Partial Molar Volumes and Partial Molar Isentropic Compressions of

Article pubs.acs.org/jced

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 Artur Purchala† and Ivan Cibulka*,‡ †

Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, Poland Department of Physical Chemistry, Institute of Chemical Technology, Technická 5, 166 28 Prague, Czech Republic

‡

ABSTRACT: Density and speed of sound data for dilute aqueous solutions of four aliphatic linear polyethers (glymes) 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 cyclic analogues, and structure−property relationships were analyzed. Group contributions of the structural segment −O−CH2−CH2− were evaluated for both homologous series and discussed.

1. INTRODUCTION This work is a continuation of a systematic study of volumetric and acoustic properties of dilute aqueous solutions of organic compounds. Recently 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 lower cyclic ethers1−3 (oxolane (tetrahydrofuran), 1,3-dioxolane, oxane (tetrahydropyran), 1,4dioxane, 1,3,5-trioxane) and large macrocycles4,5 (crown ethers: 15-crown-5, and 18-crown-6) has been completed. Present solutes belong to the family of linear polyethers of the general formula H3C−(O−CH2−CH2)(m−1)−O−CH3 with m oxygen atoms and n = 3m carbon and oxygen atoms linked together in the open nonbranched chain and can be denoted as lin(m), that is, lin(2) (2,5-dioxahexane, ethylene glycol dimethyl ether, monoglyme), lin(3) (2,5,8-trioxanonane, diethylene glycol dimethyl ether, diglyme), lin(4) (2,5,8,11-tetraoxadodecane, triethylene glycol dimethyl ether, triglyme), and lin(5) (2,5,8,11,14-pentaoxapentadecane, tetraethylene glycol dimethyl ether, tetraglyme). The first member of this series, not studied here because of low normal boiling point temperature, is dimethyl ether (2-oxapropane, m = 1, lin(1)). Then the pairs of linear and cyclic analogues, lin(m) and cyc(m), can be formed with cyclic analogues (−O−CH2−CH2)m: cyc(1) (oxirane, oxacyclopropane), cyc(2) (1,4-dioxane, 1,4-dioxacyclohexane, “6-crown-2”), cyc(3) (1,4,7-trioxacyclononane, “9-crown-3”), cyc(4) (1,4,7,10-tetraoxacyclododecane, 12-crown-4), and cyc(5) (1,4,7,10,13-pentaoxacyclopentadecane, 15-crown-5). In the present series of linear polyethers there is no analogue to the cyclic polyether for m = 6 (cyc(6), 1,4,7,10,13,16-hexaoxacyclooctadecane, 18-crown-6). Respective lin(m) and cyc(m) analogues differ by two hydrogen atoms. Compared to cyclic polyethers in which all members of the series comprise the segment −O−CH2−CH2−, the first member of the linear © 2014 American Chemical Society

polyethers series comprising this segment is monoglyme (lin(2)). A mutual comparison of standard molar volumes and standard molar isentropic compressions of pairs of linear and cyclic polyethers enables us to examine effects of cyclization on the two thermodynamic quantities. Two of the present aqueous solutes have been already studied in our laboratory: densities of dilute aqueous solutions of monoglyme and diglyme6 have been measured in the temperature range from (298 to 573) K and pressures up to 30 MPa and standard molar volumes have been evaluated. Therefore, this work also extends the temperature range of previous measurements down to 278 K.

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. At least five solutions of each solute were prepared. Uncertainty of molality was estimated to be 3·10−5 mol·kg−1. To reach this uncertainty, about 0.8 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. Received: October 1, 2014 Accepted: November 10, 2014 Published: November 24, 2014 4205

dx.doi.org/10.1021/je500914a | J. Chem. Eng. Data 2014, 59, 4205−4216

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

monoglyme diglyme triglyme tetraglyme

2,5-dioxahexane 2,5,8-trioxanonane 2,5,8,11-tetraoxadodecane 2,5,8,11,14-pentaoxapentadecane

C4H10O2 C6H14O3 C8H18O4 C10H22O5

110-71-4 111-96-6 112-49-2 143-24-8

Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Aldrich

0.995 0.995 0.99 >0.995

3.4·10−5 7.7·10−5 2.74·10−4 1.32·10−4

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 Monoglyme (aq), Diglyme (aq), Triglyme (aq), and Tetraglyme (aq) at Atmospheric Pressurea m2/(mol·kg−1)

Δρ/(kg·m−3)

T/K = 0.049210 0.050730 0.098245 0.102636 0.199994 0.202894 0.301382 0.310281 0.400846 0.405628 T/K = 0.049210 0.050730 0.098245 0.102636 0.199994 0.202894 0.301382 0.310281 0.400846 0.405628

278.15 −0.220 −0.227 −0.423 −0.446 −0.817 −0.826 −1.161 −1.187 −1.458 −1.470 313.15 −0.292 −0.302 −0.578 −0.604 −1.152 −1.170 −1.698 −1.740 −2.207 −2.232

283.15 −0.231 −0.240 −0.452 −0.471 −0.877 −0.889 −1.255 −1.284 −1.589 −1.605 318.15 −0.303 −0.312 −0.599 −0.626 −1.197 −1.214 −1.766 −1.810 −2.303 −2.328

T/K = 0.047459 0.099424 0.101928 0.193772 0.214816 0.283695 0.300396 0.408389 T/K = 0.047459 0.099424 0.101928 0.193772 0.214816 0.283695 0.300396 0.408389

278.15 0.181 0.386 0.392 0.788 0.880 1.202 1.282 1.820 313.15 0.048 0.101 0.099 0.207 0.232 0.327 0.346 0.504

283.15 0.156 0.331 0.336 0.678 0.758 1.041 1.107 1.575 318.15 0.034 0.068 0.065 0.141 0.159 0.227 0.240 0.355

T/K = 0.051868 0.100814 0.210203 0.306008 0.410034

278.15 0.595 1.166 2.461 3.623 4.898

283.15 0.558 1.093 2.302 3.383 4.571

Monoglyme (aq) 288.15 293.15 −0.242 −0.252 −0.251 −0.261 −0.475 −0.497 −0.495 −0.516 −0.927 −0.975 −0.940 −0.990 −1.338 −1.417 −1.371 −1.450 −1.708 −1.817 −1.724 −1.835 323.15 328.15 −0.313 −0.321 −0.323 −0.337 −0.619 −0.639 −0.646 −0.670 −1.240 −1.284 −1.259 −1.301 −1.834 −1.902 −1.882 −1.952 −2.397 −2.489 −2.424 −2.518 Diglyme (aq) 288.15 293.15 0.135 0.117 0.286 0.243 0.288 0.245 0.583 0.497 0.652 0.557 0.898 0.766 0.952 0.814 1.358 1.164 323.15 328.15 0.019 0.003 0.035 0.002 0.032 −0.001 0.077 0.013 0.088 0.017 0.130 0.035 0.139 0.039 0.213 0.072 Triglyme (aq) 288.15 293.15 0.525 0.497 1.031 0.972 2.162 2.038 3.173 2.986 4.280 4.020 4206

