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Densities, excess molar volumes, and refractive indices of ethyl acetate and aromatic hydrocarbon binary mixtures
J. Chem. Thermodynamics 2002, 34, 995–1004 doi:10.1006/jcht.2002.0964 Available online at http://www.idealibrary.com on
Densities, excess molar volumes, and refractive indices of ethyl acetate and aromatic hydrocarbon binary mixtures J. M. Resa,a C. Gonz´alez, S. Ortiz de Landaluce, and J. Lanz Dpto. Ingenier´ıa Qu´ımica, Facultad de Farmacia, Apdo. 450-Vitoria, Spain
Densities, excess molar volumes, refractive indices, and changes in refractive index on mixing for (ethyl acetate + benzene, or methylbenzene, or ethylbenzene, or 1-4-dimethylbenzene, or 1-methylethylbenzene, or 1-3-5-trimethylbenzene, or 1-1dimethylethylbenzene) have been determined at T = 298.15 K. The excess molar volumes and changes in refractive index have been fitted to Redlich–Kister polynomials. The π-electrons interactions of the benzene ring and the peculiar plate shape of the aromatic molecules are noticeably modified by the presence of the ethyl acetate molecules of a different nature. The intermolecular interactions are strongly modified and result in positive excess volumes except for toluene or p-xylene whose values are close to zero. The refractive indices were compared with calculated values using mixing rules proposed c 2002 Elsevier Science Ltd. All rights reserved. by several authors. KEYWORDS: density; excess volume; refractive index; ethyl acetate; aromatic hydrocarbons
1. Introduction This work is a continuation of a study of thermodynamic properties of systems formed by an ester and an organic compound. (1–4) The study examines the steric hindrance effect of various alkyl groups attached to the benzene molecule on the properties of mixtures of benzene derivatives with ethyl acetate. The study of excess volume is the first step to a fundamental understanding of the thermodynamics of an important class of molecules, the benzene derivatives in mixtures with molecules of a different nature. Here, results of refractive indices, densities and excess volumes of ethyl acetate and benzenic hydrocarbons mixtures are presented. There are no previous data in literature concerning these systems. The studied hydrocarbons are: benzene, methylbenzene, ethylbenzene, 1-4dimethylbenzene, 1-methyl-ethylbenzene, 1-3-5-trimethylbenzene and 1-1-dimethylethylbenzene. a Corresponding author: Universidad del Pais Vasco, Faclutad de Farmacia Departamento de Ingenieria Quimica, Apdo 450 C/Paseo de la Universidad 7, 01007 Vitoria, Spain
0021–9614/02
c 2002 Elsevier Science Ltd. All rights reserved.
996
J. M. Resa et al. TABLE 1. Densities ρ and refractive indices n D of the pure substances at T = 298.15 K ρ/g · cm−3
ρ/g · cm−3
nD
nD
expt
lit (5)
expt
lit (5)
Ethyl acetate
0.89426
0.89455
1.36973
1.36978
Benzene
0.87350
0.87360
1.49699
1.49792
Methylbenzene
0.86208
0.86219
1.49338
1.49413
Ethylbenzene
0.86247
0.86253
1.49304
1.49320
1-4-dimethylbenzene
0.85653
0.85661
1.49298
1.49325
1-methylethylbenzene
0.85740
0.85743
1.48840
1.48890
1-3-5-trimethylbenzene
0.86123
0.86111
1.49684
1.49684
1-1-dimethylethylbenzene
0.86217
0.86240
1.49000
1.49024
Compound
2. Experimental The chemicals used were supplied by Riedel de Ha¨en and their mole fraction purities were better than 0.995. The purities were checked by gas chromatography, using a 14-B Shimadzu gas chromatograph with a Carbowax 20M column. The mixtures were prepared by mass using a Salter ER-182A balance with an accuracy of ±1 · 10−4 g. Densities were measured with an accuracy of ±1 · 10−5 g · cm−3 using an Anton Paar DMA 58 digital vibrating-tube densimeter. Refractive indices were measured with an accuracy of ±5·10−4 for values ranging from 1.32 to 1.40 and ±1 · 10−4 for values between 1.40 and 1.58 using a Mettler Toledo RE150 refractometer. The measurement method relies on an optical detection of the critical angle at the wavelength of the sodium D line (589.3 nm). The refractometer keeps the temperature of the sample being measured constant using a builtin Peltier thermostat control. All the measurements were made at T = (298.15 ± 0.01) K and at atmospheric pressure. The densimeter was calibrated with water and air. The excess volumes were accurate to within ±2 × 10−3 cm−3 · mol−1 . The temperature was measured with an accuracy of ±0.01 K. The experimental densities and refractive indices at T = 298.15 K of the pure solvents (5) are presented in table 1 along with the corresponding literature values. (5)
3. Results and discussion The densities, excess molar volumes, refractive indices and changes in refractive index on mixing are listed in table 2. The excess molar volumes of the binary mixtures, shown in figure 1, were computed from the density measurements by using the following equation: VE =
N X i=1
xi Mi (ρ −1 − ρi−1 ),
(1)
(Ethyl acetate + hydrocarbons)
997
0.35 0.3 V E(cm3 . mol –1)
0.25 0.2 0.15 0.1 0.05 0 – 0.05 0
0.2
0.4 x1
0.6
0.8
1
•
FIGURE 1. Change of refractive indices on mixing of ethyl acetate with benzene , methylbenzene O, ethylbenzene , 1-4-dimethylbenzene , 1-methylethylbenzene ♦, 1-3-5-trimethylbenzene , 1-1-dimethylethylbenzene 4, at T = 298.15 K.
