Excess volumes of (1-pentanol  +  cyclohexane or benzene) at temperatures between 283.15 K and 328.15 K

J. Chem. Thermodynamics 2002, 34, 849–859 doi:10.1006/jcht.2001.0940 Available online at http://www.idealibrary.com on

Excess volumes of (1-pentanol + cyclohexane or benzene) at temperatures between 283.15 K and 328.15 K Ohji Hiroyuki School of High-technology for Human Welfare, Tokai University, Numazu, Shizuoka 410-0321, Japan The densities of (1-pentanol + cyclohexane or benzene) have been measured at 15 K intervals from T = 283.15 K to T = 328.15 K for comparison with the results of (2-ethoxyethanol + cyclohexane or benzene). The excess volumes V E , excess thermal expansivities α E , and the pressure derivatives of the excess enthalpies (∂ H E /∂ P)T , were estimated from the measured densities. The values of V E and their temperature dependence for the 1-pentanol systems were found to be positive over the entire concentration range. The behaviour of α E for (1-pentanol + cyclohexane) is quite different from that of (2-ethoxyethanol + cyclohexane), while the α E value for (1-pentanol + benzene) is very similar to that of (2-ethoxyethanol + benzene). The behaviour of these thermodynamic properties are discussed in terms of inter- and intra-molecular hydrogen bonds and π c 2002 Elsevier Science Ltd. All rights reserved. electrons. KEYWORDS: 1-pentanol; cyclohexane; benzene; excess volume; excess thermalexpansivity; pressure derivative of excess enthalply; hydrogen bonding

1. Introduction The excess thermodynamic properties for a series of binary mixtures containing an alkoxyalcohol have been measured by our group. (1–4) The aim of these measurements is to investigate the effect of the simultaneous presence of etheric and hydroxyl groups in the 2-ethoxyethanol(2EE) molecule on the excess thermodynamic properties. It was found that the {2-ethoxyethanol + benzene(BZ)} system showed a remarkable concentration dependence of H E and V E . (3, 4) In the present study, to obtain more insight into this phenomenon, the densities of {1-pentanol(1PN) + BZ or cyclohexane(CH)} were measured at intervals 15 K from T = 283.15 K to T = 328.15 K. The results of these systems would more clearly show the effect of the ether oxygen of 2EE on the excess thermodynamic properties. This paper reports excess volumes V E , from the measured densities and the second derivatives of the Gibbs free energy, which would be useful for studying the solution structures, such as the excess thermal expansivities α E , and the 0021–9614/02

c 2002 Elsevier Science Ltd. All rights reserved.

850

H. Ohji

pressure derivatives of the excess enthalpies (∂ H E /∂ P)T of the 1PN systems. These results are discussed in comparison with that of (2EE + BZ or CH). Incidentally, some papers have reported the V E and α E values of the (1PN + BZ or CH) systems, (5–10) however, no other data for V E of (1PN + BZ or CH) over the this entire temperature range were found in the literature.

2. Experimental All chemicals were available from Wako Pure Chemical. The 1-pentanol(special grade) and benzene(pure grade) were used without further purification. Cyclohexane(special grade) was fractionally distilled. The purities were estimated to be better than 0.997 mole fraction for 1-pentanol, 0.998 for benzene, 0.9999 for the cyclohexane from g.l.c. (Shimadzu, GC-4C). Densities were measured with a vibrating-tube densimeter (Anton Paar, DMA602 HW) between T = 283.15 K and T = 328.15 K at 15 K intervals using a thermostatted water bath with the temperature controlled within ±0.001 K. The densities, ρ, of liquids and solutions were calculated from the period, τ , of oscillation of the U-shaped sample tube in the densimeter, as follows: ρ = a + bτ 2 ,

(1)

where a and b are the characteristic constants of the oscillator and were re-determined every time system or temperature was changed. The constants, a and b, were evaluated from the densities of two standard liquids: cyclohexane and benzene, measured using a 50 mL Ostwald-type pycnometer. The accuracy and precision of the density measurements using the densimeter were estimated to be less than 1 · 10−5 . The binary mixtures for the density measurements were prepared in 50 mL flasks by measuring the masses of the components with an electronic balance (Mettler, AE200). The uncertainty of the concentration of the mixtures was believed to be less than ±2 · 10−5 .

