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Acoustical and excess properties of {1-hexanol + n-hexane, or n-octane, or n-decane} at (298.15, 303.15, and 308.15) K
Journal of Molecular Liquids 142 (2008) 124–129
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Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / m o l l i q
Acoustical and excess properties of {1-hexanol + n-hexane, or n-octane, or n-decane} at (298.15, 303.15, and 308.15) K Gyan P. Dubey ⁎, Monika Sharma Department of Chemistry, Kurukshetra University, Kurukshetra-136119, India
A R T I C L E
I N F O
Article history: Received 27 August 2007 Received in revised form 15 May 2008 Accepted 28 May 2008 Available online 5 June 2008 Keywords: Densities Excess molar volume Isentropic compressibility Alkanol PFP
A B S T R A C T Densities (ρ) and speeds of sound (u) for the binary mixtures of 1-hexanol with n-hexane, n-octane and n-decane have been measured over the entire composition range at 298.15, 303.15 and 308.15 K. The dynamic viscosities (η) E ), molar for these systems have been measured at 298.15 K. From experimental data, excess molar volumes (Vm E ), deviation in speed of sound (uD) isentropic compressibility (Ks,m), excess molar isentropic compressibility (Ks,m from their ideal values (uid) in an ideal mixture, and excess free volumes (VfE) have been calculated. The excess functions have also been correlated with the Redlich–Kister polynomial equation. The viscosity data have been analysed in terms of some semi-empirical equations. The theoretical values of speed of sound (u) and isentropic compressibility (κS) have also been estimated using the Prigogine–Flory–Patterson (PFP) theory with the van der Waals (vdW) potential energy model and the results have been compared with experimental values. The effect of chain-length of n-alkanes as well as the temperature on the excess properties has also been studied. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Studies on thermodynamic and transport properties of binary liquid mixtures provide information on the nature of interactions in the constituent binaries [1]. In order to study and understand the behaviour of alcohol + n-alkane systems under various operating conditions, their thermophysical properties are needed. Nowadays, the mixtures of alkanol + n-alkane are also of great interest because these are used as additives to petrol and in rectification processes for binary azeotropes. The binary mixtures of alcohol + alkane have also been studied extensively and systematically in recent years. The effect of alkyl chain-length of both the components on excess molar volumes, speed of sound, and isentropic compressibilities has been studied by Treszczanowicz et al. [2–4], Kiyohara and Benson [5], Handa et al. [6], and Benson and Halpin [7]. Treszczanowicz et al. [8] have reviewed in detail the existing literature on the binary mixture data of excess molar volumes of 1-alkanol + alkane and also recommended a few data sets. In literature, Heintz et al. [9] reported the excess molar volumes for 1-hexanol + n-hexane at temperatures between 283.15 and 323.15 K whereas excess molar volumes for 1hexanol + n-octane, or +n-decane at 298.15 K have also been reported by Treszczanowicz et al. [3]. In our recent studies [10–12], we have reported the experimental data about thermodynamic properties of binary mixtures containing
⁎ Corresponding author. E-mail addresses: [email protected] (G.P. Dubey), [email protected] (M. Sharma). 0167-7322/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2008.05.013
alkanols with alkanes in order to investigate the behaviour of these mixtures. Continuing our efforts, we now report the density (ρ), viscosity (η), and speeds of sound (u) data for the binary mixtures of 1hexanol with n-hexane, or n-octane, or n-decane at (298.15, 303.15 and 308.15) K. In the present work an attempt is also made to study the effect of chain-length of n-alkanes as well as the temperature on the excess properties of binary mixtures. Using experimental data, E various excess functions like excess molar volumes (Vm ), molar isentropic compressibility (KS,m), excess molar isentropic compressibility (KES,m), deviation in speed of sound (uD) from their ideal values (uid) in an ideal mixture, and excess free volumes (VfE) have been calculated. The viscosity data have been analysed in terms of some semi-empirical equations. The PFP theory of non-electrolytes liquid mixtures [13–16] has been used to analyze speed of sound and isentropic compressibility of studied binary mixtures. 2. Experimental 2.1. Chemicals Analytical reagent grade 1-hexanol, n-hexane, n-octane and n-decane (S.D. Fine Chemicals) were fractionally distilled and dried over 0.4 nm molecular sieves. They were also degassed under vacuum prior to their experimental use. The mass fraction purities tested by gas chromatography were as follows: 1-hexanol (N98.5%), n-hexane (N99%), n-octane (N99.7%) and n-decane (97%). Hexanol and n-decane were distilled before use. The purities of solvents was further ascertained by comparing their densities (ρ), viscosities (η), and speeds of sound (u) at all working temperatures with values reported in the literatures [10,11,17–33] as
G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129
125
Table 1 Experimental and literature values of densities (ρ), viscosities (η) and speeds of sound (u), isobaric expansivity (α⁎), isobaric molar heat capacities (C⁎P ) and molar isentropic compressibility (K⁎S,m ) of pure liquids ρ⁎ × 10− 3/(kg∙m− 3) Liquids 1-Hexanol
n-Hexane
n-Octane
n-Decane
a b
298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15
u/(m∙s− 1)
η/(mPa∙s)
Exptl.
Lit.
Exptl.
Lit.
Exptl.
Lit.
0.815311 0.811986 0.808355 0.655072 0.650369 0.645767 0.698580 0.694497 0.690416 0.726806 0.723042 0.719230
0.81533 [17] 0.81195 [19] 0.808482 [18] 0.6550 [20] 0.65036 [21] 0.64574 [21] 0.6986 [10,11] 0.69449 [24] 0.6904 [25] 0.7267 [26] 0.7225 [28] 0.7186 [28]
4.597
4.594 [18]
0.313
0.313 [10,11]
0.518
0.518 [10,11]
0.852
0.852 [11]
1303.8 1287.1 1270.3 1077.8 1054.2 1032.9 1172.7 1152.1 1131.7 1234.8 1215.2 1195.6
1304.72 [18] 1287.9 [18] 1271.14 [18] 1077.7 [22] 1054.6 [23] 1032.80 [11] 1173 [24] 1152 [24] 1131.52 [11] 1234.7 [27] 1215 [24] 1192.80 [11]
α⁎/(kK− 1)
C⁎P / (J K− 1 mol− 1)
⁎ /(mm3 mol− 1 MPa− 1) KS,m
0.8747 [18] 0.8861 [18] 0.9078 [18] 1.391 [29] 1.404 [32] 1.430b 1.164 [29] 1.195 [32] 1.198b 1.051 [29] 1.055 [33] 1.085b
241.64 [18] 246.52 [18] 251.47 [18] 195.48 [29] 197.4a 199.2 [30] 254.15 [29] 256.36a 258.56 [30] 314.54 [29] 316.94 [31] 319.34 [31]
90.43 93.55 96.90 172.88 182.99 193.72 170.21 178.43 187.11 176.66 184.27 192.41
Estimated using group additivity. Calculated from our measured densities.
