Arabian Journal of Chemistry (2016) xxx, xxx–xxx
King Saud University
Arabian Journal of Chemistry www.ksu.edu.sa www.sciencedirect.com
ORIGINAL ARTICLE
Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N, N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure Hossein Iloukhani *, Zahra B. Mohammadlou Department of Physical Chemistry, Faculty of Chemistry, Bu-Ali Sina University, Hamedan, Iran Received 17 March 2012; accepted 8 October 2014
KEYWORDS Excess molar volume; Deviation in the viscosity and Refractive index; Formamide; N,N-dimethylacetamide; 2-Methyl-1-butanol
Abstract This article reports experimental densities q, viscosities g, and refractive indices nD, of the ternary systems of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) and the binary systems of formamide (1) + N,N-dimethylacetamide (2), formamide (1) + 2-methyl-1butanol (3), and N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) over the entire range of composition at T = 298.15 K for the liquid region and at ambient pressure. Excess molar volumes VEm , deviations in the viscosity Dg, and deviations in the refractive index DnD, for the mixtures were derived from the experimental data. The binary and ternary data of VEm , Dg, and DnD, were correlated as a function of the mole fraction by using the Redlich–Kister and the Cibulka equations, respectively. The results are consistent with the self-association of alcohol and the polar characters of used amide. McAlister’s multibody interaction model is used for correlating the kinematic viscosity of binary mixtures, with mole fraction. The experimental and the constituted binary and ternary systems are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures. Ó 2016 Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction * Corresponding author. Fax: +98 8118282807. E-mail address:
[email protected] (H. Iloukhani). Peer review under responsibility of King Saud University.
Production and hosting by Elsevier
This paper is a part of an ongoing research program in which we study thermodynamic, and transport properties of binary and ternary mixtures (Iloukhani and Zarei, 2004; Iloukhani et al., 2000; Iloukhani and Rakhshi, 2009; Zarei and Iloukhani, 2003; Khanlarzadeh and Iloukhani, 2011; Fattahi and Iloukhani, 2010). Experimental data of properties such as density q, and viscosity g, and refractive index nD, at over the whole composition range for binary and ternary liquid
http://dx.doi.org/10.1016/j.arabjc.2016.12.004 1878-5352 Ó 2016 Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Iloukhani, H., Mohammadlou, Z.B. Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure. Arabian Journal of Chemistry (2016), http://dx.doi. org/10.1016/j.arabjc.2016.12.004
2
H. Iloukhani, Z.B. Mohammadlou
mixtures are useful for a full understanding of their thermodynamic and transport properties, as well as for practical chemical engineering purposes (Matthew and Koga, 2002; Zhang et al., 2008). On the other hand, excess thermodynamic properties and deviations of nonthermodynamic ones of binary liquid mixtures are fundamental for the design of industrial equipment and for the interpretation of the liquid state, particularly when polar components are involved. These properties have also been used as a qualitative and quantitative guide to predict the extent of complex formation in this kind of mixtures (Gomez Marigliano and Solimo, 2002). Here, we have measured densities q, viscosities g, and refractive indices nD, for the binary and ternary systems formed by formamide, N,N-dimethylacetamide, and 2methyl-1-butanol at T = 298.15 K for the liquid region and at ambient pressure for the whole composition range. The data obtained are used to calculate excess molar volumes, deviations in the viscosity, deviations in the refractive index, and excess Gibbs energies of activation of viscous flow of the binary and ternary mixtures. The excess and deviation quantities of binary mixtures have been fitted to the Redlich–Kister equation to determine the coefficients. For correlating the ternary data, the Cibulka equation was used. The kinematic viscosity data for the binary mixtures were fitted to McAllister’s interaction model and their parameters have been calculated.
