excess molar volumes for (binary mixtures of 1-alkanol and 1-alkene). i. the system 1-alkanol +...

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Journal of Solution Chemistry, Vol. 31, No. 6, June 2002 ( C 2002) Excess Molar Volumes for (Binary Mixtures of 1-Alkanol and 1-Alkene). I. The System 1-Alkanol + 1-Octene at 25 C Andrzej J. Treszczanowicz, 1,* Teresa Treszczanowicz, 1 Teresa Kasprzycka-Guttman, 2 and Tomasz S. Pawl ˆˆowski 2 Received June 6, 2001; revised February 21, 2002 Excess volumes measured at 25 C are reported for binary mixtures of the C 3 ,C 4 ,C 6 ,C 8 , and C 10 1-alkanols with 1-octene. In this series of mixtures, the excess-volume curves change from positive values over the whole concentration range for short-chain alkanols C 3 and C 4 , to sigmoid for longer-chain alkanols (with positive values in the alkanol- rich region). The positive region decreases with increasing chain length of the 1-alkanol. Excess partial molar volumes of the components are calculated. The results are compared with those for mixtures of 1-alkanols with n-octane. The model of associated mixtures proposed by Treszczanowicz and Benson 3 describes very well the size and shape of the excess volume for the class of systems considered. KEY WORDS: Excess molar volumes; 1-alkanol; 1-octene; hydrogen bonding; association. 1. INTRODUCTION The excess volumes of 1-alkanol + 1-alkene mixtures have been studied so only for the short-chain 1-alkanols C 1 to C 4 . (1,2) These data do not give systematic and extensive information for a larger series of mixtures, which is necessary in order to understand the role and magnitude of some basic effects, such as self-association, solvation, nonspecific interactions, and free volume for thermodynamic properties in a wide class of mixtures. With the present work, we are initiating a systematic investigation of the thermodynamic properties of the 1-alkanol + 1-alkane class of mixtures. We pro- pose to study two types of mixtures, A i + H and A + H i , where A and H denote 1 Department of Supramolecular Chemistry, Institute of Physical Chemistry, Polish Academy of Sci- ences, 44/52 Kasprzaka, 01-224 Warszawa, Poland; email: [email protected]. 2 Department of Chemistry, Warsaw University, 1 Pasteura, 02-093 Warszawa, Poland. 455 0095-9782/02/0600-0455/0 C 2002 Plenum Publishing Corporation

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Journal of Solution Chemistry [josc] pp582-josl-377759 August 19, 2002 4:54 Style file version June 5th, 2002

Journal of Solution Chemistry, Vol. 31, No. 6, June 2002 (C© 2002)

Excess Molar Volumes for (Binary Mixturesof 1-Alkanol and 1-Alkene). I. The System1-Alkanol + 1-Octene at 25◦C

Andrzej J. Treszczanowicz,1,∗ Teresa Treszczanowicz,1 TeresaKasprzycka-Guttman,2 and Tomasz S. PawlÃÃowski2

Received June 6, 2001; revised February 21, 2002

Excess volumes measured at 25◦C are reported for binary mixtures of the C3, C4, C6, C8,and C10 1-alkanols with 1-octene. In this series of mixtures, the excess-volume curveschange from positive values over the whole concentration range for short-chain alkanolsC3 and C4, to sigmoid for longer-chain alkanols (with positive values in the alkanol-rich region). The positive region decreases with increasing chain length of the 1-alkanol.Excess partial molar volumes of the components are calculated. The results are comparedwith those for mixtures of 1-alkanols withn-octane. The model of associated mixturesproposed by Treszczanowicz and Benson3 describes very well the size and shape of theexcess volume for the class of systems considered.

KEY WORDS: Excess molar volumes; 1-alkanol; 1-octene; hydrogen bonding;association.

1. INTRODUCTION

The excess volumes of 1-alkanol+ 1-alkene mixtures have been studied soonly for the short-chain 1-alkanols C1 to C4.(1,2) These data do not give systematicand extensive information for a larger series of mixtures, which is necessary in orderto understand the role and magnitude of some basic effects, such as self-association,solvation, nonspecific interactions, and free volume for thermodynamic propertiesin a wide class of mixtures.

