ids xx (2006) xxx–xxx

+ MODEL

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Journal of Molecular Liqu

Densities, excess molar volumes and partial molar volumes of the binarymixtures of acetic acid+alkanol (C1–C4) at 298.15 K

Hossein A. Zarei

Department of Chemistry, Faculty of Science, Bu-Ali Sina University, Hamadan, Iran

Received 13 January 2006; accepted 15 April 2006

Abstract

Densities (ρ) of the binary mixtures of acetic acid with methanol, ethanol, propan-1-ol, propan-2-ol, butan-1-ol and butan-2-ol have beenmeasured at temperature 298.15 K and ambient pressure (815 hPa) as a function of composition using an Anton Paar model DMA 4500 oscillatingdensimeter. The excess molar volume (Vm

E), partial molar volume (V i) and excess partial molar volumes (V iE) of the binary mixtures were

calculated from the density data. The excess molar volumes were correlated with the Redlich−Kister equation. The excess molar volumes arenegative for methanol, ethanol, propan-1-ol, propan-2-ol and butan-1-ol. They are positive for butan-2-ol and an inversion of sign in Vm

E isobserved for butan-2-ol around 0.9 mol fraction of acetic acid.

The results obtained in this work were interpreted in terms of intermolecular interaction between like and unlike molecules, difference in sizeand shape of unlike molecules and the steric hindrance caused by increased methylation.© 2006 Elsevier B.V. All rights reserved.

Keywords: Densities; Excess molar volume; Acetic acid; Alkanol

Table 1Densities (ρ), refractive indices (nD

25) and stated purity of the pure components attemperature 298.15 K and ambient pressure (815 hPa) and comparison withliterature

Component Purity(massfraction)

ρ/(g cm−3) nD25

Experimental Literature Experimental Literature

Acetic acid 0.998 1.04376 1.04365 [7] 1.3703 1.3698 [8]Methanol 0.995 0.78654 0.78664 [8] 1.3270 1.32652 [8]Ethanol 0.998 0.78515 0.78504 [8] 1.3595 1.35941 [8]Propan-1-ol 0.998 0.79953 0.79954 [12] 1.3833 1.38370 [8]Propan-2-ol 0.995 0.78090 0.78085 [9] 1.3751 1.3752 [8]

1. Introduction

The excess properties of binary liquid mixtures are importantto understand and interpret the nature of interaction between themolecules of the mixtures [1–4]. These properties result fromexperimental measurements or correlations. Developing accu-rate correlation requires accurate experimental measurements toensure that the equation represents the correct physical behaviorof the measured property. This paper reports on the densities(ρ), excess molar volume (Vm

E), partial molar volume (V i) andexcess partial molar volumes (V i

E) of the binary mixtures ofacetic acid with methanol, ethanol, propan-1-ol, propan-2-ol,butan-1-ol and butan-2-ol at ambient pressure (815 hPa) andtemperature (298.15 K). By extrapolation of the excess partialmolar volumes to infinite dilution, limiting excess partial molarvolumes (V i

E,0) are also obtained. These values are interestingfrom a theoretical point of view since at infinite dilution the onlyinteractions present are solute–solvent interactions. Some of ourresults of excess molar volume were compared with literaturevalues [5–7].

E-mail address: zareih@basu.ac.ir.

0167-7322/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.molliq.2006.04.009

2. Experimental

2.1. Materials

The pure components were high purity grade reagents fromMerck. The purity grades of pure components specified by themanufacturer are given in Table 1. The purity of components waschecked by comparing their measured densities (ρ) and refractive

MOLLIQ-02423; No of Pages 5

Butan-1-ol 0.998 0.80579 0.80576 [10] 1.3974 1.3973 [8]Butan-2-ol 0.99 0.80248 0.80239 [11] 1.3955 1.3950 [8]