◦
where ρ is the density of the mixture, ρi the density of pure component i, xi is the mole fraction and N stands for the number of components in the mixture. Excess molar volumes and changes in refractive index on mixing of the binary systems were fitted to Redlich– Kister polynomials of the form: X V E /(cm3 · mol−1 ), or 1n D = x1 x2 ak (x1 − x2 )k , (2) k >0
were x1 is the mole fraction of the more volatile compound, ak are adjustable parameters obtained by a least-squares method, and k is the degree of the polynomials. Table 3 presents the values of the parameters ak together with the standard deviation σ (V E ). The coefficients ak were used to calculate the solid curves in figure 1. In figure 1, are plotted the excess molar volumes of (ethyl acetate + a hydrocarbon) as a function of the mole fraction of ethyl acetate. The values are close to zero for mixtures with methylbenzene and 1-3-5-trimethylbenzene, while for the other hydrocarbons positive values are found over the whole composition range. When molecules of two components are mixed, interactions between them occur. Ethyl acetate is weakly polar and aromatic hydrocarbons are nearly non-polar. When the nonpolar molecules of a hydrocarbon intersperse among the ethyl acetate molecules, there is a decreasing interaction among the dipoles of the acetate. Hydrocarbon molecules will have increasing difficulties in establishing interactions the larger they are. If the molecules are flat or with few bulky substituents (methylbenzene, 1-35-trimethylbenzene), some interactions can persist and the excess volume is either small or close to zero. If the hydrocarbon molecules have a bulky substituent or occupy a different plane than the one for the benzenic ring, the interactions among acetate molecules are disabled and the excess volumes will be higher than in the previous case. The presence of three methylene groups in the meta position obstructs the approach of the acetate towards the ring and the steric volume is higher. In this case, the interaction among acetate
998
J. M. Resa et al. TABLE 2. Densities ρ, excess molar volume V E , refractive indices n D , changes in refractive index on mixing 1n D for binary mixtures at T = 298.15 K as a function of the mole fraction x of ethyl acetate x1
ρ/(g · cm−3 )
0.0544
0.87444
0.0952
0.87515
0.1476
0.87619
0.1852
V E /(cm3 · mol−1 )
nD
1n D
0.031
1.48953
−0.0005
0.052
1.48314
−0.0017
0.066
1.47583
−0.0024
0.87690
0.079
1.47034
−0.0031
0.2572
0.87828
0.100
1.46071
−0.0035
0.2858
0.87886
0.104
1.45654
−0.0041
0.3443
0.88007
0.109
1.44889
−0.0043
0.4053
0.88134
0.112
1.44053
−0.0049
0.4753
0.88277
0.117
1.43164
−0.0049
0.5006
0.88329
0.117
1.42845
−0.0049
0.5513
0.88434
0.117
1.42192
−0.0049
0.6092
0.88555
0.115
1.41498
−0.0045
0.6568
0.88661
0.105
1.40926
−0.0041
0.7001
0.88756
0.096
1.40400
−0.0039
0.7615
0.88893
0.080
1.39674
−0.0033
0.8234
0.89032
0.061
1.38930
−0.0029
0.8566
0.89103
0.054
1.38576
−0.0022
0.8871
0.89174
0.041
1.38363
−0.0005
0.9483
0.89312
0.018
1.37531
−0.0010
Ethyl acetate + benzene
Ethyl acetate + methylbenzene 0.0517
0.86358
0.005
1.48777
0.0008
0.1020
0.86519
−0.007
1.48210
0.0013
0.1538
0.86676
−0.008
1.47582
0.0014
0.1972
0.86815
−0.016
1.47076
0.0018
0.2515
0.86980
−0.013
1.46431
0.0020
0.3028
0.87140
−0.014
1.45798
0.0020
0.3464
0.87274
−0.012
1.45286
0.0023
0.3989
0.87436
−0.080
1.44658
0.0025
0.4499
0.87600
−0.010
1.44009
0.0023
0.5050
0.87773
−0.006
1.43328
0.0023
0.5474
0.87911
−0.008
1.42793
0.0022
0.5989
0.88081
−0.010
1.42147
0.0021
0.6485
0.88243
−0.010
1.41526
0.0021
0.7003
0.88410
−0.005
1.40865
0.0019
(Ethyl acetate + hydrocarbons)
999
TABLE 2—continued x1
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
nD
1n D
0.7502
0.88576
−0.004
1.40223
0.0016
0.7957
0.88715
0.011
1.39638
0.0014
0.8522
0.88916
0.000
1.38912
0.0011
0.9009
0.89080
0.003
1.38270
0.0007
0.9476
0.89240
0.004
1.37665
0.0004
0.0487
0.86362
0.014
1.48790
0.0009
0.1082
0.86509
0.027
1.48195
0.0022
0.1605
0.86646
0.031
1.47626
0.0030
0.1977
0.86737
0.046
1.47199
0.0033
0.2492
0.86876
0.052
1.46594
0.0036
