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Excess Gibbs energies and excess molar volumes for binary mixtures: (2-pyrrolidone + water), (2-pyrrolidone + methanol), and (2-pyrrolidone + ethanol) at the temperature 313.15 K
J. Chem. Thermodynamics 2002, 34, 1693–1701 doi:10.1016/S0021-9614(02)00231-8 Available online at http://www.idealibrary.com on
Excess Gibbs energies and excess molar volumes for binary mixtures: (2-pyrrolidone + water), (2-pyrrolidone + methanol), and (2-pyrrolidone + ethanol) at the temperature 313.15 K Jan Zielkiewicza Department of Chemistry, Technical University of Gda nsk, Narutowicza 11/12, 80-952 Gdask, Poland
Total vapour pressures and excess molar volumes, measured at the temperature 313.15 K, are reported for three binary mixtures (2-pyrrolidone+water), (2-pyrrolidone+ methanol) and (2-pyrrolidone+ethanol). The results are compared with previously obtained data for binary mixtures (amide+A), where amide ¼ N-methylformamide, N,N-dimethylformamide and N-methylacetamide, and A ¼ water, methanol, and ethanol. Ó 2002 Published by Elsevier Science Ltd.
KEYWORDS: 2-pyrrolidone; water; methanol; ethanol; amides; binary mixtures; volumes of mixing; partial molar volumes; excess Gibbs energies; correlation
1. Introduction This work continues the systematic studies for determination of the thermodynamic properties (the excess Gibbs energy, and the molar volumes of mixing) of the binary and ternary mixtures containing amide, water, and an aliphatic alcohol (methanol and ethanol). References to the previous results, describing the thermodynamic properties of other amides: N-methyl-formamide (NMF), N,N-dimethylformamide (DMF), and N methylacetamide (NMA) are given in reference.ð1Þ Based on the results obtained, it is possible to estimate the preferential solvation of amide molecule by water or alcohol by the estimation of the local mole fraction of components of the solution. It is important for understanding the interactions between the amide and hydroxyl group in the solution. A valuable tool for this investigation is a Kirkwood and BuffÕs theory of solutions. It describes thermodynamic properties of
a
(E-mail: [email protected]).
0021-9614/02/$ - see front matter
Ó 2002 Published by Elsevier Science Ltd.
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J. Zielkiewicz
solutions in an exact manner and over the whole concentration range, using the Gij parameters (called the Kirkwood–Buff integrals) defined as: Z 1 ðgij 1Þ4pr2 dr; ð1Þ Gij ¼ 0
where gij is the radial distribution function describing the distribution of the j molecules around the central i molecule. The Kirkwood–Buff theory givesð2Þ relation between Gij parameters and thermodynamic quantities such as the chemical potential, the partial molar volumes and isothermal compressibility. We can say,ð1Þ that this theory links macroscopic (thermodynamic) properties with microscopic description given by the radial distribution function, and the linkage is provided by equation (1) and the equations of the Kirkwood–Buff theory. The above considerations explain why this series of papers has been initiated.
2. Experimental SOLVENTS
The 2-Pyrrolidone, (Lancaster, >0:99 mass fraction purity) was dried over anhydrous CaSO4 , then passed through a column filled with the freshly ignited molecular sieves 0.4 nm, and finally distilled in a vacuum. The refined solvent was stored in a steel dessicator in a vacuum. Methanol and ethanol, analytical reagent grade, produced by Polish Chemical Reagents, (POCh) were distilled over freshly ignited molecular sieves 0.3 nm under nitrogen, and stored over molecular sieves. The water content was
TABLE 1. Densities d, total vapour pressures p, and refractive indices nD , of pure substances used in this work, and comparison with the literature data. Substance
T (K)
d/(g cm3 ) This work
2-Pyrrolidone
313.15
1.0957
p/kPa
Literature ð6Þ
1:0950
This work 0.008
nD
Literature
ð8Þ
0.011
This work
Literature
1.48467
1:4853ð9Þ
1.32645
1:32645ð12Þ
1.35920
1:35925ð13Þ
ð7Þ
1:0950 Methanol
313.15
0.7722
0.7725–
35.432
35:443ð11Þ
17.882
ð11Þ
ð10Þ
0.7723 298.15 Ethanol
313.15
0.7720
