# Ultrasonic Investigations of Molecular Interaction in Binary Mixtures of Cyclohexanone with Isomers of Butanol

Authors: Sk. Md Nayeem; M. Kondaiah; K. Sreekanth; D. Krishna Rao
Journal: Journal of Applied Chemistry
 (2014)

---

## Abstract

Ultrasonic speed,u, and density, ρ, have been measured in binary liquid mixtures of cyclohexanone with the isomers of butanol (n-butanol, sec-butanol, and tert-butanol) at 308.15 K over the entire range of composition. Molar volume (V
m), adiabatic compressibility (k
s),  intermolecular free length (L
f), acoustic impedance (z), and their excess/deviation along with Δ
u have been calculated from the experimental data. These values have been fitted to Redlich-Kister type polynomial equation. Positive values of V
m
E, Δ
k
s, L
f
E and negative values of z
E, Δ
u have been observed for all the liquid mixtures indicating the existence of weak interactions between components. Rupture of H-bond or reduction in H-bond strength of isomers of butanol or breaking of the structure of one or both of the components in a solution causes the existence of dispersions in the present investigated binary mixtures. The data obtained from V
-
m
,
1, V
-
m
,
2, and excess partial molar volumes V
-
m
,
1
E, V
-
m
,
2
E, reflects the inferences drawn from V
m
E. Furthermore, FTIR spectra support the conclusions drawn from excess/deviation properties. The measured values of ultrasonic speed for all the investigated mixtures have been compared with the theoretically estimated values using empirical relations such as, Nomoto, Van Dael and Vangeels, Impedance and Rao specific sound speed.


---

## Body

## 1. Introduction

Ultrasonic measurements are very useful in chemical and food processing, pharmaceuticals, material testing, and underwater ranging and cleaning and are also commonly employed in mechanical machinery of materials [1], preparation of colloids or emulsions, the pregermination of seeds, imaging of biological tissues [2], activation energy of metabolic process [3], formation and destruction of azeotropes in petrochemical industries [4], and nondestructive testing (NDT).Alcohols are self-associated organic liquids, used for the synthesis of other organic compounds. They are also widely used as coupling and dispersing agents in the chemical, pharmaceutical, and household industries and as carrier and extraction solvents for natural products. Cyclohexanone and its derivatives are used for the synthesis of pharmaceuticals, dyes, herbicides, pesticides, plasticizers, and rubber chemicals. Ketones are a class of an organic compound that contains a carbonyl group and two aliphatic or aromatic substituents containing the chemical formula RCOR1 (general chemical formula of Ketones). The chemical reactivity of the carbonyl group plays vital role in chemical reactions and is influenced considerably by steric effects. The greater electronegativity of O− and high dipole moment value make Cyclohexanone polar. Scheme 1 illustrates this polarity. Further the presence of oxygen with its nonbonding electron pairs makes cyclohexanone H-bond acceptors. Thus a study on thermophysical properties data of binary liquid mixtures containing ketones has attracted considerable interest in the literature [5–9].Scheme 1Literature survey reveals that Tsierkezos et al. [10] studied molecular interactions in cyclohexanone with methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol at 293.15 K and Sri Lakshmi et al. [11] studied molecular interactions in cyclohexanone with n-heptanol, n-octanol, and isooctanol at temperatures 303.15, 308.15, 313.15, and 318.15 K over the entire range of composition. Keeping these important aspects in mind, the present study deals with ultrasonic and thermodynamic study of cyclohexanone (CH) with the isomers of butanol (n-butanol,sec-butanol, andtert-butanol) at 308.15 K. The liquids under investigation have been chosen on the basis of their multifold applications.


## 2. Experimental Section

High purity analytical reagent (AR) grade compounds of cyclohexanone (mass fraction purity > 99%) andn-butanol,sec-butanol, andtert-butanol (mass fraction purity > 99.5%) obtained from S D Fine Chemicals are used in the present study. The chemicals are further purified by standard methods mentioned in [12, 13]. The weighing of solutions has been made using METTLER TOLEDO (Switzerland make) ABB5-S/FACT digital balance with an accuracy of ±0.01 mg. The uncertainty in the mole fraction is 10−4. The ultrasonic speeds of pure liquids and liquid mixtures have been measured using an ultrasonic interferometer (Mittal type, Model F-82) working at 2 MHz fixed frequency with an accuracy of ±0.2%. The temperature of liquid sample in the interferometer cell is maintained constant by circulating water pumped from constant temperature water bath. In the present study the constant temperature water bath (digital electronic) supplied by Concord Instruments Co. Ltd., Chennai (RAAGA type), has been used. The instrument can maintain temperature to ±0.01 K as per its specifications.Densities of pure liquids and their mixtures have been determined by using a 5 cm3 two-stem double-walled Parker & Parker type pycnometer [15]. This pycnometer is calibrated with triply distilled water. The pycnometer filled with air bubble free experimental liquids was kept in a transparent walled constant temperature bath for 20 to 30 min to attain thermal equilibrium. The positions of the liquid levels in the two arms are recorded with the help of traveling microscope. At least three to four measurements are performed, from which an average value of density of the experimental liquid is determined. The estimated accuracy in the density measurement is 3 in 105 parts. The ultrasonic speeds, u, and densities, ρ, measured at 308.15 K for the pure liquids used in this investigation are compiled in Table 1 together with the literature data [11, 14] available. These results are in good agreement with the reported data.Table 1
Comparison of experimental values of density,ρ, and ultrasonic speed, u, of pure liquids with the corresponding literature values at 308.15 K.
Liquid
ρ/(kg m−3)
u/(m s−1)
Present work
Literature
Present work
Literature
Cyclohexanone
939.60
939.6 [11]
1362.00
1362.0 [11]
n-Butanol
796.50
796.5 [14]
1209.30
1209.3 [14]
s
e
c-Butanol
793.20
793.2 [14]
1174.80
1174.8 [14]
t
e
r
t-Butanol
768.40
768.3 [14]
1086.00
1086.0 [14]


