Study of molecular interactions in ternary non electrolyte solutions

Journal of Molecular Liquids 216 (2016) 126–131

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Study of molecular interactions in ternary non electrolyte solutions C. Narasimha Rao a, L. Venkatramana b, K. Janardhanaiah a, K. Sivakumar c,⁎ a b c

Department of Chemistry, Sri Venkateswara University, Tirupati 517502, India Department of Chemistry, Indian Institute of Technology Madras, Chennai 600036, India Department of Chemistry, S.V. Arts UG &PG College (TTD'S), Tirupati 517502, India

a r t i c l e

i n f o

Article history: Received 25 September 2015 Received in revised form 20 November 2015 Accepted 6 December 2015 Available online xxxx Key words: Ternary mixture Excess volume Speed of sound 1,1,1-Trichloroethane Acetophenone Alkanols Predictive expressions

a b s t r a c t Excess volume (VE123) and speed of sound (u123) data for three ternary mixtures were reported at 303.15 K. The mixtures include 1,1,1-trichloroethane and acetophenone as common components. The non-common components were chosen as 1-alkanols namely 1-propanol, 1-butanol and 1-pentanol. The experimental speed of sound and density data of ternary mixtures were used to compute isentropic compressibility (κs123) and the quantity Δκs123, the difference between measured value and that computed from the constituent binary data. Further, experimental ternary excess volume data were compared with predictive expressions in terms of Redlich–Kister, Kohler and Tsao–Smith equations. The experimental data were analyzed on the basis of intermolecular interactions between component molecules and also in terms of constituent binary data. © 2016 Elsevier B.V. All rights reserved.

1. Introduction A thorough knowledge of the thermodynamic properties of multicomponent liquid mixtures is essential in many industrial applications, such as design calculation, heat transfer, mass transfer, fluid flow and so forth [1]. Moreover thermodynamic properties of mixed solvents have been particularly served as main tool in elucidation of solute–solute and solute–solvent interactions that exist in the liquid mixtures. Investigation of thermodynamic properties of liquid and liquid mixtures are fascinating and of high fundamental practical importance for many industrial activities. In many industrial applications, liquid mixtures rather than single component liquid system are used in processing and product formulations [2]. The mixing of different compounds gives rise to properties such as volumes, enthalpies and entropies of mixing, which reflect the extent of the deviations from non-identity. Excess thermodynamic properties of mixtures correspond to the difference between the actual property and the property in the system behaves ideally are useful in the study of molecular interactions and arrangements [3]. This work is a part of our ongoing program [4–6] to provide data for the characterization of molecular interactions between industrially important organic liquids and systematic study on thermodynamic properties of ternary liquid mixtures with molecules of significantly different sizes. Though, a number of investigations were carried out, a systematic study pertaining to alkanol as one of the components in liquid mixtures

⁎ Corresponding author. E-mail address: [email protected] (K. Sivakumar).

http://dx.doi.org/10.1016/j.molliq.2015.12.017 0167-7322/© 2016 Elsevier B.V. All rights reserved.

is scarcely reported. Further, alkanols are highly polar and they can form azeotropes with one or other components in multi component liquid mixtures. It will be interesting to study the effect of increasing in chain length of 1-alkanol on their excess thermodynamic properties. Hence, a thorough study was carried out on the molecular interaction for three ternary mixtures containing 1,1,1-trichloroethane and acetophenone as common components and 1-propanol, 1-butanol and 1-pentanol as non-common components. The selected component liquids used in the present study have various industrial applications. 1,1,1-Trichloroethane is an excellent solvent for development of photo resist polymers used in printed circuit board manufacture and the other common uses include cleaning of electrical equipment, motors, electronic components and instruments. Acetophenone is used as base for bath soaps, chemical intermediate for resins, corrosion inhibitors and as a solvent for gums. 1-Alkanols are interesting simple examples of biologically and industrially important amphiphilic materials [7]. A survey of the literature has shown that ternary excess volume data containing 1,1,1-trichloroethane with n-hexane and n-heptane with 1-alkanols were reported earlier [8,9]. The measured data in the present investigation were compared with empirical equations to check the capability of predictive expressions [10]. 2. Experimental details 2.1. Materials All the chemicals used were of analytical reagent (AR) grade (procured from Sigma-Aldrich and S.D. Fine chemicals Ltd.,) and their