0.7724–
17:908
0.7722ð10Þ 298.15 Water *
313.15
7.383
7.372
Value calculated out of recommended temperature range ð395 6 T=K 6 518Þ:
Excess Gibbs energies and excess molar
1695
TABLE 2. Experimental liquid mole fractions x, calculated {from equation (2)} vapour phase composition y, and total vapour pressure p, for the binary mixtures investigated. x
y
p (kPa)
x
y
p (kPa)
x
y
p (kPa)
2-Pyrrolidone + water, T ¼ 313.15 K 0.0442
0.0000
7.106
0.3627
0.0005
4.605
0.6772
0.0025
2.104
0.0822
0.0001
6.877
0.3984
0.0007
4.297
0.7378
0.0034
1.682
0.1217
0.0001
6.615
0.4269
0.0008
4.046
0.7732
0.0042
1.445
0.1642
0.0002
6.303
0.4805
0.0010
3.595
0.7841
0.0044
1.380
0.2028
0.0002
6.006
0.5062
0.0011
3.393
0.8516
0.0071
0.937
0.2495
0.0003
5.588
0.5442
0.0014
3.097
0.9046
0.0121
0.607
0.2770
0.0003
5.361
0.5720
0.0015
2.865
0.9188
0.0146
0.524
0.3261
0.0005
4.930
0.6003
0.0018
2.659
0.9657
0.0377
0.214
0.0476
0.0000
33.721
0.3877
0.0001
21.121
0.6959
0.0006
9.463
0.0919
0.0000
32.155
0.4273
0.0002
19.588
0.7320
0.0007
8.210
0.1440
0.0000
30.303
0.4791
0.0002
17.565
0.7717
0.0009
6.818
0.1947
0.0000
28.461
0.5405
0.0003
15.210
0.8232
0.0013
5.196
0.2409
0.0001
26.741
0.5825
0.0003
13.614
0.8481
0.0015
4.426
0.2910
0.0001
24.863
0.6265
0.0004
11.975
0.9057
0.0027
2.655
0.3377
0.0001
23.089
0.6528
0.0005
11.004
0.9492
0.0053
1.430
0.9664
0.0121
0.640
0.5962
0.0006
7.603
0.2473
0.0002
13.791
0.9361
0.0062
1.221
0.5446
0.0005
8.565
0.2001
0.0001
14.555
0.8764
0.0030
2.344
0.4846
0.0004
9.653
0.1686
0.0001
15.073
0.8228
0.0020
3.352
0.4357
0.0003
10.545
0.1177
0.0001
15.918
0.7525
0.0013
4.684
0.3845
0.0003
11.430
0.0825
0.0000
16.483
0.6985
0.0010
5.689
0.3460
0.0002
12.105
0.0454
0.0000
17.109
0.6431
0.0008
6.735
0.3031
0.0002
12.836
2-Pyrrolidone + methanol, T ¼ 313.15 K
2-Pyrrolidone + ethanol, T ¼ 313:15 K
determined in all the solvents using the Karl–Fischer reagent, and was below 0.0001 mole fraction. THE VAPOUR PRESSURE MEASUREMENTS
Total vapour pressures were determined by a modified static method. The apparatus and the experimental procedure have been described in detail elsewhere.ð3Þ During the measurements the temperature was constant within 0.002 K. The absolute error in temperature was estimated to be equal to 0:02 K. The cathetometer readings contribute less than 0.004 kPa to the error of a single pressure measurement. The binary samples of volume about 5 to 10 cm3 were prepared by weight. The errors in the mole fraction of samples were less than 0.0005.
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J. Zielkiewicz
TABLE 3. Experimental liquid mole fractions x, excess molar volumes VE , and deviations DV between experimental and calculated values, for the investigated binary mixtures. Both the VE and DV values are given in cm3 mol1 units x
V
DV
x
V
DV
0.0096
)0.0075
0.0008
0.2988
)0.4481
0.0312
)0.0337
0.0013
0.3209
)0.4633
0.0001
0.5881
)0.4199
)0.0002
)0.0006
0.6011
)0.4090
0.0467
)0.0588
0.0005
0.3264
)0.4661
0.0013
)0.0003
0.6035
)0.4093
)0.0007
0.0630
)0.0879
)0.0001
0.3475
0.0830
)0.1261
)0.0006
0.3740
)0.4762
)0.0006
0.6433
)0.3761
0.0008
)0.4842
)0.0003
0.6630
)0.3614
)0.0014
0.1077
)0.1748
)0.0011
0.1264
)0.2107
)0.0006
0.3782
)0.4851
)0.0003
0.6791
)0.3442
0.0015
0.3953
)0.4874
)0.0001
0.6967
)0.3315
)0.0020
0.1498
)0.2542
0.1632
)0.2781
)0.0003
0.4136
)0.4880
0.0002
0.7281
)0.3007
)0.0013
)0.0002
0.4538
)0.4842
)0.0002
0.7429
)0.2826
0.1785
0.0022
)0.3037
0.0002
0.4559
)0.4833
0.0002
0.7924
)0.2350
)0.0008
0.1929
)0.3267
0.0002
0.4924
)0.4723
0.0003
0.8356
)0.1877
0.0004
0.1985
)0.3350
0.0005
0.5143
)0.4636
)0.0002
0.8615
)0.1598
)0.0002
0.2066
)0.3474
0.0001
0.5287
)0.4546
0.0017
0.8965
)0.1196
0.0006
0.2150
)0.3589
0.0005
0.5289
)0.4565
)0.0003
0.9288
)0.0833
)0.0003
0.2309
)0.3799
0.0005
0.5393
)0.4509
)0.0003
0.9438
)0.0653
0.0002
0.2462
)0.3983
0.0005
0.5471
)0.4466
)0.0004
0.9563
)0.0509
0.0000
0.2707
)0.4241
0.0004
0.5737
)0.4298
)0.0002
0.9797
)0.0244
)0.0009
0.0146
)0.0790
)0.0016
0.3713
)0.7455
0.0001
0.7460
)0.4280
)0.0005
0.0404
)0.1979
0.0007
0.3725
)0.7465
)0.0009
0.7494
)0.4231
)0.0005
0.0605
)0.2803
0.0005
0.4068
)0.7415
0.0003
0.7668
)0.3973
)0.0003
