viscometric, acoustical and spectroscopic investigation of β-pinene with benzene, toluene, m-xylene...
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Viscometric, Acoustical and Spectroscopic Investigationof b-Pinene with Benzene, Toluene, m-Xyleneand Mesitylene at 303.15, 308.15 and 313.15 Kand Atmospheric Pressure
Jasmin Bhalodia • Sangita Sharma
Received: 7 November 2012 / Accepted: 23 April 2013 / Published online: 26 September 2013� Springer Science+Business Media New York 2013
Abstract The densities (q), viscosities (g), ultrasonic speeds (u) and spectroscopic data of
binary mixtures of benzene, toluene, m-xylene and mesitylene with b-pinene as a common
component, over the whole composition range of mole fraction of b-pinene including those of
pure components, have been measured at 303.15, 308.15 and 313.15 K, except for the
spectroscopic study where the temperature was maintained at 298.15 K. The experimental
results deviation in viscosity, deviation in ultrasonic velocity, isentropic compressibility and
deviation in isentropic compressibility are discussed in terms of molecular interactions
between unlike molecules. The variation of these excess parameters indicates the presence of
weak interactions between b-pinene and benzene, toluene, m-xylene and mesitylene mole-
cules. Moreover, the viscosity data are discussed in terms of interaction parameters. The
theoretical ultrasonic speed was computed using the Nomoto model, ideal mixing relation,
Jacobson’s free length theory and compared with the experimentally measured values. The
experimental values are also discussed in terms of FTIR spectroscopy.
Keywords b-Pinene � Aromatic hydrocarbons � Deviation function �Interaction parameter � Theoretical ultrasound � FTIR
1 Introduction
Solution state studies have great impact on chemical engineering and relevant fields, and
results of these studies are currently used in design of many chemical and industrial
processes. The present work is in continuation of our earlier solution state studies of binary
mixtures having one of the components of cajuput oil with different organic solvents
having several industrial applications [1, 2].
The use of this essential oil and its component in chemical industries is widely due to
the green chemistry approach. b-Pinene has been used as an antimicrobial agent because of
its growth inhibition effect against micro-organisms [3, 4]. In addition to being an
J. Bhalodia � S. Sharma (&)Department of Chemistry, Hemchandracharya North Gujarat University, Patan 384265, Indiae-mail: [email protected]
123
J Solution Chem (2013) 42:1794–1815DOI 10.1007/s10953-013-0073-z
antimicrobial agent, b-pinene is also used as a poly-b-pinene in rubber-based pressure
sensitive adhesives and in many other chemical reactions involving organic aerosols [5, 6].
A literature survey shows that less work has been done for b-pinene in terms of molecular
interactions and solution state studies [7, 8]. Mixtures of benzene, toluene, m-xylene and
mesitylene with b-pinene have not been studied using volumetric, viscometric and acoustic
studies. Therefore, a study on intermolecular interactions of b-pinene with aromatic hydro-
carbons would be interesting because of its industrial relevance and applications.
In this paper, we report the density, viscosity and ultrasonic speed of pure b-pinene,
benzene, toluene, m-xylene, mesitylene and those of their binary mixtures over the entire
composition range at 303.15, 308.15 and 313.15 K. FTIR spectra of these systems have
also been recorded at 298.15 K. From these experimental data, the deviation functions,
isentropic compressibility and intermolecular free length have been calculated and are
discussed in terms of molecular interactions between the unlike molecules. Furthermore,
the viscosity data were corrected using McAllister’s [9] three body correction parameter
and are discussed in terms of interaction parameters from the Dolezalek–Schulze [10],
Grunberg–Nissan [11] and Tamura–Kurata’s [12] methods. Acoustical data were validated
by comparing experimental values with evaluated values by using the Nomoto’s (NMT)
relation [13], the ideal mixture relation (IMR) [14, 15] and free length theory (FLT) [16].
2 Experimental
2.1 Materials
b-Pinene was imported from Sigma-Aldrich (Germany) having purity (99.9 %), and aro-
matic hydrocarbons (benzene, toluene, m-xylene and mesitylene) were purchased from S.
D. Fine (India) having purities (toluene C99.0 %, o-xylene C99.5 %, m-xylene C99.5 %
and p-xylene C99.9 %). All compounds were degassed prior to use. The purity of the
component liquids was ensured by gas chromatography and verified by comparing mea-
sured densities and boiling points of the components with those reported in the literature
[17]. The data on measured density, viscosity and ultrasonic speed along with the literature
[7, 18–49] values are given in Table 1.
2.2 Density Measurements
Densities accurate to ±0.0001 g�cm-3 were measured by using a pycnometer of bulb
volume 10 cm3 and capillary orifice with internal diameter 1 mm. The pycnometer filled
with required liquid was kept in a waterbath (High Precision Water Bath, Cat No. MSW-
274, NSW, India) with thermal stability ±0.01 K, which was checked using a calibrated
thermometer, to attain the equilibrium. An average of three measurements was taken into
account and their reproducibility is within of ±0.3 %.
2.3 Viscosity Measurements
The kinematic viscosities of both the pure liquids and liquid mixtures were measured at
303.15, 308.15 and 313.15 K at atmospheric pressure with an Ubbelohde suspended level
viscometer. During use the viscometer is filled with a liquid or liquid mixture, and its limbs
closed with Teflon caps to minimize the evaporation. The caps of the limbs were removed
during the measurements of the flow time. The flow time measurements were made using
J Solution Chem (2013) 42:1794–1815 1795
123
an electronic stopwatch with a precision of ±0.01 s. The arithmetic mean of four sets of
flow times for each sample mixture was taken for the purpose of calculation of viscosity.
The calibration of the viscometer was carried out with double distilled water and two
constants A and B of the viscometer in the equation (m = g/q = (At-B/t)) were obtained at
303.15, 308.15 and 313.15 K. The measured values of the kinematic viscosities (m) were
converted to dynamic viscosities (g) by multiplication by the density (q). The uncertainties
of the viscosity measurements are ±0.1 %.
2.4 Ultrasonic Speed Measurements
The speed of sound values were measured using a variable path single-crystal interfer-
ometer model M-81S supplied by Mittal Enterprises, New Delhi, with an accuracy
±2 m�s-1. In the present study the frequency 2 MHz was employed and the instrument
was calibrated using water and benzene.
Table 1 Comparison of experimental densities (q), viscosities (g) and ultrasonic speeds (u), of pure liquidswith their corresponding literature values at 303.15, 308.15 and 313.15 K
Compound T/K q (g�cm-3) g (mPa�s) u (m�s-1)
Experimental Literature Experimental Literature Experimental Literature
b-Pinene 303.15 0.8616 0.86195 [18] 1.420 - 1,280 1,278.6 [19]
0.86231 [20] - -
308.15 0.8586 0.8580 [21] 1.312 - 1,258 -
313.15 0.8548 0.85487 [19] 1.206 - 1,235 1,236.3 [19]
0.85395 [18] - 1,237.4 [7]
Benzene 303.15 0.8683 0.8678 [22] 0.563 0.5640 [23] 1,276 1,276 [24]
0.86823 [25] 0.5625 [26] 1,277 [27]
308.15 0.8,626 0.8624 [22] 0.538 0.5232 [23] 1,256 1,257 [28]
0.8632 [29] 0.528 [30] 1,252 [31]
313.15 0.8574 0.85738 [25] 0.506 0.5001 [23] 1,230 1,230 [24]
0.85746 [32] 0.4921 [26] -
Toluene 303.15 0.8575 0.85755 [33] 0.522 0.5226 [34] 1,282 1,289 [35]
0.85770 [24] 0.5253 [23] 1,276 [36]
308.15 0.8528 0.85285 [33] 0.493 0.4920 [34] 1,260 1,258 [31]
0.8518 [37] 0.4933 [23] 1,262 [29]
313.15 0.8483 0.84836 [33] 0.465 0.4659 [34] 1,240 1,240 [38]
0.84844 [24] 0.4717 [23] 1,239 [39]
m-Xylene 303.15 0.8556 0.85579 [40] 0.554 0.5490 [23] 1,307 1,303 [41]
0.85581 [17] 0.555 [42] -
308.15 0.8515 0.85155 [43] 0.525 0.5201 [23] 1,280 1,281 [44]
0.85157 [40] 0.5229 [28] 1,283 [45]
313.15 0.8467 0.84669 [40] 0.498 0.4967 [23] 1,255 -
0.84717 [46] 0.4780 [47] -
Mesitylene 303.15 0.8571 0.8571 [45] 0.623 0.622 [45] 1315 -
0.85754 [48] - -
308.15 0.8543 0.8530 [45] 0.586 0.586 [45] 1295 1,303.5 [31]
0.85363 [48] 0.5792 [28] -
313.15 0.8498 0.84971 [48] 0.543 - 1,276 -
0.84971 [49] -
1796 J Solution Chem (2013) 42:1794–1815
123
2.5 Infrared Spectroscopy
FTIR measurements of b-pinene with the aromatic hydrocarbons were made using an
ALPHA FTIR Spectrometer (Bruker, Germany). A spectroscopic liquid cell equipped with
KBr optical windows was used to carry out the spectral analysis. The samples were
prepared by mixing of b-pinene with aromatic hydrocarbons in 1:1 ratios. The spectra were
corrected for the water vapor and CO2 contributions and accumulated over the spectral
range 4,000–500 cm-1 with a nominal resolution of 2 cm-1 using four scans at 298.15 K.