3. Results and discussion Tables 1–3 contain the results of densities for component liquids and (1PN + CH or BZ) and calculated V E . The values of V E plotted in figures 1 and 2 were fitted to a Redlich– Kister-type equation by the least-squares method with each value of the V E assigned unit weight: V E /(cm3 · mol−1 ) = x(1 − x)

k X

Ai (1 − 2x)i−1 ,

(2)

i=1

x being the mole fraction of 1PN. The values of coefficients Ai are listed in table 4 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 Ai to be polynomials of the temperature T . Here, a linear variation with temperature should be sufficient to represent a significant difference in the temperature

Excess volumes of (1-pentanol + cyclohexane or benzene)

851

TABLE 1. Densities, ρ/(g · cm−3 ) for component liquids between T = 283.15 K and T = 328.15 K with literature values at T = 298.15 K T /K

283.15

1-Pentanol

0.82202

298.15

313.15

328.15

0.81103

0.79989

0.78842

0.75954

0.74506

0.85747

0.84115

0.81108 (6) Cyclohexane

0.78790

0.77383 0.77388 (12)

Benzene

0.88961

0.87351 0.87347 (6)

dependence for Ai as: V E /(cm3 · mol−1 ) = x(1 − x)

k X (ai + bi T )(1 − 2x)i−1 .

(3)

i=1

The excess thermal expansivities α E of mixtures at T = 298.15 K were calculated from equation (4) (11) and are shown in figure 3: X α E /(K−1 ) = αm − α id = (∂ Vm /∂ T ) P /Vm − φ j · α ∗j , (4) where the sub- and superscript, m and id, denote a mixture and an ideal mixing, respectively. φ j is the volume fraction of component liquid j in the pre-mixing state and α ∗j is the thermal expansivity of component liquid j. The values of that are given in table 5. The estimated error in α E , ε(α E ), was calculated from equation (5): ε(α E ) = [ε2 {(∂ V E /∂ T ) P }/V 2 + (α id )2 · 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 the coefficients ai and bi in equation (3). (12) In my measurement, the estimated uncertainties on α E were, using equation (5), less than 3 · 10−6 K−1 for the CH system and 2 · 10−6 K−1 for the BZ system. The dependence on pressure of excess enthalpy (∂ H E /∂ P)T , also can be determined through equation (6) from V E and its temperature derivatives; corresponding curves are represented in figure 4: (∂ H E /∂ P)T /(10−6 · J · Pa−1 · mol−1 ) = V E − T (∂ V E /∂ T ) P .

(6)

The estimated error in (∂ H E /∂ P)T , ε{(∂ H E /∂ P)T } was calculated through equation (7): ε{(∂ H E /∂ P)T } = [ε2 {T (∂ V E /∂ T ) P } + ε2 (V E )]1/2 .

(7)

The errors on my results of ε{(∂ H E /∂ P)T } were, using equation (7), less than 0.2 · 10−6 J · Pa−1 · mol−1 for the CH systems, 0.1 · 10−6 J · Pa−1 · mol−1 for the BZ systems.

