# Speeds of Sound and Excess Molar Volume for Binary Mixture of 1,4-Dioxane with 1-Heptanol at Five Temperatures

Authors: Anil Kumar Koneti; Srinivasu Chintalapati
Journal: Advances in Chemistry
 (2014)

---

## Abstract

Speed of sound and density data for dilute liquid solutions of cyclic ether 1,4-dioxane with 1-heptanol was obtained using the Anton-Paar DSA 5000 at five temperaturesT = (298.15, 303.15, 308.15, 313.15, and 318.15) K at atmospheric pressure. The excess parameters were calculated from experimental data and fitted with a Redlich-Kister polynomial function and concluded the presence of weak molecular interactions.


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## Body

## 1. Introduction

Cyclic ethers are considered some of the most important chemicals in the industry. Particularly, branched ethers (such as 2-methoxy-2-methylpropane or MTBE, 2-ethoxy-2-methyl-propane or ETBE, 2,2′-oxybis[propane] or DIPE, and 2-methoxy-2-methylbutane or TAME) have extensively been used as oxygenates in gasoline production. Cyclic ethers, in turn (e.g., 1,3-dioxolane, 1,4-dioxane, 1,3,5-trioxane, tetrahydrofuran, and tetrahydropyran), are frequently used as solvents in chemical and electrochemical processes, likewise as basic reagents (i.e., monomer) for ring-opening polymerization, and for the production of other chemical intermediaries. 1-Heptanol is often utilized in cardiac electrophysiology experiments to block gap junctions and increase axial resistance between myocytes. Increasing axial resistance will decrease conduction velocity and increase the heart’s condition to reentrant excitation and sustained arrhythmias. It has a pleasant smell and is employed in cosmetics for its fragrance.Speeds of sound and deviations in isentropic compressibilities have been previously reported by the author in their earlier studies on 1,4-dioxane + 1-butanol [1] at five temperatures T = (298.15, 303.15, 308.15, 313.15 and 318.15) K. In the continuation of investigation on excess thermodynamics functions of cyclic ethers in polar and non-polar solvents, authors are reporting the experimental values, deviations in isentropic compressibility (Δ
κ
s), excess molar volumes (V
m
E), excess free length (L
f
E), excess acoustic impedance (Z
E), and excess sound velocity (U
E) for the binary system 1,4-dioxane + 1-heptanol. The parameters are estimated using standard equations that are reported by many authors [2–5]. These excess parameters are discussed in the focus of intermolecular interactions present in the mixture at T = (298.15, 303.15, 308.15, 313.15, and 318.15) K using Anton-Paar. At the end for the best fit of the result Redlich-Kister coefficients and their related standard deviations are enclosed.


## 2. Experimental Procedure

In the present study the chemicals 1,4-dioxane and 1-heptanol are purchased from Sigma Aldrich chemical company, their mass fraction purities is >0.998. To begin with for the measurements purpose all prepared solutions were done at the same particular temperature, also changing the temperature the measurements were repeated.Speeds of sound,U, densities, ρ, of the pure compounds, and their mixtures were obtained with an Anton-Paar DSA-5000 vibrating tube densimeter and sound analyzer. All controls, adjustments, and checks were done using manufacturer’s software installed in the device. A computer connected to the U tube densimeter enabled us to read the raw data from the device memory and to perform the consequent evaluation. The temperature was automatically kept constant within ±0.01 K. The precision of the speed of sound and density measurements is ±0.1 m·s−1 and ±3 × 10−5 g·cm−3, respectively. The uncertainty of the speed of sound measurements is ±1 m·s−1 while the uncertainty for the density is ±10−5 g·cm−3. Calibration of the apparatus was carried out with air and degassed double-distilled water. Experimental values of the speed of sound of the pure compounds at five temperatures, along with literature values at temperature range of 298.15 to 318.15 K, are reported in Table 1. Mole fractions of these samples were determined by measuring the mass of each component with a precision balance Sartorius, model CP 225D, ±0.01 mg.Table 1
Experimental speed of sound and density of pure liquids with literature values atT = (298.15, 303.15, 308.15, 313.15, and 318.15) K.
System
T (K)
U (ms−1)
ρ (kgm−3)
Observed
Literature
Observed
Literature
1,4-Dioxane
298.15
1344.3
1344.8 [6]
1026.8
1027.9 [6, 7]
303.15
1322.3
1021.2
1022.5 [8, 9]
308.15
1300.5
1015.5
1016.8 [10]
313.15
1278.6
1279.8 [6]
1011.8
1011.3 [8, 9]
318.15
1257.3
1004.1
1005.1 [11]
1-Heptanol
298.15
1327.9
1327.5 [12]
819.7
818.7 [12, 13]
303.15
1310.9
1310.1 [14]
816.2
815.1 [13]
308.15
1294.1
1293.8 [15]
812.6
812.3 [15]
313.15
1277.3
809.0
318.15
1260.7
805.4