2. Experimental 2.1. Materials The mole fraction purity of the components from Merck were as follows: formamide (w P 99), N,N-dimethylacetamide (w P 99), and 2-methyl-1-butanol (w P 99), where w is mass fraction. All chemical substances were used without any further purification. Purity of each compound was checked by measuring the densities and refractive index and found to be in good agreement with values found in the literature (Nain, 2007; Cases et al., 2001; Gimenez et al., 2008; Iloukhani and Khanlarzadeh, 2006; Resa et al., 2005), reported in Table 1. 2.2. Apparatus and procedure Densities of the pure liquids and their mixture were measured with an Anton Paar DMA 4500 oscillating U-tube densimeter, operated in the static mode and the uncertainties were estimated to be within ±1 102 kg m3. The temperature in the cell was regulated to ±0.01 K with a solid-state thermostat. The apparatus was calibrated once a day with dry air and double-distilled freshly degassed water. The mixtures were
Table 1
Formamide N,N-dimethylacetamide 2-Methyl-1-butanol
c d e
ð1Þ
where k and c are the viscometer constants and t, g, and m, are the efflux time, dynamic viscosity, and kinematic viscosity, respectively. The uncertainty of the viscosity measurements was estimated to be less than ±2 103 mPa s. The viscometer was suspended in a thermostated water bath maintained to ±0.01 K. An electronic digital stopwatch with uncertainty to ±0.01 s was used for flow time measurements. At least three repetitions of each data point obtained were reproducible to ±0.05 s, and the results were averaged. Refractive indices were measured using a digital Abbe-type refractometer. Water was circulated into the prism of the refractometer by a circulation pump connected to an external thermostated water bath. The uncertainty of the refractive index is on the order of 0.0002 units. 3. Results and discussion Table 2 lists the experimental densities, viscosities, refractive indices, excess molar volumes, deviations in viscosity, deviations in refractive index and excess Gibbs energy of activation for three binary systems formamide (1) + N,Ndimethylacetamide (2), formamide (1) + 2-methyl-1-butanol (3), and N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K. The excess molar volumes VEm , were calculated from density data according to VEm ¼
n X xi Mi ðq1 q1 i Þ
ð2Þ
i¼1
where xi, Mi, and qi are the mole fraction, molar mass, and density of the pure component i, respectively. q is the density of mixture, and n is the number of components. In the system
q ðg=cm3 Þ Experimental
b
g ¼ qt ¼ qðkt c=tÞ
Comparison of measured densities and refractive indices of the pure components with literature values at 298.15 K.
Component
a
prepared by weighing amounts of the pure liquids by syringing into stoppered bottles to prevent evaporation and reducing possible errors in mole fraction calculations. Ternary mixtures were prepared by mixing the three components. Each mixture was immediately used after it was well-mixed by shaking. All the weightings were performed on an electronic balance (AB 204-N Mettler) accurate to 0.1 mg. The uncertainty in the mole fraction is estimated to be lower than ±2 104. Dynamic viscosities at 298.15 K were measured with an Ubbelohde viscometer. The equation for viscosity, according to Poiseuille’s law, is
1.12904 0.93624 0.81537
nD Literature a
1.12908 0.93634c 0.8150e
Experimental
Literature
1.4455 1.4357 1.4087
1.4468b 1.4356d 1.4086e
Nain (2007). Cases et al. (2001). Gimenez et al. (2008). Iloukhani and Khanlarzadeh (2006). Resa et al. (2005).
