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Excess molar volumes, viscosities, and speeds of sound of the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
J. Chem. Thermodynamics 39 (2007) 206–217 www.elsevier.com/locate/jct
Excess molar volumes, viscosities, and speeds of sound of the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K Hossein Iloukhani a
a,*
, Babak Samiey
b
Department of Chemistry, Faculty of Science, University of Bu-Ali Sina, Hamedan 65174, Iran b Department of Chemistry, Faculty of Science, University of Lorestan, Khoramabad, Iran Received 19 March 2006; received in revised form 12 June 2006; accepted 16 July 2006 Available online 10 August 2006
Abstract Densities (q), viscosities (g), and speeds of sound (u) of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) and the involved binary mixtures (1-heptanol + trichloroethylene), (1-heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) at 298.15 K were measured over the whole composition range. The data obtained are used to calculate excess molar volumes (VE), excess isobaric thermal expansivity (aE), viscosity deviations (Dg), excess Gibbs free energies of activation of viscous flow (DG*E), and excess isentropic compressibilities ðjES Þ of the binary and ternary mixtures. The data of the binary systems were fitted to the Redlich–Kister equation while the best correlation method for the ternary system was found using the Nagata equation. Viscosities, speeds of sound and isentropic compressibilities of the binary and ternary mixtures have been correlated by means of several empirical and semi-empirical equations. The best correlation method for viscosities of binary systems is found using the Iulan et al. equation and for the ternary system using the McAllister equation. The best correlation method for speeds of sound and isentropic compressibilities of the binary systems is found using the IMR and for the ternary system using the IMR and JR. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: 1-Heptanol; Trichloroethylene; Methylcyclohexane; Speed of sound; Excess molar volume; Viscosity
1. Introduction This paper is a continuation of our earlier work [1–5]. The number of studies on thermodynamic properties of ternary mixtures has increased in recent years due to industrial applications and the theoretical interest in studying the nature of molecular interaction and packing phenomena in ternary mixtures. In this work, we measured densities, viscosities and speeds of sound of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) and the involved binary mixtures at T = 298.15 K and over the whole composition range. The data obtained are used to calculate excess molar volumes, thermal expansivity, excess thermal expansivity, viscosity deviations, excess *
Corresponding author. Tel./fax: +98 811 8271061. E-mail address: [email protected] (H. Iloukhani).
0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.07.015
Gibbs free energies of activation of viscous flow, speed of sound deviations, isentropic compressibility, excess isentropic compressibilities of the binary and ternary mixtures. The data of the binary systems were fitted to the Redlich–Kister [6] equation. Cibulka [7], Redlich–Kister type [8], and Nagata [9] equations were tested for estimating ternary properties from binary results. The best correlation method for the ternary system was found using the Nagata equation. The viscosity data for the binary and ternary mixtures were fitted to Nissan and Grunberg [10–12], Hind et al. [11–14], Katti and Chaudhri [11,12,15], McAllister [11,12,16], Heric [11,12,17], Frenkel [11,12,18], and Iulan et al. [11,12,19] and their parameters have been calculated. Theoretical models dealing with liquid state including Jacobson free length theory (FLT) [20–23], Schaaff collision factor theory (CFT) [21,23,24], Nomoto relation (NR) [21,25], Junjie relation (JR) [21,26] and Van Deal
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
207
TABLE 1 Experimental and the literature values of densities q, viscosities g, speeds of sound u, molar isobaric heat capacity Cp, and isobaric thermal expansivity a of 1-heptanol, methylcyclohexane and trichloroethylene at T = 298.15 K Compound 1-Heptanol Methylcyclohexane Trichloroethylene
qexp/(kg Æ m3) 818.77 764.99 1454.75
qlit/(kg Æ m3) a
818.6 764.96b 1455.72c
gexp/(mPa Æ s)
glit/(mPa Æ s) d
6.041 0.684 0.527
5.810 0.679d 0.545d
uexp/(m Æ s1)
a/kK1
Cp/(J Æ mol1 Æ K1)
1329 1209 1064
0.879 1.190 1.176
272.1e 184.8e 124.4e
a values were calculated from the measured densities at different temperatures. a Reference [30]. b Reference [29]. c Reference [32]. d Reference [28]. e Reference [31].
ideal mixing relation (IMR) [21,27] have been proposed for the prediction of the speeds of sound and isentropic compressibilities of the binary and ternary mixtures. Densities and viscosities of the pure reagents were in good agreement with values found in the literature [28– 32], table 1. 2. Experimental The purity of the chemicals is on the basis of mole%. 1Heptanol (P99%) and methylcyclohexane (>99%) were supplied by Merck and trichloroethylene (>99%) was obtained from Fluka. All chemical substances were used without any further purification. All mass measurements were performed on an electronic balance (AB 204-N Mettler) accurate to 0.1 mg. The estimated accuracy in the mole fractions was ±1 Æ 104. The densities of the pure compounds and their binary and ternary mixtures were measured with an Anton Paar DMA 4500 oscillating U-tube densimeter. The density measurements accuracy was ±1 Æ 102 kg Æ m3. The temperature in the cell was automatically regulated to ±0.01 K with a solid state thermostat. The speed of sound in the pure compounds and their binary and ternary mixtures was measured with a multi-frequency ultrasonic interferometer supplied by Mittal Enterprise, New Delhi with an accuracy of ±1 m Æ s1. In this work, 1 MHz frequency was employed. Viscosities at T = 298.15 K were measured with an Ubbleohde viscometer. The equation for viscosity is g ¼ qm ¼ qðkt c=tÞ;
ð1Þ
where k and c are the viscometer constants and t, g, and m are the efflux time, dynamic and kinematic viscosities, respectively. The dynamic viscosity was reproducible to within ±2 Æ 103 mPa Æ s. The viscometer was suspended in a water bath maintained to ±0.01 K. 3. Results and discussion 3.1. Densities and excess molar volumes The excess molar volumes of the n-component mixtures are calculated from the densities of the pure liquids and their mixtures according to the following equation:
V E ðm3 mol1 Þ ¼
n n X xi M i X xi M i ; q qi i¼1 i¼1
ð2Þ
where q is the density of the mixture and xi, qi, Mi, and Vi are the mole fraction, density, molecular weight and molar volume of pure component i, respectively. Excess isobaric thermal expansivity (aE) values can be calculated as follows [33] which is the most frequent choice for this purpose: n X /i ai ; ð3Þ aE ðK1 Þ ¼ a aid ¼ ðoV m =oT ÞP =V m i¼1
where Vm is the molar volume of the mixture and /i is the ideal volume fraction of pure component i. aid and ai are the isobaric thermal expansivity of the ideal mixture and pure component i, respectively. The corresponding VE values of the binary mixtures (1-heptanol + trichloroethylene), (1-heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) measured at T = 298.15 K are presented in table 2 and plotted against mole fraction of 1-heptanol in figure 1. Each set of results were fitted using Redlich–Kister equation for the binary mixtures: N X k Y ¼ xðx 1Þ Ak ð1 2xÞ ; ð4Þ k¼1
where Y = (VE or Dg or DG*E or jES or Du) and x is the mole fraction of the first component. The coefficients Ak were calculated by the unweighted least-squares method. In each case, the optimum number of coefficients was ascertained from an examination of standard deviation (r) with hX i1=2 r¼ ðY exp Y cal Þ2 =ðn pÞ ; ð5Þ where Ycal is the calculated values of the property Y, and n and p are the experimental points and number of parameters retained in the respective equations, respectively. Adjustable parameters of VE values and standard deviations are given in table 12. The values of VE for the binary mixture (1-heptanol + methylcyclohexane) are positive over the entire composition range, due to the rupture or stretch of the hydrogen bonding of self-associated molecules of 1-heptanol. The values of VE for the
208
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
TABLE 2 Excess molar volumes VE for the binary mixtures at T = 298.15 K x1
q/ (kg Æ m3)
0.1003 0.2008 0.2682 0.2999 0.3999 0.4498 0.4995
x1
q/ (kg Æ m3)
{1-Heptanol (1) + trichloroethylene (2)} 1358.95 0.0729 0.5504 1036.48 1273.76 0.0772 0.6003 1008.26 1221.42 0.0760 0.6504 981.28 1198.18 0.0609 0.6996 955.70 1129.05 0.0379 0.8005 906.25 1096.95 0.0229 0.8489 883.87 1066.35 0.0032 0.8969 862.42
106VE/ (m3 Æ mol1) 0.0226 0.0276 0.0489 0.0556 0.0611 0.0614 0.0470
{1-Heptanol (1) + methylcyclohexane (2)} 770.20 0.1093 0.5497 795.18 773.03 0.1266 0.5999 797.98 775.76 0.1446 0.6503 800.71 781.37 0.1610 0.7007 803.42 786.91 0.1504 0.8000 808.68 789.61 0.1458 0.8495 811.24 792.45 0.1319 0.8998 813.80
0.1000 0.1506 0.2001 0.3011 0.4000 0.4490 0.5002
0.1028 0.2001 0.2201 0.2986 0.3663 0.4125 0.5008
106VE/ (m3 Æ mol1)
0.1176 0.0931 0.0777 0.0612 0.0290 0.0166 0.0080
{Trichloroethylene (1) + methylcyclohexane (2)} 815.78 0.1009 0.5513 1082.08 0.2706 866.91 0.1783 0.5999 1116.32 0.2609 877.87 0.1912 0.6491 1152.32 0.2473 922.08 0.2350 0.7008 1191.58 0.2259 962.25 0.2587 0.7996 1271.37 0.1690 990.67 0.2691 0.8497 1314.36 0.1327 1047.75 0.2754 0.9011 1360.38 0.0893
0.30
6 E 3 -1 10 V /(m . mol )
0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10 0.0
0.2
0.4
0.6
0.8
1.0
x1
FIGURE 1. Excess molar volumes for the binary mixtures of r {1heptanol (1) + trichloroethylene (2)}, m {1-heptanol (1) + methylcyclohexane (2)}, and j {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
binary mixture (trichloroethylene + methylcyclohexane) are positive over the entire composition range, as expected from dispersion effects between unlike molecules. The values of VE are negative in 1-heptanol rich region of the binary mixture (1-heptanol + trichloroethylene) due to the polar interactions between hydrogen atom of –OH group of 1-heptanol and chloro atoms of trichloroethylene (cross-associated OH–Cl bonds) and positive in 1-heptanol lower region due to the depolymerization effects of trichloroethylene on the 1-heptanol, table 2 and figure 1.
TABLE 3 Densities q, excess molar volumes VE, thermal expansivity a, and excess thermal expansivity aE for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K x1
x2
q/(kg Æ m3)
106VE/(m3 Æ mol1)
a/kK1
aE/kK1
0.0500 0.0503 0.0510 0.0501 0.0999 0.0998 0.1005 0.1008 0.1045 0.1013 0.1004 0.1000 0.1003 0.1978 0.2001 0.1985 0.1977 0.1974 0.1997 0.2001 0.2993 0.2996 0.3011 0.3000 0.3009 0.2995 0.4003 0.3981 0.3933 0.3993 0.4001 0.4973 0.4993 0.4987 0.4977 0.5998 0.6010 0.5962 0.6976 0.6959 0.7976 0.8465 0.8446 0.9003
0.9001 0.8500 0.1018 0.0505 0.1017 0.2006 0.3018 0.3965 0.4929 0.5985 0.6998 0.7986 0.8488 0.1007 0.2025 0.3009 0.4066 0.5039 0.6001 0.7061 0.1015 0.2020 0.2983 0.3999 0.5000 0.6002 0.1002 0.2039 0.3008 0.4009 0.5003 0.1038 0.2021 0.3006 0.4022 0.1008 0.1979 0.3024 0.1021 0.2026 0.1014 0.0521 0.1051 0.0499
1359.01 1314.48 817.59 791.90 820.00 871.69 928.14 984.41 1045.92 1117.93 1192.62 1271.50 1313.57 824.79 877.82 932.23 994.84 1056.64 1122.26 1200.07 830.60 882.58 935.62 995.22 1058.16 1125.61 835.34 888.60 941.43 1000.19 1062.25 842.31 892.79 946.35 1005.29 846.25 895.68 951.98 851.96 902.81 856.70 835.38 860.87 837.02
0.1052 0.1511 0.1776 0.1343 0.2605 0.2660 0.2963 0.3165 0.2997 0.2697 0.2321 0.1564 0.1462 0.2136 0.2549 0.2776 0.2781 0.2534 0.2138 0.1465 0.2076 0.2304 0.2329 0.2184 0.1822 0.1370 0.1819 0.1833 0.1772 0.1436 0.1009 0.1410 0.1268 0.1037 0.0640 0.0891 0.0637 0.0256 0.0394 0.0045 0.0043 0.0022 0.0296 0.0135
1.111 1.126 1.101 1.111 1.158 1.078 1.088 1.107 1.062 1.046 1.098 1.133
0.044 0.030 0.070 0.061 0.004 0.074 0.061 0.039 0.081 0.095 0.040 0.003
1.055 1.060 1.019 1.116 1.060 1.043 1.083 1.024 1.031 1.037 1.045 1.040 0.099 0.958 1.013 1.009 1.020 0.988 0.973 0.974 0.972 0.965 0.945 0.949 0.945 0.916 0.919 0.899 0.850 0.964 0.936
0.066 0.057 0.094 0.006 0.047 0.059 0.014 0.063 0.051 0.040 0.028 0.028 0.064 0.095 0.036 0.036 0.017 0.042 0.048 0.041 0.037 0.037 0.044 0.033 0.031 0.043 0.033 0.030 0.068 0.050 0.066
Also, the corresponding VE, a and aE values of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) are shown in table 3. The ternary excess magnitudes or deviation in ternary magnitudes were correlated using Cibulka, Redlich–Kister-type and Nagata equations. The following expression: Y 123 ¼ Y bin þ x1 x2 ð1 x1 x2 ÞD123 ;
ð6Þ
where Y bin ¼ Y 12 þ Y 13 þ Y 23
ð7Þ
is known as the binary contribution to the excess (or deviations in) ternary properties and Yij values are obtained from equation (4).
