; this work (�); cyclohexane + 1-butanol,

max(|�HE|/HE) 13.7% 28.2% 45.9%

a Equivalence between parameters: NRTL A0 = �12 and A1 = �21; UNIQUAC0 = �u12; A1 = �u21.

HE, of 2.9 J mol−1 at T = 298.15 K. The maximum value of the abso-ute deviation, max|�HE|, is 4.9 J mol−1. The remaining models givelightly worse fits. Our HE data agree to within 1.5% in the centralange of composition with the measurements for the same systemnd temperature obtained from Kammerer and Lichtenthaler [12].

The third binary system which has been studied is the sys-em TMP + 1-butanol at T = 298.15 K, showing also endothermicehaviour. The maximum value of the excess molar enthalpy of theixture at the temperature of 298.15 K is 631 J mol−1 at the mole

raction of TMP of 0.65 approximately. The experimental data haveeen fitted by the Redlich–Kister equation, the NRTL and the UNI-UAC models. The Redlich–Kister equation gives the best fit with a

oot mean square deviation, rms �HE, of 13.3 J mol−1 and the maxi-um value of the absolute deviation, max|�HE| of 30.4 J mol−1. TheRTL and UNIQUAC models show slightly higher values of fittingarameters.

The ternary mixtures DBE (1) + TMP (2) + 1-butanol (3) at= 298.15 K were formed by adding the TMP (2) to binary mixturesf fixed composition of DBE (1) + 1-butanol (3). Four different start-ng binaries were used, with values of the ratio x1/x3 of 0.2500,.6665, 1.5002 and 4.008, respectively. The experimental excessolar enthalpies listed in Table 3 are determined by Eq. (7), using

he calculated values of HE13 from the Redlich–Kister fit of the data

f the binary system DBE (1) + 1-butanol (3):

E E E

123 = H2+13 + (1 − x2)H13 (7)

he following equation was used to fit the HE measurements

E123 = HE

12 + HE13 + HE

23 + x1x2x3 �HE123 (8)

data from Ref. [1] (�); benzene + 1-butanol, data from Ref. [2] (©); (—) calcu-lated values for 2,2,4-trimethylpentane + 1-butanol at T = 298.15 K with Eq. (1) usingparameters of Table 2.

with

�HE123=B0+B1x1+B2x2+B3x2

1+B4x22+B5x1x2 + B6x3

1 + B7x32 (9)

where the parameters Bi were determined by the unweighted least-squares method. An alternative for the calculation of �HE

123 is Eq.

18 F. Aguilar et al. / Fluid Phase Equilibria 290 (2010) 15–20

Table 3Experimental excess molar enthalpies HE

2+13 at 298.15 K for the additionof 2,2,4-trimethylpentane to DBE (1) + 1-butanol (3) to form x1DBE + x22,2,4-trimethylpentane + (1 − x1 − x2)1-butanol, and values of HE

123 calculated from Eq. (7),using the smooth representation of HE

13 by Redlich–Kister equation with parametersgiven in Table 2.

x2 HE2+13/J mol−1 HE

123/J mol−1 x2 HE2+13/J mol−1 HE

123/J mol−1

x1/x3 = 0.2500; HE13/J mol−1 = 444.1

0.1004 134.0 533.5 0.6005 524.3 701.70.2004 255.0 610.1 0.7002 527.4 660.60.2997 356.1 667.0 0.8004 495.3 583.90.3997 434.7 701.3 0.9002 414.8 459.10.4999 492.2 714.2

x1/x3 = 0.6665; HE13/J mol−1 = 764.1

0.0998 114.7 802.5 0.5998 429.5 735.30.2000 215.8 827.0 0.7002 434.4 663.40.2999 297.0 832.0 0.8005 414.6 567.00.3996 358.8 817.6 0.9002 354.4 430.70.4998 403.8 786.0

x1/x3 = 1.5002; HE13/J mol−1 = 890.0

0.0998 91.8 893.0 0.5999 348.1 704.20.2000 173.8 885.9 0.6998 354.0 621.20.3002 239.7 862.5 0.8000 340.2 518.20.4004 291.1 824.8 0.9001 291.7 380.60.5004 326.9 771.5

x1/x3 = 4.0008; HE13/J mol−1 = 776.4

0.1005 73.1 771.5 0.6001 273.4 583.90.2004 137.8 758.6 0.7003 275.0 507.7

(

�

Ttmt

Table 4Summary of the data reduction and prediction results obtained for the ternarysystem DBE (1) + 2,2,4-trimethylpentane (2) + 1-butanol (3) at 298.15 K.