298.15 −0.262 −0.271 −0.517 −0.539 −1.020 −1.037 −1.490 −1.525 −1.919 −1.938 333.15 −0.336 −0.348 −0.660 −0.691 −1.327 −1.348 −1.970 −2.024 −2.584 −2.614

303.15 −0.272 −0.281 −0.538 −0.561 −1.065 −1.081 −1.562 −1.598 −2.017 −2.038 338.15 −0.344 −0.362 −0.682 −0.714 −1.372 −1.392 −2.040 −2.096 −2.679 −2.710

308.15 −0.281 −0.291 −0.558 −0.582 −1.108 −1.126 −1.631 −1.670 −2.115 −2.138 343.15 −0.354 −0.378 −0.704 −0.737 −1.418 −1.438 −2.110 −2.168 −2.774 −2.804

298.15 0.099 0.205 0.205 0.420 0.469 0.648 0.687 0.985 333.15 −0.012 −0.030 −0.033 −0.050 −0.051 −0.059 −0.060 −0.065

303.15 0.081 0.167 0.169 0.344 0.387 0.536 0.566 0.816 338.15 −0.026 −0.061 −0.063 −0.110 −0.122 −0.149 −0.158 −0.201

308.15 0.065 0.133 0.133 0.275 0.308 0.428 0.454 0.657 343.15 −0.042 −0.091 −0.094 −0.172 −0.188 −0.241 −0.255 −0.334

298.15 0.471 0.922 1.924 2.813 3.782

303.15 0.446 0.871 1.817 2.653 3.559

308.15 0.421 0.825 1.717 2.502 3.350



Article

Table 2. continued m2/(mol·kg−1)

Δρ/(kg·m−3)

T/K = 0.051868 0.100814 0.210203 0.306008 0.410034

313.15 0.399 0.780 1.619 2.357 3.152

318.15 0.378 0.736 1.526 2.218 2.960

T/K = 0.050617 0.097183 0.195888 0.249030 0.299821 0.409313 T/K= 0.050617 0.097183 0.195888 0.249030 0.299821 0.409313

278.15 0.983 1.892 3.815 4.868 5.839 7.969 313.15 0.727 1.400 2.795 3.550 4.237 5.725

283.15 0.932 1.798 3.620 4.615 5.535 7.546 318.15 0.702 1.346 2.686 3.408 4.066 5.486

323.15 328.15 0.356 0.335 0.692 0.653 1.436 1.347 2.084 1.952 2.777 2.597 Tetraglyme (aq) 288.15 293.15 0.891 0.852 1.717 1.642 3.451 3.299 4.398 4.201 5.268 5.029 7.171 6.833 323.15 328.15 0.674 0.649 1.294 1.245 2.574 2.474 3.273 3.142 3.901 3.741 5.256 5.035

333.15 0.314 0.613 1.261 1.826 2.425

338.15 0.294 0.573 1.177 1.700 2.252

343.15 0.275 0.517 1.095 1.578 2.085

298.15 0.819 1.576 3.159 4.020 4.809 6.525 333.15 0.625 1.196 2.373 3.013 3.587 4.820

303.15 0.787 1.513 3.030 3.854 4.607 6.242 338.15 0.597 1.149 2.273 2.889 3.437 4.614

308.15 0.756 1.455 2.910 3.698 4.417 5.976 343.15 0.572 1.104 2.175 2.770 3.291 4.409

Standard uncertainties are u(T) = 0.01 K, u(m2) = 2·10−5 mol·kg−1, and the combined expanded uncertainty is Uc(Δρ) = 1·10−2 kg·m−3 (level of confidence = 0.95). a

Figure 1. Plot of experimental standard molar volumes V0m,2 of glymes H3C−(O−CH2−CH2)(m−1)−O−CH3 against temperature T: ○, m = 2, monoglyme; □, m = 3, diglyme; △, m = 4, triglyme; ▲, m = 5, tetraglyme.

Figure 2. Plot of standard molar volumes of the group −O−CH2− CH2− V0m(−O−CH2−CH2−) = V0m,2(m + 1) − V0m,2(m) where m is the number of oxygen atoms against temperature T. Full lines, linear polyethers H3C−(O−CH2−CH2)(m−1)−O−CH3 (this work); dotted lines, cyclic polyethers2,4,5 (−O−CH2−CH2)m (estimated5 values for m = 3 and m = 4 were used): ○, m = 2; □, m = 3; △, m = 4; ▲, m = 5.

The vibrating-tube densimeter and sound analyzer (measuring in a low frequency range and thus providing thermodynamic speed of sound) manufactured by Anton Paar, model DSA 5000, with a built-in thermostat was used for the measurements. The experimental device was calibrated by pure water and air following the manufacturer’s instructions. An isoplethal regime of the measurements was selected to minimize the consumption of measured samples. Each solution was filled into cleaned and dried measuring cells of the DSA 5000 device, and the temperature was changed with 5 K wide steps in the entire experimental interval starting from 278.15 K. Measurement of

each solution was “bracketed” by measurements of pure water and the reproducibility of density of and speed of sound in pure water was checked; all values measured for pure water were reproducible within ± 0.003 kg·m−3 and ± 0.06 m·s−1; no significant drifts were observed. Average values of density and speed of sound for water, ρ1, c1, were calculated using the results of two consecutive measurements of water and then used in calculations of the differences Δρ = ρ − ρ1 and Δc = c − c1 where ρ and c are the density of and the speed of sound in the solution, 4207



Article

Table 3. Experimental Differences in Speed of Sound Δc = c − c1 Measured at Various Temperatures T and Molalities m2 for Monoglyme (aq), Diglyme (aq), Triglyme (aq), and Tetraglyme (aq) at Atmospheric Pressurea m2/(mol·kg−1)

Δc/(m·s−1)

T/K = 0.049210 0.050730 0.098245 0.102636 0.199994 0.202894 0.301382 0.310281 0.400846 0.405628 T/K = 0.049210 0.050730 0.098245 0.102636 0.199994 0.202894 0.301382 0.310281 0.400846 0.405628