Table 2Densities, excess molar volumes, partial molar volumes, excess partial molar volumes and excess partial molar volumes at infinite dilution for the binary systems ofacetic acid (1)+alkanol (2) at the temperature 298.15 K and ambient pressure (815 hPa)

x1 ρ (g cm−3) VmE (cm3 mol−1) V 1 (cm

3 mol−1

) V 2 (cm3 mol−

1

) V 1E (cm3 mol−

1

) V 2E (cm3 mol−

1

)

Acetic acid (1)+methanol (2)0.0000 0.78654 55.255 40.733 −2.279 0.0000.0856 0.82038 −0.192 55.416 40.724 −2.118 −0.0080.1573 0.84676 −0.331 55.622 40.695 −1.912 −0.0370.2161 0.86720 −0.435 55.813 40.651 −1.721 −0.0810.3180 0.90004 −0.579 56.152 40.527 −1.382 −0.2050.3703 0.91569 −0.635 56.318 40.440 −1.216 −0.2920.4876 0.94784 −0.710 56.656 40.185 −0.878 −0.5470.5535 0.96417 −0.720 56.824 40.003 −0.71 −0.7300.6479 0.98550 −0.691 57.040 39.677 −0.494 −1.0550.7185 0.99998 −0.637 57.184 39.365 −0.35 −1.3680.8097 1.01664 −0.511 57.348 38.830 −0.186 −1.9030.8769 1.02752 −0.378 57.446 38.298 −0.088 −2.4340.9613 1.03922 −0.141 57.524 37.392 −0.01 −3.3401.0000 1.04376 57.534 36.86 0.00 −3.873

Acetic acid (1)+ethanol (2)0.0000 0.78515 55.970 58.675 −1.564 0.0000.0788 0.80680 −0.120 56.062 58.670 −1.472 −0.0040.1642 0.83027 −0.237 56.237 58.645 −1.297 −0.0290.2344 0.84954 −0.322 56.405 58.603 −1.129 −0.0710.3132 0.87089 −0.391 56.594 58.532 −0.94 −0.1430.3994 0.89410 −0.447 56.787 58.425 −0.748 −0.2490.4646 0.91143 −0.472 56.917 58.326 −0.618 −0.3480.5573 0.93589 −0.488 57.078 58.158 −0.457 −0.5170.6393 0.95697 −0.465 57.200 57.975 −0.334 −0.7000.7227 0.97813 −0.421 57.311 57.739 −0.224 −0.9360.8039 0.99824 −0.347 57.405 57.432 −0.129 −1.2420.8803 1.01659 −0.246 57.478 57.038 −0.056 −1.6370.9610 1.03520 −0.095 57.527 56.453 −0.007 −2.2221.0000 1.04376 57.534 56.086 0.000 −2.589

Acetic acid (1)+propan-1-ol (2)0.0000 0.79953 57.355 75.163 −0.18 0.0000.0820 0.81544 −0.026 56.995 75.176 −0.54 0.0130.1573 0.83107 −0.088 56.882 75.190 −0.652 0.0270.2470 0.85023 −0.142 56.906 75.183 −0.628 0.0200.3241 0.86730 −0.176 56.994 75.147 −0.54 −0.0160.4089 0.88705 −0.227 57.112 75.078 −0.422 −0.0850.4819 0.90436 −0.241 57.209 75.000 −0.325 −0.1620.5700 0.92604 −0.247 57.306 74.893 −0.228 −0.2700.6372 0.94316 −0.242 57.365 74.803 −0.169 −0.3590.7187 0.96438 −0.211 57.421 74.685 −0.113 −0.4780.7991 0.98624 −0.178 57.467 74.542 −0.068 −0.6210.8835 1.00997 −0.124 57.506 74.331 −0.028 −0.8320.9617 1.03253 −0.049 57.530 74.028 −0.004 −1.1351.0000 1.04376 57.534 73.82 0.000 −1.343