With the present work, we are initiating a systematic investigation of thethermodynamic properties of the 1-alkanol+ 1-alkane class of mixtures. We pro-pose to study two types of mixtures,Ai + H andA+ Hi , whereA andH denote

1Department of Supramolecular Chemistry, Institute of Physical Chemistry, Polish Academy of Sci-ences, 44/52 Kasprzaka, 01-224 Warszawa, Poland; email: [email protected].

2Department of Chemistry, Warsaw University, 1 Pasteura, 02-093 Warszawa, Poland.

455

0095-9782/02/0600-0455/0C© 2002 Plenum Publishing Corporation

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456 Treszczanowicz, Treszczanowicz, Kasprzycka-Guttman, and PawlÃowski

1-alkanol and olefin, respectively, and the subscript shows a member of the ho-molog series.

This paper describes excess volumes at 25◦C for binary mixtures of1-propanol, 1-butanol, 1-hexanol, 1-octanol, and 1-decanol with 1-octene over thewhole concentration range.

A model of associated mixtures including association and equation of statecontribution, as proposed by Treszczanowicz and Benson,(3) is used to describethe excess volume of binary systems formed by 1-alkanol+ 1-octene.

2. EXPERIMENTAL

2.1. Chemical

1-Propanol, 1-butanol, 1-hexanol, and 1-octanol (Aldrich, analytical grade,99%) were further purified by distillation using a column packed with glass helixes.1-Decanol purissime A grade (99.95%) in ampules from CHEMIPAN was usedas received. 1-Octene (Sigma,>99%, analytical grade) was distilled over sodium.All liquids were stored in the dark over molecular sieves.

2.2. Apparatus and Procedure

Densitiesρ were measured using an Anton Paar densimeter (model DMA60/602) operating in static mode with an estimated accuracy better than 10−5

g-cm−3. The temperature of the oscillator chamber in the densimeter was main-tained to within±0.002◦C by circulating water using a cascade thermostatic sys-tem and a UNIPAN 560 temperature controller. The temperature in the quartz cellwas controlled to within±0.001◦C using a precision digital thermometer (Sys-temteknik AB, type S 1220) with a thermistor probe. The density was calculatedfrom the oscillation periodτ of a vibrating U-tube of the densimeter using theequation:

ρ = Aτ 2− B (1)

The apparatus constantsA and B of the oscillator were evaluated from densitymeasurements at 15–35◦C of three standard liquids, namely, twice distilled anddeionized water, benzene, and cyclohexane (99.95% mole % purity) produced andpacked in ampules by CHEMIPAN.

The mixtures were prepared by weight with a precision of 1×10−5 g in 8-cm3

bottles capped with silicone rubber septum. A needle closed by silicone rubber wasused at each bottle for equalization of the pressure during the filling of the com-ponents and collecting of the sample. The correction for vapor space was applied.Conversion to molar quantities was based on the 1995 table of atomic weightsissued by IUPAC.(4) The error in the mole fractions is estimated to be less than±1× 10−4. Measured densities of the pure liquids at 25◦C and refractive indexesat 20◦C, together with the literature values, are given in Table I.

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1-Alkanol + 1-Octene Volumes 457

Table I. Densities at 25◦C and Refractive Indexes at 20◦C for the Component Liquidsand GLC mole % Purity

ρ/g-cm−3 nD

Component Obs. Lit. Obs. Lit. Purity (moll %)

1-Octene 0.71088 0.71085a 1.40874 1.40870a 99.61-Propanol 0.79965 0.79960a 1.38552 1.38556a 99.8

0.79969c 1.38370b

1-Butanol 0.80571 0.80575a 1.39921 1.39929a 99.80.80586c

1-Hexanol 0.81540 0.81534a 1.41815 1.4172a 99.20.81589c 1.4181b

1-Octanol 0.82247 0.8221b 1.42913 1.4296b 98.90.82177c

1-Decanol 0.82631 0.8263b 1.43726 1.4373b 99.950.82698c

aRef. 5.bRef. 6.cRefs. 10 and 11.

