J Solution Chem (2006) 35:1567–1585 DOI 10.1007/s10953-006-9079-0 ORIGINAL PAPER
Volumetric Properties of Binary Mixtures of Isomeric Butanols and C8 Solvents at 298.15 K Luca Bernazzani · Maria Rita Carosi · Celia Duce · Paolo Gianni · Vincenzo Mollica
Received: 7 March 2006 / Accepted: 11 May 2006 / Published online: 27 October 2006 C Springer Science+Business Media, LLC 2006
Abstract Excess molar volumes, VmE , over the whole composition range for binary mixtures of 1-butanol, 2-butanol, and 2-methyl-2-propanol + 1-octanol, or 2-octanol, or din-butyl ether, or n-hexylacetate were determined at 298.15 K from density measurements carried out with a vibrating-tube densimeter. Small VmE values, both positive and negative, are displayed by mixtures containing 1- or 2-octanol, whereas positive and larger values are always found for mixtures containing dibutyl ether and hexylacetate. These results can be justified in terms of H-bonding interactions and/or steric hindrance due to the branched alkyl chains. Partial molar volumes at infinite dilution of the isomeric butanols in the C8 compounds were also calculated from the apparent molar volumes in dilute solution. The solute-solvent interactions and the effects of the local organisation of the solvent around the butanol molecules were discussed using the void and cavity volumes as different estimates of the intrinsic volume of the molecules. The volumetric behavior of butanols seems to be determined by the solute-solvent interactions rather than packaging effects. Keywords Density · Binary mixtures · Excess volumes · Apparent and partial molar volume · Isomeric butanols · Interactions 1 Introduction In the past years we carried out a systematic investigation of the thermodynamic properties of solvation of organic solutes in non-aqueous solvents with different amphiprotic, hydrogenbond acceptor or donor features [1, 2]. This pool of solvents with different properties, named the “critical quartet,” has been considered by many authors as a model of biological membranes in order to mimic their crossing by molecules of pharmacological or environmental relevance. Therefore, the properties of solvation are helpful devices to gain information on the factors which control this passive transport, the different solvents taking into account L. Bernazzani . M. R. Carosi . C. Duce . P. Ganni . V. Mollica () Dipartimento di Chimica e Chimica Industriale, Universit`a degli Studi di Pisa, Via Risorgimento 35, 56126 Pisa, Italy e-mail:
[email protected] Springer
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the different biophysical characteristics of the cell membranes that depend on their nature and the physiological process they are involved in [3]. Recently our attention has been extended from 1-octanol (1-OctOH) and di-n-butyl ether (DBE) solvents, traditionally belonging to the “critical quartet,” to 2-octanol (2-OctOH) and n-hexylacetate (HAC) [4, 5]. The first solvent was chosen because of its more shielded secondary –OH group with respect to 1-OctOH that produces a reduced local order that, in turn, affects the environment experienced by the solute molecules. The HAC solvent was chosen because of its low water content at saturation, the polarity of the alkoxy group and its chemical stability. From another point of view, the thermophysical properties of systems containing alkanols have been extensively analyzed both for their theoretical and experimental interest. Several papers dealt with the study of the thermodynamic behavior of systems formed by an isomeric alkanol and a given solvent [6]. It was found that the value of the properties investigated varies with the position of the hydroxyl group in the alkyl chain of the alkanol. The explanation of these results was related to a decrease of the association capability when the hydroxyl group is not located in a primary position, due to the larger steric hindrance over the hydroxyl group [7]. In this work, a comparative study of the volumetric behavior of 1-butanol (1-ButOH), 2-butanol (2-ButOH) and 2-methyl-2-propanol (t-ButOH) + 1-octanol or 2-octanol, or di-nbutyl ether or n-hexylacetate is presented. To this aim the densities of the mixtures have been measured at 298.15 K over the whole composition range and the excess molar volumes, VmE , were calculated. From these data the partial molar volumes and the excess partial molar volumes of isomeric butanols were obtained. These latter quantities were also used to characterize the molecular interactions in these mixtures and the effect of branching of the alkyl chains. Specific attention was also devoted to density measurements performed in the range of low butanol concentrations in order to obtain more accurate values of the partial molar volumes extrapolated at infinite dilution, V1∞ . Although the volumetric properties are dominated by intrinsic factors such as molecular size and shape, they are of great importance in understanding the interactions in solution and the local organization of the solvent around the solute