C.N. Rao et al. / Journal of Molecular Liquids 216 (2016) 126–131

purities were as follows: 1,1,1-trichloroethane (CAS 71-55-6) 99.5%, acetophenone (CAS 98-86-2) 99.5%, 1-propanol (CAS 71-23-8) 99.5%, 1-butanol (CAS 2346-54-1) 99.5% and 1-pentanol (CAS 71-41-0) 99.5%. Before the experimental measurements all the liquids were purified as described in the literature [11,12]. The purity of the chemical products was compared by measuring the densities and speed of sound which were in good agreement with literature values [13–15] and these were given in Table 1. 2.2. Measurements Excess volume data for ternary mixtures were measured with the dilatometer described in the literature [16,17]. The mixing cell contained three bulbs of different capacities. Mercury was used to separate three components. One of the three bulbs was fitted with a capillary and the other two fitted with ground-glass stoppers. Each bulb of the dilatometer was fitted with a component whose mass was determined directly by weighing. The full dilatometer was placed in the thermostat that could be maintained to ± 0.01 K. The densities of pure liquids were measured by using pycnometer. All the measurements were made at constant temperature employing a thermostat. The measured VE values were accurate to ±0.003 cm3 mol−1 [18]. The speed of sound of pure liquids and their mixtures were measured at 303.15 K by using a multifrequency ultrasonic interferometer (M-82 Model, Mittal Enterprise, New Delhi, India) single-crystal variable-path by using a constant temperature water bath [19]. The speeds of sound were accurate to ± 0.3%. The temperature stability was maintained to ± 0.01 K by circulating thermostatic water bath around the cell with a circulating pump.

127

at composition (x'i, x'j), such that 0

0

xi ¼ 1 − x j ¼

xi xi þ x j

wherexi and xj are the ternary mole fractions. Tsao–Smith expression [10] is of the form: V E123 ¼ x2 ð1 þ x1 Þ−1 V E12 þ x3 ð1 − x1 Þ−1 V E13 þ ð1 − x1 ÞV E23

ð3Þ

where V12E, VE13 and VE23 are the binary excess volumes at composition 0 2 (x'i, x'j), such that x'i = x1 for 1,2 and 1,3 binary systems and x2 ¼ x2xþx for 3 2,3 binary system. The quantity ΔVE123, difference between measured ternary data and computed from the constituent binary data through the Redlich–Kister relation were given Table 2. The binary VE parameters required to compute ternary VE123 data in terms of constituents binaries for the systems of 1,1,1-trichloroethane with acetophenone [13], 1,1,1-trichloroethane with 1-alkanols [20] and acetophenone with 1-alkanols [14] were taken from the literature and were given in the form of least-square parameters in Table 3. A perusal of data in Table 2 reveal that density increases with increase in mole fraction of acetophenone. The increase in density indicates the presence of solvent–solvent interactions in the ternary mixture [21]. The results in Table 2 also suggest that the ternary excess volume data in all the three mixtures were negative over the entire composition range. The sign and magnitude of excess volumes can be interpreted as composed from three contributions, namely of physical, chemical and structural effects.