Please cite this article in press as: Iloukhani, H., Mohammadlou, Z.B. Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure. Arabian Journal of Chemistry (2016), http://dx.doi. org/10.1016/j.arabjc.2016.12.004
Densities, viscosities, and refractive indices for binary and ternary mixtures
3
Table 2 Experimental densities q, viscosities g, refractive indices nD , excess molar volumes VEm , deviations in the viscosity Dg, E deviations in the Refractive Index DnD , and excess Gibbs energy of activation DG , of viscous flow for the binary systems at 298.15 K. g ðmPa sÞ
nD
VEm ðcm3 =molÞ
Dg ðmP sÞ
DG (J/mol)
DnD
1.4370 1.4381 1.4391 1.4401 1.4410 1.4418 1.4424 1.4430 1.4436 1.4441 1.4446 1.4452
0.153 0.271 0.355 0.395 0.403 0.390 0.351 0.308 0.235 0.175 0.110 0.036
0.027 0.010 0.034 0.125 0.256 0.427 0.583 0.743 0.824 0.770 0.612 0.262
192.719 409.411 609.464 811.345 993.374 1152.539 1235.356 1271.056 1208.165 1022.015 741.455 297.445
0.0005 0.0008 0.0010 0.0013 0.0014 0.0014 0.0012 0.0010 0.0008 0.0006 0.0003 0.0001
N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) 0.0803 0.82341 3.357 1.4106 0.1600 0.83174 2.661 1.4125 0.2397 0.84036 2.218 1.4145 0.3207 0.84932 1.915 1.4164 0.3987 0.85820 1.685 1.4184 0.4801 0.86769 1.510 1.4206 0.5598 0.87731 1.367 1.4228 0.6402 0.88735 1.262 1.4249 0.7200 0.89768 1.157 1.4272 0.7996 0.90826 1.073 1.4295 0.8800 0.91934 0.999 1.4315 0.9588 0.93037 0.927 1.4344
0.071 0.041 0.001 0.020 0.040 0.071 0.080 0.079 0.065 0.050 0.023 0.007
0.804 1.216 1.375 1.390 1.343 1.229 1.089 0.909 0.731 0.532 0.321 0.112
378.556 633.888 764.390 804.579 810.324 757.163 687.375 566.148 465.563 338.052 197.646 70.095
0.0003 0.0005 0.0007 0.0009 0.0010 0.0011 0.0010 0.0010 0.0009 0.0008 0.0006 0.0002
Formamide (1) + 2-methyl-1-butanol (3) 0.0801 0.82461 4.092 0.1609 0.83532 3.983 0.2398 0.84723 3.999 0.3199 0.86110 4.064 0.4005 0.87688 4.147 0.4808 0.89504 4.229 0.5609 0.91594 4.301 0.6401 0.94020 4.331 0.7200 0.96901 4.317 0.7997 1.00348 4.146 0.8809 1.04647 3.792 0.9601 1.09837 3.347
0.066 0.091 0.092 0.066 0.049 0.018 0.007 0.037 0.057 0.067 0.071 0.043
0.252 0.257 0.137 0.032 0.220 0.406 0.583 0.716 0.807 0.739 0.491 0.149
67.299 1.657 130.185 284.186 439.098 579.834 701.292 781.568 819.646 744.175 522.241 181.922
0.0020 0.0038 0.0054 0.0066 0.0075 0.0083 0.0087 0.0087 0.0078 0.0068 0.0047 0.0023
x
q ðg=cm3 Þ
Formamide (1) + N,N-dimethylacetamide (2) 0.0811 0.94490 1.049 0.1596 0.95381 1.242 0.2403 0.96353 1.469 0.3204 0.97372 1.740 0.3978 0.98431 2.045 0.4799 0.99664 2.402 0.5591 1.00974 2.735 0.6407 1.02512 3.080 0.7204 1.04190 3.340 0.7995 1.06156 3.464 0.8793 1.08485 3.485 0.9607 1.11319 3.319
1.4096 1.4108 1.4121 1.4139 1.4159 1.4181 1.4206 1.4236 1.4274 1.4313 1.4364 1.4417
studied, excess molar volumes are negative for the system formamide (1) + N,N-dimethylacetamide (2) over the whole composition range. For the system formamide (1) + 2methyl-1-butanol (3), and N,N-dimethylacetamide (2) + 2methyl-1-butanol (3) an inversion of sign of VEm , is observed over part of the concentration range. In first system values VEm , are positive at lower concentrations of alcohol and negative at higher concentrations of it. Fig. 1 shows the excess molar volumes for the three binary systems at T = 298.15 K. A plausible qualitative interpretation of the behavior of these mixtures with composition has been suggested. In the systems considered here, we can recognize four different effects as being important, (i) hydrogen bond rupture, (ii) dispersive interactions between unlike molecules, (iii) intermolecular dipolar interactions, and (iv) geometrical fitting between components. The positive contribution to VEm , is expected from first
E
