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(Vapour+liquid) equilibria in (N-methylformamide+methanol+water) at the temperature 313.15 K
J. Chem. Thermodynamics 1996, 28, 887–894
(Vapour+liquid) equilibria in (N-methylformamide+methanol+water) at the temperature 313.15 K Jan Zielkiewicz Department of Chemistry, Technical University of Gdan´sk, Narutowicza 11 /12 , 80 -952 Gdan´sk, Poland Total vapour pressure measurements made by a modified static method for binary mixtures (N-methylformamide+water) and (N-methylformamide+methanol) and for a ternary mixture (N-methylformamide+methanol+water) at the temperature T=313.15 K are presented. The results have been fitted with various correlation equations. 7 1996 Academic Press Limited
1. Introduction This work is the third of a series of papers describing thermodynamic properties such as excess molar Gibbs free energies GmE and excess molar volumes VmE of the ternary mixtures containing N-methylformamide, water, and an aliphatic alcohol. In previous articles (see reference 1 and references given therein), the GmE and VmE values for mixtures containing N,N-dimethylformamide, water, and an aliphatic alcohol were reported. Based on these results, estimates were made of the preferential solvation of the dimethylformamide molecule and local mole fractions of components in the immediate vicinity of this molecule,(2) using the Kirkwood-Buff theory of solutions. The Kirkwood-Buff theory of solutions is a valuable tool for investigations of solutions. The theory describes the thermodynamic properties of solutions in an exact manner over the whole concentration range, using the Gij quantities, defined as: Gij=
g
a
(gij−1)·4pr 2 dr,
(1)
0
where r is the distance from the central i molecule. These quantities are called the Kirkwood-Buff integrals or fluctuation integrals. These integrals may be determined from experimental values of thermodynamic quantities such as chemical potential, partial molar volumes, and isothermal compressibility.(2) It is important to note that the radial distribution function gij present in equation (1) reflects the solution structure at the microscopic level, and so we may expect that the Gij values contain some information about this structure. More information about the relation between the Kirkwood-Buff theory and the well-known idea of local composition are included in previous work.(2) 0021–9614/96/080887+08 $18.00/0
7 1996 Academic Press Limited
888
J. Zielkiewicz
The dimethylformamide molecule may interact with water or alcohol molecules, or both, only through the free electron pair on the oxygen atom, as the free electron pair on the nitrogen atom is protected by two methyl groups. Removing one of the methyl groups (to form the N-methylformamide molecule) exposes this pair, allowing it to interact with the hydrogen atoms of the hydroxyl group from alcohol and water. A comparison of the preferential solvation of N,N-dimethylformamide and N-methylformamide molecules allows us to estimate the influence of electron pairs on the nitrogen and oxygen atoms separately, on solvation of an amide group. A comparison of the local mole fractions of components around the N,Ndimethylformamide and N-methylformamide molecules may be helpful in understanding the solvation of an amide group by water and alcohol molecules. This is important in investigations of aqueous solutions of peptides; the amide group is a good model of the peptide bond. These considerations have initiated this series of papers. The application of the Kirkwood-Buff theory of solutions requires the determination of GmE and VmE values as a function of composition. Two papers containing the VmE results for (N-methylformamide + methanol + water)(3) and for (N-methylformamide + ethanol + water)(4) were published previously. In this paper, the total vapour pressure measurements for (N-methylformamide+water), (N-methylformamide + methanol), and (N-methyl-formamide + methanol + water) at T=313.15 K are reported.
2. Experimental N-methylformamide (E. Merck, product ‘‘zur synthese’’) was dried and stored over freshly ignited 0.4 nm molecular sieves. The measured conductivity of this solvent was below 2.4·10−6 V−1 m−1. Methanol (POCH, analytical reagent grade), was purified as described previously.(5) The refined solvent was stored over freshly ignited 0.3 nm molecular sieves. The mass fraction of water in both these solvents was below 0.0001, determined by titration using the Karl-Fischer reagent. Water was distilled twice in a glass apparatus. Characteristics of the pure substances are given in table 1. The apparatus for the vapour pressure measurements and the TABLE 1. Densities r, refractive indices nD , and vapour pressures p of pure liquids used in this work, measured at temperatures T Component
T/K
r/(g·cm−3 ) This work
N-methylformamide
298.15
0.9993
Methanol
313.15 298.15
0.9863 0.7864
313.15
0.7722
Water
313.15
Literature
nD
p/kPa
This work
Literature
0.9961(9) 0.9976(10)
1.43009
1.4300(9) 1.4310(10)
0.78667(11) 0.786434(12) 0.7725 to 0.7723(13)
1.32645
1.32661(11)
This work
Literature
0.095
0.093(14)
35.404
35.443(14)
7.373
7.372(14)
VLE for {x1 HCONHCH3+x2 CH3 OH+(1−x1−x2 )H2 O} at T=313.15 K
889
experimental procedure have been described in detail previously.(5,6) During the experiments, the temperature was controlled to within 20.001 K. The absolute error is estimated to be equal to 20.02 K (IPTS-68). Cathetometer readings contributed less than 0.004 kPa to the error of a single pressure measurement.