3. RESULTS

The excess volume was calculated from densities using:

VEm =

2∑i=1

Mixi

(1

ρm− 1

ρi

)(2)

wherexi is the mole fraction of componenti , andMi , ρi are the molecular massand density of the pure componenti , respectively, andρm is the density of themixture. Experimental results in the excess molar volumes for binary systems of1-octene with five homologous 1-alkanols are listed in Table II. The uncertaintyof the excess volume is estimated to be less than±0.003 cm3-mol−1. The bestoverall fit was obtained with the Neau(7) smoothing equation:

VEm = x1 (1− x1)

k∑i=1

ciYi−1 (3)

where x1 is the mole fraction of 1-alkanol,Y = x1− (1+ Dx1,)−1 with therecommended(6) valueD = 35. The Neau equation(7) was found to be more suitablefor asymmetric andS-shaped excess volumes of 1-alkanol+ n-alkane mixtures(8)

than the Redlich and Kister or Myers and Scott equations. The values of the coeffi-cientsci were obtained by the nonlinear least-squares method using the Marquard–Levenberg procedure(9) to fit the experimental results with Eq. (3). The standard

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458 Treszczanowicz, Treszczanowicz, Kasprzycka-Guttman, and PawlÃowski

Table II. Experimental Results Excess VolumeVE of (1-Alkanol+ 1-Octene) at 25◦C

xa1 VE (cm3-mol−1) xa

1 VE (cm3-mol−1) xa1 VE (cm3-mol−1)

1-Propanol+ 1-octene0.0516 0.1132 0.3534 0.2614 0.699 0.15270.1043 0.1733 0.4052 0.2543 0.7432 0.13120.1561 0.2099 0.4909 0.2318 0.8084 0.10480.2029 0.2382 0.5379 0.2175 0.8537 0.07550.2577 0.2527 0.5985 0.1917 0.9034 0.0510.3058 0.2621 0.6454 0.1717 0.9591 0.0197

1-Butanol+ 1-octene0.0548 0.1077 0.3966 0.1938 0.6391 0.11570.1008 0.1456 0.4527 0.1755 0.6951 0.09950.1535 0.1699 0.4923 0.1674 0.7528 0.07230.2009 0.1912 0.5575 0.148 0.801 0.05790.2548 0.205 0.5959 0.1333 0.8508 0.0457

0.8987 0.0369

1-Hexanol+ 1-octene0.0558 0.0495 0.34 0.0293 0.6572 −0.06520.1027 0.0568 0.4032 0.011 0.7158 −0.07390.154 0.0583 0.4454 0.0049 0.7653 −0.07350.1968 0.056 0.5095 −0.0157 0.801 −0.07680.2487 0.0479 0.5523 −0.0323 0.8539 −0.06290.2983 0.0354 0.6117 −0.0526 0.9032 −0.0503

0.9514 −0.0267

1-Octanol+ 1-octene0.0514 0.0098 0.3376 −0.1019 0.7081 −0.15730.0985 −0.0038 0.4429 −0.1363 0.7482 −0.15670.1527 −0.0228 0.491 −0.1484 0.804 −0.13450.2005 −0.0426 0.5555 −0.1542 0.8513 −0.11130.254 −0.072 0.5975 −0.1662 0.9031 −0.07930.289 −0.0847 0.6612 −0.1653 0.9491 −0.0457

1-Decanol+ 1-octene0.0508 −0.0165 0.3452 −0.2296 0.6375 −0.24640.1011 −0.0608 0.3952 −0.2430 0.7014 −0.23310.1502 −0.1012 0.4452 −0.2609 0.7494 −0.20850.2008 −0.1438 0.4979 −0.2688 0.8002 −0.18220.2594 −0.1815 0.5539 −0.2611 0.848 −0.14250.2871 −0.1997 0.6199 −0.2519 0.8998 −0.109

aMole fraction alkanol.

deviation was calculated from:

σv =(

n∑j=1

(VE,exp

m,j − VE,calm,j

)2n− k

)1/2

(4)

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1-Alkanol + 1-Octene Volumes 459

Table III. Coefficientsci and Standard Deviationσν at 25◦C for Least-SquaresRepresentations ofVE by Eq. (3) and Excess Partial Molar Volume of 1-Octene

at Infinite DilutionVE,∞2 /cm3-mol−1 for (1-Alkanol+ 1-Octene) by Eq. (5)

Component 1

1-Propanol 1-Butanol 1-Hexanol 1-Octanol 1-Decanol

c1 1.6171 1.3467 0.44989 −0.19872 −0.82069c2 −1.9791 −1.9568 −1.3299 −1.0229 −1.0709c3 0.93118 0.91782 0.56937 0.24243 1.6575c4 −0.49612 −1.0139σν 0.0023 0.0036 0.0038 0.0033 0.0047

VE∞2 0.57 0.31 −0.76 −1.02 −1.23

wherek is the number of constants smoothing Eq. (3) and the sum is extendedover alln data points. Coefficientsci , along with the standard deviation, are listedin Table III.