3 Results and Discussion
The experimental values of density are given in Table 1 at 303.15, 308.15 and 313.15 K
[1]. The experimental values of g and u of b-pinene along with those of the aromatic
hydrocarbons are given in Tables 2 and 3 in addition to experimental values for the
mixtures.
The deviations in viscosity (Dg) were calculated from the relationship:
Dg ¼ g� x1g1 � x2g2 ð1Þ
where g is the viscosity of the mixture, while g1 and g2 are the viscosities of b-pinene and
the aromatic hydrocarbon, respectively.
The isentropic compressibility (ks), deviations in isentropic compressibility (Dks) and
deviations in speed of sound (Du) are obtained from the equations,
ks ¼ ðqu2Þ�1 ð2Þ
Dks ¼ ks � /1ks;1 � /2ks;2 ð3Þ
Du ¼ u� x1u1 � x2u2 ð4Þ
where q, u, ks denote the density, ultrasound speed and isentropic compressibility of a
mixture, and ui, xi and /i denote ultrasound velocity, mole fraction and volume fraction of
ith component, respectively.
The deviation of Dg, Du and Dks were fitted in the Redlich–Kister polynomial [50]:
YE ¼ x1ð1� x1ÞXn
i¼0
Aið2x1 � 1Þi ð5Þ
where YE = (Dg, Dks and Du) and x1 is the mole fraction of the first component. The co-
efficient Ai was calculated by the unweighted least squares method. In each case, the
optimum number of coefficients was ascertained from examination of the variation in
standard deviation in YE of Eq. 5. The standard deviation (r) was calculated using the
following equation:
rðYÞ ¼PðYE
exp � YEcalÞ
2
ðN � pÞ
" #12
ð6Þ
where, YEexp is the experimentally derived excess (or deviation) function. YE
cal is the cal-
culated value of the function. N is the number of experimental points and p is the number
of coefficients used to fit the data. The estimated values of Ai and r for YE versus x1 are
J Solution Chem (2013) 42:1794–1815 1797
123
Table 2 Mole fractions (x1), viscosities (g) and deviation in viscosities (Dg) for binary mixtures of b-pinene with aromatic hydrocarbons at 303.15, 308.15 and 313.15 K
x2 g (mPa�s) Dg (mPa�s) g (mPa�s) Dg (mPa�s) g (mPa�s) Dg (mPa�s)T = 303.15 K T = 308.15 K T = 313.15 K
b-Pinene (2) ? benzene (1)
1.0000 0.573 -0.041 0.554 -0.030 0.522 -0.025
0.9405 0.593 -0.077 0.566 -0.068 0.537 -0.056
0.8754 0.614 -0.117 0.587 -0.103 0.556 -0.088
0.8039 0.646 -0.153 0.619 -0.132 0.583 -0.115
0.7249 0.691 -0.183 0.655 -0.163 0.614 -0.146
0.6373 0.759 -0.199 0.710 -0.185 0.658 -0.170
0.5395 0.867 -0.185 0.807 -0.173 0.749 -0.156
0.4296 0.998 -0.160 0.936 -0.140 0.866 -0.126
0.3052 1.187 -0.093 1.106 -0.079 1.022 -0.069
b-Pinene (2) ? toluene (1)
1.0000 0.539 -0.046 0.512 -0.038 0.486 -0.031
0.9298 0.564 -0.088 0.536 -0.076 0.505 -0.068
0.8547 0.595 -0.130 0.565 -0.113 0.534 -0.098
0.7744 0.633 -0.169 0.595 -0.153 0.560 -0.136
0.6881 0.684 -0.201 0.642 -0.183 0.598 -0.166
0.5953 0.754 -0.222 0.703 -0.203 0.654 -0.185
0.4951 0.860 -0.212 0.803 -0.192 0.745 -0.174
0.3867 0.995 -0.184 0.930 -0.162 0.863 -0.144
0.2689 1.188 -0.106 1.112 -0.085 1.027 -0.075
b-Pinene (2) ? m-xylene (1)
1.0000 0.572 -0.052 0.547 -0.042 0.522 -0.033
0.9198 0.602 -0.094 0.568 -0.087 0.542 -0.072
0.8359 0.637 -0.135 0.600 -0.123 0.563 -0.113
0.7482 0.682 -0.170 0.639 -0.156 0.593 -0.148
0.6564 0.737 -0.198 0.685 -0.186 0.637 -0.173
0.5602 0.799 -0.224 0.748 -0.203 0.697 -0.184
0.4592 0.915 -0.200 0.850 -0.184 0.787 -0.169
0.3531 1.049 -0.162 0.980 -0.142 0.910 -0.125
0.2415 1.225 -0.088 1.137 -0.078 1.050 -0.069
b-Pinene (2) ? mesitylene (1)
1.0000 0.633 -0.061 0.597 -0.055 0.555 -0.047
0.9103 0.661 -0.107 0.622 -0.096 0.576 -0.087
0.8185 0.696 -0.147 0.653 -0.133 0.606 -0.120
0.7245 0.743 -0.176 0.695 -0.161 0.645 -0.144
0.6283 0.799 -0.198 0.749 -0.179 0.698 -0.156
0.5299 0.871 -0.207 0.819 -0.181 0.768 -0.154
0.4290 0.981 -0.180 0.915 -0.160 0.854 -0.136
0.3257 1.108 -0.137 1.032 -0.120 0.959 -0.101
0.2198 1.254 -0.077 1.167 -0.064 1.082 -0.051
1798 J Solution Chem (2013) 42:1794–1815
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Table 3 Mole fractions (x2), volume fractions (/2), densities (q), ultrasonic speeds (u), deviations inultrasonic speeds (Du), and ucal by various theoretical models, isentropic compressibilities (ks) and devia-tions in isentropic compressibilities (Dks) of the binary mixture of b-pinene with aromatic hydrocarbons at303.15, 308.15 and 313.15 K
x2 /2 q(g�cm-3)
u (m�s-1) Du (m�s-1) uNMT
(m�s-1)
uIMR
(m�s-1)
uFLT
(m�s-1)
ks
(T�Pa-1)
Dks
(T�Pa-1)
b-Pinene (2) ? benzene (1)
T = 303.15 K
0.9405 0.9000 0.8674 1,273 -3 1,276 1,265 1,274 712 5
0.8754 0.8000 0.8666 1,270 -6 1,277 1,255 1,273 715 8
