Article pubs.acs.org/jced
Partial Molar Volumes and Partial Molar Isentropic Compressions of Four 2‑Alkoxyethanols at Infinite Dilution in Water at Temperatures T = 278−343 K and Atmospheric Pressure Ivan Cibulka* Department of Physical Chemistry, University of Chemistry and Technology, Technická 5, 166 28 Prague, Czech Republic ABSTRACT: Density and speed of sound data for dilute aqueous solutions of four linear 2-alkoxyethanols, H−(CH2)n−O−CH2−CH2− OH, CnE1 for n = 1, 2, 3, 4, were measured using the Anton Paar DSA 5000 vibrating-tube densimeter and sound analyzer in the temperature range from 278.15 to 343.15 K and at atmospheric pressure. Standard molar volumes and standard molar isentropic compressions were evaluated from the measured data. Present data were compared with values available for selected linear aliphatic polyethers and poly(ethylene glycols) and structure−property relationships were analyzed. Apparent molar quantities of aqueous 2-butoxyethanol in wider concentration range were evaluated and effects of aggregation of the solute molecules were considered.
1. INTRODUCTION Recently the results of the investigation of partial molar volumes at infinite dilution (standard molar volumes) and partial molar isentropic compressions at infinite dilution (standard molar isentropic compressions) of selected members of two homolous series were published: linear aliphatic polyethers (glymes)1,2 of the general formula H3C−(O−CH2−CH2)m−O−CH3 and poly(ethylene glycols)3,4 H−(O−CH2−CH2)m−OH (note that, compared to our previous studies where m denoted the number of oxygen atoms, here m is number of −O−CH2−CH2− units, i.e., number of oxygen atoms is m + 1) . In combination with some previously published data the complete set of values of standard molar volumes2,4 in the ranges from 278 to 573 K and pressures up to 30 MPa and standard molar isentropic compressions1,3 from 278 to 343 K at atmospheric pressure were obtained for m = 1, 2, 3, 4. Intermediate homologous series to those mentioned above are poly(ethylene glycol) monomethyl ethers H3C−(O−CH2−CH2)m−OH, which is a subseries of poly(ethylene glycols) monoalkyl ethers H−(CH2)n− (O−CH2−CH2)m−OH, usually denoted as CnEm. Standard molar volumes of one member of this series, H3C−(O−CH2− CH2)2−OH, C1E2, have been already studied in our laboratory5 and compared with values for respective members of the glyme series and poly(ethylene glycol) series, that is, H3C−(O−CH2− CH2)2−O−CH3 and H−(O−CH2−CH2)2−OH,4 respectively. The present study is focused to selected solutes of the series of 2-alkoxyethanols (ethylene glycol monoalkyl ethers), H−(CH2)n−O−CH2−CH2−OH, CnE1, with n = 1, 2, 3, 4. The first member of the series, 2-methoxyethanol (ethylene glycol monomethyl ether), H3C−O−CH2−CH2−OH, C1E1, is an intermediate between ethylene glycol dimethyl ether (monoglyme) and ethylene glycol (ethane-1,2-diol) and thus the effect of the end-groups can be analyzed. Results obtained for higher members of the series (n = 2, 3, 4) then enable us to examine the © 2017 American Chemical Society
effect of increase of hydrophobic (alkyl) part of the solute molecule while solubility in water still remains sufficient for accurate measurements. First three solutes (n = 1, 2, 3) are miscible with water while the “island” type of liquid−liquid phase diagram with TLCST = 321 K and TUCST = 403 K (minimum solubility 0.896 mol·kg−1 at T = 359 K) is reported for 2-butoxyethanol.6 Moreover, the experimental data for the aqueous solutes under investigations are rather scarce in the literature and thus the present measurements substantially extend the knowledge of their behavior in aqueous solutions.
2. EXPERIMENTAL SECTION The specifications of the organic solutes are summarized in Table 1. The solutes were used as obtained. Water was purified by distillation and demineralization (Millipore Synergy Purification System). Purified water was used as a calibration fluid for the DSA 5000 device and for the preparation of solutions. Solutions were prepared by mass using a Precisa 40SM-200A balance (resolution = 10−2 mg, uncertainty = ±0.1 mg) to determine the mass of the solute and an A&D Instruments GF-3000-EC balance (resolution = 10 mg, estimated uncertainty = ±2 × 10−2 percent) to determine the mass of water. Five solutions of each solute were prepared (except for 2-butoxyethanol, see below). Uncertainty of molality was estimated to be 3 × 10−5 mol·kg−1. About 1 kg of each solution was prepared. The corrections to the content of water in the solute samples determined by the Karl Fischer method (Table 1) were applied for calculations of molalities. Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 29, 2017 Accepted: April 7, 2017 Published: April 21, 2017 2649
DOI: 10.1021/acs.jced.7b00095 J. Chem. Eng. Data 2017, 62, 2649−2658
Journal of Chemical & Engineering Data
Article
Table 1. Specifications of Chemical Samples of Solutes
a
name
IUPAC name
formula
CAS RN
supplier
mass fraction puritya
mass fraction of waterb
2-methoxyethanol 2-ethoxyethanol 2-propoxyethanol 2-butoxyethanol
3-oxabutane-1-ol 3-oxapentane-1-ol 3-oxahexane-1-ol 3-oxaheptane-1-ol
C3H8O2 C4H10O2 C5H12O2 C6H14O2
109-86-4 110-80-5 2807-30-9 111-76-2
Riedel-de-Haen Riedel-de-Haen Honeywell Riedel-de-Haen
>0.999 >0.99 0.994 >0.99
2.5 × 10−5 3.8 × 10−5 1.5 × 10−4 7.8 × 10−5
Declared by the supplier. bDetermined by the Karl Fischer method.
