DOI : 10.17577/IJERTV4IS110616
- Open Access
- Total Downloads : 210
- Authors : S. Sreehari Sastry, Sk. Suriya Shihab, Ha Sie Tiong
- Paper ID : IJERTV4IS110616
- Volume & Issue : Volume 04, Issue 11 (November 2015)
- DOI : http://dx.doi.org/10.17577/IJERTV4IS110616
- Published (First Online): 27-11-2015
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Temperature Dependence of Excess Parameters for Binary Mixtures of 1-4 Butanediol and 1-Alkanols by Ultrasonic Technique
-
Sreehari Sastrya,*, Sk. Suriya shihaba,
a Department of Physics, Acharya Nagarjuna University, Nagarjunanagar -522510, India.
Ha Sie Tiongb
bDepartment of Chemical Science, Faculty of Science,
Universiti Tunku Abdul Rahman, Jalan Universiti, Bandar Barat, 31900 Kampar, Perak, Malaysia
s
f
Abstract– Speed of sound (U), Density (), and viscosity () values for the binary mixture systems of 1-4 butanediol with methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol including those of pure liquids were measured from 0.1 to 0.9 mole fraction range at different temperatures (303.15, 308.15, 313.15, 318.15 and 323.15) K. From the experimentally determined values, thermo-acoustic parameters such as excess isentropic compressibility (K E), excess molar volume (VE) and excess free length (L E), excess Gibbs free energy (G*E) and excess enthalpy (HE) have been calculated. The deviations for excess thermo-acoustic parameters have been explained on the basis of the intermolecular interactions present in these binary mixtures. The theoretical values of speed of sound in the mixtures has been evaluated using various theories and has been compared with experimentally determined speed of sound values in order to validate such theories to the liquid mixture systems under study.
Keywords—Speed Of Sound, Density, Excess Molar Volume, Isentropic Compressibility, Free Length, 1,4- Butanediol.
-
INTRODUCTION
-
Speed of sound investigations along with the volumetric and viscometric studies of liquids and liquid mixtures are of considerable importance and they play a significant role in understanding the intermolecular interactions occurring among the component molecules besides finding extensive applications in several industrial and technological processes [1,2]. Several researchers [3-8] have measured the density, viscosity, and speed of sound for a wide range of binary mixtures containing alcohols as one of the components, and these properties were interpreted in terms of specific or nonspecific interactions. Alcohols are strongly associated in solution because of dipole-dipole interaction and hydrogen bonding. They are of great importance for their relevant role in chemistry, biology and studies on hydrogen bonding in liquid mixtures. Alcohols are widely used as solvents. The molecules containing OH group form associative liquids due to hydrogen bonding. The effect shown by the molecules with other functional groups on these molecules plays an important role in understanding the behavior of hydrogen bonding. The investigations regarding the molecular association in liquid mixtures having aromatic group as one of the components are of particular interest, since aromatic group is highly non-
polar and can associate with any other group having some degree of polar attractions. Even though considerable work has been reported on alcohols as one of the component in binary and ternary mixtures, the data on binary mixtures of alcohols witp-4 butanediol with temperature variation is scanty.
s
The study of thermodynamic properties of multi component liquid mixtures and data on the analysis in terms of various models are important for industrial and pharmaceutical applications [9]. The excess thermodynamic functions [10] are sensitively dependent not only on the differences in intermolecular forces, but also on the differences in the size of the molecules. The signs and magnitudes of these excess values can throw light on the strength of interactions. So from the experimentally determined values of speed of sound density and viscosity, various thermo-acoustic parameters like excess isentropic compressibility (K E), excess molar volume (VE), excess free length (LfE), excess Gibbs free energy (G*E) and excess enthalpy (HE) have been calculated. The intermolecular interactions have been estimated in the light of these excess parameters. In the present study, theoretical speed of sound and viscosity values have been evaluated using several empirical relations in the liquid mixtures. This kind of evaluation of theoretical speed of sound values proves to be useful to verify the applicability of various postulates of these theories of liquid mixtures and to arrive at some useful inferences regarding the strength of molecular interactions between component liquids in some cases. The present study gives information on molecular interactions in the commercially important liquid mixtures 1-4 butanediol with 1-alknaols over the entire composition range. Here we report the results of speed of sound, density and viscosity for the binary liquid mixtures of 1-4 butanediol with five 1- alkanols at temperatures of (303.15, 308.15, 313.15, 318.15
and 323.15) K.
-
MATERIALS AND EXPERIMENTS
Where Ks represent the calculated value of isentropic compressibility for the mixture
-
Materials
The chemicals used in the present study are, 1-4 butanediol with methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol
Ks
1
U 2
(2)
which are of AR grade obtained from Merck Co. Inc., Germany, with purities of greater than 99%. All the chemicals were further purified by standard methods [11]and only middle fractions were collected.
K E is its excess value, K id is the ideal isentropic
s
s s
compressibility value, is the density and U represents the speed of sound. K id for an ideal mixture was calculated from the relation recommended by Benson and Kiyohara [12, 13] and Douheret et al [14].