852

H. Ohji

TABLE 2. Densities, ρ and excess volumes, V E for binary mixtures of 1-pentanol with cyclohexane between T = 283.15 K and T = 328.15 K x

ρ/(g · cm−3 )

V E /(cm3 · mol−1 )

x

x 1-pentanol + (1 − x) cyclohexane T = 298.15 K 0.125 0.0519 0.201 0.0999

ρ/(g · cm−3 )

V E /(cm3 · mol−1 )

0.77467 0.77586

0.153 0.236

T = 283.15 K 0.0519 0.0999

0.78875 0.78983

0.1510

0.79109

0.266

0.1510

0.77727

0.304

0.1988 0.2549 0.3016 0.3617 0.3965

0.79237 0.79396 0.79538 0.79731 0.79848

0.315 0.358 0.382 0.398 0.399

0.1988 0.2549 0.3016 0.3617 0.3965

0.77872 0.78050 0.78201 0.78423 0.78540

0.349 0.390 0.421 0.422 0.439

0.4457

0.80016

0.399

0.4457

0.78732

0.426

0.5030 0.5470 0.6009

0.80222 0.80383 0.80583

0.384 0.369 0.346

0.5030 0.5470 0.6009

0.78951 0.79128 0.79349

0.416 0.396 0.368

0.6456

0.80753

0.322

0.6456

0.79535

0.340

0.7030 0.7502

0.80976 0.81162

0.286 0.251

0.7030 0.8022

0.79779 0.80209

0.297 0.213

0.8022

0.81372

0.208

0.8983

0.80639

0.115

0.8516

0.81575

0.162

0.9472

0.80862

0.059

0.8983 0.9472

0.81768 0.81976

0.116 0.062

0.0519 0.0999 0.1510 0.1988

0.76028 0.76158 0.76315 0.76478

0.195 0.286 0.355 0.397

0.0519 0.0999 0.1510 0.1988

0.74567 0.74706 0.74876 0.75049

0.245 0.347 0.420 0.469

0.3016 0.3617 0.4457 0.5030 0.6009 0.6456

0.76840 0.77069 0.77409 0.77660 0.78087 0.78289

0.469 0.486 0.482 0.452 0.404 0.372

0.2549 0.3617 0.3965 0.4457 0.5030 0.5470

0.75265 0.75691 0.75840 0.76064 0.76325 0.76538

0.506 0.555 0.556 0.537 0.516 0.482

0.7030 0.7502 0.8022 0.8516 0.8983 0.9472

0.78558 0.78777 0.79025 0.79264 0.79488 0.79731

0.319 0.278 0.225 0.170 0.121 0.059

0.6009 0.6456 0.7030 0.7502 0.8516 0.8983

0.76797 0.77011 0.77303 0.77552 0.78062 0.78306

0.444 0.414 0.350 0.286 0.187 0.128

0.9472

0.78563

0.067

T = 313.15 K

T = 328.15 K

Excess volumes of (1-pentanol + cyclohexane or benzene)

853

TABLE 3. Densities, ρ and excess volumes, V E for binary mixtures of 1-pentanol with benzene between T = 283.15 K and T = 328.15 K x

ρ/(g · cm−3 )

V E /(cm3 · mol−1 )

x

ρ/(g · cm−3 )

V E /(cm3 · mol−1 )