The experimental values ofVE measured for the five 1-alkanol+ 1-octenemixtures at 25◦C are summarized in Table II and are presented graphically inFig. 1. The results for (1-propanol+ 1-octene) system agree well with those givenby Letcheret al.,(2) as shown in Fig. 1. The curves of the excess partial molarvolumes of the 1-octene in 1-alkanolsVE

2 and 1-alkanols in 1-octeneVE1 are plotted

in Fig. 2. These quantities were calculated numerically from the representationsof the results by Eq. (3) using the relation:

VEi = VE+ (1− xi )

(∂VE

∂xi

)(5)

4. DISCUSSION

The excess volumes for the systems formed by short-chain alkanols, like1-propanol and 1-butanol [cf. Letcheret al.(1) for methanol and ethanol] are positivein the whole concentration range. For the systems formed by longer-chain alkanols,the excess volume curves become sigmoid with negative values in the alkanol-richregion. The region of negativeVE increases with increasing chain length of thealkanol molecule. The excess partial molar volume of the 1-alkanols in 1-octene,VE

1 change with the increase in length of the alkanol molecule from positive inthe whole concentration range to positive-negative with a sharp minimum in thediluted alkanol region and narrow range of positive values in the high dilutionregion. The excess partial molar volumes of the 1-octene in 1-alkanolsVE

2 decreasefrom positive values in the whole concentration range for short-chain alkanolsto positive-negative for longer-chain alkanols with flat maximum in the dilutedalkanol region. The values at infinite dilutionVE,∞

2 decrease from positive to

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460 Treszczanowicz, Treszczanowicz, Kasprzycka-Guttman, and PawlÃowski

Fig. 1. Excess molar volumesVE for [x1

H(CH2)kOH+ (1− x1) 1-octene] at 25◦C vs1-alkanol mole fraction. Labels indicatek, numberC atoms of 1-alkanol molecule. Points denote ex-perimental data:1, 1-propanol;©, 1-butanol;¤,1-hexanol; ♦, 1-octanol; ∇, 1-decanol. Solidlines——, denote smoothed results by Eq. (3) withcoefficients from the Table III; dashed curve - - -denotes results for 1-propanol taken from the Ref. 2.

Fig. 2. Excess partial molar volumesVE1 of homologous

1-alkanol andVE2 of 1-octene in binary mixtures [x1

H(CH2)kOH + (1−x1) 1-octene] at 25◦C vs. 1-alkanolmole fraction. CurvesVE

1 are labeled with Ak andVE2 are

labeled with 0k wherek is the number of carbon atoms inthe alkanol molecule.

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1-Alkanol + 1-Octene Volumes 461

Fig. 3. Excess molar volumes for equimolar mixturesof homologous 1-alkanols with 1-octene orn-octane at25◦C vs. nc, the number of carbon atoms in the alkanolmolecule.©, this work;¤, Refs. 1 and 2;1, Ref. 8.

negative (cf. Table III). This behavior is similar to that observed for a series of(1-alkanol+ n-heptane) mixtures.(10−12)

The excess volumesVE at equimolar concentration for the investigated se-ries are compared in Fig. 3 with the systems formed by 1-alkanols withn-octane.The 1-octene series is lower than then-octane series ranging from about 0.2 cm3-mol−1 for short-chain alkanols to 0.07 cm3-mol−1 for longer-chain alkanols. Fig-ure 4 shows a comparison of the excess partial molar volumesVE

1 and VE2 for

the (1-decanol+ 1-octene) system with those for the (1-decanol+ n-octane)system.(13) It is shown that the minimum of excess partial molar volumeVE