## 3. Results and Discussion

The derived excess parameters such asΔ
κ
s, V
m
E, L
f
E, Z
E, and U
E at above five temperature are summarized in Tables 2
(
a
) and 2
(
b
). From the tables, it is observed that, the experimental speed of sound values of the binary liquid mixture decreases up to the mole fraction of 0.4090 (at 298.15, 303.15 K), 0.5244 (at 308.15, 313.15, 318.15 K) and then increase with increasing mole fraction of 1,4-dioxane, whereas the density increases with increasing mole fraction. This indicates that there is a dipole-induced dipole interaction between component molecules [3, 16].Table 2
(a) Experimental values (U, ρ) and excess thermodynamic parameters (Δ
κ
s, V
m
E, L
f
E, Z
E, and u
E) for 1,4-dioxane + 1-heptanol system at 298.15, 303.15, and 308.15 K. (b) Experimental values (U, ρ) and excess thermodynamic parameters (Δ
κ
s, V
m
E, L
f
E, Z
E, and u
E) for 1,4-dioxane + 1-heptanol system at 313.15 and 318.15 K.
(a)
x
1
U ms−1
ρ kgm−3
Δ
K
s * 10
-
10 m2N−1
V
m
E * 10
-
4 m3 mol−1
L
f
E * 10
-
11 m
Z
E * 10
6 kgm−2s−1
U
E ms−1
298.15 K
0.0000
1327.9
819.7
0.0000
0.0000
0.0000
0.0000
0.0000
0.1617
1318.1
838.8
0.1906
0.0206
0.0805
−0.0300
−12.4113
0.2921
1313.3
857.3
0.2919
0.0320
0.1247
−0.0480
−19.4349
0.4090
1311.7
876.2
0.3398
0.0385
0.1469
−0.0584
−22.8951
0.5244
1312.4
897.4
0.3510
0.0412
0.1538
−0.0635
−23.9247
0.6359
1315.8
920.9
0.3291
0.0398
0.1463
−0.0627
−22.8495
0.7083
1318.3
938.2
0.2966
0.0363
0.1331
−0.0584
−21.0012
0.7947
1323.6
961.1
0.2369
0.0292
0.1077
−0.0485
−17.3789
0.8687
1329.3
982.7
0.1666
0.0204
0.0767
−0.0353
−12.7616
0.9388
1336.6
1005.9
0.0837
0.0101
0.0390
−0.0183
−6.7714
1.0000
1344.3
1026.8
0.0000
0.0000
0.0000
0.0000
0.0000
303.15 K
0.0000
1310.9
816.2
0.0000
0.0000
0.0000
0.0000
0.0000
0.1617
1301.6
835.0
0.1861
0.0206
0.0781
−0.0284
−11.1370
0.2921
1296.6
853.4
0.2885
0.0321
0.1223
−0.0455
−17.7549
0.4090
1294.3
872.1
0.3400
0.0386
0.1457
−0.0558
−21.2511
0.5244
1294.3
893.1
0.3549
0.0413
0.1539
−0.0608
−22.4960
0.6359
1296.8
916.3
0.3349
0.0398
0.1472
−0.0602
−21.6492
0.7083
1298.9
933.4
0.3024
0.0363
0.1341
−0.0561
−19.9310
0.7947
1303.6
956.1
0.2415
0.0292
0.1085
−0.0465
−16.4669
0.8687
1308.7
977.5
0.1694
0.0205
0.0770
−0.0338
−12.0406
0.9388
1315.4
1000.5
0.0848
0.0102
0.0390
−0.0175
−6.3496
1.0000
1322.3
1021.2
0.0000
0.0000
0.0000
0.0000
0.0000
308.15 K
0.0000
1294.1
812.6
0.0000
0.0000
0.0000
0.0000
0.0000
0.1617
1284.4
831.2
0.1894
0.0206
0.0787
−0.0273
−10.6121
0.2921
1279.1
849.4
0.2949
0.0321
0.1237
−0.0439
−17.0206
0.4090
1276.2
868.0
0.3477
0.0386