3. Results and discussion The measured values of vapour pressures, along with the calculated compositions of the vapour phase, are given in table 2 and presented graphically in figure 1 for (N-methlyformamide + water) and (N-methylformamide + methanol), and in table 3 for (N-methylformamide + methanol + water). Unfortunately, there are no data for second viral coefficients; or for calculating these coefficients for N-methylformamide. The vapour phase behaviour was therefore assumed to be ideal. Correlation of the binary results was carried out using the Redlich-Kister equation: M
GmE /RT=x(1−x) s Ki (2x−1)i−1,
(2)
i=1
TABLE 2. Experimental mole fractions in the liquid phase, x; mole fractions in the vapour phase, y, calculated from equations (2) or (3); and measured total vapour pressures p for the binary mixtures investigated x
y
0.9667 0.9039 0.8632 0.7685 0.7628 0.6976 0.6595 0.6017 0.5859 0.5314 0.4978
0.2726 0.1137 0.0805 0.0443 0.0430 0.0308 0.0258 0.0199 0.0186 0.0147 0.0127
p/kPa
x
y
p/kPa
0.0089 0.0075 0.0067 0.0040 0.0039 0.0034 0.0020 0.0012 0.0008 0.0004
4.282 4.582 4.758 5.572 5.619 5.791 6.370 6.747 6.944 7.176
xHCONHCH3+(1−x)H2O at T=313.15 K a
0.9553 0.9462 0.9293 0.9101 0.9010 0.8835 0.8703 0.8272 0.8030 0.7653 0.7538 0.7181 0.7121 a b
0.0398 0.0346 0.0279 0.0228 0.0209 0.0180 0.0162 0.0121 0.0104 0.0085 0.0080 0.0067 0.0066
Calculated from equation (2). Calculated from equation (3).
0.344 0.758 1.016 1.663 1.698 2.164 2.432 2.860 2.962 3.387 3.653
0.4174 0.3796 0.3573 0.2537 0.2491 0.2245 0.1452 0.0933 0.0631 0.0275
xHCONHCH3+(1−x)CH3OH at T=313.15 K b 2.308 0.6594 0.0052 2.625 0.6011 0.0041 3.220 0.5550 0.0034 3.888 0.5220 0.0030 4.167 0.4595 0.0024 4.807 0.3706 0.0017 5.251 0.3275 0.0014 6.726 0.3028 0.0012 7.606 0.2103 0.0008 8.908 0.1813 0.0006 9.284 0.1245 0.0004 10.575 0.0714 0.0002 10.762
12.626 14.679 16.315 17.474 19.660 22.787 24.270 25.131 28.278 29.267 31.176 32.983
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J. Zielkiewicz
FIGURE 1. Graphical representation of the experimental total vapour pressure p against the mole fraction x of N-methylformamide for binary mixtures of (a), (N-methylformamide+methanol) and (b), (N-methylformamide+water). The solid line connecting experimental points is the best curve calculated from equation (1) for (N-methylformamide+water) and from equation (2) for (N-methylformamide+methanol) using parameters from table 5.