molecules. This information can be gained by applying simple additivity schemes to the volumetric properties at infinite dilution where the contribution of each group is assumed to be independent of the molecule being investigated, but is dependent on the solvent [8]. However, when this procedure can not be applied, alternative approaches allow the definition of a reference volume and interpretation of the relative displacement as being due to specific solute–solvent interactions, conformational effects and the packaging efficiency of the solvent molecules around the solute. Among the different kinds of the reference volume to be used [9, 10], we tried to estimate the contribution of the specific interactions to V1∞ of the examined butanols in 1-OctOH, 2-OctOH, HAC and DBE, using different approaches based on the limiting excess volume, on the model of Terasawa et al. [11] and on the Scaled Particle Theory (SPT) [12]. The results are discussed in terms of the relative ability of the solvents to discriminate between the solutes according to their different molecular structures. 2 Experimental 2.1 Materials All chemicals were commercial products of the highest quality available. Their origin, mass fraction purity and the measured density (kg·m−3 ) at T = 298.15 K were as follows: Springer
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1-butanol (C. Erba) > 0.995, 805.83; 2-butanol (Fluka) > 0.997, 802.55; t-butanol (Fluka) > 0.997, 781.21; 1-octanol (Fluka) > 0.995, 821.74; 2-octanol (Fluka) > 0.98, 816.32; din-butylether (Aldrich) > 0.99, 763.98; n-hexylacetate (Fluka) > 0.99, 869.09. The densities of the pure compounds show generally good agreement with the literature data and are consistent with our previous measurements [5, 13]. All the compounds were used without further purification and their purity, as checked from GLC analysis, was found to confirm the minimum manufacture specifications. The water content, as checked by Karl Fischer analysis, was always less than 5 × 10−4 mass fraction. 2.2 Apparatus and procedure A DMA60 Anton Paar vibrating-tube densimeter, equipped with a DMA602 cell and operating under static conditions, was used to determine the density, ρ, of the pure liquids and solutions. The measurement procedures are described in detail in ref. [14] and the reproducibility of the density values was estimated better than 3 × 10−3 kg·m−3 . By considering all possible sources of error, the accuracy of the measurements was evaluated to be within 5 × 10−3 kg·m−3 . The liquid solutions were prepared by weight and were not degassed. The composition of the solutions, expressed as molality, m, or mole fraction, x, after correction for buoyancy and for evaporation of the components in the space above the liquid, was evaluated to better than ±0.0002. The overall volume uncertainty, due to density or composition errors, was generally less than 0.04 and 0.001 cm3 ·mol−1 on the apparent molar and the excess volumes, respectively. The measurements covered the whole composition range with particular care taken in the dilute regions in order to obtain accurate partial molar volumes of the butanols extrapolated to infinite dilution. For some of the pure chemicals examined, the isobaric expansivity at 298.15 K was also determined by measuring the temperature dependence of the density in the range from 293.15 to 303.15 K. The measurements were carried out with a DMA 5000 Anton Paar densimeter with a 1 K temperature step. The precision was 0.001 K in temperature and 5 × 10−3 kg·m−3 in the density values, thus obtaining a precision of the expansivity better than 8 × 10−3 kg·m−3 ·K−1 .
3 Results 3.1 Experimental results The excess molar volumes of the mixtures were obtained from the measured values of the density through the usual equation
VmE
=
i
x i Mi
1 1 − • ρ ρi
(1)
where xi , Mi and ρi• are the mole fraction, molecular weight and density of the i component, respectively, and ρ is the density of the mixture. Experimental values of the excess molar volumes of the binary systems are listed in Table 1. The uncertainty of the molar excess volumes is estimated to be less than ±0.001 cm3 ·mol−1 . The best overall fit was obtained Springer
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with a Redlich–Kister type smoothing equation: VmE = x (1 − x)
n
Ai (2x − 1)i
(2)
i=0
where x is the mole fraction of the isomeric butanols. The values of the parameters, Ai , were obtained by a nonlinear least-squares method using the Marquardt–Levenberg procedure [15] to fit the experimental results by Eq. (2). The standard deviation, σ (VmE ), was calculated from:
2 ⎤1/2 E,exp E,calc n V − V ⎢ m, j m, j ⎥ σ VmE = ⎣ ⎦ n − k j=1 ⎡
(3)