0.0854
)0.3705
)0.0011
0.4379
)0.7322
0.0003
0.7884
)0.3649
)0.0004
0.1134
)0.4536
0.0002
0.4812
)0.7111
0.0003
0.8081
)0.3344
)0.0004
0.1421
)0.5253
0.0002
0.5154
)0.6889
)0.0004
0.8115
)0.3284
0.0002
0.1680
)0.5791
0.0001
0.5650
)0.6472
)0.0004
0.8298
)0.2988
0.0008
0.1838
)0.6072
0.0001
0.5820
)0.6295
0.0009
0.8644
)0.2419
0.0010
0.2175
)0.6565
0.0004
0.6097
)0.6006
0.0009
0.8804
)0.2163
)0.0003
0.2421
)0.6856
)0.0006
0.6223
)0.5881
)0.0005
0.8883
)0.2011
0.0014
0.2680
)0.7075
0.0006
0.6338
)0.5736
)0.0008
0.9233
)0.1408
0.0008
0.2900
)0.7230
0.0000
0.6591
)0.5437
0.0004
0.9488
)0.0946
0.0012
0.3167
)0.7350
0.0008
0.6880
)0.5088
)0.0014
0.9519
)0.0941
)0.0040
0.3401
)0.7441
)0.0016
0.7003
)0.4911
0.0000
0.9873
)0.0246
)0.0004
0.3433
)0.7430
0.0001
0.7264
)0.4555
)0.0001
x
V
DV
2-Pyrrolidone + water, T ¼ 313.15 K
2-Pyrrolidone + methanol, T ¼ 313.15 K
Excess Gibbs energies and excess molar
1697
TABLE 3—Continued x
V
DV
x
x
V
DV
0.0130
)0.0431
0.0010
0.4038
)0.5636
0.0429
)0.1301
0.0008
0.4100
)0.5680
0.0028
0.5944
)0.5076
)0.0004
0.0012
0.6215
)0.4881
0.0819
)0.2307
0.0002
0.4108
)0.0003
)0.5679
0.0010
0.6285
)0.4810
0.0013
0.1167
)0.3057
0.0002
0.1443
)0.3566
0.0001
0.4277
)0.5689
0.0018
0.6558
)0.4616
)0.0018
0.4299
)0.5634
0.0037
0.6644
)0.4526
0.1707
)0.3992
)0.0004
0.0003
0.4339
)0.5677
0.0008
0.6881
)0.4301
0.2082
0.0001
)0.4491
0.0002
0.4483
)0.5678
0.0020
0.7154
)0.4030
)0.0001
0.2380
)0.4809
0.0010
0.4588
)0.5646
0.0002
0.7564
)0.3590
)0.0007
0.2730
)0.5124
0.0003
0.4694
)0.5637
0.0012
0.7900
)0.3179
0.0008
0.3039
)0.5325
0.0011
0.4902
)0.5579
0.0004
0.8175
)0.2852
)0.0009
0.3130
)0.5416
0.0028
0.4925
)0.5568
0.0000
0.8638
)0.2224
0.0000
0.3324
)0.5464
0.0018
0.5172
)0.5480
0.0003
0.8873
)0.1878
0.0011
0.3358
)0.5521
0.0025
0.5229
)0.5452
0.0009
0.9230
)0.1338
0.0011
0.3596
)0.5598
0.0017
0.5446
)0.5367
0.0005
0.9526
)0.0872
)0.0006
0.3598
)0.5553
0.0028
0.5551
)0.5293
0.0015
0.9905
)0.0232
)0.0048
0.3795
)0.5606
0.0024
0.5722
)0.5211
0.0001
0.3837
)0.5656
0.0019
0.5923
)0.5072
0.0014
V
DV
2-Pyrrolidone + ethanol, T ¼ 313.15 K
THE MOLAR VOLUMES MEASUREMENTS
The molar volumes of pure components were determined using a pycnometer with a volume of 28 cm3 approximately, with two capillaries of i.d. 1 mm. Errors in density measurements are estimated to be equal to 0:0001 g cm3 . The excess volumes of mixing were determined using the dilution dilatometer described by Kumaran and McGlashan.ð4Þ More details on the experimental procedure are given in referenceð4Þ and in our previous papers.ð5Þ The refractive indices for the pure solvents were measured using the Carl Zeiss refractometer equipped with the exchangeable thermostasted prisms. The accuracy of determination of refractive indices was 0.00001, and the temperature during the measurements was constant within 0.1 K. The characteristics of the pure substances, and comparison with the literature data ð6–13Þ are given in table 1.
3. Results and discussion CORRELATION OF THE EXPERIMENTAL RESULTS
The experimental vapour pressures and the excess volumes of mixing were correlated using the familiar Redlich–Kister equationð14Þ
C1
C2
C3
1698
TABLE 4. Parameters Ci of equation (2) and their standard deviations for the investigated binary mixtures C4
Excess Gibbs energy 0:26313 0:01120 dp ¼ 0.022 kPa
0:26384 0:00191 dp ¼ 0.017 kPa
0:10510 0:00175 dp ¼ 0.009 kPa
0:23446 0:03100
2-Pyrrolidone + methanol, T ¼ 313.15 K 0:04453 0:00226 0:04492 0:00360
0:00485 0:00529
2-Pyrrolidone + ethanol, T ¼ 313.15 K 0:08243 0:00218 0:04904 0:00334
0:02297 0:00504
2-Pyrrolidone + water, T ¼ 313.15 K C2 C3 0:81657 0:00500 0:12989 0:02062 C6 C7 0:57310 0:03704 0:429938 0:07722
C4 0:44821 0:02990 dV 0.0008 cm3 mol1
Excess volumes of mixing C1 1:87851 0:00107 C5 0:37956 0:07991
C1 2:79770 0:00146 C5 0:30884 0:02348 C1 2:21791 0:00165 C5 0:19193 0:04078
2-Pyrrolidone + methanol, T ¼ 313.15 K C2 C3 1:35213 0:00630 0:61934 0:01413 C6 0:10472 0:04656 2-Pyrrolidone + ethanol, T ¼ 313.15 K C2 C3 0:64579 0:00898 0:24194 0:02252 C6 0:15198 0:08381
dp and dV symbolise the mean square deviation in total pressure and in excess volume of mixing, respectively.