3. Results and discussion 3.1. Excess volume The experimental ternary excess volume (VE123) data for the mixtures of 1,1,1-trichloroethane and acetophenone with 1-propanol, 1-butanol and 1-pentanol were given in Table 2 and graphically represented in Figs. 1–3. Further, the ternary excess volume data predicted from binary data using Redlich–Kister, Kohler and Tsao–Smith equations were also included in Table 2. The methods of calculation were explained as follows: Redlich–Kister equation [10] expressed as: V E123

¼

X

V Eij



xi ; x j



ð1Þ

ib j n

where V Eij ¼ xi x j ∑ ðAs Þij ðxi − x j Þs and xi , xj are the mole fractions of the s¼0

components in a ternary mixture. Kohler expression [10]: V E123 ¼ ðx1 þ x2 Þ2 V E12 þ ðx1 þ x3 Þ2 V E13 þ ðx2 þ x3 Þ2 V E23 0

0

n

0

0

ð2Þ

s

where V Eij ¼ xi x j ∑ ðAs Þij ðxi − x j Þ s¼0

Table 1 Density (ρ) and speed of sound (u) data of pure components at 303.15 K. Compound

1,1,1-Trichloroethane Acetophenone 1-Propanol 1-Butanol 1-Pentanol

Density(ρ) g·cm−3

Speed of sound (u) m s−1

Experiment

Literature

Experiment

Literature

1.32097 1.01944 0.79590 0.80196 0.80756

1.32099 [11] 1.01941 [12] 0.79592 [12] 0.80195 [12] 0.80758 [12]

944 1455 1192 1226 1255

942 [13] 1457 [12] 1190 [12] 1225 [12] 1257 [12]

i. The physical effects involve dispersion forces and nonspecific interactions in the mixture, adding positive contributions to VE. ii. The chemical and specific interactions result in decrease in volume, which includes charge transfer type forces and other complex forming interactions between the two species, thereby these chemical effects contribute negative values to VE. iii. The structural effects that arise from the geometrical fitting of one component into the other are due to the different molar volumes and free volumes of pure components, and add negative contributions to VE. The experimental results in the present investigation indicate that the factors which are responsible for contraction in volume are dominant over entire composition range in all the three ternary mixtures of 1,1,1-trichloroethane and acetophenone with 1-alkanols. In most of the thermodynamic properties of binary systems with ketones negative deviations in excess functions have been reported [22,23]. Alcohols, which exist in a highly associated form in the pure state [23,24] when mixed with polar solvents like ketones the monomerization occurs and new specific interactions appear in the solution. Dipole–dipole interactions too affect the properties of 1-alkanols [25]. The experimental results show that negative excess volume decrease with increase in chain length of 1-alkanols. Further, the strength of association in alkanol decreases [26] as the chain length of alkanol molecule increases from 1-propanol to 1-pentanol due to steric factors. Thus, it is expected that mixing of 1,1,1trichloroethane and acetophenone with 1-alkanols would cause dissociation of hydrogen bonded structures in the alkanols, releasing several dipoles of alkanol molecules, the protons of the –OH group of these dipoles are likely to interact with π-electrons of aromatic ring forming new hydrogen bonds. The degree of association in alkanols decreases as the carbon chain length in the alkanol increases because the higher alkanols possess less proton donating capacity than lower one and hence hetero association effect decrease in the mixtures with an increase in chain length of 1-alkanols.

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Table 2 Mole fractions of 1,1,1-trichloroethane (x1), acetophenone (x2), experimental and predicted excess volume data for the ternary mixtures of 1,1,1 trichloroethane (1) + acetophenone (2) + 1-alkanols (3) at 303.15 K. VE/cm3 mol−1 Exp.

Redlich–Kister

Kohler

Tsao–Smith

ΔVE123

1,1,1-Trichloroethane (1) + acetophenone (2) + 1-propanol (3) 0.0910 0.0876 0.88412 0.1025 0.1120 0.89092 0.1529 0.1120 0.95232 0.1419 0.3231 0.97053 0.1329 0.4419 0.98922 0.1217 0.5239 0.99859 0.1119 0.6118 1.00891 0.1517 0.7214 1.04328 0.1427 0.7917 1.04937 0.1029 0.8322 1.03859 0.0927 0.8602 1.03814 0.0910 0.0876 0.88408

−0.094 −0.111 −0.163 −0.195 −0.197 −0.188 −0.167 −0.150 −0.140 −0.129 −0.105 −0.094

−0.099 −0.119 −0.178 −0.208 −0.213 −0.203 −0.185 −0.176 −0.157 −0.124 −0.110 −0.099