0.8039 0.7000 0.8658 1,269 -8 1,277 1,246 1,271 717 10
0.7249 0.6000 0.8650 1,268 -9 1,278 1,238 1,271 720 12
0.6373 0.5000 0.8644 1,267 -11 1,278 1,233 1,272 721 14
0.5395 0.4000 0.8639 1,266 -11 1,278 1,230 1,274 722 14
0.4296 0.3000 0.8633 1,269 -10 1,279 1,231 1,275 720 12
0.3052 0.2000 0.8628 1,271 -7 1,279 1,237 1,277 717 9
0.1633 0.1000 0.8622 1,275 -4 1,280 1,252 1,278 713 6
T = 308.15 K
0.9405 0.9000 0.8619 1,253 -3 1,256 1,245 1,254 738 3
0.8754 0.8000 0.8613 1,252 -5 1,256 1,235 1,253 741 6
0.8039 0.7000 0.8607 1,250 -6 1,257 1,226 1,252 744 8
0.7249 0.6000 0.8602 1,248 -8 1,257 1,218 1,251 746 11
0.6373 0.5000 0.8599 1,247 -10 1,257 1,213 1,252 748 12
0.5395 0.4000 0.8597 1,247 -10 1,257 1,210 1,253 749 13
0.4296 0.3000 0.8594 1,249 -9 1,257 1,211 1,254 747 11
0.3052 0.2000 0.8592 1,251 -6 1,258 1,217 1,256 743 7
0.1633 0.1000 0.8589 1,255 -3 1,258 1,231 1,257 739 3
T = 313.15 K
0.9405 0.9000 0.8568 1,228 -2 1,230 1,219 1,229 773 3
0.8754 0.8000 0.8563 1,227 -3 1,231 1,210 1,228 775 5
0.8039 0.7000 0.8558 1,226 -5 1,231 1,201 1,227 777 8
0.7249 0.6000 0.8554 1,225 -6 1,232 1,194 1,227 779 9
0.6373 0.5000 0.8553 1,224 -8 1,232 1,188 1,228 781 12
0.5395 0.4000 0.8552 1,223 -9 1,233 1,186 1,230 781 13
0.4296 0.3000 0.8551 1,225 -8 1,233 1,187 1,231 779 11
0.3052 0.2000 0.8550 1,228 -5 1,234 1,193 1,232 775 7
0.1633 0.1000 0.8549 1,232 -2 1,234 1,208 1,234 771 3
b-Pinene (2) ? toluene (1)
T = 303.15 K
0.9298 0.9000 0.8568 1,277 -5 1,282 1,275 1,279 716 6
0.8547 0.8000 0.8569 1,274 -8 1,282 1,270 1,276 719 10
0.7744 0.7000 0.8570 1,270 -11 1,281 1,265 1,273 723 14
0.6881 0.6000 0.8573 1,267 -14 1,281 1,261 1,272 726 17
0.5953 0.5000 0.8577 1,264 -17 1,281 1,258 1,271 730 21
0.4951 0.4000 0.8584 1,262 -19 1,281 1,257 1,272 732 23
0.3867 0.3000 0.8591 1,266 -15 1,281 1,258 1,273 727 18
0.2689 0.2000 0.8600 1,270 -11 1,280 1,262 1,276 721 13
0.1405 0.1000 0.8610 1,274 -6 1,280 1,269 1,279 715 7
J Solution Chem (2013) 42:1794–1815 1799
123
Table 3 continued
x2 /2 q(g�cm-3)
u (m�s-1) Du (m�s-1) uNMT
(m�s-1)
uIMR
(m�s-1)
uFLT
(m�s-1)
ks
(T�Pa-1)
Dks
(T�Pa-1)
T = 308.15 K
0.9298 0.9000 0.8513 1,256 -3 1,260 1,254 1,257 744 5
0.8547 0.8000 0.8516 1,253 -7 1,260 1,248 1,254 748 9
0.7744 0.7000 0.8520 1,250 -9 1,259 1,243 1,252 751 12
0.6881 0.6000 0.8526 1,247 -13 1,259 1,239 1,250 754 16
0.5953 0.5000 0.8533 1,244 -15 1,259 1,237 1,250 758 20
0.4951 0.4000 0.8542 1,242 -17 1,259 1,235 1,250 759 21
0.3867 0.3000 0.8552 1,246 -13 1,259 1,236 1,251 753 16
0.2689 0.2000 0.8564 1,250 -8 1,258 1,240 1,254 747 10
0.1405 0.1000 0.8576 1,254 -4 1,258 1,247 1,256 741 5
T = 313.15 K
0.9298 0.9000 0.8490 1,237 -3 1,240 1,234 1,236 770 4
0.8547 0.8000 0.8491 1,234 -5 1,239 1,228 1,234 773 7
0.7744 0.7000 0.8494 1,231 -8 1,239 1,223 1,231 777 11
0.6881 0.6000 0.8497 1,227 -11 1,238 1,219 1,229 782 15
0.5953 0.5000 0.8502 1,224 -14 1,238 1,216 1,228 785 19
0.4951 0.4000 0.8510 1,222 -15 1,237 1,215 1,229 787 20
0.3867 0.3000 0.8518 1,227 -10 1,237 1,215 1,229 780 13
0.2689 0.2000 0.8529 1,230 -6 1,236 1,218 1,232 775 8
0.1405 0.1000 0.8539 1,232 -3 1,236 1,225 1,234 771 4
b-Pinene (2) ? m-xylene (1)
T = 303.15 K
0.9198 0.9000 0.8548 1,297 -8 1,304 1,302 1,297 695 8
0.8359 0.8000 0.8550 1,289 -13 1,302 1,298 1,287 704 14
0.7482 0.7000 0.8554 1,282 -19 1,299 1,294 1,279 712 20
0.6564 0.6000 0.8557 1,274 -24 1,296 1,290 1,272 720 26
0.5602 0.5000 0.8563 1,266 -29 1,293 1,287 1,269 729 32
0.4592 0.4000 0.8571 1,260 -32 1,291 1,284 1,268 734 36
0.3531 0.3000 0.8581 1,263 -26 1,288 1,282 1,270 730 29
0.2415 0.2000 0.8592 1,268 -19 1,285 1,281 1,273 724 21
0.1240 0.1000 0.8605 1,273 -11 1,283 1,280 1,277 717 12
T = 308.15 K
0.9198 0.9000 0.8500 1,273 -6 1,278 1,276 1,271 726 7
0.8359 0.8000 0.8504 1,266 -11 1,276 1,272 1,262 734 12
0.7482 0.7000 0.8509 1,259 -16 1,273 1,268 1,256 741 18
0.6564 0.6000 0.8515 1,252 -20 1,271 1,265 1,250 749 24
0.5602 0.5000 0.8522 1,245 -25 1,269 1,262 1,247 757 30
0.4592 0.4000 0.8532 1,240 -28 1,267 1,260 1,246 762 33
0.3531 0.3000 0.8544 1,243 -23 1,265 1,258 1,248 758 27
0.2415 0.2000 0.8557 1,248 -16 1,262 1,257 1,250 751 18
0.1240 0.1000 0.8572 1,253 -8 1,260 1,257 1,254 744 9
T = 313.15 K
0.9198 0.9000 0.8473 1,249 -4 1,253 1,251 1,246 756 5
0.8359 0.8000 0.8475 1,243 -9 1,251 1,247 1,238 764 11
0.7482 0.7000 0.8479 1,237 -13 1,249 1,244 1,232 771 17
1800 J Solution Chem (2013) 42:1794–1815
123
shown in Table 4. In all the cases, the best fit was obtained by using only three fitting
coefficients.
These values are plotted against the mole fraction of b-pinene in Figs. 1, 2 and 3.