shown in Table 1. Also given in Table 1 are our measured or literature values of those quantities which were required in the estimation of KS,m, KES,m and uD. 2.2. Apparatus and procedures The (1-hexanol + n-alkane) binary mixtures were prepared by weighing appropriate amount of the 1-hexanol and n-alkane on an electronic balance, with a precision of ± 0.05 mg, by syringing each component into air-tight stoppered bottles in order to minimize evaporation losses. Pure components were separately degassed by vacuum pump shortly before sample preparation. The accuracy of mole fractions was ±1 × 10− 4. The densities (ρ) and speeds of sound (u) of pure liquids and their binary mixtures were measured with an Anton Paar DSA-5000 digital oscillating U-tube densimeter (Austria), provided with automatic viscosity correction and two integrated Pt 100 Platinum thermometers. The temperature in the cell was regulated ±0.001 K with a solid-state thermostat. The apparatus was first calibrated with triple distilled water (ρ = 997.075 kg∙m− 3, T = 298.15 K) [29,34] and dry air. Uncertainty in density measurement is ±2 × 10− 3 kg∙m− 3, and for the speed of sound is ±0.1 ms− 1. To perform the measurement, one out of a total of ten individual measuring methods was selected and the
measuring cell was filled with the sample. An acoustic signal informs us when the measurement is completed. The results are automatically converted (including temperature compensation wherever necessary) into concentration, specific gravity, or other density-related units using the built-in conversion tables and functions. Further information about the experimental techniques has been provided in our previous work [12,35]. The dynamic viscosities (η) of pure liquids and their binary mixtures were measured at 298.15 K using an Ubbelohde suspended level viscometer, which was calibrated at 298.15 K before measurements. An electronic stop watch with readability of ±0.1 s was used for the flow time measurements. Details of the method and techniques of viscosity measurements have been described earlier [10–12,35]. The uncertainty in the viscosity measurements based on our work on several pure liquids, was ±0.003 mPa∙s. In viscosity measurements, the temperature of the samples was controlled by using a water bath equipped with a thermostat of accuracy ±0.01 K. 3. Results and discussions Tables S2–S4, ESI1, report the experimentally measured densities E (ρ), speeds of sound (u) and calculated excess molar volumes (Vm ), deviations in speed of sound (uD) from their ideal values (uid) in an ideal mixture, molar isentropic compressibilities (KS,m), excess molar E isentropic compressibilities (KS,m ), and excess molar free volumes (VfE) for the binary mixtures of 1-hexanol with n-hexane, or n-octane, or ndecane at T = (298.15, 303.15 and 308.15) K. The values of viscosity (η) at 298.15 K for these binary mixtures were recorded in Table S5, ESI1. The density, ρ values have been used to calculate excess molar E volumes (Vm ) using the following equation: E ¼ Σ xi Mi ρ−1 −ρ−1 Vm i i¼1
ð1Þ
where Mi, ρ⁎i and ρ are the molar mass, density of ith component and density of the mixture respectively. E Fig. 1 shows the variation of Vm at 298.15 K for the studied binary mixture against the mole fractions (x1) of 1-hexanol. We observe that E the Vm values for (1-hexanol + n-hexane) at 298.15 K are negative over E the entire composition range with slight positive Vm values in the
Fig. 1. Plots of excess molar volumes (VEm) vs. mole fraction of 1-hexanol (x1) for binary mixture of 1-hexanol + n-hexane (■); +n-octane (●); and +decane (▲) at 298.15 K. The solid lines are drawn from Redlich–Kister Eq. (11).
1 Electronic supplementary information (ESI) available: Tables S2–S4 provide the densities, excess molar volumes, speeds of sound, deviations in speed of sound from their values in ideal mixtures, molar isentropic compressibilities, excess molar isentropic compressibilities and excess molar free volumes at 298.15, 303.15 and 308.15 K, respectively. Table S5 reports viscosities for the studied binary mixtures at 298.15 K.
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G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129
The isentropic compressibility, κS and molar isentropic compressibility, KS,m were obtained from the equations [36,37]: −1 −1 −1 ðδVm =δP ÞS ¼ ρu2 ¼ Vm Mu2 κ S ¼ −Vm
ð2Þ
KS;m ¼ −ðδVm =δP Þs ¼ Vm κ S ¼ ∑xi Mi =ðρuÞ2
ð3Þ
where Vm the molar volume and M is the molar mass of the mixture. The excess molar isentropic compressibility KES,m was calculated from: E id KS;m ¼ KS;m −KS;m
ð4Þ
where Kid S,m, is the corresponding property of ideal solution can be calculated as [38]: h n oi id − AP;i =CP;i ¼ ∑xi KS;i −TAP;i ∑xi AP;i =∑xi CP;i KS;m Fig. 2. Plots of excess molar isentropic compressibility (KES,m) vs. mole fraction of 1-hexanol (x1) for binary mixture of 1-hexanol +n-hexane (■); +n-octane (●); and +decane (▲) at 298.15 K. The solid lines are drawn from Redlich–Kister Eq. (11). E initial range of x1 whereas with the rise of temperature Vm values become completely negative over the whole composition range. The E Vm curves for (1-hexanol + n-octane) binary mixtures display a positive deviation with a slight tendency to negative values at x1 ≈ 0.80 while for (1-hexanol + n-decane) are positive throughout the E whole composition range. It indicates that Vm values changes from negative to positive as the size of alkane molecule increases from nE hexane to n-decane. In case of (1-hexanol + n-hexane), Vm values become more negative with rise in temperature. For (1-hexanol + nE octane), Vm increases with rise in temperature and decreases at E higher mole fractions (x1) of 1-hexanol. On the other hand, the Vm curves of (1-hexanol + n-decane) show a systematic increase with temperature. E The variation of Vm with composition is the result of the contributions from several contractions and expansion processes which precede simultaneously when 1-hexanol + n-alkane mixtures are formed. Following two effects can be considered: (i) disruption of liquid order on mixing and unfavorable interactions between unlike molecules producing a positive contribution E to Vm , and (ii) contraction due to differences in free volume and molar volume of unlike molecules producing a negative contribuE tion to Vm . E The negative contributions to Vm observed in the present case may be due to differences in the size and shape of the component molecules in the mixture. The molar volumes of 1-hexanol and n-hexane at 298.15 K are 1.25 × 10− 4 and 1.32 × 10− 4 m3∙mol− 1 respectively. The E values of Vm become more negative as temperature of the system E increases. The increase in absolute values of Vm with the rise of temperature is explained by considering the differences in molar volumes of the two liquids at different temperatures. The difference in molar volumes of 1-hexanol and n-hexane is 0.062 × 10− 4 m3∙mol− 1 at 298.15 K while its value at 308.15 K is 0.067 × 10− 4 m3∙mol− 1. This means as the temperature of the mixture increases, the difference in the molar volumes two liquids also increases, hence the smaller molecules of 1-hexanol easily fit in the voids created by larger molecules of n-hexane, resulting in less increase in the volume of mixture. On the other hand, increase in temperature results ⁎ (1.253 × an appreciable increase in the molar volume of 1-hexanol, Vm,1 10− 4 m3∙mol− 1 at 298.15 K and 1.264 × 10− 4 m3∙mol− 1 at 308.15 K) due to the breaking of the hydrogen bonds. When n-alkane is added, there is an instantaneous breaking of the hydrogen bonds in 1-hexanol molecules, rendering the individual entities more disorder and hence less degree of cooperation. As a result, the net molecular order in the systems under study i.e. 1-hexanol with n-octane, or n-decane is decreased, yielding E high positive values of Vm .