-
Measurements
TV o ( o )2
o2
All binary mixtures were prepared gravimetrically
K id = K o i i -T x V o i i
p,i i p,i
(3)
s i s,i
Co
i i x Co
s,i o i
p,i
in air-tight bottles and adequate precautions have been taken to minimize evapouration losses. Before use, the
in which
K o , V i , o ,
Co are the isentropic
chemicals were stored over 0.4nm molecular sieves approximately for 72h to remove water content and then degassed. The mass measurements were performed on a digital electronic balance (Mettler Toledo AB 135, Switzerland) with an uncertainty of ±10-8 kg. The binary mixtures were prepared just before use. The uncertainty in mole fraction was estimated to be less than ±0.0001.
The viscosities were measured with Ostwald
compressibility, molar volume, isobaric thermal expansion coefficient and molar isobaric heat capacity of pure component i, T represents temperature, i is the volume fraction and xi represents the mole fraction of i in the mixture.
The density values have been used to calculate the excess volumes, VE, using the following equation,
x M x M x M x M
viscometer. The viscometer was calibrated at each
V E 1 1 2 2 1 1 2 2
(4)
temperature using redistilled water. The uncertainty in viscosity measurement is up to 0.001mPa-s. The flow time
1
2
had been measured after the attainment of bath temperature by each mixture. The flow measurements were made with an electronic stop watch with a precision of 0.01s. For all the pure components and mixtures, 3 to 4 readings were taken and the average of these values were used in all the calculations.
The densities of the pure compounds and their mixtures were determined accurately using 10 ml specific gravity bottles. The verage uncertainty in the measured density was ±0.001 kg/m3.
The speed of sound was measured with a single- crystal variable path interferometer (Mittal Enterprises,
where is the density of the mixture and x1, M1, and 1 and
x2, M2, and 2 are the mole fraction, molar mass, and density of pure components 1 and 2, respectively.
The excess values of free length (LfE), Gibbs free energy (G*E) and enthalpy (HE) were calculated by using the expressions given in literature [15] as follows,
LfE = Lf KT (Ksid)1/2 (5)
Where Lf represents the calculated value for the mixture and KT represent a temperature dependent constant whose value is KT=(91.368+0.3565T)x10-8.
Excess Gibbs free energy of activation G*E was calculated as follows,
New Delhi, India) operating at a frequency of 2 MHz that had been calibrated with water and benzene. The
G*E =RT ln V
V
1V1
– x1ln V
(6)
uncertainty in the speed of sound was found to be ±0.1m/s. In all property measurements the temperature was controlled within ± 0.1 K using a constant temperature bath (M/s Sakti Scientific Instruments Company, India) by circulating water from the thermostat.
-
Computational Details
2 2 2 2
Where R represents gas constant, T is absolute temperature,
is the viscosity of the mixture and 1,2 are the viscosities of the pure compounds, V is the molar volume of mixture
and V1, V2 are the molar volumes of the pure compounds, Excess enthalpy HE was calculated from usual relation.
The values of experimentally determined density and speed
H E H (x H
-
x H )
(7)
of sound for the binary mixtures of 1,4 Butane diol with 1- Alkanols at 303.15 K, 308.15 K, 313.15 K, 318.15 K and
323.15 K over the entire composition range.
In the present work, the excess values of isentropic compressibility and excess free length values are calculated to check the applicability of thermo dynamical ideality (the ideal mixing rules) to the components under study.
s
The excess values of isentropic compressibility K E were calculated as follows,
s s s
K E = K K id (1)
1 1 2 2
Where H represents the calculated value of enthalpy for the mixture and H1, H2 represent enthalpy of pure components 1 and 2, respectively.
-
-
RESULTS AND DISCUSSION
The experimental values of speed of sound, density and viscosity in case of the binary liquid mixtures under study over the entire range of composition and at different temperatures, T = (303.15, 308.15, 313.15, 318.15 and 323.15) K are given in Table 1.
0.000 0.7765 1135. 0.9133 0.495
0.895
1312.
22.416
0 2 2
4
6
1
0.067 0.7953 1165. 3.5921 0.604
0.919
1409.
27.372
7 0 1
9
8
7
0.140 0.8107 1228. 6.7387 0.723
0.947
1453.
32.705
5 2
4
1
7
2
0.218 0.8306 1259.
10.317
0.854
0.975
1502.
38.817
9 1
0
8
6
5
4
0.303 0.8503 1284.
14.020
1.000
1.006
1525.
45.120
6 0
5
0
4
5
0
0.395 0.8725 1299.
18.030
4 3
3
T/K = 313.15
0.889
1308.
18.865
Table 1 Densities (), Speed of sound (U) and Viscosities () for the binary
mixtures of 1,4-butanediol with 1-alkanols at different temperatures.
/
x1 10-3 kg m-3
U /
m s-1
/ 103 kg m-1 s-1
/ 10-
x1 3
kg m-3
U /
m s-1
/ 103 kg m-1 s-1
1,4-butanediol(1) + methanol (2) T/K = 303.15
0.000 0.7820
0
0.048 0.7922
5
1095. 0.5210
0.407
0.875
1296.
21.160
9
9
6
9
0.517
0.901
1348.
26.053
2
3
4
8
0.647
0.931
1412.
32.933
5
7
2
0
0.805
0.969
1486.
40.776
2
1
6
1
1.000
1.011
1578.