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
The last term stands for the ternary contribution to the magnitude. Several equations have been tested to correlate D123, the first of them suggested by Cibulka D123 ¼ ðB0 þ B1 x1 þ B2 x2 Þ:
DG
E
1
209
ðJ mol Þ ¼ RT lnðgV =hN A Þ
n X
! xi lnðgi V i =hN A Þ ;
i¼1
ð11Þ
ð8Þ
n X
ð12Þ
And the second is obtained from Redlich–Kister type equation:
Dg ðmPa sÞ ¼ g
D123 ¼ A0 þ A1 ðx2 x1 Þ þ A2 ðx3 x1 Þ þ A3 ðx3 x2 Þ;
where g and gi are the dynamic viscosities of the mixture and pure component i and V and Vi are the molar volumes of the mixture and pure component i, respectively. R is the gas constant, T is the absolute temperature, h is Planck’s constant, and NA is the Avagadro’s number. The g, DG*E, and Dg values the binary mixtures (1-heptanol + trichloroethylene), (1-heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) are presented in table 4 and the Dg and DG*E are plotted against mole fraction of 1-heptanol in figures 3 and 4, respectively. Each set of results were fitted using Redlich– Kister equation for the binary mixtures, equation (4) and the adjustable parameters and standard deviations are given in table 12. Also, The corresponding g, DG*E, and
ð9Þ
the third one proposed by Nagata D123 ¼ RT ðB0 B1 x1 B2 x2 B3 x21 B4 x22 B5 x1 x2 B6 x31 B7 x32 B8 x21 x2 Þ:
ð10Þ E
Adjustable parameters and standard deviations of V obtained from Cibulka, Redlich–Kister type and Nagata equations are given in tables 13, 14, and 15, respectively. The best correlation method for the ternary system is found using the Nagata equation. Isolines of VE from Nagata equation for the ternary system are shown in figure 2. The ternary VE values are negative in 1-heptanol rich composition range and positive in 1-heptanol lower range due to combination of interactions involved in related binary mixtures. The ternary aE values are negative over the entire composition range, table 3. a is considered to be the cross-fluctuation of volume and enthalpy [34]. a and aE values of the ternary system are given in table 3. Negative aE is due to the formation of new molecular interaction in the mixture. Negative aE means that fluctuation of the volume causing interaction energy in the mixture is lesser than in random mixing liquids. 3.2. Dynamic viscosities The excess Gibbs free energies of activation (DG*E) for viscous flow and viscosity deviations (Dg) for n-component mixtures can be calculated as: Trichloroethylene 0.0
0.1
1.0
0.05 0.9
0.2
0.8
0.3
0.7
0.4
0.6
0.5
0.5 0.25
0.6
TABLE 4 Densities q, viscosities g, viscosity deviations Dg, and excess Gibbs free energies of activation of viscous flow DG*E for the binary mixtures at T = 298.15 K x1
q/(kg Æ m3)
0.1004 0.2090 0.2996 0.4006 0.4457 0.4980 0.5977 0.6978 0.7968 0.9002
{1-Heptanol (1) + trichloroethylene (2)} 1359.05 0.643 0.438 86 1267.14 0.837 0.842 67 1198.31 1.054 1.125 33 1128.51 1.373 1.363 17 1099.49 1.544 1.441 34 1067.32 1.774 1.499 62 1006.84 2.296 1.527 100 956.65 2.979 1.395 124 907.98 3.818 1.103 127 860.90 4.856 0.635 82
0.1009 0.2007 0.3011 0.4011 0.4501 0.4985 0.6033 0.7417 0.7985 0.9006
{1-Heptanol (1) + methylcyclohexane (2)} 770.31 0.797 0.427 162 775.77 0.956 0.803 249 781.36 1.174 1.123 280 786.95 1.461 1.372 279 789.68 1.640 1.455 257 792.38 1.839 1.516 235 798.15 2.384 1.532 158 805.60 3.369 1.289 50 808.59 3.875 1.086 10 813.84 4.922 0.586 30
0.1028 0.2001 0.3015 0.3998 0.4528 0.4994 0.6504 0.6997 0.7990 0.8987
{Trichloroethylene (1) + methylcyclohexane (2)} 815.72 0.654 0.014 29 866.92 0.630 0.023 49 923.79 0.608 0.029 62 982.79 0.589 0.032 70 1016.29 0.580 0.033 73 1046.80 0.572 0.033 74 1153.26 0.551 0.031 70 1190.77 0.546 0.028 67 1270.86 0.536 0.023 57 1358.20 0.529 0.014 35
0.4 0.20 0.3
0.15 0.10
0.8
0.2 0.05 0.00
0.9
Methylcyclohexane0.0
0.10
0.15
0.1
0.2
g/(mPa Æ s)
Dg/(mPa Æ s)
DG*E/(J Æ mol1)
0.30
0.7
1.0
x i gi ;
i¼1
-0.05
0.1
0.0 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1-Heptanol
FIGURE 2. Isolines at constant excess molar volumes, 106VE (m3 Æ mol1) for the ternary mixtures of {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} correlated with equation (10) at T = 298.15 K.
210
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217 TABLE 5 Densities q, viscosities g, viscosity deviations Dg and excess Gibbs free energies of activation of viscous flow DG*E for the ternary mixture {1heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
0.0
Δη /(mPa . s)
-0.2 -0.4 -0.6 -0.8 -1.0
-1.6 -1.8 0.0
0.2
0.4
0.6
0.8
1.0
x1
/(J . mol-1)
FIGURE 3. Viscosity deviations for the binary mixtures of r {1-heptanol (1) + trichloroethylene (2)}, m {1-heptanol (1) + methylcyclohexane (2)}, and n {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
*E
x2
q/ (kg Æ m3)
g/ (mPa Æ s)
Dg/ (mPa Æ s)
DG*E/ (J Æ mol1)
0.0500 0.0500 0.0500 0.0498 0.0999 0.0994 0.1001 0.1002 0.0985 0.1000 0.0988 0.1001 0.1001 0.1992 0.1990 0.2019 0.0209 0.2007 0.1993 0.1983 0.2996 0.2965 0.3008 0.2937 0.2961 0.3004 0.3985 0.4004 0.3998 0.4000 0.3987 0.5008 0.5021 0.4986 0.5010 0.5979 0.5937 0.5992 0.6998 0.6964 0.8428 0.8454 0.8486 0.8979
0.8995 0.8503 0.1010 0.0503 0.1002 0.2012 0.3004 0.4005 0.5069 0.5985 0.7008 0.8003 0.8502 0.1009 0.2014 0.3013 0.3999 0.5014 0.6016 0.7021 0.1040 0.2078 0.3013 0.4039 0.5065 0.5980 0.1005 0.2001 0.3005 0.3985 0.5013 0.1006 0.2014 0.2992 0.3991 0.1030 0.2045 0.3004 0.0999 0.2021 0.0507 0.1048 0.0498 0.0513
1358.55 1314.84 817.13 791.82 819.32 872.03 927.34 986.94 1054.89 1117.95 1193.47 1272.92 1315.32 825.03 877.24 932.71 990.98 1055.30 1123.31 1196.93 831.93 885.61 937.42 997.50 1062.27 1124.11 835.46 886.78 941.62 998.80 1062.94 840.94 892.61 945.64 1003.54 847.24 898.80 950.91 850.98 902.57 834.50 860.76 834.44 837.58
0.571 0.574 0.699 0.712 0.765 0.736 0.718 0.702 0.677 0.668 0.651 0.644 0.644 0.924 0.898 0.885 0.860 0.845 0.833 0.819 1.138 1.108 1.101 1.067 1.060 1.066 1.427 1.413 1.392 1.382 1.373 1.826 1.815 1.787 1.800 2.329 2.298 2.318 3.014 3.009 4.263 4.288 4.321 4.840
0.240 0.245 0.237 0.231 0.438 0.449 0.455 0.456 0.455 0.458 0.452 0.450 0.443 0.811 0.820 0.834 0.838 0.836 0.824 0.817 1.134 1.131 1.147 1.127 1.130 1.133 1.376 1.385 1.386 1.382 1.368 1.525 1.527 1.521 1.505 1.542 1.534 1.529 1.403 1.374 0.928 0.908 0.902 0.647
111 124 134 127 181 192 187 164 158 161 152 127 101 243 238 212 218 183 140 123 262 226 198 162 116 77 242 203 155 105 38 187 125 73 5 99 24 30 19 78 36 148 47 47
-1.2 -1.4
ΔG
x1
150 100 50 0 -50 -100 -150 -200 -250 -300 -350 0.0
0.2
0.4
0.6
0.8
1.0
x1
FIGURE 4. Excess Gibbs free energies of activation for viscous flow for the binary mixtures of r {1-heptanol (1) + trichloroethylene (2)}, m {1heptanol (1) + methylcyclohexane (2)}, and n {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
Dg values of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) are shown in table 5. Each set of results were fitted to Cibulka, Redlich–Kister type and Nagata equations, equations (8), (9), and (10), respectively, and the adjustable parameters and standard deviations are given in tables 13, 14, and 15, respectively. The best correlation method for the ternary system is found using the Nagata equation. Isolines of Dg and DG*E from Nagata equation for the ternary system are shown in figure 5a and b. The values of Dg for the binary mixtures (1-heptanol + trichloroethylene), (1-heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) are negative over the entire composition range. In two first binary systems, negative values of Dg results from rupture or stretch of the hydrogen bonding of self-associated molecules of 1heptanol. In the binary mixture (trichloroethylene + methylcyclohexane), negative and small Dg values are due to the dispersion interactions between unlike molecules, figure 3. DG*E values for the binary mixtures (trichloroethylene + methylcyclohexane) and (1-heptanol + methylcyclo-
hexane) are negative over the entire composition range. DG*E values for the binary mixture (1-heptanol + trichloroethylene), are positive over the 1-heptanol rich region, figure 4. It seems that in the binary mixture (1-heptanol + trichloroethylene), the polar interaction between hydrogen atom of –OH group of 1-heptanol and chloro atoms of trichloroethylene results to closer packing and DG*E becomes positive in 1-heptanol rich composition range. The ternary viscosity deviations Dg, are negative over the whole composition range and the DG*E values are posi-
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217 Trichloroethylene 0.0
a
1.0
0.1
0.9
0.2
0.8
0.3
0.7
-0.3
0.4
0.6
-0.5 -0.7
0.5
0.5
-0.9 -1.1
0.6
0.4 -1.3
0.7
-1.5
0.3 -1.5
0.8
0.2
-1.3
-1.1
0.9
-0.9
0.1
-0.7 -0.5 -0.3
1.0 0.0
Methylcyclohexane
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
1-Heptanol
Trichloroethylene
b
0.0
0.1
1.0
-35
0.9
-90 0.2
0.7
ln g ¼
-145 0.4
0.6
0.5
xi ln gi þ
n X n X
xi xj Aij þ
n X n X n X
j>i
i¼1
i¼1
j>i
xi xj xk Aijk :
k>j
ð13Þ
0.5
0.4
Hind et al. equation
-200 0.7
0.3
!
75
0.8
0.2 -35
0.9
20
g¼
0.1
-255
1.0
0.0 0.1
n X i¼1
0.6
0.0
mixture compared with the behavior of pure liquids. According to Fort and Moore [38] this viscosity behavior corresponds to systems in which there is an associated component and in which solute–solvent complexes are not formed or have low stability. The breaking of hydrogen bonding of 1-heptanol makes the mixture to flow more easily. To correlate experimental data of ternary system from binary ones, different empirical and semi-empirical relations have been used. The correlation equations of Nissan and Grunberg, Hind, Frenkel, McAllister, Katti and Chaudhri, Heric, and Iulan et al. have been developed for binary mixtures. Canosa et al. [12] introduced new parameter to correlate experimental data of ternary systems from binary ones. The viscosity of n-component mixture according to correlating equations [11,12] are as follows: Nissan and Grunberg equation
0.8
0.3
Methylcyclohexane
211
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
n X
x2i gi
þ2
n X n X
i¼1
xi xj Aij þ
n X n X n X
j>i
i¼1
i¼1
j>i
xi xj xk Aijk :
k>j
1-Heptanol
FIGURE 5. Isolines at (a) constant viscosity deviations, Dg (mPa Æ s) and (b) excess Gibbs free energies of activation for viscous flow, DG*E (J Æ mol1) for the ternary mixture of {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} correlated with equation (10) at T = 298.15 K.