0.1473
−0.0538
−20.3393
0.5244
1275.9
888.7
0.3629
0.0414
0.1555
−0.0586
−21.4749
0.6359
1277.8
911.7
0.3424
0.0399
0.1486
−0.0580
−20.6255
0.7083
1279.5
928.6
0.3090
0.0364
0.1354
−0.0540
−18.9585
0.7947
1283.6
951.1
0.2463
0.0293
0.1093
−0.0447
−15.6073
0.8687
1288.1
972.3
0.1723
0.0205
0.0773
−0.0324
−11.3437
0.9388
1294.4
995.1
0.0857
0.0102
0.0390
−0.0167
−5.9248
1.0000
1300.5
1015.5
0.0000
0.0000
0.0000
0.0000
0.0000
(b)
x
1
U ms−1
ρ kgm−3
Δ
K
s * 10
-
10 m2N−1
V
m
E * 10
-
4 m3 mol−1
L
f
E * 10
-
11 m
Z
E * 10
6 kgm−2s−1
U
E ms−1
313.15 K
0.0000
1277.3
809.0
0.0000
0.0000
0.0000
0.0000
0.0000
0.1617
1267.4
827.4
0.1930
0.0206
0.0792
−0.0263
−10.1247
0.2921
1261.8
845.4
0.2969
0.0322
0.1232
−0.0420
−15.8967
0.4090
1259.0
863.8
0.3495
0.0387
0.1465
−0.0513
−18.9159
0.5244
1257.8
884.3
0.3651
0.0414
0.1547
−0.0559
−19.9470
0.6359
1259.0
907.1
0.3445
0.0400
0.1478
−0.0553
−19.1057
0.7083
1261.0
923.8
0.3106
0.0365
0.1345
−0.0514
−17.5155
0.7947
1263.8
946.1
0.2474
0.0293
0.1084
−0.0425
−14.3816
0.8687
1267.7
967.1
0.1731
0.0205
0.0767
−0.0307
−10.4522
0.9388
1273.3
989.6
0.0863
0.0101
0.0387
−0.0158
−5.4790
1.0000
1278.6
1009.8
0.0000
0.0000
0.0000
0.0000
0.0000
318.15 K
0.0000
1260.7
805.4
0.0000
0.0000
0.0000
0.0000
0.0000
0.1617
1250.4
823.6
0.1980
0.0207
0.0805
−0.0254
−9.7832
0.2921
1244.5
841.4
0.3027
0.0323
0.1243
−0.0404
−15.1454
0.4090
1241.0
859.6
0.3599
0.0388
0.1491
−0.0497
−18.3128
0.5244
1239.5
879.9
0.3777
0.0415
0.1581
−0.0542
−19.4234
0.6359
1240.2
902.4
0.3539
0.0401
0.1500
−0.0533
−18.3277
0.7083
1241.8
919.0
0.3161
0.0366
0.1352
−0.0493
−16.5045
0.7947
1244.8
941.0
0.2489
0.0294
0.1077
−0.0405
−13.2710
0.8687
1248.3
961.8
0.1732
0.0206
0.0758
−0.0292
−9.5740
0.9388
1252.4
984.2
0.0869
0.0102
0.0384
−0.0151
−5.0789
1.0000
1257.3
1004.1
0.0000
0.0000
0.0000
0.0000
0.0000The experimental data measured values of speed of sound (U) and density (ρ) various thermoacoustical parameters:isentropic compressibility:(1)
κ
s
=
1
ρ
U
2
,
molar volume:(2)
V
¯
=
M
¯
ρ
,
whereM
¯
=
M
1
X
1
+
M
2
X
2,
intermolecular free length:(3)
L
f
=
K
κ
s
1
/
2
,
whereK is Jacobson’s constant, temperature dependent,
specific acoustic impedance:(4)
Z
=
U
ρ
.The strength of interaction between the component molecules of binary liquid system is well reflected in the excess functions from ideality. The excess thermodynamic properties such as Δ
κ
s, V
m
E, L
f
E, Z
E, and U
E have been calculated using the following equation:
(5)
Y
E
=
Y
mix
-
x
1
y
1
+
x
2
y
2
,
where x
1 and x