ð5Þ
where A⁎P,i is the product of the molar volume Vi⁎ and the isobaric expansivity α⁎P,i, C⁎P,i, is the isobaric molar heat capacity, and K⁎S,i is molar isentropic compressibility of the pure liquid component i, respectively. The deviations of the speeds of sound from their values in an ideal mixture were calculated from [39,40]: uD ¼ u−uid
ð6Þ
In so far as the Newton–Laplace equation is valid, the ideal speeds of sound uid may be expressed correctly in term of thermodynamic properties of an ideal mixture: −1=2 1=2 id id : KS;m ∑ /i ρi uid ¼ Vm
ð7Þ
i
The KES,m values for studied binary mixtures at 298.15 K are plotted against x1 of 1-hexanol in Fig. 2. The trend in KES,m values is almost identical to VEm curves for all the binary mixtures. Like VEm, KES,m also depends on the strength of interaction between the molecules, on the structural effects and packing phenomenon, both related with difference in shape and size but packing phenomenon are better evidenced through KES,m values. Positive KES,m values reveal that the packing of molecules in the mixture is less compact than in the pure components while negative KES,m may correspond to interstitial accommodation of one component into another due to differences in molar masses, shape and free volumes of pure components. With
Fig. 3. Plots of deviation of speed of sound (uD) vs. mole fraction of 1-hexanol (x1) for binary mixture of 1-hexanol + n-hexane (■); + n-octane (●); and +decane (▲) at 298.15 K. The solid lines are drawn from Redlich–Kister Eq. (11).
G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129 Table 2 Values of the interaction parameters along with the standard relative deviations for (1hexanol + n-alkane) systems at 298.15 K Binary mixtures
Semi-empirical relations
Parameter
S.D.
1-Hexanol + n-hexane
Kendall–Monroe Grunberg–Nissan Tamura–Kurata Hind Katti–Chaudhri Kendall–Monroe Grunberg–Nissan Tamura–Kurata Hind Katti–Chaudhri Kendall–Monroe Grunberg–Nissan Tamura–Kurata Hind Katti–Chaudhri
– G12 = −0.996 T12 = −0.034 H12 = −0.062 Wvis / RT = −1.247 – G12 = −1.305 T12 = 0.127 H12 = 0.176 Wvis / RT = −1.305 – G12 = −1.314 T12 = 0.698 H12 = 0.360 Wvis / RT = −1.124
0.49 0.04 0.20 0.21 0.52 0.45 0.01 0.13 0.17 0.40 0.37 0.01 0.08 0.13 0.27
1-Hexanol + n-octane
1-Hexanol + n-decane
increase in temperature, the positive values become more positive and negative values become more negative. The composition dependence of uD values is shown in Fig. 3. The trend in uD values is similar to KES,m with opposite sign for all the binary systems throughout the whole composition range. The trend observed is entirely positive for 1-hexanol + n-hexane, changes sign from negative to positive for 1-hexanol + n-octane whereas entirely negative for 1-hexanol + n-decane except at higher x1. Again, the effect is that with increasing the chain-length of n-alkane, the interstitial accommodation become less important that the molecules of two components cannot be easily accommodated. The uD values for 1hexanol with n-hexane show systematic increase with rise of
127
temperature whereas in case of 1-hexanol + n-octane or +n-decane binary mixture, uD values are almost identical. The results obtained for viscosity of binary mixtures were also used to test the semi-empirical relations of Kendall and Monroe [41], Grunberg–Nissan [42], Tamura and Kurata [43], Hind–McLaughlin– Ubbelohde [44] and Katti and Chaudhry [45,46]. To perform a numerical comparison of the correlating capabilities of these relations we calculated the standard relative deviation (S.D.) using the relation: 2 1=2 2 S:D: ¼ 1=ðn−pÞ ∑ ηexp −ηcal =ηexp
ð8Þ
i¼1
where n represents the number of experimental data points and p the number of adjustable parameters in the respective relations. Table 2 shows the calculated parameters and the standard relative deviations (S.D.) between experimental values obtained for viscosities and the predicted results using the semi-empirical relations. As can be clearly seen by the results reported in Table 2, Grunberg–Nissan relation represent the behaviour of the binary mixtures satisfactorily as compared to other equations. Further interaction parameter (G12) gives an idea about quantitative estimation of interactions in the mixtures. It is well known that if G12 N 0 and higher in magnitude, there will be strong specific interactions in the mixture and if G12 b 0, it indicates the presence of weak interactions [47]. A through examination of Table 2 reveals that G12 values are negative for all the binary mixtures studied here and it provide support for the existence of weak dispersive forces in these binary mixtures. In the present study, the values of interaction parameters T12 and H12 do not differ appreciably from each other for a given binary mixture. The T12 and H12 values are also positive and negative.