ð14Þ Frenkel equation ln g ¼
n X
x2i ln gi
þ2
i¼1
n X n X
xi xj ln Aij þ
j>i
i¼1
n X n X n X i¼1
j>i
! xi xj xk ln Aijk :
k>j
ð15Þ
tive in 1-heptanol rich composition range, table 5 and figure 5 which is due to combination of interactions involved in related binary mixtures. According to Kauzman and Eyring [35], the viscosity of a mixture strongly depends on entropy of mixture, which is related to liquid structure and enthalpy (and consequently to molecular interactions between the components of the mixture). So, the viscosity deviations are functions of interactions as well as size and shape of molecules. Vogel and Weiss [36] affirm that mixtures with strong interactions between different molecules (HE < 0 and negative deviations from Raoult’s law) present positive viscosity deviations; whereas for mixtures with positive deviations of Raoult’s law and without strong specific interactions, the viscosity deviations are negative. In this way, Meyer et al. [37] state that excess Gibbs free energy of activation of viscous flow, like viscosity deviations can be used to detect molecular interactions. The negative values observed for Dg and DG*E of the ternary system under study point out the easier flow of
McAllister equation lnðgV Þ ¼
n X
x3i lnðgi V i Þ þ 3
i¼1
6
n X n X i¼1
n X n X n X j>i
i¼1
x2i xj ln Aij þ
j6¼i
ð16Þ
xi xj xk ln Aijk :
k>j
Katti and Chaudhri equation lnðgV Þ ¼
n X
xi lnðgi V i Þ þ
i¼1
n X n X i¼1
xi xj Aij þ
j>i
n X n X n X i¼1
j>i
xi xj xk Aijk :
k>j
ð17Þ
Heric equation lnðgV Þ ¼
n X
xi lnðgi V i Þ þ
i¼1
i¼1
n X n X n X i¼1
n X n X
j>i
k>j
xi xj xk Aijk :
j>i
xi xj
1 X
! Ak ðxi xj Þ
k
þ
k¼0
ð18Þ
212
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
Iulan et al. equation lnðgV Þ ¼
n X
xi lnðgi V i Þ þ
i¼1
j>i
xi xj
3 X
j>i
i¼1
n X n X n X i¼1
n X n X
! Ak ðxi xj Þ
k
þ
k¼0
ð19Þ
xi xj xk Aijk ;
k>j
where in above-mentioned equations Aij and Ak are the binary correlation parameters and Aijk is the ternary correlation parameter. The best correlation method for binary systems is found using the Iulan et al. equation and for the ternary system using the McAllister equation. Adjustable parameters of correlating equations and standard deviations are given in table 6.
TABLE 6 Adjustable parameters of viscosity correlating equations and the corresponding standard deviations for the binary mixtures and ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K {1-Heptanol Hind et al.a A12 = 0.302 Nissan and Grunbergb A12 = 0.0964 Katti and Chaudhrib A12 = 0.0819 McAllisterc A12 = 3.858 Hericb A0 = 0.0896 Frenkela A12 = 1.7636 Iulan et al.b A0 = 0.1041
3.3. Speeds of sound and excess isentropic compressibilities Isentropic compressibility jS, was calculated using Newton–Laplace equation: jS ¼ 1=qu2 :
ð20Þ
Excess isentropic compressibilities jES , n-component were calculated using the relation [27,34] jES ðTPa1 Þ ¼ jS jid S n X jid /i jS;i þ TV m a2 S ¼ i =C p;i i¼1
8 < :
T
n X
! xi V i
i¼1
n X
!2 , /i ai
i¼1
ð21Þ
n X i¼1
9 =
xi C p;i ; ;
ð22Þ
where jid S is the ideal isentropic compressibility of mixture. /i, Cp,i, jS,i, and ai are the ideal volume fraction, isobaric molar heat capacity, isentropic compressibility, and thermal expansivity of the pure component i, respectively. Duis obtained from following equations: Du ðm s1 Þ ¼ u
n X
x i ui ;
ð23Þ
i¼1
where u and ui are the speed of sound in mixture and pure component i, respectively. The data of experimental u and jS, jES and Du values of the binary mixtures (1-heptanol + trichloroethylene), (1heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) measured at 298.15 K are presented in table 7 and the Du and jES are plotted against mole fraction of 1-heptanol in figures 6 and 7. Each set of results were fitted using Redlich–Kister equation for the binary mixtures, equation (4) and the adjustable parameters and standard deviations are given in table 12. The values of jES are negative in 1-heptanol rich region of the binary mixtures (1-heptanol + trichloroethylene) and (1-heptanol + methylcyclohexane). The positive jES values of these binary mixtures are due to the depolymerization
(1) + trichloroethylene (2)} r(mPa Æ s) = 0.100 r(mPa Æ s) = 0.053 r(mPa Æ s) = 0.067 A21 = 1.1217
r(mPa Æ s) = 0.009
A1 = 0.4096
r(mPa Æ s) = 0.009
r(mPa Æ s) = 0.071 A1 = 0.3513 A2 = 0.1279 A3 = 0.1793
r(mPa Æ s) = 0.005
{1-Heptanol (1) + methylcyclohexane (2)} Hind et al.a A13 = 0.378 r(mPa Æ s) = 0.100 Nissan and Grunbergb A13 = 0.2123 r(mPa Æ s)=0.084 Katti and Chaudhrib A13 = 0.3635 r(mPa Æ s) = 0.106 McAllisterc A13 = 4.2181 A31 = 1.4073 r(mPa Æ s) = 0.014 Hericb A0 = 0.3558 A1 = 0.507 r(mPa Æ s) = 0.014 Frenkela A13 = 1.687 r(mPa Æ s) = 0.107 Iulan et al.b r(mPa Æ s) = 0.002 A0 = 0.3742 A1 = 0.4664 A2 = 0.1362 A3 = 0.1047 {Trichloroethylene (1) + methylcyclohexane (2)} Hind et al.a A23 = 0.538 r(mPa Æ s) = 0.001 Nissan and Grunbergb A23 = 0.1959 r(mPa Æ s) = 0.001 Katti and Chaudhrib A23 = 0.1230 r(mPa Æ s) = 0.001 McAllisterc A23 = 0.55688 A32 = 0.69038 r(mPa Æ s) = 0.001 Hericb A0 = 0.1233 A1 = 0.016 r(mPa Æ s)= 0.001 Frenkela A23 = 0.544 r(mPa Æ s)= 0.001 Iulan et al.b r(mPa Æ s) = 0.000 A0 = 0.1182 A1 = 0.0119 A2 = 0.0389 A3 = 0.0103 {1-Heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} A123 r(mPa Æ s) Hind et al.a 1.356 0.153 Nissan and Grunbergb 1.9353 0.058 Katti and Chaudhrib 0.7691 0.072 McAllisterc 1.2498 0.035 b Heric 0.8265 0.038 Frenkela 450.318 0.091 Iulan et al.b 0.8198 0.047 a b c
Dimension of parameter(s) is in mPa Æ s. Parameter(s) is(are) dimensionless. Dimension of parameters is in (Æ107 kg Æ m4 Æ s1 Æ mol1).
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
1
1
jES =TPa1
x1
q/(kg Æ m )
0.0000 0.1090 0.1900 0.2991 0.3967 0.4959 0.5488 0.5981 0.6928 0.7962 0.8960 1.0000
{1-Heptanol (1) + trichloroethylene (2)} 1454.75 1064 607 1351.24 1047 675 43 1282.42 1066 686 40 1198.68 1099 691 31 1131.16 1130 692 23 1068.60 1162 693 17 1037.37 1180 692 14 1009.51 1196 693 12 959.11 1228 691 7 908.29 1263 690 3 862.85 1298 688 2 818.77 1329 691
0.0000 0.1031 0.2024 0.3006 0.4033 0.4973 0.5394 0.6026 0.7045 0.7972 0.8951 1.0000
0.0000 0.1611 0.3085 0.4380 0.5206 0.6133 0.6514 0.7316 0.8075 0.8737 0.9418 1.0000
u/(m Æ s )
jS/TPa
{1-Heptanol (1) + methylcyclohexane (2)} 764.96 1215 886 770.43 1217 876 5 775.87 1225 859 3 781.33 1236 838 1 787.07 1247 817 3 792.31 1259 796 5 794.64 1264 788 5 798.11 1273 773 6 803.63 1287 751 6 808.52 1300 732 5 813.56 1315 711 4 818.77 1329 691
1
Du/(m Æ s )
46 48 44 39 33 29 27 20 12 3
-10
-25
-40
-55 0.0
0.2
0.4
0.6
0.8
1.0
x1
FIGURE 6. Speed of sound deviations for the binary mixtures of r {1heptanol (1) + trichloroethylene (2)}, m {1-heptanol (1) + methylcyclohexane (2)}, and n {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
70
10 13 13 14 13 12 11 8 6 2
{Trichloroethylene (1) + methylcyclohexane (2)} 764.96 1215 886 812.71 1190 869 16 1 866.57 1166 849 29 2 924.83 1142 829 42 7 969.09 1126 814 49 10 1027.24 1108 793 54 14 1054.36 1096 790 62 21 1118.89 1084 761 58 21 1191.62 1068 736 58 25 1267.09 1053 712 57 30 1359.71 1050 667 38 23 1454.75 1064 607
effects of trichloroethylene or methylcyclohexane on 1heptanol and the negative jES values of (1-heptanol + trichloroethylene) binary mixture is due to the polar interactions between hydrogen atom of –OH group of 1-heptanol and chloro atoms of trichloroethylene and in (1-heptanol + methylcyclohexane) binary mixture results from interstitially accommodation of methylcyclohexane molecules in a network of bonded 1-heptanol molecules leading to more dense packing of unlike molecules. The values of jES are positive over the entire composition range of the binary mixture (trichloroethylene + methylcyclohexane) due to the dispersion interactions between unlike molecules, figure 7. Also, the corresponding u and jS, jES and Du values of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) are shown in table 8. Each set of
60 50
κ SE /(TPa -1)
3
5
Δ u /(m . s-1)
TABLE 7 Densities q, speeds of sound u, isentropic compressibilities jS, excess isentropic compressibilities jES , and speed of sound deviations Du for the binary mixtures at T = 298.15 K
213
40 30 20 10 0 -10 0.0
0.2
0.4
0.6
0.8
1.0
x1
FIGURE 7. Excess isentropic compressibilities for the binary mixtures of r {1-heptanol (1) + trichloroethylene (2)}, m {1-heptanol (1) + methylcyclohexane (2)}, and n {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
results were fitted to Cibulka, Redlich–Kister–type and Nagata equations, respectively, and the adjustable parameters and standard deviations are given in tables 13, 14, and 15, respectively. The best correlation method for the ternary system is found using the Nagata equation. Isolines of jES from Nagata equation for the ternary system are shown in figure 8 and the ternary jES values are mainly positive, table 8 which results from combination of interactions involved in related binary mixtures. Speeds of sound and isentropic compressibilities of the n-component mixtures were fitted to the following polynomial equation [21]: n X m X Q¼ Bij xji ; ð24Þ i¼1
j¼1
where Q stands for u or jS and xi is the mole fraction of component i in the binary and ternary mixtures. The adjustable coefficients Bij and standard deviations are presented in table 9. Table 10 lists various basic parameters of the pure components namely molar volume, V0, molar volume at absolute zero, V0, available volume, Va, intermolecular free
214
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
TABLE 8 Densities q, speeds of sound u, isentropic compressibilities jS, excess isentropic compressibilities jES , and speed of sound deviations Du for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K x1
x2
q/ (kg Æ m3)
u/ (m Æ s1)
jS/ TPa1
jES = TPa1
Du/ (m Æ s1)
0.0500 0.5030 0.0510 0.0501 0.0999 0.0998 0.1005 0.1008 0.1045 0.1013 0.1004 0.1000 0.1003 0.1978 0.2001 0.1985 0.1977 0.1974 0.1997 0.2001 0.2993 0.2996 0.3011 0.3000 0.3009 0.2995 0.4003 0.3981 0.3933 0.3993 0.4001 0.4973 0.4993 0.4987 0.4977 0.5998 0.6010 0.5962 0.6976 0.6959 0.7976 0.8465 0.8446 0.9003
0.9001 0.8500 0.1018 0.0505 0.1017 0.2006 0.3018 0.3965 0.4929 0.5985 0.6998 0.7986 0.8488 0.1007 0.2025 0.3009 0.4066 0.5039 0.6001 0.7061 0.1015 0.2020 0.2983 0.3999 0.5000 0.6002 0.1002 0.2039 0.3008 0.4009 0.5003 0.1038 0.2021 0.3006 0.4022 0.1008 0.1979 0.3024 0.1021 0.2026 0.1014 0.0521 0.1051 0.0499
1359.01 1314.48 817.59 791.90 820.00 871.69 928.14 984.41 1045.92 1117.93 1192.62 1271.50 1313.57 824.79 877.82 932.23 994.84 1056.64 1122.26 1200.07 830.60 882.58 935.62 995.22 1058.16 1125.61 835.34 888.60 941.43 1000.19 1062.25 842.31 892.79 946.35 1005.29 846.25 895.68 951.98 851.96 902.81 856.70 835.38 860.87 837.02
1042 1048 1188 1201 1191 1168 1145 1126 1108 1089 1073 1058 1052 1200 1177 1156 1134 1116 1100 1084 1211 1188 1169 1149 1131 1115 1224 1201 1182 1163 1147 1236 1217 1198 1180 1252 1234 1213 1267 1247 1282 1298 1288 1307
678 693 867 875 860 841 822 801 779 754 728 703 688 842 822 803 782 760 736 709 821 803 782 761 739 715 799 780 760 739 716 777 756 736 714 754 733 714 731 712 710 711 700 699
39 36 8 6 8 11 15 18 21 26 30 36 39 6 9 12 17 21 26 31 3 7 10 14 19 24 0 5 7 13 17 1 1 6 10 3 1 6 4 1 3 3 1 3
43 44 17 12 20 28 36 41 44 47 48 48 46 22 30 36 42 45 47 47 23 31 35 40 43 44 22 29 32 37 38 20 24 28 31 16 20 24 12 17 9 6 7 3
length Lf, molar surface factor, Y, molecular radius, r, molar actual volume of molecule, B, and collision factor, S at 298.15 K.