C4 0:34732 0:03719 DV 0.0010 cm3 mol1 C4 0:18260 0:06199 dV 0.0016 cm3 mol1
J. Zielkiewicz
2-Pyrrolidone + water, T ¼ 313:15 K 0:03923 0:01325 0:14488 0:02212
Excess Gibbs energies and excess molar
X ¼ xð1 xÞ
N X
Ci ð2x 1Þi1 ;
1699
ð2Þ
i¼1
where X symbolises dimensionless excess Gibbs energy, GE /RT, or excess volume of mixing, VE =ðcm3 mol1 ), Ci are the adjustable parameters, N is the number of these parameters, and x is the mole fraction of 2-pyrrolidone in the mixture. The results of measurements for the investigated binary mixtures are given in table 2 (the vapour pressure results) and in table 3 (the excess volumes of mixing). The adjusted values of the Ci parameters are given in table 4, along with their standard deviations. The standard deviations of the Ci were calculated from the covariance matrix, as described previously.ð15Þ THE VAPOUR PRESSURE MEASUREMENTS
For all the investigated mixtures, small deviations from the RaoulÕs law are observed. Similar observation was made for other amides: NMF, DMF, and NMA.ð1Þ Figure 1 presents a comparison of the dimensionless Gibbs energy, GE /RT, for all the amides. As can be seen, there are no clearly visible differences between DMF and other amides;
FIGURE 1. Plot of the dimensionless excess Gibbs energy GE /RT against mole fraction of amide for (amide + solvent) binary mixtures in three solvents at T ¼ 313:15 K in plots (a), (b), and (c). Line 1, N-methylformamide; line 2, N,N-dimethylformamide; line 3, N-methylacetamide; line 4, 2-pyrrolidone. Points on the curve 4 represent our experimental results.
1700
J. Zielkiewicz
this fact indicates, that the ‘‘amide’’ hydrogen (–N–H) nearly does not affect the excess Gibbs energy of mixing. Note that the absolute values of GE /RT are small, especially for water mixtures. This is in contrast with the heat of mixing data: for the aqueous mixtures the mixing process is strongly exothermal,ð16–21Þ and for the amide mixtures with methanol or ethanol the thermal effects are comparatively large as well.ð21–26Þ Thus we can assume that distribution of molecules in the solution is nearly random and strong orientation effects within the solvation shell around the molecules are present.ð1;27Þ EXCESS VOLUMES OF MIXING
For all the amides the values of excess volumes of mixing are negative; this fact confirms that strong intermolecular interactions in the solution are present. Comparison of these values for various amides is presented in figure 2. Note, that for (2-pyrrolidone + water) mixture the VE values are relatively small, nearly the same as for the (NMF + water) mixture. Similar small differences between NMF and 2-pyrrolidone in their mixtures with water were observed by Pal and Singhð28Þ at T ¼ 303:15 K.
FIGURE 2. Plot of the excess volumes of mixing VE against mole fraction of amide for (amide + solvent) binary mixtures in three solvents at T ¼ 313.15 K in plots (a), (b), and (c). Line 1, N-methylformamide; line 2, N,N-dimethylformamide; line 3, N-methylacetamide; line 4, 2-pyrrolidone. Points on the curve 4 represent our experimental results. The open squares in plots (b) and (c) are the VE results according to Garcia et al.ð29Þ at T ¼ 313:15 K (see text).
Excess Gibbs energies and excess molar
1701
Our VE results are inconsistent with the data obtained by Garcia et al.ð29Þ Their values systematically deviate from our results, and the differences are very large: they reach even 9% for methanol and 11% for ethanol (see figure 2). Reference 29 reports the VE values at various temperatures: 298 K, 303 K, 323 K, and 333 K. Therefore, we compare the GarciaÕs et al.ð29Þ results at T ¼ 303 K with the MehtaÕs et al.ð30Þ data measured at T ¼ 303:15 K. We also found the same systematic deviations of GarciaÕs et al. results from MehtaÕs et al. data. It is difficult, however, to discuss here the observed discrepancies. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