50.450
0
3
5
0
3
1118. 3.0209
9
0.103
0
0.164
4
0.234
4
0.314
7
0.000
0.8055 1147.
0
0.8191 1178.
3
0.8358 1212.
5
0.8541 1251.
4
1080.
5.9128
8.6878
12.178
5
16.589
4
T/K = 308.15
9
4
7
5
0.517
0.897
1310.
23.950
2
4
3
6
0.647
0.926
1365.
29.719
5
9
3
8
0.805
0.965
1439.
36.467
2
9
3
5
1.000
1.006
1525.
45.120
0
4
5
0
0.407
0.871
1261.
18.882
0.000
0
0.067
7
0.140
5
0.218
9
0.7723 1124.
8
0.7882 1142.
6
0.8047 1218.
9
0.8240 1238.
5
0.8253 0.495
0.604
0.913
1369.
22.792
1
4
8
0
0.723
0.940
1467.
27.094
4
4
2
2
0.854
0.970
1524.
31.786
8
5
3
2
1.000
1.004
1473.
37.050
0
5
2
0
2 4 4 7
3.2998
5.8894
8.8550
0 0.7775
0.048 0.7887
5
2 0.4990
1101. 2.5389
4
0.303
6
0.395
0.8434 1269.
2
0.8649 1284.
11.959
9
15.203
0.103
0
0.164
4
0.234
4
0.8002 1127.
1
0.8151 1155.
0
0.834 1187.
0
5.1971
8.0598
11.287
6
4
0.000
0.067
0.7828
1132.
2.7706
0.604
0.908
1354.
18.448
7
4
6
8
1
2
2
0
0
0.7664
6
7
1111.
5
9
T/K = 318.15
0.755 0.495
2
0.883
9
1300.
5
15.217
9
0.314
7
0.000
0.8497 1222.
5
1066.
15.085
0
T/K = 313.15
0.407
0.866
1238.
15.567
0.140
5
0.218
9
0.7996 1208.
9
0.8181 1224.
8
4.8313
0.723
0.936
1439.
21.733
4
3
4
8
0.854
0.966
1514.
25.841
8
7
9
1
1.000
1.000
1424.
30.100
0
8
1
0
7.1564
0 0.7730
0.048 0.7827
5
2 0.4693
1087. 2.1738
6
0.303
6
0.395
0.8382 1254.
3
0.8598 1279.
9.8575
12.405
0.103
0
0.164
4
0.234
4
0.314
7
0.000
0.7949 1111.
7
0.8101 1140.
5
0.8273 1170.
2
0.8446 1204.
8
1053.
4.2770
9
3
4
0
0.517
0.892
1280.
19.349
2
1
2
9
0.647
0.922
1334.
24.082
5
8
5
0
0.805
0.962
1400.
29.880
2
2
7
4
1.000
1.004
1473.
37.050
0
5
2
0
6.5700
8.9799
12.134
7
T/K = 318.15
0.407
0.861
1210.
12.485
4
0.000
0
0.067
7
0.140
5
0.218
9
2
0.7637 1098.
4
0.7796 1128.
9
0.7964 1200.
0
0.8149 1214.
9
4
T/K = 323.15
0.6987 0.495
0.604
0.904
1325.
15.078
1
1
4
6
0.723
0.932
1428.
18.058
4
9
6
2
0.854
0.963
1504.
21.121
8
2
5
2
1.000
0.997
1387.
24.650
0
7
0
0
2
1.8657
3.9820
5.5414
0.880
6
1299.
3
12.377
6
0 0.7679
0.048 0.7771
5 7
4 0.4299 9 7 5 3
1072. 1.5786 0.517 0.888 1252. 15.596
0.647
0.918
1297.
19.525
5
8
5
1
0.805
0.959
1356.
24.213
2
1
3
5
1.000
1.000
1424.
30.100
0
8
1
0
9 2 2 2 1 2
0.303
6
0.395
0.8337 1249.
3
0.8560 1268.
7.8108
9.9271
0.103
0
0.164
0.7899 1092.
7
0.8060 1117.
3.3354
5.2409
4 4
1,4-butanediol(1) + 1-propanol (2) T/K = 303.15
4
0.234
4
0.314
5
0.8226 1145.
8
1177.
7.2419
0.000
0
0.086
0.7947 1192.
0
1 5
4
6
7
8
0.175 0.8354 1260.
10.022
0.772
0.964
1491.
39.264
0 9
8
4
9
7
3
0.266 0.8527 1295.
14.324
0.884
0.988
1534.
44.834
6 1
2
2
3
0
8
0.361 0.8741 1330.
18.901
1.000
1.011
1578.
50.450
2 9
3
0
3
5
0
0.459 0.8775 1370.
23.754
0 2
2
T/K =
308.15
0.000 0.7932
1171.
1.4605 0.560
0.910
1370.
25.946
0.8092 1225.
1.6121 0.560
0
5.6525 0.664
0.915
5
0.954
1409.
1
1447.
28.551
9
33.843
7 0.8398
2 9.8417
T/K = 323.15
0.000
0
0.048
5
0.103
0
0.164
4
0.234
0.7630 1040.
7
0.7728 1057.
7
0.7860 1077.
1
0.8002 1100.
2
1124.
0.3990 0.407
9
6
1
2
0.517
0.883
1223.