0.3136
0.87048
0.066
1.45890
0.0045
0.3523
0.87153
0.077
1.45492
0.0053
0.4011
0.87296
0.078
1.44927
0.0057
0.4488
0.87430
0.092
1.44338
0.0057
0.4998
0.87582
0.098
1.43743
0.0060
0.5503
0.87740
0.100
1.43149
0.0063
0.6013
0.87904
0.100
1.42474
0.0058
0.6529
0.88077
0.097
1.41820
0.0057
0.7007
0.88242
0.093
1.41169
0.0050
0.7457
0.88403
0.087
1.40573
0.0046
0.8000
0.88599
0.082
1.39831
0.0039
0.8510
0.88800
0.064
1.39121
0.0031
0.9077
0.89014
0.061
1.38312
0.0020
0.9486
0.89200
0.027
1.37724
0.0012
Ethyl acetate + ethylbenzene
Ethyl acetate + 1-4-dimethylbenzene 0.0471
0.85798
−0.003
1.48836
0.0965
0.85949
−0.001
1.48303
0.0012 0.0019
0.1472
0.86107
0.002
1.47803
0.0032
0.1988
0.86276
−0.002
1.47236
0.0039
0.2504
0.86445
−0.001
1.46705
0.0049
0.3008
0.86616
−0.002
1.46161
0.0057
0.3504
0.86788
−0.004
1.45602
0.0062
0.4042
0.86977
−0.003
1.44977
0.0066
0.4492
0.87138
−0.001
1.44428
0.0067
0.4986
0.87322
−0.004
1.43842
0.0069
0.5486
0.87506
0.001
1.43202
0.0066
1000
J. M. Resa et al. TABLE 2—continued x1
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
0.6032
0.87715
0.003
1.42520
0.0065
0.6519
0.87907
0.003
1.41880
0.0062
0.6979
0.88093
0.003
1.41248
0.0055
0.7496
0.88306
0.004
1.40577
0.0052
0.8002
0.88516
0.009
1.39885
0.0045
0.8493
0.88732
0.006
1.39182
0.0035
0.8997
0.88956
0.007
1.38457
0.0025
0.9502
0.89177
0.017
1.37703
0.0012
nD
1n D
Ethyl acetate + 1-methylethylbenzene 0.0475
0.85853
0.025
1.48383
0.0011
0.0998
0.85986
0.040
1.47925
0.0027
0.1486
0.86108
0.063
1.47452
0.0037
0.2021
0.86252
0.079
1.46946
0.0050
0.2496
0.86384
0.093
1.46457
0.0058
0.3021
0.86540
0.101
1.46006
0.0075
0.3488
0.86678
0.116
1.45518
0.0082
0.4006
0.86840
0.127
1.44948
0.0086
0.4513
0.87002
0.140
1.44401
0.0092
0.4980
0.87164
0.142
1.43915
0.0098
0.5521
0.87350
0.155
1.43202
0.0091
0.5985
0.87520
0.161
1.42616
0.0088
0.6491
0.87716
0.161
1.42000
0.0086
0.7011
0.87930
0.155
1.41293
0.0077
0.7492
0.88135
0.151
1.40668
0.0072
0.7990
0.88366
0.133
1.40005
0.0065
0.8470
0.88593
0.122
1.39326
0.0054
0.9012
0.88878
0.088
1.38535
0.0039
0.9494
0.89135
0.066
1.37788
0.0021
Ethyl acetate + 1-3-5-trimethylbenzene 0.0526
0.86217
0.049
1.49155
0.0014
0.0989
0.86294
0.105
1.48712
0.0028
0.1505
0.86392
0.152
1.48207
0.0044
0.1983
0.86483
0.199
1.47711
0.0055
0.2577
0.86619
0.229
1.47046
0.0064
0.2995
0.86708
0.265
1.46614
0.0074
0.3525
0.86841
0.287
1.46042
0.0084
0.3998
0.86956
0.317
1.45464
0.0086
(Ethyl acetate + hydrocarbons)
1001
TABLE 2—continued x1
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
0.4503
0.87094
0.333
1.44915
0.0095
0.4992
0.87241
0.336
1.44305
0.0096
0.5572
0.87420
0.343
1.43527
0.0092
0.5981
0.87561
0.334
1.42994
0.0091
0.6511
0.87756
0.315
1.42288
0.0088
0.6986
0.87931
0.305
1.41616
0.0081
0.7504
0.88152
0.267
1.40894
0.0075
0.7971
0.88356
0.235
1.40206
0.0065
0.8495
0.88589
0.206
1.39410
0.0052
0.9019
0.88851
0.155
1.38605
0.0038
0.9510
0.89136
0.074
1.37824
0.0023
nD
1n D
Ethyl acetate + 1-1-dimethylethylbenzene 0.047
0.86308
0.010
1.48637
0.0020
0.104
0.86418
0.033
1.48126
0.0038
0.150
0.86516
0.041
1.47742
0.0055
0.200
0.86624
0.053
1.47291
0.0070
0.247
0.86732
0.060
1.46844
0.0082
0.306
0.86872
0.070
1.46302
0.0098
0.352
0.86993
0.072
1.45875
0.0111
0.401
0.87117
0.082
1.45352
0.0117
0.450
0.87255
0.084
1.44838
0.0124
0.511
0.87430
0.094
1.44139
0.0129
0.553
0.87555
0.100
1.43636
0.0128
0.600
0.87704
0.103
1.43059
0.0127
0.652
0.87880
0.107
1.42384
0.0123
0.701
0.88050
0.112
1.41723
0.0116
0.748
0.88226
0.108
1.41062
0.0105
0.801
0.88440
0.103
1.40282
0.0092
0.848
0.88643
0.090
1.39547
0.0075
0.900
0.88878
0.081
1.38718
0.0054
0.951
0.89148
0.040
1.37866
0.0030
molecules will be lower and the excess volume increases. Increase in excess volume with the size of molecules has been shown in other (non-polar + polar compounds). (6) The variation of the refractive indices on mixing with the mole fraction of ethyl acetate is shown in figure 2. The experimental refractive indices of the mixtures were compared with calculated values using the mixing rules proposed by Lorentz–Lorenz {equation (3)}, (7)