two effects while opposite contribution from remaining two. The volumetric behavior of the formamide + N,Ndimethylacetamide mixture shows that effect (iii) and (iv) which leads to packing in volumes, predominates over the two (i) and (ii), which contribute to expansion. For the system of formamide (1) + 2-methyl-1-butanol (3), positive values of VEm , were observed in the region of x1 below 0.56 while negative values of VEm , were found for the other composition ranges. Mixing of formamide with alkanols would induce mutual dissociation of the hydrogen bonded structures present in pure liquids with subsequent formation of (new) H-bonds (C‚ OHAO) between proton acceptor oxygen atom (with two lone pair of electrons) of C‚O group of formamide and hydrogen atom of ‚OH group(s) of alkanol molecules. Therefore at high concentration of alcohol dissociation is dominate while at low concentration opposite contribution (associated
Please cite this article in press as: Iloukhani, H., Mohammadlou, Z.B. Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure. Arabian Journal of Chemistry (2016), http://dx.doi. org/10.1016/j.arabjc.2016.12.004
4
H. Iloukhani, Z.B. Mohammadlou
Figure 1 Variation of excess molar volume VEm with mole fraction x1 for the binary systems at T = 298.15 K: r, Formamide (1) + N,N-dimethylacetamide (2); N, N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3); d, Formamide (1) + 2-methyl-1-butanol (3). Solid curves were calculated from the Redlich–Kister equation.
Figure 2 Variation of deviation in the viscosity Dg with mole fraction x1 for the binary systems at T = 298.15 K: r, Formamide (1) + N,N-dimethylacetamide (2); N, N,N-dimethylacetamide (2) + 2-methyl-2-methyl-1-butanol (3); d, Formamide (1) + 2methyl-1-butanol (3). Solid curves were calculated from the Redlich–Kister equation.
through hydrogen bonding and leading to a contraction in volume) is dominate. For the system of N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3), negative values of VEm , were observed in the region of x1 below 0.32 while positive values of VEm , were found for the other composition ranges. A sigmoid shape observed may be attributed to the hydrogen bond effect that occurred between amide and alcohol. At low concentration of amide, hydrogen bonding is dominant resulting in negative values of VEm , whereas at higher mole fraction of amide, dispersive forces are dominant resulting in positive values of VEm . The other reason for this observation is steric hindrance of the two methyl groups of N,N-dimethylacetamide. The viscosity deviations Dg, and excess Gibbs energies of E activation of viscous flow DG , for binary mixtures can be calculated as Dg ¼ g
N X xi gi
ð3Þ
i
" DG ¼ RT lnðmMÞ E
c X xi lnðmi Mi Þ
# ð4Þ
i¼1
where M is the molecular weight, xi is the mole fraction and c refers to the number of components in the mixture g, is the absolute viscosity of the mixtures and gi , is the absolute viscosity of pure component i. The Dg, values are also graphically represented as a function of mole fraction at 298.15 K in Fig. 2. It is observed that the Dg, values for system formamide (1) + N,N-dimethylacetamide (2) and formamide (1) + 2methyl-1-butanol (3), an inversion of sign of Dg, are observed over part of the concentration range. This reveals that the strength of specific interaction is not the only factor influencing the viscosity deviation of liquid mixtures. The molecular size and shape of the components also play an equally important role. According to Meyer et al. the observed negative valE ues of DG correspond to the existence of solute–solute association.
Figure 3 Variation of deviation in the refractive index DnD with mole fraction x1 for the binary systems at T = 298.15 K: r, Formamide (1) + N,N-dimethylacetamide (2); N, N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3); d, Formamide (1) + 2methyl-1-butanol (3). Solid curves were calculated from the Redlich–Kister equation.