Zielkiewicz, J. Phys. Chem. Chem. Phys. 2000, 2, 2925–2932. Kirkwood, J. G.; Buff, F. P. J. Chem. Phys. 1951, 19, 774–777. Zielkiewicz, J.; Oracz, P.; Warycha, S. Fluid Phase Equilib. 1990, 59, 191–209. Kumaran, M. K.; McGlashan, M. L. J. Chem. Thermodyn. 1977, 7, 259–267. Zielkiewicz, J. J. Chem. Thermodyn. 1999, 31, 1597–1604. Garcia, B.; Herrera, C.; Leal, J. J. Chem. Eng. Data 1991, 36, 269–274. Jad_zyn, J.; Małecki, J.; Jad_zyn, Cz. J. Phys. Chem. 1978, 82, 2128–2130. Stephenson, R. M.; Malanowski, S. Handbook of the Thermodynamics of Organic Compounds. Elsevier: New York. 1987. Uosaki, Y.; Sogo, K.; Kunimine, T.; Moriyoshi, T. J. Chem. Thermodyn. 1990, 22, 257–262. Friedman, M. E.; Scheraga, H. A. J. Phys. Chem. 1965, 69, 3795–3800. Boublik, T.; Fried, V.; Hala, E. The Vapour Pressures of Pure Substances. Elsevier: Amsterdam. 1984. Benson, G. C.; Kiyohara, O. J. Sol. Chem. 1980, 9, 791–804. Treszczanowicz, A. J.; Benson, G. C. J. Chem. Thermodyn. 1977, 9, 1189–1197. Acree, W. E. Thermodynamic Properties of Nonelectrolyte Solutions. Academic Press: New York. 1984 [Chapter 4]. Zielkiewicz, J.; Konitz, A. Fluid Phase Equilib. 1991, 63, 129–139. Zaichikov, A. M.; Golubinskij, O. E. Zh. Fiz. Khim. 1996, 70, 1175–1179. Rehm, K.; Bittrich, H. J. Z. Phys. Chem. Leipzig 1972, 251, 109–121. de Haan, A.; Fischer, K.; Haacke, M.; Aufderhaar, O.; Petri, M.; Gmehling, J. J. Chem. Eng. Data 1997, 42, 875–881. de Haan, A.; Gmehling, J. J. Chem. Eng. Data 1996, 41, 474–478. Bougard, J.; Jadot, R. J. Chem. Thermodyn. 1975, 7, 1185–1188. Murakami, S.; Tanaka, R.; Fujishiro, R. J. Sol. Chem. 1974, 3, 71–79. Pikkarainen, L. J. Solut. Chem. 1986, 15, 473–479. Pikkarainen J. Solut. Chem. 1987, 16, 125–132. Pikkarainen, L. Thermochim. Acta 1991, 178, 311–319. Sitniyakovskii, I. B.; Semenov, L. V.; Gaile, A. A.; Koldobskaya, L. L. Zh. Prikl. Khim. (Leningrad) 1990, 63, 898–902. Oba, M.; Murakami, S.; Fujishiro, R. J. Chem. Thermodyn. 1977, 9, 407–414. Zielkiewicz, J.; Mazerski, J. J. Phys. Chem. B 2002, 106, 861–869. Pal, A.; Singh, Y. P. J. Chem. Eng. Data 1995, 40, 818–822. Garcia, B.; Herrera, C.; Leal, J. M. J. Chem. Eng. Data 1991, 36, 269–274. Mehta, S. K.; Chauhan, R. K.; Dewan, R. K. J. Chem. Soc. Faraday Trans. 1996, 92, 1167–1173. (Received 14 June 2002; in final form 11 July 2002)
WE-355
Excess Gibbs energies and excess molar volumes for binary mixtures: (2-pyrrolidone + water), (2-pyrrolidone + methanol), and (2-pyrrolidone + ethanol) at the temperature 313.15 K Jan Zielkiewicza Department of Chemistry, Technical University of Gda nsk, Narutowicza 11/12, 80-952 Gdask, Poland
Total vapour pressures and excess molar volumes, measured at the temperature 313.15 K, are reported for three binary mixtures (2-pyrrolidone+water), (2-pyrrolidone+ methanol) and (2-pyrrolidone+ethanol). The results are compared with previously obtained data for binary mixtures (amide+A), where amide ¼ N-methylformamide, N,N-dimethylformamide and N-methylacetamide, and A ¼ water, methanol, and ethanol. Ó 2002 Published by Elsevier Science Ltd.
KEYWORDS: 2-pyrrolidone; water; methanol; ethanol; amides; binary mixtures; volumes of mixing; partial molar volumes; excess Gibbs energies; correlation
1. Introduction This work continues the systematic studies for determination of the thermodynamic properties (the excess Gibbs energy, and the molar volumes of mixing) of the binary and ternary mixtures containing amide, water, and an aliphatic alcohol (methanol and ethanol). References to the previous results, describing the thermodynamic properties of other amides: N-methyl-formamide (NMF), N,N-dimethylformamide (DMF), and N methylacetamide (NMA) are given in reference.ð1Þ Based on the results obtained, it is possible to estimate the preferential solvation of amide molecule by water or alcohol by the estimation of the local mole fraction of components of the solution. It is important for understanding the interactions between the amide and hydroxyl group in the solution. A valuable tool for this investigation is a Kirkwood and BuffÕs theory of solutions. It describes thermodynamic properties of
a
(E-mail: [email protected]).
0021-9614/02/$ - see front matter
Ó 2002 Published by Elsevier Science Ltd.
1694
J. Zielkiewicz
solutions in an exact manner and over the whole concentration range, using the Gij parameters (called the Kirkwood–Buff integrals) defined as: Z 1 ðgij 1Þ4pr2 dr; ð1Þ Gij ¼ 0
where gij is the radial distribution function describing the distribution of the j molecules around the central i molecule. The Kirkwood–Buff theory givesð2Þ relation between Gij parameters and thermodynamic quantities such as the chemical potential, the partial molar volumes and isothermal compressibility. We can say,ð1Þ that this theory links macroscopic (thermodynamic) properties with microscopic description given by the radial distribution function, and the linkage is provided by equation (1) and the equations of the Kirkwood–Buff theory. The above considerations explain why this series of papers has been initiated.