## 3. Theory

Thermodynamic and acoustical parameters such as molar volume (V
m), adiabatic compressibility (k
s), intermolecular free length (L
f), and acoustic impedance (z) are evaluated using the relations given below:
(1)
V
m
=
M
eff
ρ
,
where M
eff is given by M
eff
=
(
x
1
M
1
+
x
2
M
2
), where M
1 and M
2 are the molar masses of pure components, and ρ is the density of the liquid mixture.The speed of sound (u) and the density of the medium (ρ) are related by using Newton and Laplace equation as
(2)
k
s
=
1
ρ
u
2
,
L
f
=
K
k
s
1
/
2
.
Here K is the temperature dependent constant which is equal to K
=
(
93.875
+
0.375
T
)
×
10
-
8 where T is absolute temperature. Consider
(3)
z
=
u
ρ
.
In order to understand the nature of the molecular interactions between the components of the liquid mixtures, it is of interest to discuss the same in terms of excess parameters rather than actual values. Nonideal liquid mixtures show considerable deviation from linearity in their concentrations and this has been interpreted to arise from the presence of strong or weak interactions. The difference between the properties of the real mixtures (Y
real) and those corresponding to ideal mixture (Y
ideal
=
∑
x
i
Y
i) values, namely, excess properties (Y
E), such as excess molar volume (V
m
E), free length (L
f
E), acoustic impedance (z
E), and deviations in ultrasonic speed (Δ
u), is computed by the relation
(4)
Y
E
=
Y
real
-
∑
x
i
Y
i
,
where Y
E
=
V
m
E
,
L
f
E
,
z
E and Δ
u; x
i is the mole fraction and Y
i is the value of the property of the ith component liquid of mixture.The deviation in adiabatic compressibility (Δ
k
s) has been calculated from the equation
(5)
Δ
k
s
=
k
s
-
Φ
1
k
s
1
+
Φ
2
k
s
2
,
where Φ
1
,
Φ
2, and k
s
1
,
k
s
2 are the volume fractions and adiabatic compressibilities of components 1 and 2, respectively. Since k
s is not additive on mole fraction but is additive on volume fraction, such values are calculated using volume fraction (Φ):
(6)
Φ
i
=
x
i
V
i
∑
x
i
V
i
.
The experimentally measured values of ultrasonic speed (u) and density (ρ) and calculated properties of molar volume (V
m), adiabatic compressibility (k
s), intermolecular free length (L
f), and acoustic impedance (z) and excess/deviation thermodynamic properties V
m
E, L
f
E, z
E, Δ
u, and Δ
k
s are presented in Table 2 for all binary systems over the entire composition range of CH.Table 2
Experimental values of densities,ρ, ultrasonic speeds, u, molar volume, V
m, adiabatic compressibility, k
s, intermolecular free length, L
f, acoustic impedance, z, and excess/deviation properties V
m
E, L
f
E, z
E, Δ
u, and Δ
k
s for all binary systems with mole fraction, x
1, of cyclohexanone at 308.15 K.
x
1
ρ/(kg m−3)
u/(m s−1)
V
m/(10−5 m3 mol−1)
k
s/(10−10 Pa−1)
L
f/(10−10 m)
z/(106 kg m−2 s−1)
V
m
E/(10−5 m3 mol−1)
Δ
k
s/(10−10 Pa−1)
L
f
E/(10−10 m)
z
E/(106 kg m−2 s−1)
Δ
u/(m s−1)
CH +n-butanol
1.0000
939.60
1362.00
7.2100
8.3164
0.6040
1.2797
0.0000
0.0000
0.0000
0.0000
0.00
0.9121
913.91
1331.02
7.2125
8.9952
0.6281
1.2164
0.0977
0.3231
0.0107
−0.0355
−17.55
0.8854
907.20
1322.96
7.2111
9.1843
0.6347
1.2002
0.1252
0.4008
0.0133
−0.0432
−21.54
0.7211
873.62
1283.96
7.1186
10.2048
0.6690
1.1217
0.2105
0.6763
0.0226
−0.0697
−35.45
0.6687
864.85
1274.47
7.0775
10.4903
0.6783
1.1022
0.2261
0.7151
0.0239
−0.0726
−36.94
0.5232
843.20
1252.14
6.9241
11.2327
0.7019
1.0558
0.2302
0.7516
0.0254
−0.0730
−37.05
0.4752
836.65
1246.98
6.8566
11.4565
0.7089
1.0433
0.2147
0.7367
0.0251
−0.0703
−34.88
0.3231
817.59
1230.68
6.6549
12.1558
0.7302
1.0062
0.1776
0.6877
0.0232
−0.0593
−27.95
0.2112
805.99
1220.87
6.4872
12.6087
0.7437
0.9840
0.1311
0.5914
0.0197
−0.0460
−20.68
0.1313
799.91
1215.19
6.3611
12.861
0.7511
0.9720
0.0915
0.4550
0.0150
−0.0328
−14.15
0.0000
796.50
1209.30
6.1275
13.0345
0.7561
0.9632
0.0000
0.0000
0.0000
0.0000
0.00
CH +s
e
c-butanol
1.0000
939.60
1362.00
7.2100