In Figs. 1 and 2, the points represent the data calculated from Eqs. 1, 3 and 4 respec-
tively, while the smooth curves are drawn from the data calculation using Eq. 5. The
standard percentage deviations (r %) were calculated using the relation:
Table 3 continued
x2 /2 q(g�cm-3)
u (m�s-1) Du (m�s-1) uNMT
(m�s-1)
uIMR
(m�s-1)
uFLT
(m�s-1)
ks
(T�Pa-1)
Dks
(T�Pa-1)
0.6564 0.6000 0.8483 1,230 -18 1,247 1,241 1,227 779 23
0.5602 0.5000 0.8490 1,225 -22 1,245 1,238 1,224 786 28
0.4592 0.4000 0.8498 1,220 -24 1,243 1,236 1,223 791 31
0.3531 0.3000 0.8508 1,222 -20 1,241 1,235 1,224 787 26
0.2415 0.2000 0.8520 1,226 -14 1,239 1,234 1,227 780 17
0.1240 0.1000 0.8534 1,231 -7 1,237 1,234 1,230 773 8
b-Pinene (2) ? mesitylene (1)
T = 303.15 K
0.9103 0.9000 0.8573 1,303 -9 1,311 1,311 1,309 687 8
0.8185 0.8000 0.8574 1,292 -16 1,308 1,308 1,303 698 17
0.7245 0.7000 0.8576 1,282 -23 1,304 1,304 1,297 710 25
0.6283 0.6000 0.8578 1,273 -29 1,301 1,300 1,292 720 31
0.5299 0.5000 0.8584 1,265 -34 1,297 1,297 1,290 729 37
0.4290 0.4000 0.8590 1,257 -38 1,294 1,293 1,288 736 42
0.3257 0.3000 0.8597 1,258 -33 1,290 1,290 1,286 735 36
0.2198 0.2000 0.8603 1,262 -26 1,287 1,286 1,284 730 28
0.1113 0.1000 0.8610 1,270 -14 1,283 1,283 1,282 720 15
T = 308.15 K
0.9103 0.9000 0.8536 1,285 -7 1,291 1,291 1,288 710 7
0.8185 0.8000 0.8537 1,274 -14 1,288 1,287 1,282 721 15
0.7245 0.7000 0.8539 1,265 -20 1,284 1,283 1,276 732 22
0.6283 0.6000 0.8542 1,255 -27 1,280 1,280 1,271 744 30
0.5299 0.5000 0.8549 1,246 -32 1,276 1,276 1,268 753 36
0.4290 0.4000 0.8556 1,239 -35 1,273 1,272 1,266 761 40
0.3257 0.3000 0.8563 1,240 -30 1,269 1,269 1,264 759 35
0.2198 0.2000 0.8570 1,244 -22 1,265 1,265 1,261 754 25
0.1113 0.1000 0.8578 1,252 -10 1,262 1,261 1,260 744 11
T = 313.15 K
0.9103 0.9000 0.8499 1,266 -6 1,272 1,272 1,269 734 6
0.8185 0.8000 0.8500 1,256 -12 1,268 1,268 1,262 745 14
0.7245 0.7000 0.8501 1,246 -18 1,264 1,263 1,255 757 21
0.6283 0.6000 0.8503 1,238 -23 1,259 1,259 1,249 768 27
0.5299 0.5000 0.8510 1,228 -28 1,255 1,255 1,246 779 34
0.4290 0.4000 0.8517 1,219 -33 1,251 1,251 1,244 790 40
0.3257 0.3000 0.8524 1,221 -28 1,247 1,247 1,241 787 34
0.2198 0.2000 0.8532 1,224 -20 1,243 1,243 1,239 782 24
0.1113 0.1000 0.8540 1,231 -9 1,239 1,239 1,237 773 11
J Solution Chem (2013) 42:1794–1815 1801
123
Table 4 Adjustable parameters Ai with the standard deviations r(YE) for the deviation in viscosity (Dg),deviation in ultrasonic speed (Du) and deviation in isentropic compressibility (Dks) for the binary mixtures attemperature T
Function A0 A1 A2 A3 A4 r
b-Pinene ? benzene
T = 303.15 K
Dg (mPa�s) -0.792 0.049 0.289 -0.032 -0.223 0.0009
Du (m�s-1) -42.47 18.11 11.24 -3.68 -12.93 0.10
Dks (T�Pa-1) 55.43 11.86 -27.24 -9.15 56.54 0.53
T = 308.15 K
Dg (mPa�s) -0.720 0.039 0.251 -0.001 0.018 0.001
Du (m�s-1) -40.31 17.06 50.73 -6.01 -69.95 0.08
Dks (T�Pa-1) 49.73 19.75 -25.16 -32.03 -0.75 0.38
T = 313.15 K
Dg (mPa�s) -0.658 0.028 0.376 -0.025 -0.132 0.001
Du (m�s-1) -33.43 12.09 57.39 -3.54 -59.78 0.15
Dks (T�Pa-1) 47.91 27.91 -29.24 -44.53 9.48 0.32
b-Pinene ? toluene
T = 303.15 K
Dg (mPa�s) -0.877 -0.210 0.167 0.181 -0.023 0.0006
Du (m�s-1) -72.59 9.78 84.33 0.81 -105.50 0.17
Dks (T�Pa-1) 84.77 35.91 -59.04 -47.17 61.78 0.90
T = 308.15 K
Dg (mPa�s) -0.802 -0.192 0.263 0.241 0.029 0.0007
Du (m�s-1) -63.57 21.26 74.74 -17.94 -60.75 0.18
Dks (T�Pa-1) 79.87 30.25 -86.97 -50.38 76.96 0.85
T = 313.15 K
Dg (mPa�s) -0.726 -0.170 0.273 0.200 0.044 0.0007
Du (m�s-1) -57.18 28.87 113.31 -35.08 -128.11 0.18
Dks (T�Pa-1) 76.68 22.51 -131.50 -37.35 127.30 0.96
b-Pinene ? m-xylene
T = 303.15 K
Dg (mPa�s) -0.852 -0.247 0.270 0.294 -0.155 0.001
Du (m�s-1) -123.17 -10.92 123.65 16.42 -145.52 0.22
Dks (T�Pa-1) 130.74 66.96 -98.18 -64.83 105.56 1.12
T = 308.15 K
Dg (mPa�s) -0.782 -0.172 0.251 0.163 -0.041 0.0009
Du (m�s-1) -106.27 -15.64 98.15 33.98 -77.77 0.24
Dks (T�Pa-1) 121.97 69.06 -109.21 -89.01 89.55 1.06
T = 313.15 K
Dg (mPa�s) -0.728 -0.108 0.358 0.021 -0.105 0.0005
Du (m�s-1) -92.49 -10.71 82.95 11.87 -47.92 0.19
Dks (T�Pa-1) 114.47 62.83 -82.10 -68.70 24.73 0.91
b-Pinene ? mesitylene
T = 303.15 K
Dg (mPa�s) -0.811 -0.132 0.236 0.176 -0.239 0.0007
1802 J Solution Chem (2013) 42:1794–1815
123
rð%Þ ¼ 1
N � p
X100�
YEexp � YE
cal
YEexp
!224
35
12
ð7Þ
where Yexp and Ycal are the experimental and calculated values of viscosities. The corre-
lating abilities of the theoretical models were tested by calculating the root-mean-square
deviation (RMSD) between the experimental and calculated speed of sound as:
RMSD ¼ 1
N
� �X YEexp � YE
cal
YEexp
!224
35
1=2
ð8Þ
where N represents the number of data points.
3.1 Viscosity Study
Deviations in viscosity are negative for the mixtures containing b-pinene with aromatic
hydrocarbons. It can be seen from the Fig. 1 that the Dg values show systematic increments
Table 4 continued
Function A0 A1 A2 A3 A4 r
Du (m�s-1) -142.52 -55.46 51.20 56.85 -36.73 0.22
Dks (T�Pa-1) 150.66 79.79 -21.36 -51.11 -22.25 0.94
T = 308.15 K
Dg (mPa�s) -0.727 -0.099 0.214 0.181 -0.158 0.0001
Du (m�s-1) -132.93 -51.41 71.49 70.30 -11.63 0.20
Dks (T�Pa-1) 145.79 93.64 -45.78 -104.69 -39.83 0.80
T = 313.15 K
Dg (mPa�s) -0.628 -0.031 0.108 0.117 0.042 0.0001
Du (m�s-1) -119.88 -58.15 61.40 80.15 0.95 0.32
Dks (T�Pa-1) 139.06 96.25 -39.07 -100.16 -47.98 1.44
0.0 0.2 0.4 0.6 0.8 1.0-0.25
-0.20
-0.15
Δη(m
pa.s
)
-0.10
-0.05
0.00
x2
303.15 K
Fig. 1 Deviations in theviscosity (Dg) plotted againstmole fraction (x2) for binarymixtures b-pinene (2) ? benzene(filled square), ? toluene (filledcircle), ? m-xylene (filledtriangle), and b-pinene ?mesitylene (inverted filledtriangle) at T = 303.15 K
J Solution Chem (2013) 42:1794–1815 1803
123
for b-pinene ? benzene to m-xylene, while the b-pinene ? mesitylene mixtures do not
show a systematic increment. The deviations in viscosity for the b-pinene ? mesitylene
mixtures are less negative than those with toluene and m-xylene, but are higher than those
with benzene. For all the systems, deviations in viscosity are more negative in the aromatic
hydrocarbon rich regions.
Negative deviations, in general, indicate that these mixtures behave non-ideally due to
presences of unlike interactions. The negative values of deviation in viscosity measure-
ments for these mixtures suggest that interactions in the pure compounds are weaker and
there is no important strong interaction between unlike molecules [51]. Aromatic hydro-
carbons are weak acceptors of electrons and so the expected interaction between the
aromatic ring of the hydrocarbon and the allyl group of the b-pinene is quite weak and a p–
p interaction may take place. In the present study the methyl group increment from
benzene to mesitylene enhances the electron donating tendency and the Dg values decrease
from benzene to mesitylene, which indicates that the interaction become weaker as the
electron donating tendency increases. The presence of the geminal methyl group in b-
pinene has restricted the proper orientation of the molecules and obstructed the p–pinteraction among like molecules, thus making a new interaction among unlike molecules
possible and causing less effective packing arrangements among the molecules.