where k is the number of smoothing parameters in Eq. (2) and the sum is extended to all n data points. The parameters, Ai , along with the standard deviations are reported in Table 2. The number of parameters was chosen on the basis of the σ (VmE ) values: including additional parameters produced no improvement of the fit. The experimental values of VmE are presented graphically in Fig. 1 together with the fitting curves. Figure 1 also shows the literature data, relevant to the systems 1-ButOH + 1-OctOH [16], 2-ButOH + 1-OctOH [17], 1-ButOH + DBE [13] and 2-ButOH + DBE [18]. The agreement with our values is generally good with the exception of the system 2-ButOH + 1-OctOH, for which the authors report very small excess volumes with a sigmoid trend not exhibited by our data. However, it should be stressed that in this case the overall relative uncertainties are quite high due to the very small VmE values. We did not find in the literature data relevant to the other systems investigated here. In Fig. 2 the distribution of the residuals between the experimental and calculated VmE values is reported for the 1-ButOH + 1-OctOH system, as an example. A completely random distribution of the deviations is observed. We can also evaluate the excess partial molar volumes, ViE , of the components of the liquid mixtures over the whole composition range by using the equations: V1E = VmE + (1 − x) ∂ VmE ∂ x P,T V2E = VmE − x ∂ VmE ∂ x P,T
(4) (5)
where 1 and 2 indicate the butanol isomer under investigation and the given solvent, respectively and x represents the mole fraction of the former component. The derivatives of Eqs. (4) and (5) were obtained by differentiating Eq. (2) with respect to x. This leads to the excess partial molar volumes as expressed by the following relationships: V1E = (1 − x)2
n
Ai (2x − 1)i + 2x (1 − x)2
i=0
V2E = x 2
n i=0
Ai (2x − 1)i − 2x 2 (1 − x)
n
i Ai (2x − 1)i−1
(6)
i=0 n
i Ai (2x − 1)i−1
(7)
i=0
Figure 3 shows the calculated results for excess partial molar volumes, V1E , of the butanol isomers. Springer
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Table 1 Excess molar volumes, VmE , of [butanol + organic solvent] at 298.15 K VmE (cm3 ·mol−1 )
x
VmE (cm3 ·mol−1 )
x
VmE (cm3 ·mol−1 )
x 1-Butanol + (1 − x)1-Octanol 0.0734 0.0109 0.3546 0.1252 0.0175 0.3853 0.2148 0.0255 0.4516 0.2857 0.0315 0.5501
0.0345 0.0368 0.0393 0.0418
0.6088 0.6456 0.7455 0.8523
0.0409 0.0400 0.0333 0.0219
0.9166 0.9475
0.0145 0.0101
x 2-Butanol + (1 − x)1-Octanol 0.0363 0.0083 0.2766 0.0641 0.0139 0.3639 0.1006 0.0215 0.4527 0.1843 0.0369 0.4859
0.0494 0.0590 0.0655 0.0667
0.5405 0.5542 0.6365 0.7176
0.0678 0.0676 0.0657 0.0602
0.8151 0.9176 0.9782
0.0473 0.0247 0.0067
x t-Butanol + (1 − x)1-Octanol 0.0629 −0.0153 0.2951 0.1027 −0.0232 0.3986 0.1600 −0.0371 0.4998 0.1936 −0.0445 0.5455
−0.0666 −0.0879 −0.1060 −0.1118
0.6296 0.7098 0.8106 0.9076
−0.1216 −0.1234 −0.1106 −0.0726
0.9755 −0.0243
x 1-Butanol + (1 − x)2-Octanol 0.0217 −0.0065 0.1814 0.0409 −0.0131 0.2700 0.0627 −0.0200 0.3618 0.1062 −0.0280 0.3930 0.1362 −0.0347 0.4321
−0.0430 −0.0497 −0.0512 −0.0507 −0.0499
0.4655 0.4968 0.5268 0.5634 0.6169
−0.0481 −0.0468 −0.0441 −0.0401 −0.0346
0.6503 0.7196 0.7908 0.8468 0.9443
−0.0307 −0.0244 −0.0159 −0.0106 −0.0035
x 2-Butanol + (1 − x)2-Octanol 0.0258 0.0031 0.2185 0.0667 0.0048 0.3199 0.1182 0.0093 0.4254 0.1731 0.0120 0.5216
0.0138 0.0198 0.0231 0.0245
0.6093 0.6596 0.7571 0.8591
0.0246 0.0243 0.0200 0.0135
0.9553
0.0031
x
VmE (cm3 ·mol−1 )
x
x t-Butanol + (1 − x)2-Octanol 0.1059 −0.0097 0.3977 −0.0361 0.1929 −0.0200 0.4965 −0.0421 0.2984 −0.0313 0.5844 −0.0395
0.6453 −0.0411 0.6905 −0.0400 0.7925 −0.0302
0.8904 −0.0210
x 2-Butanol + (1 − x)di−n-Butylether 0.0150 0.0130 0.1197 0.0398 0.0311 0.1648 0.0525 0.0385 0.2125 0.0673 0.0460 0.2587
0.0672 0.0898 0.1051 0.1134
0.3432 0.4220 0.4668 0.5231
0.1296 0.1348 0.1329 0.1276
0.5846 0.6736 0.7983 0.9343
0.1161 0.0920 0.0488 0.0073
x t-Butanol + (1 − x)di-n-Butylether 0.0147 0.0313 0.1305 0.0289 0.0601 0.1729 0.0420 0.0842 0.2145 0.0664 0.1239 0.3482 0.0967 0.1661 0.4432
0.2084 0.2542 0.2943 0.3953 0.4435
0.5038 0.5623 0.5826 0.6451
0.4635 0.4730 0.4746 0.4695
0.7007 0.7910 0.8850 0.9348
0.4526 0.3948 0.2941 0.2246
0.3030 0.4006 0.4952 0.5970
−0.3561 −0.3831 −0.3872 −0.3622
x 1-Octanol + (1 − x)di-n-Butylether 0.0115 −0.0227 0.0756 −0.1485 0.0256 −0.0507 0.1348 −0.2323 0.0381 −0.0832 0.2016 −0.2955 0.0503 −0.1078 0.2552 −0.3327
0.7013 −0.3102 0.7965 −0.2373 0.8823 −0.1511
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Table 1 Continued VmE (cm3 ·mol−1 )
x
VmE (cm3 ·mol−1 )
x
x
VmE (cm3 ·mol−1 )
VmE (cm3 ·mol−1 )
x
x 2-Octanol + (1 − x)di-n-Butylether 0.0134 −0.0073 0.1729 −0.0798 0.0395 −0.0227 0.2140 −0.0913 0.0628 −0.0363 0.2508 −0.0997 0.1264 −0.0624 0.3204 −0.1080
0.4235 0.5221 0.5926 0.7028
−0.1150 −0.1142 −0.1085 −0.0893
x 1-Butanol + (1 − x)n-Hexylacetate 0.0145 0.0151 0.2253 0.0614 0.0541 0.3451 0.1240 0.0942 0.4401 0.1739 0.1193 0.5194
0.1389 0.1695 0.1777 0.1765
0.5489 0.5824 0.6482 0.7456
0.1758 0.1701 0.1593 0.1323
0.8478 0.9461
0.0905 0.0370
x 2-Butanol + (1 − x)n-Hexylacetate 0.0144 0.0338 0.1764 0.0405 0.0909 0.2237 0.0678 0.1448 0.3442 0.1267 0.2500 0.4397
0.3226 0.3782 0.4770 0.5176
0.5130 0.5662 0.6423 0.7547
0.5263 0.5210 0.4947 0.4137
0.8547 0.9544
0.2919 0.1099
x t-Butanol + (1 − x)n-Hexylacetate 0.0143 0.0425 0.1783 0.0405 0.1136 0.2233 0.0705 0.1905 0.3406 0.1246 0.3063 0.4350
