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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 Ivan Cibulka* 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 two crown ethers, 15-crown-5 and 18crown-6, 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 combined with those obtained previously for lower cyclic ethers, and the predictions of standard molar volumes and standard molar isentropic compressions based on a group contribution approach were tested and analyzed. the previous works.1−3 Thus, the present study is an extension toward large cyclic ethers: 15-crown-5 (−CH2−CH2−O−)5 and 18-crown-6 (−CH2−CH2−O−)6. It should be noted that while lower members of the (−CH2−CH2−O−)m series have the oxygen atoms oriented to the outer surface of the molecule, higher members (true crown structures) may, due to the flexibility of large cyclic chain, have the oxygen atoms oriented toward the center of the cycle and thus allowing for the capture of inorganic particles (cations) inside the cycle.

1. INTRODUCTION This work is related to the previous study of volumetric and acoustic properties of dilute aqueous solutions of cyclic ethers: oxolane (tetrahydrofuran), 1,3-dioxolane, oxane (tetrahydropyran), 1,4-dioxane, and 1,3,5-trioxane. Partial molar volumes at infinite dilution (standard molar volumes) at near ambient1 and extended ranges2 of state parameters were evaluated from experimental densities and in combination with data on speed of sound measured at ambient conditions3 partial molar isentropic compressions at infinite dilution (standard molar isentropic compressions) were calculated. Group contribution approaches were designed for both partial molar quantites1−3 and predictions of standard molar volumes of several other members of the homologous series of cyclic ethers were compared1 with available experimental values. It was observed that the deviations between predicted and experimental values were increasing with the increasing size of the cycle in the solute molecule. Since the group contributions were evaluated from data for solutes with five- and six-membered cycles the predictions for solutes with large cycles are extrapolations and thus increased deviations might be expected. Large cyclic ethers in the focus of interest are predominantly crown ethers,4 cyclic substances with the −CH2−CH2−O− repeating unit. They are well-known as compounds capable to solubilize inorganic species in organic solvents with a high selectivity depending on the size of the cycle. Members of the crown ether series are usually marked with acronyms m-crown-n where m is the number of atoms (C, O) linked in the cycle and n is the number of oxygen atoms. The first member of the series (−CH2−CH2−O−)m is oxirane, (−CH2−CH2−O−)1, “3crown-1”, which, of course, does not form a “crown” structure. The second member, 1,4-dioxane (−CH2−CH2−O−)2, “6crown-2”, was included in the set of solutes already studied in © 2014 American Chemical Society

2. EXPERIMENTAL SECTION The specifications of the organic solutes are summarized in Table 1. 15-Crown-5 ether was used as obtained. 18-Crown-6 ether (solid substance at ambient conditions) was kept for 4 weeks in the desiccator over dehydrated silica gel. 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 and due to high cost of the solutes the concentration ranges were rather limited. Uncertainty of molality was estimated to be 3· 10−5 mol·kg−1. To reach this uncertainty about 0.5 kg of each solution was prepared and the unused amounts of solutions were preserved for further experiments in the near future. The Received: March 19, 2014 Accepted: May 14, 2014 Published: May 28, 2014 2075

dx.doi.org/10.1021/je500265v | J. Chem. Eng. Data 2014, 59, 2075−2086

Journal of Chemical & Engineering Data

Article

Table 1. Specifications of Chemical Samples of Solutes

a

chemical name

formula

CAS RN

supplier

mass fraction puritya

mass fraction of waterb

15-crown-5 (1,4,7,10,13-Pentaoxacyclopentadecane) 18-crown-6 (1,4,7,10,13,16-Hexaoxacyclooctadecane)

C10H20O5 C12H24O6

33100-27-5 17455-13-9

Sigma-Aldrich Fluka

0.98 > 0.99

0.0031

Declared by the supplier. bDetermined by the Karl Fischer method.

molar volumes) 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 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, i.e., ρ = Δρ(experimental) + ρ1(NIST) and c = Δc(experimental) + c1(NIST) as needed for the evaluation of standard molar isentropic compressions. The values ρ1 and c1 extracted from the NIST database7 are summarized in Table 2.

corrections to the content of water in the sample of pure liquid 15-crown-5 ether determined by the Karl Fischer method (Table 1) were applied for calculations of molalities. The vibrating-tube densimeter and sound analyzer 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 cells5 of the DSA 5000 device and temperature was scanned in the entire experimental interval from (278.15 to 343.15) K with 5 K wide steps. With the isoplethal regime the consumption of the samples was much lower compared to the isothermal regime performed using an automated sampler,6 since there was no need to ensure the complete washing-out the previous sample by a sufficient amount of the filled sample. To prevent the formation of bubbles of the dissolved air at elevated temperatures the solutions were partly degassed by decreasing the pressure in the closed syringe (by moving the piston backward) and shaking off the air bubbles immediately prior to filling the sample. Measurement of each solution was “bracketed” by measurements of pure water (degassed in the same way as the samples of solutions) 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, respectively, measured between two measurements of water. The measured differences Δρ and Δc were regarded as direct experimental data and are tabulated below (Tables 3 and 4). The effect of degassing (see above) on Δρ and Δc was also examined by measurements of aerated solutions and water in a limited temperature range from (278.15 to 313.15) K. Small shifts in densities and speeds of sound (0.002 kg·m−3 and 0.04 m·s−1 in average) were observed, the deviations in Δρ and Δc were in the limits of the reproducibility. 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). Densities measured at 278.15 K were by about 0.007 kg·m−3 lower that the NIST values and greater by about 0.008 kg·m−3 at 343.15 K with approximately linear course of deviations between the end-point temperatures; the deviations slightly exceed the uncertainty 0.005 kg·m−3 declared by the DSA 5000 manufacturer. Positive deviations between the measured and NIST values of speed of sound exhibited an Sshaped course with a minimum about 0.05 m·s−1 around 288 K and a maximum 0.35 m·s−1 around 338 K; the deviations are within the uncertainty limit 0.5 m·s−1 declared by the manufacturer. The effect of these small deviations on the goal quantities (standard molar isentropic compressions, standard

Table 2. Values of Density ρ1 of and Speed of Sound c1 in Water (NIST)7 Used in Calculations of Standard Molar Isentropic Compression and Standard Molar Volume T/K