Table 3 Coefficients Ai of Eq. (11) and corresponding standard deviation (σ) of Eq. (12) Binary mixture
T (K)
Excess property
A1
A2
A3
A4
1-Hexanol + n-hexane
298.15
E × 106/ (m3∙mol− 1) Vm uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1 MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107 /(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1 MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1)
−1.0354 124.29 −30.49 −1.8002 −2.0480 137.69 −37.78 −2.1751 −2.1107 144.26 −42.06 −2.4999 0.3405 22.60 −4.28 0.4197 0.2341 27.06 −5.75 0.4337 0.3085 25.92 −5.70 0.4847 0.9121 −13.13 4.38 0.6120 1.0998 −15.06 5.36 0.6849 1.2056 −14.17 5.61 0.7667
−0.5837 84.20 −7.85 −0.2522 −0.3633 93.75 −7.46 −0.2472 −0.3983 93.97 −6.96 −0.2158 −0.4933 38.70 −7.47 −0.2088 −0.5044 40.63 −8.12 −0.2399 −0.5773 40.82 −8.83 −0.2675 −0.3846 14.28 −4.87 0.0335 −0.3681 15.59 −5.41 0.0692 −0.2013 14.67 −5.12 0.0474
0.3697 19.01 4.59 0.2174 0.3706 20.29 5.13 0.2755 0.4662 24.92 3.92 0.2129 0.2054 14.51 0.40 −0.0186 0.3849 7.97 2.57 0.0540 0.2523 11.89 1.19 0.0138 0.1957 −1.64 1.54 0.0397 0.1661 8.72 −0.64 0.0257 0.7263 11.85 −0.62 −0.0295
− 0.9615 27.23 − 7.80 − 0.3774 − 2.3793 23.86 −10.98 − 0.4356 − 2.3006 34.13 −12.61 − 0.5186 − 0.5342 16.90 − 4.56 − 0.1219 − 0.9087 21.75 − 5.93 − 0.1598 − 0.9588 24.58 −7.07 −0.2119 −0.2109 9.39 −2.48 −0.0540 −0.1152 11.72 −3.51 −0.2108 −0.1881 18.55 −5.61 −0.1241
303.15
308.15
1-Hexanol + n-octane
298.15
303.15
308.15
1-Hexanol + n-decane
298.15
303.15
308.15
A5 −14.46 5.39 0.3145 −0.1755 −11.11 6.29 0.3293 −0.4279 5.88 0.3473 0.2098 −16.51 5.41 0.1677
1.79 −0.0363 0.3365 −6.79 5.64 0.1433 0.1578 1.30 0.0321 0.7760 −20.84 7.25 0.2068 −26.38 8.67 0.2060
σ 0.0032 0.15 0.05 0.0024 0.0040 0.21 0.05 0.0023 0.0033 0.18 0.04 0.0023 0.0020 0.07 0.02 0.0007 0.0020 0.12 0.03 0.0011 0.0016 0.15 0.04 0.0013 0.0024 0.07 0.02 0.0004 0.003 0.18 0.06 0.0063 0.0029 0.15 0.05 0.0012
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Table 4 Characteristic parameters of pure components at 298.15 K Components T/K
κT/(TPa− 1)
ν~
T˜
V⁎ × 106 / (m3∙mol− 1)
P⁎ × 106/ (J·m− 3)
T⁎/K
1-Hexanol
824.0[29] 863.0a 894.2a 1706.0 [29] 1791.7 [56] 1844.0 [50] 1280.0 [29] 1373.5 [56] 1386.0 [57] 1094.0 [29] 1196.0 [58] 1176.0 [59]
1.2587 1.2270 1.2349 1.3227 1.3292 1.3381 1.2804 1.2902 1.2946 1.2581 1.2642 1.2721
0.0528 0.0537 0.0549 0.0673 0.0681 0.0691 0.0618 0.0631 0.0637 0.0586 0.0592 0.0606
102.6022 102.5520 102.3566 99.4564 99.6842 99.7293 127.7097 127.4844 127.8032 155.6091 155.8797 155.5166
472 468 477 425 419 427 444 439 446 453 426 460
5645 5642 5603 4430 4452 4456 4826 4803 4837 5091 5120 5085
298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15
n-Hexane
n-Octane
n-Decane
a
Calculated from κT = /(ρu2) + TVα2/CP.
According to Fort and Moore, [48] the values of T12 and H12 are not very different except where the values of the component differ considerably. Furthermore, T12 and H12 show some variation with composition although this is only large for systems where there is a strong specific interaction between the components. There is a tendency of T12 and H12 at a certain composition to increase with the strength of interaction of the components. But this is not welldefined and T12 and H12 cannot generally be regarded as a measure of the strength of interactions [49]. The molar free volumes (Vf) in the binary mixtures of 1-hexanol + nalkanes were obtained according to Eyring [50,51] from the following relation:
Fig. 5. Composition dependence of experimental and calculated values of isentropic compressibility, κS in 1-hexanol + n-hexane (■); +n-octane (●); +n-decane (7) at 298.15 K. The corresponding dotted curves (........) represent PFP theory.
hexanol (x1) for binary mixtures under study is given in the Table 2S– 4S, ESI1. For each binary mixture, the excess properties (VEm,uD, KES,m, and Δη ) were fitted to the Redlich–Kister polynomial equation [52]: m
Z E ¼ x1 x2 ∑ Ai ðx1 −x2 Þi−1
ð11Þ
i¼1
Vf ¼ Vu−3 ðRTγ=M Þ3=2
ð9Þ
where γ = (CP / CV) is the ratio of isobaric and isochoric heat capacities that can be determined knowing the isentropic and isothermal compressibility coefficients, κS and κT from(CP / CV) = (κT / κS). The excess free volumes (VEf ) can be calculated by using the equation: 2
VfE ¼ Vf − ∑ xi Vf;i
ð10Þ
i¼1
where Vf is the free volume of mixture and Vf,i is that for pure component i. The variation of VEf versus the mole fractions of 1-
where ZE is any excess property, Ai's are polynomial coefficients and m is the number of estimated parameters. In each case, the optional number of coefficients was ascertained from an approximation of the variation in the standard deviations (σ). The calculated values of Ai along with the tabulated standard deviations (σ) are listed in Table 3. The standard deviations (σ) were calculated using the equation: 1=2 2 E E σ ¼ ∑ Zexp −Zcal =ðn−mÞ
ð12Þ
4. Theoretical prediction of speed of sound The theoretical values of isentropic compressibility κS and speed of sound u for both the liquid components and the liquid mixtures have been estimated using the Van der Waals (vdW) potential energy model in the Prigogine–Flory–Patterson (PFP) theory. The relevant equations are given elsewhere [13–16, 53–55].
Table 5 Comparison of experimental and calculated values of the speed of sound (u) and isentropic compressibility (κS) of binary mixtures at x1 = 0.5 and standard percentage deviation Binary mixtures
T/K
χ12 × 106/ (J·m− 3)
1-Hexanol + n-hexane
298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15
17.20 06.68 06.12 16.08 15.87 15.30 14.41 17.45 16.35
1-Hexanol + n-octane Fig. 4. Composition dependence of experimental and calculated values of speeds of sound, u in 1-hexanol + n-hexane (■); +n-octane (●); +n-decane (7) at 298.15 K. The corresponding dotted curves (........) represent PFP theory.
1-Hexanol + n-decane
u/(m s− 1)
κS/(TPa− 1)
Expt.
vdW
σ%
Expt.