1002
J. M. Resa et al.
TABLE 3. Adjustable parameters ak and standard deviation σ of the excess volume V E and change in refractive index on mixing 1n D for the studied systems System
a0
a1
a2
103 σV E /cm3 · mol−1
V E /(cm3 · mol−1 ) Ethyl acetate + benzene Ethyl acetate + methylbenzene Ethyl acetate + ethylbenzene Ethyl acetate + 1-4-dimethylbenzene
0.4732
0.0703
0.0198
−0.0422
−0.0609
0.0418
2.8 4.1
0.3759
−0.1912
0.0508
4.2
−0.0077
−0.0492
0.0850
3.4
Ethyl acetate + 1-methylethylbenzene
0.5826
−0.3210
0.2643
4.1
Ethyl acetate + 1-3-5-trimethylbenzene
1.3427
−0.2451
0.0501
6.7
Ethyl acetate + 1-1-dimethylethylbenzene
0.3698
−0.2705
0.3262
3.2
1n D 103 σ1n D −0.0197
−0.0017
0.0047
0.31
Ethyl acetate + methylbenzene
Ethyl acetate + benzene
0.0092
0.0022
0.0023
0.09 0.19
Ethyl acetate + ethylbenzene
0.0239
−0.0030
−0.0028
Ethyl acetate + 1-4-dimethylbenzene
0.0273
−0.0013
−0.0026
0.13
Ethyl acetate + 1-methylethylbenzene
0.0370
−0.0062
−0.0036
0.28
Ethyl acetate + 1-3-5-trimethylbenzene
0.0376
−0.0051
−0.0009
0.18
Ethyl acetate + 1-1-dimethylethylbenzene
0.0510
−0.0113
−0.0008
0.11
TABLE 4. Deviations σ between the experimental and calculated values of the refractive indices on mixing using several mixing rules: Lorentz–Lorenz, (7) Dale–Gladstone, (7) Eykman, (7) Newton, (7) and Oster (7) σ
System (Lorentz)
(Dale)
(Eykman)
(Newton)
(Oster)
Ethyl acetate + benzene
0.00039
0.00129
0.00098
0.00232
0.00188
Ethyl acetate + methylbenzene
0.00096
0.00023
0.00031
0.00112
0.00070
Ethyl acetate + ethylbenzene
0.00036
0.00076
0.00047
0.00173
0.00131
Ethyl acetate + 1-4-dimethylbenzene
0.00079
0.00032
0.00020
0.00126
0.00084
Ethyl acetate + 1-methylethylbenzene
0.00032
0.00100
0.00074
0.00189
0.00151
Ethyl acetate + 1-3-5-trimethylbenzene
0.00032
0.00070
0.00042
0.00162
0.00123
Ethyl acetate + 1-1-dimethylethylbenzene
0.00025
0.00125
0.00093
0.00229
0.00185
Dale–Gladstone {equation (4)}, Eykman {equation (5)}, Newton {equation (6)} and Oster {equation (7)}. n 2D − 1 n 2D + 2
=
N 2 X n −1 φi Di , n 2Di + 2 i=1
(3)
(Ethyl acetate + hydrocarbons)
1003
0.014 0.012 0.01
∆nD
0.008 0.006 0.004 0.002 0 – 0.002 – 0.004 – 0.006 0
0.2
0.4
0.6
0.8
1
x1
•
FIGURE 2. Excess molar volumes of mixtures of ethyl acetate with benzene , methylbenzene O, ethylbenzene , 1-4-dimethylbenzene , 1-methylethylbenzene ♦, 1-3-5-trimethylbenzene , 1-1dimethylethylbenzene 4, at T = 298.15 K.
◦
nD − 1 =
N X
{φi (n Di − 1)},
(4)
i=1
N 2 X n Di − 1 = φi 2 , n 2D + 0.4 i=1 n Di + 0.4 n 2D − 1
n 2D − 1 =
N X
{φi (n 2Di − 1)},
(5)
(6)
i=1
(n 2D − 1) − (2n 2D + 1) n 2D
=
N 2 X (n Di − 1) − (2n 2Di + 1) φi . n 2Di i=1
(7)
In these equations, n D is the refractive index of the mixture, and n Di , and φi are the refractive index and the volumetric fraction of component i, respectively. Deviations of the experimental and predicted refractive indices on mixing are listed in table 4. A good agreement is observed in all cases and the deviations are lesser than 5 per cent for the studied binary mixtures. We are grateful for financial assistance from the University of the Basque Country (Project UPV-069.123-EA 156/97) and Miguel Iglesias for help in computational work. REFERENCES 1. Gonz´alez, C.; Resa, J. M.; Lanz, J.; Ruiz, A. ELDATA: The International Electronic Journal of Physico-Chemical Data 1996, 2, 185–192. 2. Gonz´alez, C.; Resa, J. M.; Lanz, J.; Mtz. de Ilarduya, J. A. Fluid Phase Equilib. 1997, 137, 141–148. 3. Gonz´alez, C.; Resa, J. M.; Lanz, J.; Mtz. de Ilarduya, J. A. ELDATA: The International Electronic Journal of Physico-Chemical Data 1997, 3, 183–190.