−0.102 −0.122 −0.184 −0.213 −0.216 −0.204 −0.184 −0.170 −0.151 −0.121 −0.108 −0.102

−0.109 −0.132 −0.206 −0.236 −0.236 −0.221 −0.196 −0.177 −0.155 −0.123 −0.109 −0.109

0.005 0.008 0.015 0.013 0.016 0.016 0.018 0.026 0.017 0.011 0.006 0.005

1,1,1-Trichloroethane (1) + acetophenone (2) + 1-butanol (3) 0.1192 0.1392 0.90302 0.0912 0.0902 0.87688 0.1743 0.3179 0.97274 0.0923 0.2217 0.90929 0.1539 0.4510 0.98991 0.1011 0.5013 0.97440 0.1421 0.5517 1.00388 0.1171 0.6429 1.00920 0.1279 0.7217 1.02838 0.1314 0.7921 1.04233 0.1019 0.8319 1.03591 0.0919 0.8620 1.03662

−0.076 −0.060 −0.137 −0.097 −0.156 −0.140 −0.153 −0.136 −0.133 −0.132 −0.109 −0.099

−0.090 −0.066 −0.154 −0.106 −0.168 −0.149 −0.166 −0.150 −0.147 −0.142 −0.116 −0.104

−0.092 −0.067 −0.106 −0.108 −0.172 −0.154 −0.168 −0.150 −0.144 −0.137 −0.118 −0.102

−0.097 −0.069 −0.173 −0.114 −0.185 −0.162 −0.179 −0.157 −0.149 −0.139 −0.114 −0.102

0.014 0.006 0.017 0.009 0.012 0.009 0.013 0.014 0.014 0.010 0.007 0.005

1,1,1-Trichloroethane (1) + acetophenone (2) + 1-pentanol (3) 0.0871 0.0610 0.86519 0.0910 0.1010 0.87658 0.1176 0.1619 0.90342 0.1411 0.2529 0.93514 0.1180 0.3107 0.93653 0.1219 0.3719 0.95158 0.0919 0.4312 0.94969 0.1009 0.5109 0.97061 0.0862 0.6228 0.98640 0.0719 0.7127 0.99762 0.1039 0.7527 1.02031 0.1176 0.8061 0.86519

−0.003 −0.013 −0.023 −0.045 −0.062 −0.079 −0.081 −0.089 −0.088 −0.080 −0.099 −0.111

−0.009 −0.021 −0.039 −0.066 −0.077 −0.090 −0.091 −0.101 −0.090 −0.088 −0.109 −0.120

−0.010 −0.022 −0.041 −0.069 −0.080 −0.093 −0.093 −0.103 −0.100 −0.089 −0.107 −0.117

−0.011 −0.024 −0.044 −0.076 −0.086 −0.099 −0.098 −0.109 −0.104 −0.092 −0.110 −0.118

0.006 0.008 0.016 0.021 0.015 0.011 0.010 0.012 0.011 0.008 0.010 0.009

x1

x2

Density(ρ) g cm−3

The sign and the magnitude of ΔVE123 indicates that influence of third component on pair-wise interactions in a ternary mixtures, perhaps acetophenone being more polar than the other two compound

liquids is modifying nature and degree of interaction between constituent binaries. Further, the positive values of ΔVE123 are attributed to the weakening of charge transfer interaction by the addition of third component [27,28]. 3.2. Isentropic compressibility The isentropic compressibility of ternary mixtures (κs123) was calculated from the expression κ s123 ¼u‐2 123 ρ‐1 123

ð4Þ

where u123 and ρ123 denote speed of sound and density of ternary mixtures respectively. The density of ternary mixture was computed using the relation: ρ123 ¼ ðX 1 M1 þ X 2 M2 þ X 3 M3 Þ=V þ V E 123

Fig. 1. Excess volumes (V E 123 ) data for 1,1,1 trichloroethane (1) + acetophenone (2) + 1-propanol (3) at 303.15 K.