8.3164
0.6040
1.2797
0.0000
0.0000
0.0000
0.0000
0.00
0.9212
912.29
1329.22
7.2449
9.0394
0.6297
1.2126
0.1060
0.3836
0.0126
−0.0397
−18.02
0.8867
902.08
1316.33
7.2474
9.3357
0.6399
1.1874
0.1397
0.5194
0.0171
−0.0529
−24.46
0.7121
862.17
1263.03
7.2207
10.6512
0.6835
1.0889
0.2705
0.9784
0.0316
−0.0907
−45.07
0.6786
856.20
1254.83
7.2042
10.8709
0.6905
1.0744
0.2843
1.0245
0.0331
−0.0935
−47.00
0.5123
831.56
1221.77
7.0717
11.8365
0.7205
1.0160
0.3018
1.0967
0.0354
−0.0941
−48.93
0.4688
826.13
1215.26
7.0273
12.0569
0.7272
1.0040
0.2967
1.0794
0.0349
−0.0909
−47.29
0.3121
809.26
1196.19
6.8217
12.7651
0.7483
0.9680
0.2325
0.9202
0.0299
−0.0724
−37.03
0.2797
806.31
1193.09
6.7723
12.8921
0.7520
0.9620
0.2124
0.8684
0.0282
−0.0672
−34.06
0.1112
795.03
1180.57
6.5053
13.4011
0.7667
0.9386
0.0974
0.4604
0.0149
−0.0320
−15.04
0.0000
793.20
1174.80
6.3075
13.5292
0.7703
0.9319
0.0000
0.0000
0.0000
0.0000
0.00
CH +t
e
r
t-butanol
1.0000
939.60
1362.00
7.2100
8.3164
0.6040
1.2797
0.0000
0.0000
0.0000
0.0000
0.00
0.9221
908.29
1312.68
7.3361
9.2340
0.6364
1.1923
0.1562
0.4969
0.0150
−0.0527
−27.81
0.8895
896.42
1294.40
7.3779
9.6141
0.6494
1.1603
0.2106
0.6834
0.0207
−0.0702
−37.10
0.7012
840.30
1210.44
7.5179
11.7001
0.7164
1.0171
0.4235
1.5137
0.0457
−0.1296
−69.09
0.6814
835.51
1203.37
7.5205
11.9041
0.7226
1.0054
0.4337
1.5721
0.0475
−0.1325
−70.69
0.5112
801.79
1152.77
7.4950
13.4939
0.7693
0.9243
0.4741
1.8707
0.0562
−0.1378
−74.32
0.4777
796.61
1144.65
7.4783
13.7669
0.7771
0.9118
0.4703
1.8823
0.0566
−0.1354
−73.19
0.3321
779.12
1115.24
7.3616
14.7714
0.8049
0.8689
0.4099
1.7360
0.0519
−0.1135
−62.41
0.2635
773.60
1104.59
7.2878
15.1275
0.8146
0.8545
0.3627
1.5506
0.0463
−0.0973
−54.13
0.1323
767.78
1090.36
7.0894
15.5581
0.8261
0.8372
0.2150
0.9556
0.0285
−0.0562
−32.15
0.0000
768.40
1086.00
6.8232
15.5954
0.8271
0.8345
0.0000
0.0000
0.0000
0.0000
0.00The excess/deviation properties have been fitted to a Redlich-Kister type polynomial equation [16]
(7)
Y
E
=
x
1
x
2
∑
i
=
0
n
A
i
x
2
-
x
1
i
,
where Y
E
=
V
m
E
,
L
f
E
,
z
E
,
Δ
u and Δ
k
s; x
1 is the mole fraction of the solute.The values ofΔ
k
s have been fitted to Redlich-Kister type polynomial with volume fraction instead of mole fraction in the above polynomial and A
i are the adjustable parameters of the function and are determined using the least square method. In the present investigation “i” values are taken from 0 to 4. The corresponding standard deviation σ
(
Y
E
) was calculated using the expression
(8)
σ
Y
E
=
∑
Y
exp
⁡
E
-
Y
cal
E
2
m
-
n
1
/
2
,
where “m” is the total number of experimental points and “n” is the number of coefficients in (7). The calculated values of the coefficients A
i along with the standard deviations (σ) have been presented in Table 3.Table 3
CoefficientsA
i of Redlich-Kister type polynomial equation (7) and the corresponding standard deviations, σ, of all the systems at 308.15 K.
A
0
A
1
A
2
A
3
A
4
σ
CH +n-butanol
V
m
E/(10−5 m3 mol−1)
24.7625
−5.7880
3.6945
−3.1381
−0.8351
0.0019
Δ
k
s/(10−10 Pa−1)
0.0183
−0.0020
0.0075
0.0029
−0.0004
0.0091
L
f
E/(10−10 m)
0.8201
−0.1460
0.2529
0.0638
0.1066
0.0009
z
E/(106 kg m−2 s−1)
−0.2875
0.0836
−0.1081
0.0006
−0.0202
0.0002
Δ
u
/(ms−1)
−1.40
0.58
−0.31
−0.03
−0.18
0.0024
CH +s
e
c-butanol
V
m
E/(10−5 m3 mol−1)
27.5896
−9.594
4.2809
−2.2460
−0.7780
0.0018
Δ
k
s/(10−10 Pa−1)
0.0267
−0.001
0.0001
0.0033
0.0034
0.0001
L
f
E/(10−10 m)
1.1507
−0.1810
0.0576
0.1082
0.0684
0.0011
z
E/(106 kg m−2 s−1)
−0.3733
0.1252
−0.0791
0.0092
−0.0110
0.0001
Δ
u
/(ms−1)
−1.94
0.59
−0.04
−0.01
−0.04
0.0006
CH +t
e
r
t-butanol
V
m
E/(10−5 m3 mol−1)
36.4535
−12.3900
−0.6780
0.1003
−0.2750
0.0009
Δ
k
s/(10−10 Pa−1)
0.0428
0.0120
0.0024
0.0019
0.0011
0.0001
L
f
E/(10−10 m)
1.8117
0.1253
0.1393
0.0862
−0.0290
0.0006
z
E/(106 kg m−2 s−1)
−0.5484
0.1374
−0.0850
0.0123
−0.0032
0.0001
Δ
u
/(ms−1)
−2.96
0.62
−0.54
0.01
−0.01
0.0001


