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Excess thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) at temperatures between (283.15 and 313.15) K
J. Chem. Thermodynamics 2000, 32, 319–328 doi:10.1006/jcht.1999.0588 Available online at http://www.idealibrary.com on
Excess thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) at temperatures between (283.15 and 313.15) K Hiroyuki Ohji,a School of High-technology for Human Welfare, Tokai University Numazu, Shizuoka 410-0321, Japan
Katsutoshi Tamura, Department of Chemistry, Graduate School of Science, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
and Hideo Ogawa Faculty of Science and Engineering, Tokyo Denki University, Hatoyama, Hiki-gun, Saitama 350-0311, Japan Measurements of the excess enthalpies H E at T = 298.15 K and densities at 15 K intervals from T = (283.15 to 313.15) K are reported for (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane). Excess volumes V E , excess thermal expansivities α E , and the pressure derivatives of the excess enthalpies were estimated from the measured densities. The values of H E for both systems are positive. However, the values of V E for the 1,2-dimethoxyethane system are negative, although they are positive for the 1,4-dioxane system as expected from the sign of H E . The behaviour of these properties is discussed in c 2000 Academic Press terms of hydrogen bonds and size and shape of the ether molecules. KEYWORDS: 2-ethoxyethanol; excess enthalpy; excess volume; excess thermal expansivities; hydrogen bonds; 1,4-dioxane; 1,2-dimethoxyethane
1. Introduction Hydrogen bonds dominate many of the excess thermodynamic properties of binary mixtures and a large amount of work has been devoted to investigating the behaviour of the excess thermodynamic properties for various hydrogen bond systems. Some of a To whom correspondence should be addressed.
0021–9614/00/030319 + 10 $35.00/0
c 2000 Academic Press
320
H. Ohji, K. Tamura, and H. Ogawa
H E/(J · mol–1)
1000
500
0 0.0
0.5
1.0
x (2-ethoxyethanol) FIGURE 1. Excess enthalpies H E for {x2-ethoxyethanol + (1 − x)1,4-dioxane or 1,2dimethoxyethane} as a function of mole fraction x at T = 298.15 K. Experimental results: }, 1,4-dioxane; ◦ 1,2-dimethoxyethane; – – –, 1,4-dioxane; ——, 1,2-dimethoxyethane calculated by using equation (1) with parameters from table 1.
them, the alkoxyalkanol systems, are very interesting because these systems show the effect of the simultaneous presence of the ether and hydroxyl groups on the excess thermodynamic properties. From this point of view, the excess thermodynamic properties of some alkoxyalkanol systems have been systematically measured by our group.(1–5) In this study, the excess enthalpies H E at T = 298.15 K and densities at 15 K intervals from T = (283.15 to 313.15) K for (2-ethoxyethanol + 1,4-dioxane or 1,2dimethoxyethane) have been measured experimentally. The excess volumes V E , excess thermal expansivities α E , and the pressure derivatives of the excess enthalpies were estimated from the measured densities. The behaviour of these thermodynamic properties is discussed and compared with the results of the other 2-ethoxyethanol systems.
2. Experimental The 2-ethoxyethanol (Wako Pure Chemical, special grade) was purified by a previously described method.(2, 3) The 1,4-dioxane (Wako, pure grade) and 1,2-dimethoxyethane
Thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) TABLE 1. The coefficients of equation (1) for excess enthalpies of 2-ethoxyethanol with 1,4-dioxane or 1,2-dimethoxyethane at T = 298.15 K A1
A2
A3
2750.6
357.7
1352.4
378.4
A4
A5
σa−b−1 /(J · mol−1 )
x2-ethoxyethanol + (1 − x)1,4-dioxane 159.1
217.8
0
4.3
x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane 191.1
1.1
1.0
−132.9
a The number of values of excess volumes; b the number of coefficients of equation (1).
TABLE 2. Excess enthalpies of 2-ethoxyethanol with 1,4-dioxane and 1,2dimethoxyethane at T = 298.15 K x
H E /(J · mol−1 )
0.0250
80.9
0.3500
654.8
0.7000
549.6
0.0500
160.7
0.4000
690.1
0.7500
484.3
0.1000
291.5
0.4500
679.8
0.8000
410.9
0.1500
400.8
0.5000
687.9
0.8500
326.8
0.2000
489.9
0.5500
670.3
0.9000
222.0
0.2500
564.4
0.6000
643.6
0.9500
105.3
0.3000
617.5
0.6500
600.0
0.9750
46.1
0.0250
41.1
0.3500
333.6
0.7000
257.7
0.0500
82.1
0.4000
343.9
0.7500
224.9
0.1000
156.3
0.4500
344.4
0.8000
187.8
0.1500
215.4
0.5000
338.5
0.8500
146.4
0.2000
261.6
0.5500
326.8
0.9000
101.6
0.2500
296.0
0.6000
308.8
0.9500
51.4
0.3000
321.0
0.6500
285.1
0.9750
25.0
x
H E /(J · mol−1 )
x
H E /(J · mol−1 )
x2-ethoxyethanol + (1 − x)1,4-dioxane
x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane
321
322
H. Ohji, K. Tamura, and H. Ogawa
0.25
V E/(cm3·mol–1)
0.20 0.15 0.10 0.05 0.00 0.0
0.2
0.4
0.6
0.8
1.0
x (2-ethoxyethanol) FIGURE 2. Excess volume V E for {x2-ethoxyethanol + (1 − x)1,4-dioxane} as a function of mole fraction x at two temperatures. Experimental results: ◦, T = 298.15 K; N, T = 313.15 K; — calculated by using equation (2) with parameters from table 6.