278.15 4.61 4.77 9.11 9.56 18.54 18.70 27.58 28.38 36.52 36.83 313.15 2.16 2.21 4.28 4.45 8.60 8.65 12.70 13.08 16.81 16.90

283.15 4.15 4.29 8.21 8.61 16.68 16.83 24.81 25.55 32.87 33.14 318.15 1.91 1.95 3.76 3.92 7.58 7.62 11.15 11.48 14.72 14.78

T/K = 0.047459 0.099424 0.101928 0.193772 0.214816 0.283695 0.300396 0.408389 T/K = 0.047459 0.099424 0.101928 0.193772 0.214816 0.283695 0.300396 0.408389

278.15 6.11 12.72 13.00 24.41 26.96 35.32 37.30 50.04 313.15 3.00 6.28 6.41 12.01 13.21 17.21 18.17 24.15

283.15 5.54 11.51 11.77 22.12 24.42 31.98 33.78 45.29 318.15 2.68 5.62 5.74 10.72 11.77 15.30 16.14 21.41

T/K = 0.051868 0.100814 0.210203 0.306008 0.410034 T/K = 0.051868 0.100814 0.210203 0.306008 0.410034

278.15 8.41 16.29 33.36 47.69 62.85 313.15 4.27 8.23 16.85 23.87 31.21

283.15 7.65 14.79 30.34 43.31 57.05 318.15 3.86 7.41 15.10 21.36 27.84

T/K = 0.050617 0.097183 0.195888

278.15 9.90 18.85 37.27

283.15 9.02 17.18 33.98

Monoglyme (aq) 288.15 3.75 3.86 7.43 7.79 15.05 15.16 22.33 23.00 29.61 29.82 323.15 1.67 1.74 3.28 3.43 6.59 6.62 9.66 9.94 12.75 12.78 Diglyme (aq) 288.15 5.06 10.47 10.71 20.07 22.15 28.98 30.61 41.00 323.15 2.36 4.96 5.09 9.45 10.37 13.45 14.21 18.82 Triglyme (aq) 288.15 7.00 13.47 27.61 39.41 51.84 323.15 3.45 6.60 13.42 18.96 24.65 Tetraglyme (aq) 288.15 8.27 15.70 30.99 4208

293.15 3.37 3.47 6.69 6.99 13.54 13.64 20.08 20.68 26.63 26.82 328.15 1.45 1.51 2.81 2.95 5.61 5.69 8.26 8.49 10.89 10.88

298.15 3.03 3.11 6.01 6.28 12.16 12.26 18.02 18.56 23.88 24.02 333.15 1.22 1.31 2.36 2.50 4.71 4.76 6.89 7.09 9.12 9.06

303.15 2.73 2.80 5.39 5.65 10.90 10.96 16.11 16.61 21.35 21.48 338.15 1.01 1.12 1.94 2.08 3.85 3.92 5.62 5.76 7.28 7.33

308.15 2.43 2.51 4.80 5.02 9.69 9.76 14.33 14.77 19.00 19.10 343.15 0.81 0.90 1.52 1.69 3.05 3.17 4.45 4.48 5.60 5.67

293.15 4.55 9.49 9.71 18.19 20.07 26.24 27.72 37.08 328.15 2.05 4.34 4.45 8.26 9.05 11.72 12.37 16.33

298.15 4.13 8.60 8.78 16.46 18.17 23.71 25.06 33.47 333.15 1.76 3.71 3.86 7.09 7.80 10.08 10.63 13.98

303.15 3.73 7.79 7.94 14.88 16.37 21.38 22.57 30.15 338.15 1.46 3.12 3.30 5.99 6.61 8.50 8.99 11.76

308.15 3.35 7.01 7.15 13.39 14.72 19.23 20.31 27.05 343.15 1.17 2.62 2.81 5.00 5.51 6.97 7.41 9.60

293.15 6.34 12.24 25.11 35.80 47.04 328.15 3.05 5.82 11.83 16.67 21.63

298.15 5.76 11.13 22.82 32.47 42.65 333.15 2.68 5.10 10.33 14.51 18.75

303.15 5.24 10.12 20.67 29.43 38.55 338.15 2.33 4.41 8.88 12.43 16.01

308.15 4.75 9.11 18.69 26.56 34.76 343.15 1.94 3.70 7.41 10.45 13.38

293.15 7.55 14.36 28.25

298.15 6.88 13.06 25.71

303.15 6.27 11.87 23.36

308.15 5.70 10.77 21.20



Article

Table 3. continued m2/(mol·kg−1) T/K = 0.299821 0.409313 0.249030 T/K = 0.050617 0.097183 0.195888 0.299821 0.409313 0.249030

Δc/(m·s−1) 278.15 55.95 74.96 46.96 313.15 5.17 9.77 19.18 28.49 37.92 24.02

283.15 50.93 68.21 42.77 318.15 4.68 8.81 17.24 25.57 33.98 21.58

288.15 46.40 62.10 39.00 323.15 4.18 7.89 15.40 22.80 30.23 19.27

293.15 42.23 56.49 35.51 328.15 3.71 7.01 13.66 20.18 26.62 17.07

298.15 38.41 51.33 32.31 333.15 3.26 6.18 12.01 17.68 23.17 14.99

303.15 34.88 46.56 29.37 338.15 2.91 5.39 10.44 15.29 19.93 12.99

308.15 31.57 42.10 26.61 343.15 2.50 4.61 8.90 13.01 16.81 11.09

a Standard uncertainties are u(T) = 0.01 K, u(m2) = 2·10−5 mol·kg−1, and the combined expanded uncertainty is Uc(Δc) = 0.1 m·s−1 (level of confidence = 0.95).

Figure 4. Plot of isobaric expansivity α0p,2 = (1/V0m,2)(∂V0m,2/∂T)p of polyethers with m oxygen atoms in the molecule calculated from eq 6 against temperature T. Full lines, linear polyethers H3C−(O−CH2− CH2)(m−1)−O−CH3 (this work); dotted lines, cyclic polyethers2,4,5 (−O−CH2−CH2)m (estimated5 values for m = 3 and m = 4 were used).