and the van Laar–van Ness equation: M
GmE /RT=x(1−x)/ s Ki (2x−1)i−1,
(3)
i=1
where Ki are adjustable parameters and M is the number of such parameters. The Wilson and NRTL equations were also used for correlation of binary results. Table 4 shows the efficacy of these equations applied to the investigated binary mixtures. Table 5 includes the values of the parameters of these equations. As can be seen, equation (2) describes the (N-methylformamide+water) results with good accuracy. For the second mixture investigated, (N-methylformamide + methanol), the results obtained are best described by equation (3). Both these
VLE for {x1 HCONHCH3+x2 CH3 OH+(1−x1−x2 )H2 O} at T=313.15 K
891
TABLE 3. The ternary mixture {x1 HCONHCH3+x2CH3OH+(1−x1−x2 )H2O} at the temperature T=313.15 K; experimental mole fractions in the liquid phase, x1 , x2 ; mole fractions in the vapour phase, y1 , y2 , calculated from equations (4) and (6); and measured total vapour pressures p x1
x2
y1
y2
p/kPa
0.0692 0.1271 0.2205 0.3250 0.4300 0.5901 0.7381 0.0540 0.1228 0.1957 0.2912 0.4200 0.5222 0.0717 0.1454 0.2507 0.3502 0.4848 0.6206 0.7934 0.0391 0.0994 0.1619 0.2618 0.3738 0.5194 0.6856 0.0746 0.1681 0.2705 0.4017 0.6696 0.8394 0.4380 0.3889 0.3156 0.2389 0.1463 0.0790 0.3706 0.2670 0.1989 0.1379 0.0902 0.0497 0.0289
0.4517 0.4236 0.3783 0.3276 0.2766 0.1989 0.1271 0.2906 0.2695 0.2471 0.2177 0.1782 0.1468 0.6307 0.5806 0.5091 0.4415 0.3500 0.2578 0.1404 0.0907 0.0850 0.0791 0.0697 0.0591 0.0454 0.0297 0.8273 0.7437 0.6521 0.5349 0.2953 0.1436 0.1781 0.2702 0.4078 0.5516 0.7256 0.8518 0.3558 0.2563 0.1910 0.1323 0.0866 0.0477 0.0278
0.0003 0.0005 0.0010 0.0018 0.0029 0.0058 0.0114 0.0002 0.0006 0.0010 0.0019 0.0035 0.0055 0.0002 0.0005 0.0011 0.0017 0.0031 0.0055 0.0125 0.0003 0.0008 0.0014 0.0026 0.0047 0.0090 0.0191 0.0002 0.0006 0.0011 0.0020 0.0058 0.0138 0.0037 0.0025 0.0016 0.0010 0.0005 0.0003 0.0021 0.0015 0.0012 0.0009 0.0007 0.0005 0.0003
0.8147 0.8173 0.8216 0.8262 0.8301 0.8345 0.8370 0.7205 0.7189 0.7186 0.7192 0.7204 0.7213 0.8915 0.8956 0.9007 0.9049 0.9092 0.9118 0.9117 0.4428 0.4332 0.4265 0.4198 0.4143 0.4089 0.4054 0.9672 0.9688 0.9701 0.9714 0.9711 0.9656 0.7282 0.8071 0.8728 0.9160 0.9544 0.9772 0.8630 0.7493 0.6588 0.5524 0.4365 0.2941 0.1941
22.211 20.957 18.772 16.223 13.626 9.729 6.284 18.499 17.132 15.654 13.704 11.053 8.901 26.149 24.311 21.485 18.688 14.848 10.978 6.187 11.710 10.925 10.093 8.704 7.160 5.251 3.279 30.539 27.681 24.468 20.237 11.412 5.895 10.597 13.977 18.337 22.590 27.535 31.085 16.362 15.076 13.957 12.602 11.211 9.728 8.817
mixtures show small deviations from ideality, as can be seen in figure 1. Very similar behaviour was observed for ‘‘homologic’’ mixtures containing N,N-dimethylformamide. Comparison of the GmE values obtained for systems
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J. Zielkiewicz
TABLE 4. Comparison of the standard deviations s of different equations for the binary and ternary results investigated. M represents the number of adjusted parameters and N the number of experimental points Equation
(2) (3) Wilson NRTL, a=0.3 (2) (3) Wilson NRTL, a=0.3 (4) (4) and (6) Wilson NRTL
s{dp/kPa}
M
xHCONHCH3+(1−x)H2O at T=313.15 K (N=21) 5 0.007 5 0.017 2 0.044 2 0.045 xHCONHCH3+(1−x)CH3OH at 5 5 2 2
T=313.15 K (N=25) 0.042 0.013 0.181 0.186
102 ·s(dp/p)
0.570 1.216 2.712 2.514 1.250 0.203 4.436 4.957
x1 HCONHCH3+x2CH3OH+(1−x1−x2 )H2O at T=313.15 K (N=46) 0 0.134 1.607 3 0.091 1.197 0 0.225 2.601 0 0.188 2.109
containing N,N-dimethylformamide and N-methylformamide in their binary mixtures with water or alcohols will be presented in a future paper. The ternary results were correlated using the equation:(7) GmE =s s (GmE )ij ,
(4)
i jqi