12.572
2
6
4
9
0.647
0.913
1267.
15.961
5
4
5
4
0.805
0.953
1320.
19.992
2
5
8
5
1.000
0.997
1387.
24.650
0
7
0
0
1.3997
2.9300
4.2039
0.856
1186.
10.265
0 8
0 3 6 2
4 0.8170
0.314 0.8348
7
0.000 0.7813
0
8 5.9274
1152. 8.0744
0
1,4-butanediol(1) + ethanol (2) T/K = 303.15
0.495
0.899
1332.
25.200
2
6
4
7
0.604
0.924
1418.
30.658
1
0
3
5
0.723
0.951
1489.
36.464
1149. 0.9940
3
0.086
1
0.175
0
0.266
6
0.361
0.8059
1205. 4.9356 0.664
0.950
1406.
30.454
0 4
0
4
4
1236. 9.0164 0.772
0.960
1445.
35.224
6
4
3
4
5
1266.
12.959
0.884
0.982
1484.
40.229
9
3
2
1
5
1
1299.
17.040
1.000
1.006
1525.
45.120
3
1
0
4
5
0
1336.
21.548
3
3
0.8301
0.8478
0.8701
0.067
7
0.140
5
0.218
9
0.303
6
0.395
4
0.7992 1178.
0
0
4
5
3
4
1279.
11.542
0.854
0.979
1512.
43.133
0
2
8
9
9
5
1294.
15.746
1.000
1.011
1578.
50.450
5
9
0
3
5
0
1309.
20.285
0
8
0.8159 1256.
0.8352
0.8539
0.8769
4.2326
7.7551
2
0.459
0.000 0.7867 1152. 1.3162
0.560
0.907
1332.
21.189
0 2 0 6 4 9
0.949
1362.
25.008
1 1 4
1
7
7
0.175 0.8239 1209. 7.4585 0.772
0.954
1399.
28.689
0 5 4
9
9
7
0
0.086
0.8743
0.8015 1179.
T/K = 313.15
4.1222 0.664
T/K = 308.15
0.266 0.8420 1238. 10.505 0.884 0.982 1435. 32.977
6 4 3 2 3 7 3 0 4 0 6 5 8
0.361
2
0.459
0
0.8660 1267.
8
0.8710 1300.
1
13.965
7
17.564
0
1.000
0
1.004
5
1473.
2
37.050
0
0.103
1
0.205
4
0.7828 1181.
6
0.7954 1205.
6
3.5504 0.707
0
6.1122 0.805
3
0.891
4
0.915
3
1319.
1
1340.
0
17.751
8
19.965
6
0.000
0.7833 1139.
T/K = 318.15
1.2310 0.560
0.904
1298.
17.260
0.307
1
0.8059 1225.
3
8.2842 0.903
0
0.956
2
1364.
5
22.597
1
0
0.086
1
0.175
0
0.7971 1164.
5
0.8156 1189.
0
3.5569 0.664
4
6.2039 0.772
6
0.940
5
0.953
9
1328.
9
1360.
7
20.321
3
23.381
0.408
1
0.508
4
0.8231 1249.
9
0.8556 1270.
0
10.553
6
13.045
9
1.000
0
0.997
7
1387.
0
24.650
0
0
0.266
9
0.8397 1216.
4
8.7407 0.884
6
0.981
7
1388.
9
26.759
1,4-butanediol(1) + 1-pentnol (2) T/K = 303.15
6
0.361
2
0.459
4
0.8616 1241.
8
0.8675 1269.
11.566
9
14.186
2
1.000
0
8
1.000
8
8
1424.
1
6
30.100
0
0.000
0
0.119
4
0.8135 1253.
4
0.8414 1292.
9
3.0120 0.646
8
8.5586 0.740
2
0.941
0
0.954
7
1461.
9
1494.
2
33.603
6
38.123
1
0
0.000
0
0.086
1
0.175
0
0
0.7810 1128.
0
0.7913 1150.
5
0.8100 1173.
2
3
T/K = 323.15
1.1690 0.560
0
3.0330 0.664
4
5.2389 0.772
4
0.899
2
0.941
1
0.947
7
1272.
0
1300.
4
1327.
3
14.310
4
16.599
0
19.439
0
0.233
8
0.334
5
0.448
7
0.549
7
0.8505 1330.
0
0.8737 1362.
0
0.8936 1400.
4
0.9218 1433.
7
14.099
1
18.843
8
24.264
3
29.309
3
0.830
0
0.916
6
1.000
0
0.972
9
0.988
4
1.011
3
1523.
9
1552.
8
1578.
5
42.522
5
46.756
8
50.450
5
0.266
6
0.361
2
0.459
0.8328 1196.
3
0.8545 1221.
8
0.8591 1246.
7.3206 0.884
2
9.4024 1.000
0
11.842
0.974
5
0.997
7
1357.
0
1387.
0
21.961
9
24.650
0
0.000
0
0.119
4
0.8084 1239.
3
0.8371 1273.
6
T/K = 308.15
2.6496 0.646
8
7.5826 0.740
2
0.935
3
0.943
1
1424.
7
1450.
3
30.120
1
34.084
1
0 2 6
1,4-butanediol(1) + 1-butanol (2) T/K = 303.15
0.233
8
0.334
0.8461 1306.