1is deeper in the 1-octene system than in then-octane system. Similarly, theVE

2 curve for 1-octene in 1-decanol is lower than theVE2 curve forn-octane in

1-decanol.We can note that for any pair of binary systems formed by a given alkanol

with 1-alkene and homologousn-alkane presented in Figs. 3 and 4, the differencesbetween the free-volume contributions and nonspecific interactions are not signif-icant. The excess volume of the 1-hexene with homomorphicn-hexane at 25◦C ispositive and equal to 0.056 cm3-mol−1 at equimolar concentration,(14) the excessenthalpies of the homomorphicn-alkanes with 1-alkenes are also positive(15) andfor the (1-octene+ n-octane) system is equal to 45 J-mol−1 at the maximum.Therefore, analyzing the excess volume of the (1-alkanol+ 1-alkene) mixtures,the effect of disruption of the liquid structure of pure hydrocarbons should be

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462 Treszczanowicz, Treszczanowicz, Kasprzycka-Guttman, and PawlÃowski

taken into consideration [cf. Letcheret al.(1,2)]. It seems that the increased positivecontribution due to the larger disruption of the H bonds by 1-alkene moleculesin comparison withn-alkane and positive contribution, because of the above-mentioned disruption of liquid structure of 1-alkene, is compensated by a negativecontribution caused by the formation of specific OH· · ·π interactions. It is forthis reason that the shape of the excess volumes and their partial molar propertiesof the components are so similar and close to those observed for the 1-alkanol+n-alkane mixtures.

In order to estimate the association parameters from thermodynamicproperties of mixtures, it is necessary to know (beside excess enthalpy and ex-cess volume) excess molar isobaric heat capacity,(16) as well as excess molarisobaric thermal expansion.(17) However, the lack of suitable data, forced us toapply the model proposed by Treszczanowicz and Benson.(3) The model allowsus to take into consideration the OH· · ·π interactions by means of the Kehiaianand Guggenheim relation(18) for interaction parameters in the equation of statecontribution. Model equations and their derivation were reported in the previouspaper.(3) The parameters of association for 1-alkanols:1h0

H = −24.4 kJ-mol−1,1s0

H = −33 J-K−1-mol−1, and1ν0H = −10 cm3-mol−1, as well as the value of in-

terchange interaction parameter between hydroxyl and aliphatic contact surfaces,were adopted from the paper.(3) For this class of mixtures, three types of contactsurfaces were distinguished:a, for aliphatic CH2 and CH3 groups,o– for hydroxylgroup OH (in alkanol monomer and multimer), andb, for CH2==CH----group inthe 1-alkene molecule. Therefore, three interchange interaction parameters forthe distinguished contact surfaces were obtained:X∗o,a, X∗b,a andX∗o,b. Moreover,two independent fractions are given:α(1)

o for OH group in the alkanol moleculeand α(2)

b for CH2==CH----group in the 1-alkene molecule, while the remainingfractions areα(1)

a = 1− α(1)o , α(2)

a = 1− α(2)b andα(1)

b = α(2)o = 0. Therefore, the

modified Kehiaian–Guggenheim relation(18) for interaction parameterX12 is re-duced to:

X12 = ω[(α(1)

o

)2X∗o,a+ α(1)

o α(2)b

(X∗o,a+ X∗b,a− X∗o,b

)+ (α(2)b

)2X∗b,a

](11)

whereω is the correction parameter. The interchange interaction parameterX∗o,a =1.0135× 105 between hydroxyl and aliphatic contact surfaces andω = (V∗1 )1/3

(V∗2 )−3/2 are assumed as previously.(3) The X∗b,a = 8.621× 103 and X∗o,b =1.4146× 105 interchange interaction parameters are calculated fromVE for 1-octanol+1-octene and 1-propanol+1-octene systems at equimolar concentration,given in Table III. Equation (11) can then be rewritten in the form:

X12 = 103(V∗1)1/3 (V∗2 )−3/2

[101.35

(α(1)

o

)2− 31.493α(1)o α

(2)b + 8.621

(2)b

)2](12)

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1-Alkanol + 1-Octene Volumes 463

Table IV. Physical Properties of Component Liquids: Molar VolumeVi , Coefficients of IsobaricThermal Expansionαp,i , Isothermal CompressibilityβT,i at 25◦C, and Characteristic Parameters:

VolumeV∗i , PressureP∗i and TemperatureT∗i

Vi 103αp 106ßT V∗i P∗i T∗iComponenti (cm3-mol−1) (1/K) (1/TPa) (cm3-mol−1) (J-cm−3) (K)