where (GmE )ij are the binary constituents calculated(7) according to equation (5): M
(GmE )ij =xi xj s Kk (xi−xj )k−1,
(5)
k=1
with the Kk values taken from table 5 for appropriate binary mixtures. Equation (5) conforms to equation (1), being applicable to the multicomponent mixture.(7) The values needed for (methanol+water) at this temperature were taken from reference 5. To this expression there has also been added a term describing the ternary interactions, taking the form proposed in reference 8: M
GmE (ter)/RT=x1 x2 (1−x1−x2 ) s Ci (2x1−1)i−1,
(6)
i=1
where Ci are adjustable parameters, and M is the number of such parameters. In equations (2), (3), and (6), as well as for the Wilson and NRTL equations, values of the adjustable parameters were obtained by the least-squares method, using the optimization algorithm based on the Marquardt method. These values are given in table 5, along with their standard deviations. The ternary mixture was also described using equations based on the local composition concept (Wilson and NRTL), making it possible to predict the multicomponent VLE values directly from
VLE for {x1 HCONHCH3+x2 CH3 OH+(1−x1−x2 )H2 O} at T=313.15 K
893
TABLE 5. Parameters Ki of various equations used for correlation of the binary results, and Ci of equation (6) describing the ternary results, with their standard deviations for the mixtures investigated xHCONHCH3+(1−x)H2O at T=313.15 K Equation (2) K1=−0.0994220.00411 K4=−0.0389420.01186 Equation (3) K1=−9.4324220.65629 K4=9.7637625.02150 Wilson K1=0.62048 NRTL K1=−0.50196
K2=0.0122220.00465 K5=0.0823220.01875
K3=0.0908020.00850
K2=−1.2938920.99147 K5=−27.87532212.35541
K3=−5.8297022.54232
K2=1.61247 a=0.30
K2=0.46252
xHCONHCH3+(1−x)CH3OH at T=313.15 K Equation (2) K1=0.1526620.00282 K4=0.0728020.00992 Equation (3) K1=5.9028220.07339 K4=0.3270720.07686 Wilson K1=0.52158 NRTL K1=−0.45361
K2=0.0356720.00406 K5=0.1083820.01827
K3=−0.1083820.01827
K2=−2.0171620.04674 K5=−0.1218420.10420
K3=−3.0044920.09533
K2=1.45605 K2=0.68842
a=0.30
x1 HCONHCH3+x2CH3OH+(1−x1−x2 )H2O at T=313.15 K C1=−0.1992020.06331 C2=0.1887020.15124 C3=0.3339620.16179
the binary ones, without extra multicomponent terms. Table 4 summarizes the efficacy of describing the experimental ternary results with these formulae. As can be seen from this table, the best description, in accordance with expectations, is given by the empirical formula (4), with the adjusted ternary term defined by equation (6). The predictions of total vapour pressure for ternary mixtures obtained from the NRTL and Wilson equations are worse than the empirical formula (4) without the ternary term. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Zielkiewicz, J. J. Chem. Thermodynamics 1995, 27, 415–422. Zielkiewicz, J. J. Phys. Chem. 1995, 99, 4787–4793. Zielkiewicz, J. J. Chem. Thermodynamics 1995, 27, 1275–1279. Zielkiewicz, J. J. Chem. Thermodynamics 1996, 28, 313–318. Zielkiewicz, J.; Oracz, P. Fluid Phase Equilib. 1990, 59, 279–290. Zielkiewicz, J.; Oracz, P.; Warycha, S. Fluid Phase Equilib. 1990, 59, 191–209. Acree, W. E. Thermodynamic Properties of Nonelectrolyte Solutions. Academic Press: New York. 1984, Chap. 4. Jasin´ski, B.; Malanowski, S. Chem. Eng. Sci. 1970, 25, 913–920. Beilstein, 58, III 121, Beilstein’s Handbuch der Organische Chemie, Vol. A. Beilstein, 58, IV 170, Beilstein’s Handbuch der Organische Chemie, Vol. B. Treszczanowicz, A. J.; Benson, G. C. J. Chem. Thermodynamics 1977, 9, 1189–1197. Sakuragi, M.; Nakagawa, T. J. Chem. Thermodynamics 1984, 16, 171–174.
894
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13. Friedman, M. E.; Scheraga, H. A. J. Phys. Chem. 1965, 69, 3795–3800. 14. Boublik, T.; Fried, V.; Ha´la, E. The Vapour Pressures of Pure Substances. Elsevier: Amsterdam. 1984.