TABLE 9 Parameter values of equation (24), Bij and standard deviations for the binary mixtures and ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K B11
B12
B13
B21
B22
B23
B31
B32
B33
r
1
u/(m Æ s ) {1-Heptanol (1) + trichloroethylene (2)} 1616 277 645 397 {1-Heptanol (1) + methylcyclohexane (2)} 1695 364 798 413 {Trichloroethylene (1) + methylcyclohexane (2)} 1437 391 799 421 {1-Heptanol(1) + trichloroethylene (2)+Methylcyclohexane(3)} 1280 132 84 994 2 34 1177 28
10 2 7 6
1
jS/(TPa1) {1-Heptanol (1) + trichloroethylene (2)} 1174 495 299 336 {1-Heptanol (1) + methylcyclohexane (2)} 1192 504 414 477 {Trichloroethylene (1) + methylcyclohexane (2)} 1217 583 574 300 {1-Heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} 756 179 117 698 19 64 891 27 27
13 3 12 1
The speeds of sound were also calculated using Jacobson free length theory (FLT), Schaaff collision factor theory (CFT), Nomoto relation (NR), Junjie relation (JR), and Van Deal ideal mixing relation (IMR). The speed of sound in the n-component mixture are given by following equations. 3.3.1. Jacobson free length theory (FLT) u¼
K : Lf q1=2
ð25Þ
The value of K for the individual n-component mixture has been taken as [22] n X K¼ K i xi ; ð26Þ i¼1
where the value of Ki for each component in the mixture are obtained from equation (25). The free length of the mixture Lf is obtained by Pn 2 V i¼1 xi V 0;i Pn ; ð27Þ Lf ¼ i¼1 xi Y i where V0,i is the molar volume of pure component i at absolute zero temperature, Yi the surface area per mole
TABLE 10 Molar volume V0, molar volume at absolute zero V0, available volume Va = V0 V0, intermolecular free length Lf, molar surface factor Y, molecular radius r, molar actual volume of molecule B and collision factor S of the pure components at T = 298.15 K Compound
106V0/ (m3 Æ mol1)
106V0/ (m3 Æ mol1)
106Va/ (m3 Æ mol1)
106B/ (m3 Æ mol1)
Y/ (m2 Æ mol1)
r/ 1010 m
Lf/ 1010 m
S
1-Heptanol Methylcyclohexane Trichloroethylene
141.9202 128.3597 90.3179
117.2208 102.9173 71.1792
24.6994 25.4424 19.1387
53.7689 42.7123 28.1523
978,029 896,755 701,322
2.7727 2.5682 2.2354
0.5051 0.5674 0.5458
2.1924 2.2821 2.1335
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217 TABLE 11 Standard deviations of predicted speeds of sound and isentropic compressibilities by means of FLT, CFT, NR, JR, and IMR theories of the binary mixtures and ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K FLT
CFT
NR
JR
r(u)/(m Æ s1) {1-Heptanol (1) + trichloroethylene (2)} 38 47 47 29 {1-Heptanol (1) + methylcyclohexane (2)} 4 15 11 8 {Trichloroethylene (1) + methylcyclohexane (2)} 130 27 24 39 {1-Heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} 31 43 46 22 r(jS)/(TPa1) {1-Heptanol (1) + trichloroethylene (2)} 43 53 48 34 {1-Heptanol (1) + methylcyclohexane (2)} 6 17 15 11 {Trichloroethylene (1) + methylcyclohexane (2)} 235 41 32 51 {1-Heptanol (1) + Tichloroethylene (2) + methylcyclohexane (3)} 39 53 57 28
IMR
21
1=3
6
E
3
1
10 V /(m Æ mol ) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
B0
B1
B2
r
0.2206 0.379 142 920 737
0.6176 0.386 94 2108 836
0.1573 0.305 349 1599 873
0.0081 0.009 25 8 3
13 22
TABLE 14 Parameters of equation (9) and standard deviations for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
25 4 17 29
ð28Þ
;
TABLE 13 Parameters of equation (8) and standard deviations for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
3
for pure component i and V is the molar volume of mixture. For spherical molecules the surface area per mole of the pure liquid is given by Y i ¼ ð36pN A V 20;i Þ
215
where NA is the Avogadro’s number. The molar volume of pure component i at absolute zero temperature V0,i is obtained by Sugden formula 0:3 T ; ð29Þ V 0;i ¼ V i 1 TC
106VE/(m3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
A0
A1
A2
A3
r
0.4477 0.149 227 753 168
1.1166 0.989 149 1227 12
0.6326 1.144 30 698 279
1.2328 0.914 116 544 291
0.0079 0.009 25 8 3
where TC and Vi are the critical temperature and molar volume of pure component i. 3.3.2. Schaaff collision factor theory (CFT) Pn Pn i¼1 xi S i i¼1 xi Bi ¼ u1 Srf ; u ¼ u1 V
ð30Þ
where u1 = 1600 m s1, S = collision factor and rf = B/V, space filling factor. B is the actual volume of the molecules per mole. For n-component mixtures S and B are related to pure component values through
TABLE 12 Parameters of equation (4) and standard deviations for the binary mixtures at T = 298.15 K A0
A1
106VE/(m3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
0.0107 6.006 271 58 124
{1-Heptanol (1) + trichloroethylene (2)} 0.7346 0.0137 0.1369 1.629 0.095 0.390 865 410 465 85 237 328 98 203 286
106VE/(m3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
0.5282 6.089 925 20 50
{1-Heptanol 0.6198 1.839 1151 22 22
106VE/(m3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
1.1006 0.133 293 183 33
{Trichloroethylene (1) + methylcyclohexane (2)} 0.0627 0.0077 0.0838 0.003 0.028 0.003 33 94 15 99 216 336 31 171 301
A2
A3
(1) + methylcyclohexane (2)} 0.1669 0.3437 0.677 1.073 318 275 5 59 21 49
A4
A5
r
0.3441
0.4484
0.0042 0.004 7 2 2
0.5434
0.7343
0.0029 0.005 3 1 0
0.1401
0.1128
0.0004 0.000 1 4 4
r
0.0059 0.008 26 1 2 7.6489 Æ 103 0.0111 36.8229 4.001 1.6473
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
B8
216
Trichloroethylene 0.0
1.0
0.1
0.9
0.2
0.8 30
0.3
0.7
0.4
25
0.6
0.5
0.5 20
5.689 Æ 103 3.7113 Æ 103 14.1288 7.8072 4.8591
B7 B6
3.0733 Æ 103 9.1358 Æ 103 8.8784 3.3679 4.4799
B5
8.9201 Æ 103 5.1429 Æ 103 21.8586 4.6022 2.5207
B4
3.8569 Æ 103 3.9799 Æ 103 14.1122 8.5307 5.8512
B3
8.9841 Æ 103 8.6488 Æ 103 19.2449 5.6049 6.7535 1.8134 Æ 103 6.8191 Æ 104 1.0535 4.157 2.9184 6.6222 Æ 103 2.5936 Æ 103 9.1943 2.8836 3.5923
B2 B1
1.1729 Æ 103 2.3773 Æ 104 0.7684 0.3125 0.9324
0.3
10 0.8
5
0.2
0.9
0.1
1.0
Methylcyclohexane
0.0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1-Heptanol
FIGURE 8. Isolines at constant excess isentropic compressibilities, jES ðTPa1 Þ for the ternary mixture of {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} correlated with equation (10) at T = 298.15 K.
S¼ B¼
B0
0.4
15 0.7
0.0
106VE/(m3 Æ mol1) Dg (mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
TABLE 15 Parameters of equation (10) and standard deviations for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
0.6
n X i¼1 n X
xi S i ;
ð31Þ
x i Bi ;
ð32Þ
i¼1
where Bi can be evaluated as 4 Bi ¼ pr3 N A ; 3
ð33Þ
where r is the molecular radius of the pure component. Molecular radius is calculated as 1=3 3b r¼ ð34Þ 16pN A where b is the van der Waals constant. 3.3.3. Nomoto relation (NR) Pn 3 x i Ri u ¼ Pni¼1 ; i¼1 xi V i 1=3
Ri ¼ V i u i ;
ð35Þ ð36Þ
where Ri and ui stand for Rao molar sound velocity and speed of sound of the pure component i, respectively. 3.3.4. Junjie relation (JR) Pn i¼1 xi V u ¼ Pn 1=2 Pn : 2 1=2 i¼1 xi M i i¼1 xi V i =qi ui 3.3.5. Van Deal ideal mixing relation (IMR) n X 1 1 xi Pn ¼ : 2 M i u2i i¼1 xi M i u i¼1
ð37Þ
ð38Þ
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
The best correlation method for the binary systems is found using the IMR and for the ternary system using the IMR and JR. The standard deviations for speeds of sound r(u) and isentropic compressibilities r(jS) predicted by above mentioned equations are given in table 11. Acknowledgements The authors thank of the Bu-Ali Sina University authorities for the necessary facilities to carry out the work. References [1] H. Iloukhani, B. Samiey, M.A. Moghaddasi, J. Chem. Thermodyn. 38 (2006) 190–200. [2] H. Iloukhani, H.A. Zarei, J. Chem. Eng. Data 47 (2002) 195–197. [3] H. Iloukhani, B. Samiey, J. Chem. Eng. Data 50 (2005) 1911–1916. [4] H.A. Zarei, H. Iloukhani, Thermochim. Acta 405 (2003) 123–128. [5] H. Iloukhani, M. Rezaei-Sameti, J. Chem. Thermodyn. 37 (2005) 1151–1161. [6] O.J. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [7] I. Cibulka, Collect. Czech. Chem. Commun. 47 (1982) 1414–1419. [8] F. Olive, K.R. Patil, J. Fernandez, A. Coronas, Thermochim. Acta 259 (1995) 57–70. [9] I. Nagata, K. Tamura, J. Chem. Thermodyn. 22 (1990) 279–283. [10] L. Grunberg, A.H. Nissan, Trans. Faraday Soc. 45 (1949) 125–137. [11] M. Dominguez, J.I. Pardo, I.G. Gascon, F.M. Royo, J.S. Urieta, Fluid Phase Equilibr. 169 (2000) 277–292. [12] J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 43 (1998) 961– 966. [13] R.K. Hind, E. McLaughlin, A.R. Ubbelohde, Trans. Faraday Soc. 56 (1960) 328–330. [14] R.K. Hind, E. McLaughlin, A.R. Ubbelohde, Trans. Faraday Soc. 56 (1960) 331–334. [15] P.K. Katti, M.M. Chaudhri, J. Chem. Eng. Data 9 (1964) 442–443. [16] R.A. McAllister, AIChE J. 6 (1960) 427–431.
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[17] E.L. Heric, J. Chem. Eng. Data 11 (1966) 66–68. [18] Y.I. Frenkel, Kinematic Theory of Liquids, Oxford University Press, London, 1946. [19] O. Iulan, M.C. Iulita, G. Loresco, in: Proceeding of the 11th International Congress of Chemical Engineering, Chemical Equipment Design and Automation, CHISA93, Prague, Czech Republic, August 29–September 3, 1993, paper F2-386. [20] B. Jacobson, Acta Chem. Scand. A 6 (1952) 1485–1498. [21] G. Savaroglu, E. Aral, Fluid Phase Equilibr. 215 (2004) 253–262. [22] S.L. Oswal, S.G. Patel, R.L. Gradas, N.Y. Ghael, Fluid Phase Equilibr. 215 (2004) 61–70. [23] N.Y. Sastry, M.C. Patel, S.R. Patel, Fluid Phase Equilibr. 155 (1999) 261–276. [24] W. Schaaff, Molekularakustic, Springer, Berlin, 1963. [25] O. Nomoto, J. Phys. Soc. Jpn. 13 (1958) 1528. [26] Z. Junjie, J. Chem. Univ. Sci. Technol. 14 (1984) 298. [27] W. Van Deal, E. Vageel, in: Proceedings of the First International Conference on Calorimetry and Thermodynamics, Warsaw, 1969. [28] Handbook of Chemistry and Physics, 81st ed., CRC Press, Boca Raton, FL, 2000, pp. 170–174, Section 6. [29] C. Kretschmer, R. Wiebe, J. Am. Chem. Soc. 71 (1949) 3176–3179. [30] T. Shinomiya, Bull. Chem. Soc. Jpn. 62 (1989) 908–914. [31] Handbook of Chemistry and Physics, 81st ed., CRC Press, Boca Raton, FL, 2000, pp. 5–60, Section 5. [32] R. Francesconi, F. Comelli, Thermochim. Acta 260 (1995) 95–103. [33] G.C. Benson, O. Kiyohara, J. Chem. Thermodyn. 11 (1979) 1061– 1064. [34] A. Ben-Naiem, Water and Aqueous Solutions, Plenum Press, New York, 1974. [35] W. Kauzman, H. Eyring, J. Am. Chem. Soc. 62 (1940) 3113–3125. [36] H. Vogel, A. Weiss, Ber. Bunsenges. Phys. Chem. 86 (1982) 193–198. [37] R. Meyer, M. Meyer, J. Metzger, A. Peneloux, J. Chim. Phys. Physicochim. Biol. 68 (1971) 406–412. [38] R.J. Fort, W.R. Moore, Trans. Faraday Soc. 62 (1966) 1112–1119.