Figure 3. Plot of standard molar volumes of two hydrogen atoms V0m(−H,−H) = V0m,2[lin(m)] − V0m,2[cyc(m)] where m is the number of oxygen atoms against temperature T. Linear polyethers H3C−(O− CH2−CH2)(m−1)−O−CH3 (this work); cyclic polyethers2,4,5 (−O− CH2−CH2)m (estimated5 values for m = 3 and m = 4 were used): ○, m = 2; □, m = 3; △, m = 4; ▲, m = 5.

the evaluation of standard molar volumes and standard molar isentropic compressions as well as for the calculations of densities of and speeds of sound in solutions; that is, ρ = Δρ(experimental) + ρ1(NIST) and c = Δc(experimental) + c1(NIST) as needed for the evaluation of standard molar isentropic compressions.

respectively, measured between two measurements of water. The measured differences Δρ and Δc were regarded as direct experimental data and are tabulated in the tables. Since lower glymes are rather volatile (normal boiling point temperature of monoglyme is about 358 K) the solutions were not degassed4 to prevent the composition changes due to evaporation. At higher temperatures (above 333 K) formations of air bubbles were observed several times and the measurements were repeated. Similarly as in the previous measurements it was observed that values ρ1 and c1 measured for water exhibited small systematic deviations from the values presented by the National Institute of Standards and Technology7 (NIST) (for details and NIST values see ref 4). The effect of these small deviations on the goal quantities (standard molar volumes, standard molar isentropic compressions) is negligible since in the differences Δρ and Δ[(ρc)2] (eqs 2 and 5) these systematic deviations cancel out. The values ρ1(NIST) and c1(NIST) were used for

3. RESULTS 3.1. Direct Experimental Data. The measured 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. 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 equation8 0 app = lim (V m,2 V m,2 )= m2 → 0

4209

a ⎞ 1⎛ ⎜⎜M 2 − V ⎟⎟ ρ1 ⎝ ρ1 ⎠

(1)



Article

Table 4. Coefficients aV and bV of eq 2, Standard Molar Volumes V0m,2, Coefficients aK, and bK of eq 5, and Standard Molar Isentropic Compressions K0S,m,2, for {Monoglyme (2) or Diglyme (2) or Triglyme (2) or Tetraglyme (2) + Water(1)}. The Uncertainties σ(V0m,2) and σ(K0S,m,2) Represent the Combined Expanded Uncertainties T K

aV −3

−3

−2

kg ·m ·mol 3

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

−4.570 −4.813 −5.022 −5.219 −5.411 −5.612 −5.805 −6.012 −6.217 −6.414 −6.630 −6.842 −7.031 −7.252

2.3646 2.1324 1.9120 1.7204 1.5572 1.4459 1.3192 1.2604 1.1865 1.0854 1.0580 1.0021 0.8694 0.8310

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

3.699 3.169 2.733 2.331 1.967 1.606 1.271 0.944 0.633 0.315 −0.012 −0.323 −0.612 −0.924

1.8689 1.6973 1.4520 1.2569 1.0639 0.9389 0.8040 0.6875 0.5526 0.4798 0.4618 0.3868 0.2701 0.2405

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

11.423 10.720 10.110 9.560 9.081 8.603 8.143 7.720 7.301 6.881 6.492 6.103 5.717 5.271

1.3134 1.0679 0.8231 0.6205 0.3571 0.2026 0.0916 −0.0686 −0.1873 −0.2494 −0.3784 −0.4585 −0.5411 −0.4265

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

19.451 18.479 17.665 16.915 16.260 15.636 15.043 14.479 13.967 13.430 12.938

0.1195 −0.0265 −0.2754 −0.4444 −0.7006 −0.8716 −1.0039 −1.1215 −1.3219 −1.3806 −1.5054

aK·10−12

V0m,2 ± σ(V0m,2)

bV −1

kg ·m ·mol 2

−1

cm ·mol 3

Monoglyme (aq) 94.70 ± 0.06 94.96 ± 0.08 95.23 ± 0.08 95.52 ± 0.08 95.83 ± 0.08 96.18 ± 0.08 96.54 ± 0.08 96.93 ± 0.08 97.35 ± 0.07 97.78 ± 0.08 98.25 ± 0.11 98.74 ± 0.11 99.22 ± 0.17 99.76 ± 0.22 Diglyme (aq) 130.48 ± 0.10 131.04 ± 0.11 131.56 ± 0.11 132.08 ± 0.12 132.59 ± 0.13 133.14 ± 0.11 133.69 ± 0.11 134.27 ± 0.11 134.85 ± 0.12 135.48 ± 0.12 136.13 ± 0.10 136.80 ± 0.11 137.47 ± 0.12 138.19 ± 0.10 Triglyme (aq) 166.81 ± 0.09 167.55 ± 0.09 168.26 ± 0.10 168.95 ± 0.09 169.62 ± 0.09 170.33 ± 0.08 171.06 ± 0.10 171.78 ± 0.10 172.54 ± 0.08 173.34 ± 0.08 174.13 ± 0.08 174.96 ± 0.09 175.82 ± 0.08 176.77 ± 0.17 Tetraglyme (aq) 202.84 ± 0.13 203.86 ± 0.14 204.78 ± 0.14 205.70 ± 0.14 206.58 ± 0.13 207.48 ± 0.13 208.39 ± 0.13 209.32 ± 0.14 210.23 ± 0.11 211.21 ± 0.13 212.19 ± 0.12 4210

−4 −2

bK·10−12

kg ·m ·s ·mol 3

−1

−4 −2

kg ·m ·s ·mol 4

K0S,m,2 ± σ(K0S,m,2) −2

cm3·mol−1·GPa−1

0.2495 0.2244 0.2023 0.1800 0.1596 0.1409 0.1222 0.1044 0.0882 0.0730 0.0576 0.0420 0.0287 0.0153

−0.0065 −0.0062 −0.0097 −0.0081 −0.0092 −0.0116 −0.0115 −0.0104 −0.0124 −0.0154 −0.0158 −0.0135 −0.0163 −0.0163

−16.0 −8.2 −2.0 3.6 8.3 12.3 16.0 19.4 22.5 25.3 28.1 31.0 33.5 36.1

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.7 0.8 0.6

0.3843 0.3527 0.3250 0.2960 0.2698 0.2449 0.2203 0.1973 0.1759 0.1545 0.1334 0.1113 0.0931 0.0755

−0.0238 −0.0247 −0.0313 −0.0280 −0.0297 −0.0310 −0.0290 −0.0290 −0.0306 −0.0303 −0.0278 −0.0178 −0.0204 −0.0201

−26.9 −16.4 −8.1 −0.5 5.8 11.4 16.5 21.0 25.1 29.1 33.0 37.1 40.5 43.9

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.4 0.4 0.6 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5 0.7 0.7 1.1