(Received 15 January 1996; in final form 6 March 1996)
WE-053
(Vapour+liquid) equilibria in (N-methylformamide+methanol+water) at the temperature 313.15 K Jan Zielkiewicz Department of Chemistry, Technical University of Gdan´sk, Narutowicza 11 /12 , 80 -952 Gdan´sk, Poland Total vapour pressure measurements made by a modified static method for binary mixtures (N-methylformamide+water) and (N-methylformamide+methanol) and for a ternary mixture (N-methylformamide+methanol+water) at the temperature T=313.15 K are presented. The results have been fitted with various correlation equations. 7 1996 Academic Press Limited
1. Introduction This work is the third of a series of papers describing thermodynamic properties such as excess molar Gibbs free energies GmE and excess molar volumes VmE of the ternary mixtures containing N-methylformamide, water, and an aliphatic alcohol. In previous articles (see reference 1 and references given therein), the GmE and VmE values for mixtures containing N,N-dimethylformamide, water, and an aliphatic alcohol were reported. Based on these results, estimates were made of the preferential solvation of the dimethylformamide molecule and local mole fractions of components in the immediate vicinity of this molecule,(2) using the Kirkwood-Buff theory of solutions. The Kirkwood-Buff theory of solutions is a valuable tool for investigations of solutions. The theory describes the thermodynamic properties of solutions in an exact manner over the whole concentration range, using the Gij quantities, defined as: Gij=
g
a
(gij−1)·4pr 2 dr,
(1)
0
where r is the distance from the central i molecule. These quantities are called the Kirkwood-Buff integrals or fluctuation integrals. These integrals may be determined from experimental values of thermodynamic quantities such as chemical potential, partial molar volumes, and isothermal compressibility.(2) It is important to note that the radial distribution function gij present in equation (1) reflects the solution structure at the microscopic level, and so we may expect that the Gij values contain some information about this structure. More information about the relation between the Kirkwood-Buff theory and the well-known idea of local composition are included in previous work.(2) 0021–9614/96/080887+08 $18.00/0
7 1996 Academic Press Limited
888
J. Zielkiewicz
The dimethylformamide molecule may interact with water or alcohol molecules, or both, only through the free electron pair on the oxygen atom, as the free electron pair on the nitrogen atom is protected by two methyl groups. Removing one of the methyl groups (to form the N-methylformamide molecule) exposes this pair, allowing it to interact with the hydrogen atoms of the hydroxyl group from alcohol and water. A comparison of the preferential solvation of N,N-dimethylformamide and N-methylformamide molecules allows us to estimate the influence of electron pairs on the nitrogen and oxygen atoms separately, on solvation of an amide group. A comparison of the local mole fractions of components around the N,Ndimethylformamide and N-methylformamide molecules may be helpful in understanding the solvation of an amide group by water and alcohol molecules. This is important in investigations of aqueous solutions of peptides; the amide group is a good model of the peptide bond. These considerations have initiated this series of papers. The application of the Kirkwood-Buff theory of solutions requires the determination of GmE and VmE values as a function of composition. Two papers containing the VmE results for (N-methylformamide + methanol + water)(3) and for (N-methylformamide + ethanol + water)(4) were published previously. In this paper, the total vapour pressure measurements for (N-methylformamide+water), (N-methylformamide + methanol), and (N-methyl-formamide + methanol + water) at T=313.15 K are reported.
2. Experimental N-methylformamide (E. Merck, product ‘‘zur synthese’’) was dried and stored over freshly ignited 0.4 nm molecular sieves. The measured conductivity of this solvent was below 2.4·10−6 V−1 m−1. Methanol (POCH, analytical reagent grade), was purified as described previously.(5) The refined solvent was stored over freshly ignited 0.3 nm molecular sieves. The mass fraction of water in both these solvents was below 0.0001, determined by titration using the Karl-Fischer reagent. Water was distilled twice in a glass apparatus. Characteristics of the pure substances are given in table 1. The apparatus for the vapour pressure measurements and the TABLE 1. Densities r, refractive indices nD , and vapour pressures p of pure liquids used in this work, measured at temperatures T Component
T/K
r/(g·cm−3 ) This work
N-methylformamide
298.15
0.9993
Methanol
313.15 298.15
0.9863 0.7864
313.15
0.7722
Water
313.15
Literature
nD
p/kPa
This work
Literature
0.9961(9) 0.9976(10)
1.43009
1.4300(9) 1.4310(10)
0.78667(11) 0.786434(12) 0.7725 to 0.7723(13)
1.32645
1.32661(11)
This work
Literature
0.095
0.093(14)
35.404
35.443(14)
7.373
7.372(14)
VLE for {x1 HCONHCH3+x2 CH3 OH+(1−x1−x2 )H2 O} at T=313.15 K
889
experimental procedure have been described in detail previously.(5,6) During the experiments, the temperature was controlled to within 20.001 K. The absolute error is estimated to be equal to 20.02 K (IPTS-68). Cathetometer readings contributed less than 0.004 kPa to the error of a single pressure measurement.