0.05
V E/(cm3 · mol–1)
0.00
–0.05
–0.10
–0.15 0.0
0.2
0.4 0.6 x (2-ethoxyethanol)
0.8
1.0
FIGURE 3. Excess volume V E for {x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane} as a function of mole fraction x at four temperatures. Experimental results: ◦, T = 283.15 K; N, T = 298.15 K; , T = 313.15 K; —, calculated by using equation (2) with parameters from table 6.
(Wako, special grade) were used without further purification. The purities were estimated to be better than mass fraction 0.9997 for 2-ethoxyethanol, 0.9999 for 1,2-dimethoxyethane from g.l.c. (Shimadzu, GC-4C), and 0.998 for 1,4-dioxane, as certified by Wako. The excess enthalpies were measured at T = 298.15 K using an LKB flow microcalorimeter
Thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane)
323
2.0
α E/(10–5 K–1)
1.0
1,4-dioxane
0.0
–1.0 1,2-dimethoxyethane
–2.0 0.0
0.2
0.6 0.4 x (2-ethoxethanol)
0.8
1.0
FIGURE 4. Excess thermal expansivities calculated by using equation (4) for {2-ethoxyethanol + 1,4-dioxane or + 1,2-dimethoxyethane} as a function of mole fraction x of 2-ethoxyethanol at T = 298.15 K.
(δH E/δP)T /(10–6 J · Pa–1 · mol–1)
0.2
0.1
0.0
–0.1
–0.2
–0.3 0.0
0.2
0.4
0.6
0.8
1.0
x (2-ethoxyethanol) FIGURE 5. Dependence of excess enthalpies with pressure (∂ H E /∂ P)T for {2-ethoxyethanol + 1,4-dioxane or + 1,2-dimethoxyethane} as a function of mole fraction x of 2-ethoxyethanol at T = 298.15 K calculated by using equation (6): - - -, 1,4-dioxane; ——, 1,2-dimethoxyethane.
(LKB 107001) immersed in a waterbath and the temperature was controlled to within ±0.001 K. The precision of H E was believed to be ±0.3 per cent. Details of the flow
324
H. Ohji, K. Tamura, and H. Ogawa TABLE 3. Densitiesa ρ for liquid components between T = (283.15 and 313.15) K T /(K)
283.15
2-Ethoxyethanol
0.93910
298.15
1,4-Dioxane 1,2-Dimethoxyethane
0.87771
313.15
0.92537
0.91165
1.02815
1.01107
0.86124
0.84464
a Units: g · cm−3 .
microcalorimeter have been previously described.(6) Densities were measured with a vibrating-tube densimeter (Anton Paar DMA602 HW) using a thermostated water bath with the temperature controlled within ±0.001 K. The accuracy and precision of the density measurements using the densimeter were estimated to be less than 1 · 10−5 and 5 · 10−6 , respectively. The uncertainty of the concentration of the mixtures for the density measurements was believed to be less than ±5 · 10−5 . The details of the instruments and experimental procedure were previously described.(2, 7)
3. Results and discussion Table 2 presents the observed values of the excess enthalpies H E for (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane), which are plotted in figure 1 together with the curves calculated by using adjustable parameters in table 1. The parameters are fitted to the following Redlich–Kister equation using the least-squares method: H E /(J · mol−1 ) = x(1 − x)
k X
Ai (1 − 2x)i−1 .
(1)
i=1
Tables 3, 4, and 5 contain the densities obtained for the liquid components and mixtures (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) and calculated V E . The values of V E plotted in figures 2 and 3 were fitted to a Redlich–Kister type equation by the leastsquares method with each value of V E assigned a unit weight: V E /(cm3 · mol−1 ) = x(1 − x)
k X
Bi (1 − 2x)i−1 .