vdW
σ%
1169.1 1151.9 1132.8 1216.9 1195.3 1176.8 1249.3 1225.7 1210.9
1189.2 1162.8 1150.1 1239.0 1206.2 1196.5 1270.4 1230.8 1229.6
1.3 0.7 1.4 1.7 0.5 1.4 1.4 1.2 1.3
997.8 1034.5 1077.5 905.6 937.9 977.3 842.0 879.9 907.6
996.6 1011.2 1040.8 871.1 924.5 942.5 813.0 875.9 874.7
2.8 1.5 2.8 3.4 1.1 3.0 3.0 2.4 2.7
G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129
The derived parameters for the pure liquid components using Flory theory are presented in Table 4. The contact interaction parameter χ12 for each liquid mixture is obtained according to the PFP theory from the excess molar volume values at x1 = 0.5. Figs. 4 and 5 compare the experimental values of speed of sound u and isentropic compressibility κS with the calculated one over the entire composition range for the three binary mixtures at 298.15 K. Similar trend is observed at other two working temperatures. The experimental and the PFP estimates of both u and κS with the vdW energy model for all the binary mixtures at equimolar comparison are summarized in Table 5. In order to perform a numerical composition of the estimation capability of the vdW energy model in the PFP theory, we calculated the standard percentage deviations (σ %) using the relation h i1=2 2 σ k ¼ ∑f100ðexptl:−theor:Þ=exptl:g =ðn−1Þ
ð13Þ
where n represents the number of experimental data points. The values of σ % are also given in Table 5. Acknowledgement Financial support for this project (Grant No. F.30-58/2004-SR dated 2/11/04) by University Grants Commission, New Delhi, India is fully acknowledged. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.molliq.2008.05.013. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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Contents lists available at ScienceDirect
Journal of Molecular Liquids j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / m o l l i q
Acoustical and excess properties of {1-hexanol + n-hexane, or n-octane, or n-decane} at (298.15, 303.15, and 308.15) K Gyan P. Dubey ⁎, Monika Sharma Department of Chemistry, Kurukshetra University, Kurukshetra-136119, India
A R T I C L E
I N F O
Article history: Received 27 August 2007 Received in revised form 15 May 2008 Accepted 28 May 2008 Available online 5 June 2008 Keywords: Densities Excess molar volume Isentropic compressibility Alkanol PFP
A B S T R A C T Densities (ρ) and speeds of sound (u) for the binary mixtures of 1-hexanol with n-hexane, n-octane and n-decane have been measured over the entire composition range at 298.15, 303.15 and 308.15 K. The dynamic viscosities (η) E ), molar for these systems have been measured at 298.15 K. From experimental data, excess molar volumes (Vm E ), deviation in speed of sound (uD) isentropic compressibility (Ks,m), excess molar isentropic compressibility (Ks,m from their ideal values (uid) in an ideal mixture, and excess free volumes (VfE) have been calculated. The excess functions have also been correlated with the Redlich–Kister polynomial equation. The viscosity data have been analysed in terms of some semi-empirical equations. The theoretical values of speed of sound (u) and isentropic compressibility (κS) have also been estimated using the Prigogine–Flory–Patterson (PFP) theory with the van der Waals (vdW) potential energy model and the results have been compared with experimental values. The effect of chain-length of n-alkanes as well as the temperature on the excess properties has also been studied. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Studies on thermodynamic and transport properties of binary liquid mixtures provide information on the nature of interactions in the constituent binaries [1]. In order to study and understand the behaviour of alcohol + n-alkane systems under various operating conditions, their thermophysical properties are needed. Nowadays, the mixtures of alkanol + n-alkane are also of great interest because these are used as additives to petrol and in rectification processes for binary azeotropes. The binary mixtures of alcohol + alkane have also been studied extensively and systematically in recent years. The effect of alkyl chain-length of both the components on excess molar volumes, speed of sound, and isentropic compressibilities has been studied by Treszczanowicz et al. [2–4], Kiyohara and Benson [5], Handa et al. [6], and Benson and Halpin [7]. Treszczanowicz et al. [8] have reviewed in detail the existing literature on the binary mixture data of excess molar volumes of 1-alkanol + alkane and also recommended a few data sets. In literature, Heintz et al. [9] reported the excess molar volumes for 1-hexanol + n-hexane at temperatures between 283.15 and 323.15 K whereas excess molar volumes for 1hexanol + n-octane, or +n-decane at 298.15 K have also been reported by Treszczanowicz et al. [3]. In our recent studies [10–12], we have reported the experimental data about thermodynamic properties of binary mixtures containing
⁎ Corresponding author. E-mail addresses: [email protected] (G.P. Dubey), [email protected] (M. Sharma). 0167-7322/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2008.05.013
alkanols with alkanes in order to investigate the behaviour of these mixtures. Continuing our efforts, we now report the density (ρ), viscosity (η), and speeds of sound (u) data for the binary mixtures of 1hexanol with n-hexane, or n-octane, or n-decane at (298.15, 303.15 and 308.15) K. In the present work an attempt is also made to study the effect of chain-length of n-alkanes as well as the temperature on the excess properties of binary mixtures. Using experimental data, E various excess functions like excess molar volumes (Vm ), molar isentropic compressibility (KS,m), excess molar isentropic compressibility (KES,m), deviation in speed of sound (uD) from their ideal values (uid) in an ideal mixture, and excess free volumes (VfE) have been calculated. The viscosity data have been analysed in terms of some semi-empirical equations. The PFP theory of non-electrolytes liquid mixtures [13–16] has been used to analyze speed of sound and isentropic compressibility of studied binary mixtures. 2. Experimental 2.1. Chemicals Analytical reagent grade 1-hexanol, n-hexane, n-octane and n-decane (S.D. Fine Chemicals) were fractionally distilled and dried over 0.4 nm molecular sieves. They were also degassed under vacuum prior to their experimental use. The mass fraction purities tested by gas chromatography were as follows: 1-hexanol (N98.5%), n-hexane (N99%), n-octane (N99.7%) and n-decane (97%). Hexanol and n-decane were distilled before use. The purities of solvents was further ascertained by comparing their densities (ρ), viscosities (η), and speeds of sound (u) at all working temperatures with values reported in the literatures [10,11,17–33] as
G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129
125
Table 1 Experimental and literature values of densities (ρ), viscosities (η) and speeds of sound (u), isobaric expansivity (α⁎), isobaric molar heat capacities (C⁎P ) and molar isentropic compressibility (K⁎S,m ) of pure liquids ρ⁎ × 10− 3/(kg∙m− 3) Liquids 1-Hexanol
n-Hexane
n-Octane
n-Decane
a b
298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15
u/(m∙s− 1)
η/(mPa∙s)
Exptl.
Lit.
Exptl.
Lit.
Exptl.
Lit.
0.815311 0.811986 0.808355 0.655072 0.650369 0.645767 0.698580 0.694497 0.690416 0.726806 0.723042 0.719230
0.81533 [17] 0.81195 [19] 0.808482 [18] 0.6550 [20] 0.65036 [21] 0.64574 [21] 0.6986 [10,11] 0.69449 [24] 0.6904 [25] 0.7267 [26] 0.7225 [28] 0.7186 [28]
4.597
4.594 [18]
0.313
0.313 [10,11]
0.518
0.518 [10,11]
0.852
0.852 [11]
1303.8 1287.1 1270.3 1077.8 1054.2 1032.9 1172.7 1152.1 1131.7 1234.8 1215.2 1195.6
1304.72 [18] 1287.9 [18] 1271.14 [18] 1077.7 [22] 1054.6 [23] 1032.80 [11] 1173 [24] 1152 [24] 1131.52 [11] 1234.7 [27] 1215 [24] 1192.80 [11]
α⁎/(kK− 1)
C⁎P / (J K− 1 mol− 1)
⁎ /(mm3 mol− 1 MPa− 1) KS,m
0.8747 [18] 0.8861 [18] 0.9078 [18] 1.391 [29] 1.404 [32] 1.430b 1.164 [29] 1.195 [32] 1.198b 1.051 [29] 1.055 [33] 1.085b
241.64 [18] 246.52 [18] 251.47 [18] 195.48 [29] 197.4a 199.2 [30] 254.15 [29] 256.36a 258.56 [30] 314.54 [29] 316.94 [31] 319.34 [31]
90.43 93.55 96.90 172.88 182.99 193.72 170.21 178.43 187.11 176.66 184.27 192.41
Estimated using group additivity. Calculated from our measured densities.