0.0 0.2 0.4 0.6 0.8 1.0-40
-30
-20
-10
0
Δu(m
.s-1
)x2
303.15 K
Fig. 2 Deviations in theultrasonic speed (Du) plottedagainst mole fraction (x2) forbinary mixtures b-pinene(2) ? benzene (filled square),? toluene (filled circle),? m-xylene (filled triangle),and b-pinene ? mesitylene(inverted filled triangle) atT = 303.15 K
0.0 0.2 0.4 0.6 0.8 1.00
5
10
15
20
25
30
35
40
45
Δks(T
P.a
-1)
φ2
303.15 KFig. 3 Deviations in theisentropic compressibility (Dks)plotted against volume fraction(/2) for binary mixtures b-pinene(2) ? benzene (filled square),? toluene (filled circle), ?m-xylene (filled triangle),and b-pinene ? mesitylene(inverted filled triangle) atT = 303.15 K
1804 J Solution Chem (2013) 42:1794–1815
123
The viscosities of all the four binary mixtures were correlated and predicted theoreti-
cally in terms of pure component data by using various theoretical relations. The following
theoretical models have been tested for the mixtures under study and presented in Tables 5
and 6.
(i) The McAllister equation [9] based on Eyring’s theory of absolute reaction rates and
three body interaction model is:
ln t12 ¼ x31 ln t1 þ 3x2
1x2 ln M12 þ 3x1x22 ln M12 þ x3
2 ln t2 � ln x1 þx2M2
M1
� �� �
þ 3x21x2 ln
2
3
� �þ M2
3M1
� �� �þ 3x1x2
2 ln2
3
� �þ M2
3M1
� �� �þ x2
2 lnM2
M1
� � ð9Þ
where m, m1 and m2 are the kinematic viscosities of the mixture and of the 1st and 2nd
components of the mixture, respectively. The M12 and M21 are fitting parameters that
denote viscosity contributions from interactions between mixture components, which were
calculated for each mixture by a least-squares method.
(ii) Dolezalek–Schulze [10] have suggested the following equation for the viscosity of
binary liquid mixtures:
g12 ¼ x21g1 þ x2
2g2 þ 2x1x2D12 ð10Þ
where x1 and x2 are mole fractions of component 1 and 2, respectively. g1, g2 and g12 are
the dynamic viscosities of component 1, component 2 and binary mixtures. D12 is a
constant that is regarded as a measure of the strength of the molecular interactions between
the components of the mixture.
(iii) Grunberg and Nissan [11] have suggested the following logarithmic relation between
the viscosity of the binary liquid mixture and pure components:
ln g12 ¼ x1 ln g1 þ x2 ln g2 þ x1x2G12 ð11Þ
where G12 is a constant, proportional to energy exchange. g1, g2 and g12 are the dynamic
viscosities of component 1, component 2 and binary mixtures, respectively.
(iv) Tamura–Kurata [12] have developed the following equation for the viscosity of
binary liquid mixtures:
ln g ¼ x1/1g1 þ x2/2g2 þ 2ðx1x2/1/2Þ0:5T12 ð12Þ
where, T12 is the interaction parameter. /1, /2 are the volume fractions of component 1 and
2, respectively.
An attempt has been made to check the suitability of equations for experimental data
sets by taking into account the number of empirical adjustable parameters.
The standard percentage deviation (r %) for one-parameter relations lies within the range
0.02–0.21 % for the Dolezalek–Schulze [10] relation; 0.11–0.20 % for the Grunberg-Nissan
[11] relation; and 0.06–0.79 % for the Tamura–Kurata [12] relation for the binary mixtures
under study. The analysis of the results for the one-parameter relations (Eqs. 10–12) reveals
that the Dolezalek–Schulze equation shows minimum r %, followed by that of Grunberg-
Nissan, whereas the Tamura–Kurata model exhibits maximum values of r %. The McAll-
ister [9] three body equation was also applied to the experimental viscosities.
The interaction parameters play an important role to ascertain the extent of interaction
in binary mixtures. It has been reported earlier by Fort and Moore [52] and Ramamoorthy
J Solution Chem (2013) 42:1794–1815 1805
123
Table 5 The interaction parameters along with the standard percentage deviations (r %) for b-pinene ?aromatic hydrocarbon mixtures at 303.15, 308.15 and 313.15 K
Semi-empirical relation Parameter r (%)
b-Pinene ? benzene
T = 303.15 K
Dolezaleck D12 = 0.609 0.021
Grunberg G12 = -0.476 0.209
Tamura T12 = 0.529 0.214
McAllister M12 = 1.167, M21 = 0.713 0.063
T = 308.15 K
Dolezaleck D12 = 0.582 0.112
Grunberg G12 = -0.463 0.193
Tamura T12 = 0.511 0.248
McAllister M12 = 1.081, M21 = 0.690 0.107
T = 313.15 K
Dolezaleck D12 = 0.550 0.147
Grunberg G12 = -0.448 0.183
Tamura T12 = 0.486 0.279
McAllister M12 = 0.992, M21 = 0.622 0.141
b-Pinene ? toluene
T = 303.15 K
Dolezaleck D12 = 0.548 0.053
Grunberg G12 = -0.516 0.110
Tamura T12 = 0.482 0.325
McAllister M12 = 1.056, M21 = 0.696 0.067
T = 308.15 K
Dolezaleck D12 = 0.523 0.200
Grunberg G12 = -0.494 0.136
Tamura T12 = 0.464 0.334
McAllister M12 = 0.990, M21 = 0.664 0.119
T = 313.15 K
Dolezaleck D12 = 0.495 0.216
Grunberg G12 = -0.484 0.145
Tamura T12 = 0.442 0.341
McAllister M12 = 0.916, M21 = 0.631 0.140
b-Pinene ? m-xylene
T = 303.15 K
Dolezaleck D12 = 0.579 0.056
Grunberg G12 = -0.502 0.114
Tamura T12 = 0.536 0.267
McAllister M12 = 1.067, M21 = 0.732 0.096
T = 308.15 K
Dolezaleck D12 = 0.546 0.184
Grunberg G12 = -0.505 0.124
Tamura T12 = 0.506 0.417
1806 J Solution Chem (2013) 42:1794–1815
123
Table 5 continued
Semi-empirical relation Parameter r (%)
McAllister M12 = 1.000, M21 = 0.688 0.107
T = 313.15 K
Dolezaleck D12 = 0.512 0.204
Grunberg G12 = -0.513 0.151
Tamura T12 = 0.477 0.277
McAllister M12 = 0.927, M21 = 0.651 0.145
b-Pinene ? mesitylene
T = 303.15 K
Dolezaleck D12 = 0.627 0.028
Grunberg G12 = -0.530 0.131
Tamura T12 = 0.606 0.129
McAllister M12 = 1.124, M21 = 0.761 0.057
T = 308.15 K
Dolezaleck D12 = 0.614 0.209
Grunberg G12 = -0.407 0.164
Tamura T12 = 0.595 0.799
McAllister M12 = 1.062, M21 = 0.715 0.052
T = 313.15 K
Dolezaleck D12 = 0.568 0.050
Grunberg G12 = -0.465 0.162
Tamura T12 = 0.550 0.069
McAllister M12 = 1.010, M21 = -0.407 0.043
Table 6 Root mean squaredeviation (RMSD) of ultrasonicspeed for the binary systems of b-pinene ? aromatic hydrocarbonsat 303.15, 308.15 and 313.15 K
System uNMT uIMR uFLT
T = 303.15 K
b-Pinene ? benzene 0.01 2.04 0.32
b-Pinene ? toluene 0.90 0.42 0.42
b-Pinene ? m-xylene 1.45 1.10 0.31
b-Pinene ? mesitylene 1.82 1.79 1.45
T = 308.15 K
b-Pinene ? benzene 0.53 2.10 0.28
b-Pinene ? toluene 0.78 0.54 0.31
b-Pinene ? m-xylene 1.26 0.88 0.25
b-Pinene ? mesitylene 1.65 1.62 1.23
T = 313.15 K
b-Pinene ? benzene 0.47 2.20 0.25
b-Pinene ? toluene 0.67 0.62 0.21
b-Pinene ? m-xylene 1.11 0.72 0.23
b-Pinene ? mesitylene 1.52 1.50 1.06
J Solution Chem (2013) 42:1794–1815 1807
123
[53] that negative values of G12 indicate the presence of weak interaction and positive
values indicate strong interaction between the binary components. These interaction
parameters indicate the presence of interactions between unlike molecules but do not
predict the extent of interaction amongst heteromolecules of liquid mixtures. The values of
D12 and T12 show similar behavior and have positive values.