(2)
i=1
The values of the coefficients Bi are listed in table 6, along with the corresponding standard deviations σ . Equation (2) can be extended in order to represent V E as a function of temperature as well as of composition by considering the coefficients Bi to be polynomials of the temperature T . Here, a linear variation with temperature should be sufficient to represent a significant difference in the temperature dependence for Bi as: V E /(cm3 · mol−1 ) = x(1 − x)
k X (ai + bi T )(1 − 2x)i−1 . i=1
(3)
Thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane)
325
TABLE 4. Densities ρ and excess volumes V E for binary mixtures of 2-ethoxyethanol with 1,4-dioxane at T = (298.15 and 313.15) K x
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
x
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
x2-ethoxyethanol + (1 − x)1,4-dioxane T = 298.15 K
T = 313.15 K
0.0594
1.02048
0.067
0.0594
1.00364
0.068
0.0996
1.01551
0.099
0.0996
0.99880
0.104
0.1443
1.01009
0.132
0.1443
0.99361
0.132
0.2017
1.00331
0.166
0.2017
0.98706
0.167
0.2548
0.99731
0.182
0.2548
0.98117
0.192
0.3041
0.99183
0.196
0.3041
0.97590
0.203
0.3317
0.98878
0.205
0.3317
0.97299
0.209
0.4096
0.98049
0.212
0.4096
0.96494
0.219
0.4568
0.97563
0.210
0.4568
0.96025
0.216
0.4892
0.97236
0.204
0.4892
0.95704
0.214
0.5493
0.96632
0.198
0.5493
0.95123
0.206
0.5966
0.96170
0.186
0.5966
0.94678
0.193
0.6468
0.95691
0.170
0.6468
0.94210
0.181
0.7035
0.95158
0.149
0.7035
0.93695
0.160
0.7520
0.94719
0.121
0.7520
0.93261
0.140
0.8012
0.94257
0.114
0.8012
0.92824
0.123
0.8606
0.93748
0.063
0.8606
0.92316
0.087
0.9435
0.93008
0.035
The excess thermal expansivities α E of mixtures at T = 298.15 K were calculated by using equation (4) and are shown in figure 4: α E /(K−1 ) = α − α id = {(∂ V E /∂ T ) P − V E α id }/(V id + V E ).
(4)
The estimated error in α E , ε(α E ), was calculated by using equation (5), 2
ε(α E ) = [ε2 {(∂ V E /∂ T ) P }/V 2 + α id ε2 (V E )/V 2 ]1/2 ,
(5)
where ε2 (V E ) and ε2 {(∂ V E /∂ T ) P } are the mean square errors which were calculated from the most probable errors in coefficients ai and bi in equation (3). The error ε(α E ) was less than 0.11 · 10−5 K−1 for the 1,2-dimethoxyethane system. These estimations for α E and ε(α E ) were described in detail elsewhere.(8, 9) The dependence on the pressure of the excess enthalpies H E can also be determined through equation (6) from V E and its temperature derivatives. The corresponding curves are represented in figure 5: (∂ H E /∂ P)T /(10−6 · J · Pa−1 · mol−1 ) = V E − T (∂ V E /∂ T ) P .
(6)
326
H. Ohji, K. Tamura, and H. Ogawa TABLE 5. Densities ρ and excess volumes V E for binary mixtures of 2-ethoxyethanol with 1,2-dimethoxyethane between T = (283.15 and 313.15) K x
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
x
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane T = 283.15 K
T = 298.15 K
0.0555
0.88107
−0.019
0.0555
0.86477
−0.024
0.1010
0.88385
−0.035
0.1010
0.86768
−0.043
0.1499
0.88686
−0.053
0.1499
0.87084
−0.065
0.2001
0.88995
−0.069
0.2001
0.87403
−0.078
0.2531
0.89321
−0.083
0.2531
0.87746
−0.096
0.2980
0.89596
−0.091
0.2980
0.88032
−0.103
0.3502
0.89916
−0.099
0.3502
0.88373
−0.120
0.3937
0.90183
−0.104
0.3937
0.88636
−0.107
0.4447
0.90496
−0.107
0.4447
0.88958
−0.104
0.5020
0.90847
−0.106
0.5020
0.89341
−0.123
0.5475
0.91124
−0.103
0.6509
0.90292
−0.104
0.6009
0.91449
−0.096
0.7016
0.90618
−0.094
0.7602
0.92419
−0.062
0.7602
0.90992
−0.077
0.7816
0.92551
−0.056
0.7816
0.91124
−0.066
0.8490
0.92960
−0.032
0.8490
0.91556
−0.043
0.8977
0.93253
−0.010
0.8977
0.91865
−0.020
0.9489
0.92207
−0.012
T = 313.15 K 0.0555
0.84826
−0.019
0.5475
0.88162
−0.177
0.1010
0.85137
−0.050
0.6009
0.88507
−0.156
0.1499
0.85473
−0.083
0.6509
0.88815
−0.117
0.2001
0.85792
−0.080
0.7016
0.89155
−0.106
0.2531
0.86152
−0.104
0.7602
0.89543
−0.084
0.2980
0.86453
−0.115
0.7816
0.89684
−0.073
0.3502
0.86806
−0.129
0.8490
0.90132
−0.044
0.3937
0.87095
−0.132
0.8977
0.90456
−0.020
0.4447
0.87434
−0.133
0.9489
0.90821
−0.019
0.5020
0.87820
−0.136
The estimated error in (∂ H E /∂ P)T , ε{(∂ H E /∂ P)T } was calculated by using equation (7): ε{(∂ H E /∂ P)T } = [ε 2 {T (∂ V E /∂ T ) P } + ε2 (V E )]1/2 .