Acetic acid (1)+propan-2-ol (2)0.0000 0.78090 57.428 76.956 −0.107 0.0000.0799 0.79718 −0.025 57.071 76.969 −0.463 0.0130.1580 0.81399 −0.069 56.939 76.986 −0.595 0.0300.2443 0.83349 −0.123 56.942 76.984 −0.592 0.0280.3194 0.85120 −0.169 57.012 76.956 −0.523 −0.0000.3961 0.86990 −0.200 57.107 76.902 −0.427 −0.0540.4744 0.88975 −0.224 57.206 76.826 −0.328 −0.1300.5594 0.91211 −0.232 57.300 76.725 −0.234 −0.2310.6397 0.93409 −0.227 57.371 76.619 −0.163 −0.3370.7256 0.95854 −0.203 57.431 76.491 −0.103 −0.4650.7993 0.98038 −0.170 57.472 76.360 −0.063 −0.5960.8817 1.00573 −0.117 57.508 76.165 −0.026 −0.7910.9613 1.03113 −0.045 57.531 75.889 0.003 −1.0671.0000 1.04376 57.534 75.707 0.000 −1.250

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x1 ρ (g cm−3) VmE (cm3 mol−1) V 1 (cm

3 mol−1

) V 2 (cm3 mol−

1

) V 1E (cm3 mol−

1

) V 2E (cm3 mol−

1

)

Acetic acid (1)+butan-1-ol (2)0.0000 0.80579 57.528 91.986 −0.006 0.0000.0778 0.81775 −0.004 57.372 91.992 −0.162 0.0060.1502 0.82970 −0.024 57.307 91.100 −0.228 0.0140.2380 0.84515 −0.046 57.294 92.002 −0.240 0.0160.3143 0.85950 −0.065 57.318 91.993 −0.217 0.0070.3946 0.87895 −0.077 57.358 91.971 −0.177 −0.0150.4739 0.89556 −0.088 57.400 91.938 −0.134 −0.0480.5668 0.91404 −0.092 57.446 91.889 −0.089 −0.0970.6502 0.93490 −0.088 57.478 91.839 −0.056 −0.1470.7256 0.95522 −0.080 57.500 91.791 −0.035 −0.1950.7579 0.96438 −0.074 57.507 91.770 −0.027 −0.2170.8791 1.00160 −0.045 57.527 91.680 −0.008 −0.3060.9460 1.02417 −0.018 57.533 91.618 −0.002 −0.3681.0000 1.04376 57.534 91.556 0.000 −0.431

Acetic acid (1)+butan-2-ol (2)0.0000 0.80248 58.732 92.366 1.198 0.0000.0735 0.81329 0.062 58.152 92.386 0.618 0.0210.1526 0.82591 0.094 57.782 92.432 0.248 0.0660.2487 0.84273 0.099 57.562 92.485 0.027 0.1190.3380 0.85981 0.083 57.487 92.515 −0.047 0.1490.3979 0.87206 0.071 57.474 92.522 −0.060 0.1570.4703 0.88775 0.055 57.476 92.520 −0.058 0.1550.5451 0.90515 0.037 57.487 92.510 −0.048 0.1440.6286 0.92598 0.024 57.498 92.494 −0.036 0.1280.7169 0.94997 0.013 57.507 92.474 −0.027 0.1090.8106 0.97790 0.002 57.516 92.444 −0.018 0.0780.8750 0.99881 −0.004 57.524 92.404 −0.011 −0.0380.9595 1.02863 −0.010 57.533 92.299 −0.002 −0.0661.0000 1.04376 57.534 92.214 0.000 −0.152

Table 2 (continued)

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indices (nD25) with those reported in the literature [7–12]. The

determined densities and refractive indices of pure componentsagree with the literature data very well which are given in Table 1.Therefore, no further purification and other contaminant speciesdetermination were attempted owing to their high purity grade.Before measurements, chemicals were degassed by heating andcooling.