Table 2. Experimental Differences in Density Δρ = ρ − ρ1 Measured at Various Temperatures T and Molalities m2 for 2-Methoxyethanol (aq), 2-Ethoxyethanol (aq), 2-Propoxyethanol (aq), and 2-Butoxyethanol (aq) at Atmospheric Pressurea m2/(mol·kg−1)
Δρ/(kg·m−3)
T/K = 0.055865 0.101589 0.206781 0.295917 0.412952 T/K = 0.055865 0.101589 0.206781 0.295917 0.412952
278.15 0.109 0.198 0.423 0.621 0.903 313.15 0.038 0.069 0.153 0.227 0.326
283.15 0.096 0.174 0.373 0.548 0.796 318.15 0.031 0.055 0.122 0.182 0.262
T/K = 0.056171 0.115494 0.209787 0.318859 0.420331 T/K = 0.056171 0.115494 0.209787 0.318859 0.420331
278.15 0.001 0.017 0.073 0.161 0.272 313.15 −0.078 −0.154 −0.258 −0.374 −0.471
283.15 −0.012 −0.010 0.016 0.083 0.142 318.15 −0.088 −0.178 −0.302 −0.443 −0.564
T/K = 0.055942 0.111411 0.202801 0.305848 0.405558 T/K = 0.055942 0.111411 0.202801 0.305848 0.405558
278.15 −0.078 −0.134 −0.196 −0.221 −0.209 313.15 −0.203 −0.374 −0.658 −0.959 −1.233
283.15 −0.096 −0.172 −0.273 −0.345 −0.382 318.15 −0.214 −0.406 −0.718 −1.053 −1.361
T/K = 0.053585 0.105052 0.204516 0.296274 0.408189 0.622189 0.835410 1.091036 1.293825
278.15 −0.145 −0.262 −0.438 −0.552 −0.643 −0.701 −0.677 −0.670 −0.883
283.15 −0.168 −0.313 −0.546 −0.716 −0.880 −1.100 −1.259 −1.548 −2.117
2-methoxyethanol (aq) 288.15 293.15 0.084 0.075 0.155 0.134 0.332 0.290 0.485 0.426 0.701 0.616 323.15 328.15 0.024 0.014 0.041 0.026 0.092 0.060 0.138 0.095 0.197 0.135 2-Ethoxyethanol (aq) 288.15 293.15 −0.024 −0.034 −0.038 −0.063 −0.032 −0.082 −0.014 −0.092 0.027 −0.082 323.15 328.15 −0.110 −0.099 −0.201 −0.223 −0.344 −0.388 −0.510 −0.579 −0.655 −0.747 2-Propoxyethanol (aq) 288.15 293.15 −0.114 −0.132 −0.210 −0.246 −0.343 −0.413 −0.458 −0.566 −0.543 −0.691 323.15 328.15 −0.223 −0.239 −0.436 −0.470 −0.777 −0.837 −1.145 −1.239 −1.488 −1.617 2-Butoxyethanol (aq)b 288.15 293.15 −0.192 −0.216 −0.361 −0.406 −0.645 −0.735 −0.867 −1.007 −1.099 −1.305 −1.468 −1.816 −1.807 −2.329 −2.413 −3.272 −3.308 −4.420 2650
298.15 0.064 0.116 0.255 0.372 0.538 333.15 0.006 0.011 0.030 0.053 0.073
303.15 0.055 0.101 0.219 0.321 0.463 338.15 −0.002 −0.004 −0.001 0.009 0.009
308.15 0.049 0.085 0.185 0.272 0.393 343.15 −0.010 −0.017 −0.035 −0.045 −0.058
298.15 −0.045 −0.087 −0.128 −0.164 −0.185 333.15 −0.122 −0.248 −0.433 −0.646 −0.839
303.15 −0.056 −0.111 −0.172 −0.236 −0.283 338.15 −0.133 −0.269 −0.476 −0.715 −0.932
308.15 −0.068 −0.135 −0.216 −0.306 −0.377 343.15 −0.144 −0.292 −0.520 −0.784 −1.024
298.15 −0.149 −0.279 −0.477 −0.668 −0.832 333.15 −0.254 −0.502 −0.897 −1.332 −1.743
303.15 −0.167 −0.312 −0.538 −0.768 −0.968 338.15 −0.269 −0.533 −0.957 −1.425 −1.868
308.15 −0.184 −0.341 −0.598 −0.864 −1.100 343.15 −0.285 −0.565 −1.017 −1.516 −1.994
298.15 −0.236 −0.447 −0.823 −1.142 −1.502 −2.147 −2.838 −4.107 −5.438
303.15 −0.256 −0.487 −0.907 −1.272 −1.692 −2.469 −3.344 −4.898 −6.373
308.15 −0.274 −0.528 −0.992 −1.400 −1.876 −2.783 −3.843 −5.634 −7.224
DOI: 10.1021/acs.jced.7b00095 J. Chem. Eng. Data 2017, 62, 2649−2658
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Table 2. continued m2/(mol·kg−1) T/K = 0.053585 0.105052 0.204516 0.296274 0.408189 0.622189 0.835410 1.091036 1.293825
Δρ/(kg·m−3) 313.15 −0.295 −0.565 −1.071 −1.526 −2.058 −3.090 −4.331 −6.315 −8.003
318.15 −0.314 −0.606 −1.154 −1.645 −2.236 −3.392 −4.804 −6.946 −8.719
2-Butoxyethanol (aq)b 323.15 328.15 −0.334 −0.353 −0.642 −0.686 −1.232 −1.317 −1.768 −1.886 −2.412 −2.583 −3.687 −3.976 −5.254 −5.676 −7.529 −8.066 −9.380 −9.992
333.15 −0.373 −0.726 −1.396 −2.006 −2.755 −4.257 −6.076 -8.565 −10.663
338.15 −0.391 −0.766 −1.477 −2.126 −2.923 −4.530 −6.451 -9.085 −11.278
343.15 −0.411 −0.805 −1.555 −2.243 −3.090 −4.796 −6.803 -9.581 −11.829
Standard uncertainties are u(T) = 0.01 K, u(m2) = 3 × 10−5 mol·kg−1, and the combined expanded uncertainty is Uc(Δρ) = 1 × 10−2 kg·m−3 (level of confidence = 0.95, systematic errors7 not included). bValues for solutions at conditions close to or within the miscibility gap are written in italics. a
Table 3. Experimental Differences in Speed of Sound Δc = c − c1 Measured at Various Temperatures T and Molalities m2 for 2-Methoxyethanol (aq), 2-Ethoxyethanol (aq), 2-Propoxyethanol (aq), and 2-Butoxyethanol (aq) at Atmospheric Pressurea m2/(mol·kg−1)
Δc/(m·s−1)
T/K = 0.055865 0.101589 0.206781 0.295917 0.412952 T/K = 0.055865 0.101589 0.206781 0.295917 0.412952