0
0.8715 1335.
12.612
6
17.012
0.830
0
0.916
0.968
9
0.986
1478.
5
1500.
38.063
1
41.651
0.000
0
0.103
1
0.8040 1226.
4
0.8124 1261.
6
2.0540 0.608
0
7.4906 0.707
0
0.887
1
0.914
3
1438.
4
1478.
6
31.730
6
35.963
1
5
0.448
7
0.549
2
0.8867 1368.
9
0.9192 1395.
0
21.876
9
26.231
6
1.000
0
8
1.006
4
8
1525.
5
7
45.120
0
0.205
4
0.307
1
0.408
1
0.8161 1301.
9
0.8256 1335.
8
0.8495 1372.
7
12.377
6
16.902
5
21.803
4
0.805
3
0.903
0
1.000
0
0.935
7
0.979
7
1.011
3
1508.
5
1546.
6
1578.
5
41.198
2
45.653
6
50.450
0
7
0.000
0
0.119
4
9
0.8059 1218.
6
0.8352 1248.
3
2
T/K = 313.15
2.3079 0.646
8
6.1111 0.740
2
0.920
0
0.936
0
1382.
6
1409.
0
24.384
4
27.807
8
0.508
4
0.000
0
0.103
1
0.8843 1407.
7
0.7935 1201.
8
0.8013 1235.
5
26.774
0
T/K = 308.15
1.9030 0.608
0
6.3628 0.707
0
0.883
7
0.910
6
1396.
5
1429.
5
28.319
4
32.454
6
0.233
8
0.334
5
0.448
7
0.549
0.8415 1278.
0
0.8612 1301.
8
0.8770 1334.
5
0.9140 1357.
10.180
2
13.918
9
17.702
7
21.006
0.830
0
0.916
6
1.000
0
0.954
6
0.984
9
1.004
5
1429.
4
1453.
7
1473.
2
30.946
0
33.918
9
37.050
0
0.205
4
0.8138 1266.
1
10.553
6
0.805
3
0.931
6
1460.
9
36.798 7
5
9 0
T/K = 318.15
0.307
1
0.8224 1299.
9
14.967
2
0.903
0
0.976
2
1492.
0
41.086
8
0.000
0
0.8025 1202 2.0759 0.646
8
0.915
6
1342.
8
20.390
4
0.408
1
0.8436 1332.
1
19.478
3
1.000
0
1.006
4
1525.
5
45.120
0
0.119
4
0.8294 1227.
8
5.0150
2
0.740
2
0.919
1
1364.
7
23.213
2
0.508
4
0.8794 1365.
2
23.822
3
0.233
8
0.8341 1252.
7
8.3033 0.830
0
0.939
4
1384.
5
25.615
6
0.000
0
0.103
1
0.205
0.7916 1192.
6
0.7958 1220.
2
0.8103 1248.
T/K = 313.15
1.6200 0.608
0
5.0680 0.707
0
8.8968 0.805
0.879
1
0.907
6
0.929
1361.
0
1389.
0
1415.
22.819
8
26.342
3
30.059
0.334
5
0.448
7
0.549
7
0.8510 1274.
5
0.8605 1300.
2
0.9119 1321.
8
11.246
3
14.549
6
17.567
6
0.916
6
1.000
0
0.982
6
1.000
8
1403.
4
1424.
1
27.958
0
30.100
0
4
0.307
1
0.408
1
0.508
4
1
0.8192 1275.
9
0.8379 1305.
3
0.8746 1331.
8
12.224
4
15.746
9
19.380
8
3
0.903
0
1.000
0
0
0.973
2
1.004
5
5
1445.
3
1473.
2
8
33.540
5
37.050
0
0.000
0
0.119
4
0.233
8
0.7986 1192.
0
0.8231 1212.
8
0.8285 1237.
3
T/K = 323.15
1.8530 0.646
8
4.3994 0.740
2
6.8318 0.830
0
0.912
5
0.916
6
0.927
5
1316.
6
1333.
7
1352.
2
16.456
5
18.783
8
20.270
3
0.000
0.7883 1169.
T/K = 318.15
1.4564 0.608
0.874
1321.
18.768
0.334
5
0.8298 1256.
1
9.2192 0.916
6
0.980
2
1369.
9
22.792
8
0
0.103
1
6
0.7908 1196.
2
0
4.2326 0.707
0
7
0.902
4
8
1346.
2
2
21.719
9
0.448
7
0.549
0.8574 1276.
3
0.9073 1297.
11.831
8
14.159
1.000
0
0.997
7
1387.
0
24.650
0
0.205
4
0.8054 1220.
9
7.2400 0.805
3
0.925
1
1373.
6
24.476
7
7 4 2
0.307
1
0.8129 1245.
9
10.052
4
0.903
0
0.969
0
1398.
0
27.247
3
From the data of speed of sound, density and viscosity, the
values of excess isentropic compressibility (K E), excess
0.408
0.8317 1271.
13.171
1.000
1.000
1424.
-
s
E E
1
0.508
4
2
0.8690 1296.