## 4. Results and Discussion

Figure1 represents the variation of excess molar volume (V
m
E) with mole fraction of CH. The sign of V
m
E depends upon the contraction and expansion of volume of the liquids due to mixing. The factors that are mainly responsible for the expansion of molar volume, that is, positive values of V
m
E, are the following: (i) breaking of the structure of one or both of the components in a solution, that is, the loss of dipolar association between the molecules (dispersion forces); (ii) H-bond rupture and stretching of self-associated molecules (like alcohols); (iii) the geometry of molecular structures which does not favour the fitting of molecules of one component into void space of another molecule; (iv) steric hindrance of the molecules. The negative values of V
m
E are due to the (i) association of molecules through the formation of hydrogen bond, that is, strong specific interactions, and (ii) accommodation of molecules because of large differences in their molar volumes. In other words, V
m
E arises due to the result of physical, chemical, and structural contributions. Physical interactions involving mainly nonspecific interactions such as dispersion or weak forces (breaking of the liquid order on mixing, i.e., loss of dipolar association between the molecules) contribute to positive V
m
E. The chemical or specific interactions such as complex formation and hydrogen bond formation between constituent molecules contribute to negative V
m
E. The structural effects arise from interstitial accommodation due to the difference in the molar volumes and free volumes between the liquid components on mixing contributing to negative V
m
E [17]. The variation of V
m
E is found to be positive over the entire composition range in the present investigation which indicates that weak forces exist. Sri Lakshmi et al. [11] reported similar results in CH with n-heptanol, n-octanol, andiso-octanol at temperatures of 303.15, 308.15, 313.15, and 318.15 K. The V
m
E data obtained by Tsierkezos et al. [10] for CH + 1-butanol binary system are negative at 293.15 K whereas in our investigations they are found to be positive when performed at 308.15 K. Such behaviour may arise due to the fact that as temperature increases the effective collision between the component molecules increases. Thus larger number of free dipoles of component molecules may be available due to declusttering of molecules in the pure state.Figure 1
Variation of excess molar volume,V
m
E, with mole fraction, x
1, of cyclohexanone in (◆), n-butanol/(■),sec-butanol/(▲), andtert-butanol at 308.15 K and Tsierkezos et al. [10] for cyclohexanone + 1-butanol (dotted lines) at 293.15 K.The nature of interaction in binary liquids can be analysed by knowing their chemical and physical properties (physicochemical properties). Generally, butanols are associated through the hydrogen bonding as shown below and in the pure state, they exhibit equilibrium between the monomer and multimer species. Also, they can be associated with any other groups having some degree of polar attractions. As discussed earlier, butanol exhibits strong intermolecular interactions (H-bond). Alcohol size, chain length, and physical properties (boiling point, density, hydrophobic property, viscosity, insolubility, and refractive index) are important parameters that must be taken into account to explain the behaviour of the interactions (Scheme2).Scheme 2CH is a polar molecule because of the presence of carbonyl group (C=O); this is due to the fact that oxygen is more electronegative (O
-) than carbon (C+). Thus they cause strong dipole-dipole interactions in chemical reactions. Moreover CH lacks hydroxyl groups, so it is incapable of creating intermolecular hydrogen bonds. In CH + isomers of butanol binary systems, the negatively charged oxygen (O
-) in CH tries to drag the positively charged H+ which were bounded in very strong intermolecular interactions of butanol (Scheme 3). An equilibrium stage is reached where rupturing of hydrogen bond or reduction in H-bond strength of butanol or breaking of the structure of one or both of the components in a solution, that is, the loss of dipolar association between the molecules (dispersion forces) [18], will be favourable leading to weak interactions. This causes increase in volume of binary liquid and explains the observed positive values V
m
E in the systems.Scheme 3Kiyohara and Benson [19] have suggested that Δ
k