ρ1/kg·m−3

c1/m·s−1

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

999.967 999.702 999.103 998.207 997.048 995.649 994.033 992.216 990.213 988.035 985.693 983.196 980.551 977.765

1447.27 1465.93 1482.35 1496.70 1509.15 1519.85 1528.90 1536.45 1542.58 1547.39 1550.97 1553.40 1554.75 1447.27

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 3 and 4, 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

a ⎞ 1⎛ ⎜⎜M 2 − V ⎟⎟ ρ1 ⎝ ρ1 ⎠

(1)

Vapp m,2

where M2 is the molar mass, apparent molar volume, and m2 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) The values of the coefficients aV and bV obtained by using a least-squares method with unit weights are recorded in Table 5 along with the calculated standard molar volumes and estimated uncertainties. 3.3. Standard Molar Isentropic Compressions. Partial molar isentropic compression at infinite dilution (standard 2076



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Table 3. Experimental Differences in Density Δρ = ρ − ρ1 Measured at Various Temperatures T and molalities m2 for 15Crown-5 (aq) and 18-Crown-6 (aq) at Atmospheric Pressurea m2/mol·kg−1

Δρ/kg·m−3

T/K = 0.055 724 0.101 838 0.176 907 0.229 722 0.298 682 T/K = 0.055 724 0.101 838 0.176 907 0.229 722 0.298 682

278.15 2.101 3.821 6.572 8.485 10.950 313.15 1.817 3.296 5.654 7.282 9.372

283.15 2.045 3.717 6.393 8.249 10.642 318.15 1.789 3.243 5.562 7.164 9.217

T/K = 0.051 773 0.091 089 0.151 327 0.206 616 0.278 466 T/K = 0.051 773 0.091 089 0.151 327 0.206 616 0.278 466

278.15 2.327 4.073 6.721 9.112 12.166 313.15 2.028 3.541 5.827 7.881 10.494

283.15 2.269 3.970 6.545 8.870 11.841 318.15 1.999 3.488 5.735 7.755 10.322

15-Crown-5 (aq) 288.15 1.997 3.626 6.235 8.043 10.371 323.15 1.764 3.195 5.478 7.054 9.072 18-Crown-6 (aq) 288.15 2.217 3.877 6.393 8.662 11.555 323.15 1.970 3.437 5.649 7.636 10.160

293.15 1.953 3.549 6.096 7.861 10.132 328.15 1.738 3.149 5.396 6.947 8.933

298.15 1.915 3.476 5.970 7.696 9.917 333.15 1.713 3.106 5.321 6.846 8.801

303.15 1.879 3.412 5.856 7.548 9.720 338.15 1.692 3.064 5.245 6.751 8.676

308.15 1.847 3.352 5.751 7.410 9.540 343.15 1.670 3.022 5.177 6.659 8.557

293.15 2.173 3.798 6.259 8.478 11.305 328.15 1.940 3.386 5.566 7.522 10.005

298.15 2.132 3.726 6.138 8.310 11.077 333.15 1.914 3.341 5.488 7.413 9.855

303.15 2.095 3.659 6.028 8.156 10.869 338.15 1.890 3.294 5.412 7.308 9.713

308.15 2.062 3.599 5.923 8.013 10.673 343.15 1.863 3.251 5.337 7.206 9.576

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). a

volume of 15-crown-5 ether is rather scarce.9−15 Our value at T = 298.15 K agree within the experimental uncertainties with standard molar volumes reported by Tyczyńska and Józw ́ iak10 15 and Høiland. At other temperatures the deviations are greater than the experimental uncertainties being both negative9,11−14 and positive.10 Our experimental data for temperatures (288.15, 298.15, and 313.15) K were tentatively recalculated using molalities uncorrected with respect to the content of water in the sample of pure 15-crown-5 ether (see Table 1) and standard molar volumes by 0.11 cm3·mol−1 higher were obtained. The values were still lower than literature data9,11−14 but more close being within the limits of experimental uncertainties. Thus, it seem likely that one of the reasons for observed negative deviations might be the presence of small amounts of water in solute samples despite that some authors13 mentioned drying. On the other hand, rather large positive deviations from data10 at temperatures other than 298.15 K are difficult to explain. A larger number of published values were found for standard molar volumes of aqueous 18-crown-6 ether. Few papers present values for temperatures other than 298 K; our standard molar volumes in the low temperature range are systematically greater, the deviations are slightly above the experimental uncertainties. Our values in the range from (293.15 to 308.15) K agree perfectly with data published recently by Tyczyńska and Józw ́ iak.17 Larger deviations from data by Kolhapurkar et 18 al. are observed in the entire temperature range. Smoothed values calculated from the equation presented by Niederhauser et al.16 agree, with the exception of the lowest temperatures, with our values within the estimated experimental uncertainties,

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 app ⎞ ⎛ ∂V 0 ⎞ ⎛ −∂V m,2 m,2 ⎟ KS0,m,2 = lim ⎜ ⎟ = −⎜⎜ m2 → 0⎝ ∂p ⎠ ∂p ⎟⎠ ⎝ S S

(3) 6

Based on this definition it is possible to derive the expression for standard molar isentropic compression KS0,m,2 =

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

(4)

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

(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 5 along with calculated values of K0S,m,2. Uncertainties σ(K0S,m,2) are affected mainly by the uncertainty in the speed of sound which was estimated to be about ± 0.1 m·s−1.

4. DISCUSSION 4.1. Comparison with Data in Literature. Measured standard molar volumes are compared in Table 6 with the values found in the literature. Information on standard molar 2077



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Table 4. Experimental Differences in Speed of Sound Δc = c − c1 Measured at Various Temperatures T and molalities m2 for 15Crown-5 (aq) and 18-Crown-6 (aq) at Atmospheric Pressurea m2/mol·kg−1