2.2. Apparatus and procedures

Binary mixtures were prepared just before use by mass using aMettler AB-204 balance with a precision of ±1·10−4 g. Con-version to molar quantities was based on the relative atomic masstable of 1996 issued by IUPAC [13]. The average uncertainty inthe mole fraction is estimated to be 1.5 ·10−5. The densities of thepure components and mixtures were measured using an AntonPaar DMA 4500 digital vibrating U-tube densimeter, withautomatic viscosity correction. The densities of the sampleswere observed with a reproducibility of ±1·10−5 g cm−3. Totaluncertainty in the density measurement, as reported by theequipment manufacturer, was 1·10−5 g cm−3 at a confidencelevel of 95% and the accuracy for the density measurement was±5·10−5 g cm−3. The following relationship holds for the periodof vibration (τ) and the density (ρ)

q ¼ aþ bs2 ð1Þ

where a and b are the instrument constants which are de-termined by calibration with bidistilled and degassed water,and dry air [14]. The temperature in the cell was regulatedto ±0.01 K with a solid state thermostat (Peltier). The ope-rative temperature range is 273.15 K to 363.15 K. The ref-ractive indices were measured at 298.15 K with an Abbérefractometer. The accuracy of the refractive index measured isin the order of ±0.0002, and for the temperature of mea-surement it was ±0.01 K. Each mixture was used immediatelyafter it was well mixed by shaking.

3. Results and discussions

The densities of pure components and binary mixtures ofacetic acid with methanol, ethanol, propan-1-ol, propan-2-ol,butan-1-ol and butan-2-ol are listed in Table 2.

The values of excess molar volumes (VmE) of binary mixtures

were computed by applying the equation

VEm ¼

X2i¼1

xiMiðq−1−q−1i Þ ð2Þ

where ρ is the density of a mixture andMi, ρi are the molar massand density of pure component, respectively. The average un-certainty in the excessmolar volume is estimated to be ±0.006 cm3

mol−1. Calculated excess molar volumes at temperature 298.15 K

Fig. 1. Excess molar volume at 298.15 K and ambient pressure (815 hPa) ofacetic acid (1) with alkanols (2). Solid lines were calculated from coefficient ofEq. (3) given in Table 2. Methanol(▴), ethanol(▿), propan-1-ol (▪), propan-2-ol (⋄), butan-1-ol (×), butan-2-ol (+) (methanol (○) [5]; methanol (|) [7]; ethanol(✩) [7]; propan-1-ol (▵) [6]).

Table 3The least-squares parameters (Ai) and standard deviations (σ(Vm

E ))

System A0 A1 A2 A3 σ(VmE )

Acetic acid+methanol −2.8486 −0.5317 −0.2274 −0.2649 0.002Acetic acid+ethanol −1.9229 −0.2894 −0.1533 −0.2230 0.002Acetic acid+propan-1-ol −0.9737 −0.2393 0.2126 −0.3422 0.006Acetic acid+propan-2-ol −0.9137 −0.2782 0.2355 −0.2934 0.001Acetic acid+butan-1-ol −0.3630 −0.1183 0.1446 −0.0939 0.002Acetic acid+butan-2-ol 0.1938 −0.4106 0.3290 −0.2641 0.003

Fig. 2. Excess partial molar volume and their values at infinite dilution at 298.15Kand ambient pressure (815 hPa) of acetic acid (1) with alkanols (2). Methanol (▴),ethanol (▿), propan-1-ol (▪), propan-2-ol (⋄), butan-1-ol (×), butan-2-ol (+).

4 H.A. Zarei / Journal of Molecular Liquids xx (2006) xxx–xxx

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and ambient pressure (815 hPa) appear in Table 2, and aregraphically represented in Fig. 1. The experimental data werecorrelated by a least squares method to the Redlich−Kisterequation [15] of the type

VEm ðcm3 mol−1Þ ¼ x1ð1−x1Þ

Xki¼0

Aið1−2x1Þi ð3Þ

where x1 is the mole fraction of acetic acid. The coefficients Ai arethe adjustable parameters and in each case the optimum number ofcoefficients is ascertained from examination of the variation in thestandard deviation σ(Vm

E) as given by

rðVEmÞ ¼

Xni¼1

ðVEm;expt:;i−V

Em;calc:;iÞ2=ðn−kÞ

" #1=2

ð4Þ

where n is the number of experimental data and k is the number ofparameters retained in Eq. (3). The values of the parameters areincluded in Table 3 along with the standard deviations σ(Vm

