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Topological studies of molecular interactions of formamide with propanol and butanol at 298.15 K
Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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Topological studies of molecular interactions of formamide with propanol and butanol at 298.15 K Manju Rani a, Sanjeev Maken b,* a b
Department of Chemical Engineering, Deenbandhu Chhotu Ram University of Science and Technology, Murthal 131 039, India Department of Chemistry, Deenbandhu Chhotu Ram University of Science and Technology, Murthal 131 039, India
A R T I C L E I N F O
Article history: Received 15 January 2012 Accepted 7 March 2012 Available online 28 March 2012 Keywords: Molar excess volume Partial molar volume Formamide Alkanol Graph theoretical approach
A B S T R A C T
Molar excess volumes have been measured at 298.15 K for formamide + 1-propanol, 2-propanol, 1butanol, 2-methyl-1-propanol or 2-methyl-2-propanol mixtures. For an equimolar mixture, molar excess volumes follow the sequence: 1-butanol > 1-propanol > 2-methyl-1-propanol > 2-methyl-2E ) values have been fitted to Redlich–Kister propanol > 2-propanol. The excess molar volume (Vm polynomial equation and other volumetric properties like apparent molar volume, partial molar volume, excess partial molar volume were calculated. The excess volume data have also been rationalized by E calculated by this approach agree well with graph-theoretical arguments. It has been observed that Vm the corresponding experimental values. This analysis has further yielded information about the state of aggregation of pure components that is consistent with the existing views on their nature of association. The infrared spectral studies lend further credence to the graph theoretical arguments. ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
1. Introduction The thermo-physical properties of mixtures would be of great importance in processing engineering designs and also helpful in getting information about molecular structure and intermolecular forces in liquid mixture, which can be very helpful in making the choice of solvent in various applications. Alcohols are self associated organic compound through hydrogen bonding of their hydroxyl groups. These are biologically and industrially important amphiphilic materials. Branching of alkyl group attached to the hydroxyl group results in abnormal behaviour of alcohols [1]. Amides are known as an important class of bio-organic solvents and are convenient model systems for investigating peptide and protein–solvent interactions. The H-bond formation ability of these solvents with other H-bonded self-associating solvents is useful in understanding the peptide linkage in complex biosystems [2]. Formamide is selected for this study, as it is the simplest amide that contains a peptide linkage, the fundamental building block of proteins. Formamide molecules are highly polar [3] and are strongly self-associated through extensive threedimensional network of hydrogen bonds, through its three hydrogen bond donors (3 H-atoms) and three acceptors (two lone pairs of electrons at oxygen and one on nitrogen atom). Since the components of these binary mixtures have both proton-donating/ accepting abilities, significant interaction through hydrogen
bonding between unlike molecules is expected [4]. Further in view of the two well known resonance structures [5] of the amide group, the lower amides in pure state may exist like alkanols [6,7], dimers and higher r-mers, though Davies [8] favors dimeric state for them in solution. Although such a situation can be handled by the ideal association model approach [9,10] yet the result would be strongly dependent on the particular type of model assumed for formamide and alkanols. This calls for an entirely different approach. Since binary mixture is formed by the replacement of like contacts in the pure state by unlike contact in the mixture and as the formations of molecular entities in the present mixtures may be visualized [11] due to the changes in the topology of formamide brought on by alkanol, it appears that a recent graph theoretical approach [12,13] should provide valuable information about the state of formamide and alkanol in an binary mixture. This prompted us to perform molar excess volume studies at 298.15 K on formamide + 1-propanol, 2-propanol, 1-butanol, 2methyl-1-propanol or 2-methyl-2-propanol mixtures. The Redlich–Kister equation was used to correlate the experimental data and to obtain the partial molar volumes at 298.15 K and at atmospheric pressure [14]. The excess volume data have also been rationalized by graph-theoretical arguments. It has been observed E that Vm calculated by this approach agree well with the corresponding experimental values. 2. Experimental
* Corresponding author. E-mail address: [email protected] (S. Maken).
Formamide, 1-propanol, 2-propanol, 1-butanol, 2-methyl-1propanol or 2-methyl-2-propanol mixtures (Merck or Sigma) were
1226-086X/$ – see front matter ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2012.03.011
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704 0.05
Molar excess volume, (cm3mol-1)
purified by standard procedures [15,16]. The purities of the purified samples were checked by measuring their densities and refractive indices at 298.15 K. The densities were measured with a precision of 5 105 g cm3 by a specially designed densimeter, consisting of a bulb of approximate volume 35 cm3 attached to a calibrated capillary through a B-10 standard joint in the manner described by Weissenberger [17]. Air buoyancy correction was also applied to achieve a greater accuracy. Refractive indices were measured with a thermostatically controlled Abbe refractometer (OSAW, India) using sodium D-line with an accuracy of 0.0001. Our experimental values for the density, and refractive index of the pure compounds compared well with the literature values as shown in E Table 1. Molar excess volumes, Vm , for the binary mixtures have been measured by V-shaped dilatometer at 298.15 K in the manner described elsewhere [18]. The temperature of water thermostat was controlled to 0.01 K by a mercury-in-toluene regulator. The change in the position of the liquid level in the capillary was noted with a cathetometer (OSAW, Ambala) that could read to 0.001 cm. The performance of dilatometer was checked by measuring the molar excess volume of the benzene + cyclohexane mixture at 298.15 K and these agreed to within the experimental limits with corresponding E literature. The uncertainty in the measured Vm values was 1%.
1695
0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 0.0
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol 0.2
0.4
0.6
0.8
1.0
x1 E Fig. 1. Molar excess volume (Vm ) of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K; symbols represent experimental value and lines represent value calculated from Eq. (2).
E ðs ðVm ÞÞ.
3. Results The excess molar volume is defined by E Vm ¼ V m x1 V1o x2 V2o
s ðVmE Þ ðcm3 mol1 Þ ¼ (1)
where Vm represents the volume of a mixture containing one mole of (formamide + alkanol), x1 and x2 are the mole fraction of formamide and alkanol, respectively and V1o and V2o are the molar volume of pure components. E The measured Vm data at 298.15 K are recorded in Table 2 and are fitted to the following Redlick and Kister equation
E Vm
3
ðcm
1
mol
2 3 n X j Þ ¼ x1 ð1 x1 Þ4 A j ð2x1 1Þ 5
(2)
j¼0
where Aj are the adjustable parameters, and x1 is the mole fraction of formamide in formamide + alkanol mixture. These parameters E were evaluated by fitting Vm data to Eq. (2) by the least squares E method and recorded in Table 3 with the standard deviations of Vm ,
8" 2 #91=2 P > > > > E E > > Vexpt: V > > = < cal:ð Eq: ð2ÞÞ > > > > :
mn
> > > > ;
(3)
where m is the number of experimental values, and n is the number of adjustable parameters in Eq. (2). The choice of n to have 0–3 values was dictated by the consideration that the maximum E deviation sm(VE) of Vm (as calculated from Eq. (2) from the E corresponding experimental Vm values satisfied the relation s ðVmE Þ 2s ðVmE Þ. E Comparison of Vm experimental for the studied system together with smoothing curves using Eq. (2) is shown in Fig. 1. E We have also calculated the excess partial molar volumes, V¯ 1 ¼ o E o E ðV¯ 1 V¯ 1 Þ and V¯ 2 ¼ ðV¯ 2 V¯ 2 Þ, from Vm . The excess molar volumes, E E V¯ 1 and V¯ 2 , were evaluated using following equations: E o V¯ 1 ¼ V¯ m þ V¯ 1 þ ð1 x1 Þ
E
@V¯m @x1
! (4) p;T
Table 1 Measured densities (r) and refractive indices (nD) of the pure components at 298.15 K. Compound
Temperature (K)
r (kg m3)
nD
This work
Literature
This work
Literature
1129.01 [25] 1129.1 [26] 799.75 [27] 799.79 [29] 799.48 [30] 781.28 [29] 781.01 [30] 781.06 [32] 805.565 [33] 805.98 [29] 805.83 [30] 797.37 [33] 797.8 [34] 798.52 [35] 780.59 [33] 781.2 [34]
1.4461
1.44597 [26]
1.914
1.915 [28]
2.0650
2.0652 [31]
1.3972