Δc/m·s−1

T/K = 0.055 724 0.101 838 0.176 907 0.229 722 0.298 682 T/K = 0.055 724 0.101 838 0.176 907 0.229 722 0.298 682

278.15 9.43 17.10 29.32 37.69 48.48 313.15 5.10 9.25 15.82 20.27 25.93

283.15 8.64 15.65 26.85 34.48 44.33 318.15 4.66 8.44 14.40 18.40 23.59

T/K = 0.051 773 0.091 089 0.151 327 0.206 616 0.278 466 T/K = 0.051 773 0.091 089 0.151 327 0.206 616 0.278 466

278.15 11.09 19.27 31.59 42.72 56.83 313.15 6.09 10.61 17.33 23.36 31.03

283.15 10.17 17.66 28.96 39.14 52.08 318.15 5.60 9.72 15.83 21.33 28.32

15-Crown-5 (aq) 288.15 7.94 14.33 24.58 31.59 40.60 323.15 4.25 7.66 13.07 16.68 21.37 18-Crown-6 (aq) 288.15 9.35 16.24 26.58 35.93 47.82 323.15 5.11 8.84 14.40 19.41 25.75

293.15 7.26 13.16 22.53 28.93 37.17 328.15 3.83 6.90 11.79 15.05 19.29

298.15 6.66 12.05 20.66 26.50 34.04 333.15 3.45 6.21 10.60 13.52 17.32

303.15 6.11 11.06 18.91 24.26 31.15 338.15 3.08 5.56 9.48 12.06 15.46

308.15 5.57 10.09 17.28 22.19 28.47 343.15 2.74 4.96 8.39 10.66 13.66

293.15 8.58 14.93 24.42 33.01 43.88 328.15 4.65 8.01 13.05 17.59 23.31

298.15 7.87 13.71 22.46 30.30 40.32 333.15 4.21 7.24 11.78 15.87 21.01

303.15 7.22 12.60 20.60 27.83 37.00 338.15 3.79 6.50 10.55 14.22 18.81

308.15 6.61 11.55 18.90 25.52 33.91 343.15 3.38 5.79 9.40 12.64 16.69

Standard uncertainties are u(T) = 0.01 K, u(m2) = 3·10−5 mol·kg−1, and the combined expanded uncertainty is Uc(Δc) = 0.1 m·s−1 (level of confidence = 0.95). a

Compared to 15-crown-5 ether one more source18 of standard molar isentropic compression at 298.15 K is available for 18-crown-6 ether, the value disagrees with both the measured value and the data from other sources.9,12,13 Agreement of other published values with the measurements in this work can be regarded as very satisfactory except for T = 313.15 K where the deviation −3.4 cm3·mol−1·GPa−1 is observed. 4.2. Dependences of Standard Molar Volumes on Temperature. The dependences themselves would not show anything interesting, just the differences related to the different numbers of (−CH2−CH2−O−) segments. The courses of the V0m,2(T) dependences indicate, however, concave shape at low temperatures and therefore the examination of the relative change of standard molar volume with respect to unit change of temperature in the form of the analogue of isobaric thermal expansivity α0p,2 = (1/V0m,2)(∂V0m,2/∂T)p is more interesting. Figure 1 presents a plot of α0p,2 for both crown ethers evaluated from the three-order polynomial fits of values in Table 5 along with the values for lower cyclic ethers obtained for p = 0.1 MPa from the V0m,2(T,p) fits.2 The lines are denoted by n-m marks where n is the number of the members of the cycle (methylene groups, ether oxygen atom) and m is the number of oxygen atoms. Thus, the ratio m/n expresses relative portion of hydrophilic part of the molecule. Obviously the ethers with low ratio m/n (oxolane, 5−1; oxane, 6−1) exhibit distinctly different course of α0p,2(T) compared to ethers with larger m/ n. The relations between the ether molecular structure and the shape of V0m,2(T) dependence have been already discussed in more detail in the previous papers.1,2 The present results show

the deviations are positive in the low temperature range and negative at higher temperatures. The effect of the difference in experimental pressure is, in regard to uncertainties of Niederhauser measurements,16 negligible. Literature values of standard molar volume at T = 298.15 K cover rather large interval 2 cm3·mol−1 wide. Our value is in the middle of this interval, the deviations lower than 0.1 cm3·mol−1 are observed for data.9,11,15,17,20,21 Bakshi et al.21 examined the effect of drying 18-crown-6 ether on standard molar volume and found out that drying the solute resulted in lower values of standard molar volume. This observation is related to the positive value of the parameter aV, i.e., the presence of water in the solute would cause lower value of aV and consequently higher value of standard molar volume (see eq 1). The value measured at T = 298.15 K agrees perfectly with that obtained by Bakshi et al.21 for dried solute sample. On the other hand, the explanation of lower values is, similarly as with 15-crown-5 ether, uncertain. Table 7 presents a comparison of measured standard molar isentropic compressions with data published in the literature. Three sources9,12,13 of data for aqueous 15-crown-5 ether were found. Deviations at T = (288.15 and 313.15) K are slightly higher than estimated uncertainties, largest one is observed at T = 313.15 K. Similarly as with standard molar volumes tentative calculations were performed using “uncorrected” molalities and standard molar isentropic compressions higher by (0.3 to 0.4) cm3·mol−1·GPa−1 were obtained which are closer to the published values at T = (288.15 and 313.15) K while the deviation for the measured value at T = 298.15 K remains within the uncertainty limits. 2078



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Table 5. 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 {15-Crown-5 (2) or 18-Crown-6 (2) + Water (1)}a T K

a

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

37.946 36.942 36.078 35.314 34.620 33.993 33.407 32.880 32.369 31.919 31.454 31.034 30.641 30.245

−4.3543 −4.4462 −4.5991 −4.7099 −4.8137 −4.9076 −4.9670 −5.0833 −5.1136 −5.2451 −5.2434 −5.3153 −5.4184 −5.4239

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

45.236 44.110 43.114 42.271 41.484 40.771 40.139 39.495 38.934 38.382 37.806 37.311 36.837 36.335

−5.5192 −5.6999 −5.7977 −6.0275 −6.1295 −6.2615 −6.5502 −6.5365 −6.7442 −6.8632 −6.7631 −6.9110 −7.0700 −7.0266

aK · 10−12

V0m,2 ± σ (V0m,2)

bV −1

kg ·m ·mol 2

cm ·mol 3

−1

−4 −2

bK·10−12 −1

kg ·m ·s ·mol 3

15-Crown-5 (aq) ± 0.06 ± 0.05 ± 0.05 ± 0.05 ± 0.05 ± 0.05 ± 0.05 ± 0.05 ± 0.05 ± 0.05 ± 0.05 ± 0.05 ± 0.06 ± 0.06 18-Crown-6 (aq) 219.09 ± 0.06 220.26 ± 0.06 221.36 ± 0.06 222.37 ± 0.06 223.37 ± 0.06 224.34 ± 0.06 225.28 ± 0.06 226.27 ± 0.06 227.22 ± 0.06 228.20 ± 0.06 229.24 ± 0.05 230.24 ± 0.05 231.25 ± 0.06 232.32 ± 0.05 182.32 183.37 184.32 185.22 186.09 186.94 187.78 188.59 189.43 190.23 191.09 191.92 192.76 193.64