JCT 06-72
Excess molar volumes, viscosities, and speeds of sound of the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K Hossein Iloukhani a
a,*
, Babak Samiey
b
Department of Chemistry, Faculty of Science, University of Bu-Ali Sina, Hamedan 65174, Iran b Department of Chemistry, Faculty of Science, University of Lorestan, Khoramabad, Iran Received 19 March 2006; received in revised form 12 June 2006; accepted 16 July 2006 Available online 10 August 2006
Abstract Densities (q), viscosities (g), and speeds of sound (u) of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) and the involved binary mixtures (1-heptanol + trichloroethylene), (1-heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) at 298.15 K were measured over the whole composition range. The data obtained are used to calculate excess molar volumes (VE), excess isobaric thermal expansivity (aE), viscosity deviations (Dg), excess Gibbs free energies of activation of viscous flow (DG*E), and excess isentropic compressibilities ðjES Þ of the binary and ternary mixtures. The data of the binary systems were fitted to the Redlich–Kister equation while the best correlation method for the ternary system was found using the Nagata equation. Viscosities, speeds of sound and isentropic compressibilities of the binary and ternary mixtures have been correlated by means of several empirical and semi-empirical equations. The best correlation method for viscosities of binary systems is found using the Iulan et al. equation and for the ternary system using the McAllister equation. The best correlation method for speeds of sound and isentropic compressibilities of the binary systems is found using the IMR and for the ternary system using the IMR and JR. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: 1-Heptanol; Trichloroethylene; Methylcyclohexane; Speed of sound; Excess molar volume; Viscosity
1. Introduction This paper is a continuation of our earlier work [1–5]. The number of studies on thermodynamic properties of ternary mixtures has increased in recent years due to industrial applications and the theoretical interest in studying the nature of molecular interaction and packing phenomena in ternary mixtures. In this work, we measured densities, viscosities and speeds of sound of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) and the involved binary mixtures at T = 298.15 K and over the whole composition range. The data obtained are used to calculate excess molar volumes, thermal expansivity, excess thermal expansivity, viscosity deviations, excess *
Corresponding author. Tel./fax: +98 811 8271061. E-mail address: [email protected] (H. Iloukhani).
0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.07.015
Gibbs free energies of activation of viscous flow, speed of sound deviations, isentropic compressibility, excess isentropic compressibilities of the binary and ternary mixtures. The data of the binary systems were fitted to the Redlich–Kister [6] equation. Cibulka [7], Redlich–Kister type [8], and Nagata [9] equations were tested for estimating ternary properties from binary results. The best correlation method for the ternary system was found using the Nagata equation. The viscosity data for the binary and ternary mixtures were fitted to Nissan and Grunberg [10–12], Hind et al. [11–14], Katti and Chaudhri [11,12,15], McAllister [11,12,16], Heric [11,12,17], Frenkel [11,12,18], and Iulan et al. [11,12,19] and their parameters have been calculated. Theoretical models dealing with liquid state including Jacobson free length theory (FLT) [20–23], Schaaff collision factor theory (CFT) [21,23,24], Nomoto relation (NR) [21,25], Junjie relation (JR) [21,26] and Van Deal
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
207
TABLE 1 Experimental and the literature values of densities q, viscosities g, speeds of sound u, molar isobaric heat capacity Cp, and isobaric thermal expansivity a of 1-heptanol, methylcyclohexane and trichloroethylene at T = 298.15 K Compound 1-Heptanol Methylcyclohexane Trichloroethylene
qexp/(kg Æ m3) 818.77 764.99 1454.75
qlit/(kg Æ m3) a
818.6 764.96b 1455.72c
gexp/(mPa Æ s)
glit/(mPa Æ s) d
6.041 0.684 0.527
5.810 0.679d 0.545d
uexp/(m Æ s1)
a/kK1
Cp/(J Æ mol1 Æ K1)
1329 1209 1064
0.879 1.190 1.176
272.1e 184.8e 124.4e
a values were calculated from the measured densities at different temperatures. a Reference [30]. b Reference [29]. c Reference [32]. d Reference [28]. e Reference [31].
ideal mixing relation (IMR) [21,27] have been proposed for the prediction of the speeds of sound and isentropic compressibilities of the binary and ternary mixtures. Densities and viscosities of the pure reagents were in good agreement with values found in the literature [28– 32], table 1. 2. Experimental The purity of the chemicals is on the basis of mole%. 1Heptanol (P99%) and methylcyclohexane (>99%) were supplied by Merck and trichloroethylene (>99%) was obtained from Fluka. All chemical substances were used without any further purification. All mass measurements were performed on an electronic balance (AB 204-N Mettler) accurate to 0.1 mg. The estimated accuracy in the mole fractions was ±1 Æ 104. The densities of the pure compounds and their binary and ternary mixtures were measured with an Anton Paar DMA 4500 oscillating U-tube densimeter. The density measurements accuracy was ±1 Æ 102 kg Æ m3. The temperature in the cell was automatically regulated to ±0.01 K with a solid state thermostat. The speed of sound in the pure compounds and their binary and ternary mixtures was measured with a multi-frequency ultrasonic interferometer supplied by Mittal Enterprise, New Delhi with an accuracy of ±1 m Æ s1. In this work, 1 MHz frequency was employed. Viscosities at T = 298.15 K were measured with an Ubbleohde viscometer. The equation for viscosity is g ¼ qm ¼ qðkt c=tÞ;
ð1Þ
where k and c are the viscometer constants and t, g, and m are the efflux time, dynamic and kinematic viscosities, respectively. The dynamic viscosity was reproducible to within ±2 Æ 103 mPa Æ s. The viscometer was suspended in a water bath maintained to ±0.01 K. 3. Results and discussion 3.1. Densities and excess molar volumes The excess molar volumes of the n-component mixtures are calculated from the densities of the pure liquids and their mixtures according to the following equation:
V E ðm3 mol1 Þ ¼
n n X xi M i X xi M i ; q qi i¼1 i¼1
ð2Þ
where q is the density of the mixture and xi, qi, Mi, and Vi are the mole fraction, density, molecular weight and molar volume of pure component i, respectively. Excess isobaric thermal expansivity (aE) values can be calculated as follows [33] which is the most frequent choice for this purpose: n X /i ai ; ð3Þ aE ðK1 Þ ¼ a aid ¼ ðoV m =oT ÞP =V m i¼1
where Vm is the molar volume of the mixture and /i is the ideal volume fraction of pure component i. aid and ai are the isobaric thermal expansivity of the ideal mixture and pure component i, respectively. The corresponding VE values of the binary mixtures (1-heptanol + trichloroethylene), (1-heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) measured at T = 298.15 K are presented in table 2 and plotted against mole fraction of 1-heptanol in figure 1. Each set of results were fitted using Redlich–Kister equation for the binary mixtures: N X k Y ¼ xðx 1Þ Ak ð1 2xÞ ; ð4Þ k¼1
where Y = (VE or Dg or DG*E or jES or Du) and x is the mole fraction of the first component. The coefficients Ak were calculated by the unweighted least-squares method. In each case, the optimum number of coefficients was ascertained from an examination of standard deviation (r) with hX i1=2 r¼ ðY exp Y cal Þ2 =ðn pÞ ; ð5Þ where Ycal is the calculated values of the property Y, and n and p are the experimental points and number of parameters retained in the respective equations, respectively. Adjustable parameters of VE values and standard deviations are given in table 12. The values of VE for the binary mixture (1-heptanol + methylcyclohexane) are positive over the entire composition range, due to the rupture or stretch of the hydrogen bonding of self-associated molecules of 1-heptanol. The values of VE for the
208
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TABLE 2 Excess molar volumes VE for the binary mixtures at T = 298.15 K x1
q/ (kg Æ m3)
0.1003 0.2008 0.2682 0.2999 0.3999 0.4498 0.4995
x1
q/ (kg Æ m3)
{1-Heptanol (1) + trichloroethylene (2)} 1358.95 0.0729 0.5504 1036.48 1273.76 0.0772 0.6003 1008.26 1221.42 0.0760 0.6504 981.28 1198.18 0.0609 0.6996 955.70 1129.05 0.0379 0.8005 906.25 1096.95 0.0229 0.8489 883.87 1066.35 0.0032 0.8969 862.42
106VE/ (m3 Æ mol1) 0.0226 0.0276 0.0489 0.0556 0.0611 0.0614 0.0470
{1-Heptanol (1) + methylcyclohexane (2)} 770.20 0.1093 0.5497 795.18 773.03 0.1266 0.5999 797.98 775.76 0.1446 0.6503 800.71 781.37 0.1610 0.7007 803.42 786.91 0.1504 0.8000 808.68 789.61 0.1458 0.8495 811.24 792.45 0.1319 0.8998 813.80
0.1000 0.1506 0.2001 0.3011 0.4000 0.4490 0.5002
0.1028 0.2001 0.2201 0.2986 0.3663 0.4125 0.5008
106VE/ (m3 Æ mol1)
0.1176 0.0931 0.0777 0.0612 0.0290 0.0166 0.0080
{Trichloroethylene (1) + methylcyclohexane (2)} 815.78 0.1009 0.5513 1082.08 0.2706 866.91 0.1783 0.5999 1116.32 0.2609 877.87 0.1912 0.6491 1152.32 0.2473 922.08 0.2350 0.7008 1191.58 0.2259 962.25 0.2587 0.7996 1271.37 0.1690 990.67 0.2691 0.8497 1314.36 0.1327 1047.75 0.2754 0.9011 1360.38 0.0893
0.30
6 E 3 -1 10 V /(m . mol )
0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10 0.0
0.2
0.4
0.6
0.8
1.0
x1
FIGURE 1. Excess molar volumes for the binary mixtures of r {1heptanol (1) + trichloroethylene (2)}, m {1-heptanol (1) + methylcyclohexane (2)}, and j {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
binary mixture (trichloroethylene + methylcyclohexane) are positive over the entire composition range, as expected from dispersion effects between unlike molecules. The values of VE are negative in 1-heptanol rich region of the binary mixture (1-heptanol + trichloroethylene) due to the polar interactions between hydrogen atom of –OH group of 1-heptanol and chloro atoms of trichloroethylene (cross-associated OH–Cl bonds) and positive in 1-heptanol lower region due to the depolymerization effects of trichloroethylene on the 1-heptanol, table 2 and figure 1.
TABLE 3 Densities q, excess molar volumes VE, thermal expansivity a, and excess thermal expansivity aE for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K x1
x2
q/(kg Æ m3)
106VE/(m3 Æ mol1)
a/kK1
aE/kK1
0.0500 0.0503 0.0510 0.0501 0.0999 0.0998 0.1005 0.1008 0.1045 0.1013 0.1004 0.1000 0.1003 0.1978 0.2001 0.1985 0.1977 0.1974 0.1997 0.2001 0.2993 0.2996 0.3011 0.3000 0.3009 0.2995 0.4003 0.3981 0.3933 0.3993 0.4001 0.4973 0.4993 0.4987 0.4977 0.5998 0.6010 0.5962 0.6976 0.6959 0.7976 0.8465 0.8446 0.9003
0.9001 0.8500 0.1018 0.0505 0.1017 0.2006 0.3018 0.3965 0.4929 0.5985 0.6998 0.7986 0.8488 0.1007 0.2025 0.3009 0.4066 0.5039 0.6001 0.7061 0.1015 0.2020 0.2983 0.3999 0.5000 0.6002 0.1002 0.2039 0.3008 0.4009 0.5003 0.1038 0.2021 0.3006 0.4022 0.1008 0.1979 0.3024 0.1021 0.2026 0.1014 0.0521 0.1051 0.0499
1359.01 1314.48 817.59 791.90 820.00 871.69 928.14 984.41 1045.92 1117.93 1192.62 1271.50 1313.57 824.79 877.82 932.23 994.84 1056.64 1122.26 1200.07 830.60 882.58 935.62 995.22 1058.16 1125.61 835.34 888.60 941.43 1000.19 1062.25 842.31 892.79 946.35 1005.29 846.25 895.68 951.98 851.96 902.81 856.70 835.38 860.87 837.02
0.1052 0.1511 0.1776 0.1343 0.2605 0.2660 0.2963 0.3165 0.2997 0.2697 0.2321 0.1564 0.1462 0.2136 0.2549 0.2776 0.2781 0.2534 0.2138 0.1465 0.2076 0.2304 0.2329 0.2184 0.1822 0.1370 0.1819 0.1833 0.1772 0.1436 0.1009 0.1410 0.1268 0.1037 0.0640 0.0891 0.0637 0.0256 0.0394 0.0045 0.0043 0.0022 0.0296 0.0135
1.111 1.126 1.101 1.111 1.158 1.078 1.088 1.107 1.062 1.046 1.098 1.133
0.044 0.030 0.070 0.061 0.004 0.074 0.061 0.039 0.081 0.095 0.040 0.003
1.055 1.060 1.019 1.116 1.060 1.043 1.083 1.024 1.031 1.037 1.045 1.040 0.099 0.958 1.013 1.009 1.020 0.988 0.973 0.974 0.972 0.965 0.945 0.949 0.945 0.916 0.919 0.899 0.850 0.964 0.936
0.066 0.057 0.094 0.006 0.047 0.059 0.014 0.063 0.051 0.040 0.028 0.028 0.064 0.095 0.036 0.036 0.017 0.042 0.048 0.041 0.037 0.037 0.044 0.033 0.031 0.043 0.033 0.030 0.068 0.050 0.066
Also, the corresponding VE, a and aE values of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) are shown in table 3. The ternary excess magnitudes or deviation in ternary magnitudes were correlated using Cibulka, Redlich–Kister-type and Nagata equations. The following expression: Y 123 ¼ Y bin þ x1 x2 ð1 x1 x2 ÞD123 ;
ð6Þ
where Y bin ¼ Y 12 þ Y 13 þ Y 23
ð7Þ
is known as the binary contribution to the excess (or deviations in) ternary properties and Yij values are obtained from equation (4).