The deviation in the refractive index from the mole fraction average DnD , is given by DnD ¼ nD
n X xi nD;i
ð5Þ
i
where nD and nD;i are the refractive index of the mixture and the refractive index of pure component i, respectively. For the whole composition range, the DnD , values are negative for systems formamide (1) + 2-methyl-1-butanol (3) and N, N-dimethylacetamide (2) + 2-methyl-1-butanol (3). The DnD , values for system formamide (1) + N,N-dimethylacetamide
Please cite this article in press as: Iloukhani, H., Mohammadlou, Z.B. Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure. Arabian Journal of Chemistry (2016), http://dx.doi. org/10.1016/j.arabjc.2016.12.004
Densities, viscosities, and refractive indices for binary and ternary mixtures (2) are positive. Figs. 3 and 4 show the results of DnD , and E DG for the three binary mixtures at T = 298.15 K respectively. The mixing functions VEm , Dg, and DnD were represented mathematically by the Redlich–Kister equation for correlating the experimental data (Redlich and Kister, 1948): DQij ¼ xi xj
m X Ak ðxj xi Þk
5
Ak were determined by a multiple regression analysis based on the least squares method and are summarized along with the standard deviations between the experimental and the fitted values of the respective functions in Table 3. The standard deviation is defined by " #12 n X r¼ ðDQexp;i þ DQcal;i Þ=ðn pÞ ð7Þ
ð6Þ
i¼1
k¼0
where DQij refers to VEm =cm3 mol1 , Dg=mPa s, and DnD for each i–j binary pair; xi is the mole fraction of component i; and Ak values are the coefficients. The values of coefficients
where n is the number of experimental points and p is the number of adjustable parameters. The experimental densities, viscosities, excess molar volumes, deviations in the viscosity, deviations in refractive index and excess Gibbs energy of activation of the ternary mixtures system formamide (1) + N,Ndimethylacetamide (2) + 2-methy1-butanol (3) at 298.15 K are listed in Table 4. The derived data (VEm , Dg, and DnD ) as defined in Eqs. (2)–(5) for the ternary system were correlated respectively using the equation DQ123 ¼ DQbin þ x1 x2 x3 D123
ð8Þ
3 X 3 X DQij
ð9Þ
DQbin ¼
i¼1
j:i
where DQ123 refers to VEm , Dg, and DnD , for the ternary system formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1butanol (3). DQij in Eq. (9) is the binary contribution of each i–j pair to the VEm , Dg, and DnD , given by Eq. (6) with the parameters shown in Table 3. The ternary contribution term D123 was correlated using the expression suggested by Cibulka (1982): Figure 4 Excess Gibs energies of the binary mixtures vs. mole fraction x1 for the binary systems at T = 298.15 K: r, Formamide (1) + N,N-dimethylacetamide (2); N, N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3); d, Formamide (1) + 2-methyl-1-butanol (3).
D123 ¼ B0 þ B1 x1 þ B2 x2
ð10Þ
where the ternary parameters B0, B1, and B2 were determined with the optimization algorithm similar to that for the binary parameters. The fitting parameters and the corresponding
Table 3 Binary coefficients of the RedlichKister equation Ak, at 298.15 K and ternary coefficients of the Cibulka equation for VEm , Dg, and DnD at 298.15 K. DQij