2 are mole fractions of 1,4-dioxane and 1-heptanol, respectively.Further, the excess parameters were fitted to Redlich-Kister polynomial equation to estimate the adjustable parameters:(6)
Y
E
=
x
1
x
2
∑
i
=
0
n
a
i
1
-
2
x
i
.
Using least-squares regression method, the a
i coefficients are obtained by fitting the above equation to the experimental values. The optimum number of coefficients are ascertained from an examination of the variation in standard deviation σ
(
Y
) equation as
(7)
σ
(
Y
)
=
∑
Y
exp
⁡
t
-
Y
calc
2
N
-
n
1
/
2
,
where N is the number of data points and n is the degree of fitting (i.e. number of coefficients) these values are reported in Table 3.Table 3
Coefficients (a
i) and standard deviation (σ) for 1,4-dioxane + 1-heptanol.
Property
T (K)
a
0
a
1
a
2
a
3
a
4
σ (102)
Δ
κ
s (10−10 m2N−1)
298.15
1.4061
−0.0223
0.1258
−0.0355
−0.1509
0.1961
303.15
1.4189
−0.0816
0.0851
−0.0024
−0.1395
0.1805
308.15
1.4507
−0.0821
0.0879
−0.0061
−0.1734
0.2665
313.15
1.4594
−0.0886
0.0780
0.0403
−0.1142
0.3415
318.15
1.5097
−0.1010
−0.0949
0.1229
0.1178
0.0559
V
m
E (m3 mol−1)
298.15
0.1639
−0.0278
0.0103
0.0165
−0.0149
0.0158
303.15
0.1643
−0.0268
0.0100
0.0139
−0.0151
0.0191
308.15
0.1645
−0.0278
0.0099
0.0156
−0.0154
0.0183
313.15
0.1648
−0.0275
0.0115
0.0146
−0.0194
0.0169
318.15
0.1651
−0.0282
0.0110
0.0163
−0.0173
0.0189
L
f
E (10−11 m)
298.15
0.6143
−0.0463
0.0645
−0.0173
−0.0628
0.0829
303.15
0.6135
−0.0686
0.0502
−0.0041
−0.0619
0.0756
308.15
0.6201
−0.0676
0.0510
−0.0055
−0.0753
0.1129
313.15
0.6169
−0.0683
0.0466
0.0117
−0.0528
0.1452
318.15
0.6306
−0.0726
−0.0252
0.0482
0.0448
0.0227
Z
E (106 kgm−2s−1)
298.15
−0.2516
0.0606
−0.0368
0.0014
0.0260
0.0290
303.15
−0.2409
0.0620
−0.0324
−0.0020
0.0249
0.0265
308.15
−0.2321
0.0592
−0.0314
−0.0025
0.0274
0.0341
313.15
−0.2214
0.0564
−0.0303
−0.0065
0.0260
0.0399
318.15
−0.2148
0.0540
−0.0123
−0.0125
0.0017
0.0128
U
E (ms−1)
298.15
−95.5643
6.7116
−14.1963
14.3672
7.2122
16.5048
303.15
−89.6441
10.8671
−9.7419
10.8158
5.9228
13.5179
308.15
−85.6186
9.4617
−9.8055
10.9174
9.7175
20.3881
313.15
−79.5527
8.3222
−7.9463
6.7460
3.7143
24.8586
318.15
−77.5029
8.1303
8.6723
−0.8418
−18.5150
7.7314Generally, the values of the excess functionsΔ
κ
s, V
m
E, and L
f
E depend upon several physical and chemical contributions [3, 17]. The physical contribution depends mainly on two factors, namely,(a)
the dispersion forces or weak dipole-dipole interaction that leads to positive values,
(b)
the geometrical effect allowing the fitting of molecules of two different sizes into each other’s structure resulting in negative values.The chemical contributions include breaking up of the associates present in pure liquids, resulting in positiveΔ