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
The last term stands for the ternary contribution to the magnitude. Several equations have been tested to correlate D123, the first of them suggested by Cibulka D123 ¼ ðB0 þ B1 x1 þ B2 x2 Þ:
DG
E
1
209
ðJ mol Þ ¼ RT lnðgV =hN A Þ
n X
! xi lnðgi V i =hN A Þ ;
i¼1
ð11Þ
ð8Þ
n X
ð12Þ
And the second is obtained from Redlich–Kister type equation:
Dg ðmPa sÞ ¼ g
D123 ¼ A0 þ A1 ðx2 x1 Þ þ A2 ðx3 x1 Þ þ A3 ðx3 x2 Þ;
where g and gi are the dynamic viscosities of the mixture and pure component i and V and Vi are the molar volumes of the mixture and pure component i, respectively. R is the gas constant, T is the absolute temperature, h is Planck’s constant, and NA is the Avagadro’s number. The g, DG*E, and Dg values the binary mixtures (1-heptanol + trichloroethylene), (1-heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) are presented in table 4 and the Dg and DG*E are plotted against mole fraction of 1-heptanol in figures 3 and 4, respectively. Each set of results were fitted using Redlich– Kister equation for the binary mixtures, equation (4) and the adjustable parameters and standard deviations are given in table 12. Also, The corresponding g, DG*E, and
ð9Þ
the third one proposed by Nagata D123 ¼ RT ðB0 B1 x1 B2 x2 B3 x21 B4 x22 B5 x1 x2 B6 x31 B7 x32 B8 x21 x2 Þ:
ð10Þ E
Adjustable parameters and standard deviations of V obtained from Cibulka, Redlich–Kister type and Nagata equations are given in tables 13, 14, and 15, respectively. The best correlation method for the ternary system is found using the Nagata equation. Isolines of VE from Nagata equation for the ternary system are shown in figure 2. The ternary VE values are negative in 1-heptanol rich composition range and positive in 1-heptanol lower range due to combination of interactions involved in related binary mixtures. The ternary aE values are negative over the entire composition range, table 3. a is considered to be the cross-fluctuation of volume and enthalpy [34]. a and aE values of the ternary system are given in table 3. Negative aE is due to the formation of new molecular interaction in the mixture. Negative aE means that fluctuation of the volume causing interaction energy in the mixture is lesser than in random mixing liquids. 3.2. Dynamic viscosities The excess Gibbs free energies of activation (DG*E) for viscous flow and viscosity deviations (Dg) for n-component mixtures can be calculated as: Trichloroethylene 0.0
0.1
1.0
0.05 0.9
0.2
0.8
0.3
0.7
0.4
0.6
0.5
0.5 0.25
0.6
TABLE 4 Densities q, viscosities g, viscosity deviations Dg, and excess Gibbs free energies of activation of viscous flow DG*E for the binary mixtures at T = 298.15 K x1
q/(kg Æ m3)
0.1004 0.2090 0.2996 0.4006 0.4457 0.4980 0.5977 0.6978 0.7968 0.9002
{1-Heptanol (1) + trichloroethylene (2)} 1359.05 0.643 0.438 86 1267.14 0.837 0.842 67 1198.31 1.054 1.125 33 1128.51 1.373 1.363 17 1099.49 1.544 1.441 34 1067.32 1.774 1.499 62 1006.84 2.296 1.527 100 956.65 2.979 1.395 124 907.98 3.818 1.103 127 860.90 4.856 0.635 82
0.1009 0.2007 0.3011 0.4011 0.4501 0.4985 0.6033 0.7417 0.7985 0.9006
{1-Heptanol (1) + methylcyclohexane (2)} 770.31 0.797 0.427 162 775.77 0.956 0.803 249 781.36 1.174 1.123 280 786.95 1.461 1.372 279 789.68 1.640 1.455 257 792.38 1.839 1.516 235 798.15 2.384 1.532 158 805.60 3.369 1.289 50 808.59 3.875 1.086 10 813.84 4.922 0.586 30
0.1028 0.2001 0.3015 0.3998 0.4528 0.4994 0.6504 0.6997 0.7990 0.8987
{Trichloroethylene (1) + methylcyclohexane (2)} 815.72 0.654 0.014 29 866.92 0.630 0.023 49 923.79 0.608 0.029 62 982.79 0.589 0.032 70 1016.29 0.580 0.033 73 1046.80 0.572 0.033 74 1153.26 0.551 0.031 70 1190.77 0.546 0.028 67 1270.86 0.536 0.023 57 1358.20 0.529 0.014 35
0.4 0.20 0.3
0.15 0.10
0.8
0.2 0.05 0.00
0.9
Methylcyclohexane0.0
0.10
0.15
0.1
0.2
g/(mPa Æ s)
Dg/(mPa Æ s)
DG*E/(J Æ mol1)
0.30
0.7
1.0
x i gi ;
i¼1
-0.05
0.1
0.0 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1-Heptanol
FIGURE 2. Isolines at constant excess molar volumes, 106VE (m3 Æ mol1) for the ternary mixtures of {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} correlated with equation (10) at T = 298.15 K.
210
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217 TABLE 5 Densities q, viscosities g, viscosity deviations Dg and excess Gibbs free energies of activation of viscous flow DG*E for the ternary mixture {1heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
0.0
Δη /(mPa . s)
-0.2 -0.4 -0.6 -0.8 -1.0
-1.6 -1.8 0.0
0.2
0.4
0.6
0.8
1.0
x1
/(J . mol-1)
FIGURE 3. Viscosity deviations for the binary mixtures of r {1-heptanol (1) + trichloroethylene (2)}, m {1-heptanol (1) + methylcyclohexane (2)}, and n {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
*E
x2
q/ (kg Æ m3)
g/ (mPa Æ s)
Dg/ (mPa Æ s)
DG*E/ (J Æ mol1)
0.0500 0.0500 0.0500 0.0498 0.0999 0.0994 0.1001 0.1002 0.0985 0.1000 0.0988 0.1001 0.1001 0.1992 0.1990 0.2019 0.0209 0.2007 0.1993 0.1983 0.2996 0.2965 0.3008 0.2937 0.2961 0.3004 0.3985 0.4004 0.3998 0.4000 0.3987 0.5008 0.5021 0.4986 0.5010 0.5979 0.5937 0.5992 0.6998 0.6964 0.8428 0.8454 0.8486 0.8979
0.8995 0.8503 0.1010 0.0503 0.1002 0.2012 0.3004 0.4005 0.5069 0.5985 0.7008 0.8003 0.8502 0.1009 0.2014 0.3013 0.3999 0.5014 0.6016 0.7021 0.1040 0.2078 0.3013 0.4039 0.5065 0.5980 0.1005 0.2001 0.3005 0.3985 0.5013 0.1006 0.2014 0.2992 0.3991 0.1030 0.2045 0.3004 0.0999 0.2021 0.0507 0.1048 0.0498 0.0513
1358.55 1314.84 817.13 791.82 819.32 872.03 927.34 986.94 1054.89 1117.95 1193.47 1272.92 1315.32 825.03 877.24 932.71 990.98 1055.30 1123.31 1196.93 831.93 885.61 937.42 997.50 1062.27 1124.11 835.46 886.78 941.62 998.80 1062.94 840.94 892.61 945.64 1003.54 847.24 898.80 950.91 850.98 902.57 834.50 860.76 834.44 837.58
0.571 0.574 0.699 0.712 0.765 0.736 0.718 0.702 0.677 0.668 0.651 0.644 0.644 0.924 0.898 0.885 0.860 0.845 0.833 0.819 1.138 1.108 1.101 1.067 1.060 1.066 1.427 1.413 1.392 1.382 1.373 1.826 1.815 1.787 1.800 2.329 2.298 2.318 3.014 3.009 4.263 4.288 4.321 4.840
0.240 0.245 0.237 0.231 0.438 0.449 0.455 0.456 0.455 0.458 0.452 0.450 0.443 0.811 0.820 0.834 0.838 0.836 0.824 0.817 1.134 1.131 1.147 1.127 1.130 1.133 1.376 1.385 1.386 1.382 1.368 1.525 1.527 1.521 1.505 1.542 1.534 1.529 1.403 1.374 0.928 0.908 0.902 0.647
111 124 134 127 181 192 187 164 158 161 152 127 101 243 238 212 218 183 140 123 262 226 198 162 116 77 242 203 155 105 38 187 125 73 5 99 24 30 19 78 36 148 47 47
-1.2 -1.4
ΔG
x1
150 100 50 0 -50 -100 -150 -200 -250 -300 -350 0.0
0.2
0.4
0.6
0.8
1.0
x1
FIGURE 4. Excess Gibbs free energies of activation for viscous flow for the binary mixtures of r {1-heptanol (1) + trichloroethylene (2)}, m {1heptanol (1) + methylcyclohexane (2)}, and n {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
Dg values of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) are shown in table 5. Each set of results were fitted to Cibulka, Redlich–Kister type and Nagata equations, equations (8), (9), and (10), respectively, and the adjustable parameters and standard deviations are given in tables 13, 14, and 15, respectively. The best correlation method for the ternary system is found using the Nagata equation. Isolines of Dg and DG*E from Nagata equation for the ternary system are shown in figure 5a and b. The values of Dg for the binary mixtures (1-heptanol + trichloroethylene), (1-heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) are negative over the entire composition range. In two first binary systems, negative values of Dg results from rupture or stretch of the hydrogen bonding of self-associated molecules of 1heptanol. In the binary mixture (trichloroethylene + methylcyclohexane), negative and small Dg values are due to the dispersion interactions between unlike molecules, figure 3. DG*E values for the binary mixtures (trichloroethylene + methylcyclohexane) and (1-heptanol + methylcyclo-
hexane) are negative over the entire composition range. DG*E values for the binary mixture (1-heptanol + trichloroethylene), are positive over the 1-heptanol rich region, figure 4. It seems that in the binary mixture (1-heptanol + trichloroethylene), the polar interaction between hydrogen atom of –OH group of 1-heptanol and chloro atoms of trichloroethylene results to closer packing and DG*E becomes positive in 1-heptanol rich composition range. The ternary viscosity deviations Dg, are negative over the whole composition range and the DG*E values are posi-
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217 Trichloroethylene 0.0
a
1.0
0.1
0.9
0.2
0.8
0.3
0.7
-0.3
0.4
0.6
-0.5 -0.7
0.5
0.5
-0.9 -1.1
0.6
0.4 -1.3
0.7
-1.5
0.3 -1.5
0.8
0.2
-1.3
-1.1
0.9
-0.9
0.1
-0.7 -0.5 -0.3
1.0 0.0
Methylcyclohexane
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
1-Heptanol
Trichloroethylene
b
0.0
0.1
1.0
-35
0.9
-90 0.2
0.7
ln g ¼
-145 0.4
0.6
0.5
xi ln gi þ
n X n X
xi xj Aij þ
n X n X n X
j>i
i¼1
i¼1
j>i
xi xj xk Aijk :
k>j
ð13Þ
0.5
0.4
Hind et al. equation
-200 0.7
0.3
!