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4. Resa, J. M.; Gonz´alez, C.; Lanz, J.; Mtz. de Ilarduya, J. A. J. Therm. Anal. 1998, 52, 895–901. 5. Riddick, J.; Bunger, W.; Sakano, T. K. Organic Solvents: Physical Properties and Methods of Purification. Wiley Interscience: New York. 1986. 6. Gonz´alez, C.; Resa, J. M.; Ruiz, A.; Betolaza, M. A.; Mtz. de Ilarduya, J. A. ELDATA: The International Electronic Journal of Physico-Chemical Data 1995, 1, 275–280. 7. Tasic; DjordjevicB. D.; GrozdanicD. K. J. Chem. Eng. Data 1992, 37, 310–313. (Received 19 September 2000; revised 7 March 2001; accepted 14 May 2001)
WA00/049
Densities, excess molar volumes, and refractive indices of ethyl acetate and aromatic hydrocarbon binary mixtures J. M. Resa,a C. Gonz´alez, S. Ortiz de Landaluce, and J. Lanz Dpto. Ingenier´ıa Qu´ımica, Facultad de Farmacia, Apdo. 450-Vitoria, Spain
Densities, excess molar volumes, refractive indices, and changes in refractive index on mixing for (ethyl acetate + benzene, or methylbenzene, or ethylbenzene, or 1-4-dimethylbenzene, or 1-methylethylbenzene, or 1-3-5-trimethylbenzene, or 1-1dimethylethylbenzene) have been determined at T = 298.15 K. The excess molar volumes and changes in refractive index have been fitted to Redlich–Kister polynomials. The π-electrons interactions of the benzene ring and the peculiar plate shape of the aromatic molecules are noticeably modified by the presence of the ethyl acetate molecules of a different nature. The intermolecular interactions are strongly modified and result in positive excess volumes except for toluene or p-xylene whose values are close to zero. The refractive indices were compared with calculated values using mixing rules proposed c 2002 Elsevier Science Ltd. All rights reserved. by several authors. KEYWORDS: density; excess volume; refractive index; ethyl acetate; aromatic hydrocarbons
1. Introduction This work is a continuation of a study of thermodynamic properties of systems formed by an ester and an organic compound. (1–4) The study examines the steric hindrance effect of various alkyl groups attached to the benzene molecule on the properties of mixtures of benzene derivatives with ethyl acetate. The study of excess volume is the first step to a fundamental understanding of the thermodynamics of an important class of molecules, the benzene derivatives in mixtures with molecules of a different nature. Here, results of refractive indices, densities and excess volumes of ethyl acetate and benzenic hydrocarbons mixtures are presented. There are no previous data in literature concerning these systems. The studied hydrocarbons are: benzene, methylbenzene, ethylbenzene, 1-4dimethylbenzene, 1-methyl-ethylbenzene, 1-3-5-trimethylbenzene and 1-1-dimethylethylbenzene. a Corresponding author: Universidad del Pais Vasco, Faclutad de Farmacia Departamento de Ingenieria Quimica, Apdo 450 C/Paseo de la Universidad 7, 01007 Vitoria, Spain
0021–9614/02
c 2002 Elsevier Science Ltd. All rights reserved.
996
J. M. Resa et al. TABLE 1. Densities ρ and refractive indices n D of the pure substances at T = 298.15 K ρ/g · cm−3
ρ/g · cm−3
nD
nD
expt
lit (5)
expt
lit (5)
Ethyl acetate
0.89426
0.89455
1.36973
1.36978
Benzene
0.87350
0.87360
1.49699
1.49792
Methylbenzene
0.86208
0.86219
1.49338
1.49413
Ethylbenzene
0.86247
0.86253
1.49304
1.49320
1-4-dimethylbenzene
0.85653
0.85661
1.49298
1.49325
1-methylethylbenzene
0.85740
0.85743
1.48840
1.48890
1-3-5-trimethylbenzene
0.86123
0.86111
1.49684
1.49684
1-1-dimethylethylbenzene
0.86217
0.86240
1.49000
1.49024
Compound
2. Experimental The chemicals used were supplied by Riedel de Ha¨en and their mole fraction purities were better than 0.995. The purities were checked by gas chromatography, using a 14-B Shimadzu gas chromatograph with a Carbowax 20M column. The mixtures were prepared by mass using a Salter ER-182A balance with an accuracy of ±1 · 10−4 g. Densities were measured with an accuracy of ±1 · 10−5 g · cm−3 using an Anton Paar DMA 58 digital vibrating-tube densimeter. Refractive indices were measured with an accuracy of ±5·10−4 for values ranging from 1.32 to 1.40 and ±1 · 10−4 for values between 1.40 and 1.58 using a Mettler Toledo RE150 refractometer. The measurement method relies on an optical detection of the critical angle at the wavelength of the sodium D line (589.3 nm). The refractometer keeps the temperature of the sample being measured constant using a builtin Peltier thermostat control. All the measurements were made at T = (298.15 ± 0.01) K and at atmospheric pressure. The densimeter was calibrated with water and air. The excess volumes were accurate to within ±2 × 10−3 cm−3 · mol−1 . The temperature was measured with an accuracy of ±0.01 K. The experimental densities and refractive indices at T = 298.15 K of the pure solvents (5) are presented in table 1 along with the corresponding literature values. (5)
3. Results and discussion The densities, excess molar volumes, refractive indices and changes in refractive index on mixing are listed in table 2. The excess molar volumes of the binary mixtures, shown in figure 1, were computed from the density measurements by using the following equation: VE =
N X i=1
xi Mi (ρ −1 − ρi−1 ),
(1)
(Ethyl acetate + hydrocarbons)
997
0.35 0.3 V E(cm3 . mol –1)
0.25 0.2 0.15 0.1 0.05 0 – 0.05 0
0.2
0.4 x1
0.6
0.8
1
•
FIGURE 1. Change of refractive indices on mixing of ethyl acetate with benzene , methylbenzene O, ethylbenzene , 1-4-dimethylbenzene , 1-methylethylbenzene ♦, 1-3-5-trimethylbenzene , 1-1-dimethylethylbenzene 4, at T = 298.15 K.