0.5142 0.4763 0.4419 0.4070 0.3753 0.3452 0.3153 0.2872 0.2616 0.2352 0.2102 0.1859 0.1634 0.1380

−0.0342 −0.0365 −0.0417 −0.0400 −0.0424 −0.0449 −0.0438 −0.0441 −0.0486 −0.0478 −0.0478 −0.0466 −0.0481 −0.0388

−36.7 −23.6 −12.9 −3.5 4.4 11.2 17.6 23.2 28.2 33.1 37.8 42.3 46.5 51.3

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.6 0.5 0.4 0.5 0.5 0.4 0.4 0.5 0.3 0.3 0.3 0.3 0.4 0.4

0.6422 0.5983 0.5587 0.5196 0.4814 0.4452 0.4106 0.3779 0.3469 0.3152 0.2848

−0.0444 −0.0486 −0.0582 −0.0628 −0.0635 −0.0645 −0.0657 −0.0679 −0.0716 −0.0691 −0.0674

−46.0 −30.3 −17.8 −6.9 2.7 11.1 18.6 25.2 31.3 37.3 42.9

± ± ± ± ± ± ± ± ± ± ±

0.4 0.4 0.4 0.5 0.4 0.4 0.4 0.4 0.5 0.4 0.3



Article

Table 4. continued T

aV

bV

V0m,2 ± σ(V0m,2)

aK·10−12

bK·10−12

K0S,m,2 ± σ(K0S,m,2)

K

kg2·m−3·mol−1

kg3·m−3·mol−2

cm3·mol−1

kg3·m−4·s−2·mol−1

kg4·m−4·s−2·mol−2


333.15 338.15 343.15

12.452 11.927 11.444

−1.6171 −1.5371 −1.5630

0.2560 0.2301 0.2029

−0.0670 −0.0718 −0.0688

Tetraglyme (aq) 213.20 ± 0.11 214.28 ± 0.15 215.36 ± 0.17

Figure 6. Plot of experimental standard molar isentropic compressions K0S,m,2 of glymes H3C−(O−CH2−CH2)(m−1)−O−CH3 against temperature T: ○, m = 2, monoglyme; □, m = 3, diglyme; △, m = 4, triglyme; ▲, m = 5, tetraglyme.

Figure 5. Plot of the derivative (∂c0p,m,2/∂p)T of polyethers with m oxygen atoms in the molecule calculated from eq 6 against temperature T. Full lines, linear polyethers H3C−(O−CH2−CH2)(m−1)−O−CH3 (this work); dotted lines, cyclic polyethers2,4,5 (−O−CH2−CH2)m (estimated5 values for m = 3 and m = 4 were used).

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

where M2 is the molar mass, Vapp m,2 is the apparent molar volume, and m2 is the molality of the solute. The coefficient aV is an adjustable parameter of the fit of experimental values Δρ/m2 ρ − ρ1 Δρ = = aV + bV m2 m2 m2 (2)

(ρc)2 − (ρ1c1)2 Δ[(ρc)2 ] = = aK + bK m2 m2 m2

app ⎞ ⎛ ∂V 0 ⎞ ⎛ −∂V m,2 m,2 ⎟ = lim ⎜ ⎟ = −⎜⎜ m2 → 0⎝ ∂p ⎠ ∂p ⎟⎠ ⎝ S S

4. DISCUSSION 4.1. Comparison with Data in Literature. Experimental standard molar volumes are compared in Table 5 with the values found in the literature. Values obtained previously in this laboratory for monoglyme6 agree with the present data within experimental uncertainties. Excellent agreement is observed for data measured by Harada et al.10 and some others.15−18 On the other hand, the volumes calculated from the smoothing function11 and those reported by Sikora12 exhibit large systematic deviations. Standard molar volumes measured in this work for diglyme agree within experimental uncertainties with data published by Harada et al.,10 Lepori et al.,18,22 and Raju and Sailaja.25 Agreement with our previous data6 is within experimental uncertainties at lower temperatures; slightly higher deviations are observed for T > 328 K. In the case of triglyme the

(3) 9

On the basis of this definition it is possible to derive the expression for standard molar isentropic compression KS0,m,2 =

aK ⎞ 1 ⎛ ⎜M − ⎟⎟ 2⎜ 2 (ρ1c1) ⎝ (ρ1c1)2 ⎠

(5)

The values of the coefficients aK and 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 0 0 KS,m,2 . Uncertainties σ(KS,m,2 ) are affected mainly by the uncertainty in the speed of sound which was estimated to be about ± 0.1 m·s−1.

The values of the coefficients aV and bV obtained by using a leastsquares method with unit weights are recorded in Table 4 along with the calculated standard molar volumes and estimated uncertainties. 3.3. Standard Molar Isentropic Compressions. Partial molar isentropic compression at infinite dilution (standard molar isentropic compression) of the solute 2 is defined as the derivative of standard molar volume V0m,2 with respect to pressure at constant entropy KS0,m,2

48.2 ± 0.3 53.1 ± 0.5 58.2 ± 0.5

(4) 4211



Article

Table 5. Comparison of Standard Molar Volumes Obtained in This Work with Data Taken from the Literature T

V0m,2 (this work)

V0m,2 (lit.)

K

cm3·mol−1

cm3·mol−1

278.15 283.15 288.15 293.15 298.15

303.15 308.15

313.15 313.25 318.15

323.15 323.25 328.15 333.15 338.15 343.15 278.15 298.15

303.15

Monoglyme (aq) 94.71 ± 0.05 94.39b 94.74b 95.0 95.52 ± 0.08 95.09b 95.83 ± 0.08 95.4c 95.45b 95.6 95.6 ± 0.1 95.7 ± 0.4 95.77 ± 0.15 95.85 ± 0.05 95.88 ± 0.03 95.90d 95.9 96.26 96.18 ± 0.08 95.83b 96.18d 96.54 ± 0.08 96.1 96.24b 96.52d 96.93 ± 0.08 96.68b 96.90d 96.95e 96.6 97.35 ± 0.07 97.18b 97.32d 97.34 ± 0.05 97.78 ± 0.08 97.74b 97.77d e 97.80 97.7 98.25 ± 0.11 98.25d 98.74 ± 0.11 98.75d 99.22 ± 0.17 99.27d 99.76 ± 0.22 99.82d Diglyme (aq) 130.48 ± 0.10 130.64 ± 0.05 132.59 ± 0.13 131.6 ± 0.1 132.0c 132.1c 132.4 ± 0.4 132.42 132.69 ± 0.05 132.7 132.71d 132.72 ± 0.05 133.19f 133.8 ± 0.1g 133.8h 133.14 ± 0.11 133.21d 133.25 94.70 ± 0.06 94.96 ± 0.08 95.23 ± 0.08

deva

T

V0m,2 (this work)