0.3995 0.4620 0.5740 0.6209
0.5089 0.5691 0.6448 0.7480
0.6325 0.6276 0.5964 0.5137
0.8482 0.9478
0.3721 0.1500
0.7992 −0.0699 0.9145 −0.0369
Table 2 Parameters, Ai , of Eq. (2) for [x butanol + (1 − x) organic compound] at 298.15 K and maximum values of x and (VmE )a E A1 A2 A3 σ VmE b (xmax ) c (Vm,max )c 1-octanol 1-butanol 2-butanol t-butanol
0.16271 0.26838 −0.42217
0.02445 0.0548 −0.34984
0.01062 0.02165 −0.20430
0.0008 0.0003 0.0013
0.5394 0.5535 0.6861
0.0409 0.0678 −0.1251
2-octanol 1-butanol 2-butanol t-butanol
−0.18238 0.09869 −0.16388
0.15028 0.02039 −0.05196
−0.00968 −0.00391 0.00816
0.0006 0.0008 0.0014
0.3460 0.5483 0.5711
−0.0520 0.0249 −0.0419
di-n-butyl ether 1-butanold 2-butanol t-butanol 1-octanol 2-octanol
−0.94653 0.51535 1.82100 −1.53183 −0.45763
−0.07717 −0.26898 0.61521 0.31097 0.08848
−0.32037 −0.11286 0.92415 −0.36812 −0.09362
0.0014 0.0032 0.0114 0.0045 0.0011
0.5304 0.4036 0.6241 0.4370 0.4421
−0.2372 0.1355 0.4764 −0.3880 −0.1157
n-hexyl acetate 1-butanol 2-butanol t-butanol
0.71114 2.10309 2.52963
−0.09511 0.07602 0.08969
0.13597 0.37888 0.60189
0.0012 0.0009 0.0012
0.4596 0.5110 0.5116
0.1788 0.5260 0.6327
quantities in units of cm3 ·mol−1 . deviation of the fitting procedure. c Maximum value of excess volume as calculated by Eq. (2) at x max mole fraction. d The A parameters and σ (V E ) value are taken from ref. [13]. i m
a All
b Standard
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Fig. 1 Plots of the excess molar volumes, VmE , against the mole fraction x for [x alcohol + (1 − x) S] binary mixtures at 298.15 K. S: (a) 1-OctOH; (b) 2-OctOH; (c) DBE; (d) HAC. Alcohol: (), 1-ButOH; (䊐), 2-ButOH; × 䊐, t-ButOH; (•), 1-OctOH; (◦), 2-OctOH (this work). Literature data: (a) 1-ButOH + 1-OctOH ((), ref. [16]), 2-ButOH + 1-OctOH ((), ref. [17]); (c), 1-ButOH + DBE ((), ref. [13].), 2-ButOH + DBE ((), ref. [18].)
Fig. 2 Plot of the distribution of the residuals [= VmE (exp) − VmE (calc)] against the mole fraction x for [x 1-ButOH + (1−x) 1-OctOH] binary mixtures
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Fig. 3 Excess partial molar volumes, V1E , against the mole fraction x for [x alcohol + (1 − x) S] binary mixtures at 298.15 K. S: (a) 1-OctOH; (b) 2-OctOH; (c) DBE; (d) HAC. Alcohol: (), 1-ButOH; (䊐), 2-ButOH; (× 䊐), t-ButOH; (•), 1-OctOH; ◦, 2-OctOH
Equation (6) can be used to calculate the excess partial molar volumes at infinite dilution of the butanols, V1E,∞ , by simply setting x = 0. These limiting partial properties are very interesting because, having been calculated for the condition of vanishing solute-solute interactions, they provide selective information on the interactions of the solute with the solvent. Table 3 reports the V1E,∞ values of the examined butanols with the corresponding partial molar volumes at infinite dilution, V1∞ , calculated from the molar volume of the pure alcohol, V1∗ , through the well-known relation V1∞ = V1∗ + V1E,∞ . However, the values in Table 3 must be regarded with caution. As a matter of fact, the VmE data collected over the whole composition range can easily mask inflection points or even sign changes of the function in the very dilute region, thus possibly yielding completely wrong values of the limiting excess volumes. More accurate values of V1∞ can be obtained by extrapolation to infinite dilution of properly measured apparent molar volumes of butanols in a given solvent, 1 . Values of 1 were calculated from the measured densities of the dilute solutions, ρ, through the Eq. (8): 1 =
M1 1000(ρ2• − ρ) + ρ mρρ2•
(8)
where ρ2• and M1 are the density and molecular weight of the pure solvent, respectively, whereas m is the concentration of the solution in mol·kg−1 . Table 4 reports the experimental quantities m, ρ = (ρ2• − ρ), and 1 of the examined solutions. The 1 values are shown in Fig. 4 as a function of the concentration, m, of the solutions. As can be seen, the values of 1 are almost constant in the examined concentration range Springer
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Table 3 Excess partial molar volumes, V1E,∞ , and partial molar volumes, V1∞ , at infinite dilution of the examined compoundsa (V1E,∞ ) b
(V1∞ ) c
(V1E,∞ ) d
1-octanol 1-butanol 2-butanol t-butanol
0.149 0.235 −0.277
92.14 92.60 94.66
0.154 0.233 −0.218
2-octanol 1-butanol 2-butanol t-butanol
−0.342 0.074 −0.104
91.66 92.46 94.88
−0.326 0.096 −0.003
di-n-butyl ether 1-butanol 2-butanol t-butanol 1-octanol 2-octanol
−1.190 0.671 2.130 −2.211 −0.640
90.84 93.29 96.99 156.28 158.91
−1.141 0.926 2.109 −2.193 −0.622
n-hexyl acetate 1-butanol 2-butanol t-butanol
0.942 2.406 3.042
93.05 94.76 97.96
1.069 2.397 3.081
298.15 K. All data are in cm3 ·mol−1 . from values in Table 2 setting x = 0 in Eq. (6). c Calculated by linear extrapolation to infinite dilution of the values of Table 4. 1 d Calculated by V E,∞ = V ∞ − V ∗ using the V ∞ values of this table and the molar volumes, V ∗ , of the pure 1 1 1 1 1 alcohols obtained from density values described in Section 2.1.