1.39741 [16]
1.3937
1.3939 [34]
1.3854
1.3852 [34]
Formamide
298.15
1129.02
1-Propanol
298.15
799.77
2-Propanol
298.15
781.2
1-Butanol
298.15
805.85
2-Methyl-1-propanol
298.15
797.6
2-Methyl-2-propanol
298.15
780.8
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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Table 2 Experimental excess volume, apparent molar volumes, partial molar volumes and excess partial molar volumes of binary liquid mixtures of formamide (1) + alkanol (2) at 298.15 K. Vf1 (cm3 mol1)
Vf2 (cm3 mol1)
1 V¯ 1 ðcm3 mol Þ
1 V¯ 2 ðcm3 mol Þ
E 1 V¯ 1 ðcm3 mol Þ
E 1 V¯ 2 ðcm3 mol Þ
Formamide (1) + 1-propanol (2) 0.0499 0.011 0.0921 0.024 0.1532 0.037 0.1835 0.044 0.2251 0.056 0.066 0.2663 0.3219 0.081 0.3856 0.097 0.4082 0.105 0.4420 0.118 0.5091 0.135 0.5621 0.146 0.147 0.6258 0.7068 0.135 0.7493 0.122 0.7852 0.112 0.8227 0.095 0.8621 0.072 0.053 0.8917 0.9250 0.034 0.9563 0.018
39.593 39.626 39.651 39.656 39.657 39.653 39.643 39.633 39.630 39.627 39.628 39.637 39.658 39.700 39.728 39.753 39.781 39.810 39.832 39.854 39.873
75.131 75.120 75.103 75.093 75.078 75.059 75.028 74.983 74.965 74.936 74.872 74.818 74.754 74.681 74.653 74.636 74.627 74.631 74.643 74.670 74.708
39.554 39.557 39.550 39.545 39.539 39.538 39.546 39.570 39.582 39.603 39.654 39.700 39.756 39.819 39.846 39.864 39.878 39.888 39.892 39.894 39.894
75.150 75.153 75.150 75.142 75.125 75.100 75.057 74.998 74.977 74.946 74.894 74.865 74.852 74.868 74.887 74.907 74.926 74.938 74.937 74.920 74.884
0.339 0.336 0.343 0.348 0.354 0.355 0.347 0.323 0.311 0.290 0.239 0.193 0.137 0.074 0.047 0.029 0.015 0.005 0.001 0.001 0.001
0.003 0.007 0.003 0.004 0.022 0.047 0.090 0.148 0.169 0.200 0.253 0.281 0.295 0.279 0.259 0.240 0.221 0.209 0.210 0.226 0.263
Formamide (1) + 2-propanol (2) 0.0455 0.019 0.1021 0.043 0.1327 0.060 0.1725 0.079 0.2155 0.102 0.2692 0.136 0.3269 0.172 0.3535 0.190 0.3867 0.213 0.4245 0.232 0.4850 0.262 0.5191 0.271 0.5729 0.289 0.6237 0.295 0.6951 0.283 0.7543 0.260 0.7907 0.233 0.8250 0.215 0.8735 0.168 0.8999 0.139 0.9331 0.102 0.9745 0.036
39.519 39.479 39.458 39.433 39.408 39.381 39.361 39.355 39.350 39.348 39.357 39.367 39.391 39.424 39.484 39.547 39.590 39.635 39.702 39.740 39.790 39.853
76.915 76.886 76.866 76.837 76.800 76.744 76.674 76.638 76.590 76.531 76.428 76.365 76.260 76.155 76.001 75.870 75.790 75.715 75.611 75.556 75.489 75.411
38.462 38.612 38.688 38.781 38.877 38.991 39.109 39.162 39.226 39.298 39.407 39.466 39.553 39.629 39.721 39.784 39.815 39.840 39.866 39.877 39.886 39.892
76.929 76.912 76.896 76.868 76.830 76.773 76.701 76.665 76.620 76.569 76.491 76.451 76.398 76.361 76.336 76.342 76.359 76.382 76.428 76.458 76.500 76.556
1.431 1.281 1.205 1.112 1.016 0.902 0.784 0.731 0.667 0.595 0.486 0.427 0.340 0.264 0.172 0.109 0.078 0.053 0.027 0.016 0.007 0.001
0.004 0.021 0.037 0.065 0.103 0.160 0.232 0.267 0.312 0.364 0.442 0.481 0.535 0.572 0.597 0.591 0.574 0.551 0.505 0.475 0.433 0.377
Formamide (1) + 1-butanol (2) 0.0499 0.016 0.0862 0.030 0.1629 0.016 0.2111 0.002 0.2571 0.020 0.2983 0.037 0.3254 0.050 0.3629 0.061 0.4092 0.079 0.4363 0.089 0.4675 0.098 0.5166 0.108 0.5799 0.109 0.6482 0.110 0.7025 0.103 0.7446 0.093 0.7699 0.088 0.8183 0.073 0.8544 0.060 0.8873 0.047 0.9218 0.033 0.9654 0.015
40.315 40.192 39.985 39.889 39.818 39.770 39.745 39.718 39.697 39.690 39.686 39.687 39.700 39.723 39.747 39.767 39.780 39.805 39.823 39.840 39.856 39.877
92.000 92.006 91.995 91.976 91.951 91.925 91.906 91.878 91.842 91.820 91.796 91.757 91.711 91.665 91.633 91.611 91.600 91.579 91.567 91.556 91.547 91.536
39.487 39.517 39.571 39.600 39.622 39.639 39.649 39.661 39.675 39.682 39.690 39.704 39.723 39.748 39.771 39.792 39.805 39.830 39.848 39.863 39.877 39.890
91.977 91.975 91.968 91.959 91.945 91.929 91.915 91.893 91.861 91.839 91.813 91.768 91.711 91.660 91.641 91.647 91.662 91.725 91.807 91.914 92.066 92.328
0.406 0.376 0.322 0.293 0.271 0.254 0.244 0.232 0.218 0.211 0.203 0.189 0.170 0.145 0.122 0.101 0.088 0.063 0.045 0.030 0.016 0.003
0.001 0.002 0.009 0.019 0.032 0.049 0.062 0.084 0.117 0.138 0.165 0.209 0.266 0.317 0.337 0.331 0.315 0.252 0.170 0.063 0.089 0.350
Formamide (1) + 2-methyl-1-propanol 0.0408 0.003 0.1027 0.010 0.1751 0.029 0.2364 0.045
(2) 39.841 39.793 39.739 39.698
92.927 92.917 92.896 92.868
38.640 38.796 38.967 39.102
92.924 92.901 92.856 92.807
1.253 1.097 0.926 0.791
0.005 0.028 0.073 0.122
x1
1
E Vm ðcm3 mol
Þ
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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Table 2 (Continued ) Vf1 (cm3 mol1)
Vf2 (cm3 mol1)
1 V¯ 1 ðcm3 mol Þ
1 V¯ 2 ðcm3 mol Þ
E 1 V¯ 1 ðcm3 mol Þ
E 1 V¯ 2 ðcm3 mol Þ
0.065 0.082 0.100 0.117 0.132 0.150 0.159 0.170 0.185 0.186 0.174 0.165 0.146 0.135 0.115 0.085 0.068 0.031
39.668 39.644 39.626 39.610 39.602 39.595 39.593 39.593 39.603 39.636 39.659 39.687 39.717 39.740 39.764 39.804 39.825 39.859
92.838 92.803 92.767 92.722 92.686 92.635 92.599 92.543 92.428 92.260 92.174 92.080 91.994 91.930 91.867 91.769 91.718 91.641
39.206 39.298 39.374 39.450 39.501 39.563 39.600 39.648 39.727 39.803 39.829 39.851 39.866 39.875 39.881 39.888 39.890 39.892
92.763 92.721 92.686 92.651 92.629 92.605 92.592 92.579 92.571 92.596 92.620 92.654 92.690 92.719 92.750 92.800 92.827 92.869
0.687 0.595 0.519 0.443 0.392 0.330 0.293 0.245 0.166 0.090 0.064 0.042 0.027 0.018 0.012 0.005 0.003 0.001
0.166 0.207 0.243 0.278 0.300 0.324 0.337 0.350 0.358 0.333 0.309 0.275 0.239 0.210 0.179 0.128 0.102 0.059
Formamide (1) + 2-methyl-2-propanol 0.0593 0.009 0.1129 0.020 0.1521 0.035 0.1926 0.059 0.2202 0.073 0.2615 0.100 0.2983 0.123 0.3299 0.145 0.3673 0.170 0.4055 0.200 0.4501 0.220 0.4849 0.235 0.5285 0.248 0.5658 0.260 0.6385 0.265 0.7081 0.250 0.7446 0.231 0.779 0.215 0.8183 0.183 0.8586 0.155 0.8917 0.118 0.9516 0.057
(2) 39.813 39.714 39.650 39.591 39.555 39.509 39.475 39.451 39.429 39.415 39.407 39.409 39.418 39.433 39.479 39.541 39.580 39.619 39.666 39.717 39.759 39.835
94.923 94.905 94.885 94.856 94.833 94.792 94.750 94.710 94.659 94.602 94.531 94.472 94.396 94.329 94.197 94.075 94.015 93.962 93.906 93.857 93.824 93.782
38.857 38.947 39.005 39.060 39.096 39.149 39.195 39.235 39.283 39.332 39.391 39.437 39.496 39.545 39.638 39.720 39.758 39.791 39.823 39.850 39.868 39.888
94.926 94.916 94.901 94.877 94.856 94.817 94.776 94.736 94.685 94.630 94.564 94.514 94.455 94.411 94.351 94.336 94.350 94.379 94.431 94.508 94.589 94.778
1.036 0.946 0.888 0.833 0.797 0.744 0.698 0.658 0.610 0.561 0.502 0.456 0.397 0.348 0.255 0.173 0.135 0.102 0.070 0.043 0.025 0.005
0.002 0.012 0.027 0.051 0.072 0.111 0.152 0.192 0.243 0.298 0.364 0.414 0.473 0.517 0.578 0.592 0.578 0.550 0.497 0.421 0.339 0.150
x1
E Vm ðcm3 mol
0.2873 0.3353 0.3772 0.4225 0.4548 0.4967 0.5238 0.5622 0.6334 0.7224 0.7631 0.805 0.8412 0.8669 0.8917 0.9285 0.9469 0.9745
1
Þ
Table 3 Adjustable parameters of Eq. (2) and standard deviation (sm). System Formamide Formamide Formamide Formamide Formamide
(1) + 1-propanol (2) (1) + 2-propanol (2) (1) + 1-butanol (2) (1) + 2-methyl-1-propanol (2) (1) + 2-methyl-2-propanol (2)
E
@V¯m @x1
E o V¯ 2 ¼ V¯ m þ V¯2 x1
A0
A1
A2
A3
sm
0.5312 1.0650 0.4145 0.5966 0.9645
0.4551 0.7735 0.3608 0.7067 0.7774
0.1704 0.1107 0.5013 0.0938 0.4063
0.4551 0.1616 0.1754 0.0351 0.1778
0.0021 0.0027 0.0019 0.0021 0.0025
! (5) p;T
Differentiation of Eq. (2) with respect to x1 and combination of the results of Eqs. (4) and (5) leads to the following equation for the partial molar volumes of formamide (V¯1 ) and alkanols (V¯ 2 ) V¯ 1 ¼ V1o þ ð1 x1 Þ2
n X A j ð1 2x1 Þ j j¼0
n X þ 2x1 ð1 x1 Þ A j ð jÞð1 2x1 Þ j1 2
(6)
j¼0
V¯ 2 ¼ V2o þ x21
n X A j ð1 2x1 Þ j þ 2x21 ð1
j¼0
1 V¯ 1 ¼ V1o þ
1 V¯ 2 ¼ V2o þ
j¼0 n X x1 Þ A j ð jÞð1 2x1 Þ j1
The calculated results for partial molar volume and excess partial molar volumes are plotted in Figs. 2–5. Much of our present interest is focused on the partial molar volume at infinite dilution. The partial properties at infinite dilution are of interest since, at the limit of infinite dilution, the solute–solute interactions disappear. The values of partial molar volume at infinite dilution provide information about solute solvent interaction, independent of the composition effect. Therefore, we get from Eq. (6), by setting x2 = 1 and x1 = 0 n X Aj
j¼0 n X
A j ð1Þ j
(8) (9)
j¼0
(7)
Eqs. (8) and (9) represent the partial molar volume of formamide 1 1 V¯ 1 and alkanols V¯ 2 at infinite dilution, respectively. These
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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39.8
39.4 39.2 39.0 1-propanol
38.8
2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
38.6 38.4 38.2 0.0
0.2
0.4
0.6
0.8
-1
39.6
0.0
3
Excess partial molar volume, (cm mol )
Partial molar volume, (cm 3 .mol -1 )
0.2
-0.2 -0.4 -0.6 -0.8
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
-1.0 -1.2 -1.4 -1.6 0.0
1.0
0.2
0.4
0.6
0.8
1.0
x1
x1 Fig. 2. Partial molar volume of formamide (V¯ 1 ) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K.