278.15 3.80 6.62 14.09 19.24 26.65 313.15 1.77 3.26 6.75 9.52 13.15
283.15 3.43 5.97 12.81 17.40 24.13 318.15 1.54 2.93 6.04 8.55 11.75
T/K = 0.056171 0.115494 0.209787 0.318859 0.420331 T/K = 0.056171 0.115494 0.209787 0.318859 0.420331
278.15 5.07 10.35 18.55 28.29 36.34 313.15 2.63 5.36 9.40 14.29 18.66
283.15 4.60 9.41 16.80 25.51 33.10 318.15 2.37 4.79 8.48 12.81 16.74
T/K = 0.055942 0.111411 0.202801 0.305848 0.405558 T/K = 0.055942 0.111411 0.202801 0.305848 0.405558
278.15 6.22 12.31 22.26 33.12 43.58 313.15 3.40 6.43 11.52 16.92 22.05
283.15 5.53 11.23 20.31 30.24 39.71 318.15 3.05 5.80 10.34 15.13 19.69
T/K = 0.053585 0.105052
278.15 7.20 13.88
283.15 6.56 12.64
2-Methoxyethanol (aq) 288.15 293.15 3.11 2.80 5.41 4.91 11.69 10.60 15.81 14.35 21.87 19.83 323.15 328.15 1.33 1.13 2.60 2.28 5.34 4.67 7.58 6.69 10.41 9.14 2-Ethoxyethanol (aq) 288.15 293.15 4.28 3.84 8.62 7.84 15.25 13.83 23.22 21.17 30.23 27.56 323.15 328.15 2.15 1.91 4.30 3.82 7.63 6.82 11.42 10.09 14.91 13.16 2-Propoxyethanol (aq) 288.15 293.15 5.13 4.77 10.32 9.48 18.59 16.99 27.64 25.12 36.32 32.97 323.15 328.15 2.67 2.33 5.17 4.56 9.20 8.09 13.40 11.73 17.42 15.24 2-Butoxyethanol (aq)b 288.15 293.15 6.06 5.53 11.61 10.54 2651
298.15 2.52 4.45 9.45 12.99 17.95 333.15 0.94 1.99 4.01 5.82 7.95
303.15 2.27 4.04 8.47 11.74 16.21 338.15 0.79 1.73 3.42 5.04 6.80
308.15 2.00 3.63 7.54 10.57 14.60 343.15 0.66 1.50 2.85 4.34 5.74
298.15 3.47 7.15 12.58 19.24 25.11 333.15 1.65 3.33 6.02 8.78 11.51
303.15 3.21 6.57 11.43 17.47 22.80 338.15 1.42 2.80 5.24 7.54 9.92
308.15 2.91 5.99 10.37 15.82 20.66 343.15 1.18 2.30 4.48 6.36 8.42
298.15 4.40 8.64 15.49 22.88 29.93 333.15 2.01 3.98 7.04 10.17 13.15
303.15 4.07 7.86 14.08 20.77 27.13 338.15 1.74 3.43 6.04 8.65 11.18
308.15 3.73 7.12 12.74 18.78 24.49 343.15 1.50 2.88 5.06 7.18 9.25
298.15 5.06 9.57
303.15 4.63 8.70
308.15 4.15 7.85
DOI: 10.1021/acs.jced.7b00095 J. Chem. Eng. Data 2017, 62, 2649−2658
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Table 3. continued m2/(mol·kg−1) 0.204516 0.296274 0.408189 0.622189 0.835410 1.091036 1.293825 T/K = 0.053585 0.105052 0.204516 0.296274 0.408189 0.622189 0.835410 1.091036 1.293825
Δc/(m·s−1) 26.66 38.11 51.49 75.34 96.47 116.06 121.64 313.15 3.81 7.08 13.44 19.06 25.05 33.78 33.19 22.09 13.47
24.28 34.75 46.87 68.23 86.63 100.93 99.93 318.15 3.46 6.39 12.01 16.85 22.08 28.86 25.41 13.22 4.07
2-Butoxyethanol (aq)b 22.14 20.12 31.66 28.81 42.61 38.64 61.66 55.53 77.31 68.24 85.34 70.00 80.12 63.01 323.15 328.15 3.11 2.78 5.70 5.05 10.63 9.30 14.76 12.79 19.21 16.46 24.11 19.56 18.29 11.85 5.16 −2.19 −4.61 −12.61
18.28 26.13 34.92 49.70 59.25 55.76 48.23 333.15 2.45 4.41 8.03 10.90 13.80 15.25 6.03 −8.91 −11.62
16.56 23.62 31.46 44.17 50.31 43.12 35.30 338.15 2.15 3.80 6.80 9.07 11.28 11.18 0.77 −11.21 −12.18
14.94 21.28 28.16 38.87 41.55 31.96 23.82 343.15 1.83 3.23 5.61 7.29 8.83 7.35 −4.03 −13.27 −14.47
Standard uncertainties are u(T) = 0.01 K, u(m2) = 3× 10−5 mol·kg−1, and the combined expanded uncertainty is Uc(Δc) = 0.2 m·s−1 (level of confidence = 0.95, systematic errors7 not included). bValues for solutions at conditions close to or within the miscibility gap are written in italics. a
ρ − ρ1 Δρ = = aV + bV m2 m2 m2
The vibrating-tube densimeter and sound analyzer manufactured by Anton Paar, model DSA 5000, with a built-in thermostat was used for the measurements. Experimental methodology and procedures were essentially same as those used for previous measurements.1,3,7 Measurements were performed in the isoplethal regime when temperature is scanned for a particular sample filled in the device over entire temperature range with 5 K wide steps. The samples were partly degassed7 before filling into the measuring device to avoid the formation of air bubbles at higher temperatures. The measured differences Δρ = ρ − ρ1 and Δc = c − c1 where ρ and c are experimental density of and speed of sound in the solution, respectively, and ρ1 and c1 are experimental density of and speed of sound in pure water, respectively, are presented as direct experimental data and tabulated below. To eliminate the effect of the drift of the device the density of and speed of sound in pure water were repeatedly measured between measurements of solutions and used for calculations of experimental differences Δρ and Δc.