shown in Table 1. Also given in Table 1 are our measured or literature values of those quantities which were required in the estimation of KS,m, KES,m and uD. 2.2. Apparatus and procedures The (1-hexanol + n-alkane) binary mixtures were prepared by weighing appropriate amount of the 1-hexanol and n-alkane on an electronic balance, with a precision of ± 0.05 mg, by syringing each component into air-tight stoppered bottles in order to minimize evaporation losses. Pure components were separately degassed by vacuum pump shortly before sample preparation. The accuracy of mole fractions was ±1 × 10− 4. The densities (ρ) and speeds of sound (u) of pure liquids and their binary mixtures were measured with an Anton Paar DSA-5000 digital oscillating U-tube densimeter (Austria), provided with automatic viscosity correction and two integrated Pt 100 Platinum thermometers. The temperature in the cell was regulated ±0.001 K with a solid-state thermostat. The apparatus was first calibrated with triple distilled water (ρ = 997.075 kg∙m− 3, T = 298.15 K) [29,34] and dry air. Uncertainty in density measurement is ±2 × 10− 3 kg∙m− 3, and for the speed of sound is ±0.1 ms− 1. To perform the measurement, one out of a total of ten individual measuring methods was selected and the
measuring cell was filled with the sample. An acoustic signal informs us when the measurement is completed. The results are automatically converted (including temperature compensation wherever necessary) into concentration, specific gravity, or other density-related units using the built-in conversion tables and functions. Further information about the experimental techniques has been provided in our previous work [12,35]. The dynamic viscosities (η) of pure liquids and their binary mixtures were measured at 298.15 K using an Ubbelohde suspended level viscometer, which was calibrated at 298.15 K before measurements. An electronic stop watch with readability of ±0.1 s was used for the flow time measurements. Details of the method and techniques of viscosity measurements have been described earlier [10–12,35]. The uncertainty in the viscosity measurements based on our work on several pure liquids, was ±0.003 mPa∙s. In viscosity measurements, the temperature of the samples was controlled by using a water bath equipped with a thermostat of accuracy ±0.01 K. 3. Results and discussions Tables S2–S4, ESI1, report the experimentally measured densities E (ρ), speeds of sound (u) and calculated excess molar volumes (Vm ), deviations in speed of sound (uD) from their ideal values (uid) in an ideal mixture, molar isentropic compressibilities (KS,m), excess molar E isentropic compressibilities (KS,m ), and excess molar free volumes (VfE) for the binary mixtures of 1-hexanol with n-hexane, or n-octane, or ndecane at T = (298.15, 303.15 and 308.15) K. The values of viscosity (η) at 298.15 K for these binary mixtures were recorded in Table S5, ESI1. The density, ρ values have been used to calculate excess molar E volumes (Vm ) using the following equation: E ¼ Σ xi Mi ρ−1 −ρ−1 Vm i i¼1
ð1Þ
where Mi, ρ⁎i and ρ are the molar mass, density of ith component and density of the mixture respectively. E Fig. 1 shows the variation of Vm at 298.15 K for the studied binary mixture against the mole fractions (x1) of 1-hexanol. We observe that E the Vm values for (1-hexanol + n-hexane) at 298.15 K are negative over E the entire composition range with slight positive Vm values in the
Fig. 1. Plots of excess molar volumes (VEm) vs. mole fraction of 1-hexanol (x1) for binary mixture of 1-hexanol + n-hexane (■); +n-octane (●); and +decane (▲) at 298.15 K. The solid lines are drawn from Redlich–Kister Eq. (11).
1 Electronic supplementary information (ESI) available: Tables S2–S4 provide the densities, excess molar volumes, speeds of sound, deviations in speed of sound from their values in ideal mixtures, molar isentropic compressibilities, excess molar isentropic compressibilities and excess molar free volumes at 298.15, 303.15 and 308.15 K, respectively. Table S5 reports viscosities for the studied binary mixtures at 298.15 K.
126
G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129
The isentropic compressibility, κS and molar isentropic compressibility, KS,m were obtained from the equations [36,37]: −1 −1 −1 ðδVm =δP ÞS ¼ ρu2 ¼ Vm Mu2 κ S ¼ −Vm
ð2Þ
KS;m ¼ −ðδVm =δP Þs ¼ Vm κ S ¼ ∑xi Mi =ðρuÞ2
ð3Þ
where Vm the molar volume and M is the molar mass of the mixture. The excess molar isentropic compressibility KES,m was calculated from: E id KS;m ¼ KS;m −KS;m
ð4Þ
where Kid S,m, is the corresponding property of ideal solution can be calculated as [38]: h n oi id − AP;i =CP;i ¼ ∑xi KS;i −TAP;i ∑xi AP;i =∑xi CP;i KS;m Fig. 2. Plots of excess molar isentropic compressibility (KES,m) vs. mole fraction of 1-hexanol (x1) for binary mixture of 1-hexanol +n-hexane (■); +n-octane (●); and +decane (▲) at 298.15 K. The solid lines are drawn from Redlich–Kister Eq. (11). E initial range of x1 whereas with the rise of temperature Vm values become completely negative over the whole composition range. The E Vm curves for (1-hexanol + n-octane) binary mixtures display a positive deviation with a slight tendency to negative values at x1 ≈ 0.80 while for (1-hexanol + n-decane) are positive throughout the E whole composition range. It indicates that Vm values changes from negative to positive as the size of alkane molecule increases from nE hexane to n-decane. In case of (1-hexanol + n-hexane), Vm values become more negative with rise in temperature. For (1-hexanol + nE octane), Vm increases with rise in temperature and decreases at E higher mole fractions (x1) of 1-hexanol. On the other hand, the Vm curves of (1-hexanol + n-decane) show a systematic increase with temperature. E The variation of Vm with composition is the result of the contributions from several contractions and expansion processes which precede simultaneously when 1-hexanol + n-alkane mixtures are formed. Following two effects can be considered: (i) disruption of liquid order on mixing and unfavorable interactions between unlike molecules producing a positive contribution E to Vm , and (ii) contraction due to differences in free volume and molar volume of unlike molecules producing a negative contribuE tion to Vm . E The negative contributions to Vm observed in the present case may be due to differences in the size and shape of the component molecules in the mixture. The molar volumes of 1-hexanol and n-hexane at 298.15 K are 1.25 × 10− 4 and 1.32 × 10− 4 m3∙mol− 1 respectively. The E values of Vm become more negative as temperature of the system E increases. The increase in absolute values of Vm with the rise of temperature is explained by considering the differences in molar volumes of the two liquids at different temperatures. The difference in molar volumes of 1-hexanol and n-hexane is 0.062 × 10− 4 m3∙mol− 1 at 298.15 K while its value at 308.15 K is 0.067 × 10− 4 m3∙mol− 1. This means as the temperature of the mixture increases, the difference in the molar volumes two liquids also increases, hence the smaller molecules of 1-hexanol easily fit in the voids created by larger molecules of n-hexane, resulting in less increase in the volume of mixture. On the other hand, increase in temperature results ⁎ (1.253 × an appreciable increase in the molar volume of 1-hexanol, Vm,1 10− 4 m3∙mol− 1 at 298.15 K and 1.264 × 10− 4 m3∙mol− 1 at 308.15 K) due to the breaking of the hydrogen bonds. When n-alkane is added, there is an instantaneous breaking of the hydrogen bonds in 1-hexanol molecules, rendering the individual entities more disorder and hence less degree of cooperation. As a result, the net molecular order in the systems under study i.e. 1-hexanol with n-octane, or n-decane is decreased, yielding E high positive values of Vm .