75
0.8
0.2 -35
0.9
20
g¼
0.1
-255
1.0
0.0 0.1
n X i¼1
0.6
0.0
mixture compared with the behavior of pure liquids. According to Fort and Moore [38] this viscosity behavior corresponds to systems in which there is an associated component and in which solute–solvent complexes are not formed or have low stability. The breaking of hydrogen bonding of 1-heptanol makes the mixture to flow more easily. To correlate experimental data of ternary system from binary ones, different empirical and semi-empirical relations have been used. The correlation equations of Nissan and Grunberg, Hind, Frenkel, McAllister, Katti and Chaudhri, Heric, and Iulan et al. have been developed for binary mixtures. Canosa et al. [12] introduced new parameter to correlate experimental data of ternary systems from binary ones. The viscosity of n-component mixture according to correlating equations [11,12] are as follows: Nissan and Grunberg equation
0.8
0.3
Methylcyclohexane
211
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
n X
x2i gi
þ2
n X n X
i¼1
xi xj Aij þ
n X n X n X
j>i
i¼1
i¼1
j>i
xi xj xk Aijk :
k>j
1-Heptanol
FIGURE 5. Isolines at (a) constant viscosity deviations, Dg (mPa Æ s) and (b) excess Gibbs free energies of activation for viscous flow, DG*E (J Æ mol1) for the ternary mixture of {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} correlated with equation (10) at T = 298.15 K.
ð14Þ Frenkel equation ln g ¼
n X
x2i ln gi
þ2
i¼1
n X n X
xi xj ln Aij þ
j>i
i¼1
n X n X n X i¼1
j>i
! xi xj xk ln Aijk :
k>j
ð15Þ
tive in 1-heptanol rich composition range, table 5 and figure 5 which is due to combination of interactions involved in related binary mixtures. According to Kauzman and Eyring [35], the viscosity of a mixture strongly depends on entropy of mixture, which is related to liquid structure and enthalpy (and consequently to molecular interactions between the components of the mixture). So, the viscosity deviations are functions of interactions as well as size and shape of molecules. Vogel and Weiss [36] affirm that mixtures with strong interactions between different molecules (HE < 0 and negative deviations from Raoult’s law) present positive viscosity deviations; whereas for mixtures with positive deviations of Raoult’s law and without strong specific interactions, the viscosity deviations are negative. In this way, Meyer et al. [37] state that excess Gibbs free energy of activation of viscous flow, like viscosity deviations can be used to detect molecular interactions. The negative values observed for Dg and DG*E of the ternary system under study point out the easier flow of
McAllister equation lnðgV Þ ¼
n X
x3i lnðgi V i Þ þ 3
i¼1
6
n X n X i¼1
n X n X n X j>i
i¼1
x2i xj ln Aij þ
j6¼i
ð16Þ
xi xj xk ln Aijk :
k>j
Katti and Chaudhri equation lnðgV Þ ¼
n X
xi lnðgi V i Þ þ
i¼1
n X n X i¼1
xi xj Aij þ
j>i
n X n X n X i¼1
j>i
xi xj xk Aijk :
k>j
ð17Þ
Heric equation lnðgV Þ ¼
n X
xi lnðgi V i Þ þ
i¼1
i¼1
n X n X n X i¼1
n X n X
j>i
k>j
xi xj xk Aijk :
j>i
xi xj
1 X
! Ak ðxi xj Þ
k
þ
k¼0
ð18Þ
212
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
Iulan et al. equation lnðgV Þ ¼
n X
xi lnðgi V i Þ þ
i¼1
j>i
xi xj
3 X
j>i
i¼1
n X n X n X i¼1
n X n X
! Ak ðxi xj Þ
k
þ
k¼0
ð19Þ
xi xj xk Aijk ;
k>j
where in above-mentioned equations Aij and Ak are the binary correlation parameters and Aijk is the ternary correlation parameter. The best correlation method for binary systems is found using the Iulan et al. equation and for the ternary system using the McAllister equation. Adjustable parameters of correlating equations and standard deviations are given in table 6.
TABLE 6 Adjustable parameters of viscosity correlating equations and the corresponding standard deviations for the binary mixtures and ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K {1-Heptanol Hind et al.a A12 = 0.302 Nissan and Grunbergb A12 = 0.0964 Katti and Chaudhrib A12 = 0.0819 McAllisterc A12 = 3.858 Hericb A0 = 0.0896 Frenkela A12 = 1.7636 Iulan et al.b A0 = 0.1041
3.3. Speeds of sound and excess isentropic compressibilities Isentropic compressibility jS, was calculated using Newton–Laplace equation: jS ¼ 1=qu2 :
ð20Þ
Excess isentropic compressibilities jES , n-component were calculated using the relation [27,34] jES ðTPa1 Þ ¼ jS jid S n X jid /i jS;i þ TV m a2 S ¼ i =C p;i i¼1
8 < :
T
n X
! xi V i
i¼1
n X
!2 , /i ai
i¼1
ð21Þ
n X i¼1
9 =
xi C p;i ; ;
ð22Þ
where jid S is the ideal isentropic compressibility of mixture. /i, Cp,i, jS,i, and ai are the ideal volume fraction, isobaric molar heat capacity, isentropic compressibility, and thermal expansivity of the pure component i, respectively. Duis obtained from following equations: Du ðm s1 Þ ¼ u
n X
x i ui ;
ð23Þ
i¼1
where u and ui are the speed of sound in mixture and pure component i, respectively. The data of experimental u and jS, jES and Du values of the binary mixtures (1-heptanol + trichloroethylene), (1heptanol + methylcyclohexane), and (trichloroethylene + methylcyclohexane) measured at 298.15 K are presented in table 7 and the Du and jES are plotted against mole fraction of 1-heptanol in figures 6 and 7. Each set of results were fitted using Redlich–Kister equation for the binary mixtures, equation (4) and the adjustable parameters and standard deviations are given in table 12. The values of jES are negative in 1-heptanol rich region of the binary mixtures (1-heptanol + trichloroethylene) and (1-heptanol + methylcyclohexane). The positive jES values of these binary mixtures are due to the depolymerization
(1) + trichloroethylene (2)} r(mPa Æ s) = 0.100 r(mPa Æ s) = 0.053 r(mPa Æ s) = 0.067 A21 = 1.1217
r(mPa Æ s) = 0.009
A1 = 0.4096
r(mPa Æ s) = 0.009
r(mPa Æ s) = 0.071 A1 = 0.3513 A2 = 0.1279 A3 = 0.1793
r(mPa Æ s) = 0.005
{1-Heptanol (1) + methylcyclohexane (2)} Hind et al.a A13 = 0.378 r(mPa Æ s) = 0.100 Nissan and Grunbergb A13 = 0.2123 r(mPa Æ s)=0.084 Katti and Chaudhrib A13 = 0.3635 r(mPa Æ s) = 0.106 McAllisterc A13 = 4.2181 A31 = 1.4073 r(mPa Æ s) = 0.014 Hericb A0 = 0.3558 A1 = 0.507 r(mPa Æ s) = 0.014 Frenkela A13 = 1.687 r(mPa Æ s) = 0.107 Iulan et al.b r(mPa Æ s) = 0.002 A0 = 0.3742 A1 = 0.4664 A2 = 0.1362 A3 = 0.1047 {Trichloroethylene (1) + methylcyclohexane (2)} Hind et al.a A23 = 0.538 r(mPa Æ s) = 0.001 Nissan and Grunbergb A23 = 0.1959 r(mPa Æ s) = 0.001 Katti and Chaudhrib A23 = 0.1230 r(mPa Æ s) = 0.001 McAllisterc A23 = 0.55688 A32 = 0.69038 r(mPa Æ s) = 0.001 Hericb A0 = 0.1233 A1 = 0.016 r(mPa Æ s)= 0.001 Frenkela A23 = 0.544 r(mPa Æ s)= 0.001 Iulan et al.b r(mPa Æ s) = 0.000 A0 = 0.1182 A1 = 0.0119 A2 = 0.0389 A3 = 0.0103 {1-Heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} A123 r(mPa Æ s) Hind et al.a 1.356 0.153 Nissan and Grunbergb 1.9353 0.058 Katti and Chaudhrib 0.7691 0.072 McAllisterc 1.2498 0.035 b Heric 0.8265 0.038 Frenkela 450.318 0.091 Iulan et al.b 0.8198 0.047 a b c
Dimension of parameter(s) is in mPa Æ s. Parameter(s) is(are) dimensionless. Dimension of parameters is in (Æ107 kg Æ m4 Æ s1 Æ mol1).
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
1
1
jES =TPa1
x1
q/(kg Æ m )
0.0000 0.1090 0.1900 0.2991 0.3967 0.4959 0.5488 0.5981 0.6928 0.7962 0.8960 1.0000
{1-Heptanol (1) + trichloroethylene (2)} 1454.75 1064 607 1351.24 1047 675 43 1282.42 1066 686 40 1198.68 1099 691 31 1131.16 1130 692 23 1068.60 1162 693 17 1037.37 1180 692 14 1009.51 1196 693 12 959.11 1228 691 7 908.29 1263 690 3 862.85 1298 688 2 818.77 1329 691
0.0000 0.1031 0.2024 0.3006 0.4033 0.4973 0.5394 0.6026 0.7045 0.7972 0.8951 1.0000
0.0000 0.1611 0.3085 0.4380 0.5206 0.6133 0.6514 0.7316 0.8075 0.8737 0.9418 1.0000
u/(m Æ s )
jS/TPa
{1-Heptanol (1) + methylcyclohexane (2)} 764.96 1215 886 770.43 1217 876 5 775.87 1225 859 3 781.33 1236 838 1 787.07 1247 817 3 792.31 1259 796 5 794.64 1264 788 5 798.11 1273 773 6 803.63 1287 751 6 808.52 1300 732 5 813.56 1315 711 4 818.77 1329 691
1
Du/(m Æ s )
46 48 44 39 33 29 27 20 12 3
-10
-25
-40
-55 0.0
0.2
0.4
0.6
0.8
1.0
x1
FIGURE 6. Speed of sound deviations for the binary mixtures of r {1heptanol (1) + trichloroethylene (2)}, m {1-heptanol (1) + methylcyclohexane (2)}, and n {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
70
10 13 13 14 13 12 11 8 6 2
{Trichloroethylene (1) + methylcyclohexane (2)} 764.96 1215 886 812.71 1190 869 16 1 866.57 1166 849 29 2 924.83 1142 829 42 7 969.09 1126 814 49 10 1027.24 1108 793 54 14 1054.36 1096 790 62 21 1118.89 1084 761 58 21 1191.62 1068 736 58 25 1267.09 1053 712 57 30 1359.71 1050 667 38 23 1454.75 1064 607
effects of trichloroethylene or methylcyclohexane on 1heptanol and the negative jES values of (1-heptanol + trichloroethylene) binary mixture is due to the polar interactions between hydrogen atom of –OH group of 1-heptanol and chloro atoms of trichloroethylene and in (1-heptanol + methylcyclohexane) binary mixture results from interstitially accommodation of methylcyclohexane molecules in a network of bonded 1-heptanol molecules leading to more dense packing of unlike molecules. The values of jES are positive over the entire composition range of the binary mixture (trichloroethylene + methylcyclohexane) due to the dispersion interactions between unlike molecules, figure 7. Also, the corresponding u and jS, jES and Du values of the ternary mixture (1-heptanol + trichloroethylene + methylcyclohexane) are shown in table 8. Each set of
60 50
κ SE /(TPa -1)
3
5
Δ u /(m . s-1)
TABLE 7 Densities q, speeds of sound u, isentropic compressibilities jS, excess isentropic compressibilities jES , and speed of sound deviations Du for the binary mixtures at T = 298.15 K
213
40 30 20 10 0 -10 0.0
0.2
0.4
0.6
0.8
1.0
x1
FIGURE 7. Excess isentropic compressibilities for the binary mixtures of r {1-heptanol (1) + trichloroethylene (2)}, m {1-heptanol (1) + methylcyclohexane (2)}, and n {trichloroethylene (1) + methylcyclohexane (2)}, at T = 298.15 K. The solid curves were calculated from coefficients of equation (4) given in table 12.