A2
A3
A4
r
Formamide (1) + N,N-dimethylacetamide (2) 1.5233 0.8383 VEm (cm3/mol) Dg ðmPa sÞ 1.8886 4.1602 0.0054 0.0018 DnD
0.0966 1.4651 0.0028
0.2925 0.2627 0.001
0.1409 0.1721 0.0024
0.0039 0.0114 0.000036
N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) 0.2899 0.1039 VEm (cm3/mol) Dg ðmPa sÞ 4.7762 3.3975 0.0042 0.0008 DnD
0.2824 2.4403 0.0017
0.8259 1.9729 0.0003
0.9068 0.9216 0.0027
0.0069 0.00474 0.000036
Formamide (1) + 2-methyl-1-butanol (3) 0.0363 VEm (cm3/mol) Dg ðmPa sÞ 1.7763 0.0344 DnD
0.3016 1.3156 0.0072
0.5868 0.3651 0.0097
0.5001 4.5054 0.0228
0.0043 0.0143 0.000227
A0
DQ123 VEm
3
(cm /mol) Dg=ðmPa sÞ DnD
A1
0.6418 4.9465 0.0078
B0
B1
B2
r
1.6013 5.02495 0199.0
3.5073 16.6239 0.0106
2.8107 10.6946 0.0007
0.0372 0.0229 0.0002
Please cite this article in press as: Iloukhani, H., Mohammadlou, Z.B. Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure. Arabian Journal of Chemistry (2016), http://dx.doi. org/10.1016/j.arabjc.2016.12.004
6
H. Iloukhani, Z.B. Mohammadlou Table 4 Experimental densities q, viscosities g, refractive Indices nD , excess molar volumes VEm , deviation in the viscosity Dg, E deviations in the refractive index DnD , and excess Gibbs energy of activation DG , of viscous flow for the ternary for the system formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K. x1
x2
q ðg=cm3 Þ
g ðmPa sÞ
nD
VEm ðcm3 =molÞ
Dg ðmPa sÞ
DG (J/mol)
DnD
0.1015 0.1014 0.1016 0.1025 0.1009 0.1013 0.1000 0.0999 0.2067 0.2060 0.2055 0.2048 0.2037 0.2023 0.2009 0.3128 0.3106 0.3107 0.3088 0.3057 0.3026 0.4193 0.4170 0.4112 0.4098 0.4048 0.5243 0.5196 0.5122 0.5068 0.6262 0.6195 0.6091 0.7231 0.7118 0.8146
0.0834 0.1867 0.2894 0.3915 0.4918 0.5960 0.6974 0.7984 0.0703 0.1752 0.2801 0.3854 0.4901 0.5952 0.6989 0.0609 0.1720 0.2765 0.3830 0.4898 0.5964 0.0561 0.1659 0.2743 0.3851 0.4940 0.0560 0.1690 0.2813 0.3913 0.0608 0.1749 0.2894 0.0704 0.1866 0.0835
0.8368 0.8490 0.8617 0.8748 0.8879 0.9023 0.9167 0.9315 0.8510 0.8649 0.8792 0.8942 0.9097 0.9257 0.9420 0.8686 0.8848 0.9009 0.9179 0.9351 0.9530 0.8901 0.9082 0.9258 0.9459 0.9652 0.9165 0.9371 0.9575 0.9788 0.9487 0.9721 0.9913 0.9875 1.0132 1.0352
3.295 2.605 2.183 1.875 1.658 1.472 1.331 1.201 3.463 2.856 2.410 2.102 1.860 1.651 1.486 3.665 3.083 2.658 2.351 2.074 1.852 3.846 3.328 2.906 2.566 2.280 3.986 3.498 3.105 2.764 4.058 3.617 3.189 4.002 3.616 3.772
1.4123 1.4153 1.4181 1.4211 1.4243 1.4274 1.4306 1.434 1.4138 1.4174 1.4207 1.4242 1.4277 1.4314 1.4351 1.4161 1.4200 1.4239 1.4280 1.4319 1.436 1.4187 1.4231 1.4274 1.4323 1.4366 1.4221 1.4272 1.4321 1.4371 1.4264 1.4319 1.4369 1.4314 1.4376 1.4378
0.066 0.061 0.039 0.025 0.013 0.051 0.115 0.151 0.062 0.013 0.027 0.079 0.147 0.208 0.267 0.028 0.046 0.099 0.180 0.248 0.327 0.008 0.095 0.174 0.264 0.338 0.048 0.148 0.237 0.321 0.085 0.195 0.068 0.101 0.218 0.139
0.720 1.044 1.101 1.046 0.909 0.724 0.507 0.278 0.463 0.698 0.772 0.708 0.579 0.417 0.216 0.156 0.347 0.401 0.332 0.234 0.081 0.146 0.015 0.029 0.021 0.116 0.422 0.329 0.325 0.367 0.643 0.598 0.563 0.746 0.759 0.682