2. Experimental SOLVENTS
The 2-Pyrrolidone, (Lancaster, >0:99 mass fraction purity) was dried over anhydrous CaSO4 , then passed through a column filled with the freshly ignited molecular sieves 0.4 nm, and finally distilled in a vacuum. The refined solvent was stored in a steel dessicator in a vacuum. Methanol and ethanol, analytical reagent grade, produced by Polish Chemical Reagents, (POCh) were distilled over freshly ignited molecular sieves 0.3 nm under nitrogen, and stored over molecular sieves. The water content was
TABLE 1. Densities d, total vapour pressures p, and refractive indices nD , of pure substances used in this work, and comparison with the literature data. Substance
T (K)
d/(g cm3 ) This work
2-Pyrrolidone
313.15
1.0957
p/kPa
Literature ð6Þ
1:0950
This work 0.008
nD
Literature
ð8Þ
0.011
This work
Literature
1.48467
1:4853ð9Þ
1.32645
1:32645ð12Þ
1.35920
1:35925ð13Þ
ð7Þ
1:0950 Methanol
313.15
0.7722
0.7725–
35.432
35:443ð11Þ
17.882
ð11Þ
ð10Þ
0.7723 298.15 Ethanol
313.15
0.7720
0.7724–
17:908
0.7722ð10Þ 298.15 Water *
313.15
7.383
7.372
Value calculated out of recommended temperature range ð395 6 T=K 6 518Þ:
Excess Gibbs energies and excess molar
1695
TABLE 2. Experimental liquid mole fractions x, calculated {from equation (2)} vapour phase composition y, and total vapour pressure p, for the binary mixtures investigated. x
y
p (kPa)
x
y
p (kPa)
x
y
p (kPa)
2-Pyrrolidone + water, T ¼ 313.15 K 0.0442
0.0000
7.106
0.3627
0.0005
4.605
0.6772
0.0025
2.104
0.0822
0.0001
6.877
0.3984
0.0007
4.297
0.7378
0.0034
1.682
0.1217
0.0001
6.615
0.4269
0.0008
4.046
0.7732
0.0042
1.445
0.1642
0.0002
6.303
0.4805
0.0010
3.595
0.7841
0.0044
1.380
0.2028
0.0002
6.006
0.5062
0.0011
3.393
0.8516
0.0071
0.937
0.2495
0.0003
5.588
0.5442
0.0014
3.097
0.9046
0.0121
0.607
0.2770
0.0003
5.361
0.5720
0.0015
2.865
0.9188
0.0146
0.524
0.3261
0.0005
4.930
0.6003
0.0018
2.659
0.9657
0.0377
0.214
0.0476
0.0000
33.721
0.3877
0.0001
21.121
0.6959
0.0006
9.463
0.0919
0.0000
32.155
0.4273
0.0002
19.588
0.7320
0.0007
8.210
0.1440
0.0000
30.303
0.4791
0.0002
17.565
0.7717
0.0009
6.818
0.1947
0.0000
28.461
0.5405
0.0003
15.210
0.8232
0.0013
5.196
0.2409
0.0001
26.741
0.5825
0.0003
13.614
0.8481
0.0015
4.426
0.2910
0.0001
24.863
0.6265
0.0004
11.975
0.9057
0.0027
2.655
0.3377
0.0001
23.089
0.6528
0.0005
11.004
0.9492
0.0053
1.430
0.9664
0.0121
0.640
0.5962
0.0006
7.603
0.2473
0.0002
13.791
0.9361
0.0062
1.221
0.5446
0.0005
8.565
0.2001
0.0001
14.555
0.8764
0.0030
2.344
0.4846
0.0004
9.653
0.1686
0.0001
15.073
0.8228
0.0020
3.352
0.4357
0.0003
10.545
0.1177
0.0001
15.918
0.7525
0.0013
4.684
0.3845
0.0003
11.430
0.0825
0.0000
16.483
0.6985
0.0010
5.689
0.3460
0.0002
12.105
0.0454
0.0000
17.109
0.6431
0.0008
6.735
0.3031
0.0002
12.836
2-Pyrrolidone + methanol, T ¼ 313.15 K
2-Pyrrolidone + ethanol, T ¼ 313:15 K
determined in all the solvents using the Karl–Fischer reagent, and was below 0.0001 mole fraction. THE VAPOUR PRESSURE MEASUREMENTS
Total vapour pressures were determined by a modified static method. The apparatus and the experimental procedure have been described in detail elsewhere.ð3Þ During the measurements the temperature was constant within 0.002 K. The absolute error in temperature was estimated to be equal to 0:02 K. The cathetometer readings contribute less than 0.004 kPa to the error of a single pressure measurement. The binary samples of volume about 5 to 10 cm3 were prepared by weight. The errors in the mole fraction of samples were less than 0.0005.
1696
J. Zielkiewicz
TABLE 3. Experimental liquid mole fractions x, excess molar volumes VE , and deviations DV between experimental and calculated values, for the investigated binary mixtures. Both the VE and DV values are given in cm3 mol1 units x
V
DV
x
V
DV
0.0096
)0.0075
0.0008
0.2988
)0.4481
0.0312
)0.0337
0.0013
0.3209
)0.4633
0.0001
0.5881
)0.4199
)0.0002
)0.0006
0.6011
)0.4090
0.0467
)0.0588
0.0005
0.3264
)0.4661
0.0013
)0.0003
0.6035
)0.4093
)0.0007
0.0630
)0.0879
)0.0001
0.3475
0.0830
)0.1261
)0.0006
0.3740