results were fitted to Cibulka, Redlich–Kister–type and Nagata equations, respectively, and the adjustable parameters and standard deviations are given in tables 13, 14, and 15, respectively. The best correlation method for the ternary system is found using the Nagata equation. Isolines of jES from Nagata equation for the ternary system are shown in figure 8 and the ternary jES values are mainly positive, table 8 which results from combination of interactions involved in related binary mixtures. Speeds of sound and isentropic compressibilities of the n-component mixtures were fitted to the following polynomial equation [21]: n X m X Q¼ Bij xji ; ð24Þ i¼1
j¼1
where Q stands for u or jS and xi is the mole fraction of component i in the binary and ternary mixtures. The adjustable coefficients Bij and standard deviations are presented in table 9. Table 10 lists various basic parameters of the pure components namely molar volume, V0, molar volume at absolute zero, V0, available volume, Va, intermolecular free
214
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
TABLE 8 Densities q, speeds of sound u, isentropic compressibilities jS, excess isentropic compressibilities jES , and speed of sound deviations Du for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K x1
x2
q/ (kg Æ m3)
u/ (m Æ s1)
jS/ TPa1
jES = TPa1
Du/ (m Æ s1)
0.0500 0.5030 0.0510 0.0501 0.0999 0.0998 0.1005 0.1008 0.1045 0.1013 0.1004 0.1000 0.1003 0.1978 0.2001 0.1985 0.1977 0.1974 0.1997 0.2001 0.2993 0.2996 0.3011 0.3000 0.3009 0.2995 0.4003 0.3981 0.3933 0.3993 0.4001 0.4973 0.4993 0.4987 0.4977 0.5998 0.6010 0.5962 0.6976 0.6959 0.7976 0.8465 0.8446 0.9003
0.9001 0.8500 0.1018 0.0505 0.1017 0.2006 0.3018 0.3965 0.4929 0.5985 0.6998 0.7986 0.8488 0.1007 0.2025 0.3009 0.4066 0.5039 0.6001 0.7061 0.1015 0.2020 0.2983 0.3999 0.5000 0.6002 0.1002 0.2039 0.3008 0.4009 0.5003 0.1038 0.2021 0.3006 0.4022 0.1008 0.1979 0.3024 0.1021 0.2026 0.1014 0.0521 0.1051 0.0499
1359.01 1314.48 817.59 791.90 820.00 871.69 928.14 984.41 1045.92 1117.93 1192.62 1271.50 1313.57 824.79 877.82 932.23 994.84 1056.64 1122.26 1200.07 830.60 882.58 935.62 995.22 1058.16 1125.61 835.34 888.60 941.43 1000.19 1062.25 842.31 892.79 946.35 1005.29 846.25 895.68 951.98 851.96 902.81 856.70 835.38 860.87 837.02
1042 1048 1188 1201 1191 1168 1145 1126 1108 1089 1073 1058 1052 1200 1177 1156 1134 1116 1100 1084 1211 1188 1169 1149 1131 1115 1224 1201 1182 1163 1147 1236 1217 1198 1180 1252 1234 1213 1267 1247 1282 1298 1288 1307
678 693 867 875 860 841 822 801 779 754 728 703 688 842 822 803 782 760 736 709 821 803 782 761 739 715 799 780 760 739 716 777 756 736 714 754 733 714 731 712 710 711 700 699
39 36 8 6 8 11 15 18 21 26 30 36 39 6 9 12 17 21 26 31 3 7 10 14 19 24 0 5 7 13 17 1 1 6 10 3 1 6 4 1 3 3 1 3
43 44 17 12 20 28 36 41 44 47 48 48 46 22 30 36 42 45 47 47 23 31 35 40 43 44 22 29 32 37 38 20 24 28 31 16 20 24 12 17 9 6 7 3
length Lf, molar surface factor, Y, molecular radius, r, molar actual volume of molecule, B, and collision factor, S at 298.15 K.
TABLE 9 Parameter values of equation (24), Bij and standard deviations for the binary mixtures and ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K B11
B12
B13
B21
B22
B23
B31
B32
B33
r
1
u/(m Æ s ) {1-Heptanol (1) + trichloroethylene (2)} 1616 277 645 397 {1-Heptanol (1) + methylcyclohexane (2)} 1695 364 798 413 {Trichloroethylene (1) + methylcyclohexane (2)} 1437 391 799 421 {1-Heptanol(1) + trichloroethylene (2)+Methylcyclohexane(3)} 1280 132 84 994 2 34 1177 28
10 2 7 6
1
jS/(TPa1) {1-Heptanol (1) + trichloroethylene (2)} 1174 495 299 336 {1-Heptanol (1) + methylcyclohexane (2)} 1192 504 414 477 {Trichloroethylene (1) + methylcyclohexane (2)} 1217 583 574 300 {1-Heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} 756 179 117 698 19 64 891 27 27
13 3 12 1
The speeds of sound were also calculated using Jacobson free length theory (FLT), Schaaff collision factor theory (CFT), Nomoto relation (NR), Junjie relation (JR), and Van Deal ideal mixing relation (IMR). The speed of sound in the n-component mixture are given by following equations. 3.3.1. Jacobson free length theory (FLT) u¼
K : Lf q1=2
ð25Þ
The value of K for the individual n-component mixture has been taken as [22] n X K¼ K i xi ; ð26Þ i¼1
where the value of Ki for each component in the mixture are obtained from equation (25). The free length of the mixture Lf is obtained by Pn 2 V i¼1 xi V 0;i Pn ; ð27Þ Lf ¼ i¼1 xi Y i where V0,i is the molar volume of pure component i at absolute zero temperature, Yi the surface area per mole
TABLE 10 Molar volume V0, molar volume at absolute zero V0, available volume Va = V0 V0, intermolecular free length Lf, molar surface factor Y, molecular radius r, molar actual volume of molecule B and collision factor S of the pure components at T = 298.15 K Compound
106V0/ (m3 Æ mol1)
106V0/ (m3 Æ mol1)
106Va/ (m3 Æ mol1)
106B/ (m3 Æ mol1)
Y/ (m2 Æ mol1)
r/ 1010 m
Lf/ 1010 m
S
1-Heptanol Methylcyclohexane Trichloroethylene
141.9202 128.3597 90.3179
117.2208 102.9173 71.1792
24.6994 25.4424 19.1387
53.7689 42.7123 28.1523
978,029 896,755 701,322
2.7727 2.5682 2.2354
0.5051 0.5674 0.5458
2.1924 2.2821 2.1335
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217 TABLE 11 Standard deviations of predicted speeds of sound and isentropic compressibilities by means of FLT, CFT, NR, JR, and IMR theories of the binary mixtures and ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K FLT
CFT
NR
JR
r(u)/(m Æ s1) {1-Heptanol (1) + trichloroethylene (2)} 38 47 47 29 {1-Heptanol (1) + methylcyclohexane (2)} 4 15 11 8 {Trichloroethylene (1) + methylcyclohexane (2)} 130 27 24 39 {1-Heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} 31 43 46 22 r(jS)/(TPa1) {1-Heptanol (1) + trichloroethylene (2)} 43 53 48 34 {1-Heptanol (1) + methylcyclohexane (2)} 6 17 15 11 {Trichloroethylene (1) + methylcyclohexane (2)} 235 41 32 51 {1-Heptanol (1) + Tichloroethylene (2) + methylcyclohexane (3)} 39 53 57 28
IMR
21
1=3
6
E
3
1
10 V /(m Æ mol ) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
B0
B1
B2
r
0.2206 0.379 142 920 737
0.6176 0.386 94 2108 836
0.1573 0.305 349 1599 873
0.0081 0.009 25 8 3
13 22
TABLE 14 Parameters of equation (9) and standard deviations for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
25 4 17 29
ð28Þ
;
TABLE 13 Parameters of equation (8) and standard deviations for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
3
for pure component i and V is the molar volume of mixture. For spherical molecules the surface area per mole of the pure liquid is given by Y i ¼ ð36pN A V 20;i Þ
215
where NA is the Avogadro’s number. The molar volume of pure component i at absolute zero temperature V0,i is obtained by Sugden formula 0:3 T ; ð29Þ V 0;i ¼ V i 1 TC
106VE/(m3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
A0
A1
A2
A3
r
0.4477 0.149 227 753 168
1.1166 0.989 149 1227 12
0.6326 1.144 30 698 279
1.2328 0.914 116 544 291
0.0079 0.009 25 8 3
where TC and Vi are the critical temperature and molar volume of pure component i. 3.3.2. Schaaff collision factor theory (CFT) Pn Pn i¼1 xi S i i¼1 xi Bi ¼ u1 Srf ; u ¼ u1 V
ð30Þ
where u1 = 1600 m s1, S = collision factor and rf = B/V, space filling factor. B is the actual volume of the molecules per mole. For n-component mixtures S and B are related to pure component values through
TABLE 12 Parameters of equation (4) and standard deviations for the binary mixtures at T = 298.15 K A0
A1
106VE/(m3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
0.0107 6.006 271 58 124
{1-Heptanol (1) + trichloroethylene (2)} 0.7346 0.0137 0.1369 1.629 0.095 0.390 865 410 465 85 237 328 98 203 286
106VE/(m3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
0.5282 6.089 925 20 50
{1-Heptanol 0.6198 1.839 1151 22 22
106VE/(m3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
1.1006 0.133 293 183 33
{Trichloroethylene (1) + methylcyclohexane (2)} 0.0627 0.0077 0.0838 0.003 0.028 0.003 33 94 15 99 216 336 31 171 301
A2
A3
(1) + methylcyclohexane (2)} 0.1669 0.3437 0.677 1.073 318 275 5 59 21 49
A4
A5
r
0.3441
0.4484
0.0042 0.004 7 2 2
0.5434
0.7343
0.0029 0.005 3 1 0
0.1401
0.1128
0.0004 0.000 1 4 4
r
0.0059 0.008 26 1 2 7.6489 Æ 103 0.0111 36.8229 4.001 1.6473
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
B8
216
Trichloroethylene 0.0
1.0
0.1
0.9
0.2
0.8 30
0.3
0.7
0.4
25
0.6
0.5
0.5 20
5.689 Æ 103 3.7113 Æ 103 14.1288 7.8072 4.8591
B7 B6
3.0733 Æ 103 9.1358 Æ 103 8.8784 3.3679 4.4799
B5
8.9201 Æ 103 5.1429 Æ 103 21.8586 4.6022 2.5207
B4
3.8569 Æ 103 3.9799 Æ 103 14.1122 8.5307 5.8512
B3
8.9841 Æ 103 8.6488 Æ 103 19.2449 5.6049 6.7535 1.8134 Æ 103 6.8191 Æ 104 1.0535 4.157 2.9184 6.6222 Æ 103 2.5936 Æ 103 9.1943 2.8836 3.5923
B2 B1
1.1729 Æ 103 2.3773 Æ 104 0.7684 0.3125 0.9324
0.3
10 0.8
5
0.2
0.9
0.1
1.0
Methylcyclohexane
0.0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1-Heptanol
FIGURE 8. Isolines at constant excess isentropic compressibilities, jES ðTPa1 Þ for the ternary mixture of {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} correlated with equation (10) at T = 298.15 K.
S¼ B¼
B0
0.4
15 0.7
0.0
106VE/(m3 Æ mol1) Dg (mPa Æ s) DG*E/(J Æ mol1) jES =TPa1 Du/(m Æ s1)
TABLE 15 Parameters of equation (10) and standard deviations for the ternary mixture {1-heptanol (1) + trichloroethylene (2) + methylcyclohexane (3)} at T = 298.15 K
0.6
n X i¼1 n X
xi S i ;
ð31Þ
x i Bi ;
ð32Þ
i¼1
where Bi can be evaluated as 4 Bi ¼ pr3 N A ; 3
ð33Þ
where r is the molecular radius of the pure component. Molecular radius is calculated as 1=3 3b r¼ ð34Þ 16pN A where b is the van der Waals constant. 3.3.3. Nomoto relation (NR) Pn 3 x i Ri u ¼ Pni¼1 ; i¼1 xi V i 1=3
Ri ¼ V i u i ;
ð35Þ ð36Þ
where Ri and ui stand for Rao molar sound velocity and speed of sound of the pure component i, respectively. 3.3.4. Junjie relation (JR) Pn i¼1 xi V u ¼ Pn 1=2 Pn : 2 1=2 i¼1 xi M i i¼1 xi V i =qi ui 3.3.5. Van Deal ideal mixing relation (IMR) n X 1 1 xi Pn ¼ : 2 M i u2i i¼1 xi M i u i¼1
ð37Þ
ð38Þ
H. Iloukhani, B. Samiey / J. Chem. Thermodynamics 39 (2007) 206–217
The best correlation method for the binary systems is found using the IMR and for the ternary system using the IMR and JR. The standard deviations for speeds of sound r(u) and isentropic compressibilities r(jS) predicted by above mentioned equations are given in table 11. Acknowledgements The authors thank of the Bu-Ali Sina University authorities for the necessary facilities to carry out the work. References [1] H. Iloukhani, B. Samiey, M.A. Moghaddasi, J. Chem. Thermodyn. 38 (2006) 190–200. [2] H. Iloukhani, H.A. Zarei, J. Chem. Eng. Data 47 (2002) 195–197. [3] H. Iloukhani, B. Samiey, J. Chem. Eng. Data 50 (2005) 1911–1916. [4] H.A. Zarei, H. Iloukhani, Thermochim. Acta 405 (2003) 123–128. [5] H. Iloukhani, M. Rezaei-Sameti, J. Chem. Thermodyn. 37 (2005) 1151–1161. [6] O.J. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [7] I. Cibulka, Collect. Czech. Chem. Commun. 47 (1982) 1414–1419. [8] F. Olive, K.R. Patil, J. Fernandez, A. Coronas, Thermochim. Acta 259 (1995) 57–70. [9] I. Nagata, K. Tamura, J. Chem. Thermodyn. 22 (1990) 279–283. [10] L. Grunberg, A.H. Nissan, Trans. Faraday Soc. 45 (1949) 125–137. [11] M. Dominguez, J.I. Pardo, I.G. Gascon, F.M. Royo, J.S. Urieta, Fluid Phase Equilibr. 169 (2000) 277–292. [12] J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 43 (1998) 961– 966. [13] R.K. Hind, E. McLaughlin, A.R. Ubbelohde, Trans. Faraday Soc. 56 (1960) 328–330. [14] R.K. Hind, E. McLaughlin, A.R. Ubbelohde, Trans. Faraday Soc. 56 (1960) 331–334. [15] P.K. Katti, M.M. Chaudhri, J. Chem. Eng. Data 9 (1964) 442–443. [16] R.A. McAllister, AIChE J. 6 (1960) 427–431.
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JCT 06-72