236.041 408.908 439.286 411.146 322.437 205.464 60.532 82.433 0.500 65.313 74.981 2.705 102.201 214.427 354.827 256.269 256.998 295.196 401.388 499.750 626.389 491.786 552.277 626.429 739.573 857.658 691.211 791.397 914.353 1036.467 837.740 973.379 1089.410 892.271 1061.625 811.692
0.0024 0.0022 0.0022 0.0019 0.0014 0.0011 0.0006 0.0001 0.0044 0.0036 0.0031 0.0024 0.0017 0.0008 0.0001 0.0058 0.0048 0.0037 0.0024 0.0013 0.0001 0.0069 0.0054 0.0038 0.0019 0.0003 0.0074 0.0052 0.0030 0.0008 0.0070 0.0043 0.0020 0.0058 0.0023 0.0031
E
Table 5 Binary coefficients of McAlister,s multibody-interaction equations and standard deviations r, for kinematic viscosities at 298.15 K. Three-body m12 ðmm2 =sÞ
Four-body m2;1 ðmm2 =sÞ
r ðmm2 =sÞ
m1112 ðmm2 =sÞ
m1122 ðmm2 =sÞ
m2221 ðmm2 =sÞ
r ðmm2 =sÞ
Formamide (1) + N,N-dimethylacetamide (2) 5.0746 1.7067 0.0135
1.49633
1.02288
0.414879
0.0095
N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) 1.4621 1.5566 0.0297
0.203471
0.535476
0.685996
0.0071
Formamide (1) + 2-methyl-1-butanol (3) 7.3493 3.6403 0.0355
1.72536
1.67282
1.37031
0.0349
standard deviations are given in Table 3. As can be expected, the ternary system shows the same change in binary systems. McAllister’s multibody-interaction model (McAllister, 1960)
is widely used for correlating the kinematic viscosity of binary mixtures with mole fraction. The three-body model is defined as
Please cite this article in press as: Iloukhani, H., Mohammadlou, Z.B. Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure. Arabian Journal of Chemistry (2016), http://dx.doi. org/10.1016/j.arabjc.2016.12.004
Densities, viscosities, and refractive indices for binary and ternary mixtures ln m ¼ x31 ln m1 þ 3x21 x2 ln v12 þ 3x1 x22 ln v21 þ x32 ln m2 x2 M2 M2 þ 3x21 x2 ln 2=3 þ ln x1 þ M1 3M1 2M 2 þ 3x1 x22 ln 1=3 þ þ x32 lnðM2 =M1 Þ 3M1
ð11Þ
and the four-body model is given by ln m ¼ x41 ln m1 þ 4x31 x2 ln m1112 þ 6x21 x22 ln m1122 x2 M2 þ 4x1 x32 ln m2221 þ x42 ln m2 ln x1 þ M1 1 þ 3M2 =M1 3 4 þ x2 lnðM2 =M1 Þ þ 4x1 x2 ln 4 3 þ M2 =M1 1 þ M2 =M1 3 2 2 þ 6x1 x2 ln þ 4x1 x2 ln 4 2 ð12Þ where m, m1 , and m2 are the kinematic viscosities of the mixture and the viscosities of pure components 1 and 2, respectively. m12 , m21 , m1112 , m1122 and m2221 are the model parameters. Table 5 records the calculated results with the standard deviation defined as in Eq. (7). It is shown that McAllister’s four-body equation gave a better result for those three systems. 4. Conclusions Excess molar volumes, viscosities, and refractive index deviations for mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2methyl-1-butanol (3) were obtained from experimental results and fitted by the Redlich–Kister and Cibulka equations. Positive quantities show that dominant factors are physical interactions, and negative values suggested that the main factor in the interactional forces is chemical interactions. McAllister’s multibody-interaction model was used for correlating the kinematic viscosity of binary mixtures with mole fraction. Results showed that McAllister’s four-body equation gave a better result for those three systems.