Correlationa �HE123, Eq. (9) �HE

123, Eq. (10) NRTL UNIQUAC

B0 3289.8 8729.2 −0.1020 −705.5B1 −26,267.8 15,771.4 0.5728 1371.5B2 43,717.1 −7852.5 2.0861 2169.4B3 2538.2 0.7733 −620.5B4 −229,673.3 2.8942 2155.2B5 91,359.5 0.0832 −776.7B6 32,537.6B7 25,7847.7˛ 0.32rms �HE/J mol−1 39.3 65.5 32.6 41.7max|�HE|/J mol−1 91.7 158.2 78.0 115.0max(|�HE|/HE) 31.9% 49.1% 26.4% 25.1%

Predictiona NRTL UNIQUAC

B0 0.0772 −174.7B1 0.1745 270.5B2 2.4081 2160.1B3 0.8333 −629.7B4 2.4838 2159.1B5 0.7237 −765.0˛12 1.47˛13 0.31˛23 0.40rms �HE/J mol−1 42.9 90.7max|�HE|/J mol−1 115.0 181.0max(|�HE|/HE) 40.0% 55.1%

0.2999 190.0 733.5 0.7999 259.3 414.7

0.3998 229.1 695.1 0.8998 209.9 287.70.5002 257.4 645.4

10):

HE123 = B1x1 + B2x2 + B3x3 (10)

able 4 presents the summary of correlation results obtained forhe ternary systems with Eqs. (8)–(10) and the NRTL and UNIQUAC

odels. Table 4 also shows the prediction results obtained for theernary systems using the parameters of the binary systems.

Fig. 2. Contours for constant values of HE123 for DBE (1) + 2,2,

a Equivalence between parameters: NRTL B0 = �12; B1 = �21; B2 = �13; B3 = �31;B4 = �23; B5 = �32; UNIQUAC B0 = �u12; B1 = �u21; B2 = �u13; B3 = �u31; B4 = �u23;B5 = �u32.

For the measured ternary system, DBE (1) + TMP (2) + 1-butanol(3) at a temperature of 298.15 K, the best fit of experimental data isobtained with the NRTL model. The root mean square deviation, rms

�HE, is 32.6 J mol−1, and the maximum value of the absolute devi-ation, max|�HE|, is 78.0 J mol−1. Correlated results with the NRTLmodel for the excess molar enthalpy HE

123 are shown in Fig. 2. TheUNIQUAC model gives also a good fit, as well as the one with Eqs.

4–trimethylpentane (2) + 1-butanol (3) at T = 298.15 K.

F. Aguilar et al. / Fluid Phase Equilibria 290 (2010) 15–20 19

utano

(wr

2tobitQ5

nietudwbt

Fig. 3. Excess molar enthalpy HE for DBE (1) + 2,2,4-trimethylpentane (2) + 1-b

8) and (9). The results obtained with Eqs. (8) and (10) are slightlyorse. This system shows endothermic behaviour in the whole

ange of composition. The maximum value of HE is 893 J mol−1.Concerning the prediction of data at the temperature of

98.15 K, Fig. 3 shows the graphical comparison of experimen-al ternary data and prediction data using the binary parametersf the NRTL and UNIQUAC models. The NRTL model presents theest qualitative description of ternary HE curves. Value of the max-

mum relative deviation, max(|�HE|/HE), is 40.0%. Prediction ofhe ternary data from binary parameters obtained with the UNI-UAC model is slightly worse, with values of max(|�HE|/HE) of5.1%.