(7)
The uncertainty ε{(∂ H E /∂ P)T } was less than 0.05 · 10−6 J · Pa−1 · mol−1 for the 1,2-dimethoxyethane system. The 1,4-dioxane and 1,2-dimethoxyethane have the same
Thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane)
327
TABLE 6. The coefficients of equation (2) and standard deviations σ for mixtures between T = (283.15 and 318.15) K B1
B2
B3
B4
σa−b−1 /(cm3 · mol−1 )
x2-ethoxyethamol + (1 − x)1,4-dioxane T = 298.15 K 0.821
0.26
0.04
0.11
0.004
T = 313.15 K 0.850
0.24
0.13
0.02
0.002
x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane T = 283.15 K −0.431
−0.07
0.21
−0.12
0.003
T = 298.15 K −0.499
−0.07
0.18
−0.55
−0.07
0.15
−0.10
0.004
T = 313.15 K −0.1
0.005
a The number of values of excess volumes; b the number of coefficients of equation (2).
number and species of elementary segments (ether, methyl, and methylane groups). The (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) systems show the effect of molecular shape and size of the ether on the excess thermodynamic properties of 2ethoxyethanol systems. The values of H E for both systems are positive and the magnitude of H E for the 1,2-dimethoxyethane system at the maximum is about half as much as that for the 1,4-dioxane system. The difference between the two systems is attributed to the effect of the ether’s molecular shape and size and the difference of unlike intermolecular interactions, which therefore occur. The 1,2-dimethoxyethane, an isomer of 2-ethoxyethanol, has a linear molecular shape similar to the latter, and will form good packing with 2-ethoxyethanol in solution and will reform the hydrogen bonds with 2ethoxyethanol, thus reducing excess enthalpies compared to the 1,4-dioxane systems. On the other hand, the cyclic molecular shape of 1,4-dioxane is not ideal to accept the hydroxyl groups of 2-ethoxyethanol resulting in an increase in the excess enthalpies and molecular distance. The fact that the excess volume of 1,2-dimethoxyethane is negative and that for 1,4-dioxane is positive and the α E , the pressure dependence of the enthalpies, support the above explanation. Comparing these results with those of the n-octane and cyclohexane systems, which were previously reported,(2) is very interesting from the point of view as to whether an ether oxygen could exist. The H E and V E of the n-octane and cyclohexane systems are about 1100 J · mol−1 and about 1 cm3 · mol−1 , respectively, which are rather large compared with non-polar solutions, and show the similar dependencies of concentration. The difference in the effect of molecular shape and size does not appear. On the other hand,
328
H. Ohji, K. Tamura, and H. Ogawa
in the cases of the 1,4-dioxane and 1,2-dimethoxyethane systems, each molecule having two ether oxygens, the magnitude of V E for these systems decreases to about one-fifth. The difference in the sign of excess volumes and the excess enthalpies for these systems arises because the molecular shape and size and the ether oxygen produces a multiplier effect, which affects H E and V E . REFERENCES 1. Tamura, K.; Osaki, A.; Murakami, S.; Ohji, H.; Ogawa, H.; Laurent, B.; Grolier, J.-P. E. Fluid Phase Equilib. 1999, 156, 137–147. 2. Ohji, H.; Ogawa, H.; Murakami, S.; Tamura, K.; Grolier, J.-P. E. Fluid Phase Equilib. 1999, 156, 101–114. 3. Ohji, H.; Osaki, A.; Tamura, K.; Murakami, S.; Ogawa, H. J. Chem. Thermodynamics 1998, 30, 761–765. 4. Nishimoto, M.; Tamura, K.; Murakami, S. Fluid Phase Equilib. 1997, 136, 235–247. 5. Kimura, F.; Murakami, S.; Fujishiro, R.; Toshiyasu, Y. Bull. Chem. Soc. Jpn. 1977, 50, 791–794. 6. Fujihara, I.; Kobayashi, M.; Murakami, S. Fluid Phase Equilib. 1983, 15, 81–89. 7. Ogawa, H.; Murase, N.; Murakami, S. Thermochim. Acta 1995, 253, 41–49. 8. Kiyohara, O.; D’Arcy, P. J.; Benson, G. C. Can. J. Chem. 1978, 56, 2803–2807. 9. Arimoto, A.; Ogawa, H.; Murakami, S. Thermochim. Acta 1993, 163, 191–202. (Received 4 June 1999; in final form 4 August 1999)
WE-165
Excess thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) at temperatures between (283.15 and 313.15) K Hiroyuki Ohji,a School of High-technology for Human Welfare, Tokai University Numazu, Shizuoka 410-0321, Japan
Katsutoshi Tamura, Department of Chemistry, Graduate School of Science, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