ð5Þ
where A⁎P,i is the product of the molar volume Vi⁎ and the isobaric expansivity α⁎P,i, C⁎P,i, is the isobaric molar heat capacity, and K⁎S,i is molar isentropic compressibility of the pure liquid component i, respectively. The deviations of the speeds of sound from their values in an ideal mixture were calculated from [39,40]: uD ¼ u−uid
ð6Þ
In so far as the Newton–Laplace equation is valid, the ideal speeds of sound uid may be expressed correctly in term of thermodynamic properties of an ideal mixture: −1=2 1=2 id id : KS;m ∑ /i ρi uid ¼ Vm
ð7Þ
i
The KES,m values for studied binary mixtures at 298.15 K are plotted against x1 of 1-hexanol in Fig. 2. The trend in KES,m values is almost identical to VEm curves for all the binary mixtures. Like VEm, KES,m also depends on the strength of interaction between the molecules, on the structural effects and packing phenomenon, both related with difference in shape and size but packing phenomenon are better evidenced through KES,m values. Positive KES,m values reveal that the packing of molecules in the mixture is less compact than in the pure components while negative KES,m may correspond to interstitial accommodation of one component into another due to differences in molar masses, shape and free volumes of pure components. With
Fig. 3. Plots of deviation of speed of sound (uD) vs. mole fraction of 1-hexanol (x1) for binary mixture of 1-hexanol + n-hexane (■); + n-octane (●); and +decane (▲) at 298.15 K. The solid lines are drawn from Redlich–Kister Eq. (11).
G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129 Table 2 Values of the interaction parameters along with the standard relative deviations for (1hexanol + n-alkane) systems at 298.15 K Binary mixtures
Semi-empirical relations
Parameter
S.D.
1-Hexanol + n-hexane
Kendall–Monroe Grunberg–Nissan Tamura–Kurata Hind Katti–Chaudhri Kendall–Monroe Grunberg–Nissan Tamura–Kurata Hind Katti–Chaudhri Kendall–Monroe Grunberg–Nissan Tamura–Kurata Hind Katti–Chaudhri
– G12 = −0.996 T12 = −0.034 H12 = −0.062 Wvis / RT = −1.247 – G12 = −1.305 T12 = 0.127 H12 = 0.176 Wvis / RT = −1.305 – G12 = −1.314 T12 = 0.698 H12 = 0.360 Wvis / RT = −1.124
0.49 0.04 0.20 0.21 0.52 0.45 0.01 0.13 0.17 0.40 0.37 0.01 0.08 0.13 0.27
1-Hexanol + n-octane
1-Hexanol + n-decane
increase in temperature, the positive values become more positive and negative values become more negative. The composition dependence of uD values is shown in Fig. 3. The trend in uD values is similar to KES,m with opposite sign for all the binary systems throughout the whole composition range. The trend observed is entirely positive for 1-hexanol + n-hexane, changes sign from negative to positive for 1-hexanol + n-octane whereas entirely negative for 1-hexanol + n-decane except at higher x1. Again, the effect is that with increasing the chain-length of n-alkane, the interstitial accommodation become less important that the molecules of two components cannot be easily accommodated. The uD values for 1hexanol with n-hexane show systematic increase with rise of
127
temperature whereas in case of 1-hexanol + n-octane or +n-decane binary mixture, uD values are almost identical. The results obtained for viscosity of binary mixtures were also used to test the semi-empirical relations of Kendall and Monroe [41], Grunberg–Nissan [42], Tamura and Kurata [43], Hind–McLaughlin– Ubbelohde [44] and Katti and Chaudhry [45,46]. To perform a numerical comparison of the correlating capabilities of these relations we calculated the standard relative deviation (S.D.) using the relation: 2 1=2 2 S:D: ¼ 1=ðn−pÞ ∑ ηexp −ηcal =ηexp
ð8Þ
i¼1
where n represents the number of experimental data points and p the number of adjustable parameters in the respective relations. Table 2 shows the calculated parameters and the standard relative deviations (S.D.) between experimental values obtained for viscosities and the predicted results using the semi-empirical relations. As can be clearly seen by the results reported in Table 2, Grunberg–Nissan relation represent the behaviour of the binary mixtures satisfactorily as compared to other equations. Further interaction parameter (G12) gives an idea about quantitative estimation of interactions in the mixtures. It is well known that if G12 N 0 and higher in magnitude, there will be strong specific interactions in the mixture and if G12 b 0, it indicates the presence of weak interactions [47]. A through examination of Table 2 reveals that G12 values are negative for all the binary mixtures studied here and it provide support for the existence of weak dispersive forces in these binary mixtures. In the present study, the values of interaction parameters T12 and H12 do not differ appreciably from each other for a given binary mixture. The T12 and H12 values are also positive and negative.
Table 3 Coefficients Ai of Eq. (11) and corresponding standard deviation (σ) of Eq. (12) Binary mixture
T (K)
Excess property
A1
A2
A3
A4
1-Hexanol + n-hexane
298.15
E × 106/ (m3∙mol− 1) Vm uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1 MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107 /(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1 MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1) E Vm × 106/(m3∙mol− 1) uD/(m∙s− 1) E KS,m /(mm3 mol− 1MPa− 1) VfE × 107/(m3∙mol− 1)
−1.0354 124.29 −30.49 −1.8002 −2.0480 137.69 −37.78 −2.1751 −2.1107 144.26 −42.06 −2.4999 0.3405 22.60 −4.28 0.4197 0.2341 27.06 −5.75 0.4337 0.3085 25.92 −5.70 0.4847 0.9121 −13.13 4.38 0.6120 1.0998 −15.06 5.36 0.6849 1.2056 −14.17 5.61 0.7667
−0.5837 84.20 −7.85 −0.2522 −0.3633 93.75 −7.46 −0.2472 −0.3983 93.97 −6.96 −0.2158 −0.4933 38.70 −7.47 −0.2088 −0.5044 40.63 −8.12 −0.2399 −0.5773 40.82 −8.83 −0.2675 −0.3846 14.28 −4.87 0.0335 −0.3681 15.59 −5.41 0.0692 −0.2013 14.67 −5.12 0.0474
0.3697 19.01 4.59 0.2174 0.3706 20.29 5.13 0.2755 0.4662 24.92 3.92 0.2129 0.2054 14.51 0.40 −0.0186 0.3849 7.97 2.57 0.0540 0.2523 11.89 1.19 0.0138 0.1957 −1.64 1.54 0.0397 0.1661 8.72 −0.64 0.0257 0.7263 11.85 −0.62 −0.0295
− 0.9615 27.23 − 7.80 − 0.3774 − 2.3793 23.86 −10.98 − 0.4356 − 2.3006 34.13 −12.61 − 0.5186 − 0.5342 16.90 − 4.56 − 0.1219 − 0.9087 21.75 − 5.93 − 0.1598 − 0.9588 24.58 −7.07 −0.2119 −0.2109 9.39 −2.48 −0.0540 −0.1152 11.72 −3.51 −0.2108 −0.1881 18.55 −5.61 −0.1241
303.15
308.15
1-Hexanol + n-octane
298.15
303.15
308.15
1-Hexanol + n-decane
298.15
303.15
308.15
A5 −14.46 5.39 0.3145 −0.1755 −11.11 6.29 0.3293 −0.4279 5.88 0.3473 0.2098 −16.51 5.41 0.1677
1.79 −0.0363 0.3365 −6.79 5.64 0.1433 0.1578 1.30 0.0321 0.7760 −20.84 7.25 0.2068 −26.38 8.67 0.2060
σ 0.0032 0.15 0.05 0.0024 0.0040 0.21 0.05 0.0023 0.0033 0.18 0.04 0.0023 0.0020 0.07 0.02 0.0007 0.0020 0.12 0.03 0.0011 0.0016 0.15 0.04 0.0013 0.0024 0.07 0.02 0.0004 0.003 0.18 0.06 0.0063 0.0029 0.15 0.05 0.0012
128
G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129
Table 4 Characteristic parameters of pure components at 298.15 K Components T/K
κT/(TPa− 1)
ν~
T˜
V⁎ × 106 / (m3∙mol− 1)
P⁎ × 106/ (J·m− 3)
T⁎/K
1-Hexanol
824.0[29] 863.0a 894.2a 1706.0 [29] 1791.7 [56] 1844.0 [50] 1280.0 [29] 1373.5 [56] 1386.0 [57] 1094.0 [29] 1196.0 [58] 1176.0 [59]
1.2587 1.2270 1.2349 1.3227 1.3292 1.3381 1.2804 1.2902 1.2946 1.2581 1.2642 1.2721
0.0528 0.0537 0.0549 0.0673 0.0681 0.0691 0.0618 0.0631 0.0637 0.0586 0.0592 0.0606
102.6022 102.5520 102.3566 99.4564 99.6842 99.7293 127.7097 127.4844 127.8032 155.6091 155.8797 155.5166
472 468 477 425 419 427 444 439 446 453 426 460
5645 5642 5603 4430 4452 4456 4826 4803 4837 5091 5120 5085
298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15
n-Hexane
n-Octane
n-Decane
a
Calculated from κT = /(ρu2) + TVα2/CP.