s is the resultant of several opposing effects. Negative values of Δ
k
s contribute to charge transfer, dipole-induced dipole and dipole-dipole interactions, interstitial accommodation, and breaking up of the alcohol structures leads to positive values of Δ
k
s. From Figure 2, the observed positive values of Δ
k
s for binary mixtures of CH with n-butanol, s
e
c-butanol, and t
e
r
t-butanol are due to declustering of alcohols in the presence of CH. The positive deviation in Δ
k
s for the binary systems follows the order CH +, t
e
r
t-butanol > s
e
c-butanol > n-butanol. Figure 3 represents the variation of L
f
E with mole fraction (x
1) of CH. The observed values of L
f
E are positive. According to Fort and Moore [20], positive L
f
E should be attributed to the dispersive forces. As mentioned earlier, positive values of Δ
k
s and L
f
E are mainly attributed to weak forces between the component molecules in the mixture [21].Figure 2
Variation of deviation in adiabatic compressibility,Δ
k
s, with mole fraction, x
1, of cyclohexanone in (◆), n-butanol/(■),sec-butanol/(▲), andtert-butanol at 308.15 K.Figure 3
Variation of excess free length,L
f
E, with mole fraction, x
1, of cyclohexanone in (◆), n-butanol/(■),sec-butanol/(▲), andtert-butanol at 308.15 K.The variations of excess acoustic impedance (z
E) and deviation in ultrasonic speed (Δ
u) have been presented in Figures 4 and 5, respectively. From Figure 4, it has been observed that the values of z
E are negative over the entire mole fraction range indicating the decreasing strength of interactions between component molecules of the mixture. According to Gowrisankar et al. [22], the negative values for Δ
u indicate the decrease in the strength of interaction between the molecules and the negative deviations in Δ
u from linear dependence suggest the presence of weak interaction between the component molecules. These deviation/excess properties further support the conclusions drawn from V
m
E, L
f
E, and Δ
k
s.Figure 4
Variation of excess acoustic impedance,z
E, with mole fraction, x
1, of cyclohexanone in (◆), n-butanol/(■),sec-butanol/(▲), andtert-butanol at 308.15 K.Figure 5
Variation of deviation in ultrasonic speed,Δ
u, with mole fraction, x
1, of cyclohexanone in (◆), n-butanol/(■),sec-butanol/(▲), andtert-butanol at 308.15 K.The existing molecular interactions in the systems are well reflected in the properties of partial molar volumes. The partial molar volumesV
-
m
,
1 of component 1 (CH) and V
-
m
,
2 of component 2 (isomers of butanol) in the mixtures over the entire composition range have been calculated by using the following relations:
(9)
V
-
m
,
1
=
V
m
E
+
V
1
*
+
x
2
∂
V
m
E
∂
x
T
,
P
,
V
-
m
,
2
=
V
m
E
+
V
2
*
+
x
1
∂
V
m
E
∂
x
T
,
P
,
where V
1
* and V
2
* are the molar volumes of the pure components of CH and butanols, respectively. The derivates in the above equations are obtained by differentiating Redlich-Kister equation (7) which leads to the following equations for V
-
m
,
1 and V
-
m
,
2:
(10)
V
-
m
,
1
=
V
1
*
+
x
2
2
∑
i
=
0
j
A
i
x
2
-
x
1
i
-
2
x
1
x
2
2
∑
i
=
1
j
A
i
x
2
-
x
1
i
-
1
,
(11)
V
-
m
,
2
=
V
2
*
+
x
1
2
∑
i
=
0
j
A
i
x
2
-
x
1
i
+
2
x
2
x
1
2
∑
i
=
1
j
A
i
x
2
-
x
1
i
-
1
;
using the above equations V
-
m
,
1
E, V
-
m
,
2
E have been calculated using
(12)
V
-
m
,
1
E
=
V
-
m
,
1
-
V
1
*
,
V
-
m
,
2
E
=
V
-
m
,
2
-
V
2
*
.
The pertinent values of V
-
m
,
1 and V
-
m
,
2 are furnished in Table 4. From this table, the values of V
-
m
,
1 and V
-
m
,
2 for both the components in the mixtures are greater than their respective molar volumes in the pure state; that is, an expansion of volume takes place on mixing alcohols with ketone. These results also support the observed positive values of V
m
E in all the binary systems. Figures 6 and 7 represent the variation of excess partial molar volumes of V
-
m
,
1
E (CH), V
-
m
,
2
E (isomers of butanol) in the binary mixtures. Examination of these figures reveals that dispersion forces exist between the unlike molecules. These figures support the conclusions drawn from V
m
E. The partial molar volumes and excess partial molar volumes of CH and isomers of butanols in all the binary liquid mixtures at infinite dilution, V
-
m
,
1
∞, V
-
m
,
2
∞, V
-
m
,
1
E
,
∞, and V
-
m
,
2
E
,
∞, respectively, were obtained by putting x
=
0 in (10) and x
=
1 in (11). Consider
(13)
V
-
m
,
1
E
,
∞
=
A
0
+
A
1
+
A
2
+
A
3
+
⋯
=
V
-
m
,
1
∞
-
V
1
*
,
V
-
m
,
2
E
,
∞
=
A
0
-
A
1
+
A
2
-
A
3
+
⋯
=
V
-
m
,
2
∞
-
V
2
*
.
The pertinent values of V