a At
b Calculated
except for all butanols in HAC, and 2-ButOH and t-ButOH in DBE. In these cases, the 1 values decrease markedly when m increases. The limiting partial molar volumes of the solutes, V1∞ , were then obtained by linear extrapolation of the 1 values to infinite dilution by a simple least-squares fitting method and are reported in Table 3. The uncertainty of the limiting partial molar volumes, estimated as the standard deviation of the intercept of the linear fit, is less than ±0.03 cm3 ·mol−1 . The slopes of the straight lines are both positive and negative, small in magnitude for the isomeric butanols in 1-OctOH and 2-OctOH whereas higher in HAC and DBE, and are generally negative indicating the presence of attractive solute-solute short-range interactions. To the best of our knowledge, V1∞ data obtained from the 1 values, which are directly comparable with ours, have not been reported in the literature. The comparison of the V1∞ values calculated from data over the whole composition range and those calculated from the apparent molar volumes in the dilute region can give useful indications in regard to the accuracy of fitting the VmE data and, more specifically, may suggest the presence in the dilute region of a “critical” zone where a significant deviation from the random distribution of the molecules may occur. The V1E,∞ values calculated by the two approaches always have the same sign and their differences are generally small, only being significant for 2-ButOH in DBE and 1-ButOH in HAC. The excellent agreement between the two sets indicates that the trends of VmE versus x are well defined even in the very dilute region and sigmoid shapes can be excluded. Springer
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Table 4 Experimental m, ρ, and 1 values of the examined solutionsa
m mol·kg−3
ρ kg·m−3
b
1 cm3 ·mol−1
c
m mol·kg−3
ρ kg·m−3
1 cm3 ·mol−1
1-octanol 1-butanol 0.0812 0.1320 0.1691 0.2528 0.3118 0.3480 0.4409 0.5125
0.105 0.171 0.216 0.322 0.396 0.445 0.560 0.645
92.13 92.14 92.12 92.13 92.12 92.15 92.15 92.14
0.5553 0.8288 1.0036 1.1600 1.4653 1.5374 1.9706
0.686 1.000 1.209 1.364 1.703 1.758 2.203
92.11 92.10 92.12 92.10 92.12 92.09 92.11
2-butanol 0.0877 0.1870 0.2865 0.2892 0.3908 0.4889 0.5091 0.5256
0.143 0.298 0.452 0.455 0.607 0.755 0.783 0.808
92.64 92.60 92.59 92.58 92.57 92.57 92.57 92.57
0.8592 0.9878 1.1290 1.4847 1.4919 1.7348 1.9661
1.288 1.460 1.650 2.112 2.126 2.436 2.706
92.56 92.56 92.55 92.55 92.55 92.55 92.55
t-butanol 0.0734 0.1251 0.1721 0.2701 0.3813 0.4464 0.5158 0.8059
0.219 0.376 0.509 0.801 1.114 1.300 1.500 2.300
94.65 94.69 94.64 94.69 94.66 94.67 94.68 94.69
0.8786 0.9220 1.1160 1.3695 1.4625 1.8161 1.8439
2.497 2.615 3.112 3.763 3.981 4.840 4.893
94.70 94.70 94.69 94.71 94.69 94.71 94.70
2-octanol 1-butanol 0.1096 0.1702 0.2210 0.3106 0.3277 0.4233 0.4611 0.5133 0.6759
0.064 0.100 0.125 0.182 0.183 0.233 0.262 0.283 0.386
91.68 91.69 91.66 91.69 91.66 91.65 91.68 91.66 91.67
0.7850 0.9127 1.1863 1.3861 1.5783 1.7016 1.8592 2.0663
91.71 91.71 91.73 91.74 91.75 91.75 91.76 91.76
0.459 0.521 0.678 0.789 0.898 0.985 1.049 1.150
2-butanol 0.2036 0.3248 0.4344 0.4719 0.5491
0.225 0.353 0.461 0.499 0.575
92.48 92.47 92.44 92.44 92.44
0.6829 1.0295 1.6075 2.0388 2.1470
0.704 1.046 1.560 1.924 2.003
92.43 92.44 92.43 92.43 92.43
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Table 4 Continued
m mol·kg−3
t-butanol 0.1116 0.1673 0.2162 0.3143 0.4240 0.5201 0.5842 0.8177
ρ kg·m−3
0.298 0.450 0.578 0.833 1.118 1.371 1.536 2.128
b
1 cm3 ·mol−1
94.85 94.86 94.88 94.88 94.89 94.88 94.93 94.92
c
m mol·kg−3
1.0588 1.1053 1.1503 1.4396 1.7295 1.9746 2.0925 2.2961
ρ kg·m−3
1 cm3 ·mol−1
2.716 2.783 2.899 3.532 4.181 4.683 4.936 5.337
94.93 94.87 94.93 94.86 94.92 94.90 94.88 94.91
di-n-butyl ether 1-butanol 0.0225 0.0957 0.2148 0.3350 0.4130 0.5653
−0.081 −0.339 −0.759 −1.170 −1.436 −1.932
90.84 90.90 90.87 90.89 90.88 90.92
0.8196 0.8563 1.3356 1.8119 2.3437
−2.733 −2.851 −4.239 −5.509 −6.816
90.97 90.97 91.07 91.15 91.22
2-butanol 0.1011 0.1169 0.2072 0.2613 0.3183 0.3304 0.4251 0.5340 0.5554
−0.218 −0.256 −0.454 −0.579 −0.700 −0.739 −0.940 −1.183 −1.244
93.28 93.23 93.18 93.14 93.14 93.09 93.09 93.05 93.02
0.7906 0.8126 0.9936 1.0440 1.1106 1.3501 1.5154 2.0723
−1.767 −1.821 −2.179 −2.320 −2.472 −2.957 −3.268 −4.368
92.97 92.97 92.97 92.92 92.92 92.90 92.90 92.85