κ
s, V
m
E, and L
f
E. In the present mixture the graphical representations for deviation isentropic compressibilities (Δ
κ
s), excess molar volumes (V
m
E), and excess free length (L
f
E) are positive, presented in Figures 1, 2, and 3.The positive values reveal that there are present weak interactions in the mixture.Figure 1
Variation of deviations in isentropic compressibility (Δ
κ
s) with mole fraction of 1,4-dioxane + 1-heptanol system at different temperatures.Figure 2
Variation of excess molar volumes (V
m
E) with mole fraction of 1,4-dioxane + 1-heptanol system at different temperatures.Figure 3
Variation of excess free length (L
f
E) with mole fraction of 1,4-dioxane + 1-heptanol system at different temperatures.Figure4 shows that the excess acoustic impedance becomes more negative at 0.5244 mole fraction of the binary mixture. The negative values of Z
E [1, 18] indicate that the breaking of hydrogen bond in 1-heptanol leads to weak packing of the structure. Also, Figure 5 shows U
E values exhibiting negative deviations over the entire composition range of 1,4-dioxane in the mixture at all five temperatures studied. The negative deviations of Z
E and U
E suggest that dispersion forces are operative in the system. Similar reports are made by Ali et al. [19]. Further, Bahadur et al. [20] and Sumathi and Govindarajan [3]. According to their reports the negative values of U
E indicates the decrease in the strength of interaction between the molecules in the mixture. In the present work the negative deviations of Z
E and U
E suggests the presence of weak interaction dispersive forces between the unlike molecules.Figure 4
Variation of excess acoustic impedance (Z
E) with mole fraction of 1,4-dioxane + 1-heptanol system at different temperatures.Figure 5
Variation of excess ultrasonic velocity (u
E) with mole fraction of 1,4-dioxane + 1-heptanol system at different temperatures.


## 4. Conclusion

Speed of sound and density for binary mixture that consist of 1,4-dioxane with 1-heptanol system are measured atT = (298.15, 303.15, 308.15, 313.15, and 318.15) K using Anton-Paar. The derived acoustical parameters and their excess parameters Δ
κ
s, V
m
E, and L
f
E are positive and Z
E, U
E are negative which hint to the presence of weak dispersive forces between the component molecules in the mixture at all five temperatures studied.



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*Source: 343012-2014-11-05.xml*