The values of M12 and M21 were evaluated using the least squares method. M12 and M21
are positive but values of M21 are smaller than the M12 values, which also supports the
existence of weak interactions. The interaction parameter M12 values vary in the order
benzene [ mesitylene [ m-xylene [ toluene. Use of the two parameter equation (Mc-
Allister) reduces r % values significantly below those of the single parameter equations.
From these comparisons, it is concluded that correlating ability significantly improves for
these non-ideal systems as the number of parameters increases.
3.2 Speed of Sound Study
It can be seen from the Figs. 2 and 3 that, for binaries of b-pinene in benzene to mesitylene
mixtures, Du is negative and Dks is positive. Deviations in speed of sound values become more
negative when going from benzene to mesitylene mixtures of b-pinene. The major deviation of
speed of sound (minima of the curves) lies toward the high b-pinene concentrated region. The
graphical variation of Dks as a function of the b-pinene mole fraction for the binary mixtures is
negative with systematic increase from benzene to mesitylene. The observed positive values of
Dks, with systematic increase over whole composition range of b-pinene ? aromatic hydro-
carbons, suggest that dispersion force are dominant in the weak interactions between unlike
molecules. Negative values of Du and positive values of Dks support the negative Dg values.
Furthermore, positive Du deviations indicate that the mixed species are overall more com-
pressible and hence have large volume due to structure disruption.
Theoretical velocities of sound were calculated for all binaries using three well estab-
lished equations: NMT, the ideal mixing rule (IMR) and Jacobson’s Free Length Theory
(FLT).
Nomoto [13] established an empirical formula for study of ultrasonic speed, uNMT in
binary mixtures:
uNMT ¼x1R1 þ x2R2
x1V1 þ x1V2
� �3
ð13Þ
where xi is mole fraction, Ri is the molar sound velocity calculated using the equation
Ri ¼ uiV1=3i , Vi the molar volume and ui is the sound velocity of the ith component.
Van Deal and Van Geel [14, 15] proposed the following expression for the estimation of
speed of sound, uIMR, in an ideal mixture using the sound velocities of pure components:
uIMR ¼ u1u2
M1M2
ðx1M2u22 þ x2M1u2
1Þðx1M1 þ x2M2Þ� �" #
ð14Þ
According to Jacobson’s theory [16] of free length, the ultrasonic speed is given by:
u ¼ K
ðLfq1=2Þ ð15Þ
For a binary liquid mixture, the above equation is:
1808 J Solution Chem (2013) 42:1794–1815
123
u ¼ Kðx1Y1 þ x2Y2Þ2½VM � ðx1V0:1 þ x2V0:2Þ�q1=2
ð16Þ
where Y is an adjustable parameter. Y was obtained from the velocities in the pure liquids
using the equation:
Y ¼ 2Vauq1=2
Kð17Þ
where K is the temperature dependent Jacobson’s constant [54]. Va is the available molar
volume, the difference between the molar volume at T (K) and 0 (K), which is a direct
measure of the compactness and the strength of bonding between the molecules of a liquid
mixture. Va is given by:
Va ¼ VM � V0 ð18ÞWhen Y in the Eq. 16 is replaced according to Eq. 17 and when the resulting expression
is rearranged, one gets:
uFLT ¼½fx1ðVM1 � V0:1Þu1q
1=21 g þ fx2ðVM2 � V0:2Þu2q
1=22 g�
½VM � ðx1V0:1 þ x2V0:2Þ�q1=2ð19Þ
The above expression reveals that according to the free length theory, the square root of
the inverse of the adiabatic compressibility of a liquid mixture (uq1/2) is the sum of the
available volume fraction average of the square root of the inverse of adiabatic com-
pressibilities of the individual components.
The values of theoretical speeds of sound given in Table 3 are in good agreement with
the experimental data taken for the binary mixtures. The ability of the models to predict the
experimental speed of sound given in Table 5 can be tested by comparing the RMSDs. The
predictive abilities of various ultrasonic theories depend upon the strength of interaction in
systems; that is, these theories are not accurate where strong interactions arise. The study
of RMSD shows that the resultant speed of sound for the (b-pinene ? benzene), (b-pinene ?
m-xylene) and (b-pinene ? mesitylene) systems can be best explained by the FLT for-
mulation with minimum values of r that are 0.32 to 1.45 % at 303.15 K. On the other
hand, the IMR relation gives good predictions of the speed of sound in the (b-
pinene ? toluene) system having a minimum r of 0.42 % at 303.15 K.
For each system, the deviations in viscosity (Dg) and in ultrasound speed increase while
the isentropic compressibility (ks) and deviations in isentropic compressibility (Dks)
decrease over the whole mole fraction range with increasing temperature. There is a weak
dispersive type of interactions between b-pinene and hydrocarbon mixtures. These inter-
actions become weaker with increasing temperature because the kinetic energy of the
molecules increases. This leads to a decrease in interaction between unlike molecules, so
the viscosity decreases and molecules become less compressible.
3.3 IR Analysis
FTIR spectroscopy gives additional evidence for weak interactions. To explain the results
obtained at a molecular level, it was decided to study the spectra of the binary mixtures at
equimolar composition by FTIR spectroscopy, operating with a resolution of 2 cm-1,
under the assumption that the possible molecular interactions will alter the spectroscopic
characteristics of the mixture as compared to their pure components (Figs. 4, 5, 6 and 7).
J Solution Chem (2013) 42:1794–1815 1809
123
The test is focused on the aromatic C–H stretching at 3,070 cm-1 and aromatic ring
stretching at 1,475 cm-1 for the aromatic hydrocarbons. The frequencies of toluene, m-
xylene and mesitylene at 728, 764, 686, 827 and 687 cm-1 are due to presence of mono-,
di- and trimethyl groups on the phenyl ring.
In the case of b-pinene, the typical absorption band of the exocyclic double bond, =CH2
moiety is observed at 875 cm-1. The exocyclic double bond, =CH2 shows olefinic
asymmetric stretching at 3,020 cm-1 accompanied by symmetric stretching at 2,982 cm-1
[55].
From the IR data, it is clear that position and shape of the peak is not modified and no
new peak appeared. The intensity of a peak in the mixture decreased for all selected wave
numbers when b-pinene was mixed with benzene or toluene or m-xylene or mesitylene.
There is no shift in wave number, only the intensity has decreased at all the selected test
frequencies. It seems there is no significant interaction between the components of the
mixtures.
The mC–H stretching frequency at 3,070 cm-1 for hydrocarbons has decreased in all the
binaries, which is a clear indication that the hydrocarbons are not self associated in the pure
state and there is hetero-association between b-pinene and aromatic hydrocarbons. Simi-
larly, the m =CH2 wagging frequency of b-pinene also has decreased intensity. This also
proves that there is only weak interaction between b-pinene and aromatic hydrocarbons.
The decrease in the intensity of selected peaks has the order: benzene [ toluene [ m-
xylene [ mesitylene.
As the –CH3 group increases in the order benzene to toluene to mesitylene, the electron
density increases in the aromatic ring. So the p–p interaction between b-pinene and
hydrocarbon decreases from benzene to mesitylene. Therefore the intensity of peak has
decreased in the above order.
4000 3500 3000 2500 2000 1500 1000 5000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
% T
rans
mitt
ance
s
Wave number (cm-1)
Fig. 4 Experimental IR transmittances spectra at 298.15 K for b-pinene (continuous lines), benzene (thickcontinuous lines) and b-pinene ? benzene (dashed lines)
1810 J Solution Chem (2013) 42:1794–1815
123
4 Conclusions
The viscometric, acoustical and FTIR studies on liquid binary mixtures provide a com-
parative investigation of molecular interactions between b-pinene ? benzene, ? toluene,
4000 3500 3000 2500 2000 1500 1000 5000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
% T
rans
mitt
ance
s
Wave number (cm-1)
Fig. 5 Experimental IR transmittances spectra at 298.15 K for b-pinene (continuous lines), toluene (thickcontinuous lines) and b-pinene ? toluene (dashed lines)
4000 3500 3000 2500 2000 1500 1000 5000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
% T
rans
mitt
ance
s
Wave number (cm-1)
Fig. 6 Experimental IR transmittances spectra at 298.15 K for b-pinene (continuous lines), m-xylene (thickcontinuous lines) and b-pinene ? m-xylene (dashed lines)
J Solution Chem (2013) 42:1794–1815 1811
123
? m-xylene and ? mesitylene. A systematic study of b-pinene with aromatic hydrocarbons
has been carried out at different concentrations and different temperatures using viscom-
etry, acoustical and spectroscopic studies. The FTIR study was carried out only at
298.15 K.
Negative Dg and Du values and positive Dks values support the view that there is weak
or dispersive types of interactions between b-pinene ? aromatic hydrocarbons. Positive
values of interaction parameters (D12) and (T12) along with negative values of (G12)
indicate the presence of weak interactions between b-pinene and aromatic hydrocarbons. A
comparisons of one adjustable parameter equations like Eqs. 10, 11 and 12 with the two
parameteric, Eq. 9, has been made to check the suitability of the equations predicting the
experimental speeds of sound. This analysis shows that the correlating ability was sig-
nificantly improved in the two parameter model as compared to the one parameter models.