−4 −2

K0S,m,2 ± σ (K0S,m,2) −2

kg ·m ·s ·mol 4

cm3·mol−1·GPa−1

0.6420 0.6076 0.5756 0.5442 0.5140 0.4862 0.4573 0.4317 0.4070 0.3829 0.3582 0.3350 0.3130 0.2919

−0.0369 −0.0418 −0.0481 −0.0501 −0.0513 −0.0561 −0.0519 −0.0556 −0.0600 −0.0631 −0.0597 −0.0583 −0.0577 −0.0583

−46.9 −33.4 −22.4 −12.9 −4.7 2.2 8.7 14.2 19.2 23.9 28.5 32.8 36.8 40.7

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.4 0.5 0.5

0.8002 0.7579 0.7183 0.6799 0.6424 0.6066 0.5726 0.5414 0.5118 0.4811 0.4513 0.4225 0.3951 0.3677

−0.0504 −0.0564 −0.0625 −0.0661 −0.0642 −0.0639 −0.0653 −0.0724 −0.0820 −0.0829 −0.0827 −0.0820 −0.0833 −0.0809

−63.5 −46.7 −32.9 −21.1 −10.8 −1.9 5.9 12.6 18.7 24.6 30.2 35.5 40.5 45.5

± ± ± ± ± ± ± ± ± ± ± ± ± ±

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

The uncertainties σ(V0m,2) and σ(K0S,m,2) represent the combined expanded uncertainties.

employed for the evaluations of group contributions to estimate standard molar volumes (first in the low pressure range1 and then extended to wide ranges of temperature and pressure2) and standard molar isentropic compressions at p = 0.1 MPa.3 In the case of volumes it was observed1 that predictions toward large cycles (n = 12, 15, 16) show, as could be expected, increasing deviations from the experiment with increasing size of the cycle. No such test was performed for standard molar isentropic compression due to lack of sufficient set of experimental values for large cycles. Results obtained for predictions of standard molar quantities of crown ethers using group contributions for volumes2 (smoothed contributions) and isentropic compressions3 (discrete contributions evaluated for each experimental temperature) are compared with the experimental data either obtained in this work (15-crown-5, 18crown-6) or taken from the literature (12-crown-4) in Figures 3 and 4. Obviously the deviations exhibit a monotonous trends within the homologous series, large values are a consequence of the extrapolations from the narrow range of lower cycles (n = 5, 6) toward the macrocycles. New group contributions were evaluated using an extended set of data consisting of the previously measured values1−3 for oxolane, oxane, and 1,4-dioxane combined with data measured in this work. Data for 1,3-dioxolane were omitted since it was proved that the structure −O−CH2−O− requires particular structural contribution,1−3 and thus, if one solute only having

that lines for large cycles 15−5 and 18−6 follow the pattern observed for solutes with higher ratio m/n (both crown ethers have the same value of m/n as 1,4-dioxane, 6−2). 4.3. Dependences of Standard Molar Isentropic Compression on Temperature. Since the discussion on the K0S,m,2(T) dependences of lower cyclic ethers has been already presented3 the available experimental values for the solute series (−CH2−CH2−O−)m only are shown in Figure 2. Experimental data obtained in this work are supplemented with both the values obtained previously for 1,4-dioxane3 and the data found in the literature for 12-crown-4 ether: Bernal et al.9 in the range from (288.15 to 313.15) K and values9,12,13 in the interval from (−0.2 to 1.2) cm3·mol−1·GPa−1 at T = 298.15 K. The K0S,m,2(T) dependence for 12-crown-4 ether is nearly linear while the curves for other ethers are distinctly concave; a question concerning the reliability of data may thus arise which is discussed in relation to group contribution predictions below. Except for the value reported for 12-crown-4 ether at T = 313.15 K9 the dependences for all four solutes (m = 2, 4, 5, 6) follow monotonous trends within the homologous series crossing each other at temperature around 320 K. The phenomenon of crossing the temperature dependences has been observed also for some other homologous series as aliphatic diols and triols.27,28 4.4. Group Contribution Predictions. Previously measured data for lower cyclic ethers1−3 (n = 5, 6) has been already 2079



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Table 6. Comparison of Standard Molar Volumes Measured in This Work with Data Taken from the Literature T

V0m,2 (this work)

V0m,2 (lit)

K

cm3·mol−1

cm3·mol−1

288.15 293.15 298.15

184.32 ± 0.05 185.22 ± 0.05 186.09 ± 0.05

303.15 308.15 313.15

186.94 ± 187.78 ± 188.59 ±

278.15 283.15 288.15

219.09 ± 220.26 ± 221.36 ±

293.15

222.37 ±

295.15 297.15 298.15

222.76b 223.15b 223.37 ±

15-Crown-5 (aq) 184.60 ± 0.3 185.02 ± 0.04 186.50 ± 0.3 186.46 ± 0.05 186.40 ± 0.3 186.30 186.22 186.06 ± 0.1 186.02 ± 0.02 0.05 186.79 ± 0.02 0.05 187.59 ± 0.01 0.05 189.00 ± 0.3 18-Crown-6 (aq) 0.06 218.55 ± 0.3d 0.06 219.86 ± 0.3d 0.06 221.01 ± 0.3d 220.90 ± 0.3 0.06 222.30 ± 0.02 222.10 ± 0.3d 221.63c 222.01c 222.47c 0.06 224.40 ± 0.5 223.60 ± 0.3 223.40 223.35 ± 0.1 223.35 ± 0.05 223.35 ± 0.03 223.33 ± 0.06 223.30 ± 0.3

Deva

T

V0m,2 (this work)