V0m,2 (lit.)

ref

cm3·mol−1

K

cm3·mol−1

cm3·mol−1

10 11 11 12 11 13 11 12 14 15 16 10 17 6 18 19 11 6 12 11 6 11 6 12 11 6 10 11 6 12 6 6 6 6

−0.01 0.57 0.49 0.23 0.43 0.43 0.38 0.23 0.23 0.13 0.06 −0.02 −0.05 −0.07 −0.07 −0.43 0.35 0.00 0.44 0.31 0.02 0.25 0.03 0.35 0.17 0.03 0.01 0.05 0.01 0.10 0.00 −0.01 −0.05 −0.06

308.15

133.69 ± 0.11

313.15

134.27 ±

318.15

134.85 ±

323.15

135.48 ±

328.15 333.15 338.15 343.15

136.13 136.80 137.47 138.19

278.15 288.15

166.81 ± 168.26 ±

298.15

169.62 ±

308.25 313.15 315.05 318.15 323.25

171.08e 171.78 ± 172.08e 172.54 ± 173.34e

10 14 16 21 15 19 22 18 6 10 23 24 24 6 25

−0.16 0.99 0.59 0.49 0.19 0.17 −0.10 −0.11 −0.12 −0.13 −0.60 −1.21 −1.21 −0.07 −0.11

278.15 287.95 288.15 298.15

202.84 ± 204.74e 204.78 ± 206.58 ±

298.25 308.35 313.15 315.15 318.15 323.05

206.62e 208.45e 209.32 ± 209.69e 210.23 ± 211.19e

± ± ± ±

Diglyme (aq) 133.76d 133.83 0.11 134.35d 134.38 0.12 134.94 ± 0.05 134.94 134.96d 0.12 135.49 135.60d 0.10 136.27d 0.11 136.95d 0.12 137.66d 0.10 138.38d Triglyme (aq) 0.09 167.02 ± 0.05 0.10 167.7 168.5 ± 0.3 0.09 169.0 169.2 169.36 169.57 ± 0.15 169.63 ± 0.05 169.7 169.83 ± 0.05 169.9 ± 0.3 170.24f 170.3 ± 0.3 170.0 0.10 171.15 ± 0.05 171.4 0.08 172.66 ± 0.05 172.7 Tetraglyme (aq) 0.13 203.18 ± 0.05 204.6 0.14 205.6 ± 0.3 0.13 205.95 206.66 ± 0.05 206.7 206.88 ± 0.05 207.0 ± 0.3 207.05f 207.3 ± 0.3 206.6 207.7 0.14 208.9 ± 0.2 209.0 0.11 210.27 ± 0.05 210.9

deva ref

cm3·mol−1

6 25 6 25 10 25 6 25 6 6 6 6 6

−0.07 −0.14 −0.08 −0.11 −0.09 −0.09 −0.11 −0.01 −0.12 −0.14 −0.15 −0.19 −0.19

10 12 26 27 12 19 16 22 18 10 26 23 28 12 26 12 10 12

−0.21 0.56 −0.24 0.62 0.42 0.26 0.05 −0.01 −0.08 −0.21 −0.28 −0.62 −0.68 1.08 0.63 0.68 −0.12 0.64

10 12 26 19 22 18 10 28 23 26 12 12 26 12 10 12

−0.34 0.14 −0.82 0.63 −0.08 −0.12 −0.30 −0.42 −0.47 −0.72 0.02 0.75 0.42 0.69 −0.04 0.29

a

Deviation between this work and the literature value. bCalculated from smoothing equation. cEvaluated by present method using data for two most diluted solutions (m2 up to 2.36 mol·kg−1). dSmoothed values, p = 0.1 MPa. eInterpolated by a polynomial interpolation. fEvaluated by present method for m2 up to 0.4 mol·kg−1. gOriginal value. hEvaluated by present method using data for three most diluted solutions (m2 up to 0.7 mol·kg−1).

for triglyme by Sikora12 deviate significantly from the present data. Data published for standard molar volumes of tetraglyme are rather scarce. Our values agree within experimental uncertainties with data reported by Lepori,18,22 Bernal and

agreement within experimental uncertainties is observed for data reported by Schrödle et al.,16 Lepori et al.,18,22 and Bernal et al.26 at T = 298.15 K, and that reported by Harada et al.10 at T = 318.15 K. Similarly as with monoglyme the values measured 4212



Article

Table 6. Comparison of Standard Molar Isentropic Compressions Obtained in This Work with Data Taken from the Literature T

K0S,m,2 (this work)

K0S,m,2(lit.)

K



278.15 298.15

−16.0 ± 0.5 8.3 ± 0.4

318.15

22.5 ± 0.4

278.15 298.15

−26.9 ± 0.4 5.8 ± 0.3

303.15 308.15 313.15 318.15

11.4 ± 0.4 16.5 ± 0.4 21.0 ± 0.4 25.1 ± 0.4

323.15

29.1 ± 0.4

278.15 288.15 298.15

−36.7 ± 0.6 −12.9 ± 0.4 4.4 ± 0.5

313.15 318.15

23.2 ± 0.5 28.2 ± 0.3

278.15 288.15 298.15

−46.0 ± 0.4 −17.8 ± 0.4 2.7 ± 0.4

313.15 318.15

25.2 ± 0.4 31.3 ± 0.5

Monoglyme (aq) −16.0 ± 0.5 8.6 ± 0.5 6.73 13.5 22.9 ± 0.5 Diglyme (aq) −27.1 ± 0.5 5.91 6.3 ± 0.5 −9.57 ± 1.0b −7.7c 11.19 16.00 20.88 25.7 ± 0.5 25.69 30.10 Triglyme (aq) −37.2 ± 0.5 −13.2 ± 0.8 4.8 ± 0.1 4.4 ± 0.5 3.8 ± 0.8 4.6 ± 0.8 25.5 ± 0.8 28.5 ± 0.5 Tetraglyme (aq) −47.3 ± 0.5 −17.5 ± 0.8 3.18 2.8 ± 0.5 2.9 ± 0.8 2.2 ± 0.8 25.4 ± 0.8 31.5 ± 0.5

deva ref


10 10 19 20 10

0.0 −0.3 1.6 −5.2 −0.4

10 19 10 24 24 25 25 25 10 25 25

0.2 −0.1 −0.5 15.4 13.5 0.2 0.5 0.1 −0.6 −0.6 −1.0

10 26 19 10 26 28 26 10

0.5 0.3 −0.4 0.0 0.6 −0.2 −2.3 −0.3

10 26 19 10 28 26 26 10

1.3 −0.3 −0.5 −0.1 −0.2 0.5 −0.2 −0.2

Figure 7. Plot of standard molar isentropic compressions of the group −O−CH2−CH2− K0S,m(−O−CH2−CH2−) = K0S,m,2(m + 1) − K0S,m,2(m) where m is the number of oxygen atoms against temperature T. Full lines, linear polyethers H3C−(O−CH2−CH2)(m−1)−O−CH3 (this work); dotted lines, cyclic polyethers3,4 (−O−CH2−CH2)m (estimated4 values for m = 3 and m = 4 were used): ○, m = 2; □, m = 3; △, m = 4; ▲, m = 5.