E
Fig. 4. Excess partial molar volume of formamide (V¯ 1 ) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K. 0.8 0.6
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
Partial molar volume, (cm 3mol-1)
3
-1
Excess partial molar volume , (cm mol )
100
95
90
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
85
80
75
70
0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 0.0
0.0
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
1.0
x2
1.0
E Fig. 5. Excess partial molar volume of alkanol (V¯ 2 ) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of alkanol (x2) at 298.15 K.
x2 Fig. 3. Partial molar volume of alkanol (V¯ 2 ) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of alkanol (x2) at 298.15 K.
properties are listed in Table 4. Partial molar volumes were calculated using Redlich–Kister equation and its derivatives do not always provide best representation of properties of either component at infinite dilution in the other component. Instead of using the Redlich–Kister equation, we have also considered another approach, which may be more convenient and accurate, by calculating the partial molar volume at infinite dilution through apparent volumes of formamide in alkanol Vf1 and the apparent molar volume of alkanol in formamide Vf2 can be expressed as V m x2 V2o V f1 ¼ x1
(10)
V f2 ¼
V m x1 V1o x2
(11)
Combination of Eqs. (1), (10) and (11) leads to V f1 ¼ V1o þ
E Vm x1
(12)
V f2 ¼ V2o þ
E Vm x2
(13)
Simple graphic or analytical extrapolation of Vf1 to x1 = 0 1 (x2 = 1) leads to desired value of V 1 and a simple extrapolation of
Table 4 Partial molar volumes and excess partial molar volumes at infinite dilution at 298.15 K. System Formamide Formamide Formamide Formamide Formamide
(1) + 1-propanol (2) (1) + 2-propanol (2) (1) + 1-butanol (2) (1) + 2-methyl-1-propanol (2) (1) + 2-methyl-2-propanol (2)
V1o
V2o
1 V¯ 1 , Eq. (8)
1 V¯ 2 , Eq. (9)
E1 V¯ 1 , Eq. (4)
E1 V¯ 2 , Eq. (5)
39.8930 39.8930 39.8930 39.8930 39.8930
75.1466 76.9329 91.97741 92.92878 94.9282
39.5322 38.3268 39.4436 38.5308 38.7352
74.7858 76.5905 92.6004 92.90998 94.9697
0.3608 1.5662 0.449 1.3622 1.15878
0.3608 0.3424 0.623 0.0188 0.0414
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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Apparent molar volume, (cm mol )
40.0
-1
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
40.2
39.8
39.6
39.4
39.2 0.0
0.2
0.4
0.6
0.8
95
3
Apparent molar volume, (cm 3mol -1 )
100
90
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
85
80
75
70 0.0
1.0
0.2
0.4
x1
1
1 Vf2 to x2 = 0 (x1 = 1) leads to the desired value of V 2 . The V¯ i results are shown in Figs. 6 and 7.
4. Discussion E Vm values for formamide + 1-propanol or 2-propanol or 2methyl-1-propanol or 2-methyl-2-propanol systems are negative over the whole composition range, except for formamide + 1butanol where these are positive for <0.17 and then change sign. E At equimolar composition, Vm values follow the sequence: 1butanol > 1-propanol > 2-methyl-1-propanol > 2-methyl-2-propanol > 2-propanol. At the simplest qualitative level, VE values may be attributed to the resultant of two opposing effects. The E positive contribution to Vm values arises from the breaking selfassociated formamide and alkanol and negative contribution arises due to the presence of intermolecular H-bonding between alkanol and formamide. In spite of this qualitative description of the E present Vm data, the degree of association of formamide and influence of alkanol on it remains to be investigated. For this E purpose we analyzed the present Vm data in terms of an approach [12,13,19], that employs [20] the graph theoretical concept of molecular connectivity parameter of the third degree, 3j, of the constituents of these mixtures.
4.1. Conceptual aspects of graph theoretical approach and results According to mathematical discipline of graph theory [21], if the atoms in a structural formula of a molecule are represented by vertices and bonds joining them by edges, then the resulting graph describes the totality of information contained in that v v molecule [20,22–24]. Consequently, if dm , dn , etc. represents the degrees of mth and nth vertices of the graph of a molecule, then connectivity parameters of third degree, 3 ji , is defined [11] by Eq. (14): 3
ji ¼
X
v
v v v 0:5
ðdm dn do d p Þ
(14)
m
where dm , etc. reflects explicitly the valency of mth vertex in molecular graph of i (i = 1 or 2) and is related [24] to maximum valency, Zm, and number of H-atoms, hm, attached to mth, etc. vertex by the relation:
dvm ¼ Z m hm
(15)
1.0
Further Kier [20] has suggested that the information regarding effect of branching in the molecules can be obtained by evaluation of 3 ji of molecules. E Since Vm of an (1 + 2) mixture reflects interactional effects on 1 the packing of molecules and as ð3 ji Þ of i determines [12] the effectiveness with which the molecular surface of i interacts with that of another i molecule, the interactional part of the molar 1 volume of pure i has been taken to ð3 ji Þ . The ideal interactional molar volume of an (1 + 2) mixture would then be proportional to P 3 1 xi ð ji Þ , where xi and ð3 ji Þ denote mole fraction and connectivity parameter of third degree respectively of i. The interactional molar volume of a (1 + 2) mixture should also be proportional to 1/(3j)m of the mixture. If (3j)m of the real mixture in P the molecular graph is expressed by fxi ð3 ji Þm g (where ð3 ji Þm 3 denotes j of i in the mixture) and if the proportionality constant a12 is assume to be the same for the mixture and its pure E components then, Vm may be expressed by [12]. E Vm
3
ðcm
1
mol
" # 2 2 X X xi 1 3 Þ ¼ a12 fxi ð ji Þm g 3 i¼1
i¼1
(16)
ji
where a12 is the constant characteristic of the (1 + 2) mixture and E can be evaluated using equimolar experimental Vm value. 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 0.0
v
0.8
Fig. 7. Apparent molar volume of alkanol (Vf2) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of alkanol (x2) at 298.15 K.
Excess molar volume, (cm3 mol-1 )
Fig. 6. Apparent molar volume of formamide (Vf1) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K.
0.6
x2
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol 0.2
0.4
0.6
0.8
1.0
x1 E Fig. 8. Molar excess volume (Vm ) of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K; symbol represent values calculated from Eq. (2) and solid lines represent values calculated from graph theory: 1-propanol; 2-propanol; 1-butanol; 2-methyl-1propanol; 2-methyl-2-propanol.
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As the degree of association of 1 and 2 is not known in the mixture and pure state, we regarded ð3 ji Þ and ð3 ji Þm (i = 1 or 2) as adjustable E parameters and evaluated them by employing Vm data to Eq. (16). Only those values of ð3 ji Þ and ð3 ji Þm were retained that best reproduced the VE data. Various ð3 ji Þ or ð3 ji Þm (i = 1 or 2) parameters E along with a12 are recorded in Table 5 along with Vm values obtained
from Eq. (16) for the various binary mixtures as a function of x1 and are also compared with the values calculated from Eq. (2). E Examination of Table 5 and Fig. 8 reveals that Vm values agree well with their corresponding experimental values and thus ð3 ji Þ or ð3 ji Þm (i = 1 or 2) values can be relied upon to extract information about the state of pure components as well as their mixture.
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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Table 5 Comparison of smoothened VE values from Eq. (2) with their corresponding values calculated from graph theory (Eq. (14)) along with the various ð3 ji Þ and ð3 ji Þm (i = 1 or 2) values and a12. VE (cm3 mol1)
Mole fraction of formamide (x1) 0.1
0.2
0.3
0.4
0.6
0.7
0.8
0.9
Formamide (1) + 1-propanol (2)a Eq. (2) 0.026 0.004 Eq. (14)
0.047 0.051
0.074 0.089
0.105 0.116
0.147 0.137
0.138 0.127
0.103 0.102
0.050 0.061
Formamide (1) + 2-propanol (2)b Eq. (2) 0.041 Eq. (14) 0.016
0.095 0.108
0.157 0.181
0.218 0.235
0.291 0.274
0.283 0.254
0.233 0.204
0.138 0.121
Formamide (1) + 1-butanol (2)c Eq. (2) 0.026 Eq. (14) 0.030
0.003 0.015
0.038 0.053
0.077 0.083
0.112 0.114
0.103 0.112
0.078 0.094
0.042 0.058
Formamide (1) + 2-methyl-1-propanol (2)d Eq. (2) 0.010 Eq. (14) 0.003
0.034 0.053
0.070 0.096
0.110 0.128
0.178 0.157
0.187 0.149
0.167 0.123
0.108 0.075
Formamide (1) + 2-methyl-2-propanol (2)e Eq. (2) 0.016 Eq. (14) 0.014
0.062 0.093
0.126 0.158
0.191 0.209
0.265 0.253
0.252 0.240
0.199 0.198
0.111 0.121
a b c d e
(3j1) = (3j1)m = 1; (3j2) = 1.41, (3j2)m = 1.395; a12 = 6.7974. (3j1) = (3j1)m = 1; (3j2) = 1.43; (3j2)m = 1.415; a12 = 12.388. (3j1) = (3j1)m = 0.8; (3j2) = 1.485, (3j2)m = 1.4; a12 = 1.9697. (3j1) = (3j1)m = 0.8; (3j2) = 1.4; (3j2)m = 1.36; a12 = 2.6531. (3j1) = (3j1)m = 0.8; (3j2) = 1.44; (3j2)m = 1.4; a12 = 3.8194.