V0m,2 (lit)

ref

cm3·mol−1

K

cm3·mol−1

cm3·mol−1

9 10 9 11 12 13 14 15 10 10 10 9

−0.28 0.20 −0.41 −0.37 −0.31 −0.21 −0.13 0.03 0.07 0.22 0.19 −0.41

16 16 16 9 17 16 18 18 18 19 12 20 15 17 21 11 9

0.54 0.39 0.35 0.46 0.07 0.27 0.74 0.75 0.68 −1.03 −0.23 −0.03 0.02 0.02 0.02 0.04 0.07

299.15 301.15 303.15

223.54b 223.93b 224.34 ±

308.15

225.28 ±

313.15

226.27 ±

318.15 323.15 328.15 333.15 338.15 343.15

227.22 228.20 229.24 230.24 231.25 232.32

± ± ± ± ± ±

18-Crown-6 (aq) 223.20 223.17 223.16 ± 0.3d 223.16c 223.03 222.54 ± 0.77 222.50 ± 0.3 222.40 ± 0.3 223.29c 223.88c 0.06 224.38 ± 0.05 224.21 ± 0.3d 224.04c 0.06 225.28 ± 0.05 225.25 ± 0.3d 225.04c 0.06 226.28 ± 0.3d 226.10 ± 0.3 226.01c 0.06 227.31 ± 0.3d 0.06 228.33 ± 0.3d 0.05 229.36 ± 0.3d 0.05 230.38 ± 0.3d 0.06 231.40 ± 0.3d 0.05 232.42 ± 0.3d

Deva ref

cm3·mol−1

13 22 16 18 23 24 25 26 18 18 17 16 18 17 16 18 16 9 18 16 16 16 16 16 16

0.17 0.20 0.21 0.21 0.34 0.83 0.87 0.97 0.25 0.05 −0.04 0.13 0.30 0.00 0.03 0.24 −0.01 0.17 0.26 −0.09 −0.13 −0.12 −0.14 −0.15 −0.10

a

Deviation between this work and the literature value. bInterpolated by a polynomial interpolation. cValues were obtained by the present method using published densities. dAt p = 0.35 MPa, calculated from fitting equation.

Table 7. Comparison of Standard Molar Isentropic Compressions Measured in This Work with Data Taken from the Literature T

K0S,m,2 (this work)

K

cm ·mol ·GPa 3

−1

−1

288.15 298.15

−22.4 ± 0.5 −4.7 ± 0.4

313.15

14.2 ± 0.3

288.15 298.15

−32.9 ± 0.5 −10.8 ± 0.2

313.15

12.6 ± 0.2

Deva

K0S,m,2 (lit) −1

−1

cm ·mol ·GPa 3

15-Crown-5 (aq) −20.8 ± 0.8 −5.2 −5.2 ± 0.8 −5.7 ± 0.8 16.9 ± 0.8 18-Crown-6 (aq) −32.0 ± 0.8 −10.5 −11.0 ± 0.8 −12.4 ± 0.8 −17.0b 16.0 ± 0.8

ref

cm ·mol−1·GPa−1

9 13 9 12 9

−1.6 0.5 0.5 1.0 −2.7

9 13 9 12 18 9

−0.9 −0.3 0.2 1.6 6.2 −3.4

3

Deviation between this work and the literature value. bValue −18 cm3·mol−1·GPa−1 was obtained by the present method using published densities and sound speeds. a

Figure 1. Plot of α0p,2 = (1/V0m,2)(∂V0m,2/∂T)p against temperature T. 5−1, oxolane;2 6−1, oxane;2 5−2, 1,3-dioxolane;2 6−2, 1,4-dioxane;2 6−3, 1,3,5-trioxane;2 15−5, 15-crown-5; 18−6, 18-crown-6.

the structure −O−CH2−O− in its molecule is included in the data set, the inclusion of the contribution for this structure does not affect the group contributions for other groups. Similarly the data for 1,3,5-trioxane were not employed due to uncertain 2080



Article

Figure 2. Plot of experimental values of standard molar isentropic compression K0S,m,2 against temperature T. The lines are to aid the eye. ●, 6−2, 1,4-dioxane;3 ■, 12−4, 12-crown-4;9,12,13 ▲, 15−5, 15-crown5; Δ, 18−6, 18-crown-6.

Figure 4. Plot of deviations between predicted and experimental standard molar isentropic compressions ΔK0S,m,2 = K0S,m,2 (predicted) − K0S,m,2 (experimental) against temperature T. Nonsmoothed contributions3 were used for predictions. The lines are to aid the eye. ■, 12−4, 12-crown-4;9,12,15 ▲, 15−5, 15-crown-5; Δ, 18−6, 18-crown-6.

respectively. Values of contributions at each experimental temperature were obtained using the weighted least-squares method by minimizing the objective function 0 0 0 , Y m,CH , Y m,O ) ϕ(Y m,c 2 0 0 0 0 ⎧ ⎫2 ⎪ (Y m,2)exp , i − [Y m,c + (ni − mi )Y m,CH + mi Y m,O] ⎪ 2 ⎬ 0 ⎪ ⎪ )i σ(Y m,2 ⎭ i=1 ⎩ Ns

=

∑⎨

(7)

where the summation is performed over all solutes (Ns = 5) and σ(Y0m,2)i is the experimental uncertainty of the property Y0m,2 of ith solute. “Experimental” values of standard molar volumes for oxolane, oxane, and 1,4-dioxane were generated from polynomial T,p fits2 for p = 0.1 MPa and experimental temperatures of this work. Uncertainties were derived from the uncertainties estimated for original experimental values.1,2 Temperature set of standard molar isentropic compression is identical with the experimental one3 (278.15, 283.15, 288.15, 293.15, 298.15, and 318.15) K. Values of group contributions obtained from eq 6 are recorded in the upper part of Table 8. Deviation plots analogous to those in Figures 3 and 4 are shown in Figures 5 and 6. It should be noted that values shown in Figures 3 and 4 are true predictions while the deviations shown in Figures 5 and 6 represent, except for 12-crown-4 ether, the results of back calculations. Standard molar volumes of lower cycles (oxolane, oxane, 1,4dioxane) exhibit, with an exception for oxane at low temperatures, deviations within ± 0.5 cm−3·mol−1 (Figure 5). Compared to true predictions (Figure 3) the deviations for macrocycles (15−5, 18−6) naturally decreased in magnitude, being, however, 1 cm−3·mol−1 and of the opposite sign. Temperature has a moderate influence on the deviations. True predictions for 12-crown-4 ether worsened, deviations from the experiment are in the interval from (1 to 2) cm−3·mol−1 compared to ± 1 cm−3·mol−1 in Figure 3. Extrapolations