The values of the coefficients aV and bV obtained by using a least-squares method with unit weights are recorded in Table 4 along with the calculated standard molar volumes and estimated uncertainties. Some experimental evidence indicate that 2-butoxyethanol, as the molecule with larger hydrophobic part (butyl) on one side and hydrophilic hydroxyl group and ether oxygen atom on the other, is capable to form aggregates (micelles) in aqueous solutions.10,11 This phenomenon is discussed below using measured data for higher concentrations, standard molar volumes presented in Table 4 were evaluated using data for five most diluted solutions (molalities up to 0.408 mol·kg−1), that is, in the concentration range approximately same as those for other three 2-alkoxyethanols. 3.3. Standard Molar Isentropic Compressions. Partial molar isentropic compression at infinite dilution (standard molar isentropic compression) of the solute 2 is a limiting apparent molar isentropic compression Kapp S,m,2 and can be calculated from the expression12
3. RESULTS 3.1. Direct Experimental Data. The experimental values of differences of density Δρ = ρ − ρ1 and of speed of sound Δc = c − c1 along with the molalities of organic solutes m2 are recorded in Tables 2 and 3, respectively. Values of density of and speed of sound in pure water needed for calculations of standard molar quantities (including density of and speed of sound in solutions, ρ = Δρ + ρ1 and c = Δc + c1) were taken from the NIST database;8 for details and values, see ref 7. 3.2. Standard Molar Volumes. The partial molar volume at infinite dilution (m2 → 0) of a solute V0m,2 (standard molar volume) can be calculated from the equation9 0 V m,2
⎡ ⎛ ⎤ a ⎞ Δρ ⎞⎥ 1 1⎛ app ⎟⎟ = ⎜⎜M 2 − V ⎟⎟ = lim [V m,2 ] = lim ⎢ ⎜⎜M 2 − m2 → 0 m2 → 0⎢ ρ1 ⎝ ρ1 ⎠ m2ρ1 ⎠⎥⎦ ⎣ ρ⎝
(2)
⎡ 2 ⎞⎤ ⎛ ⎢ 1 ⎜⎜M 2 − Δ[(ρc) ] ⎟⎟⎥ KS0,m,2 = lim [KSapp ,m,2] = lim 2 m2 → 0 m2 → 0⎢ m2(ρ1c1)2 ⎠⎥⎦ ⎣ (ρc) ⎝ =
aK ⎞ 1 ⎛ ⎟⎟ ⎜M − 2⎜ 2 (ρ1c1) ⎝ (ρ1c1)2 ⎠
(3)
where aK is an adjustable parameter of the fit of experimental values of the differences Δ[(ρc)2] = (ρc)2 − (ρ1c1)2 in the form (ρc)2 − (ρ1c1)2 Δ[(ρc)2 ] = = aK + bK m2 m2 m2
(4)
The values of the coefficients aK, bK were obtained from measured data by using a least-squares method with unit weights and are recorded in Table 4 along with calculated values of K0S,m,2. Uncertainties σ(K0S,m,2) are affected mainly by the uncertainty in the speed of sound; the uncertainty in the difference Δc was estimated to be about ±0.2 m·s−1.
(1)
where M2 is the molar mass, Vapp m,2 apparent molar volume, and m2 molality of the solute. The coefficient aV is an adjustable parameter of the fit of experimental values Δρ/m2 2652
DOI: 10.1021/acs.jced.7b00095 J. Chem. Eng. Data 2017, 62, 2649−2658
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Table 4. Coefficients aV and bV of Equation 2, Standard Molar Volumes V0m,2, Coefficients aK and bK of Equation 4, and Standard Molar Isentropic Compressions K0S,m,2, for {2-Methoxyethanol (2) or 2-Ethoxyethanol (2) or 2-Propoxyethanol (2) or 2-Butoxyethanol (2) + Water(1)}a V0m,2 ± σ(V0m,2) cm3·mol−1
T/K
aV kg2·m−3·mol−1
bV kg3·m−3·mol−2
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15
1.901 1.661 1.473 1.292 1.114 0.969 0.833 0.667 0.529 0.407 0.241 0.094 −0.041 −0.183
0.681 0.645 0.555 0.490 0.472 0.381 0.286 0.314 0.263 0.179 0.226 0.227 0.180 0.102
74.20 74.46 74.69 74.93 75.20 75.45 75.71 76.01 76.31 76.60 76.95 77.30 77.65 78.02
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15
−0.052 −0.272 −0.475 −0.661 −0.846 −1.047 −1.253 −1.412 −1.598 −1.792 −1.974 −2.188 −2.373 −2.572
1.716 1.549 1.331 1.148 1.004 0.931 0.892 0.727 0.637 0.586 0.488 0.482 0.394 0.347
90.18 90.42 90.68 90.95 91.24 91.57 91.93 92.26 92.64 93.05 93.46 93.92 94.38 94.86
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15
−1.497 −1.812 −2.119 −2.428 −2.718 −3.013 −3.297 −3.608 −3.831 −4.022 −4.301 −4.577 −4.847 −5.117
2.484 2.194 1.980 1.834 1.697 1.610 1.521 1.512 1.245 0.891 0.801 0.711 0.605 0.503
105.65 105.99 106.36 106.77 107.19 107.64 108.11 108.63 109.08 109.53 110.09 110.66 111.25 111.87
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15
−2.837 −3.274 −3.707 −4.118 −4.469 −4.840 −5.177 −5.532 −5.886 −6.229 −6.611 −6.980
3.191 2.811 2.554 2.344 2.009 1.781 1.468 1.258 1.062 0.848 0.751 0.628
121.02 121.49 121.99 122.52 123.02 123.57 124.12 124.72 125.35 125.99 126.69 127.42
aK × 10−12 kg3·m−4·s−2·mol−1
2-Methoxyethanol (aq) ±0.06 ±0.04 ±0.04 ±0.04 ±0.04 ±0.05 ±0.04 ±0.04 ±0.04 ±0.06 ±0.04 ±0.05 ±0.07 ±0.07 2-Ethoxyethanol (aq) ±0.05 ±0.06 ±0.05 ±0.04 ±0.04 ±0.04 ±0.04 ±0.03 ±0.03 ±0.03 ±0.03 ±0.03 ±0.03 ±0.03 2-Propoxyethanol (aq) ±0.05 ±0.05 ±0.05 ±0.04 ±0.06 ±0.07 ±0.07 ±0.07 ±0.07 ±0.05 ±0.04 ±0.04 ±0.06 ±0.06 2-Butoxyethanol (aq)b ±0.07 ±0.05 ±0.06 ±0.07 ±0.06 ±0.07 ±0.05 ±0.07 ±0.07 ±0.08 ±0.06 ±0.07 2653