and Hideo Ogawa Faculty of Science and Engineering, Tokyo Denki University, Hatoyama, Hiki-gun, Saitama 350-0311, Japan Measurements of the excess enthalpies H E at T = 298.15 K and densities at 15 K intervals from T = (283.15 to 313.15) K are reported for (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane). Excess volumes V E , excess thermal expansivities α E , and the pressure derivatives of the excess enthalpies were estimated from the measured densities. The values of H E for both systems are positive. However, the values of V E for the 1,2-dimethoxyethane system are negative, although they are positive for the 1,4-dioxane system as expected from the sign of H E . The behaviour of these properties is discussed in c 2000 Academic Press terms of hydrogen bonds and size and shape of the ether molecules. KEYWORDS: 2-ethoxyethanol; excess enthalpy; excess volume; excess thermal expansivities; hydrogen bonds; 1,4-dioxane; 1,2-dimethoxyethane
1. Introduction Hydrogen bonds dominate many of the excess thermodynamic properties of binary mixtures and a large amount of work has been devoted to investigating the behaviour of the excess thermodynamic properties for various hydrogen bond systems. Some of a To whom correspondence should be addressed.
0021–9614/00/030319 + 10 $35.00/0
c 2000 Academic Press
320
H. Ohji, K. Tamura, and H. Ogawa
H E/(J · mol–1)
1000
500
0 0.0
0.5
1.0
x (2-ethoxyethanol) FIGURE 1. Excess enthalpies H E for {x2-ethoxyethanol + (1 − x)1,4-dioxane or 1,2dimethoxyethane} as a function of mole fraction x at T = 298.15 K. Experimental results: }, 1,4-dioxane; ◦ 1,2-dimethoxyethane; – – –, 1,4-dioxane; ——, 1,2-dimethoxyethane calculated by using equation (1) with parameters from table 1.
them, the alkoxyalkanol systems, are very interesting because these systems show the effect of the simultaneous presence of the ether and hydroxyl groups on the excess thermodynamic properties. From this point of view, the excess thermodynamic properties of some alkoxyalkanol systems have been systematically measured by our group.(1–5) In this study, the excess enthalpies H E at T = 298.15 K and densities at 15 K intervals from T = (283.15 to 313.15) K for (2-ethoxyethanol + 1,4-dioxane or 1,2dimethoxyethane) have been measured experimentally. The excess volumes V E , excess thermal expansivities α E , and the pressure derivatives of the excess enthalpies were estimated from the measured densities. The behaviour of these thermodynamic properties is discussed and compared with the results of the other 2-ethoxyethanol systems.
2. Experimental The 2-ethoxyethanol (Wako Pure Chemical, special grade) was purified by a previously described method.(2, 3) The 1,4-dioxane (Wako, pure grade) and 1,2-dimethoxyethane
Thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) TABLE 1. The coefficients of equation (1) for excess enthalpies of 2-ethoxyethanol with 1,4-dioxane or 1,2-dimethoxyethane at T = 298.15 K A1
A2
A3
2750.6
357.7
1352.4
378.4
A4
A5
σa−b−1 /(J · mol−1 )
x2-ethoxyethanol + (1 − x)1,4-dioxane 159.1
217.8
0
4.3
x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane 191.1
1.1
1.0
−132.9
a The number of values of excess volumes; b the number of coefficients of equation (1).
TABLE 2. Excess enthalpies of 2-ethoxyethanol with 1,4-dioxane and 1,2dimethoxyethane at T = 298.15 K x
H E /(J · mol−1 )
0.0250
80.9
0.3500
654.8
0.7000
549.6
0.0500
160.7
0.4000
690.1
0.7500
484.3
0.1000
291.5
0.4500
679.8
0.8000
410.9
0.1500
400.8
0.5000
687.9
0.8500
326.8
0.2000
489.9
0.5500
670.3
0.9000
222.0
0.2500
564.4
0.6000
643.6
0.9500
105.3
0.3000
617.5
0.6500
600.0
0.9750
46.1
0.0250
41.1
0.3500
333.6
0.7000
257.7
0.0500
82.1
0.4000
343.9
0.7500
224.9
0.1000
156.3
0.4500
344.4
0.8000
187.8
0.1500
215.4
0.5000
338.5
0.8500
146.4
0.2000
261.6
0.5500
326.8
0.9000
101.6
0.2500
296.0
0.6000
308.8
0.9500
51.4
0.3000
321.0
0.6500
285.1
0.9750
25.0
x
H E /(J · mol−1 )
x
H E /(J · mol−1 )
x2-ethoxyethanol + (1 − x)1,4-dioxane
x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane
321
322
H. Ohji, K. Tamura, and H. Ogawa
0.25
V E/(cm3·mol–1)
0.20 0.15 0.10 0.05 0.00 0.0
0.2
0.4
0.6
0.8
1.0
x (2-ethoxyethanol) FIGURE 2. Excess volume V E for {x2-ethoxyethanol + (1 − x)1,4-dioxane} as a function of mole fraction x at two temperatures. Experimental results: ◦, T = 298.15 K; N, T = 313.15 K; — calculated by using equation (2) with parameters from table 6.