-
m
,
1
∞, V
-
m
,
2
∞, V
-
m
,
1
E
,
∞, and V
-
m
,
2
E
,
∞ are reported in Table 5. From this table it is seen that these values are positive, from which we conclude that weak interactions exist among the unlike molecules of the liquid mixtures.Table 4
Partial molar volumes of CH (V
-
m
,
1/10−5 m3 mol−1) and butanols (V
-
m
,
2/10−5 m3 mol−1) of all the binary systems with mole fraction (x
1) of CH at 308.15 K.
CH +n-butanol
CH +s
e
c-butanol
CH +t
e
r
t-butanol
x
1
V
-
m
,
1
V
-
m
,
2
x
1
V
-
m
,
1
V
-
m
,
2
x
1
V
-
m
,
1
V
-
m
,
2
1.0000
7.210
42.676
1.0000
7.210
49.234
1.0000
7.210
54.612
0.9121
7.699
32.512
0.9212
7.681
38.378
0.9221
7.606
44.590
0.8854
7.999
30.035
0.8867
8.130
34.445
0.8895
7.997
40.788
0.7211
10.600
19.303
0.7121
11.586
20.460
0.7012
12.366
23.413
0.6687
11.554
17.041
0.6786
12.354
18.636
0.6814
12.989
22.023
0.5232
14.365
12.385
0.5123
16.219
12.221
0.5112
19.004
13.087
0.4752
15.378
11.198
0.4688
17.234
11.058
0.4777
20.247
11.893
0.3231
19.092
8.232
0.3121
20.995
8.043
0.3321
25.389
8.416
0.2112
22.264
6.843
0.2797
21.794
7.619
0.2635
27.459
7.562
0.1313
24.403
6.314
0.1112
25.586
6.406
0.1323
30.211
6.874
0.0000
25.905
6.128
0.0000
26.462
6.307
0.0000
30.421
6.823Table 5
Partial molar volumes (V
-
m
,
1
∞, V
-
m
,
2
∞) and excess partial molar volumes (V
-
m
,
1
E
,
∞, V
-
m
,
2
E
,
∞) of the components at infinite dilution for all the systems at 308.15 K.
System
V
-
m
,
1
∞
V
-
m
,
2
∞
V
-
m
,
1
E
,
∞
V
-
m
,
2
E
,
∞
/(10−5 m3 mol−1)
CH +n
-butanol
25.519
43.758
18.696
36.548
CH +s
e
c
-butanol
25.561
50.9205
19.253
42.933
CH +t
e
r
t
-butanol
30.034
55.000
23.211
47.790Figure 6
Variation of excess partial molar volume,V
-
m
,
2
E, with mole fraction, x
1, of cyclohexanone in (◆), n-butanol/(■),sec-butanol/(▲), andtert-butanol at 308.15 K.Figure 7
Variation of excess partial molar volume,V
-
m
,
1
E, with mole fraction, x
1, of cyclohexanone in (◆), n-butanol/(■),sec-butanol/(▲), andtert-butanol at 308.15 K.FT-IR spectra of pure CH, butanols, and binary mixtures of CH with butanols at equal concentrations are depicted in Figures8, 9, and 10. According to Karunakar and Srinivas [23], the intensity of an absorption in the IR spectrum is related to the change in dipole moment that occurs during the vibration. Consequently, vibrations that produce a large change in dipole moment (e.g., C=O stretch) result in a more intense absorption than those that result in a relatively modest change in dipole (e.g., C=C). Vibrations that do not result in a change in dipole moment (e.g., a symmetrical alkyne C≡C stretch) will show little or no absorption for this vibration. In the present FT-IR spectra liquid mixture shows very small variations in the intensity of the respective bonds, that is, dipole moment, and hence it supports that weak interactions take place between the components of liquid molecules.Figure 8
Fourier transform infrared spectra of pure cyclohexanone (red), cyclohexanone andn-butanol in the ratio 5 : 5 (green), and pure n-butanol (blue).Figure 9
Fourier transform infrared spectra of pure cyclohexanone (red), cyclohexanone andsec-butanol in the ratio 5 : 5 (green), and puresec-butanol (blue).Figure 10
Fourier transform infrared spectra of pure cyclohexanone (red), cyclohexanone andtert-butanol in the ratio 5 : 5 (green), and puretert-butanol (blue).Theoretical evaluation of ultrasonic speed in binary liquid mixtures and its correlation to study molecular interaction has been successfully done in recent years. Ultrasonic speeds in liquid mixtures have been calculated and compared with experimental values using various theories. Such an evaluation offers a simple method to investigate molecular interactions besides verifying the applicability of various theories to liquid mixtures.Nomoto [24] established the following relation for sound speed (U
N) based on the assumption of the linearity of the molecular sound speed and the additivity of molar volume:
(14)
U
N
=
∑
x
i
R
i
∑
x
i
V
i
3
,
where R
i is molar sound speed and V
i is molar volume.van Dael and Vangeel [25] obtained the ideal mixture relation
(15)
∑
x
i
M
i
u
i
2
=
1
∑
x
i
M
i
1
U
V
2
.
Baluja and Parsania [26] have given impedance relation on the basis of force of resistance for sound speed by the interacting molecules
(16)
U
imp
=
∑
x
i
Z
i
∑
x
i
ρ
i
.
Rao’s (specific sound speed) [27] relation is given by
(17)
U
R
=
∑
x
i
r
i
ρ
3
,
where r
i
=
u
i
1
/
3
/
ρ