x 1-pentanol + (1 − x) benzene T = 283.15 K

T = 298.15 K

0.0506

0.88456

0.092

0.0506

0.86873

0.102

0.0840

0.88152

0.129

0.0840

0.86589

0.143

0.1558

0.87533

0.191

0.1558

0.86009

0.212

0.2019

0.87158

0.218

0.2019

0.85660

0.242

0.2514

0.86769

0.241

0.2514

0.85302

0.264

0.2938

0.86450

0.252

0.2938

0.85005

0.277

0.3592

0.85980

0.258

0.3592

0.84568

0.287

0.4215

0.85551

0.255

0.4215

0.84170

0.286

0.4543

0.85331

0.251

0.4543

0.83968

0.282

0.4815

0.85157

0.241

0.4815

0.83810

0.270

0.5579

0.84673

0.219

0.5579

0.83365

0.245

0.6033

0.84396

0.202

0.6033

0.83110

0.227

0.6625

0.84044

0.176

0.6625

0.82790

0.196

0.7008

0.83823

0.157

0.7008

0.82586

0.178

0.7466

0.83562

0.134

0.7466

0.82350

0.149

0.7960

0.83289

0.105

0.8439

0.81857

0.093

0.8439

0.83024

0.083

0.8989

0.81587

0.060

0.8989

0.82729

0.054

0.9473

0.81354

0.031

0.9473

0.82474

0.029

0.0506

0.85286

0.121

0.0506

0.83670

0.142

0.0840

0.85014

0.172

0.0840

0.83411

0.203

0.1558

0.84475

0.246

0.1558

0.82908

0.287

0.2019

0.84150

0.280

0.2019

0.82610

0.321

0.2514

0.83818

0.304

0.2514

0.82293

0.361

0.2938

0.83541

0.323

0.2938

0.82044

0.374

0.3592

0.83140

0.331

0.3592

0.81679

0.380

0.4215

0.82776

0.328

0.4215

0.81349

0.374

0.4543

0.82585

0.330

0.4543

0.81178

0.371

0.4815

0.82445

0.311

0.5579

0.80676

0.333

0.5579

0.82033

0.292

0.7008

0.80033

0.251

0.6033

0.81806

0.266

0.7466

0.79839

0.218

0.6625

0.81511

0.235

0.7960

0.79640

0.173

0.7008

0.81327

0.212

0.8439

0.79447

0.133

T = 313.15 K

T = 328.15 K

854

H. Ohji TABLE 3—continued x

ρ/(g · cm−3 )

V E /(cm3 · mol−1 )

x

ρ/(g · cm−3 )

V E /(cm3 · mol−1 )

0.7466

0.81113

0.180

0.8989

0.79229

0.088

0.7960

0.80886

0.145

0.9473

0.79042

0.046

0.8439

0.80670

0.111

0.8989

0.80427

0.072

0.9473

0.80215

0.038

0.6

0.5

V E /(cm3 . mol − 1)

0.4

0.3

0.2

0.1

0.0 0.0

0.2

0.4 0.6 x(1-pentanol)

0.8

1.0

FIGURE 1. Excess volumes for {x 1-pentanol + (1 − x) cyclohexane} plotted 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; , T = 328.15 K; —, calculated with equation (2) with parameters from table 4.

•

◦

THE (1PN + CH OR BZ) SYSTEMS

Both systems show a positive V E over the entire composition range at four temperatures and also a positive (∂ V E /∂ T ) P . Taking into account the large positive H E at T = 298.15 K (the maximum values are about 620–680 J · mol−1 for the CH system and about 1120– 1160 J · mol−1 for the BZ system), (13–15) disruption of the hydrogen bonding dominates the excess thermodynamic properties in these 1PN systems. The positive α E and negative (∂ H E /∂ P)T , which suggest that the expansivity of the solution is greater than that of pure liquids and the average intermolecular distance is prolonged upon mixing, support the above explanation. However, there are two differences between the CH systems and the BZ systems. First, while the maximum values of H E for the BZ systems exceed that of the CH systems, the CH systems exceed the BZ systems in the maximum value of V E . Second, the

Excess volumes of (1-pentanol + cyclohexane or benzene)

855

0.40 0.35 0.30 V E /(cm3 . mol − 1)

0.25 0.20 0.15 0.10 0.05 0.00 0.0

0.2

0.4 0.6 x(1-pentanol)

0.8

1.0

FIGURE 2. Excess volumes for {x 1-pentanol + (1 − x) benzene} plotted as a function of mole fraction x at four temperatures. Experimental results: , T = 283.15 K; N, T = 298.15K; , T = 313.15 K; , T = 328.15 K; —, calculated with equation (2) with parameters from table 4.

◦

•

4.0

αE /(10 − 5 K − 1)

3.0

2.0

1.0

0.0

− 1.0 0.0

0.2

0.4 0.6 x(1-pentanol)

0.8

1.0

FIGURE 3. Excess thermal expansivities for {1-pentanol + cyclohexane, or + benzene} plotted as a function of mole fraction x of 1-pentanol at T = 298.15 K calculated with equation (4): ——, cyclohexane; , benzene.