E).The excess molar volumes for the systems of acetic acid with

methanol, ethanol, propan-1-ol, propan-2-ol and butan-1-ol arenegative over the whole range of compositions. They arepositive for the system of acetic acid+butan-2-ol and inversionof sign is observed at the rich concentration of acetic acid. TheVmE vs. x1 curves for the systems of acetic acid with methanol,

ethanol, propan-1-ol, propan-2-ol and butan-1-ol are almost

symmetrical with a minimum around x1≈0.56. Butan-2-ol pre-sents a maximum around x1≈0.25. The excess molar volumesof acetic acid with methanol, ethanol and propan-1-ol are ingood agreement with the reported data at 298.15 K [5–7].

The excess molar enthalpies (HmE) which have previously

been reported by Hasse et al. [17] for the systems of acetic acidwith ethanol, propan-1-ol, propan-2-ol and butan-1-ol are posi-tive. They are negative for acetic acid+methanol, and inversionof sign has been observed at a rich concentration of acetic acid.The Hm

E values increase with increasing chain length of alkanol.Also Fig. 1 shows that the Vm

E becomes more positive withincreasing chain length of the alkanols.

The following factors influence the excess volume: (a) dis-sociation of self-associated acetic acid and alkanol, (b) inter-stitial accommodation of alkanol in hydrogen-bonded aceticacid aggregates and (c) weak hydrogen-bonding interaction(positive excess enthalpies) between unlike molecules. Whilethe first factor contributes increase in excess volume, the last

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two factors contribute decrease in excess volumes. From thesereported excess volumes and excess enthalpies data it can bepointed out that the second factor (b) is dominant in thesesystems. From the experimental results, it can also be said thatacetic acid+alkan-2-ol complex formation is relatively weakerthan the formation of complex between acetic acid+alkan-1-oldue to the steric hindrance.

The partial molar volumes (V̄ i) can be determined fromexcess molar volumes data using [16]

V i ¼ VEm þ Vi

⁎þ ð1−xiÞðAVEm=AxiÞT ;P ð5Þ

where (∂VmE/∂xi)xj≠i,p,T is calculated from Eq. (3) using the para-

meters in Table 3 and Vi

⁎

represent the molar volumes of thecomponent 1 (acetic acid) or 2 (alkanol).The excess partial molarvolumes (V i

E) of a component in a binary mixture can be deter-mined from the relation

VEi ¼ V i−Vi

⁎ ð6Þ

The partial molar volumes (V i) and excess partial molarvolumes (V i

E) are given in Table 2 and the excess partial molarvolumes are represented in Fig. 2. The excess partial molarvolume (V i

E) of methanol, ethanol, propan-1-ol propan-2-ol andbutan-1-ol is negative over the whole range of acetic acid con-centration. It is positive for butan-2-ol, and inversion of sign isobserved after x1≈0.25. The V 2

E values of methanol and ethanolare negative. They are positive for propan-1-ol, propan-2-ol,butan-1-ol and butan-2-ol and inversion of sign is observed withincreasing mole fraction of acetic acid.

The excess partial molar volume at infinite dilution (V iE,0)

can be determined from the equation

VE;0

i ¼ ðAVEm=AxiÞxi¼0;p;T ð7Þ

The excess partial molar volume at infinite dilution (V iE,0)

appears to be of particular interest. In the limit of infinite dilu-

tion, solute–solute interactions disappear. Thus, the values of theexcess partial molar volumes at infinite dilution provide insightinto solute–solvent interactions. We can consider acetic acid atinfinite dilution (x1=0) in alcohols and alcohols at infinite di-lution (x1=1) in acetic acid. All excess partial molar volumes atinfinite dilution (V i

E,0) are given in Table 2 and are represented inFig. 2.

Acknowledgment

The author would like to thank the Bu-Ali-Sina Universityfor providing the necessary facilities to carry out the research.

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