3. Results and discussion The measured values of vapour pressures, along with the calculated compositions of the vapour phase, are given in table 2 and presented graphically in figure 1 for (N-methlyformamide + water) and (N-methylformamide + methanol), and in table 3 for (N-methylformamide + methanol + water). Unfortunately, there are no data for second viral coefficients; or for calculating these coefficients for N-methylformamide. The vapour phase behaviour was therefore assumed to be ideal. Correlation of the binary results was carried out using the Redlich-Kister equation: M
GmE /RT=x(1−x) s Ki (2x−1)i−1,
(2)
i=1
TABLE 2. Experimental mole fractions in the liquid phase, x; mole fractions in the vapour phase, y, calculated from equations (2) or (3); and measured total vapour pressures p for the binary mixtures investigated x
y
0.9667 0.9039 0.8632 0.7685 0.7628 0.6976 0.6595 0.6017 0.5859 0.5314 0.4978
0.2726 0.1137 0.0805 0.0443 0.0430 0.0308 0.0258 0.0199 0.0186 0.0147 0.0127
p/kPa
x
y
p/kPa
0.0089 0.0075 0.0067 0.0040 0.0039 0.0034 0.0020 0.0012 0.0008 0.0004
4.282 4.582 4.758 5.572 5.619 5.791 6.370 6.747 6.944 7.176
xHCONHCH3+(1−x)H2O at T=313.15 K a
0.9553 0.9462 0.9293 0.9101 0.9010 0.8835 0.8703 0.8272 0.8030 0.7653 0.7538 0.7181 0.7121 a b
0.0398 0.0346 0.0279 0.0228 0.0209 0.0180 0.0162 0.0121 0.0104 0.0085 0.0080 0.0067 0.0066
Calculated from equation (2). Calculated from equation (3).
0.344 0.758 1.016 1.663 1.698 2.164 2.432 2.860 2.962 3.387 3.653
0.4174 0.3796 0.3573 0.2537 0.2491 0.2245 0.1452 0.0933 0.0631 0.0275
xHCONHCH3+(1−x)CH3OH at T=313.15 K b 2.308 0.6594 0.0052 2.625 0.6011 0.0041 3.220 0.5550 0.0034 3.888 0.5220 0.0030 4.167 0.4595 0.0024 4.807 0.3706 0.0017 5.251 0.3275 0.0014 6.726 0.3028 0.0012 7.606 0.2103 0.0008 8.908 0.1813 0.0006 9.284 0.1245 0.0004 10.575 0.0714 0.0002 10.762
12.626 14.679 16.315 17.474 19.660 22.787 24.270 25.131 28.278 29.267 31.176 32.983
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J. Zielkiewicz
FIGURE 1. Graphical representation of the experimental total vapour pressure p against the mole fraction x of N-methylformamide for binary mixtures of (a), (N-methylformamide+methanol) and (b), (N-methylformamide+water). The solid line connecting experimental points is the best curve calculated from equation (1) for (N-methylformamide+water) and from equation (2) for (N-methylformamide+methanol) using parameters from table 5.