t-butanol 0.1147 0.2282 0.3369 0.5047 0.5463 0.7235 0.8220
−0.005 −0.016 −0.038 −0.086 −0.103 −0.127 −0.220
96.94 96.89 96.81 96.71 96.68 96.66 96.53
1.1521 1.3490 1.6048 1.8241 2.0969 2.2094
−0.374 −0.413 −0.613 −0.654 −0.880 −0.851
96.41 96.40 96.28 96.28 96.18 96.21
1-octanol 0.0977 0.1919 0.2855 0.3032 0.3927 0.4018 0.4892
−0.803 −1.541 −2.275 −2.395 −3.081 −3.137 −3.788
156.24 156.41 156.36 156.45 156.40 156.46 156.44
0.4987 0.6277 1.1961 1.6511 1.9389 2.1535
−3.842 −4.762 −8.385 −10.906 −12.365 −13.404
156.49 156.51 156.75 156.93 157.01 157.06
2-octanol 0.1042 0.2111 0.2288
−0.693 −1.389 −1.499
158.93 158.92 158.94
1.1112 1.6051 1.9645
−6.571 −8.990 −3.112
158.98 159.01 159.05
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Table 4 Continued
m mol·kg−3
0.2940 0.3154 0.4902
ρ kg·m−3
−1.917 −2.053 −3.112
b
1 cm3 ·mol−1
158.91 158.90 158.95
c
m mol·kg−3
2.0903 2.5706
ρ kg·m−3
1 cm3 ·mol−1
−11.122 −13.036
159.05 159.08
n-hexyl acetate 1-butanol 0.1019 0.2136 0.3049 0.3974 0.4538
0.590 1.215 1.712 2.207 2.503
93.02 92.95 92.90 92.87 92.86
0.4929 0.9816 1.4597 1.8374 2.0169
2.706 5.118 7.277 8.859 9.577
92.84 92.74 92.66 92.62 92.59
2-butanol 0.1012 0.1969 0.2929 0.3988
0.714 1.371 2.012 2.701
94.71 94.65 94.61 94.55
1.0062 1.4854 1.8384 1.9975
6.351 8.905 10.627 11.367
94.34 94.19 94.09 94.05
3.370
94.50
0.953 1.795 2.688 3.660 4.473
97.92 97.83 97.76 97.69 97.63
0.5263 0.9867 1.5050 1.8064 1.9934
4.704 8.336 12.003 13.951 15.120
97.65 97.41 97.19 97.07 97.02
0.5046 t-butanol 0.1007 0.1926 0.2925 0.4040 0.5001 a At
298.15 K. = (ρ1• − ρ) with ρ2• and ρ being the densities of the solvent and the solution, respectively. c Calculated from Eq. (8). b ρ
4 Discussion 4.1 Excess volumes Figure 1 shows that VmE for isomeric butanols + 1-OctOH or 2- OctOH mixtures assumes both positive and negative values that are very small in magnitude (VmE ≤ 0.1 cm3 ·mol−1 ) over the whole composition range, whereas the VmE values are always positive in mixtures with DBE and HAC, except for 1-butanol in DBE [13], with values ranging from 0.1 to 0.6 cm3 ·mol−1 . As it is known, the VmE values are the result of several opposing effects: attractive like-like interactions lead to an increase in the excess volume, whereas interactions between unlike molecules, free volume effects and interstitial accommodation decrease the VmE values. On this basis, a qualitative explanation for the behavior of these mixtures can be suggested. As stated earlier [19], both butanol and octanol molecules are self-associated through hydrogen bonding in their pure states. Mixing of these components induce mutual dissociation of the hydrogen-bonded structures in the pure liquids with subsequent formation of new Hbonds among unlike molecules. As expected, the observed trends in VmE values indicate that the butanol-octanol interaction is practically coincident with those existing among like molecules. t-ButOH exhibits a slightly different behavior that may arise from the markedly different molecular size and shape of this component and 1-octanol/2-octanol that might allow Springer
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Fig. 4 Apparent molar volumes, 1 , of the examined butanols versus the concentration, m, of the solutions in: (a) 1-OctOH; (b) 2-OctOH; (c) DBE; (d) HAC. Solutes: (), 1-ButOH; (䊐), 2-ButOH; (× 䊐), t-ButOH; (•), 1-OctOH; (◦), 2-OctOH
a more favorable fitting of the smaller molecules of t-ButOH into the voids or interstitial spaces present among the octanol aggregates. In the case of mixtures containing DBE or HAC, the VmE values become more positive as the branching in the alcohol molecules increases. This result might be the consequence of steric interactions associated with the branched alkyl chains that reduce the extent of hydrogen bonding. An alternative explanation takes into account the inductive electronrepelling effect of the alkyl chains that causes the electron density at the oxygen atom of hydroxyl group of the alcohol molecules to increase in the sequence: 1-butanol < 2-butanol < 2-methyl-2-propanol. This indicates that the H-bond basicity of the -OH group increases in the same order, whereas the H-bond acidity decreases. As a consequence, when the second component can act only as a proton-acceptor, the strength of the H-bond decreases following the order: 1-ButOH > 2-ButOH > t-ButOH, thus justifying a corresponding increase in the VmE values.