856

H. Ohji

(δHE /δP)T / (10 − 6J . Pa − 1 . mol − 1)

0.5

0.0

− 0.5

− 1.0

0.0

0.2

0.4 0.6 x(1-pentanol)

0.8

1.0

FIGURE 4. Dependence of excess enthalpies on pressure for {1-pentanol + cyclohexane, or + benzene} plotted as a function of mole fraction x of 1-pentanol at T = 298.15 K calculated with equation (6): ——, cyclohexane; , benzene.

values of (∂ V E /∂ T ) P , α E and (∂ H E /∂ P)T are nearly zero, which suggest less breaking of the hydrogen bonding, in the 1PN rich region for the CH systems. These are due to the larger local concentration fluctuation in the CH systems than in the BZ systems. That is, the intermolecular π–HO interaction promotes the dispersion in (1PN + BZ) more than in (1PN + CH) , leading to more disruption of self-associated molecules in the pure states for the BZ systems. Furthermore, the π–HO interaction would have a negative contribution to V E. THE 1PN AND 2EE SYSTEMS

The 2EE + BZ systems show a rather large negative contribution or much less positive contribution to the V E and H E in the region: x2EE = about 0.8 to 1.0. (3, 4) The fact that this phenomenon emerges only in the 2EE rich region, and that the values of α E and (∂ H E /∂ P)T are nearly zero in this region suggest the difficulty in breaking the 2EE intermolecular hydrogen bonding. The other feature is that the dependence of (∂ V E /∂ T ) P on solvents for the 2EE systems differ from that of the CH systems (figures 5 and 6). That is, the values of (∂ V E /∂ T ) P for the 2EE systems in the CH solvent (x2EE 6 0.5) are much larger than the other three systems. This means a larger expansion of the solutions with increasing temperature and the more disruption of the hydrogen bonded self-association leading to a significant loss of intermolecular interaction energy and the increase in the average intermolecular distance compared to the other three systems. The above explanation would become understandable in the light of the following facts

Excess volumes of (1-pentanol + cyclohexane or benzene)

857

TABLE 4. The coefficients of equation (2) and standard deviations, σ for mixtures between T = 283.15 K and T = 328.15 K A1

A2

A3

A4

σ/(cm3 · mol−1 )

x 1-pentanol + (1 − x) cyclohexane T = 283.15 K 1.542

0.53

0.32

0.13

0.003

0.60

0.40

0.40

0.006

0.74

0.56

0.66

0.010

0.95

0.75

0.89

0.015

T = 298.15 K 1.649 T = 313.15 K 1.82 T = 328.15 K 2.03

x 1-pentanol + (1 − x) benzene T = 283.15 K 0.947

0.54

0.22

0.17

0.003

0.57

0.22

0.22

0.004

0.59

0.29

0.38

0.005

0.63

0.43

0.52

0.005

T = 298.15 K 1.060 T = 313.15 K 1.234 T = 328.15 K 1.421

TABLE 5. Themal expansivities, α/K−1 for component liquids between T = 283.15 K and T = 328.15 K T /K

283.15

298.15

313.15

328.15

1-Pentanol

0.00088

0.00091

0.00094

0.00097

Cyclohexane

0.00118

0.00122

0.00126

0.00130

Benzene

0.00119

0.00123

0.00126

0.00129

that the value of α E at the maximum for (2EE + CH) is two times higher than that of the other three systems, the values of the isobaric excess heat capacities, C EP at x = 0.5 are 14.5 J · K−1 · mol−1 for (2-methoxyethanol + CH) and 6.8 J · K−1 · mol−1 for (2-methoxyethanol + BZ) at T = 298.15 K (16) and the values of (∂ H E /∂ P)T are quite negative for (2EE + CH) compared to (1PN + CH). These results led to the conclusion that, for the 2EE systems, which have the effect of the simultaneous presence of etheric and hydroxyl groups in the same molecule, the