bK × 10−12 kg4·m−4·s−2·mol−2
K0S,m,2 ± σ(K0S,m,2) cm3·mol−1·GPa−1
0.2008 0.1839 0.1690 0.1538 0.1393 0.1260 0.1122 0.0995 0.0877 0.0762 0.0649 0.0543 0.0456 0.0379
−0.0124 −0.0108 −0.0105 −0.0075 −0.0058 −0.0050 −0.0007 0.0032 0.0066 0.0089 0.0124 0.0151 0.0139 0.0112
−11.1 −5.6 −1.3 2.7 6.1 9.0 11.8 14.3 16.5 18.6 20.7 22.7 24.3 25.8
±0.9 ±0.9 ±0.8 ±0.7 ±0.5 ±0.3 ±0.2 ±0.2 ±0.3 ±0.4 ±0.4 ±0.5 ±0.5 ±0.5
0.2586 0.2369 0.2205 0.1993 0.1808 0.1668 0.1510 0.1348 0.1200 0.1066 0.0935 0.0786 0.0644 0.0502
−0.0111 −0.0109 −0.0204 −0.0121 −0.0093 −0.0176 −0.0182 −0.0154 −0.0155 −0.0177 −0.0193 −0.0145 −0.0106 −0.0050
−18.2 −11.0 −5.9 −0.4 4.0 7.2 10.5 13.7 16.5 19.0 21.5 24.2 26.9 29.6
±0.9 ±0.8 ±0.8 ±0.6 ±0.5 ±0.7 ±0.6 ±0.4 ±0.4 ±0.4 ±0.4 ±0.6 ±0.5 ±0.6
0.3128 0.2828 0.2627 0.2441 0.2238 0.2043 0.1850 0.1657 0.1466 0.1263 0.1069 0.0885 0.0720 0.0572
0.0097 0.0041 −0.0068 −0.0233 −0.0294 −0.0358 −0.0399 −0.0411 −0.0410 −0.0361 −0.0320 −0.0286 −0.0288 −0.0328
−24.4 −14.8 −8.5 −3.4 1.6 6.1 10.1 14.0 17.6 21.4 25.0 28.4 31.5 34.4
±1.1 ±0.8 ±0.6 ±0.4 ±0.4 ±0.5 ±0.6 ±0.6 ±0.6 ±0.4 ±0.4 ±0.4 ±0.4 ±0.4
0.3734 0.3421 0.3163 0.2877 0.2613 0.2369 0.2101 0.1885 0.1677 0.1463 0.1263 0.1057
−0.0340 −0.0345 −0.0469 −0.0480 −0.0523 −0.0591 −0.0556 −0.0652 −0.0752 −0.0814 −0.0888 −0.0918
−32.2 −21.6 −13.6 −6.0 0.4 5.9 11.4 15.8 19.8 23.8 27.5 31.3
±0.6 ±0.6 ±0.7 ±0.8 ±0.9 ±1.0 ±0.7 ±0.9 ±0.9 ±0.8 ±0.9 ±0.8
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Table 4. continued aV kg2·m−3·mol−1
T/K
−7.318 −7.682
338.15 343.15
bV kg3·m−3·mol−2 0.422 0.310
V0m,2 ± σ(V0m,2) cm3·mol−1
aK × 10−12 kg3·m−4·s−2·mol−1
2-Butoxyethanol (aq)b 128.13 ±0.06 128.90 ±0.07
bK × 10−12 kg4·m−4·s−2·mol−2
K0S,m,2 ± σ(K0S,m,2) cm3·mol−1·GPa−1
−0.0983 −0.1001
0.0870 0.0677
34.8 38.5
±0.9 ±0.7
a The uncertainties σ(V0m,2) and σ(K0S,m,2) represent the combined expanded uncertainties. bExperimental values (Tables 2 and 3) for five most diluted solutions (molalities up to 0.408189 mol·kg−1) were used.
Table 5. Comparison of Standard Molar Volumes Obtained in This Work with Data Taken from the Literature T/K
V0m,2 (this work) cm3·mol−1
278.15 298.15
74.20 ± 0.06 75.20 ± 0.04
308.15
75.71 ± 0.04
318.15
76.31 ± 0.04
278.15 283.15 298.15
90.18 ± 0.05 90.42 ± 0.06 91.24 ± 0.04
313.15 318.15
92.26 ± 0.03 92.64 ± 0.03
278.15 298.15
105.65 ± 0.05 107.19 ± 0.06
318.15
109.08 ± 0.07
278.15 298.15
121.02 ± 0.07 123.02 ± 0.06
313.15 318.15 328.15
124.72 ± 0.07 125.35 ± 0.07 126.69 ± 0.06
V0m,2 (lit.) cm3·mol−1 2-Methoxyethanol (aq) 74.25 ± 0.05 75.20 ± 0.05 75.11 76.55b 74.17c 74.00d 76.37 ± 0.05 2-Ethoxyethanol (aq) 90.18 ± 0.05 90.18 91.29 ± 0.05 90.97 90.94e 92.02 92.67 ± 0.05 2-Propoxyethanol (aq) 105.64 ± 0.05 107.10 107.13 ± 0.05 106.84f 108.95 ± 0.05 2-Butoxyethanol (aq) 120.97 ± 0.05 122.91 122.76g 122.98 ± 0.05 124.54 125.29 ± 0.05 126.37
reference
deva cm3·mol−1
13 13 14 15 16 16 13
−0.05 0.00 0.09 −1.35 1.54 1.71 −0.06
13 14 13 14 15 14 13
0.00 0.24 −0.05 0.27 0.30 0.24 −0.03
13 14 13 17 13
0.01 0.09 0.06 0.35 0.13
13 14 15 13 14 13 14
0.05 0.11 0.26 0.04 0.18 0.06 0.32
Deviation between this work and the literature value. bEvaluated by present method for three most diluted solutions (m2 up to 3.5 mol·kg−1). Evaluated from data on excess volume for three most diluted solutions (m2 up to 3.47 mol·kg−1). dEvaluated from the Redlich−Kister fit of excess volume over entire concentration range. eEvaluated by present method for five most diluted solutions (m2 up to 2.95 mol·kg−1). fEvaluated from data on excess volume for three most diluted solutions (m2 up to 0.83 mol·kg−1). gEvaluated by present method for three most diluted solutions (m2 up to 0.56 mol·kg−1). a c
number of data points is low). Details are given in the footnote to Table 5. Three sources of data13,17,18 on standard molar isentropic compression were found in the literature (Table 6). Good agreement is observed for values reported by Harada et al.,13 rather large deviations are, however, obtained for 2-propoxyethanol and 2-butoxyethanol at 278 K. 4.2. Dependences of Standard Molar Volumes on Molecular Structure and Temperature. Standard molar volumes obtained in this work are plotted in Figure 1. The lines for individual solutes are nearly equidistant, the differences correspond to the volume of methylene group −CH2−. The lines do not show any significant differences between solutes. More interesting features are obtained using derivative quantities as the analog of isobaric thermal expansivity (further named shortly
Similarly as with volumes (see above), standard molar isentropic compressions of aqueous 2-butoxyethanol recorded in Table 4 were evaluated using measured data for five most diluted solutions (molalities up to 0.408 mol·kg−1).