4.2 Limiting partial molar volumes at infinite dilute solution The observations of the previous section can be confirmed by the examination of the V1E,∞ and V1∞ data in Table 3. The butanol isomers in all the considered solvents assume V1∞ values very close to their molar volumes in the pure liquid state. When the solvent is 1-OctOH or 2-OctOH, the V1E,∞ values may be both positive and negative, but are always very small in magnitude. As expected, these quantities increase with increasing VmE , maintaining the same sign. In the cases of DBE and HAC, on going from primary to secondary to tertiary butanol, Springer
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an increase of the partial molar excess volume is observed that can be also justified according to Patterson in terms of conformational effects [20]. When the tertiary alcohol, exhibiting a more globular shape with respect to the n-alkanol isomers, is added to solvents characterized by elongated molecules, a disruption of the order present in the pure liquid state is produced with consequent expansion effects. On the other hand, the more negative value of V1E,∞ exhibited by 1-ButOH in DBE can be justified by particularly favorable packaging effects due to the same alkyl chain length of the n-alkanol and the ether. It has also to be stressed that the values of V1E,∞ become more negative when the alkyl chain length of the solute molecule increases (f.i., compare V1E,∞ values for the pairs 1-ButOH/1-OctOH and those for 2-ButOH/2-OctOH, when DBE is the solvent). This result can be explained by assuming that the longer the hydrocarbon skeleton of the solute molecule, the stronger is the interaction with the corresponding alkyl chain of the solvent producing more negative V1E,∞ values. Since the partial molar volume reflects to only a minor extent the solute–solvent interactions, an estimation of the intrinsic volume of the solute molecule is needed in order to obtain information on the interactions in solution and on their correlation with the molecular structure. Various approaches can be applied based on the van der Waals intrinsic volume and on the cavity volume as deduced from SPT. As regards the intrinsic volume approach, according to Terasawa et al. [11] the partial molar volume can be split into two terms: V1∞ = VW + Vvoid
(9)
where the intrinsic volume, VW , is approximated by the van der Waals volume, i.e., the volume actually occupied by the solute molecules and impenetrable to the solvent molecules, whereas Vvoid is a measure of the volume of the empty spaces or interstices between the solute molecular surface and the solvent molecules, thus containing all the effects due to solute– solvent interactions. The intrinsic volumes of the solutes can be calculated by our usual procedure [5] and the Vvoid values are so obtained by Eq. (9). In Fig. 5 the reduced void volumes, V˜void = Vvoid VW , are reported for all solutes in their pure liquid state and in the examined solvents. As can be seen, the V˜void values of the solutes are generally close to those of their pure liquid states and are practically coincident in the cases of 1-OctOH and 2-OctOH. Furthermore, we can note that in all the solvents, V˜void systematically increases on going from primary to secondary to tertiary alcohols. In other words, the primary alcohol shows, in all the solvents examined, Vvoid values that are lower than those of the corresponding secondary and tertiary ones with the same intrinsic volume. As a final observation, in DBE and HAC the spread of the V˜void values is larger than in 1-OctOH and 2-OctOH, thus indicating a more extensive capability of the former two solvents to distinguish between the solutes on the basis of packing effects. These results are in agreement with the observed behavior of the limiting excess partial molar volumes.
4.3 Application of SPT According to a widely accepted model for describing dilute solutions, the process of introducing a solute molecule into a given solvent consists of two steps, the first being the creation in the solvent of a cavity of a suitable size to host the solute molecule, and the second being the introduction of the solute into the cavity and the switching on of the interactions with the Springer
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Fig. 5 Reduced void volumes, V˜void , of the considered compounds in the solvents 1-OctOH, 2-OctOH, DBE, HAC, and in their own pure liquid state. Compounds: (), 1-ButOH; (䊐), 2-ButOH; (× 䊐), t-ButOH; (•), 1-OctOH; (◦), 2-OctOH
solvent. The limiting partial molar volume of the solute, V1∞ , can then be expressed by: V1∞ = Vcav + Vint + βT RT
(10)
where Vcav is the contribution to V1∞ associated with the cavity formation in the solvent, Vint is the contribution from solute–solvent interactions and the term βT RT (βT isothermal compressibility of the solvent) is the volume change corresponding to the “liberation” of a solute molecule from a fixed position [21]. The cavity term was calculated following Pierotti’s approach to the Scaled Particle Theory [12] using the hard-sphere diameters, σ , of both the solute and solvent molecules, the isothermal compressibility values and the thermal expansion coefficients of the solvents. The quantities used in the calculation are taken from our previous paper in regards to the solvents [5], whereas the data related to the solutes are reported in Table 5 together with the determined Vcav values. The results show that in each solvent the cavity volumes increase linearly with the size of the solute molecule independently of the way it is expressed (van der Waals or hard-sphere Table 5 Hard-sphere diameters, σ , thermal expansion coefficients, α p , and cavity volumes, Vcav , of the solutes in 1-OctOH, 2-OctOH, DBE and HACa
Compound
σ b / × 1010 m
αPc / × 103 K −1
Vcav /(cm3 · mol−1 ) 1-OctOH 2-OctOH DBE
HAC
1-butanol 2-butanol t-butanol
5.57 5.53 5.47
0.949 1.043 1.296
192.57 189.36 185.23
158.50 155.79 152.30
193.78 190.54 186.37
163.68 160.92 157.36
a At