)0.4762
)0.0006
0.6433
)0.3761
0.0008
)0.4842
)0.0003
0.6630
)0.3614
)0.0014
0.1077
)0.1748
)0.0011
0.1264
)0.2107
)0.0006
0.3782
)0.4851
)0.0003
0.6791
)0.3442
0.0015
0.3953
)0.4874
)0.0001
0.6967
)0.3315
)0.0020
0.1498
)0.2542
0.1632
)0.2781
)0.0003
0.4136
)0.4880
0.0002
0.7281
)0.3007
)0.0013
)0.0002
0.4538
)0.4842
)0.0002
0.7429
)0.2826
0.1785
0.0022
)0.3037
0.0002
0.4559
)0.4833
0.0002
0.7924
)0.2350
)0.0008
0.1929
)0.3267
0.0002
0.4924
)0.4723
0.0003
0.8356
)0.1877
0.0004
0.1985
)0.3350
0.0005
0.5143
)0.4636
)0.0002
0.8615
)0.1598
)0.0002
0.2066
)0.3474
0.0001
0.5287
)0.4546
0.0017
0.8965
)0.1196
0.0006
0.2150
)0.3589
0.0005
0.5289
)0.4565
)0.0003
0.9288
)0.0833
)0.0003
0.2309
)0.3799
0.0005
0.5393
)0.4509
)0.0003
0.9438
)0.0653
0.0002
0.2462
)0.3983
0.0005
0.5471
)0.4466
)0.0004
0.9563
)0.0509
0.0000
0.2707
)0.4241
0.0004
0.5737
)0.4298
)0.0002
0.9797
)0.0244
)0.0009
0.0146
)0.0790
)0.0016
0.3713
)0.7455
0.0001
0.7460
)0.4280
)0.0005
0.0404
)0.1979
0.0007
0.3725
)0.7465
)0.0009
0.7494
)0.4231
)0.0005
0.0605
)0.2803
0.0005
0.4068
)0.7415
0.0003
0.7668
)0.3973
)0.0003
0.0854
)0.3705
)0.0011
0.4379
)0.7322
0.0003
0.7884
)0.3649
)0.0004
0.1134
)0.4536
0.0002
0.4812
)0.7111
0.0003
0.8081
)0.3344
)0.0004
0.1421
)0.5253
0.0002
0.5154
)0.6889
)0.0004
0.8115
)0.3284
0.0002
0.1680
)0.5791
0.0001
0.5650
)0.6472
)0.0004
0.8298
)0.2988
0.0008
0.1838
)0.6072
0.0001
0.5820
)0.6295
0.0009
0.8644
)0.2419
0.0010
0.2175
)0.6565
0.0004
0.6097
)0.6006
0.0009
0.8804
)0.2163
)0.0003
0.2421
)0.6856
)0.0006
0.6223
)0.5881
)0.0005
0.8883
)0.2011
0.0014
0.2680
)0.7075
0.0006
0.6338
)0.5736
)0.0008
0.9233
)0.1408
0.0008
0.2900
)0.7230
0.0000
0.6591
)0.5437
0.0004
0.9488
)0.0946
0.0012
0.3167
)0.7350
0.0008
0.6880
)0.5088
)0.0014
0.9519
)0.0941
)0.0040
0.3401
)0.7441
)0.0016
0.7003
)0.4911
0.0000
0.9873
)0.0246
)0.0004
0.3433
)0.7430
0.0001
0.7264
)0.4555
)0.0001
x
V
DV
2-Pyrrolidone + water, T ¼ 313.15 K
2-Pyrrolidone + methanol, T ¼ 313.15 K
Excess Gibbs energies and excess molar
1697
TABLE 3—Continued x
V
DV
x
x
V
DV
0.0130
)0.0431
0.0010
0.4038
)0.5636
0.0429
)0.1301
0.0008
0.4100
)0.5680
0.0028
0.5944
)0.5076
)0.0004
0.0012
0.6215
)0.4881
0.0819
)0.2307
0.0002
0.4108
)0.0003
)0.5679
0.0010
0.6285
)0.4810
0.0013
0.1167
)0.3057
0.0002
0.1443
)0.3566
0.0001
0.4277
)0.5689
0.0018
0.6558
)0.4616
)0.0018
0.4299
)0.5634
0.0037
0.6644
)0.4526
0.1707
)0.3992
)0.0004
0.0003
0.4339
)0.5677
0.0008
0.6881
)0.4301
0.2082
0.0001
)0.4491
0.0002
0.4483
)0.5678
0.0020
0.7154
)0.4030
)0.0001
0.2380
)0.4809
0.0010
0.4588
)0.5646
0.0002
0.7564
)0.3590
)0.0007
0.2730
)0.5124
0.0003
0.4694
)0.5637
0.0012
0.7900
)0.3179
0.0008
0.3039
)0.5325
0.0011
0.4902
)0.5579
0.0004
0.8175
)0.2852
)0.0009
0.3130
)0.5416
0.0028
0.4925
)0.5568
0.0000
0.8638
)0.2224
0.0000
0.3324
)0.5464
0.0018
0.5172
)0.5480
0.0003
0.8873
)0.1878
0.0011
0.3358
)0.5521
0.0025
0.5229
)0.5452
0.0009
0.9230
)0.1338
0.0011
0.3596
)0.5598
0.0017
0.5446
)0.5367
0.0005
0.9526
)0.0872
)0.0006
0.3598
)0.5553
0.0028
0.5551
)0.5293
0.0015
0.9905
)0.0232
)0.0048
0.3795
)0.5606
0.0024
0.5722
)0.5211
0.0001
0.3837
)0.5656
0.0019
0.5923
)0.5072
0.0014
V
DV
2-Pyrrolidone + ethanol, T ¼ 313.15 K
THE MOLAR VOLUMES MEASUREMENTS
The molar volumes of pure components were determined using a pycnometer with a volume of 28 cm3 approximately, with two capillaries of i.d. 1 mm. Errors in density measurements are estimated to be equal to 0:0001 g cm3 . The excess volumes of mixing were determined using the dilution dilatometer described by Kumaran and McGlashan.ð4Þ More details on the experimental procedure are given in referenceð4Þ and in our previous papers.ð5Þ The refractive indices for the pure solvents were measured using the Carl Zeiss refractometer equipped with the exchangeable thermostasted prisms. The accuracy of determination of refractive indices was 0.00001, and the temperature during the measurements was constant within 0.1 K. The characteristics of the pure substances, and comparison with the literature data ð6–13Þ are given in table 1.