a

Deviation between this work and the literature value. bOriginal value. Evaluated by the present method using data for the three most diluted solutions (m2 up to 0.7 mol·kg−1). c

McCluan,28 and Harada et al.10 at T = 318.15 K, and with data reported by Sikora12 at T = 298.25 K. At other temperatures the values of Sikora12 deviate in similar manner as for other glymes. Table 6 presents a comparison of measured standard molar isentropic compressions with data published in the literature. With the exception of tetraglyme at T = 278.15 K the agreement within experimental uncertainties is observed for data published by Harada et al.10 for all four glymes. Except for monoglyme the agreement within experimental uncertainties is seen also for data reported by Douheret et al.19 for the other three glymes. Values from other two sources of compressions of monoglyme19,20 exhibit large deviations (both signs). Agreement of the present values of diglyme with the literature data is very satisfactory, the three sources10,19,25 provide values with deviations either within or close to experimental uncertainties. Extremely large deviations are observed for data by Dhondge et al.;24 it should be noted, however, that standard molar volumes from this source deviate

Figure 8. Comparison of standard molar isentropic compressions K0S,m,2 of linear H3C−(O−CH2−CH2)(m−1)−O−CH3 (full lines, this work) and cyclic (−O−CH2−CH2)m (dotted lines3,4) polyethers: ○, m = 2; ▲, m = 5.

largely from the present data as well (Table 5). Standard molar compressions obtained in this work for triglyme agree, except for the value reported by Bernal et al.26 for T = 313.15 K, with data taken from the literature within experimental uncertainties. With the exception of value by Harada et al.10 at T = 278.15 K the deviations between standard molar compressions measured for tetraglyme and those available in the literature data are within the limits of experimental uncertainties. 4213



Article

Table 7. Parameters aij of Equation 6a monoglyme (aq)

diglyme (aq)

triglyme (aq)

tetraglyme (aq)

i

j

aij

aij

aij

aij

1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 T/K p/MPa std.dev.b w.std.dev.c Nd

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

95.831 −6.1532083 ·10−3 −2.1525789 ·10−4 6.7530293 ·10−2 −2.6797111 ·10−3 6.1369617 ·10−5 5.4281767 ·10−4 8.2321232 ·10−5 −2.6229017 ·10−6 −4.1447541 ·10−6 −1.1737887 ·10−6 4.1284053 ·10−8 5.8688375 ·10−8 7.0405715 ·10−9 −2.9049602 ·10−10 −3.2531468 ·10−10 −1.7264050 ·10−11 9.1947283 ·10−13 6.8897813 ·10−13 8.9535026 ·10−15 −1.0181611 ·10−15 278 to 573 0.1 to 30 0.10 1.12 47

132.641 5.6475768 ·10−3 −4.4135449 ·10−4 1.1039927 ·10−1 −3.2703930 ·10−3 6.2772613 ·10−5 3.5902782 ·10−4 9.9295036 ·10−5 −2.7523286 ·10−6 −1.8015855 ·10−6 −1.6093381 ·10−6 4.8424797 ·10−8 4.7919304 ·10−8 1.1136506 ·10−8 −3.6955747 ·10−10 −3.0310704 ·10−10 −3.3012948 ·10−11 1.2419028 ·10−12 6.8150371 ·10−13 2.9944993 ·10−14 −1.4623222 ·10−15 278 to 573 0.1 to 30 0.12 1.58 47

169.637

206.592

1.4053232 ·10−1

1.8071885 ·10−1

1.2208150 ·10−4

−9.5229172 ·10−5

5.9455605 ·10−6

9.3242899 ·10−6

278 to 343 0.1 0.02 0.19 14

278 to 343 0.1 0.02 0.15 14

a

In the region T < 298 K the data at p = 0.1 MPa only obtained in this work were included in the experimental data sets, data at elevated pressures for T ≥ 298 K were taken from ref6. bstd.dev. = standard deviation/(cm3·mol−1). cw.std.dev. = weighted standard deviation. dN = number of data points.

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 linear polyethers are nearly equidistant, the differences correspond to the volume of the segment −O−CH2−CH2−. Full lines in Figure 2 show that the volume of this segment calculated as V0m(−O−CH2−CH2−) = V0m,2[lin(m + 1)] − V0m,2[lin(m)] where m is the number of oxygen atoms (the number of −O−CH2− CH2− segments in glymes is equal to m − 1) is nearly independent of the length of the chain. Volumes of this segment in cyclic polyethers (crown ethers) V0m(−O−CH2−CH2−) = V0m,2[cyc(m + 1)] − V0m,2[cyc(m)] are plotted in the figure as well (dotted lines). They were evaluated using experimental data for m = 2 (dioxane, “6-crown-2”2), m = 5 (15-crown-54,5) and m = 6 (18-crown-64,5) and values estimated by a group contribution method5 for m = 3 (“9-crown-3”) and m = 4 (12-crown-4). Evidently, the volume of the −O−CH2−CH2− segment in cyclic polyethers is increasing with the size of the cycle and for large cycles is approaching the values in linear chains of glymes. Standard molar volumes of glymes are larger than those in corresponding cyclic counterparts. They differ by two hydrogen atoms and thus the volumes V0m(−H,−H) = V0m,2[lin(m)] − V0m,2[cyc(m)] could be expected to be same for each m. This is not the case as Figure 3 shows, and the effect of cyclization may be considered. The differences between lines in Figure 3 are decreasing with increasing m and the hypothesis that V0m(−H,−H) may approach a constant value (depending on temperature, of course) for large linear/cyclic chains seems to be quite reasonable.