298.15 K. from the vaporization enthalpies of [22] according to Pierotti [12]. c Calculated from the temperature dependence of the density of the pure liquids determined in this work as indicated in the Section 2.2. b Calculated
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Fig. 6 Cavity volumes, Vcav , and interaction volumes, Vint , in 1-OctOH, 2-OctOH, DBE, HAC versus the molar hard-sphere volumes, σ , of examined butanols
volume or surface). Figure 6 shows the cavity contributions to the partial molar volume versus the hard-sphere volume of the solute molecules calculated from the σ diameters. The straight lines obtained are parallel and the cavity volumes for a given solute vary in the order HAC < DBE < 2-OctOH ≈ 1-OctOH, indicating that in order to insert a hard sphere of fixed size it is necessary to create a larger cavity in 1-OctOH or 2-OctOH than in DBE or HAC. This can be related to the particular structure of the molecule aggregates occurring in pure octanol [23], thus determining a molecular packaging different with respect to those in DBE or in HAC. In these latter cases, the lack of hydrogen bonding should obviously be taken into account. The identical values of Vcav in 1-OctOH and 2-OctOH indicate very similar liquid structures for these compounds. The interaction contributions to V1∞ , calculated by Eq. (10) and plotted in Fig. 6, are strongly negative showing a parallel linear decrease as the solute size increases. The Vint values for each solute vary exactly in the reverse order with respect to that observed for Vcav . When the solvent is 1-OctOH or 2-OctOH, interaction to a similar extent is proven to occur with isomeric butanols, i.e., the nature of the functional groups is the characterizing factor of the interaction, whereas branching of the alkyl chain of the solute and solvent molecules plays only a secondary role. As for Vvoid , the reduced cavity, V˜cav , and interaction, V˜int , terms were calculated by normalizing the corresponding contributions with respect to the VW volume of each solute. The values obtained are plotted in Fig. 7. As can be observed, the negative V˜int values compensate for a significant amount of the cavity volume. Moreover, unlike the limiting partial molar volumes and reduced void volumes, both the cavity and interaction terms show no significant changes when going from one solvent to another, with all the solutes showing exactly the same trend. Butanol isomers present the same V˜cav and V˜int values in 1-OctOH, and in 2-OctOH, indicating that the nature of the functional groups is the characterizing aspect of the solute-solvent interaction. Therefore, in these solvents the conformational and packaging effects, as well as the differently buried OH group of the alcohol, play a secondary Springer
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Fig. 7 Reduced cavity volumes, V˜cav , and reduced interaction volumes, V˜int , of the isomeric butanols examined in 1-OctOH, 2-OctOH, DBE, HAC. Isomeric butanols: (䊏), 1-ButOH; (䊐), 2-ButOH; (× 䊐), t-ButOH
role. In regards DBE and HAC, the V˜cav and V˜int values are lower in magnitude with respect to those in 1-OctOH and in 2-OctOH, with very small differences observed between the two solvents. The volumetric properties confirm previous observations that the four examined solvents interact in different ways with the solutes [1,2,5]. The isomeric octanols show the most noticeable interaction effects, probably due to their amphiprotic nature. On the other hand, HAC and DBE interact less strongly with the hydroxyl solutes, but are nonetheless effective in discriminating them according to their structure.
5 Conclusion Either the excess volumes of the mixtures or the excess partial molar volume of butanols at infinite dilution in the C8 solvents are much lower in magnitude when 1-OctOH and 2OctOH are involved. This indicates that the solute-solvent interactions produce no significant shrinking or expansion with respect to the pure liquid solutes. Moreover, the branching of the solute molecule only plays a secondary role in affecting the volumetric properties of mixtures containing 1-OctOH or 2-OctOH, despite the fact that it alters significantly the steric and electronic properties of the solute molecule, as well as the accessibility of the −OH group. This appears to be a somewhat unexpected result particularly in the case of 1-OctOH where the insertion of a globular shape molecule like t-ButOH is expected to be a high cost process in terms of the disruption of the local order. On the other hand, mixtures containing DBE or HAC as solvents show significantly large and positive values of VmE as well as V1E,∞ , indicating that the solute molecule is involved in a framework of weaker solute–solvent interactions with respect to the pure liquid solute. It is worth noting that weakening of solute-solvent interactions enhances the effect of branching; as a matter of fact DBE and HAC are much more effective in discriminating among the isomeric butanols according to their structure. Springer
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As a general conclusion we can stress that the nature of functional groups plays the central role in determining the volumetric behavior of the mixtures investigated in the present work. The topology of the −OH group of the isomeric butanols also represents a secondary effect in the sense that the weaker are the specific interactions between the butanol –OH group and the solvent, the stronger is the effect of its topology. This conclusion is supported by the trends of the interaction volumes that we have deduced by applying the SPT model, and is also consistent with the observed trends of the enthalpies of solvation of isomeric butanols in the solvents examined here [1,2,4]. Acknowledgements The authors are grateful to the Universit`a di Pisa and to the Ministero dell’Istruzione, dell’Universit`a e della Ricerca (MIUR) for financial support (PRIN 2005).
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