◦
where ρ is the density of the mixture, ρi the density of pure component i, xi is the mole fraction and N stands for the number of components in the mixture. Excess molar volumes and changes in refractive index on mixing of the binary systems were fitted to Redlich– Kister polynomials of the form: X V E /(cm3 · mol−1 ), or 1n D = x1 x2 ak (x1 − x2 )k , (2) k >0
were x1 is the mole fraction of the more volatile compound, ak are adjustable parameters obtained by a least-squares method, and k is the degree of the polynomials. Table 3 presents the values of the parameters ak together with the standard deviation σ (V E ). The coefficients ak were used to calculate the solid curves in figure 1. In figure 1, are plotted the excess molar volumes of (ethyl acetate + a hydrocarbon) as a function of the mole fraction of ethyl acetate. The values are close to zero for mixtures with methylbenzene and 1-3-5-trimethylbenzene, while for the other hydrocarbons positive values are found over the whole composition range. When molecules of two components are mixed, interactions between them occur. Ethyl acetate is weakly polar and aromatic hydrocarbons are nearly non-polar. When the nonpolar molecules of a hydrocarbon intersperse among the ethyl acetate molecules, there is a decreasing interaction among the dipoles of the acetate. Hydrocarbon molecules will have increasing difficulties in establishing interactions the larger they are. If the molecules are flat or with few bulky substituents (methylbenzene, 1-35-trimethylbenzene), some interactions can persist and the excess volume is either small or close to zero. If the hydrocarbon molecules have a bulky substituent or occupy a different plane than the one for the benzenic ring, the interactions among acetate molecules are disabled and the excess volumes will be higher than in the previous case. The presence of three methylene groups in the meta position obstructs the approach of the acetate towards the ring and the steric volume is higher. In this case, the interaction among acetate
998
J. M. Resa et al. TABLE 2. Densities ρ, excess molar volume V E , refractive indices n D , changes in refractive index on mixing 1n D for binary mixtures at T = 298.15 K as a function of the mole fraction x of ethyl acetate x1
ρ/(g · cm−3 )
0.0544
0.87444
0.0952
0.87515
0.1476
0.87619
0.1852
V E /(cm3 · mol−1 )
nD
1n D
0.031
1.48953
−0.0005
0.052
1.48314
−0.0017
0.066
1.47583
−0.0024
0.87690
0.079
1.47034
−0.0031
0.2572
0.87828
0.100
1.46071
−0.0035
0.2858
0.87886
0.104
1.45654
−0.0041
0.3443
0.88007
0.109
1.44889
−0.0043
0.4053
0.88134
0.112
1.44053
−0.0049
0.4753
0.88277
0.117
1.43164
−0.0049
0.5006
0.88329
0.117
1.42845
−0.0049
0.5513
0.88434
0.117
1.42192
−0.0049
0.6092
0.88555
0.115
1.41498
−0.0045
0.6568
0.88661
0.105
1.40926
−0.0041
0.7001
0.88756
0.096
1.40400
−0.0039
0.7615
0.88893
0.080
1.39674
−0.0033
0.8234
0.89032
0.061
1.38930
−0.0029
0.8566
0.89103
0.054
1.38576
−0.0022
0.8871
0.89174
0.041
1.38363
−0.0005
0.9483
0.89312
0.018
1.37531
−0.0010
Ethyl acetate + benzene
Ethyl acetate + methylbenzene 0.0517
0.86358
0.005
1.48777
0.0008
0.1020
0.86519
−0.007
1.48210
0.0013
0.1538
0.86676
−0.008
1.47582
0.0014
0.1972
0.86815
−0.016
1.47076
0.0018
0.2515
0.86980
−0.013
1.46431
0.0020
0.3028
0.87140
−0.014
1.45798
0.0020
0.3464
0.87274
−0.012
1.45286
0.0023
0.3989
0.87436
−0.080
1.44658
0.0025
0.4499
0.87600
−0.010
1.44009
0.0023
0.5050
0.87773
−0.006
1.43328
0.0023
0.5474
0.87911
−0.008
1.42793
0.0022
0.5989
0.88081
−0.010
1.42147
0.0021
0.6485
0.88243
−0.010
1.41526
0.0021
0.7003
0.88410
−0.005
1.40865
0.0019
(Ethyl acetate + hydrocarbons)
999
TABLE 2—continued x1
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
nD
1n D
0.7502
0.88576
−0.004
1.40223
0.0016
0.7957
0.88715
0.011
1.39638
0.0014
0.8522
0.88916
0.000
1.38912
0.0011
0.9009
0.89080
0.003
1.38270
0.0007
0.9476
0.89240
0.004
1.37665
0.0004
0.0487
0.86362
0.014
1.48790
0.0009
0.1082
0.86509
0.027
1.48195
0.0022
0.1605
0.86646
0.031
1.47626
0.0030
0.1977
0.86737
0.046
1.47199
0.0033
0.2492
0.86876
0.052
1.46594