0.05
V E/(cm3 · mol–1)
0.00
–0.05
–0.10
–0.15 0.0
0.2
0.4 0.6 x (2-ethoxyethanol)
0.8
1.0
FIGURE 3. Excess volume V E for {x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane} as a function of mole fraction x at four temperatures. Experimental results: ◦, T = 283.15 K; N, T = 298.15 K; , T = 313.15 K; —, calculated by using equation (2) with parameters from table 6.
(Wako, special grade) were used without further purification. The purities were estimated to be better than mass fraction 0.9997 for 2-ethoxyethanol, 0.9999 for 1,2-dimethoxyethane from g.l.c. (Shimadzu, GC-4C), and 0.998 for 1,4-dioxane, as certified by Wako. The excess enthalpies were measured at T = 298.15 K using an LKB flow microcalorimeter
Thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane)
323
2.0
α E/(10–5 K–1)
1.0
1,4-dioxane
0.0
–1.0 1,2-dimethoxyethane
–2.0 0.0
0.2
0.6 0.4 x (2-ethoxethanol)
0.8
1.0
FIGURE 4. Excess thermal expansivities calculated by using equation (4) for {2-ethoxyethanol + 1,4-dioxane or + 1,2-dimethoxyethane} as a function of mole fraction x of 2-ethoxyethanol at T = 298.15 K.
(δH E/δP)T /(10–6 J · Pa–1 · mol–1)
0.2
0.1
0.0
–0.1
–0.2
–0.3 0.0
0.2
0.4
0.6
0.8
1.0
x (2-ethoxyethanol) FIGURE 5. Dependence of excess enthalpies with pressure (∂ H E /∂ P)T for {2-ethoxyethanol + 1,4-dioxane or + 1,2-dimethoxyethane} as a function of mole fraction x of 2-ethoxyethanol at T = 298.15 K calculated by using equation (6): - - -, 1,4-dioxane; ——, 1,2-dimethoxyethane.
(LKB 107001) immersed in a waterbath and the temperature was controlled to within ±0.001 K. The precision of H E was believed to be ±0.3 per cent. Details of the flow
324
H. Ohji, K. Tamura, and H. Ogawa TABLE 3. Densitiesa ρ for liquid components between T = (283.15 and 313.15) K T /(K)
283.15
2-Ethoxyethanol
0.93910
298.15
1,4-Dioxane 1,2-Dimethoxyethane
0.87771
313.15
0.92537
0.91165
1.02815
1.01107
0.86124
0.84464
a Units: g · cm−3 .
microcalorimeter have been previously described.(6) Densities were measured with a vibrating-tube densimeter (Anton Paar DMA602 HW) using a thermostated water bath with the temperature controlled within ±0.001 K. The accuracy and precision of the density measurements using the densimeter were estimated to be less than 1 · 10−5 and 5 · 10−6 , respectively. The uncertainty of the concentration of the mixtures for the density measurements was believed to be less than ±5 · 10−5 . The details of the instruments and experimental procedure were previously described.(2, 7)
3. Results and discussion Table 2 presents the observed values of the excess enthalpies H E for (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane), which are plotted in figure 1 together with the curves calculated by using adjustable parameters in table 1. The parameters are fitted to the following Redlich–Kister equation using the least-squares method: H E /(J · mol−1 ) = x(1 − x)
k X
Ai (1 − 2x)i−1 .
(1)
i=1
Tables 3, 4, and 5 contain the densities obtained for the liquid components and mixtures (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) and calculated V E . The values of V E plotted in figures 2 and 3 were fitted to a Redlich–Kister type equation by the leastsquares method with each value of V E assigned a unit weight: V E /(cm3 · mol−1 ) = x(1 − x)
k X
Bi (1 − 2x)i−1 .