0
2 0 8 1 0
15.830
5
molar volume (V ), excess free length (Lf ), excess Gibbs
free energy (G*E) and excess enthalpy (HE) were
T/K = 323.15
0.000 0.7878 1157. 1.3341 0.608 0.865 1296. 15.593
calculated. These excess parameters were plotted against
mole fractions separately over the entire range and at different temperatures. The plots are shown in Fig 1-5.
s
s
s
s
s
Figs. 1(a) to 1(e) show the excess isentropic compressibility (K E) for the binary liquid mixtures of 1-4 butanediol with 1-alknaols over the entire mole fraction range and at different temperatures T= (303.15, 308.15, 313.15, 318.15, 323.15) K. It is clear from Figs. 1(a) to 1(e) that the K E values are negative over the entire mole fraction range for the systems under study and at investigated temperatures, This indicates the presence of strong interactions in these mixtures. As the temperature increases, it has been observed that the, the negative K E values are found to increase in these systems and the changes in K E values with respect to temperature are small in these mixtures. Also with the increase in temperature the solute-solvent interactions get weaker causing the excess values to decrease at higher temperature. The sign of excess isentropic compressibility plays a relevant role in assessing the compactness due to molecular interaction in liquid mixtures through charge transfer, dipole-dipole interactions, and dipole induced dipole interactions interstitial accommodation and orientational ordering leading to more compact structure making, which enhances excess isentropic compressibility to have negative values. Fort and Moore [17] suggested that the liquids having different molecular sizes and shapes mix well there by reducing the volume which causes the values of K E to be negative.
(a)
(b)
(c)
(d)
(e)
Fig.1 a e Excess isentropic compressibility with respect to mole fraction at various temperatures for (a) 1-4 butanediol + methanol (b) 1-4 butanediol + ethanol (c) 1-4 butanediol + propanol (d) 1-4 butanediol + butanol and (e) 1-4 butanediol +pentanol at temperatures
,303.15K;,308.15K;,313.15K; ,318.15K;,323.15K.
It also suggests that the liquids are less compressible when compared to their ideal mixtures signifying the chemical effects including charge transfer forces, formation of hydrogen bond and other complex forming interactions. It can also be said that the molecular interactions are strong in these binary liquid mixtures and that the medium is highly packed.
(a)
(b)
2(c)
The variation of excess molar volume (VE), with respect to mole fraction, x1, is given in Figs. 2(a) to 2(e) over the entire composition range and at different T = (303.15, 308.15, 313.15, 318.15 and 323.15) K. The
strength of the intermolecular interactions in binary liquid mixtures can be explained using the sign and magnitude of the VE values .The factors that are mainly responsible for the contraction of volume causing the VE values negative are due to strong specific interactions
(d)
2(e)
Fig.2 a e Excess molar volume with respect to mole fraction at various temperatures for (a) 1-4 butanediol + methanol (b) 1-4 butanediol + ethanol (c) 1-4 butanediol + propanol (d) 1-4 butanediol + butanol and (e) 1-4 butanediol +pentanol at temperatres,303.15K,308.15K
,313.15K
,318.15K;,323.15K.
like the association of component molecules through hydrogen bonds, due to dipole-dipole interactions or it may be due to the induced dipole-dipole interactions. Whereas the expansion of volumes, leading to positive VE values is due to breaking of one or both of the components in a solution. The geometry of molecular structure does not allow the fitting of one component molecules into the voids created by the molecules of other component and the steric hinderance of the molecules. In our present study the VE values are mostly negative in both the cases. So this kind of behavior of VE can be attributed to the formation of hydrogen bond, disruption of alcohol self-associations and the structural characteristics like geometrical fitting of one component into the other as a result of the increase in difference of size and shape of the component molecules. As the temperature increases, it has been observed that, the negative values of VE are found to decrease indicating the decrease of interactions between the unlike molecules. The expansion in molar volume can be attributed to the presence of weak intermolecular forces of attraction [18]. Similar results were reported by Garcia et al [19]. The negative values of VE indicate that there is more compact packing of the molecules which implies that the molecular
interactions are strong whereas the positive values indicate a loose packing of molecules in the binary mixture compared to those in the pure component. Similar results were observed by earlier workers [20].
(a)
(b)
s
It can be observed from Figs. 3(a) to 3(e) that the LfE values have a negative trend similar to what we have observed in case of the K E at all the temperatures under study. The negative values of LfE suggest that specific interactions are present between unlike molecules in these binary systems [21].
Figs. 4(a) to 4(e) represent the excess Gibbs free energy of activation (G*E) with respect to mole fraction x1, over the entire composition range and at T = (303.15, 308.15, 313.15, 318.51, and 323.15) K. It can be observed that the
G*E values are positive at all temperatures and over the entire range of mole fraction. These positive values indicate
(c)
(d)
(e)
Fig.3 a e Excess free length with respect to mole fraction at various temperatures for (a) 1-4 butanediol + methanol (b) 1-4 butanediol + ethanol (c) 1-4 butanediol + propanol (d) 1-4 butanediol + butanol and (e) 1-4 butanediol + pentanol at temperatures
-
,303.15K;,308.15K;,313.15K; ,318.15K;,323.15K.