Acknowledgment The authors would like to thank the Bu-Ali Sina University for providing the necessary facilities to carry out the research. References Cases, A.M., Gomez Marigliano, A.C., Solimo, H.N., 2001. Density, viscosity and refractive index of formamide three carboxylic acids and formamide + carboxylic acid binary mixtures. J. Chem. Eng. Data 46, 712–715. Cibulka, I., 1982. Estimation of excess volume and density of ternary liquid mixtures of non electrolytes from binary data. Collect. Czech. Chem. Commun. 47, 1414–1419. Fattahi, M., Iloukhani, H., 2010. Excess molar volume, viscosity, and refractive index study for the ternary mixture 2-methyl-2-butanol
7
(1) + tetrahydrofuran (2) + propylamine (3) at different temperatures. Application of the ERAS-model and Peng–Robinson– Stryjek–Vera equation of state. J. Chem. Thermodyn. 42, 1335– 1345. Gimenez, P.G., Lopez, J.F., Velasco, I., 2008. Excess molar enthalpies and (vapour + liquid) equilibria for mixtures containing N,Ndialkylamides and a,x-dichloroalkanes. J. Chem. Thermodyn. 40, 212–219. Gomez Marigliano, A.C., Solimo, H.N., 2002. Density, viscosity, excess molar volume, viscosity deviation and their correlations for formamide + three alkane-1-ols binary systems. J. Chem. Eng. Data 47, 796–800. Iloukhani, H., Parsa, J.B., Saboury, A.A., 2000. Excess molar enthalpies of binary mixtures containing N,N-dimethylformamide + six 2-alkanols (c3–c8) at 300.15 K. J. Chem. Eng. Data 45, 1016– 1021. Iloukhani, H., Zarei, H.A., 2004. Excess molar enthalpies of amides + some alkan-2-ols at 298.15 K. Phys. Chem. Liq. 42, 75–79. Iloukhani, H., Khanlarzadeh, H., 2006. Densities, viscosities, and refractive indices for binary and ternary mixtures of N,N-dimethylacetamide (1) + 2-methylbutan-2-ol (2) + ethyl acetate (3) at 298.15 K for the liquid region and at ambient pressure. J. Chem. Eng. Data 51, 1226–1231. Iloukhani, H., Rakhshi, M., 2009. Excess molar volumes, viscosities, and refractive indices for binary and ternary mixtures of cyclohexanone (1) + N,N-dimethylacetamide (2) + N,N-diethylethanolamine (3) at 298.15, 308.15, and 318.15 K. J. Mol. Liq. 149, 86–95. Khanlarzadeh, K., Iloukhani, H., 2011. Application of ERAS-model and Prigogine–Flory–Patterson theory to excess molar volumes for ternary mixtures of 2-chlorobutane (1) + butylacetate (2) + isobutanol (3) at T = 298.15 K. J. Chem. Thermodyn. 43, 1583–1590. Matthew, T.P., Koga, Y., 2002. Interactions in 1-propanol-(1,2- and 1,3-)propanediol-H2O: the effect of hydrophobic vs hydrophilic moiety on the molecular organization of H2O. J. Phys. Chem. B 106, 7090–7095. McAllister, R.A., 1960. The viscosity of liquid mixtures. AIChE J. 6, 427–431. Nain, A.K., 2007. Densities and volumetric properties of (formamide + ethanol, or 1-propanol, or 1,2-ethanediol, or 1,2-propanediol) mixtures at temperatures between 293.15 K and 318.15 K. J. Chem. Eng. Data 46, 712–715. Redlich, O.J., Kister, A.T., 1948. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 40, 345–348. Resa, J.M., Gonzalez, C., Goenaga, J.M., 2005. Density, refractive index, speed of sound at 298.15 K and vapour-liquid equilibria at 101.3 kPa for binary mixtures of methanol + 2-methyl-1-butanol and ethanol + 2-methyl-1-butanol. J. Chem. Eng. Data 50, 1570– 1575. Zarei, H.A., Iloukhani, H., 2003. Excess molar enthalpies of formamide + some alkan-1-ols (c1–c6) and their correlation at 298.15 K. Thermochim. Acta 405, 123–128. Zhang, R., Zheng, D., Pan, Y., Lou, S., Wu, W., Li, H., 2008. Allatom simulation and excess properties study on intermolecular interactions of amide-water system. J. Mol. Struct. 875, 96–100.
Please cite this article in press as: Iloukhani, H., Mohammadlou, Z.B. Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure. Arabian Journal of Chemistry (2016), http://dx.doi. org/10.1016/j.arabjc.2016.12.004