0.0036
0.3136
0.87048
0.066
1.45890
0.0045
0.3523
0.87153
0.077
1.45492
0.0053
0.4011
0.87296
0.078
1.44927
0.0057
0.4488
0.87430
0.092
1.44338
0.0057
0.4998
0.87582
0.098
1.43743
0.0060
0.5503
0.87740
0.100
1.43149
0.0063
0.6013
0.87904
0.100
1.42474
0.0058
0.6529
0.88077
0.097
1.41820
0.0057
0.7007
0.88242
0.093
1.41169
0.0050
0.7457
0.88403
0.087
1.40573
0.0046
0.8000
0.88599
0.082
1.39831
0.0039
0.8510
0.88800
0.064
1.39121
0.0031
0.9077
0.89014
0.061
1.38312
0.0020
0.9486
0.89200
0.027
1.37724
0.0012
Ethyl acetate + ethylbenzene
Ethyl acetate + 1-4-dimethylbenzene 0.0471
0.85798
−0.003
1.48836
0.0965
0.85949
−0.001
1.48303
0.0012 0.0019
0.1472
0.86107
0.002
1.47803
0.0032
0.1988
0.86276
−0.002
1.47236
0.0039
0.2504
0.86445
−0.001
1.46705
0.0049
0.3008
0.86616
−0.002
1.46161
0.0057
0.3504
0.86788
−0.004
1.45602
0.0062
0.4042
0.86977
−0.003
1.44977
0.0066
0.4492
0.87138
−0.001
1.44428
0.0067
0.4986
0.87322
−0.004
1.43842
0.0069
0.5486
0.87506
0.001
1.43202
0.0066
1000
J. M. Resa et al. TABLE 2—continued x1
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
0.6032
0.87715
0.003
1.42520
0.0065
0.6519
0.87907
0.003
1.41880
0.0062
0.6979
0.88093
0.003
1.41248
0.0055
0.7496
0.88306
0.004
1.40577
0.0052
0.8002
0.88516
0.009
1.39885
0.0045
0.8493
0.88732
0.006
1.39182
0.0035
0.8997
0.88956
0.007
1.38457
0.0025
0.9502
0.89177
0.017
1.37703
0.0012
nD
1n D
Ethyl acetate + 1-methylethylbenzene 0.0475
0.85853
0.025
1.48383
0.0011
0.0998
0.85986
0.040
1.47925
0.0027
0.1486
0.86108
0.063
1.47452
0.0037
0.2021
0.86252
0.079
1.46946
0.0050
0.2496
0.86384
0.093
1.46457
0.0058
0.3021
0.86540
0.101
1.46006
0.0075
0.3488
0.86678
0.116
1.45518
0.0082
0.4006
0.86840
0.127
1.44948
0.0086
0.4513
0.87002
0.140
1.44401
0.0092
0.4980
0.87164
0.142
1.43915
0.0098
0.5521
0.87350
0.155
1.43202
0.0091
0.5985
0.87520
0.161
1.42616
0.0088
0.6491
0.87716
0.161
1.42000
0.0086
0.7011
0.87930
0.155
1.41293
0.0077
0.7492
0.88135
0.151
1.40668
0.0072
0.7990
0.88366
0.133
1.40005
0.0065
0.8470
0.88593
0.122
1.39326
0.0054
0.9012
0.88878
0.088
1.38535
0.0039
0.9494
0.89135
0.066
1.37788
0.0021
Ethyl acetate + 1-3-5-trimethylbenzene 0.0526
0.86217
0.049
1.49155
0.0014
0.0989
0.86294
0.105
1.48712
0.0028
0.1505
0.86392
0.152
1.48207
0.0044
0.1983
0.86483
0.199
1.47711
0.0055
0.2577
0.86619
0.229
1.47046
0.0064
0.2995
0.86708
0.265
1.46614
0.0074
0.3525
0.86841
0.287
1.46042
0.0084
0.3998
0.86956
0.317
1.45464
0.0086
(Ethyl acetate + hydrocarbons)
1001
TABLE 2—continued x1
ρ/(g · cm−3 )
V E /(cm3 · mol−1 )
0.4503
0.87094
0.333
1.44915
0.0095
0.4992
0.87241
0.336
1.44305
0.0096
0.5572
0.87420
0.343
1.43527
0.0092
0.5981
0.87561
0.334
1.42994
0.0091
0.6511
0.87756
0.315
1.42288
0.0088
0.6986
0.87931
0.305
1.41616
0.0081
0.7504
0.88152
0.267
1.40894
0.0075
0.7971
0.88356
0.235
1.40206
0.0065
0.8495
0.88589
0.206
1.39410
0.0052
0.9019
0.88851
0.155
1.38605
0.0038
0.9510
0.89136
0.074
1.37824
0.0023
nD
1n D
Ethyl acetate + 1-1-dimethylethylbenzene 0.047
0.86308
0.010
1.48637
0.0020
0.104
0.86418
0.033
1.48126
0.0038
0.150
0.86516
0.041
1.47742
0.0055
0.200
0.86624
0.053
1.47291
0.0070
0.247
0.86732
0.060
1.46844
0.0082
0.306
0.86872
0.070
1.46302
0.0098
0.352
0.86993
0.072
1.45875
0.0111
0.401
0.87117
0.082
1.45352
0.0117
0.450
0.87255
0.084
1.44838
0.0124
0.511
0.87430
0.094
1.44139
0.0129
0.553
0.87555
0.100
1.43636
0.0128
0.600
0.87704
0.103
1.43059
0.0127
0.652
0.87880
0.107
1.42384
0.0123
0.701
0.88050
0.112
1.41723
0.0116
0.748
0.88226
0.108
1.41062
0.0105
0.801
0.88440
0.103
1.40282
0.0092
0.848
0.88643
0.090
1.39547
0.0075
0.900
0.88878
0.081
1.38718
0.0054
0.951
0.89148
0.040
1.37866
0.0030
molecules will be lower and the excess volume increases. Increase in excess volume with the size of molecules has been shown in other (non-polar + polar compounds). (6) The variation of the refractive indices on mixing with the mole fraction of ethyl acetate is shown in figure 2. The experimental refractive indices of the mixtures were compared with calculated values using the mixing rules proposed by Lorentz–Lorenz {equation (3)}, (7)