1-Octene 157.858 1.173 1297.3 123.121 443.1 4808.2Ethanol 58.678 1.093 1162.2 46.332 449.7 4987.51-Propanol 75.161 0.995 1015.2 60.289 454.1 5245.61-Butanol 91.984 0.932 942.4 74.566 448.7 5442.01-Hexanol 125.316 0.870 839.4 102.682 460.3 5663.91-Octanol 158.474 0.827 775.7 130.848 466.2 5837.81-Decanol 191.503 0.812 738.0 158.549 478.6 5903.0

where the fraction of OH and of CH2==CH----groups are given by:

α(1)OH = VvdW

OH

/[VvdW

OH + VvdWCH3+ (n(1)

C − 1)VvdW

CH2

](13)

α(2)b = VvdW

CH2=CH

/[VvdW

CH2=CH+ VvdWCH3+ (n(2)

C − 3)VvdW

CH2

](14)

Fig. 4. Excess partial molar volumesVE1 of 1-alkanol

andVE2 of hydrocarbon at 25◦C vs. the mole fraction of

1-decanol in binary mixtures: ——, for [x1 1-decanol+(1−x1) 1-octene] and· · · · · ·, for [x1 1-decanol+(1− x1) 1-octane] (Ref. 13).

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464 Treszczanowicz, Treszczanowicz, Kasprzycka-Guttman, and PawlÃowski

Fig. 5. Excess molar volumesVE for binarymixtures of a 1-alkanol (CkH2k+1OH) with 1-octene at 25◦C vs the mole fractionsx1 of the1-alkanol: ——, smoothed experimental resultsfrom sources given in Table III; - - - - - -, cal-culated from presented theory. Curves are labeledwith values ofk.

n(1)C andn(2)

C are numbers of C atoms in alkanol and alkene molecules,VvdWOH = 8.04,

VvdWCH3= 13.67 andVvdW

CH2= 10.23 andVvdW

CH2=CH = 20.41 cm3-mol−1 are van derWaals volume for respective groups.(19) It should be noted that the Kehiaian andGuggenheim relation allows us to obtain the negative constituent ofX12 in thecase of active solvents, whenX∗o,b > X∗o,a+ X∗b,a.

Physical properties and characteristic parameters of pure components arelisted in Table IV. The data for 1-alkanol are taken from the literature.(3) The coef-ficient of isobaric thermal expansionαp for 1-octene was estimated from densitydata(5) usingdρ/dT = 0.000943 g-cm−3-K−1. The coefficient of isothermal com-pressibilityβT for 1-octene was obtained by the Manzini and Crescenzi method(20)

assumingβT = 1711 TPa−1 for 1-hexene(5) to evaluate the new----CH==CH2

group parameter. Figure 4 shows a comparison of experimental and predictedVE. The model predicts correctly the shape of excess volumeVE, includingthe position of extremes and the sign of inversion points in the whole investi-gated series of systems. Larger deviations are observed only in diluted alkanolregion.

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1-Alkanol + 1-Octene Volumes 465

5. CONCLUSIONS

The excess volumeVE in a series of systems formed by 1-alkanol with 1-octene shows similar character as concentration function like in series of systemsformed by 1-alkanol with ann-alkane.(3) For both these classes of mixtures, achange can be seen from positiveVE values in the whole concentration range forshort-chain alkanols to positive-negative for longer-chain alkanols. The values ofexcess volumesVE for the 1-alkanol+ 1-octene system are lower than the valuesfor respective 1-alkanol+ n-octane systems. The excess volumeVE data are de-scribed by means of the associated mixture model, where OH· · ·π interactionsare represented by nonspecific interactions contribution. The agreement betweenmodel prediction and experiment (Fig. 5) seems reasonable in view of the approx-imations involved in the model. The model properly describesVE changes over awide concentration range in the whole series of systems, including a shift of theextremums, as well as theVE sign inversion points. Larger deviations are observedfor the diluted alkanol region.

Finally, it should be noted that the difference between specific interaction ofπ electrons and OH groups in monomer and multimer could play an importantrole for sharpness of the positive lobe in the diluted alkanol region. However,comparison prediction of the 1-alkanol+ n-heptane systems (see, Ref. 3, andFig. 3) and of the series investigated here (see Fig. 5) in the diluted alkanol regionshows that the character of deviations is similar.

A more refined model of the associated mixture for this class of mixturesneeds excess enthalpy, excess molar heat capacity, and excess molar isobaricthermal expansion. These data will be presented in further papers of thisseries.

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