Data obtained in this work for monoglyme and diglyme were combined with those reported previously for extended ranges of temperature and pressure6 and equation 0 V m,2 /( cm 3· mol−1) NT

=

3

∑ ∑ aij(T /K − 298.15)(i− 1)(p/MPa − 0.1)(j − 1) i=1 j=1

(6)

was then fitted to the resulting data sets. Adjustable parameters aij reported in Table 7 were evaluated using the weighted leastsquares method with weights expressed in terms of estimated experimental uncertainties as 1/[σ(V0(exp) m,2 )]. A similar procedure was adopted for data measured at atmospheric pressure (p = 0.1 MPa) for triglyme and tetraglyme in this work by setting aij = 0 for j = 2 and j = 3. Respective nonzero parameters are recorded in Table 7 as well. Function 6 was also fitted to V0m,2(T,p) surfaces estimated for cyc(m = 3) (“9-crown-3”) and cyc(m = 4) (12-crown-4) using the group contribution method.5 Function 6 enable us easy evaluation of derivative quantities which may show tiny variations of structure−property relationships. Values of the analogue of isobaric expansivity α0p,2 = (1/V0m,2)(∂V0m,2/∂T)p (called “expansivity” in the following text) at atmospheric pressure were evaluated from function 6 and are plotted in Figure 4. Evidently, there is a distinct dependence between the shape of the curves and the size of the solute molecule, particularly at lower temperatures. The trends in the homologous series of linear (full lines) and cyclic (dotted lines) polyethers 4214



Article

for m = 2 and m = 5 in Figure 8; similar plots can be obtained for m = 3 and m = 4 using values estimated4 for cyclic polyethers. The slopes (∂K0S,m,2/∂T)p of linear polyethers are systematically greater than those of cyclic counterparts. On the basis of previous observations,9,29 it is likely that more hydrophilic solutes would exhibit smaller slopes, and thus the plots in Figure 8 are in accord to curves depicted in Figure 4; that is, that cyclic polyethers are more hydrophilic than their respective linear counterparts.

are, however, opposite. It is already proven that at low temperatures hydrophilic solutes exhibit convex shapes of the α0p,2(T) dependence while those for hydrophobic solutes are concave.29 According to this rule the cyclic 1,4-dioxane (m = 2) is the most hydrophilic solute while its linear counterpart monoglyme (m = 2) is the most hydrophobic one. It is likely that oxygen atoms in a somewhat rigid structure of 1,4-dioxane are more exposed to interactions with water compared to oxygen atoms rather protected by methylene groups in a more flexible linear chain of monoglyme. Flexibility of the cyclic chain increases with its increasing length and thus the expansivities of solutes in both homologous series become closer to each other for large m. Figure 5 shows temperature dependences of the derivative (∂c0p,m,2/∂p)T which is related to the second derivative of standard molar volume with respect to temperature, (∂c0p,m,2/∂p)T = −T(∂2V0m,2/∂T2)p. A monotonous trend in the series of linear polyethers can be observed while that in the series of cyclic polyethers is not, except for 1,4-dioxane, distinct. According to Hepler’s classification30 based on the sign of the second derivative (∂2V0m,2/∂T2)p and the shape of its temperature dependence, monoglyme (m = 2) and diglyme (m = 3) with positive (∂2V0m,2/ 0 /∂p)T) are structure makers ∂T2)p (i.e., negative (∂cp,m,2 (prevailing hydrophobic hydration) within this homologous series while larger glymes (m = 4 and 5) and cyclic polyethers with negative (∂2V0m,2/∂T2)p (i.e., positive (∂c0p,m,2/∂p)T) are, at least at low temperatures, structure breakers (prevailing hydrophilic hydration). It should be, however, noted that the second derivative (∂2V0m,2/∂T2)p is sensitive to both the input experimental data V0m(T) or V0m(T,p) and the way of fitting (order of the polynomial in this case) and therefore the values shown in Figure 5 should be regarded as illustrative only. On the other hand, the trends are clearly seen and correspond to the structures of the solute molecules. 4.3. Dependences of Standard Molar Isentropic Compression on Molecular Structure and Temperature. Experimental values of standard molar isentropic compression are plotted as functions of temperature in Figure 6. The plots exhibit a monotonous trend within the homologous series with mutual crossing of the dependences at temperatures around 305 K. Similar behavior was observed for some other homologous series as propane-1,3-diol and its 2-methyl- and 2,2-dimethylderivatives,29 alcohols derived from 2,2-dimethylpropane29 {(H3C)(4−n)C(CH2OH)n, n = 1, 2, 3, 4}, and linear alkaneα,ω-diols.31 Figure 7 shows that the contribution of the segment −O−CH2−CH2− to the standard molar isentropic compression calculated as K0S,m(−O−CH2−CH2−) = K0S,m,2[lin(m + 1)] − K0S,m,2[lin(m)] is nearly independent of the number of the segments (size of a glyme molecule); the deviations between curves are close to the experimental uncertainty of the contribution derived from experimental uncertainties of the experimental compressions (Table 4). This is not the case for cyclic polyethers (dotted lines in Figure 7) where the dependence on the cycle size is obvious (note that values shown for all m except for m = 5 were calculated using standard molar isentropic compressions estimated from the group contribution approach4). Contrary to standard molar volumes (Figure 2), the full and dotted curves at low temperatures for large m do not approach each other, the opposite trend is observed. On the other hand, since the dotted dependences exhibit mutual crossing it might seem likely that at higher temperatures and large m the contribution of the cyclic segment −O−CH2−CH2− becomes closer to that in linear polyethers. Experimental standard molar isentropic compressions of linear (this work) and cyclic polyethers3,4 are compared

5. CONCLUSIONS New data on density and speed of sound in a dilute region were reported for four aqueous linear aliphatic polyethers H3C−(O− CH2−CH2)(m−1)−O−CH3 with m ranging from 2 to 5 (monoglyme to tetraglyme). Analysis of the temperature dependences of standard molar volumes and standard molar isentropic compression and of the structure−property relationships was performed. Comparison with the solute analogues in the series of cyclic polyethers was also presented, and some effects of the cyclization on standard molar volumes and standard molar isentropic compressions were revealed. As a conclusion it seems probable that cyclization results in a higher hydrophlilic character of polyethers.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +420 220444063. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Institutional support from the Institute of Chemical Technology (ICT), Prague is acknowledged. The stay of A.P. at ICT Prague was arranged within the ERASMUS Program. A.P. is deeply grateful for the hospitality of the staff of ICT where the experimental part was performed. Authors express their thanks to Dr. Edward Zorebski for valuable comments on the manuscript.

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REFERENCES

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