(2)
i=1
The values of the coefficients Bi are listed in table 6, along with the corresponding standard deviations σ . Equation (2) can be extended in order to represent V E as a function of temperature as well as of composition by considering the coefficients Bi to be polynomials of the temperature T . Here, a linear variation with temperature should be sufficient to represent a significant difference in the temperature dependence for Bi as: V E /(cm3 · mol−1 ) = x(1 − x)
k X (ai + bi T )(1 − 2x)i−1 . i=1
(3)
Thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane)
325
TABLE 4. Densities ρ and excess volumes V E for binary mixtures of 2-ethoxyethanol with 1,4-dioxane at T = (298.15 and 313.15) K x
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
x
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
x2-ethoxyethanol + (1 − x)1,4-dioxane T = 298.15 K
T = 313.15 K
0.0594
1.02048
0.067
0.0594
1.00364
0.068
0.0996
1.01551
0.099
0.0996
0.99880
0.104
0.1443
1.01009
0.132
0.1443
0.99361
0.132
0.2017
1.00331
0.166
0.2017
0.98706
0.167
0.2548
0.99731
0.182
0.2548
0.98117
0.192
0.3041
0.99183
0.196
0.3041
0.97590
0.203
0.3317
0.98878
0.205
0.3317
0.97299
0.209
0.4096
0.98049
0.212
0.4096
0.96494
0.219
0.4568
0.97563
0.210
0.4568
0.96025
0.216
0.4892
0.97236
0.204
0.4892
0.95704
0.214
0.5493
0.96632
0.198
0.5493
0.95123
0.206
0.5966
0.96170
0.186
0.5966
0.94678
0.193
0.6468
0.95691
0.170
0.6468
0.94210
0.181
0.7035
0.95158
0.149
0.7035
0.93695
0.160
0.7520
0.94719
0.121
0.7520
0.93261
0.140
0.8012
0.94257
0.114
0.8012
0.92824
0.123
0.8606
0.93748
0.063
0.8606
0.92316
0.087
0.9435
0.93008
0.035
The excess thermal expansivities α E of mixtures at T = 298.15 K were calculated by using equation (4) and are shown in figure 4: α E /(K−1 ) = α − α id = {(∂ V E /∂ T ) P − V E α id }/(V id + V E ).
(4)
The estimated error in α E , ε(α E ), was calculated by using equation (5), 2
ε(α E ) = [ε2 {(∂ V E /∂ T ) P }/V 2 + α id ε2 (V E )/V 2 ]1/2 ,
(5)
where ε2 (V E ) and ε2 {(∂ V E /∂ T ) P } are the mean square errors which were calculated from the most probable errors in coefficients ai and bi in equation (3). The error ε(α E ) was less than 0.11 · 10−5 K−1 for the 1,2-dimethoxyethane system. These estimations for α E and ε(α E ) were described in detail elsewhere.(8, 9) The dependence on the pressure of the excess enthalpies H E can also be determined through equation (6) from V E and its temperature derivatives. The corresponding curves are represented in figure 5: (∂ H E /∂ P)T /(10−6 · J · Pa−1 · mol−1 ) = V E − T (∂ V E /∂ T ) P .
(6)
326
H. Ohji, K. Tamura, and H. Ogawa TABLE 5. Densities ρ and excess volumes V E for binary mixtures of 2-ethoxyethanol with 1,2-dimethoxyethane between T = (283.15 and 313.15) K x
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
x
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane T = 283.15 K
T = 298.15 K
0.0555
0.88107
−0.019
0.0555
0.86477
−0.024
0.1010
0.88385
−0.035
0.1010
0.86768
−0.043
0.1499
0.88686
−0.053
0.1499
0.87084
−0.065
0.2001
0.88995
−0.069
0.2001
0.87403
−0.078
0.2531
0.89321
−0.083
0.2531
0.87746
−0.096
0.2980
0.89596
−0.091
0.2980
0.88032
−0.103
0.3502
0.89916
−0.099
0.3502
0.88373
−0.120
0.3937
0.90183
−0.104
0.3937
0.88636
−0.107
0.4447
0.90496
−0.107
0.4447
0.88958
−0.104
0.5020
0.90847
−0.106
0.5020
0.89341
−0.123
0.5475
0.91124
−0.103
0.6509
0.90292
−0.104
0.6009
0.91449
−0.096
0.7016
0.90618
−0.094
0.7602
0.92419
−0.062
0.7602
0.90992
−0.077
0.7816
0.92551
−0.056
0.7816
0.91124
−0.066
0.8490
0.92960
−0.032
0.8490
0.91556
−0.043
0.8977
0.93253
−0.010
0.8977
0.91865
−0.020
0.9489
0.92207
−0.012
T = 313.15 K 0.0555
0.84826
−0.019
0.5475
0.88162
−0.177
0.1010
0.85137
−0.050
0.6009
0.88507
−0.156
0.1499
0.85473
−0.083
0.6509
0.88815
−0.117
0.2001
0.85792
−0.080
0.7016
0.89155
−0.106
0.2531
0.86152
−0.104
0.7602
0.89543
−0.084
0.2980
0.86453
−0.115
0.7816
0.89684
−0.073
0.3502
0.86806
−0.129
0.8490
0.90132
−0.044
0.3937
0.87095
−0.132
0.8977
0.90456
−0.020
0.4447
0.87434
−0.133
0.9489
0.90821
−0.019
0.5020
0.87820
−0.136
The estimated error in (∂ H E /∂ P)T , ε{(∂ H E /∂ P)T } was calculated by using equation (7): ε{(∂ H E /∂ P)T } = [ε 2 {T (∂ V E /∂ T ) P } + ε2 (V E )]1/2 .