i is Rao’s specific sound speed of ith component of the mixture.Percentage deviation in ultrasonic speed is given by(18)
%
Δ
u
=
100
*
1
-
U
cal
u
exp
⁡
t
.
Table 6 shows the values of ultrasonic speed computed by various theories along with their percentage error for all the systems. The variations between the evaluated and experimental values may be due to interactions occurring between the hetero molecules of the binaries. From the observed values of all three systems, there is a good agreement between theoretical and experimental values through van Deal and Vangeel relation. It can be seen from Table 6 that the theoretical values of ultrasonic speed calculated by using various theories show deviation from experimental values. The limitations and approximation incorporated in these theories are responsible for the deviations of theoretical values from experimental values. Nomoto’s theory proposes that the volume does not change upon mixing. Therefore, no interaction between the components of liquid mixtures has been taken into account. Similarly, the assumption for the formation of ideal mixing relation is that the ratios of specific heats of ideal mixtures and the volumes are also equal. Again no molecular interactions are taken into account. But upon mixing, interactions between the molecules occur because of the presence of various types of forces such as dispersion forces, charge transfer, and hydrogen bonding dipole-dipole and dipole-induced dipole interactions. Thus, the observed deviation of theoretical values of speed from the experimental values shows that the molecular interactions are taking place between the CH and isomers of butanol molecules. The deviations of experimental values and values calculated from impedance relation and Rao’s relation imply nonadditivity of acoustic impedance and Rao’s speed in the liquid mixtures. Among all the empirical theories van Dael and Vangeels relation gives better estimate of experimental values of sound speed in all the systems. In the present binary systems, the difference between experimental and theoretical speeds is greater where the mole fraction of CH varies in the region 0.3 to 0.6. Hence it can be qualitatively inferred that the strength of interaction in the binary mixtures is more in this range of composition of CH with isomers of butanol liquid system.Table 6
Theoretical values of ultrasonic speed from various equations and percentage error with mole fractionx
1 of CH for all binary systems at 308.15 K.
x
1
U
N
U
V
U
Imp
U
R
%U
N
%U
V
%U
Imp
%U
R
CH +n-butanol
1.0000
1362.00
1362.00
1362.00
1362.00
0.00
0.00
0.00
0.00
0.9121
1350.01
1345.47
1350.43
1298.06
1.43
1.09
1.46
2.48
0.8854
1346.32
1340.60
1346.87
1283.17
1.77
1.33
1.81
3.01
0.7211
1323.09
1311.99
1324.27
1221.96
3.05
2.18
3.14
4.83
0.6687
1315.49
1303.34
1316.81
1209.73
3.22
2.27
3.32
5.08
0.5232
1293.86
1280.42
1295.42
1185.02
3.33
2.26
3.46
5.36
0.4752
1286.56
1273.19
1288.14
1178.71
3.17
2.10
3.30
5.48
0.3231
1262.83
1251.29
1264.29
1163.93
2.61
1.68
2.73
5.42
0.2112
1244.78
1236.09
1245.94
1161.66
1.96
1.25
2.05
4.85
0.1313
1231.58
1225.67
1232.39
1168.83
1.35
0.86
1.42
3.82
0.0000
1209.30
1209.30
1209.30
1209.30
0.00
0.00
0.00
0.00
CH +s
e
c
-butanol
1.0000
1362.00
1362.00
1362.00
1362.00
0.00
0.00
0.00
0.00
0.9212
1348.36
1344.12
1349.36
1284.64
1.44
1.12
1.52
3.35
0.8867
1342.34
1336.50
1343.75
1258.30
1.98
1.53
2.08
4.41
0.7121
1311.30
1299.73
1314.35
1172.55
3.82
2.91
4.06
7.16
0.6786
1305.24
1293.00
1308.52
1162.63
4.02
3.04
4.28
7.35
0.5123
1274.65
1260.97
1278.60
1131.58
4.33
3.21
4.65
7.38
0.4688
1266.50
1252.96
1270.49
1127.05
4.22
3.10
4.55
7.26
0.3121
1236.66
1225.24
1240.27
1120.04
3.38
2.43
3.69
6.37
0.2797
1230.39
1219.72
1233.81
1120.51
3.13
2.23
3.41
6.08
0.1112
1197.22
1192.10
1199.01
1138.85
1.41
0.98
1.56
3.53
0.0000
1174.80
1174.80
1174.80
1174.80
0.00
0.00
0.00
0.00
CH +t
e
r
t-butanol
1.0000
1362.00
1362.00
1362.00
1362.00
0.00
0.00
0.00
0.00
0.9221
1340.13
1335.38
1344.13
1269.23
2.09
1.73
2.40
3.31
0.8895
1330.99
1324.56
1336.51
1236.00
2.83
2.33
3.25
4.51
0.7012
1278.40
1265.44
1290.65
1095.88
5.61
4.54
6.63
9.46
0.6814
1272.89
1259.53
1285.64
1085.50
5.78
4.67
6.84
9.80
0.5112
1225.70
1211.04
1240.87
1023.59
6.33
5.06
7.64
11.21
0.4777
1216.45
1201.95
1231.70
1016.61
6.27
5.01
7.61
11.19
0.3321
1176.38
1164.00
1190.36
1004.06
5.48
4.37
6.74
9.97
0.2635
1157.60
1146.96
1170.00
1007.94
4.80
3.84
5.92
8.75
0.1323
1121.83
1115.75
1129.39
1033.39
2.89
2.33
3.58
5.23
0.0000
1086.00
1086.00
1086.00
1086.00
0.00
0.00
0.00
0.00