Figure 3. Plot of deviations between predicted and experimental 0 0 0 = V m,2 (predicted) − V m,2 standard molar volumes, ΔV m,2 (experimental) against temperature T. Smoothed values of group contributions2 were used for predictions. The lines are to aid the eye. ■, 12−4, 12-crown-4;9,11−13,15 ▲, 15−5, 15-crown-5; Δ, 18−6, 18crown-6.

mutual correlation of three structures −O−CH2−O−.2,3 The group additivity scheme for the property Y0m,2 (Y = V or KS) is identical with the previous one1−3 0 0 0 0 (Y m,2 )calc = Y m,c + (n − m)Y m,CH + mY m,O 2

(6)

where the subscripts c, CH2, and O denote the contributions for covolume, methylene group, and ether oxygen atom, 2081



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Table 8. Values of Group Contributions T

V0m,c

V0m,O

V0m,cycle

K0S,m,c

−1

cm ·mol 3

K

a

V0m,CH2

̀

K0S,m,CH2

K0S,m,O −1

cm ·mol ·GPa 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

8.997 9.221 9.450 9.678 9.902 10.110 10.335 10.522 10.714 10.894 10.873 11.057 11.407 11.431

15.691 15.661 15.635 15.622 15.621 15.635 15.653 15.687 15.730 15.782 15.893 15.958 15.973 16.091

3.496 3.687 3.884 4.041 4.173 4.273 4.358 4.419 4.461 4.487 4.471 4.475 4.550 4.519

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

9.619 9.822 10.048 10.265 10.487 10.690 10.905 11.105 11.290 11.483 11.639 11.836 12.019 12.193

15.409 15.376 15.351 15.344 15.344 15.360 15.383 15.411 15.457 15.503 15.566 15.625 15.696 15.773

3.937 4.169 4.363 4.512 4.642 4.737 4.815 4.886 4.923 4.959 4.979 4.991 4.984 4.977

K0S,m,cycle

−1

Contributions in eq 6 14.950 16.914 17.268 18.357 19.082

−7.968 −7.069 −5.590 −4.769 −3.738

3.194 3.745 2.986 3.057 2.549

(21.012)a 21.435

(−1.239)a −0.549

(1.252)a 0.642

−7.603 −6.707 −5.303 −4.524 −3.515

2.518 3.146 2.511 2.705 2.235

−0.1002 −0.0870 −0.0690 −0.0607 −0.0443

(−1.158)a −0.502

(1.141)a 0.574

(−0.0131)a −0.0040

Contributions in eq 8 0.0641 14.442 0.0623 16.290 0.0620 16.774 0.0608 17.819 0.0606 18.551 0.0600 0.0591 0.0604 (20.754)a 0.0596 21.301 0.0610 0.0622 0.0633 0.0631 0.0646

Interpolated values (2nd order polynomial) used for prediction of K0S,m,c for 12-crown-4 ether (see Figures 6 and 8).

contributions (upper part of Table 8, eq 6) result in lower deviations as shown in Figure 6. Compared to volumes an opposite trend of deviations with respect to the cycle size can be observed: positive deviations for small (n = 5) and large (n = 18) cycles and negative ones for the middle range (n = 6, 12, 15). Similarly as with volumes the results indicate a need for a structural parameter related to the size of the cycle. Deviations of values predicted (true predictions) for 12-crown-4 ether from the experiment9,12,13 exhibit rather peculiar dependence on temperature with large negative deviations for T = (288.15 and 313.15) K. Somewhat speculative considerations might lead to the conclusion that the experimental values9 for temperatures (288.15 and 313.15) K are too large, i.e., lower values (more negative one for T = 288.15 K; less positive one for T = 313.15 K) would result in smaller deviations in Figure 6 and fit better to the character of the concave K0S,m,2(T) dependences observed for other solutes (see Figure 2). An attempt to incorporate the effect of the size of cycle has been performed. As follows from Figures 5 and 6 the dependences of deviations on n are not monotonous and therefore an addition of the term depending linearly on n would not be a solution. Since the deviations are moderately dependent on temperature (less dependent for volumes, more dependent for compressions) the sum of deviations shown in Figures 5 and 6 (bias) was calculated for each solute 0 0 and each quantity (Vm,2 , KS,m,2 ) over the experimental temperature range and the resulting values of bias were

toward very small cycles (oxirane, 3−1; oxetane, 4−1) also worsened when compared to predictions based on group contributions evaluated from data for cycles with n = 5 and 61,2 as can be seen in Table 9. Deviations observed for oxepane (7− 1) are also larger when present group contributions (Table 8, eq 6) are used. Based on the above observations it seems likely that due to larger flexibility of macrocyclic chains and accommodation of water molecules inside the cycles the assumption of group additivity is fulfilled in a lesser extent compared to the solute series with similar size. Regardless of the lack of data for very small cycles in wider temperature ranges it can be concluded that negative deviations are observed for both the small (n = 3, 4, 5) and large (n = 18) cycles while for n around a middle of the range (n = 6, 7, 12, 15) predicted values are greater than experimental ones. Thus, a structural contribution reflecting the size of the cycle might improve the performance of the group additivity scheme. Somewhat similar situation is observed for standard molar isentropic compression. Values calculated (predicted) for crown ethers using previous group contributions3 lead to large deviations (Figure 4) which are, however, strongly dependent on temperature. Rather large scatter of the data points for 15-crown-5 and 18-crown-6 ethers is caused by the fact that the three contributions K0S,m,c, K0S,m,CH2, and K0S,m,O were evaluated using data for three solutes (for details see ref 3), i.e., no averaging over larger set of solutes was performed. New 2082



Article 0 0 0 0 (Y m,2 )calc = Y m,c + (n − m)Y m,CH + mY m,O 2 0 + fY (n)Y m,cycle , Y = V or KS

(8)

After normalization to the unit value of the parameter of the quadratic term, two very close functions, f V(n) = n2 − 22.4278n + 95.3097 and f Ks(n) = n2 − 22.4934n + 94.7143 were obtained. This might seem surprising but V0m,2 and K0S,m,2(T) are mutually related through eq 3. If the effect of the cycle size is manifested in the similar way for both quantities then the function f(n) can be identical and K0S,m,cycle = −(∂V0m,cycle/∂p)S. The differences between the functions f V(n) and f Ks(n)are small and therefore the average function fV (n) = fK (n) = n2 − 22.4606n + 95.0120 S