For each system, the deviations in viscosity (Dg), deviation in ultrasound velocity
(Du) increase while isentropic the compressibility (ks) and deviations in isentropic com-
pressibility (Dks) are decrease over the whole mole fraction range with increasing
temperature.
In the IR, no new peak has emerged and the position and shape of the test peaks were
not modified. The intensity of the peaks in the mixture decreased for all the selected wave
numbers. This indicates that the aromatic hydrocarbons are not self associated in the pure
state and there is weak hetero-association between b-pinene and aromatic hydrocarbons.
Moreover, the electron donating tendency increases as the -CH3 groups increase from
benzene to mesitylene. So as the p–p interaction increases, the intensity of test frequencies
decreases in the order: benzene \ toluene \ m-xylene \ mesitylene.
Acknowledgments Financial support for work was given by the Gujarat Council of Sciences and Tech-nology (GUJCOST) (Letter No. GUJCOST/SSP/201657/2010-11/19), Gandhinagar under the SCITECHscheme, is highly acknowledged.
4000 3500 3000 2500 2000 1500 1000 5000.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
% T
rans
mitt
ance
s
Wave number (cm-1)
Fig. 7 Experimental IR transmittances spectra at 298.15 K for b-pinene (continuous lines), mesitylene(thick continuous lines) and b-pinene ? mesitylene (dashed lines)
1812 J Solution Chem (2013) 42:1794–1815
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References
1. Sharma, S., Bhalodia, J., Ramani, J., Patel, R.: Density, excess molar volumes and refractive indices ofb-pinene with o, m, p-xylene and toluene at 303.15, 308.15 and 313.15 K. Phys. Chem. Liq. 49,765–776 (2011)
2. Sharma, S., Bhalodia, J., Ramani, J., Patel, R.: Volumetric, viscometric and ultrasonic studies on binarymixtures of oleic acid with alkyl esters at 303.15, 308.15 and 313.15 K. Int. J. Phys. Sci. 7, 1205–1214(2012)
3. Carolina, A., Moreira, P., Lima, E.D.O., Souza, E.L.D., Dingenen, M.A.V., Trajano, V.N.: Inhibitoryeffect of cinnamomum zeylanicum blume (lauraceae) essential oil and b-pinene on the growth ofdematiaceous moulds. Braz. J. Micro. 38, 33–38 (2007)
4. Leite, A., Lima, E., Souza, E., Dinz, M., Trajano, V., Medeiros, I.: Inhibitory effect of b-pinene, a-pinene and eugenol on the growth of potential infectious endocarditis causing Gram-positive bacteria.Braz. J. Pharm. Sci. 43, 121–126 (2007)
5. Kumooka, Y.: Analysis of polyb-pinene in rubber-based pressure-sensitive adhesives by matrix-assistedlaser desorption/ionization time-of-flight mass spectrometry. J. Mass Spectrom. Soc. Jpn. 55, 287–291(2007)
6. Seinfeld, J., Erdakos, G., Asher, W., Pankow, J.: Modeling the formation of secondary organic aerosol(soa). 2. The predicted effects of relative humidity on aerosol formation in the a-pinene-, b-pinene-,sabinene-, D3-carene-, and cyclohexene–ozone systems. Environ. Sci. Technol. 35, 1806–1817 (2001)
7. Langa, E., Mainar, A.M., Pardo, J.I., Urieta, S.: Excess enthalpy, density, and speed of sound for themixtures b-pinene ? 1-butanol or 2-butanol at (283.15, 298.15, and 313.15) K. J. Chem. Eng. Data 51,392–397 (2006)
8. Reich, R., Sanhueza, V.: Vapor–liquid equilibria for a-pinene and b-pinene and for these pinenes withheptane, cyclohexane, 1-octene and cyclohexene. Fluid Phase Equilib. 77, 313–325 (1992)
9. McAllister, R.A.: The viscosity of liquid mixtures. AIChE J. 6, 427–431 (1960)10. Dolezalek, F., Schulze, A.: On the theory of mixtures and binary concentrated solution IV. Z. Phys.
Chem. 83, 45–78 (1913)11. Grunberg, L., Nissan, A.H.: Mixture law for viscosity. Nature 164, 799–800 (1949)12. Tamura, M., Kurata, M.: On the viscosity of binary mixture of liquids. Bull. Chem. Soc. Jpn. 25, 32–38
(1952)13. Nomoto, O.: Empirical formula for sound velocity in liquid mixtures. J. Phys. Soc. Jpn. 13, 1528–1532
(1958)14. Van Deal, W., Vangeel, E.: Abstract Pap. In: Proceeding 1st International Conference on Calorimetry
and Thermodynamics. Warsaw, p. 555 (1969)15. Van Deal, W.: Thermodynamic properties and velocity of sound. Exp. Thermodyn. 2, 542 (1975)16. Jacobson, B.: Ultrasonic velocity in liquids and liquid mixtures. J. Chem. Phys. 20, 927–928 (1952)17. Riddick, J.A., Bunger, W.B., Weissberger, A.: Organic Solvents: Physical Properties and Methods of
Purification. Wiley, Hoboken (1970)18. Wilhoit, R.C., Hong, X., Frenkel, M., Hall, K.R.: Thermodynamic Properties of Organic Compounds
and Their Mixtures. Subvolume F: Densities of Polycyclic Hydrocarbons. Landolt-Borstein NumericalData and Functional Relationships in Science and Technology, Group 4. Springer, Berlin (1999)
19. Langa, E., Mainar, A.M., Pardo, J.I., Urieta, J.S.: Excess enthalpy, density, and speed of sound for themixtures b-pinene ? 2-methyl-1-propanol or 2-methyl-2-propanol at several temperatures. J. Chem.Eng. Data 52, 2182–2187 (2007)
20. Comelli, F., Francesconi, R., Castellari, C.: Excess molar enthalpies and excess molar volumes ofbinary mixtures containing dialkyl carbonates ? pine resins at (298.15 and 313.15) K. J. Chem. Eng.Data 46, 63–68 (2001)
21. Ribeiro, A., Bernardo-Gil, G.: Densities and refractive indices of components of pine resin. J. Chem.Eng. Data 35, 204–206 (1990)
22. Aminabhavi, T.M., Banerjee, K.: Density, viscosity, refractive index, and speed of sound in binarymixtures of 1-chloronaphthalene with benzene, methylbenzene, 1,4-dimethylbenzene, 1,3,5-trimethyl-benzene, and methoxybenzene at (298.15, 303.15, and 308.15) K. J. Chem. Eng. Data 44, 547–552(1999)
23. Song, C.Y., Shen, H.Z., Zhao, J.H., Wang, L.C., Wang, F.A.: Densities and viscosities of binarymixtures of vitamin K3 with benzene, toluene, ethylbenzene, o-xylene, m-xylene, and p-xylene from(303.15 to 333.15) K. J. Chem. Eng. Data 53, 1110–1115 (2008)
24. Reddy, K.S.: Isentropic compressibilities of binary liquid mixtures at 303.15 and 313.15 K. J. Chem.Eng. Data 31, 238–240 (1986)
J Solution Chem (2013) 42:1794–1815 1813
123
25. Awwad, A., Daabes, M.: Densities, viscosities, and excess properties of (N-methylmorpholine ?cyclohexane, ? benzene and ? toluene) at T = (298.15, 303.15, 313.15, 323.15) K. J. Chem. Ther-modyn. 40, 645–652 (2008)
26. Oswal, S.L., Desai, J.S., Ijardar, S.P.: Studies of viscosities of dilute solutions of alkylamine in non-electrolyte solvents I. Aliphatic and aromatic hydrocarbons. Thermochim. Acta 423, 29–41 (2004)