858

H. Ohji 1.2

V E / (cm3 . mol − 1)

1.0

0.8

0.6

0.4

0.2

0.0 280

290

300

310

320

330

T/K

FIGURE 5. Excess volumes plotted against temperature for {x 1-pentanol + (1 − x) cyclohexane, or + benzene} at three mole fractions: cyclohexane solvent , x = 0.1; N, x = 0.5; , x = 0.9 benzene solvent , x = 0.1; 4, x = 0.5; , x = 0.9; ——, calculated line by the least-squares method.

•

◦

1.2

V E / (cm3 . mol − 1)

1.0

0.8

0.6

0.4

0.2

0.0 280

290

300

310

320

330

T/K

FIGURE 6. Excess volumes plotted against temperature for {x 2-ethoxyethanol + (1 − x) cyclohexane, or + benzene} at three mole fractions: cyclohexane solvent , x = 0.1; N, x = 0.5; , x = 0.9 benzene solvent , x = 0.1; 4, x = 0.5; , x = 0.9; ——, calculated line by the least-squares method.

◦

•

Excess volumes of (1-pentanol + cyclohexane or benzene)

859

behaviour of the hydrogen bonded association upon mixing and the increasing temperature significantly varies according to the kinds of solvents and composition. This would be assigned to a specific interaction between the ether oxygen and benzene, (17) and the ability of forming inter- and intra-molecular hydrogen bonds of 2EE. The author thanks Dr H. Ogawa for the use of his vibrating-tube densimeter and technical assistance and Dr K. Tamura for his support. REFERENCES 1. Kimura, F.; Murakami, S.; Fujishiro, F.; Toshiyasu, Y. Bull. Chem. Soc. Jpn. 1977, 50, 791–794. 2. Tamura, K.; Osaki, A.; Murakami, S.; Ohji, H.; Ogawa, H.; Laurent, B.; 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. Ohji, H.; Ogawa, H.; Murakami, S.; Tamura, K.; Grolier, J.-P. E. Fluid Phase Equilib. 1999, 156, 137–147. 5. Yu, C-H.; Tsai, F-N. J. Chem. Eng. Data 1994, 39, 441–443. 6. Ortega, J.; Paz-Andrade, M. I. J. Chem. Eng. Data 1986, 31, 231–235. 7. Tsierkezos, N. G.; Palaiologou, M. M.; Molinou, I. E. J. Chem. Eng. Data 2000, 45, 272–275. 8. Munk, P.; Qin, A.; Hoffman, D. E. Collect. Czech. Chem. Cmmun. 1993, 58, 2612–2624. 9. Kumar, K. S.; Reddy, N. V. Phys. Chem. Liq. 2001, 39, 117–123. 10. Janssens, J-M.; Ruel, M. Can. J. Chem. Eng. 1972, 50, 591–594. 11. Kiyohara, O.; D’Arcy, P. J.; Benson, G. C. Can. J. Chem. 1978, 56, 2803–2807. 12. Arimoto, A.; Ogawa, H.; Murakami, S. Thermochim. Acta 1990, 163, 191–202. 13. Saris, P.; Rosenholm, J. B.; Sj¨oblom, E.; Henriksson, U. J. Phy. Chem. 1986, 90, 660–665. 14. Thermodynamics Research Center, Texas A & M Univ. Int. Data Ser., Selec. Data Mixtures, Ser. A 1976, 26. 15. Posa, C. G.; Nu˜nez, L.; Villar, E. J. Chem. Thermodynamics 1972, 4, 275–281. 16. Valero, J.; Gracia, M.; Losa, C. G. J. Chem. Thermodynamics 1979, 11, 1101–1105. 17. Morimoto, S.; Takahta, J. Bull. Sch. High-Tech. Tokai Univ. 1991, 1, 65–73. (Received 4 September 2001; in final form 3 December 2001)

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