Figs. 4(a) to 4(e) represent the excess Gibbs free energy of activation (G*E) with respect to mole fraction x1, over the entire composition range and at T = (303.15, 308.15, 313.15, 318.51, and 323.15) K. It can be observed that the
G*E values are positive at all temperatures and over the entire range of mole fraction. These positive values indicate the existence of strong intermolecular interaction through hydrogen bonding between the component molecules of the liquid mixtures under study. The maximum deviation is observed for 1-4 butanediol
+methanol system indicating the strength of bond formation in this system is more compared to that of other system. Similar results were observed by earlier workers [22].
(a)
(b)
(c)
(d)
(e)
Fig.4 a e Excess Gibbs free energy with respect to mole fraction at various temperatures for (a) 1-4 butanediol + methanol (b) 1-4 butanediol
+ ethanol (c) 1-4 butanediol + propanol (d) 1-4 butanediol + butanol and
-
1-4 butanediol +pentanol at temperatures ,303.15K;, 308.15K;
,313.15K; ,318.15K;,323.15K.
From Figs. 5(a) to 5(e) it is clear that the excess values of Enthalpy (HE) are positive with respect to the mole fraction, x1, over the entire composition range and at T = (303.15, 308.15, 313.15, 318.15, and 323.15) K.
(a)
(b)
(c)
(d)
(e)
Fig.5 a e Excess enthalpy with respect to mole fraction at various temperatures for (a) 1-4 butanediol + methanol (b) 1-4 butanediol + ethanol (c) 1-4 butanediol + propanol (d) 1-4 butanediol + butanol and (e) 1-4 butanediol + pentanol at temperatures
-
-
,303.15K;,308.15K;,313.15K;, 318.15K;,323.15K.
-
The positive values of HE tend to decrease with increase in temperature, this insists the fact that there are strong specific interactions between unlike molecules in these liquid mixtures [23]. The positive HE values also suggest the existence of inter molecular hydrogen bond and the breaking of associated structures in both cases.
The variations in these above excess parameters with mole fraction and temperature predict the presence of hydrogen bonding between the compounds in these binary mixtures. The strength of bond formation between the compounds in the present mixtures decrease, this is because of the increased chain length. Also the excess parameters calculated in the present study are correlated with one another and at the same time each parameter supporting the formation of hydrogen bonding in these binary liquid mixtures.
The deviations observed in the excess parameters indicate the strength of interactions present between the component molecules of the binary mixtures under study [16]. The variations in these excess parameter values reflect the interactions between the mixing species, depending upon the composition, molecular sizes and shapes of the components and temperature. The effects which influence the values of excess thermodynamic functions may be the result of physical, chemical and structural contributions such as:
S f
S f
-
The chemical effects, like the breaking of molecular association present in the pure liquid have resulted in the positive values of VE, K E, L E and negative G*E, on the other hand charge transfer forces, formation of hydrogen bonds and other complex forming interactions have resulted in the negative values of VE, K E, L E and positive
G*E [15].
S f
-
Physical contributions are from dispersion forces or weak dipole-dipole interactions causing the positive values of VE, K E, L E and negativeG*E.
S
-
The structural contribution arising from the geometrical fitting of one component into the other because of the differences in the size and shape of the component molecules are resulting in the negative values of VE, K E, LfE and positive G*E.
In the present study, theoretical values for speed of sound have been evaluated in the binary mixtures considering 1-4 butanediol as one component and 1- alkanols as the other component at that of all investigated temperatures. This kind of evaluation of theoretical speed of sound values proves to be useful to verify the applicability of various postulates of these theories of liquid mixtures and to arrive at some useful inferences regarding the strength of molecular interactions between component liquids in some cases. The theories due to Nomoto (UNOM) [24], Impedance relation(UIMP) [25], Van Dael and Vangeel (UVDV) [26], Junjies (UJM) [27], Free length theory (UFLT) [28] and Raos (UR) [29] are employed and the Average percentage error along with the Chi square fit values for the binary mixture and at all investigated temperatures are compiled in Table.2.
Table 2: Average percentage error (APE) and Chi Square fit values for
APE 0.0000 -0.7099 1.4645 0.7430 0.0000 -1.1747
Speed of sound computed from different theoretical models.
Chi square
0.0000 0.9748 4.0801 1.0578 0.0000 3.1353
UNOM UIMP UVDV UJM UFLT UR
1,4-butanediol + methanol
1,4-butanediol + 1-pentanol T/K = 303.15
APE 0.0000 -0.7137 1.2854 1.8626 0.0000 0.8352
T/K = 303.15
APE 0.0000 -1.1914 13.1395 -2.5444 0.0000 -0.7319
Chi square
0.0000 1.0905 3.5217 7.4758 0.0000 1.7958
Chi square
T/K = 308.15
APE 0.0000 -0.6679 10353 1.5609 0.0000 0.6966
T/K = 308.15
APE 0.0000 -1.2821 12.6040 -2.7728 0.0000 -1.2108
Chi square
0.0000 0.9124 2.2454 5.1514 0.0000 1.3689
Chi square
0.0000 3.1084 391.0114 13.856 0.0000 3.2437
T/K = 313.15
APE 0.0000 -0.6138 0.8706 1.3551 0.0000 0.6032
T/K = 313.15
APE 0.0000 -0.8473 12.4805 -2.5362 0.0000 -0.6557
Chi square
0.0000 0.7744 1.5387 3.7767 0.0000 1.0706
Chi square
0.0000 1.4228 372.182 11.4882 0.0000 1.4244
T/K = 318.15
APE 0.0000 -0.6640 0.5909 1.0264 0.0000 0.3910
T/K = 318.15
APE 0.0000 -0.8711 11.9793 -2.6785 0.0000 -1.0005
Chi square
0.0000 0.8381 0.7012 2.1155 0.0000 0.7623
Chi square
0.0000 1.3538 332.990 12.290 0.0000 2.4992
T/K = 323.15
APE 0.0000 -0.6085 0.4569 0.8499 0.0000 0.3081
T/K = 323.15
Chi
0.0000 0.6953 0.4187 1.4410 0.0000 0.6533
APE 0.0000 -0.9734 11.5913 -2.8871 0.0000 -1.0805 square
Chi square
0.0000 1.6465 302.786 13.9597 0.0000 2.4519
1,4-butanediol + ethanol T/K = 303.15
The error for average percentage values is small. On comparison, the Nomotos relation and Free length theory
APE 0.0000 -0.5817 8.4311 0.2942 0.0000 -1.5.279
Chi 0.0000 4.8904 161.239 3.7999 0.0000 9.5029
square
T/K = 308.15
relation are found to give some valuable estimate of the
experimental values of speed of sound values in these binary mixtures at all the temperatures.