27. Oswal, S.L., Gardas, R.L., Phalak, R.P.: Densities, speeds of sound, isentropic compressibilities,refractive indices and viscosities of binary mixtures of tetrahydrofuran with hydrocarbons at 303.15 K.J. Mol. Liq. 116, 109–118 (2005)
28. Nain, A.: Ultrasonic and viscometric studies of molecular interactions in binary mixtures of tetrahy-drofuran with some aromatic hydrocarbons at temperatures from 288.15 to 318.15 K. Phys. Chem. Liq.45, 371–388 (2007)
29. Bahadur, P., Sastry, N.: Densities, sound speeds, excess volumes and excess isentropic compressibilitiesof methyl acrylate ? 1-propanol (or 1-butanol) ? hydrocarbons (n-hexane, n-heptane, cyclohexane,benzene and toluene) at 308.15 K. Int. J. Thermophys. 24, 447–462 (2003)
30. Aralaguppi, M.I., Jadar, C.V., Aminabhavi, T.M.: Density, refractive index, viscosity and speed ofsound in binary mixtures of cyclohexanone with benzene, methylbenzene, 1,4-dimethylbenzene, 1,3,5-trimethylbenzene and methoxybenzene in the temperature interval (298.15 to 308.15) K. J. Chem. Eng.Data 44, 446–450 (1999)
31. Kumar, B.R., Satyanarayana, B., Banu, S.A., Jyothi, K.A., Jyostna, T.S., Satyanarayana, N.: Volumetricand transport properties of binary liquid mixtures of aromatic hydrocarbons with N-methylacetamide at308.15 K. Indian J. Pure Appl. Phys. 47, 511–516 (2009)
32. Yang, C., Liu, Z., Lai, H., Ma, P.: Thermodynamic properties of binary mixtures of N-methyl-2-pyrrolidinone with cyclohexane, benzene, toluene at (303.15 to 353.15) K and atmospheric pressure.J. Chem. Thermodyn. 39, 28–38 (2007)
33. Sastry, N.V., Thakor, R.R., Patel, M.C.: Excess molar volumes, viscosity deviations, excess isentropiccompressibilities and deviations inrelative permittivities of (alkyl acetates (methyl, ethyl, butyl andisoamyl) ? n-hexane, ? benzene, ? toluene, ? (o-, m-, p-) xylenes, ? (chloro-, bromo-, nitro-)benzenes at temperatures from 298.15 to 313.15 K. J. Mol. Liq. 144, 13–22 (2009)
34. Exarchos, N., Tasioula-Margari, M., Demetropoulos, I.: Viscosities and densities of dilute solutions ofglycerol trioleate ? octane, ? p-xylene, ? toluene, and ? chloroform. J. Chem. Eng. Data 40, 567–571(1995)
35. Ali, A., Nain, A.K., Sharma, V.K., Ahmad, S.: Study of molecular interaction in ternary mixturesthrough ultrasonic speed measurements. Phys. Chem. Liq. 42, 375–383 (2004)
36. Thirumaran, S., Jayakumar, J.E.: Ultrasonic study of n-alkanols in toluene with nitrobenzene. Indian J.Pure Appl. Phys. 47, 265–272 (2009)
37. Nikam, P.S., Jagdale, B.S., Sawant, A.B., Hasan, M.: Densities and viscosities for binary mixtures ofbenzonitrile with methanol, ethanol, propan-1-ol, butan-1-ol, pentan-1-ol and 2-methylpropan-2-ol at(303.15, 308.15, and 313.15) K. J. Chem. Eng. Data 45, 214–218 (2000)
38. Calvar, N., Gonzalez, B., Gomez, E., Canosa, J.: Density, speed of sound and refractive index for binarymixtures containing cycloalkanes and aromatic compounds at T = 313.15 K. J. Chem. Eng. Data 54,1334–1339 (2009)
39. Resa, J., Gonzalez, C., Concha, R.: Ultrasonic velocity measurements for butyl acetate ? hydrocarbonmixtures. Phys. Chem. Liq. 42, 521–543 (2004)
40. George, J., Sastry, N.V.: Densities, excess molar volumes, viscosities, speeds of sound, excess isen-tropic compressibilities and relative permittivities for CmH2m?1(OCH2CH2)nOH (m = 1 or 2 or 4 andn = 1) ? benzene, ? toluene, ? (o-, m-, and p-) xylenes, ? ethylbenzene, and ? cyclohexane.J. Chem. Eng. Data 48, 977–989 (2003)
41. Prabhavathi, C., Kumar, K.S., Venkateswarlu, P., Raman, G.: Speed of sound and isentropic com-pressibilities of n-methylcyclohexylamine with benzene and substituted benzenes at 303.15 K. Phys.Chem. Liq. 38, 705–712 (2000)
42. Moumouzias, G., Ritzoulis, C., Ritzoulis, G.: A study in mixtures of butyrolactone with o-xylene and m-xylene: densities and viscosities. J. Chem. Eng. Data 44, 1187–1191 (1999)
43. Verma, N., Maken, S., Singh, K.C.: Volumetric properties of sec- and tert-butyl chloride with benzene,toluene and xylenes at 308.15 K. J. Mol. Liq. 141, 35–38 (2008)
44. Ali, A., Nain, A.K., Chand, D., Ahmad, R.: Volumetric, ultrasonic, viscometric and refractive indexbehavior of binary mixtures of 2,2,4-trimethylpentane with aromatic hydrocarbons: an experimental andtheoretical study. J. Mol. Liq. 128, 32–41 (2006)
45. Baragi, J.G., Aralaguppi, M.I.: Excess and deviation properties for the binary mixtures of methylcy-clohexane with benzene, toluene, p-xylene, mesitylene, and anisole at T = (298.15, 303.15, and 308.15)K. J. Chem. Thermodyn. 38, 1717–1724 (2006)
1814 J Solution Chem (2013) 42:1794–1815
123
46. Kumar, A., Sharma, R., Ali, A., Gopal, S.: Densities and volumetric properties of methyl acry-late ? benzene, or toluene, or o-xylene, or m-xylene, or p-xylene, or mesitylene binary mixtures attemperatures from 293.15 to 318.15 K. J. Mol. Liq. 144, 124–130 (2009)
47. Prasad, T., Chandrika, K., Haritha, M., Geetha, N., Prasad, D.: Density and viscosity of ethanol ? o-xylene, ethanol ? m-xylene, ethanol ? p-xylene and methanol ? o-xylene mixtures. Phys. Chem. Liq.37, 429–434 (1999)
48. Nain, A.K.: Densities and volumetric properties of binary mixtures of tetrahydrofuran with somearomatic hydrocarbons at temperatures from 278.15 to 318.15 K. J. Solution Chem. 35, 1417–1439(2006)
49. Nain, A.K., Chandra, P., Pandey, J.D., Gopal, S.: Densities, refractive indices, and excess properties ofbinary mixtures of 1, 4-dioxane with benzene, toluene, o-xylene, m-xylene, p-xylene, and mesitylene attemperatures from (288.15 to 318.15) K. J. Chem. Eng. Data 53, 2654–2665 (2008)
50. Redlich, O., Kister, A.T.: Algebraic representation of thermodynamic properties and the classification ofsolutions. Ind. Eng. Chem. 40, 345–348 (1948)
51. Ali, A., Tariq, M., Nabi, F.: Sahjahan.: density, viscosity, refractive index, and speed of sound in binarymixtures of pyridine and 1-alkanols (C6, C7, C8, C10) at 303.15 K. Chin. J. Chem. 26, 2009–2015 (2008)
52. Fort, R., Moore, W.: Viscosities of binary liquid mixtures. Trans. Faraday Soc. 62, 1112–1119 (1966)53. Ramamoorthy, K.: Excess free-energy of mixing (DFm) and strength of interaction in binary liquid
mixtures from viscosity studies. Indian J. Pure Appl. Phys. 11, 554–555 (1973)54. Jacobson, B.: Intermolecular free lengths in the liquid state. I. Adiabatic and isothermal compress-
ibilities. Acta Chem. Scand. 6, 1485–1498 (1952)55. Cataldo, F., Keheyan, Y.: Radiopolymerization of b-(-)pinene: a case of chiral amplification. Radiat.
Phys. Chem. 75, 572–582 (2006)
J Solution Chem (2013) 42:1794–1815 1815
123