(7)
The uncertainty ε{(∂ H E /∂ P)T } was less than 0.05 · 10−6 J · Pa−1 · mol−1 for the 1,2-dimethoxyethane system. The 1,4-dioxane and 1,2-dimethoxyethane have the same
Thermodynamic properties of (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane)
327
TABLE 6. The coefficients of equation (2) and standard deviations σ for mixtures between T = (283.15 and 318.15) K B1
B2
B3
B4
σa−b−1 /(cm3 · mol−1 )
x2-ethoxyethamol + (1 − x)1,4-dioxane T = 298.15 K 0.821
0.26
0.04
0.11
0.004
T = 313.15 K 0.850
0.24
0.13
0.02
0.002
x2-ethoxyethanol + (1 − x)1,2-dimethoxyethane T = 283.15 K −0.431
−0.07
0.21
−0.12
0.003
T = 298.15 K −0.499
−0.07
0.18
−0.55
−0.07
0.15
−0.10
0.004
T = 313.15 K −0.1
0.005
a The number of values of excess volumes; b the number of coefficients of equation (2).
number and species of elementary segments (ether, methyl, and methylane groups). The (2-ethoxyethanol + 1,4-dioxane or 1,2-dimethoxyethane) systems show the effect of molecular shape and size of the ether on the excess thermodynamic properties of 2ethoxyethanol systems. The values of H E for both systems are positive and the magnitude of H E for the 1,2-dimethoxyethane system at the maximum is about half as much as that for the 1,4-dioxane system. The difference between the two systems is attributed to the effect of the ether’s molecular shape and size and the difference of unlike intermolecular interactions, which therefore occur. The 1,2-dimethoxyethane, an isomer of 2-ethoxyethanol, has a linear molecular shape similar to the latter, and will form good packing with 2-ethoxyethanol in solution and will reform the hydrogen bonds with 2ethoxyethanol, thus reducing excess enthalpies compared to the 1,4-dioxane systems. On the other hand, the cyclic molecular shape of 1,4-dioxane is not ideal to accept the hydroxyl groups of 2-ethoxyethanol resulting in an increase in the excess enthalpies and molecular distance. The fact that the excess volume of 1,2-dimethoxyethane is negative and that for 1,4-dioxane is positive and the α E , the pressure dependence of the enthalpies, support the above explanation. Comparing these results with those of the n-octane and cyclohexane systems, which were previously reported,(2) is very interesting from the point of view as to whether an ether oxygen could exist. The H E and V E of the n-octane and cyclohexane systems are about 1100 J · mol−1 and about 1 cm3 · mol−1 , respectively, which are rather large compared with non-polar solutions, and show the similar dependencies of concentration. The difference in the effect of molecular shape and size does not appear. On the other hand,
328
H. Ohji, K. Tamura, and H. Ogawa
in the cases of the 1,4-dioxane and 1,2-dimethoxyethane systems, each molecule having two ether oxygens, the magnitude of V E for these systems decreases to about one-fifth. The difference in the sign of excess volumes and the excess enthalpies for these systems arises because the molecular shape and size and the ether oxygen produces a multiplier effect, which affects H E and V E . REFERENCES 1. Tamura, K.; Osaki, A.; Murakami, S.; Ohji, H.; Ogawa, H.; Laurent, B.; Grolier, J.-P. E. Fluid Phase Equilib. 1999, 156, 137–147. 2. Ohji, H.; Ogawa, H.; Murakami, S.; Tamura, K.; Grolier, J.-P. E. Fluid Phase Equilib. 1999, 156, 101–114. 3. Ohji, H.; Osaki, A.; Tamura, K.; Murakami, S.; Ogawa, H. J. Chem. Thermodynamics 1998, 30, 761–765. 4. Nishimoto, M.; Tamura, K.; Murakami, S. Fluid Phase Equilib. 1997, 136, 235–247. 5. Kimura, F.; Murakami, S.; Fujishiro, R.; Toshiyasu, Y. Bull. Chem. Soc. Jpn. 1977, 50, 791–794. 6. Fujihara, I.; Kobayashi, M.; Murakami, S. Fluid Phase Equilib. 1983, 15, 81–89. 7. Ogawa, H.; Murase, N.; Murakami, S. Thermochim. Acta 1995, 253, 41–49. 8. Kiyohara, O.; D’Arcy, P. J.; Benson, G. C. Can. J. Chem. 1978, 56, 2803–2807. 9. Arimoto, A.; Ogawa, H.; Murakami, S. Thermochim. Acta 1993, 163, 191–202. (Received 4 June 1999; in final form 4 August 1999)
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