ð5Þ

where X1, X2 and X3 denote mole fractions and M1, M2 and M3 are the molecular weights of 1,1,1-trichloroethane, acetophenone and 1-alkanols respectively; V is the molar volume and VE123 is experimental ternary excess volume.

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129

Table 3 The binary parameters and standard deviation σ(VE) values of Redlich–Kister equation at 303.15 K. System cm3 mol−1 23231,1,1-Trichloroethane(1) + acetophenone(2) Acetophenone(2) + 1-propanol(3) Acetophenone(2) + 1-butanol(3) Acetophenone(2) + 1-pentanol(3) 1,1,1-Trichloroethane(1) + 1-propanol(3) 1,1,1-Trichloroethane(1) + 1-butanol(3) 1,1,1-Trichloroethane(1) + 1-pentanol(3)

a0

a1

a2

σ(VE)

−1.369

−0.353

−0.142

0.001

0.125 0.046 0.503 −0.719 −0.404 −0.255

0.842 0.740 0.674 0.371 0.026 0.037

0.494 0.174 0.267 −0.003 0.179 0.081

0.001 0.002 0.005 0.003 0.003 0.002

where κs12, κs13 and κs23 denote the deviation in isentropic compressibilities for the three binary mixtures and these are estimated using the smoothing equation h i ð9Þ κ sij ¼ 1 2 a0 þ a1 ð 1 ‐ 2 Þ þ a2 ð 1 ‐ 2 Þ2 Fig. 2. Excess volumes (V E 123 ) data for 1,1,1 trichloroethane (1) + acetophenone (2) + 1-butanol (3) at 303.15 K.

The deviation in isentropic compressibility (κs’123) was estimated using the relation κs

0

123

¼ κ s123 –

1 κ s1

–

2 κ s2

–

3 κ s3

ð6Þ

where ø1, ø2, ø3, κs1, κs2 and κs3 are the volume fractions and isentropic compressibilities of the pure components 1, 2 and 3 respectively. The magnatitude Δκs123, the difference between measured value of κs’123 and that of computed from binary data κs’123(b) has been calculated using the relation Δκ s123 ¼κ s

0

123 –

κs

0

123ðbÞ

ð7Þ

The latter magnatitude, κs’123(b) was computed using Redlich–Kister [10] relation κs

0

123ðbÞ

¼ κ s12 þ κ s13 þ κ s23

ð8Þ

where a0, a1and a2 are the constants obtained by Redlich–Kister equation. The binary parameters that were required to compute ḱs123(b) for the mixtures of 1,1,1-trichloroethane with acetophenone [15], 1,1,1trichloroethane with 1-alkanols [29] and acetophenone with 1alkanols [14] were collected from the literature and these were given in Table 4 along with standard deviation σ(Δκs123). The speed of sound (u), density of the mixture (ρ123), isentropic compressibility (κs123) and deviation in isentropic compressibility (κs’123) for three ternary mixtures were given in Table 6. Further, the quantity Δκs123, the difference between measured data of κs’123 and that of computed from the constituent binary data κs’123(b) is also included in Table 5. Moreover, the deviation in isentropic compressibility (Δκs123) for the three ternary mixtures were also graphically represented in Figs. 4 to 6. The results in Table 5 indicate that speed of sound in ternary mixture increases with increase in mole fraction of acetophenone. The structural changes occurring in the ternary mixture with the increase in concentration cause the increase in speed of sound which may result in the increase in intermolecular forces [30]. An examination of Δκs123 values that were tabulated in Table 5 suggest that the values were positive over the entire composition range in all the ternary mixtures of 1,1,1 trichloroethane and acetophenone with 1-alkanols and these were 3 to 4 times to the experimental error. This suggests that Redlich–Kister equation is capable of giving good estimation of deviation in isentropic compressibility of ternary mixtures from that of constituent binaries [14,15,29]. An examination of κs’123 values that were present in Table 5 suggest that the values were negative over the entire composition range in all the ternary mixtures of 1,1,1 trichloroethane and acetophenone with 1-alkanols. The deviation in isentropic compressibility data can be interpreted in terms of two opposing effects namely structure breaking and Table 4 The binary parameters and standard deviation σ(Δκs123) values of Redlich-Kister eq. at 303.15 K.