A number of structures (I–XIII) were then assumed for 1 and 2 0 and their ð3 ji Þ values were calculated from structural considerations of Eq. (14). These values were then compared with corresponding values, ð3 ji Þ obtained from Eq. (16). Any structure 0 or combination of structures that yielded ð3 ji Þ values which 3 compared well with the corresponding ð ji Þ obtained from Eq. (16) were considered as representative structure of that component. For this purpose we assumed 1-propanol, 2-propanol, 1butanol, 2-methyl-1-propanol, 2-methyl-2-propanol and formamide to exist in various configurations (I–XIII) (ranging from monomers to di-mers (for alkanols), di-mers and r-mers (both 0 cyclic as well as open for formamide and then calculated ð3 ji Þ values (from Eq. (14)) in the manner explained elsewhere for these 0 configurations. These ð3 ji Þ values when compared with the 3 corresponding ji values of pure components (obtained from an E analysis of the Vm data of the appropriate mixture in terms of Eq. (16)) then suggested that while 1-propanol (3j = 1.41) exists as II (3j0 = 1.314), 2-propanol (3j = 1.43) exists as IV (3j0 = 1.5856). The present treatment further suggests that while 1-butanol (3j = 1.485) exists as an equilibrium mixture of V (3j0 = 0.7020) and dimer VI (3j0 = 1.8994), 2-methyl-1-propanol (3j = 1.4) exists as VIII (3j0 = 1.1435) and 2-methyl-2-propanol (3j0 = 1.440) exists as an equilibrium mixture of IX (3j0 = 0.6123) and X (3j0 = 1.946). Again the 3j value 1.0 of formamide in propanol isomers mixtures compare well with the 3j0 value of 0.94 calculated for it from
Eq. (14) for the configuration XII. 3j Value of 0.8 for formamide in butanol isomers mixtures compare well with the 3j0 value of 0.856 calculated for it from Eq. (14) for the configuration XIII. This suggests that the present approach can be relied upon to yield meaningful information about the state of aggregation of the component of binary mixtures. Again as alkanol can undergo specific interactions with formamide in these mixtures to yield molecular entities, and as ð3 ji Þm depends on the valences of the vertices in the molecular graph of the molecular entities, it would be instructive to see if the present approach could be utilized to know the vertices in the molecular graph of formamide and alkanol that get influenced in these mixture formation. Formamide + 1-propanol mixture (with ð3 j2 Þm ¼ 1:395) should contain an equilibrium mixture of XIV (3j0 = 0.6695) or XVI 0 (3j0 = 1.8453), formamide + 2-propanol ð3 j2 Þm ¼ 1:415 should con0 tain XVIII. Formamide + 1-butanol ð3 jB Þm ¼ 1:4Þ mixture should contain XXI (3j0 = 1.4619) or should contain an equilibrium mixture of XX (3j0 = 0.9633) and XXII (3j0 = 1.9808), formamide + 2-methyl0 1-propanol ðð3 j2 Þm ¼ 1:36Þ should contain equilibrium mixture of 3 0 XXIV ( j = 0.7681) and XXVI (3j0 = 1.8337) and formamide + 20 methyl-2-propanol ðð3 j2 Þm ¼ 1:4Þ should contain equilibrium 3 0 mixture of XXVII ( j = 0.7693) and XXIX (3j0 = 1.8252). This suggests that the present approach can be relied upon to yield meaningful information about the state of aggregation of the component of binary mixtures.
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M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
If interpretation of excess volume data in terms of graph theoretical approach is correct then it should also be reflected in the infrared spectra of these binary mixtures and should influence the characteristics vibrations of formamide and alkanol in these binaries. For this purpose we compared the infrared spectral data of the pure formamide and alkanol (1propanol, 1-butanol and 2 propanol) with their equimolar binary mixtures and observed that in formamide + 1-propanol mixture, the absorption band at 3307 cm1 (asym. NH2 stretch), 3197 cm1 (sym. NH2 stretch), 1664 cm1 (C5 5O) got shifted to 3329, 3190, 1686 cm1, respectively. In case of formamide + 1butanol, these absorption bands of pure formamide got influenced and shifted in the mixture to 3320, 3190 and 1677 cm1. For formamide + 2-propanol mixture, the infrared spectral data reveal the shifting of absorption bands of formamide (asym. NH2 stretch, sym. NH2 stretch and C5 5O) to 3360, 3190 and 1692 cm1 in the mixture. The OH absorption band for 1-propanol, 1-butanol and 2-propanol exists at 3332, 3316 and 3329 cm1. Thus the addition of alkanol to formamide not only influences the hydrogen atom of the NH2 group of formamide, but also affects the carbonyl group of formamide as well as the hydroxyl group of alcohols. In mixtures OH band of alkanol were merged with the NH2 bands of formamide so it is hard to know the position of OH bands in these mixtures. However, the maximum shifting was observed in the mixture of formamide + 2-propanol and minimum in 1-butanol. This may be due to the presence of two electron donating –CH3 groups (in 2-propanol) at C-atom attached to hydroxyl oxygen that interact with H-atom of –NH2 group of formamide. Thus the infrared spectral data of formamide (1), 1-propanol, 1-butanol and 2propanol (2) and their binary (1 + 2) mixtures evidently point to the presence of (XIV, XVI), (XXI, XX, XXII) and XVIII in the mixtures containing 1-propanol, 1-butanol and 2-propanol, respectively. This lends further credence to the graph theoretical arguments. Acknowledgements Authors thank Mr H. S. Chahal, Vice Chancellor, Deenbandhu Chhotu Ram University of Science & Technology, Murthal, India for moral support. One of them (Manju Rani) thanks University Grant Commission, New Delhi, India for the award of Teacher fellowship under Faculty Improvement Program.
References [1] M. Gupta, I. Vibhu, J.P. Shukla, Fluid Phase Equilibria 244 (1) (2006) 26. [2] R.J. Sengwa, V. Khatri, S. Sankhla, Fluid Phase Equilibria 266 (1–2) (2008) 54. [3] Y. Marcus, Introduction to Liquid State Chemistry, Wiley Interscience, New York, 1977. [4] N. Anil Kumar, Fluid Phase Equilibria 265 (1–2) (2008) 46. [5] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, New York, 1960. [6] E.M. Woolley, et al. The Journal of Physical Chemistry 75 (23) (1971) 3591. [7] J.R. Johnson, S.D. Christian, H.E. Affsprung, Journal of the Chemical Society A: Inorganic, Physical, Theoretical (1967) 764. [8] M. Davies, in: H.W.T.E.D. Hadzi (Ed.), Hydrogen Bonding, Pergamon Press, New York, 1952. [9] L.G. Hepler, D.V. Fenby, The Journal of Chemical Thermodynamics 5 (4) (1973) 471. [10] D.V. Fenby, L.G. Hepler, The Journal of Chemical Thermodynamics 6 (2) (1974) 185. [11] P.P. Singh, Thermochimica Acta 66 (1–3) (1993) 37. [12] S. Kumar, et al. Journal of Molecular Liquids 155 (2–3) (2010) 115. [13] A. Maken, S. Maken, Journal of Industrial and Engineering Chemistry 18 (3) (2012) 1013. [14] O. Redlich, A.T. Kister, Industrial and Engineering Chemistry 40 (2) (1948) 345. [15] A.I. Vogel, A Text Book of Practical Organic Chemistry, 4th ed., ELBS Longman, London, 1978. [16] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents. Physical Properties and Methods of Purification, vol. 1, Wiley, New York, 1986. [17] A. Weissenberger, Physical Methods of Organic Chemistry, vol. 1, Interscience, New York, 1959. [18] S. Maken, et al. Journal of Industrial and Engineering Chemistry 13 (7) (2007) 1098. [19] S. Maken, et al. Fluid Phase Equilibria 235 (1) (2005) 42. [20] L.B. Kier, in: S.H. Yalkowaski, S.C. Valvani (Eds.), Physical Chemical Properties of Drugs, Marcel Dekker Inc., New York, Bessel, 1980. [21] F. Harary, Graph Theory, Addison Wesley, Reading, MA, 1969. [22] A.T. Balaban (Ed.), Chemical Applications of Graph Theory, Academic Press, London, 1976. [23] D.H. Rouvray, Reviews 4 (2) (1971) 173. [24] L.B. Kier, L.H. Hall, Molecular Connectivity in Chemistry and Drug Research, Academic Press, New York, 1976. [25] D. Papamatthaiakis, F. Aroni, V. Havredaki, The Journal of Chemical Thermodynamics 40 (1) (2008) 107. [26] A.M. Cases, et al. Journal of Chemical and Engineering Data 46 (3) (2001) 712. [27] N. Anil Kumar, The Journal of Chemical Thermodynamics 39 (3) (2007) 462. [28] N. Anil Kumar, Journal of Molecular Liquids 140 (1–3) (2008) 108. [29] I.-C. Hwang, et al. Journal of Industrial and Engineering Chemistry 18 (1) (2012) 499. [30] S.-J. Park, K.-J. Han, J. Gmehling, Fluid Phase Equilibria 200 (2) (2002) 399. [31] N. Anil Kumar, Fluid Phase Equilibria 259 (2) (2007) 218. [32] H. Iloukhani, B. Samiey, M.A Moghaddasi, The Journal of Chemical Thermodynamics 38 (2) (2006) 190. [33] A.K. Nain, et al. Journal of Molecular Liquids 144 (3) (2009) 138. [34] T.E. Vittal Prasad, et al. Fluid Phase Equilibria 249 (1–2) (2006) 49. [35] G.P. Dubey, M. Sharma, S. Oswal, The Journal of Chemical Thermodynamics 41 (7) (2009) 849.