and the van Laar–van Ness equation: M
GmE /RT=x(1−x)/ s Ki (2x−1)i−1,
(3)
i=1
where Ki are adjustable parameters and M is the number of such parameters. The Wilson and NRTL equations were also used for correlation of binary results. Table 4 shows the efficacy of these equations applied to the investigated binary mixtures. Table 5 includes the values of the parameters of these equations. As can be seen, equation (2) describes the (N-methylformamide+water) results with good accuracy. For the second mixture investigated, (N-methylformamide + methanol), the results obtained are best described by equation (3). Both these
VLE for {x1 HCONHCH3+x2 CH3 OH+(1−x1−x2 )H2 O} at T=313.15 K
891
TABLE 3. The ternary mixture {x1 HCONHCH3+x2CH3OH+(1−x1−x2 )H2O} at the temperature T=313.15 K; experimental mole fractions in the liquid phase, x1 , x2 ; mole fractions in the vapour phase, y1 , y2 , calculated from equations (4) and (6); and measured total vapour pressures p x1
x2
y1
y2
p/kPa
0.0692 0.1271 0.2205 0.3250 0.4300 0.5901 0.7381 0.0540 0.1228 0.1957 0.2912 0.4200 0.5222 0.0717 0.1454 0.2507 0.3502 0.4848 0.6206 0.7934 0.0391 0.0994 0.1619 0.2618 0.3738 0.5194 0.6856 0.0746 0.1681 0.2705 0.4017 0.6696 0.8394 0.4380 0.3889 0.3156 0.2389 0.1463 0.0790 0.3706 0.2670 0.1989 0.1379 0.0902 0.0497 0.0289
0.4517 0.4236 0.3783 0.3276 0.2766 0.1989 0.1271 0.2906 0.2695 0.2471 0.2177 0.1782 0.1468 0.6307 0.5806 0.5091 0.4415 0.3500 0.2578 0.1404 0.0907 0.0850 0.0791 0.0697 0.0591 0.0454 0.0297 0.8273 0.7437 0.6521 0.5349 0.2953 0.1436 0.1781 0.2702 0.4078 0.5516 0.7256 0.8518 0.3558 0.2563 0.1910 0.1323 0.0866 0.0477 0.0278
0.0003 0.0005 0.0010 0.0018 0.0029 0.0058 0.0114 0.0002 0.0006 0.0010 0.0019 0.0035 0.0055 0.0002 0.0005 0.0011 0.0017 0.0031 0.0055 0.0125 0.0003 0.0008 0.0014 0.0026 0.0047 0.0090 0.0191 0.0002 0.0006 0.0011 0.0020 0.0058 0.0138 0.0037 0.0025 0.0016 0.0010 0.0005 0.0003 0.0021 0.0015 0.0012 0.0009 0.0007 0.0005 0.0003
0.8147 0.8173 0.8216 0.8262 0.8301 0.8345 0.8370 0.7205 0.7189 0.7186 0.7192 0.7204 0.7213 0.8915 0.8956 0.9007 0.9049 0.9092 0.9118 0.9117 0.4428 0.4332 0.4265 0.4198 0.4143 0.4089 0.4054 0.9672 0.9688 0.9701 0.9714 0.9711 0.9656 0.7282 0.8071 0.8728 0.9160 0.9544 0.9772 0.8630 0.7493 0.6588 0.5524 0.4365 0.2941 0.1941
22.211 20.957 18.772 16.223 13.626 9.729 6.284 18.499 17.132 15.654 13.704 11.053 8.901 26.149 24.311 21.485 18.688 14.848 10.978 6.187 11.710 10.925 10.093 8.704 7.160 5.251 3.279 30.539 27.681 24.468 20.237 11.412 5.895 10.597 13.977 18.337 22.590 27.535 31.085 16.362 15.076 13.957 12.602 11.211 9.728 8.817
mixtures show small deviations from ideality, as can be seen in figure 1. Very similar behaviour was observed for ‘‘homologic’’ mixtures containing N,N-dimethylformamide. Comparison of the GmE values obtained for systems
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TABLE 4. Comparison of the standard deviations s of different equations for the binary and ternary results investigated. M represents the number of adjusted parameters and N the number of experimental points Equation
(2) (3) Wilson NRTL, a=0.3 (2) (3) Wilson NRTL, a=0.3 (4) (4) and (6) Wilson NRTL
s{dp/kPa}
M
xHCONHCH3+(1−x)H2O at T=313.15 K (N=21) 5 0.007 5 0.017 2 0.044 2 0.045 xHCONHCH3+(1−x)CH3OH at 5 5 2 2
T=313.15 K (N=25) 0.042 0.013 0.181 0.186
102 ·s(dp/p)
0.570 1.216 2.712 2.514 1.250 0.203 4.436 4.957
x1 HCONHCH3+x2CH3OH+(1−x1−x2 )H2O at T=313.15 K (N=46) 0 0.134 1.607 3 0.091 1.197 0 0.225 2.601 0 0.188 2.109
containing N,N-dimethylformamide and N-methylformamide in their binary mixtures with water or alcohols will be presented in a future paper. The ternary results were correlated using the equation:(7) GmE =s s (GmE )ij ,
(4)
i jqi
where (GmE )ij are the binary constituents calculated(7) according to equation (5): M
(GmE )ij =xi xj s Kk (xi−xj )k−1,