(9)

was used for both standard molar quantities in all subsequent calculations. The use of eq 9 brings no substantial differences in results compared to their separate use for particular standard molar quantities. Group contributions Y0m,c, Y0m,CH2, Y0m,O, and 0 Ym,cycle in eq 8 combined with eq 9 were obtained by minimizing the objective function analogous to eq 7 and are recorded in the lower part of Table 8. The deviation plots are shown in Figures 7 and 8. Introduction of the term related to the size of the cycle does not lead to dramatic changes of values of group contributions (see also Figures 9 and 10 and the discussion below) but significant improvement of the agreement between calculated and experimental values is obvious. Also the true predictions calculated for 12-crown-4 ether are in much better agreement with the experiment, particularly perfect for values at T = 298.15 K. Deviations in volumes for other temperatures are quite satisfactory. Large deviations in compressions for T = (288.15 and 313.15) K appear here and some doubts concerning the experimental values9 may arise as already discussed above in relation to Figure 6. Extrapolation of function f(n) down to n < 5 leads to larger deviations compared to both the previous group contributions1 and contributions related to eq 6 as can be seen from Table 9. Due to lack of experimental data the extrapolations toward n > 18 cannot be examined. Interpolation for oxepane (n = 7) leads to calculated standard molar volume which is slightly closer to the experiment than that predicted using both the contributions1 and eq 6. Contributions V0m,cycle and K0S,m,cycle are of the opposite sign which is a s consequence of opposite trends of deviations with n when applying eq 6 (Figures 5 and 6). Unlike K0S,m,cycle, the contribution V0m,cycle exhibits very moderate dependence on temperature as follows from Table 8. It was verified that the use of the constant value averaged over the experimental temperature range V0m,cycle = 0.06164 cm3·mol−1 results in nonsignificant changes of calculated standard molar volumes. Then the volume correction reflecting the size of the cycle (last term in eq 8) is temperature independent. This is not the case for compressions, obviously due to stronger temperature dependency of deviations when applying eq 6 (Figure 6). Any group additivity scheme issues from the assumption that a value of the particular property (standard molar volume and standard molar isentropic compression in this case) can be assigned to a particular segment of the molecule (atom or group of atoms) independently of the surrounding segments. Since this assumption is fulfilled in a more or less extent (depending on the order of the group additivity approach) the values of group contributions are dependent on definitions of

Figure 5. Plot of deviations between predicted and experimental 0 0 0 = V m,2 (predicted) − V m,2 standard molar volumes, ΔV m,2 (experimental) against temperature T. Values of group contributions from Table 8 (eq 6) were used for predictions. The lines are to aid the eye. ○, 5−1, oxolane;2 ●, 6−1, oxane;2 □, 6−2, 1,4-dioxane;2 ■, 12− 4, 12-crown-4;9,11−13,15 ▲, 15−5, 15-crown-5; Δ, 18−6, 18-crown-6.

Figure 6. Plot of deviations between predicted and experimental standard molar isentropic compressions ΔK0S,m,2 = K0S,m,2 (predicted) 0 (experimental) against temperature T. Values of group −KS,m,2 contributions from Table 8 (eq 6) were used for predictions. The lines are to aid the eye. ○, 5−1, oxolane;3 ●, 6−1, oxane;3 □, 6−2, 1,4-dioxane;3 ■, 12−4, 12-crown-4;9,12,15 ▲, 15−5, 15-crown-5; Δ, 18−6, 18-crown-6.

correlated with n using a quadratic function f(n). This function was then employed for the additional term in the group additivity scheme, i.e., 2083



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Table 9. Comparison of Predicted and Experimental Values of Standard Molar Volumes of Small Cyclic Solutes

a

T

V0m,2(exp) cm ·mol

solute

n−m

K

oxirane oxetane

3−1 4−1

283.15 298.15

oxepane

7−1

298.15

3

−1

45.42 61.40 ± 0.20 61.35 ± 0.01 104.10 ± 0.60 105.46 ± 0.02

Deva ref 1

cm ·mol 3

ref 29 30 31 30 31

Deva eq 6

−0.03 0.12 0.17 2.96 1.60

−1.19 −0.46 −0.41 3.70 2.34

Deva eq 8

−1

1.60 1.04 1.09 2.29 0.93

Deviation between predicted and experimental value.

Figure 7. Plot of deviations between predicted and experimental standard molar volumes, ΔV0m,2 = V0m,2(predicted) − V0m,2 (experimental) against temperature T. Values of group contributions from Table 8 (eq 8) were used for predictions. The lines are to aid the eye. ○, 5−1, oxolane;2 ●, 6−1, oxane;2 □, 6−2, 1,4-dioxane;2 ■, 12−4, 12crown-4;9,11−13,15 ▲, 15−5, 15-crown-5; Δ, 18−6, 18-crown-6.

Figure 8. Plot of deviations between predicted and experimental standard molar isentropic compressions ΔK0S,m,2 = K0S,m,2 (predicted) − 0 (experimental) against temperature T. Values of group KS,m,2 contributions from Table 8 (eq 8) were used for predictions. The lines are to aid the eye. ○, 5−1, oxolane;3 ●, 6−1, oxane;3 □, 6−2, 1,4-dioxane;3 ■, 12−4, 12-crown-4;9,12,15 ▲, 15−5, 15-crown-5; Δ, 18−6, 18-crown-6.