4. DISCUSSION 4.1. Comparison with Data in Literature. Experimental standard molar volumes are compared in Table 5 with the values reported in the literature. Excellent agreement close to or within experimental uncertainties is seen for data reported by Harada et al.13 and Roux et al.14 (except for 2-ethoxyethanol and 2-butoxyethanol at higher temperatures). Deviations from other data available in the literature are larger. The reason can be seen in limited data sets available for highly diluted region (either the concentration range is wide or the 2654
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Table 6. Comparison of Standard Molar Isentropic Compressions Obtained in This Work with Data Taken from the Literature T/K
K0S,m,2 (this work) cm3·mol−1·GPa−1
278.15 298.15 318.15
−11.1 ± 0.9 6.1 ± 0.5 16.5 ± 0.3
278.15 298.15 318.15
−18.2 ± 0.9 4.0± 0.5 16.5 ± 0.4
278.15 298.15
−24.4 ± 1.1 1.6 ± 0.4
318.15
17.6 ± 0.6
278.15 298.15
−32.2 ± 0.6 0.4 ± 0.9
318.15
19.8 ± 0.9
K0S,m,2 (lit) cm3·mol−1·GPa−1
reference
deva cm3·mol−1·GPa−1
13 13 13
−0.1 0.1 1.4
13 13 13
0.3 0.6 0.1
13 13 17 13
2.3 0.1 0.0 −0.4
13 13 18 13
2.1 0.8 1.6 −0.4
2-Methoxyethanol (aq) −11.0± 0.5 6.0 ± 0.5 15.1 ± 0.5 2-Ethoxyethanol (aq) −18.5 ± 0.5 3.4 ± 0.5 16.4 ± 0.5 2-Propoxyethanol (aq) −26.7 ± 0.5 1.5 ± 0.5 1.6b 18.0 ± 0.5 2-Butoxyethanol (aq) −34.3 ± 0.5 −0.4 ± 0.5 −1.2 ± 0.1 20.2 ± 0.5
a
Deviation between this work and the literature value. bEvaluated from data on excess volume and speed of sound for three most diluted solutions (m2 up to 0.83 mol·kg−1)
isobaric expansivity) α0p,2 = (1/Vom,2)(∂Vom,2/∂T)p and the pressure derivative of standard isobaric molar heat capacity (∂C0p,m,2/ ∂p)T = −T(∂2V0m,2/∂T2)p related to the second derivative of standard molar volume with respect to temperature. These quantities were evaluated from the fits of experimental standard molar volumes using equation 4 0 V m,2 /(cm 3·mol‐1) =
∑ ai(T /K − 298.15)(i− 1) i=1
(5)
Adjustable parameters ai evaluated using the weighted leastsquares method with weights expressed in terms of estimated 0(exp) experimental uncertainties (Table 4) as 1/[σ(Vm,2 )] are recorded in Table 7. Isobaric expansivity is shown in Figure 2. Values obtained for the solutes investigated are mutually compared in Figure 2a. Obviously, the curve for most hydrophilic solute (2-methoxyethanol) shows most convex shape; the solutes with larger hydrophobic part (2-propoxyethanol, 2-butoxyethanol) tend, however, to convex shape as well. Except for lowest temperatures expansivity exhibits monotonous increasing dependence on the size of alkyl group. Figure 3a shows derivatives (∂c0p,m,2/∂p)T = −T(∂2V0m,2/T2)p. As expected the values for most hydrophilic solute are higher (i.e., less negative). All values of (∂c0p,m,2/∂p)T are, however, negative which indicate a convex shape of the
Figure 1. Plot of experimental standard molar volumes V0m,2 of 2-alkoxyethanols H−(CH2)n−O−CH2−CH2−OH against temperature T. ●, n = 1, 2-methoxyethanol; ■, n = 2, 2-ethoxyethanol; ▲, n = 3, 2-propoxyethanol; ⧫, n = 4, 2-butoxyethanol.
Table 7. Parameters ai of Equation 5a
a
2-Methoxyethanol (aq)
2-Ethoxyethanol (aq)
2-Propoxyethanol (aq)
2-Butoxyethanol (aq)
i
ai
ai
ai
ai
1 2 3 4 std devb w std devc Nd
75.189 5.155801 × 10−2 1.808529 × 10−4 1.723502 × 10−6 0.01 0.24 14
91.250 6.154200 × 10−2 4.083252 × 10−4 1.861666 × 10−7 0.01 0.27 14
107.195 8.504322 × 10−2 3.628101 × 10−4 1.080119 × 10−6 0.03 0.50 14
123.018 1.073124 × 10−1 4.253425 × 10−4 2.238145 × 10−6 0.02 0.24 14
The fits cover the temperature range from (278 to 343) K. bstd dev: standard deviation/(cm3·mol−1). cw std dev: weighted standard deviation. N: number of data points.