Fig. 3. Excess volumes (V E 123 ) data for 1,1,1 trichloroethane (1) + acetophenone (2) + 1-pentanol (3) at 303.15 K.

System

a0

a1

a2

σ(ks)

TPa−1 1,1,1-Trichloroethane(1) + acetophenone(2) Acetophenone(2) + 1-propanol(3) Acetophenone(2) + 1-butanol(3) Acetophenone (2) + 1pentanol(3) 1,1,1-Trichloroethane (1) + 1-propanol(3) 1,1,1-Trichloroethane (1) + 1-butanol(3) 1,1,1-Trichloroethane (1) + 1-pentanol(3)

−174.76 83.30 100.50 −130.85 −298.31 −232.42 −155.90

53.53 153.90 148.70 −5.96 59.01 61.30 33.31

−92.60 −18.30 71.90 −18.69 11.91 41.30 23.51

2 3 2 1 0.3 0.3 0.4

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Table 5 Volume fractions of 1,1,1-trichloroethane (ϕ1), acetophenone (ϕ2), density(ρ), speed of sound (u), isentropic compressibility (κs123), deviation in isentropic compressibility(ḱs123), deviation in isentropic compressibility computed from computed constituent binary data and (ḱs123(b)) and Δκs123 values for ternary systems 1,1,1-trichloroethane (1) + acetophenone (2) + 1-alkanols (3). Φ1

Φ2

ρ g cm−3

ḱs123(b)

Δκs123

1,1,1-Trichloroethane (1) + acetophenone (2) + 1-propanol (3) 0.1126 0.1260 0.88412 1168 829 2 0.1248 0.1592 0.89092 1194 781 −32 0.1745 0.2826 0.95232 1206 722 −37 0.1543 0.4102 0.97053 1224 688 −18 0.1374 0.5335 0.98922 1256 641 −13 0.1218 0.6125 0.99859 1271 620 −1 0.1083 0.6915 1.00891 1292 594 6 0.1393 0.7735 1.04328 1324 547 −5 0.1278 0.8282 1.04937 1355 519 −1 0.0916 0.8651 1.03859 1422 476 −38 0.0818 0.8870 1.03814 1444 462 −43 0.1126 0.126 0.88408 1168 829 2

−17 −22 −35 −45 −48 −47 −43 −38 −33 −28 −25 −17

19 −10 −2 28 35 46 49 33 23 −11 −19 19

1,1,1-Trichloroethane (1) + acetophenone (2) + 1-butanol (3) 0.1240 0.1692 0.90302 1198 771 1 0.0964 0.1119 0.87688 1209 780 −11 0.1725 0.3674 0.97274 1234 675 −23 0.0942 0.2643 0.90929 1260 693 −42 0.1476 0.5053 0.98991 1291 606 −40 0.0962 0.5572 0.97440 1306 602 −24 0.1332 0.6040 1.00388 1324 568 −41 0.1077 0.6903 1.00920 1341 551 −26 0.1154 0.7604 1.02838 1365 522 −29 0.1166 0.8212 1.04233 1378 505 −24 0.0899 0.8567 1.03591 1422 477 −38 0.806 0.824 1.03662 1449 459 −46

−19 −12 −37 −32 −41 −42 −40 −37 −33 −30 −26 −23

20 1 14 −9 1 18 −1 10 4 7 −12 −23

1,1,1-Trichloroethane (1) + acetophenone (2) + 1-pentanol (3) 0.0839 0.0687 0.86519 1224 771 −1 0.0872 0.1141 0.87658 1249 731 −27 0.1120 0.1800 0.90342 1265 692 −46 0.1329 0.2781 0.93514 1296 637 −70 0.1102 0.3390 0.93653 1325 608 −77 0.1130 0.4026 0.95158 1342 583 −81 0.0845 0.4636 0.94969 1374 558 −85 0.0919 0.5433 0.97061 1422 509 −107 0.0774 0.6530 0.98640 1436 492 −88 0.0638 0.7388 0.99762 1441 483 −67 0.0919 0.7773 1.02031 1452 465 −74 771 −1 0.0687 0.86519 1224 0.0839