1002
J. M. Resa et al.
TABLE 3. Adjustable parameters ak and standard deviation σ of the excess volume V E and change in refractive index on mixing 1n D for the studied systems System
a0
a1
a2
103 σV E /cm3 · mol−1
V E /(cm3 · mol−1 ) Ethyl acetate + benzene Ethyl acetate + methylbenzene Ethyl acetate + ethylbenzene Ethyl acetate + 1-4-dimethylbenzene
0.4732
0.0703
0.0198
−0.0422
−0.0609
0.0418
2.8 4.1
0.3759
−0.1912
0.0508
4.2
−0.0077
−0.0492
0.0850
3.4
Ethyl acetate + 1-methylethylbenzene
0.5826
−0.3210
0.2643
4.1
Ethyl acetate + 1-3-5-trimethylbenzene
1.3427
−0.2451
0.0501
6.7
Ethyl acetate + 1-1-dimethylethylbenzene
0.3698
−0.2705
0.3262
3.2
1n D 103 σ1n D −0.0197
−0.0017
0.0047
0.31
Ethyl acetate + methylbenzene
Ethyl acetate + benzene
0.0092
0.0022
0.0023
0.09 0.19
Ethyl acetate + ethylbenzene
0.0239
−0.0030
−0.0028
Ethyl acetate + 1-4-dimethylbenzene
0.0273
−0.0013
−0.0026
0.13
Ethyl acetate + 1-methylethylbenzene
0.0370
−0.0062
−0.0036
0.28
Ethyl acetate + 1-3-5-trimethylbenzene
0.0376
−0.0051
−0.0009
0.18
Ethyl acetate + 1-1-dimethylethylbenzene
0.0510
−0.0113
−0.0008
0.11
TABLE 4. Deviations σ between the experimental and calculated values of the refractive indices on mixing using several mixing rules: Lorentz–Lorenz, (7) Dale–Gladstone, (7) Eykman, (7) Newton, (7) and Oster (7) σ
System (Lorentz)
(Dale)
(Eykman)
(Newton)
(Oster)
Ethyl acetate + benzene
0.00039
0.00129
0.00098
0.00232
0.00188
Ethyl acetate + methylbenzene
0.00096
0.00023
0.00031
0.00112
0.00070
Ethyl acetate + ethylbenzene
0.00036
0.00076
0.00047
0.00173
0.00131
Ethyl acetate + 1-4-dimethylbenzene
0.00079
0.00032
0.00020
0.00126
0.00084
Ethyl acetate + 1-methylethylbenzene
0.00032
0.00100
0.00074
0.00189
0.00151
Ethyl acetate + 1-3-5-trimethylbenzene
0.00032
0.00070
0.00042
0.00162
0.00123
Ethyl acetate + 1-1-dimethylethylbenzene
0.00025
0.00125
0.00093
0.00229
0.00185
Dale–Gladstone {equation (4)}, Eykman {equation (5)}, Newton {equation (6)} and Oster {equation (7)}. n 2D − 1 n 2D + 2
=
N 2 X n −1 φi Di , n 2Di + 2 i=1
(3)
(Ethyl acetate + hydrocarbons)
1003
0.014 0.012 0.01
∆nD
0.008 0.006 0.004 0.002 0 – 0.002 – 0.004 – 0.006 0
0.2
0.4
0.6
0.8
1
x1
•
FIGURE 2. Excess molar volumes of mixtures of ethyl acetate with benzene , methylbenzene O, ethylbenzene , 1-4-dimethylbenzene , 1-methylethylbenzene ♦, 1-3-5-trimethylbenzene , 1-1dimethylethylbenzene 4, at T = 298.15 K.
◦
nD − 1 =
N X
{φi (n Di − 1)},
(4)
i=1
N 2 X n Di − 1 = φi 2 , n 2D + 0.4 i=1 n Di + 0.4 n 2D − 1
n 2D − 1 =
N X
{φi (n 2Di − 1)},
(5)
(6)
i=1
(n 2D − 1) − (2n 2D + 1) n 2D
=
N 2 X (n Di − 1) − (2n 2Di + 1) φi . n 2Di i=1
(7)
In these equations, n D is the refractive index of the mixture, and n Di , and φi are the refractive index and the volumetric fraction of component i, respectively. Deviations of the experimental and predicted refractive indices on mixing are listed in table 4. A good agreement is observed in all cases and the deviations are lesser than 5 per cent for the studied binary mixtures. We are grateful for financial assistance from the University of the Basque Country (Project UPV-069.123-EA 156/97) and Miguel Iglesias for help in computational work. REFERENCES 1. Gonz´alez, C.; Resa, J. M.; Lanz, J.; Ruiz, A. ELDATA: The International Electronic Journal of Physico-Chemical Data 1996, 2, 185–192. 2. Gonz´alez, C.; Resa, J. M.; Lanz, J.; Mtz. de Ilarduya, J. A. Fluid Phase Equilib. 1997, 137, 141–148. 3. Gonz´alez, C.; Resa, J. M.; Lanz, J.; Mtz. de Ilarduya, J. A. ELDATA: The International Electronic Journal of Physico-Chemical Data 1997, 3, 183–190.
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