d
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Figure 3. Plots of the derivative (∂c0p,m,2/∂p)T against temperature T. (a) 2-alkoxyethanols: ●, n = 1, 2-methoxyethanol; ■, n = 2, 2-ethoxyethanol; ▲, n = 3, 2-propoxyethanol; ⧫, n = 4, 2-butoxyethanol. (b) G1−O−CH2−CH2−O−G2: ●, 2-methoxyethanol (G1 = CH3, G2 = H); □, ethylene glycol dimethyl ether1 (G1 = CH3, G2 = CH3); Δ, ethylene glycol3 (G1 = H, G2 = H).
o (1/Vom,2)(∂Vm,2 /∂T)p
Figure 2. Plots of isobaric expansivity = against temperature T. (a) 2-alkoxyethanols: ●, n = 1, 2-methoxyethanol; ■, n = 2, 2-ethoxyethanol; ▲, n = 3, 2-propoxyethanol; ⧫, n = 4, 2-butoxyethanol. (b) G1−O−CH2−CH2−O-G2: ●, 2-methoxyethanol (G1 = CH3, G2 = H) ; □, ethylene glycol dimethyl ether1 (G1 = CH3, G2 = CH3); Δ, ethylene glycol3 (G1 = H, G2 = H).
were obtained from the comparisons3,4 performed for other glymes and poly(ethylene glycols) in wider temperature interval combined with data available for diethylene glycol monomethyl ether.5 4.3. Dependences of Standard Molar Isentropic Compressions on Molecular Structure and Temperature. Standard molar isentropic compressions obtained in this work are plotted in Figure 4a. Similarly as observed for other homologous series of solutes with trends in hydrophilic/hydrophobic character (see, e.g., refs 1 and 4 where references to other examples can be found), the slopes (∂K0S,m,2/∂T)p distinctly decrease with increasing hydrophilic character of the solute molecule. Similarly as in Figures 2b and 3b, a comparison for the same series of solutes G1−O−CH2−CH2−O−G2 presented in Figure 4b confirms this rule. 4.4. Aggregation of 2-Butoxyethanol. Compared to other three solutes, density and speed of sound data for aqueous
fits using eq 5. Thus, from the point of view of Hepler’s classification, all solutes investigated here can be regarded as structure makers.19 The effect of the size of the hydrophilic part of solute molecules on the derivative quantities can be regarded as moderate only. Significant differences can be observed when solutes with different end-groups are compared. Figures 2b and 3b present plots for three solutes of the general formula G1−O−CH2− CH2−O−G2 with various end-groups G1 and G2: G1 = CH3 and G2 = H (present 2-methoxyethanol, ethylene glycol monomethyl ether), G1 = G2 = CH3 (ethylene glycol dimethyl ether, glyme),1 and G1 = G2 = H (ethylene glycol).3 The trend in the shape of curves from most hydrophilic solute (ethylene glycol) toward the most hydrophobic one (glyme) is obvious. Similar characteristics 2656
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Figure 5. Plots of experimental apparent molar quantities of aqueous 2-butoxyethanol against molality m2. (a) apparent molar volume; (b) apparent molar isentropic compression. Lines are isotherms in 5 K interval. Open symbols (○) correspond to data points close to or within miscibility gap. Dotted lines approximately show the course of critical micelle concentration (CMC).10
Figure 4. Plots of experimental standard molar isentropic compressions K0S,m,2 against temperature T. (a) 2-alkoxyethanols: ●, n = 1, 2-methoxyethanol; ■, n = 2, 2-ethoxyethanol; ▲, n = 3, 2-propoxyethanol; ⧫, n = 4, 2-butoxyethanol. (b) G1−O−CH2−CH2−O−G2: ●, 2-methoxyethanol (G1 = CH3, G2 = H) ; □, ethylene glycol dimethyl ether1 (G1 = CH3, G2 = CH3); Δ, ethylene glycol3 (G1 = H, G2 = H).
centration range seems to be moderate while apparent molar isentropic compressions are more affected at higher molalities. Obviously, the convex curves at low molalities tend to change to concave ones beyond the lines representing the critical micelle concentration. The curves in Figure 5b are in agreement (at least semiquantitatively) with the plot presented by D’Angelo et al.10 The plots in Figure 5 also indicate that extrapolations of data measured for the five most diluted solutions resulted in standard molar quantities (Table 4) that are not affected by the aggregation of the solute molecules. To check this conclusion standard molar quantities were also obtained by the extrapolations of apparent molar quantities to infinite dilution. Linear extrapolations of apparent molar volumes and apparent molar isentropic compressions evaluated for the molality range up to 0.408 mol·kg−1 (i.e., for the same range as that used for the fits by eqs 2 and 4) resulted in values of standard quantities differing
2-butoxyethanol were measured in wider concentration range (up to 1.29 mol·kg−1) that extends to the region where formation of solute micelles is reported.10,11 Critical micelle concentration (CMC) decreases with increasing temperature and data published by D’Angelo et al.10 for the temperature ranging from 275 to 328 K can be represented by the polynomial fit m2(CMC)/(mol·kg−1) = 1.8031 × 10−4(T/K)2 − 0.12110(T/ K) + 21.061 which gives (with slight extrapolation) m2(CMC) in the range between 1.33 mol·kg−1 (at 278 K) and 0.73 mol·kg−1 (at 343 K). To observe the effect of aggregation apparent molar quantities, that is, apparent molar volumes Vapp m,2 (for expression see eq 1) and apparent molar isentropic compressions Kapp S,m,2 (for expression see eq 3), were evaluated for each solution. The plots of apparent molar quantities are shown in Figure 5a,b. The effect of aggregation on apparent molar volumes in the present con2657