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Topological studies of molecular interactions of formamide with propanol and butanol at 298.15 K Manju Rani a, Sanjeev Maken b,* a b
Department of Chemical Engineering, Deenbandhu Chhotu Ram University of Science and Technology, Murthal 131 039, India Department of Chemistry, Deenbandhu Chhotu Ram University of Science and Technology, Murthal 131 039, India
A R T I C L E I N F O
Article history: Received 15 January 2012 Accepted 7 March 2012 Available online 28 March 2012 Keywords: Molar excess volume Partial molar volume Formamide Alkanol Graph theoretical approach
A B S T R A C T
Molar excess volumes have been measured at 298.15 K for formamide + 1-propanol, 2-propanol, 1butanol, 2-methyl-1-propanol or 2-methyl-2-propanol mixtures. For an equimolar mixture, molar excess volumes follow the sequence: 1-butanol > 1-propanol > 2-methyl-1-propanol > 2-methyl-2E ) values have been fitted to Redlich–Kister propanol > 2-propanol. The excess molar volume (Vm polynomial equation and other volumetric properties like apparent molar volume, partial molar volume, excess partial molar volume were calculated. The excess volume data have also been rationalized by E calculated by this approach agree well with graph-theoretical arguments. It has been observed that Vm the corresponding experimental values. This analysis has further yielded information about the state of aggregation of pure components that is consistent with the existing views on their nature of association. The infrared spectral studies lend further credence to the graph theoretical arguments. ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
1. Introduction The thermo-physical properties of mixtures would be of great importance in processing engineering designs and also helpful in getting information about molecular structure and intermolecular forces in liquid mixture, which can be very helpful in making the choice of solvent in various applications. Alcohols are self associated organic compound through hydrogen bonding of their hydroxyl groups. These are biologically and industrially important amphiphilic materials. Branching of alkyl group attached to the hydroxyl group results in abnormal behaviour of alcohols [1]. Amides are known as an important class of bio-organic solvents and are convenient model systems for investigating peptide and protein–solvent interactions. The H-bond formation ability of these solvents with other H-bonded self-associating solvents is useful in understanding the peptide linkage in complex biosystems [2]. Formamide is selected for this study, as it is the simplest amide that contains a peptide linkage, the fundamental building block of proteins. Formamide molecules are highly polar [3] and are strongly self-associated through extensive threedimensional network of hydrogen bonds, through its three hydrogen bond donors (3 H-atoms) and three acceptors (two lone pairs of electrons at oxygen and one on nitrogen atom). Since the components of these binary mixtures have both proton-donating/ accepting abilities, significant interaction through hydrogen
bonding between unlike molecules is expected [4]. Further in view of the two well known resonance structures [5] of the amide group, the lower amides in pure state may exist like alkanols [6,7], dimers and higher r-mers, though Davies [8] favors dimeric state for them in solution. Although such a situation can be handled by the ideal association model approach [9,10] yet the result would be strongly dependent on the particular type of model assumed for formamide and alkanols. This calls for an entirely different approach. Since binary mixture is formed by the replacement of like contacts in the pure state by unlike contact in the mixture and as the formations of molecular entities in the present mixtures may be visualized [11] due to the changes in the topology of formamide brought on by alkanol, it appears that a recent graph theoretical approach [12,13] should provide valuable information about the state of formamide and alkanol in an binary mixture. This prompted us to perform molar excess volume studies at 298.15 K on formamide + 1-propanol, 2-propanol, 1-butanol, 2methyl-1-propanol or 2-methyl-2-propanol mixtures. The Redlich–Kister equation was used to correlate the experimental data and to obtain the partial molar volumes at 298.15 K and at atmospheric pressure [14]. The excess volume data have also been rationalized by graph-theoretical arguments. It has been observed E that Vm calculated by this approach agree well with the corresponding experimental values. 2. Experimental
* Corresponding author. E-mail address: [email protected] (S. Maken).
Formamide, 1-propanol, 2-propanol, 1-butanol, 2-methyl-1propanol or 2-methyl-2-propanol mixtures (Merck or Sigma) were
1226-086X/$ – see front matter ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2012.03.011
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704 0.05
Molar excess volume, (cm3mol-1)
purified by standard procedures [15,16]. The purities of the purified samples were checked by measuring their densities and refractive indices at 298.15 K. The densities were measured with a precision of 5 105 g cm3 by a specially designed densimeter, consisting of a bulb of approximate volume 35 cm3 attached to a calibrated capillary through a B-10 standard joint in the manner described by Weissenberger [17]. Air buoyancy correction was also applied to achieve a greater accuracy. Refractive indices were measured with a thermostatically controlled Abbe refractometer (OSAW, India) using sodium D-line with an accuracy of 0.0001. Our experimental values for the density, and refractive index of the pure compounds compared well with the literature values as shown in E Table 1. Molar excess volumes, Vm , for the binary mixtures have been measured by V-shaped dilatometer at 298.15 K in the manner described elsewhere [18]. The temperature of water thermostat was controlled to 0.01 K by a mercury-in-toluene regulator. The change in the position of the liquid level in the capillary was noted with a cathetometer (OSAW, Ambala) that could read to 0.001 cm. The performance of dilatometer was checked by measuring the molar excess volume of the benzene + cyclohexane mixture at 298.15 K and these agreed to within the experimental limits with corresponding E literature. The uncertainty in the measured Vm values was 1%.
1695
0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 0.0
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol 0.2
0.4
0.6
0.8
1.0
x1 E Fig. 1. Molar excess volume (Vm ) of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K; symbols represent experimental value and lines represent value calculated from Eq. (2).
E ðs ðVm ÞÞ.
3. Results The excess molar volume is defined by E Vm ¼ V m x1 V1o x2 V2o
s ðVmE Þ ðcm3 mol1 Þ ¼ (1)
where Vm represents the volume of a mixture containing one mole of (formamide + alkanol), x1 and x2 are the mole fraction of formamide and alkanol, respectively and V1o and V2o are the molar volume of pure components. E The measured Vm data at 298.15 K are recorded in Table 2 and are fitted to the following Redlick and Kister equation
E Vm
3
ðcm
1
mol
2 3 n X j Þ ¼ x1 ð1 x1 Þ4 A j ð2x1 1Þ 5
(2)
j¼0
where Aj are the adjustable parameters, and x1 is the mole fraction of formamide in formamide + alkanol mixture. These parameters E were evaluated by fitting Vm data to Eq. (2) by the least squares E method and recorded in Table 3 with the standard deviations of Vm ,
8" 2 #91=2 P > > > > E E > > Vexpt: V > > = < cal:ð Eq: ð2ÞÞ > > > > :
mn
> > > > ;
(3)
where m is the number of experimental values, and n is the number of adjustable parameters in Eq. (2). The choice of n to have 0–3 values was dictated by the consideration that the maximum E deviation sm(VE) of Vm (as calculated from Eq. (2) from the E corresponding experimental Vm values satisfied the relation s ðVmE Þ 2s ðVmE Þ. E Comparison of Vm experimental for the studied system together with smoothing curves using Eq. (2) is shown in Fig. 1. E We have also calculated the excess partial molar volumes, V¯ 1 ¼ o E o E ðV¯ 1 V¯ 1 Þ and V¯ 2 ¼ ðV¯ 2 V¯ 2 Þ, from Vm . The excess molar volumes, E E V¯ 1 and V¯ 2 , were evaluated using following equations: E o V¯ 1 ¼ V¯ m þ V¯ 1 þ ð1 x1 Þ
E
@V¯m @x1
! (4) p;T
Table 1 Measured densities (r) and refractive indices (nD) of the pure components at 298.15 K. Compound
Temperature (K)
r (kg m3)
nD
This work
Literature
This work
Literature
1129.01 [25] 1129.1 [26] 799.75 [27] 799.79 [29] 799.48 [30] 781.28 [29] 781.01 [30] 781.06 [32] 805.565 [33] 805.98 [29] 805.83 [30] 797.37 [33] 797.8 [34] 798.52 [35] 780.59 [33] 781.2 [34]
1.4461
1.44597 [26]
1.914
1.915 [28]
2.0650
2.0652 [31]
1.3972
1.39741 [16]
1.3937
1.3939 [34]
1.3854
1.3852 [34]
Formamide
298.15
1129.02
1-Propanol
298.15
799.77
2-Propanol