3. Results and discussion CORRELATION OF THE EXPERIMENTAL RESULTS
The experimental vapour pressures and the excess volumes of mixing were correlated using the familiar Redlich–Kister equationð14Þ
C1
C2
C3
1698
TABLE 4. Parameters Ci of equation (2) and their standard deviations for the investigated binary mixtures C4
Excess Gibbs energy 0:26313 0:01120 dp ¼ 0.022 kPa
0:26384 0:00191 dp ¼ 0.017 kPa
0:10510 0:00175 dp ¼ 0.009 kPa
0:23446 0:03100
2-Pyrrolidone + methanol, T ¼ 313.15 K 0:04453 0:00226 0:04492 0:00360
0:00485 0:00529
2-Pyrrolidone + ethanol, T ¼ 313.15 K 0:08243 0:00218 0:04904 0:00334
0:02297 0:00504
2-Pyrrolidone + water, T ¼ 313.15 K C2 C3 0:81657 0:00500 0:12989 0:02062 C6 C7 0:57310 0:03704 0:429938 0:07722
C4 0:44821 0:02990 dV 0.0008 cm3 mol1
Excess volumes of mixing C1 1:87851 0:00107 C5 0:37956 0:07991
C1 2:79770 0:00146 C5 0:30884 0:02348 C1 2:21791 0:00165 C5 0:19193 0:04078
2-Pyrrolidone + methanol, T ¼ 313.15 K C2 C3 1:35213 0:00630 0:61934 0:01413 C6 0:10472 0:04656 2-Pyrrolidone + ethanol, T ¼ 313.15 K C2 C3 0:64579 0:00898 0:24194 0:02252 C6 0:15198 0:08381
dp and dV symbolise the mean square deviation in total pressure and in excess volume of mixing, respectively.
C4 0:34732 0:03719 DV 0.0010 cm3 mol1 C4 0:18260 0:06199 dV 0.0016 cm3 mol1
J. Zielkiewicz
2-Pyrrolidone + water, T ¼ 313:15 K 0:03923 0:01325 0:14488 0:02212
Excess Gibbs energies and excess molar
X ¼ xð1 xÞ
N X
Ci ð2x 1Þi1 ;
1699
ð2Þ
i¼1
where X symbolises dimensionless excess Gibbs energy, GE /RT, or excess volume of mixing, VE =ðcm3 mol1 ), Ci are the adjustable parameters, N is the number of these parameters, and x is the mole fraction of 2-pyrrolidone in the mixture. The results of measurements for the investigated binary mixtures are given in table 2 (the vapour pressure results) and in table 3 (the excess volumes of mixing). The adjusted values of the Ci parameters are given in table 4, along with their standard deviations. The standard deviations of the Ci were calculated from the covariance matrix, as described previously.ð15Þ THE VAPOUR PRESSURE MEASUREMENTS
For all the investigated mixtures, small deviations from the RaoulÕs law are observed. Similar observation was made for other amides: NMF, DMF, and NMA.ð1Þ Figure 1 presents a comparison of the dimensionless Gibbs energy, GE /RT, for all the amides. As can be seen, there are no clearly visible differences between DMF and other amides;
FIGURE 1. Plot of the dimensionless excess Gibbs energy GE /RT against mole fraction of amide for (amide + solvent) binary mixtures in three solvents at T ¼ 313:15 K in plots (a), (b), and (c). Line 1, N-methylformamide; line 2, N,N-dimethylformamide; line 3, N-methylacetamide; line 4, 2-pyrrolidone. Points on the curve 4 represent our experimental results.
1700
J. Zielkiewicz
this fact indicates, that the ‘‘amide’’ hydrogen (–N–H) nearly does not affect the excess Gibbs energy of mixing. Note that the absolute values of GE /RT are small, especially for water mixtures. This is in contrast with the heat of mixing data: for the aqueous mixtures the mixing process is strongly exothermal,ð16–21Þ and for the amide mixtures with methanol or ethanol the thermal effects are comparatively large as well.ð21–26Þ Thus we can assume that distribution of molecules in the solution is nearly random and strong orientation effects within the solvation shell around the molecules are present.ð1;27Þ EXCESS VOLUMES OF MIXING
For all the amides the values of excess volumes of mixing are negative; this fact confirms that strong intermolecular interactions in the solution are present. Comparison of these values for various amides is presented in figure 2. Note, that for (2-pyrrolidone + water) mixture the VE values are relatively small, nearly the same as for the (NMF + water) mixture. Similar small differences between NMF and 2-pyrrolidone in their mixtures with water were observed by Pal and Singhð28Þ at T ¼ 303:15 K.
FIGURE 2. Plot of the excess volumes of mixing VE against mole fraction of amide for (amide + solvent) binary mixtures in three solvents at T ¼ 313.15 K in plots (a), (b), and (c). Line 1, N-methylformamide; line 2, N,N-dimethylformamide; line 3, N-methylacetamide; line 4, 2-pyrrolidone. Points on the curve 4 represent our experimental results. The open squares in plots (b) and (c) are the VE results according to Garcia et al.ð29Þ at T ¼ 313:15 K (see text).
Excess Gibbs energies and excess molar
1701
Our VE results are inconsistent with the data obtained by Garcia et al.ð29Þ Their values systematically deviate from our results, and the differences are very large: they reach even 9% for methanol and 11% for ethanol (see figure 2). Reference 29 reports the VE values at various temperatures: 298 K, 303 K, 323 K, and 333 K. Therefore, we compare the GarciaÕs et al.ð29Þ results at T ¼ 303 K with the MehtaÕs et al.ð30Þ data measured at T ¼ 303:15 K. We also found the same systematic deviations of GarciaÕs et al. results from MehtaÕs et al. data. It is difficult, however, to discuss here the observed discrepancies. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
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