(5)
k=1
with the Kk values taken from table 5 for appropriate binary mixtures. Equation (5) conforms to equation (1), being applicable to the multicomponent mixture.(7) The values needed for (methanol+water) at this temperature were taken from reference 5. To this expression there has also been added a term describing the ternary interactions, taking the form proposed in reference 8: M
GmE (ter)/RT=x1 x2 (1−x1−x2 ) s Ci (2x1−1)i−1,
(6)
i=1
where Ci are adjustable parameters, and M is the number of such parameters. In equations (2), (3), and (6), as well as for the Wilson and NRTL equations, values of the adjustable parameters were obtained by the least-squares method, using the optimization algorithm based on the Marquardt method. These values are given in table 5, along with their standard deviations. The ternary mixture was also described using equations based on the local composition concept (Wilson and NRTL), making it possible to predict the multicomponent VLE values directly from
VLE for {x1 HCONHCH3+x2 CH3 OH+(1−x1−x2 )H2 O} at T=313.15 K
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TABLE 5. Parameters Ki of various equations used for correlation of the binary results, and Ci of equation (6) describing the ternary results, with their standard deviations for the mixtures investigated xHCONHCH3+(1−x)H2O at T=313.15 K Equation (2) K1=−0.0994220.00411 K4=−0.0389420.01186 Equation (3) K1=−9.4324220.65629 K4=9.7637625.02150 Wilson K1=0.62048 NRTL K1=−0.50196
K2=0.0122220.00465 K5=0.0823220.01875
K3=0.0908020.00850
K2=−1.2938920.99147 K5=−27.87532212.35541
K3=−5.8297022.54232
K2=1.61247 a=0.30
K2=0.46252
xHCONHCH3+(1−x)CH3OH at T=313.15 K Equation (2) K1=0.1526620.00282 K4=0.0728020.00992 Equation (3) K1=5.9028220.07339 K4=0.3270720.07686 Wilson K1=0.52158 NRTL K1=−0.45361
K2=0.0356720.00406 K5=0.1083820.01827
K3=−0.1083820.01827
K2=−2.0171620.04674 K5=−0.1218420.10420
K3=−3.0044920.09533
K2=1.45605 K2=0.68842
a=0.30
x1 HCONHCH3+x2CH3OH+(1−x1−x2 )H2O at T=313.15 K C1=−0.1992020.06331 C2=0.1887020.15124 C3=0.3339620.16179
the binary ones, without extra multicomponent terms. Table 4 summarizes the efficacy of describing the experimental ternary results with these formulae. As can be seen from this table, the best description, in accordance with expectations, is given by the empirical formula (4), with the adjusted ternary term defined by equation (6). The predictions of total vapour pressure for ternary mixtures obtained from the NRTL and Wilson equations are worse than the empirical formula (4) without the ternary term. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Zielkiewicz, J. J. Chem. Thermodynamics 1995, 27, 415–422. Zielkiewicz, J. J. Phys. Chem. 1995, 99, 4787–4793. Zielkiewicz, J. J. Chem. Thermodynamics 1995, 27, 1275–1279. Zielkiewicz, J. J. Chem. Thermodynamics 1996, 28, 313–318. Zielkiewicz, J.; Oracz, P. Fluid Phase Equilib. 1990, 59, 279–290. Zielkiewicz, J.; Oracz, P.; Warycha, S. Fluid Phase Equilib. 1990, 59, 191–209. Acree, W. E. Thermodynamic Properties of Nonelectrolyte Solutions. Academic Press: New York. 1984, Chap. 4. Jasin´ski, B.; Malanowski, S. Chem. Eng. Sci. 1970, 25, 913–920. Beilstein, 58, III 121, Beilstein’s Handbuch der Organische Chemie, Vol. A. Beilstein, 58, IV 170, Beilstein’s Handbuch der Organische Chemie, Vol. B. Treszczanowicz, A. J.; Benson, G. C. J. Chem. Thermodynamics 1977, 9, 1189–1197. Sakuragi, M.; Nakagawa, T. J. Chem. Thermodynamics 1984, 16, 171–174.
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13. Friedman, M. E.; Scheraga, H. A. J. Phys. Chem. 1965, 69, 3795–3800. 14. Boublik, T.; Fried, V.; Ha´la, E. The Vapour Pressures of Pure Substances. Elsevier: Amsterdam. 1984.
(Received 15 January 1996; in final form 6 March 1996)
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