298.15
781.2
1-Butanol
298.15
805.85
2-Methyl-1-propanol
298.15
797.6
2-Methyl-2-propanol
298.15
780.8
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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Table 2 Experimental excess volume, apparent molar volumes, partial molar volumes and excess partial molar volumes of binary liquid mixtures of formamide (1) + alkanol (2) at 298.15 K. Vf1 (cm3 mol1)
Vf2 (cm3 mol1)
1 V¯ 1 ðcm3 mol Þ
1 V¯ 2 ðcm3 mol Þ
E 1 V¯ 1 ðcm3 mol Þ
E 1 V¯ 2 ðcm3 mol Þ
Formamide (1) + 1-propanol (2) 0.0499 0.011 0.0921 0.024 0.1532 0.037 0.1835 0.044 0.2251 0.056 0.066 0.2663 0.3219 0.081 0.3856 0.097 0.4082 0.105 0.4420 0.118 0.5091 0.135 0.5621 0.146 0.147 0.6258 0.7068 0.135 0.7493 0.122 0.7852 0.112 0.8227 0.095 0.8621 0.072 0.053 0.8917 0.9250 0.034 0.9563 0.018
39.593 39.626 39.651 39.656 39.657 39.653 39.643 39.633 39.630 39.627 39.628 39.637 39.658 39.700 39.728 39.753 39.781 39.810 39.832 39.854 39.873
75.131 75.120 75.103 75.093 75.078 75.059 75.028 74.983 74.965 74.936 74.872 74.818 74.754 74.681 74.653 74.636 74.627 74.631 74.643 74.670 74.708
39.554 39.557 39.550 39.545 39.539 39.538 39.546 39.570 39.582 39.603 39.654 39.700 39.756 39.819 39.846 39.864 39.878 39.888 39.892 39.894 39.894
75.150 75.153 75.150 75.142 75.125 75.100 75.057 74.998 74.977 74.946 74.894 74.865 74.852 74.868 74.887 74.907 74.926 74.938 74.937 74.920 74.884
0.339 0.336 0.343 0.348 0.354 0.355 0.347 0.323 0.311 0.290 0.239 0.193 0.137 0.074 0.047 0.029 0.015 0.005 0.001 0.001 0.001
0.003 0.007 0.003 0.004 0.022 0.047 0.090 0.148 0.169 0.200 0.253 0.281 0.295 0.279 0.259 0.240 0.221 0.209 0.210 0.226 0.263
Formamide (1) + 2-propanol (2) 0.0455 0.019 0.1021 0.043 0.1327 0.060 0.1725 0.079 0.2155 0.102 0.2692 0.136 0.3269 0.172 0.3535 0.190 0.3867 0.213 0.4245 0.232 0.4850 0.262 0.5191 0.271 0.5729 0.289 0.6237 0.295 0.6951 0.283 0.7543 0.260 0.7907 0.233 0.8250 0.215 0.8735 0.168 0.8999 0.139 0.9331 0.102 0.9745 0.036
39.519 39.479 39.458 39.433 39.408 39.381 39.361 39.355 39.350 39.348 39.357 39.367 39.391 39.424 39.484 39.547 39.590 39.635 39.702 39.740 39.790 39.853
76.915 76.886 76.866 76.837 76.800 76.744 76.674 76.638 76.590 76.531 76.428 76.365 76.260 76.155 76.001 75.870 75.790 75.715 75.611 75.556 75.489 75.411
38.462 38.612 38.688 38.781 38.877 38.991 39.109 39.162 39.226 39.298 39.407 39.466 39.553 39.629 39.721 39.784 39.815 39.840 39.866 39.877 39.886 39.892
76.929 76.912 76.896 76.868 76.830 76.773 76.701 76.665 76.620 76.569 76.491 76.451 76.398 76.361 76.336 76.342 76.359 76.382 76.428 76.458 76.500 76.556
1.431 1.281 1.205 1.112 1.016 0.902 0.784 0.731 0.667 0.595 0.486 0.427 0.340 0.264 0.172 0.109 0.078 0.053 0.027 0.016 0.007 0.001
0.004 0.021 0.037 0.065 0.103 0.160 0.232 0.267 0.312 0.364 0.442 0.481 0.535 0.572 0.597 0.591 0.574 0.551 0.505 0.475 0.433 0.377
Formamide (1) + 1-butanol (2) 0.0499 0.016 0.0862 0.030 0.1629 0.016 0.2111 0.002 0.2571 0.020 0.2983 0.037 0.3254 0.050 0.3629 0.061 0.4092 0.079 0.4363 0.089 0.4675 0.098 0.5166 0.108 0.5799 0.109 0.6482 0.110 0.7025 0.103 0.7446 0.093 0.7699 0.088 0.8183 0.073 0.8544 0.060 0.8873 0.047 0.9218 0.033 0.9654 0.015
40.315 40.192 39.985 39.889 39.818 39.770 39.745 39.718 39.697 39.690 39.686 39.687 39.700 39.723 39.747 39.767 39.780 39.805 39.823 39.840 39.856 39.877
92.000 92.006 91.995 91.976 91.951 91.925 91.906 91.878 91.842 91.820 91.796 91.757 91.711 91.665 91.633 91.611 91.600 91.579 91.567 91.556 91.547 91.536
39.487 39.517 39.571 39.600 39.622 39.639 39.649 39.661 39.675 39.682 39.690 39.704 39.723 39.748 39.771 39.792 39.805 39.830 39.848 39.863 39.877 39.890
91.977 91.975 91.968 91.959 91.945 91.929 91.915 91.893 91.861 91.839 91.813 91.768 91.711 91.660 91.641 91.647 91.662 91.725 91.807 91.914 92.066 92.328
0.406 0.376 0.322 0.293 0.271 0.254 0.244 0.232 0.218 0.211 0.203 0.189 0.170 0.145 0.122 0.101 0.088 0.063 0.045 0.030 0.016 0.003
0.001 0.002 0.009 0.019 0.032 0.049 0.062 0.084 0.117 0.138 0.165 0.209 0.266 0.317 0.337 0.331 0.315 0.252 0.170 0.063 0.089 0.350
Formamide (1) + 2-methyl-1-propanol 0.0408 0.003 0.1027 0.010 0.1751 0.029 0.2364 0.045
(2) 39.841 39.793 39.739 39.698
92.927 92.917 92.896 92.868
38.640 38.796 38.967 39.102
92.924 92.901 92.856 92.807
1.253 1.097 0.926 0.791
0.005 0.028 0.073 0.122
x1
1
E Vm ðcm3 mol
Þ
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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Table 2 (Continued ) Vf1 (cm3 mol1)
Vf2 (cm3 mol1)
1 V¯ 1 ðcm3 mol Þ
1 V¯ 2 ðcm3 mol Þ
E 1 V¯ 1 ðcm3 mol Þ
E 1 V¯ 2 ðcm3 mol Þ
0.065 0.082 0.100 0.117 0.132 0.150 0.159 0.170 0.185 0.186 0.174 0.165 0.146 0.135 0.115 0.085 0.068 0.031
39.668 39.644 39.626 39.610 39.602 39.595 39.593 39.593 39.603 39.636 39.659 39.687 39.717 39.740 39.764 39.804 39.825 39.859
92.838 92.803 92.767 92.722 92.686 92.635 92.599 92.543 92.428 92.260 92.174 92.080 91.994 91.930 91.867 91.769 91.718 91.641
39.206 39.298 39.374 39.450 39.501 39.563 39.600 39.648 39.727 39.803 39.829 39.851 39.866 39.875 39.881 39.888 39.890 39.892
92.763 92.721 92.686 92.651 92.629 92.605 92.592 92.579 92.571 92.596 92.620 92.654 92.690 92.719 92.750 92.800 92.827 92.869
0.687 0.595 0.519 0.443 0.392 0.330 0.293 0.245 0.166 0.090 0.064 0.042 0.027 0.018 0.012 0.005 0.003 0.001
0.166 0.207 0.243 0.278 0.300 0.324 0.337 0.350 0.358 0.333 0.309 0.275 0.239 0.210 0.179 0.128 0.102 0.059
Formamide (1) + 2-methyl-2-propanol 0.0593 0.009 0.1129 0.020 0.1521 0.035 0.1926 0.059 0.2202 0.073 0.2615 0.100 0.2983 0.123 0.3299 0.145 0.3673 0.170 0.4055 0.200 0.4501 0.220 0.4849 0.235 0.5285 0.248 0.5658 0.260 0.6385 0.265 0.7081 0.250 0.7446 0.231 0.779 0.215 0.8183 0.183 0.8586 0.155 0.8917 0.118 0.9516 0.057
(2) 39.813 39.714 39.650 39.591 39.555 39.509 39.475 39.451 39.429 39.415 39.407 39.409 39.418 39.433 39.479 39.541 39.580 39.619 39.666 39.717 39.759 39.835
94.923 94.905 94.885 94.856 94.833 94.792 94.750 94.710 94.659 94.602 94.531 94.472 94.396 94.329 94.197 94.075 94.015 93.962 93.906 93.857 93.824 93.782
38.857 38.947 39.005 39.060 39.096 39.149 39.195 39.235 39.283 39.332 39.391 39.437 39.496 39.545 39.638 39.720 39.758 39.791 39.823 39.850 39.868 39.888
94.926 94.916 94.901 94.877 94.856 94.817 94.776 94.736 94.685 94.630 94.564 94.514 94.455 94.411 94.351 94.336 94.350 94.379 94.431 94.508 94.589 94.778
1.036 0.946 0.888 0.833 0.797 0.744 0.698 0.658 0.610 0.561 0.502 0.456 0.397 0.348 0.255 0.173 0.135 0.102 0.070 0.043 0.025 0.005
0.002 0.012 0.027 0.051 0.072 0.111 0.152 0.192 0.243 0.298 0.364 0.414 0.473 0.517 0.578 0.592 0.578 0.550 0.497 0.421 0.339 0.150
x1
E Vm ðcm3 mol
0.2873 0.3353 0.3772 0.4225 0.4548 0.4967 0.5238 0.5622 0.6334 0.7224 0.7631 0.805 0.8412 0.8669 0.8917 0.9285 0.9469 0.9745
1
Þ
Table 3 Adjustable parameters of Eq. (2) and standard deviation (sm). System Formamide Formamide Formamide Formamide Formamide
(1) + 1-propanol (2) (1) + 2-propanol (2) (1) + 1-butanol (2) (1) + 2-methyl-1-propanol (2) (1) + 2-methyl-2-propanol (2)
E
@V¯m @x1
E o V¯ 2 ¼ V¯ m þ V¯2 x1
A0
A1
A2
A3
sm
0.5312 1.0650 0.4145 0.5966 0.9645
0.4551 0.7735 0.3608 0.7067 0.7774
0.1704 0.1107 0.5013 0.0938 0.4063
0.4551 0.1616 0.1754 0.0351 0.1778
0.0021 0.0027 0.0019 0.0021 0.0025
! (5) p;T
Differentiation of Eq. (2) with respect to x1 and combination of the results of Eqs. (4) and (5) leads to the following equation for the partial molar volumes of formamide (V¯1 ) and alkanols (V¯ 2 ) V¯ 1 ¼ V1o þ ð1 x1 Þ2
n X A j ð1 2x1 Þ j j¼0
n X þ 2x1 ð1 x1 Þ A j ð jÞð1 2x1 Þ j1 2
(6)
j¼0
V¯ 2 ¼ V2o þ x21
n X A j ð1 2x1 Þ j þ 2x21 ð1
j¼0
1 V¯ 1 ¼ V1o þ
1 V¯ 2 ¼ V2o þ
j¼0 n X x1 Þ A j ð jÞð1 2x1 Þ j1
The calculated results for partial molar volume and excess partial molar volumes are plotted in Figs. 2–5. Much of our present interest is focused on the partial molar volume at infinite dilution. The partial properties at infinite dilution are of interest since, at the limit of infinite dilution, the solute–solute interactions disappear. The values of partial molar volume at infinite dilution provide information about solute solvent interaction, independent of the composition effect. Therefore, we get from Eq. (6), by setting x2 = 1 and x1 = 0 n X Aj
j¼0 n X
A j ð1Þ j
(8) (9)
j¼0
(7)
Eqs. (8) and (9) represent the partial molar volume of formamide 1 1 V¯ 1 and alkanols V¯ 2 at infinite dilution, respectively. These
M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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39.8
39.4 39.2 39.0 1-propanol
38.8
2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
38.6 38.4 38.2 0.0
0.2
0.4
0.6
0.8
-1
39.6
0.0
3
Excess partial molar volume, (cm mol )
Partial molar volume, (cm 3 .mol -1 )
0.2
-0.2 -0.4 -0.6 -0.8
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
-1.0 -1.2 -1.4 -1.6 0.0
1.0
0.2
0.4
0.6
0.8
1.0
x1
x1 Fig. 2. Partial molar volume of formamide (V¯ 1 ) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K.