In the mixtures presented in this work, containing someon-polar + polar and polar + polar compounds, interaction effects

nfluence the excess molar enthalpy data. In mixtures ofther + hydrocarbon substances, which are non-polar substances,he dispersion forces are the most significant attractive molec-

E

lar forces. The positive contribution to H associated with theisruption of interaction between like molecules in connectionith the negative contribution due to the creation of interaction

etween unlike molecules explains the endothermic character ofhe mixtures DBE + TMP. The HE curve is slightly skewed towards

l (3) at T = 298.15 K: (©) experiment; (—) NRTL model; (- - -) UNIQUAC model.

small mole fractions of ether, reflecting the more active behaviourof ether molecules. Comparison shown in Fig. 1a with data ofother mixtures DBE + hydrocarbon taken from [1,2], shows that theendothermic character of the mixture increases for cyclic or aro-matic hydrocarbons with respect to a branched hydrocarbon suchas TMP.

The binary mixture DBE + 1-butanol contains one strong self-associating component (1-butanol) and a non-self-associatingcomponent (DBE) which, however, can form associates with thealkanol through hydrogen bonding. In this case, the chemicalcontribution dominates the excess properties. The endothermicbehaviour of the mixture is explained by the greater positive con-tribution of the destruction of alkanol–alkanol hydrogen bondsupon mixing with reference to the negative term due to the forma-tion of alkanol–ether complexes. The HE curve is skewed towardslow mole fractions of alcohol, reflecting the strong self-associationcharacter of the alcohol.

E

With respect to the binary mixture TMP + 1-butanol, the Hcurve is skewed towards low mole fractions of alcohol, reflect-ing again its strong self-association character. The chemical forcesof the hydrogen bonds in the alkanol are stronger than the dis-persion forces of the hydrocarbon, which explain the endothermic

2 se Equ

chatcrh

4

t(t(Abbiotem

LA

HimqRr

0 F. Aguilar et al. / Fluid Pha

haracter of the mixture. When compared with the mixture cyclo-exane + 1-butanol [1], Fig. 1c shows that both mixtures presentvery similar endothermic character, but when compared with

he mixture benzene + 1-butanol [2], the mixture aromatic hydro-arbon + 1-alkanol reveals a greater endothermic character withespect to the mixtures of the 1-alkanol with cyclic or branchedydrocarbons.

. Conclusions

Isothermal excess molar enthalpies at T = 298.15 K for theernary system DBE (1) + 2,2,4-trimethylpentane (2) + 1-butanol3) and two of its constituent binary systems DBE (1) + 2,2,4-rimethylpentane (2) and 2,2,4-trimethylpentane (2) + 1-butanol3) were determined by using an isothermal flow calorimeter.ll the binary systems show endothermic and asymmetric HE

ehaviour at the measured temperature. The asymmetric HE

ehaviour is more pronounced in the binary mixtures contain-ng the alkanol, due to the hydrogen bonding association effectf the alkanol. Intermolecular and association effects involved inhese systems have been discussed. The measured excess molarnthalpies data were correlated well with the NRTL and UNIQUACodels and polynomial equations.

ist of symbols

i, Bi adjustable parameters of the correlation equations andmodels

E molar excess enthalpy

,j constituent identification: 1, 2 or 3

ax maximum value of the indicated quantitymolecular surface areauniversal gas constant

ms root mean square

[[

[

ilibria 290 (2010) 15–20

T absolute temperaturex mole fraction

Greek letters� difference˛ non-randomness parameter in the NRTL model� energy interaction parameter in the NRTL and the UNI-

QUAC models

Acknowledgements

This paper is part of the Doctoral Thesis of F. Aguilar.Support for this work came from the Dirección General de Inves-

tigación (DGI), Ministerio de Educación y Ciencia, Spain, ProjectsENE2006-12620, and from the Consejería de Educación, Junta deCastilla y León, Spain, Project BU021A08.

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