## 5. Conclusion

(i)
Ultrasonic speeds,u, and densities, ρ, of mixtures of cyclohexanone with n-butanol orsec-butanol ortert-butanol over the entire composition range have been measured at T
=
308.15 K.
(ii)
The values ofV
m
E, Δ
k
s, L
f
E, z
E, and Δ
u are calculated from experimental data of density and ultrasonic speed. The excess and deviation properties have been fitted to Redlich-Kister type polynomial and corresponding standard deviations have been evaluated. The observed positive values of V
m
E, Δ
k
s, and L
f
E and negative values of z
E, Δ
u for all the liquid mixtures studied clearly indicate the presence of weak interactions such as rupturing of hydrogen bond or reduction in H-bond strength of butanol or breaking of the structure of one or both of the components in a solution.
(iii)
The deviation/excess properties have been fitted to Redlich-Kister type polynomial and the corresponding standard deviations have been calculated.
(iv)
The calculated values of partial molar volumes have also been examined. The observed higher partial molar volumes in the liquid mixture when compared to the respective molar volumes of pure components indicate weak interactions present in the systems.
(v)
The strength of interaction in the mixtures follows the order CH +,tert-butanol >sec-butanol > n-butanol.
(vi)
FT-IR spectra for the present binary mixture also support the conclusions drawn from theV
m
E, L
f
E, Δ
k
s, Δ
u, and z
E.
(vii)
Further theoretical values of sound speed in the mixtures have been evaluated using various theories and have been compared with experimental sound speeds to verify the applicability of such theories to the systems studied.



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*Source: 741795-2014-12-18.xml*