E
Fig. 4. Excess partial molar volume of formamide (V¯ 1 ) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K. 0.8 0.6
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
Partial molar volume, (cm 3mol-1)
3
-1
Excess partial molar volume , (cm mol )
100
95
90
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
85
80
75
70
0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 0.0
0.0
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
1.0
x2
1.0
E Fig. 5. Excess partial molar volume of alkanol (V¯ 2 ) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of alkanol (x2) at 298.15 K.
x2 Fig. 3. Partial molar volume of alkanol (V¯ 2 ) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of alkanol (x2) at 298.15 K.
properties are listed in Table 4. Partial molar volumes were calculated using Redlich–Kister equation and its derivatives do not always provide best representation of properties of either component at infinite dilution in the other component. Instead of using the Redlich–Kister equation, we have also considered another approach, which may be more convenient and accurate, by calculating the partial molar volume at infinite dilution through apparent volumes of formamide in alkanol Vf1 and the apparent molar volume of alkanol in formamide Vf2 can be expressed as V m x2 V2o V f1 ¼ x1
(10)
V f2 ¼
V m x1 V1o x2
(11)
Combination of Eqs. (1), (10) and (11) leads to V f1 ¼ V1o þ
E Vm x1
(12)
V f2 ¼ V2o þ
E Vm x2
(13)
Simple graphic or analytical extrapolation of Vf1 to x1 = 0 1 (x2 = 1) leads to desired value of V 1 and a simple extrapolation of
Table 4 Partial molar volumes and excess partial molar volumes at infinite dilution at 298.15 K. System Formamide Formamide Formamide Formamide Formamide
(1) + 1-propanol (2) (1) + 2-propanol (2) (1) + 1-butanol (2) (1) + 2-methyl-1-propanol (2) (1) + 2-methyl-2-propanol (2)
V1o
V2o
1 V¯ 1 , Eq. (8)
1 V¯ 2 , Eq. (9)
E1 V¯ 1 , Eq. (4)
E1 V¯ 2 , Eq. (5)
39.8930 39.8930 39.8930 39.8930 39.8930
75.1466 76.9329 91.97741 92.92878 94.9282
39.5322 38.3268 39.4436 38.5308 38.7352
74.7858 76.5905 92.6004 92.90998 94.9697
0.3608 1.5662 0.449 1.3622 1.15878
0.3608 0.3424 0.623 0.0188 0.0414
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Apparent molar volume, (cm mol )
40.0
-1
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
40.2
39.8
39.6
39.4
39.2 0.0
0.2
0.4
0.6
0.8
95
3
Apparent molar volume, (cm 3mol -1 )
100
90
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol
85
80
75
70 0.0
1.0
0.2
0.4
x1
1
1 Vf2 to x2 = 0 (x1 = 1) leads to the desired value of V 2 . The V¯ i results are shown in Figs. 6 and 7.
4. Discussion E Vm values for formamide + 1-propanol or 2-propanol or 2methyl-1-propanol or 2-methyl-2-propanol systems are negative over the whole composition range, except for formamide + 1butanol where these are positive for <0.17 and then change sign. E At equimolar composition, Vm values follow the sequence: 1butanol > 1-propanol > 2-methyl-1-propanol > 2-methyl-2-propanol > 2-propanol. At the simplest qualitative level, VE values may be attributed to the resultant of two opposing effects. The E positive contribution to Vm values arises from the breaking selfassociated formamide and alkanol and negative contribution arises due to the presence of intermolecular H-bonding between alkanol and formamide. In spite of this qualitative description of the E present Vm data, the degree of association of formamide and influence of alkanol on it remains to be investigated. For this E purpose we analyzed the present Vm data in terms of an approach [12,13,19], that employs [20] the graph theoretical concept of molecular connectivity parameter of the third degree, 3j, of the constituents of these mixtures.
4.1. Conceptual aspects of graph theoretical approach and results According to mathematical discipline of graph theory [21], if the atoms in a structural formula of a molecule are represented by vertices and bonds joining them by edges, then the resulting graph describes the totality of information contained in that v v molecule [20,22–24]. Consequently, if dm , dn , etc. represents the degrees of mth and nth vertices of the graph of a molecule, then connectivity parameters of third degree, 3 ji , is defined [11] by Eq. (14): 3
ji ¼
X
v
v v v 0:5
ðdm dn do d p Þ
(14)
m
where dm , etc. reflects explicitly the valency of mth vertex in molecular graph of i (i = 1 or 2) and is related [24] to maximum valency, Zm, and number of H-atoms, hm, attached to mth, etc. vertex by the relation:
dvm ¼ Z m hm
(15)
1.0
Further Kier [20] has suggested that the information regarding effect of branching in the molecules can be obtained by evaluation of 3 ji of molecules. E Since Vm of an (1 + 2) mixture reflects interactional effects on 1 the packing of molecules and as ð3 ji Þ of i determines [12] the effectiveness with which the molecular surface of i interacts with that of another i molecule, the interactional part of the molar 1 volume of pure i has been taken to ð3 ji Þ . The ideal interactional molar volume of an (1 + 2) mixture would then be proportional to P 3 1 xi ð ji Þ , where xi and ð3 ji Þ denote mole fraction and connectivity parameter of third degree respectively of i. The interactional molar volume of a (1 + 2) mixture should also be proportional to 1/(3j)m of the mixture. If (3j)m of the real mixture in P the molecular graph is expressed by fxi ð3 ji Þm g (where ð3 ji Þm 3 denotes j of i in the mixture) and if the proportionality constant a12 is assume to be the same for the mixture and its pure E components then, Vm may be expressed by [12]. E Vm
3
ðcm
1
mol
" # 2 2 X X xi 1 3 Þ ¼ a12 fxi ð ji Þm g 3 i¼1
i¼1
(16)
ji
where a12 is the constant characteristic of the (1 + 2) mixture and E can be evaluated using equimolar experimental Vm value. 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 0.0
v
0.8
Fig. 7. Apparent molar volume of alkanol (Vf2) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of alkanol (x2) at 298.15 K.
Excess molar volume, (cm3 mol-1 )
Fig. 6. Apparent molar volume of formamide (Vf1) in a mixture of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K.
0.6
x2
1-propanol 2-propanol 1-butanol 2-methyl-1-propanol 2-methyl-2-propanol 0.2
0.4
0.6
0.8
1.0
x1 E Fig. 8. Molar excess volume (Vm ) of formamide (1) + alkanol (2) mixtures as a function of mole fraction of formamide (x1) at 298.15 K; symbol represent values calculated from Eq. (2) and solid lines represent values calculated from graph theory: 1-propanol; 2-propanol; 1-butanol; 2-methyl-1propanol; 2-methyl-2-propanol.
1700
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As the degree of association of 1 and 2 is not known in the mixture and pure state, we regarded ð3 ji Þ and ð3 ji Þm (i = 1 or 2) as adjustable E parameters and evaluated them by employing Vm data to Eq. (16). Only those values of ð3 ji Þ and ð3 ji Þm were retained that best reproduced the VE data. Various ð3 ji Þ or ð3 ji Þm (i = 1 or 2) parameters E along with a12 are recorded in Table 5 along with Vm values obtained
from Eq. (16) for the various binary mixtures as a function of x1 and are also compared with the values calculated from Eq. (2). E Examination of Table 5 and Fig. 8 reveals that Vm values agree well with their corresponding experimental values and thus ð3 ji Þ or ð3 ji Þm (i = 1 or 2) values can be relied upon to extract information about the state of pure components as well as their mixture.
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Table 5 Comparison of smoothened VE values from Eq. (2) with their corresponding values calculated from graph theory (Eq. (14)) along with the various ð3 ji Þ and ð3 ji Þm (i = 1 or 2) values and a12. VE (cm3 mol1)
Mole fraction of formamide (x1) 0.1
0.2
0.3
0.4
0.6
0.7
0.8
0.9
Formamide (1) + 1-propanol (2)a Eq. (2) 0.026 0.004 Eq. (14)
0.047 0.051
0.074 0.089
0.105 0.116
0.147 0.137
0.138 0.127
0.103 0.102
0.050 0.061
Formamide (1) + 2-propanol (2)b Eq. (2) 0.041 Eq. (14) 0.016
0.095 0.108
0.157 0.181
0.218 0.235
0.291 0.274
0.283 0.254
0.233 0.204
0.138 0.121
Formamide (1) + 1-butanol (2)c Eq. (2) 0.026 Eq. (14) 0.030
0.003 0.015
0.038 0.053
0.077 0.083
0.112 0.114
0.103 0.112
0.078 0.094
0.042 0.058
Formamide (1) + 2-methyl-1-propanol (2)d Eq. (2) 0.010 Eq. (14) 0.003
0.034 0.053
0.070 0.096
0.110 0.128
0.178 0.157
0.187 0.149
0.167 0.123
0.108 0.075
Formamide (1) + 2-methyl-2-propanol (2)e Eq. (2) 0.016 Eq. (14) 0.014
0.062 0.093
0.126 0.158
0.191 0.209
0.265 0.253
0.252 0.240
0.199 0.198
0.111 0.121
a b c d e
(3j1) = (3j1)m = 1; (3j2) = 1.41, (3j2)m = 1.395; a12 = 6.7974. (3j1) = (3j1)m = 1; (3j2) = 1.43; (3j2)m = 1.415; a12 = 12.388. (3j1) = (3j1)m = 0.8; (3j2) = 1.485, (3j2)m = 1.4; a12 = 1.9697. (3j1) = (3j1)m = 0.8; (3j2) = 1.4; (3j2)m = 1.36; a12 = 2.6531. (3j1) = (3j1)m = 0.8; (3j2) = 1.44; (3j2)m = 1.4; a12 = 3.8194.