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(6) Christensen, S. P.; Donate, F. A.; Frank, T. C.; LaTulip, R. J.; Wilson, L. C. Mutual Solubility and Lower Critical Solution Temperature for Water + Glycol Ether Systems. J. Chem. Eng. Data 2005, 50, 869−877. (7) Cibulka, I. Partial Molar Volumes and Partial Molar Isentropic Compressions of 15-Crown-5 and 18-Crown-6 Ethers at Infinite Dilution in Water at Temperatures T = (278 to 343) K and Atmospheric Pressure. J. Chem. Eng. Data 2014, 59, 2075−2086. Correction in Cibulka, I. J. Chem. Eng. Data 2016, 61, 3387−3387. (8) Harvey, A. H.; Peskin, A. P.; Klein, S. A. NIST/ASME Steam Properties, Formulation for General and Scientific Use. NIST Standard Reference Database 10, Version 2.11; NIST: Washington, DC, 1996. (9) Hynek, V.; Hnědkovský, L.; Cibulka, I. A New Design of a Vibrating-tube Densimeter and Partial Molar Volumes of Phenol(aq) at Temperatures from 298 to 573 K. J. Chem. Thermodyn. 1997, 29, 1237− 1252. (10) D’Angelo, M.; Onori, G.; Santucci, A. Study of Aggregation of nButoxyethanol in Water by Compressibility and Surface Tension Measurements. Chem. Phys. Lett. 1994, 220, 59−63. (11) Onori, G.; Santucci, A. Calorimetric Study of the Micellization of n-Butoxyethanol in Water. J. Phys. Chem. B 1997, 101, 4662−4666. (12) Katriňaḱ , T.; Hnědkovský, L.; Cibulka, I. Partial Molar Volumes and Partial Molar Isentropic Compressions of Three Polyhydric Alcohols Derived from Propane at Infinite Dilution in Water at Temperatures T = (278 to 318) K and Atmospheric Pressure. J. Chem. Eng. Data 2012, 57, 1152−1159. (13) Harada, S.; Nakajima, T.; Komatsu, T.; Nakagawa, T. Apparent Molal Volumes and Adiabatic Compressibilities of Ethylene Glycol Derivatives in Water at 5, 25, and 45°C. J. Solution Chem. 1978, 7, 463− 474. (14) Roux, G.; Perron, G.; Desnoyers, J. E. Model Systems for Hydrophobic Interactions: Volumes and Heat Capacities of n-Alkoxyethanols in Water. J. Solution Chem. 1978, 7, 639−654. (15) Douhéret, G.; Pal, A. Dielectric Constants and Densities of Aqueous Mixtures of 2-Alkoxyethanols at 25°C. J. Chem. Eng. Data 1988, 33, 40−43. (16) Pal, A.; Singh, Y. P. Excess Molar Volumes and Viscosities for Glycol Ether − Water Solutions at the Temperature 308.15 K: Ethylene Glycol Monomethyl, Diethylene Glycol Monomethyl, and Triethylene Glycol Monomethyl Ethers. J. Chem. Eng. Data 1996, 41, 425−427. (17) Douhéret, G.; Davis, M. I.; Høiland, H. Speeds of Sound and Excess Volumetric Properties of Mixtures of Water with Ethylene Glycol Monopropyl Ether at 298.15 K. J. Mol. Liq. 1999, 80, 1−18. (18) Lara, J.; Desnoyers, J. E. Isentropic Compressibilities of Alcohol − Water Mixtures at 25°C. J. Solution Chem. 1981, 10, 465−478. (19) Hepler, L. G. Thermal Expansion and Structure in Water and Aqueous Solutions. Can. J. Chem. 1969, 47, 4613−4617.
from those recorded in Table 4 less than estimated uncertainties (maximum deviations 0.02 cm3·mol−1 and RMSD = 0.01 cm3· mol−1 for volumes; maximum deviations 0.11 cm3·mol−1·GPa−1 and RMSD = 0.04 cm3·mol−1·GPa−1 for compressions). Slight deviations from the linearity of the apparent molar isentropic compression of two most diluted solutions (systematic, similar at all temperatures, see Figure 5b) are likely to be caused by larger sensitivity to concentration in highly diluted region rather than a specific feature of the system.
5. CONCLUSIONS New data on density and speed of sound in dilute region were reported for four 2-alkoxyethanols H−(CH2)n−O−CH2−CH2− OH with n ranging from 1 to 4 and standard molar volumes and standard molar isentropic compressions were evaluated from experimental data. Analysis of the temperature dependences of standard molar volumes and standard molar isentropic compressions and of the structure−property relationships was performed. Comparison of data obtained for 2-methoxyethanol with selected solute analogs (glyme, ethylene glycol) was also performed. The effect of the size of hydrophobic part (alkyl group) was found to be moderate in the series of 2-alkoxyethanols while distinct effects of the end groups (hydrophobic methyl, hydrophilic hydroxyl) was observed when compared with selected members of linear aliphatic polyethers (glymes) and poly(ethylene glycols). The effect of aggregation of molecules of 2-butoxyethanol in aqueous solutions was investigated using apparent molar volumes and isentropic compressions in wider concentration range.
■
AUTHOR INFORMATION
Corresponding Author
*Phone: +420 220444063. E-mail:
[email protected]. ORCID
Ivan Cibulka: 0000-0002-7435-136X Notes
The author declares no competing financial interest.
■ ■
ACKNOWLEDGMENTS Institutional support from the University of Chemistry and Technology (UCT), Prague is acknowledged. REFERENCES
(1) Purchala, A.; Cibulka, I. Partial Molar Volumes and Partial Molar Isentropic Compressions of Four Aliphatic Linear Polyethers at Infinite Dilution in Water at Temperatures T = (278 to 343) K and Atmospheric Pressure. J. Chem. Eng. Data 2014, 59, 4205−4216. (2) Cibulka, I. Partial molar volumes of organic solutes in water. XXVII. Two aliphatic polyethers (triglyme, tetraglyme) at temperatures T = 298 to 573 K and pressures up to 30 MPa. J. Chem. Thermodyn. 2016, 101, 78−83. (3) Cibulka, I. Partial Molar Volumes and Partial Molar Isentropic Compressions of Four Poly(Ethylene Glycols) at Infinite Dilution in Water at Temperatures T = (278 to 343) K and Atmospheric Pressure. J. Chem. Eng. Data 2016, 61, 748−759. (4) Cibulka, I. Partial molar volumes of organic solutes in water. XXVIII. Three aliphatic poly(ethylene glycols) at temperatures T = 298 to 573 K and pressures up to 30 MPa. J. Chem. Thermodyn. 2017, 109, 2−10. (5) Cibulka, I.; Hnědkovský, L.; Marek, T. Partial molar volumes of organic solutes in water. XVIII. Selected polyethers(aq) and 3,6-dioxa-1heptanol(aq) at temperatures T = 298 to 573 K and at pressures up to 30 MPa. J. Chem. Thermodyn. 2007, 39, 1292−1299. 2658
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