According to Fort and Moore, [48] the values of T12 and H12 are not very different except where the values of the component differ considerably. Furthermore, T12 and H12 show some variation with composition although this is only large for systems where there is a strong specific interaction between the components. There is a tendency of T12 and H12 at a certain composition to increase with the strength of interaction of the components. But this is not welldefined and T12 and H12 cannot generally be regarded as a measure of the strength of interactions [49]. The molar free volumes (Vf) in the binary mixtures of 1-hexanol + nalkanes were obtained according to Eyring [50,51] from the following relation:
Fig. 5. Composition dependence of experimental and calculated values of isentropic compressibility, κS in 1-hexanol + n-hexane (■); +n-octane (●); +n-decane (7) at 298.15 K. The corresponding dotted curves (........) represent PFP theory.
hexanol (x1) for binary mixtures under study is given in the Table 2S– 4S, ESI1. For each binary mixture, the excess properties (VEm,uD, KES,m, and Δη ) were fitted to the Redlich–Kister polynomial equation [52]: m
Z E ¼ x1 x2 ∑ Ai ðx1 −x2 Þi−1
ð11Þ
i¼1
Vf ¼ Vu−3 ðRTγ=M Þ3=2
ð9Þ
where γ = (CP / CV) is the ratio of isobaric and isochoric heat capacities that can be determined knowing the isentropic and isothermal compressibility coefficients, κS and κT from(CP / CV) = (κT / κS). The excess free volumes (VEf ) can be calculated by using the equation: 2
VfE ¼ Vf − ∑ xi Vf;i
ð10Þ
i¼1
where Vf is the free volume of mixture and Vf,i is that for pure component i. The variation of VEf versus the mole fractions of 1-
where ZE is any excess property, Ai's are polynomial coefficients and m is the number of estimated parameters. In each case, the optional number of coefficients was ascertained from an approximation of the variation in the standard deviations (σ). The calculated values of Ai along with the tabulated standard deviations (σ) are listed in Table 3. The standard deviations (σ) were calculated using the equation: 1=2 2 E E σ ¼ ∑ Zexp −Zcal =ðn−mÞ
ð12Þ
4. Theoretical prediction of speed of sound The theoretical values of isentropic compressibility κS and speed of sound u for both the liquid components and the liquid mixtures have been estimated using the Van der Waals (vdW) potential energy model in the Prigogine–Flory–Patterson (PFP) theory. The relevant equations are given elsewhere [13–16, 53–55].
Table 5 Comparison of experimental and calculated values of the speed of sound (u) and isentropic compressibility (κS) of binary mixtures at x1 = 0.5 and standard percentage deviation Binary mixtures
T/K
χ12 × 106/ (J·m− 3)
1-Hexanol + n-hexane
298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15
17.20 06.68 06.12 16.08 15.87 15.30 14.41 17.45 16.35
1-Hexanol + n-octane Fig. 4. Composition dependence of experimental and calculated values of speeds of sound, u in 1-hexanol + n-hexane (■); +n-octane (●); +n-decane (7) at 298.15 K. The corresponding dotted curves (........) represent PFP theory.
1-Hexanol + n-decane
u/(m s− 1)
κS/(TPa− 1)
Expt.
vdW
σ%
Expt.
vdW
σ%
1169.1 1151.9 1132.8 1216.9 1195.3 1176.8 1249.3 1225.7 1210.9
1189.2 1162.8 1150.1 1239.0 1206.2 1196.5 1270.4 1230.8 1229.6
1.3 0.7 1.4 1.7 0.5 1.4 1.4 1.2 1.3
997.8 1034.5 1077.5 905.6 937.9 977.3 842.0 879.9 907.6
996.6 1011.2 1040.8 871.1 924.5 942.5 813.0 875.9 874.7
2.8 1.5 2.8 3.4 1.1 3.0 3.0 2.4 2.7
G.P. Dubey, M. Sharma / Journal of Molecular Liquids 142 (2008) 124–129
The derived parameters for the pure liquid components using Flory theory are presented in Table 4. The contact interaction parameter χ12 for each liquid mixture is obtained according to the PFP theory from the excess molar volume values at x1 = 0.5. Figs. 4 and 5 compare the experimental values of speed of sound u and isentropic compressibility κS with the calculated one over the entire composition range for the three binary mixtures at 298.15 K. Similar trend is observed at other two working temperatures. The experimental and the PFP estimates of both u and κS with the vdW energy model for all the binary mixtures at equimolar comparison are summarized in Table 5. In order to perform a numerical composition of the estimation capability of the vdW energy model in the PFP theory, we calculated the standard percentage deviations (σ %) using the relation h i1=2 2 σ k ¼ ∑f100ðexptl:−theor:Þ=exptl:g =ðn−1Þ
ð13Þ
where n represents the number of experimental data points. The values of σ % are also given in Table 5. Acknowledgement Financial support for this project (Grant No. F.30-58/2004-SR dated 2/11/04) by University Grants Commission, New Delhi, India is fully acknowledged. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.molliq.2008.05.013. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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