A number of structures (I–XIII) were then assumed for 1 and 2 0 and their ð3 ji Þ values were calculated from structural considerations of Eq. (14). These values were then compared with corresponding values, ð3 ji Þ obtained from Eq. (16). Any structure 0 or combination of structures that yielded ð3 ji Þ values which 3 compared well with the corresponding ð ji Þ obtained from Eq. (16) were considered as representative structure of that component. For this purpose we assumed 1-propanol, 2-propanol, 1butanol, 2-methyl-1-propanol, 2-methyl-2-propanol and formamide to exist in various configurations (I–XIII) (ranging from monomers to di-mers (for alkanols), di-mers and r-mers (both 0 cyclic as well as open for formamide and then calculated ð3 ji Þ values (from Eq. (14)) in the manner explained elsewhere for these 0 configurations. These ð3 ji Þ values when compared with the 3 corresponding ji values of pure components (obtained from an E analysis of the Vm data of the appropriate mixture in terms of Eq. (16)) then suggested that while 1-propanol (3j = 1.41) exists as II (3j0 = 1.314), 2-propanol (3j = 1.43) exists as IV (3j0 = 1.5856). The present treatment further suggests that while 1-butanol (3j = 1.485) exists as an equilibrium mixture of V (3j0 = 0.7020) and dimer VI (3j0 = 1.8994), 2-methyl-1-propanol (3j = 1.4) exists as VIII (3j0 = 1.1435) and 2-methyl-2-propanol (3j0 = 1.440) exists as an equilibrium mixture of IX (3j0 = 0.6123) and X (3j0 = 1.946). Again the 3j value 1.0 of formamide in propanol isomers mixtures compare well with the 3j0 value of 0.94 calculated for it from
Eq. (14) for the configuration XII. 3j Value of 0.8 for formamide in butanol isomers mixtures compare well with the 3j0 value of 0.856 calculated for it from Eq. (14) for the configuration XIII. This suggests that the present approach can be relied upon to yield meaningful information about the state of aggregation of the component of binary mixtures. Again as alkanol can undergo specific interactions with formamide in these mixtures to yield molecular entities, and as ð3 ji Þm depends on the valences of the vertices in the molecular graph of the molecular entities, it would be instructive to see if the present approach could be utilized to know the vertices in the molecular graph of formamide and alkanol that get influenced in these mixture formation. Formamide + 1-propanol mixture (with ð3 j2 Þm ¼ 1:395) should contain an equilibrium mixture of XIV (3j0 = 0.6695) or XVI 0 (3j0 = 1.8453), formamide + 2-propanol ð3 j2 Þm ¼ 1:415 should con0 tain XVIII. Formamide + 1-butanol ð3 jB Þm ¼ 1:4Þ mixture should contain XXI (3j0 = 1.4619) or should contain an equilibrium mixture of XX (3j0 = 0.9633) and XXII (3j0 = 1.9808), formamide + 2-methyl0 1-propanol ðð3 j2 Þm ¼ 1:36Þ should contain equilibrium mixture of 3 0 XXIV ( j = 0.7681) and XXVI (3j0 = 1.8337) and formamide + 20 methyl-2-propanol ðð3 j2 Þm ¼ 1:4Þ should contain equilibrium 3 0 mixture of XXVII ( j = 0.7693) and XXIX (3j0 = 1.8252). This suggests that the present approach can be relied upon to yield meaningful information about the state of aggregation of the component of binary mixtures.
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M. Rani, S. Maken / Journal of Industrial and Engineering Chemistry 18 (2012) 1694–1704
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If interpretation of excess volume data in terms of graph theoretical approach is correct then it should also be reflected in the infrared spectra of these binary mixtures and should influence the characteristics vibrations of formamide and alkanol in these binaries. For this purpose we compared the infrared spectral data of the pure formamide and alkanol (1propanol, 1-butanol and 2 propanol) with their equimolar binary mixtures and observed that in formamide + 1-propanol mixture, the absorption band at 3307 cm1 (asym. NH2 stretch), 3197 cm1 (sym. NH2 stretch), 1664 cm1 (C5 5O) got shifted to 3329, 3190, 1686 cm1, respectively. In case of formamide + 1butanol, these absorption bands of pure formamide got influenced and shifted in the mixture to 3320, 3190 and 1677 cm1. For formamide + 2-propanol mixture, the infrared spectral data reveal the shifting of absorption bands of formamide (asym. NH2 stretch, sym. NH2 stretch and C5 5O) to 3360, 3190 and 1692 cm1 in the mixture. The OH absorption band for 1-propanol, 1-butanol and 2-propanol exists at 3332, 3316 and 3329 cm1. Thus the addition of alkanol to formamide not only influences the hydrogen atom of the NH2 group of formamide, but also affects the carbonyl group of formamide as well as the hydroxyl group of alcohols. In mixtures OH band of alkanol were merged with the NH2 bands of formamide so it is hard to know the position of OH bands in these mixtures. However, the maximum shifting was observed in the mixture of formamide + 2-propanol and minimum in 1-butanol. This may be due to the presence of two electron donating –CH3 groups (in 2-propanol) at C-atom attached to hydroxyl oxygen that interact with H-atom of –NH2 group of formamide. Thus the infrared spectral data of formamide (1), 1-propanol, 1-butanol and 2propanol (2) and their binary (1 + 2) mixtures evidently point to the presence of (XIV, XVI), (XXI, XX, XXII) and XVIII in the mixtures containing 1-propanol, 1-butanol and 2-propanol, respectively. This lends further credence to the graph theoretical arguments. Acknowledgements Authors thank Mr H. S. Chahal, Vice Chancellor, Deenbandhu Chhotu Ram University of Science & Technology, Murthal, India for moral support. One of them (Manju Rani) thanks University Grant Commission, New Delhi, India for the award of Teacher fellowship under Faculty Improvement Program.
References [1] M. Gupta, I. Vibhu, J.P. Shukla, Fluid Phase Equilibria 244 (1) (2006) 26. [2] R.J. Sengwa, V. Khatri, S. Sankhla, Fluid Phase Equilibria 266 (1–2) (2008) 54. [3] Y. Marcus, Introduction to Liquid State Chemistry, Wiley Interscience, New York, 1977. [4] N. Anil Kumar, Fluid Phase Equilibria 265 (1–2) (2008) 46. [5] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, New York, 1960. [6] E.M. Woolley, et al. The Journal of Physical Chemistry 75 (23) (1971) 3591. [7] J.R. Johnson, S.D. Christian, H.E. Affsprung, Journal of the Chemical Society A: Inorganic, Physical, Theoretical (1967) 764. [8] M. Davies, in: H.W.T.E.D. Hadzi (Ed.), Hydrogen Bonding, Pergamon Press, New York, 1952. [9] L.G. Hepler, D.V. Fenby, The Journal of Chemical Thermodynamics 5 (4) (1973) 471. [10] D.V. Fenby, L.G. Hepler, The Journal of Chemical Thermodynamics 6 (2) (1974) 185. [11] P.P. Singh, Thermochimica Acta 66 (1–3) (1993) 37. [12] S. Kumar, et al. Journal of Molecular Liquids 155 (2–3) (2010) 115. [13] A. Maken, S. Maken, Journal of Industrial and Engineering Chemistry 18 (3) (2012) 1013. [14] O. Redlich, A.T. Kister, Industrial and Engineering Chemistry 40 (2) (1948) 345. [15] A.I. Vogel, A Text Book of Practical Organic Chemistry, 4th ed., ELBS Longman, London, 1978. [16] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents. Physical Properties and Methods of Purification, vol. 1, Wiley, New York, 1986. [17] A. Weissenberger, Physical Methods of Organic Chemistry, vol. 1, Interscience, New York, 1959. [18] S. Maken, et al. Journal of Industrial and Engineering Chemistry 13 (7) (2007) 1098. [19] S. Maken, et al. Fluid Phase Equilibria 235 (1) (2005) 42. [20] L.B. Kier, in: S.H. Yalkowaski, S.C. Valvani (Eds.), Physical Chemical Properties of Drugs, Marcel Dekker Inc., New York, Bessel, 1980. [21] F. Harary, Graph Theory, Addison Wesley, Reading, MA, 1969. [22] A.T. Balaban (Ed.), Chemical Applications of Graph Theory, Academic Press, London, 1976. [23] D.H. Rouvray, Reviews 4 (2) (1971) 173. [24] L.B. Kier, L.H. Hall, Molecular Connectivity in Chemistry and Drug Research, Academic Press, New York, 1976. [25] D. Papamatthaiakis, F. Aroni, V. Havredaki, The Journal of Chemical Thermodynamics 40 (1) (2008) 107. [26] A.M. Cases, et al. Journal of Chemical and Engineering Data 46 (3) (2001) 712. [27] N. Anil Kumar, The Journal of Chemical Thermodynamics 39 (3) (2007) 462. [28] N. Anil Kumar, Journal of Molecular Liquids 140 (1–3) (2008) 108. [29] I.-C. Hwang, et al. Journal of Industrial and Engineering Chemistry 18 (1) (2012) 499. [30] S.-J. Park, K.-J. Han, J. Gmehling, Fluid Phase Equilibria 200 (2) (2002) 399. [31] N. Anil Kumar, Fluid Phase Equilibria 259 (2) (2007) 218. [32] H. Iloukhani, B. Samiey, M.A Moghaddasi, The Journal of Chemical Thermodynamics 38 (2) (2006) 190. [33] A.K. Nain, et al. Journal of Molecular Liquids 144 (3) (2009) 138. [34] T.E. Vittal Prasad, et al. Fluid Phase Equilibria 249 (1–2) (2006) 49. [35] G.P. Dubey, M. Sharma, S. Oswal, The Journal of Chemical Thermodynamics 41 (7) (2009) 849.