6 2 −2 −10 −16 −20 −23 −25 −25 −23 −25 6

−8 −29 −44 −60 −61 −61 −62 −82 −62 −45 −50 −8

u m s−1

ks123

ḱs123 TPa−1

Fig. 4. Deviation in isentropic compressibility (Δks123) data for1,1,1 trichloroethane (1) + acetophenone (2) + 1-propanol (3) at 303.15 K.

Fig. 5. Deviation in isentropic compressibility (Δks123) data for 1,1,1 trichloroethane (1) + acetophenone (2) + 1-butanol (3) at 303.15 K.

structure making effects on mixing the component molecules and the consequent change in geometrical factors [31]. Former effects include loss of dipolar association and difference in size and shape of the component molecules which lead to positive deviation in isentropic compressibility. Whereas the latter effects arise due to dipole–dipole, dipole-induced dipole, electron-donor–acceptor interactions and interstitial accommodation of molecule lattice which contribute to negative deviation in isentropic compressibility. Structure breaking effects contribute to an increase in free spaces [32] between the molecules and structure making effects cause to decrease in free spaces of the component molecules leading to positive and negative deviations in isentropic compressibility respectively. The sign and magnitude of the actual deviation depends on the relative strengths of the two opposing effects as reported by Benson and Kiyohara [33]. The experimental Δks123values indicate that the factors which are responsible for structure making effect were prevailing in all the three ternary mixtures.

Fig. 6. Deviation in isentropic compressibility (Δks123) data for 1,1,1 trichloroethane (1) + acetophenone (2) + 1-pentanol (3) at 303.15 K.

C.N. Rao et al. / Journal of Molecular Liquids 216 (2016) 126–131

131

Table 6 The standard deviation values σ(ΔVE123) and σ(Δκs123) for ternary systems of 1,1,1-trichloroethane (1) + acetophenone (2) + 1-alkanols(3). System

A

B

C

σ(ΔVE123)

cm3 mol−1 1,1,1-Trichloroethane(1) + acetophenone (2) + 1-propanol(3) 1,1,1-Trichloroethane(1) + acetophenone(2) + 1-butanol(3) 1,1,1-Trichloroethane(1) + acetophenone (2) + 1-pentanol(3)

0.6008 0.4690 0.5547

4.9436 0.0856 −1.3496

The dependence of ΔVE123 and Δκs123 were fitted to the following empirical equation proposed by Redlich–Kister [10]: h i ‐1 ΔV E 123 =cm3 mol ¼ x1 x2 x3 AþBx1 ðx2 ‐x3 ÞþC x1 2 ðx2 ‐x3 Þ2 h

Δκ s123 =TPa‐1 ¼ ϕ1 ϕ2 ϕ3 AþBϕ1 ðϕ2 ‐ ϕ3 ÞþCϕ1 2 ðϕ2 ‐ ϕ3 Þ2

i

ð10Þ ð11Þ

where A, B and C are the ternary constants which were obtained by least square method. The values of coefficients were in turn used to compute standard deviation σ(YE123) as follows:   1=2   2 σ Y E 123 ¼ΔV E 123 =Δks123 ¼ Σ Y E 123 exp ‐ Y E 123 cal =ðm‐nÞ

A

B

C

σ(Δκs123)

2093.37 1888.98 912.53

2527.21 53,509.61 56,506.57

3 2 1

TPa−1 115.4709 112.0098 123.7403

[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

ð12Þ

[19]

where ‘m’ is the total number of experimental points and ‘n’ is the number of coefficients in Eqs.(10) and (11) and the corresponding data were presented in Table 6.

[20] [21] [22] [23] [24]

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