the segments, the character of the compounds (solutes) and the extent of the experimental data set employed for the evaluation of contributions. Figures 9 and 10 present comparisons of the contributions of the methylene group and ether oxygen atom obtained in this work for the extended set of cyclic ethers (n = 5, 6, 15, 18) with those evaluated previously2,3 for limited set of cyclic ethers (n = 5, 6). Values for the contributions obtained for noncyclic (open-chain) aliphatic aqueous solutes (dashed lines in the figures) taken from the literature are shown for a comparison as well. The values of K0S,m,O for open-chain solutes (dashed line in Figure 10) were approximated as K0S,m,O = K0S,m (−CH2−O−CH2−) − 2K0S,m(−CH2−) using the values for segments −CH2−O−CH2− and −CH2− reported by Santos et al.36 No proper data to confirm/reject this approximation were found. It should be noted that the covolume term which must be a priori defined for open-chain solute molecules32 has no effect on the contributions of the segments incorporated in the chains of the molecular frame (like −CH2− or −O− groups) of open-chain molecules (contrary to substituent groups like −OH) and therefore the contributions of −CH2− or −O− groups in open-chain and cyclic molecules are comparable. Obviously, the values for groups incorporated in cycles differ from those in open-chain molecules. The extension of the

experimental data set for cyclic ethers from n = 5, 6 (thick full lines in Figure 9 or open circles in Figure 10) to n = 5, 6, 15, 18 (open squares) is significant for the contribution of the methylene group, the effect for the oxygen atom is rather moderate. The inclusion of the term accounting for the size of cycle (full squares in Figures 9 and 10) affects the values of the contributions but it is difficult to observe any evident regularity. Taking into account the experimental uncertainties of the source data which may result in the uncertainties of the group contributions about 0.1 cm3·mol−1 for volumes and 1 cm3· mol−1·GPa−1 for compressions it seems, however, that the effect is more pronounced for standard molar volumes rather than for standard molar isentropic compressions.

5. CONCLUSIONS New data on density and speed of sound in dilute region were reported for two aqueous crown ethers and employed for the evaluation of standard molar volumes and standard molar isentropic compressions of the solutes in the temperature range (278 to 343.15) K. In combination with data measured previously for several other cyclic ethers the contributions of two group contribution schemes were evaluated and the results 2084



Article

molar volumes and standard molar isentropic compressions of aqueous cyclic ethers in the near ambient temperature range and at atmospheric pressure.

■

AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

■

REFERENCES

(1) Cibulka, I.; Alexiou, C. Partial Molar Volumes of Organic Solutes in Water. XXI. Cyclic Ethers at Temperatures T = 278 to 373 K and at Low Pressure. J. Chem. Thermodyn. 2010, 42, 274−285. (2) Cibulka, I. Partial Molar Volumes of Organic Solutes in Water. XXII. Cyclic Ethers at Temperatures T = 298 to 573 K and Pressures up to 30 MPa. J. Chem. Thermodyn. 2010, 42, 502−512. (3) Cibulka, I. Partial Molar Isentropic Compressions of Selected Cyclic Ethers at Infinite Dilution in Water at Temperatures T = (278 to 318) K and Atmospheric Pressure. J. Chem. Eng. Data 2013, 58, 1249−1254. (4) Pedersen, C. J. In Nobel Lectures, Chemistry 1981−1990; Malmström, B. G., Ed.; World Scientific Publishing Co.: Singapore, 1992; pp 495−511. (5) Fortin, T. J.; Laesecke, A.; Freund, M.; Outcalt, S. Advanced Calibration, Adjustment, and Operation of a Density and Sound Speed Analyzer. J. Chem. Thermodyn. 2013, 57, 276−285. (6) 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. (7) 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, 1996. (8) 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. (9) Bernal, P.; Bunn, A.; Logan, J.; McCluan, J. Apparent Molar Volumes and Adiabatic Compressibilities of Crown Ethers and Glymes in Aqueous Solutions at Various Temperatures. J. Solution Chem. 2000, 29, 651−665. (10) Tyczyńska, M.; Józw ́ iak, M. Partial Molar Volumes of 15Crown-5 Ether in the Mixtures of N,N-Dimethylformamide with Water. J. Solution Chem. 2014, 43, 388−403. (11) Zielenkiewicz, W.; Kulikov, O. V.; Kulis-Cwikla, I. Excess Enthalpies and Apparent Molar Volumes of Aqueous Solutions of Crown Ethers and Cryptand(222) at 25°C. J. Solution Chem. 1993, 22, 963−973. (12) Bernal, P.; McCluan, J. Apparent Molar Volumes and Adiabatic Compressibilities of Crown Ethers and Glymes in H2O and D2O at 25°C. J. Solution Chem. 2001, 30, 119−131. (13) Vikingstad, E.; Bakken, J. Effect of Complex Forming Crown Ethers on the Micelle Formation of Sodium Decanoate at 25°C. J. Colloid Interface Sci. 1980, 74, 8−15. (14) Dagade, D. H.; Shetake, P. K.; Patil, K. J. Thermodynamic Studies of Aqueous and CCl4 Solutions of 15-Crown-5 at 298.15 K: An Application of McMillan-Mater and Kirkwood-Buff Theories of Solutions. J. Phys. Chem. B 2007, 111, 7610−7619. (15) Høiland, H. In Thermodynamic Data for Biochemistry and Biotechnology; Hinz, H.-J., Ed.; Springer-Verlag: Berlin, 1986; Chapter 2, pp 17−44. (16) Niederhauser, T. L.; Brown, B. R.; Ziemer, S. P.; Sargent, J. D.; Woolley, E. M. Thermodynamics of Complexation of Aqueous 18Crown-6 with Potassium Ion: Apparent Molar Volumes and Apparent Heat Capacities of Aqueous 18-Crown-6 and the (18-Crown-6 + Potassium Chloride) Complex at Temperatures (278.15 to 393.15) K,

Figure 9. Plot of contributions of methylene group and ether oxygen atom to standard molar volume against temperature T. The lines are to aid the eye. Dashed lines - aliphatic open-chain solutes;32 full lines, cyclic solutes; thick full lines, smoothed contributions2 for cyclic ethers n = 5, 6. □, cyclic ethers n = 5, 6, 15, 18, eq 6; ■, cyclic ethers n = 5, 6, 15, 18, eq 8

Figure 10. Plot of contributions of methylene group and ether oxygen atom to standard molar isentropic compression against temperature T. The lines are to aid the eye. Dashed lines, aliphatic open-chain solutes; full lines, cyclic solutes. ○, cyclic ethers3 n = 5,6; □, cyclic ethers n = 5, 6, 15, 18, eq 6; ■, cyclic ethers n = 5, 6, 15, 18, eq 8; Δ, Høiland;33,34 ▲, Nakajima;35 ∇, Santos.36

were analyzed. The introduction of the term that accounts for the size of the cycle in the solute molecule improves substantially the agreement between calculated and experimental values. Thus, the proposed group contribution approach may serve as a tool for the estimation of standard 2085



Article

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