APE 0.0000 0.3050 8.7269 0.9620 0.0000 -1.0436
Chi 0.0000 3.0137 171.916 4.2026 0.0000 5.9474
square
T/K = 313.15
APE 0.0000 1.4348 9.1919 1.6983 0.0000 0.6915
-
-
CONCLUSIONS
The excess parameters like K E, VE, L E, G*E and
S f
Chi square
0.0000 11.5639 197.744 12.971 0.0000 9.4830
T/K = 318.15
HE are calculated from the experimentally determined speed of sound, density and viscosity values. The
APE 0.0000 2.5027 9.7117 2.5825 0.0000 1.5084
Chi 0.0000 21.5625 219.943 22.365 0.0000 14.400
square
T/K = 323.15
APE 0.0000 3.4250 10.262 3.3537 0.0000 2.4808
Chi 0.0000 34.027 243.499 33.271 0.0000 23.501
formation of hydrogen bond between the mixtures is identified by studying the variations in these parameters. The values of excess isentropic compressibility, excess free length are found to be negative, excess enthalpy, excess
square
1,4-butanediol + 1-propanol T/K = 303.15
APE 0.0000 -1.0030 4.4820 1.0404 0.0000 -2.7384
Gibbs free energy of activation is positive over the entire range of composition at all temperatures for the liquid mixture systems considered in the present study. The
Chi
square
0.0000 2.0293 44.180 2.2421 0.0000 14.771
T/K = 308.15
excess molar volume values have changed from positive to negative for the binary systems over the entire range of
APE 0.0000 -0.8803 4.2454 0.9078 0.0000 -2.7202
Chi 0.0000 1.5677 38.157 1.6160 0.0000 14.413
square
T/K = 313.15
APE 0.0000 -0.9163 3.8843 0.6916 0.0000 -2.9786
Chi 0.0000 1.5915 31.161 0.9475 0.0000 16.579
square
T/K = 318.15
composition and at all the temperatures considered in the present study. This is a clear indication for the presence of hydrogen bonding between the component molecules. The difference in molar masses of the liquid molecules is also responsible for the existing specific interactions between
the molecules of the component liquids. Besides, the
APE 0.0000 -0.8059 3.5714 0.5367 0.0000 -3.0532
Chi 0.0000 1.2182 25.5559 0.5608 0.0000 17.047
square
T/K = 323.15
computed speed of sound values from different theories have been correlated with the experimentally measured values. Speed of sound values obtained from Nomotos and
APE 0.0000 -0.7810 3.2935 0.3744 0.0000 -3.1588
Chi
0.0000 1.1208 21.2309 0.2716 0.0000 17.886
free length theory relations are in good agreement with the
square 1,4-butanediol + 1-butanol
T/K = 303.15
APE 0.0000 -0.7979 2.4709 1.5844 0.0000 -0.6349
experimental values.
-
ACKNOWLEDGEMENTS
Chi square
0.0000 1.3261 13.182 5.3886 0.0000 1.2501
T/K = 308.15
The authors gratefully acknowledge University Grants
APE 0.0000 -0.9348 2.1364 1.3047 0.0000 -0.9036
Chi 0.0000 1.7240 9.5490 3.5589 0.0000 2.0242
square
T/K = 313.15
APE 0.0000 -0.8878 1.7478 0.9712 0.0000 -1.1030
Chi 0.0000 1.5237 6.2145 1.9355 0.0000 2.7703
square
T/K = 318.15
Commission Departmental Special Assistance at Level I program No. F.530/1/DSA- 1/2015 (SAP-1), dated 12 May 2015, and Department of Science and Technology-Fund for Improving Science and Technology program No.DST/FIST/ PSI002/2011 dated 20-12-2011, New
Delhi, to the Department of Physics, Acharya Nagarjuna
APE 0.0000 -0.8139 1.6019 0.8546 0.0000 -1.1501
Chi 0.0000 1.2724 4.9993 1.4202 0.0000 3.0405
square
University for providing financial assistance.
T/K = 323.15
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