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Thermophysical properties of binary mixtures (dimethyl carbonate + ketones) at T = (303.15, 308.15 and 313.15) K
Journal of Molecular Liquids 163 (2011) 170–177
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Thermophysical properties of binary mixtures (dimethyl carbonate + ketones) at T = (303.15, 308.15 and 313.15) K M.V. Rathnam a,⁎, Sudhir Mohite a, M.S.S. Kumar b a b
Physical Chemistry Research Laboratory, B.N. Bandodkar College of Science; Thane, 400 601, India Zulal Bhilajirao Patil College, Deopur, Dhule, 424 002, India
a r t i c l e
i n f o
Article history: Received 29 June 2011 Received in revised form 8 August 2011 Accepted 1 September 2011 Available online 17 September 2011 Keywords: Dimethyl carbonate Ketones Binary mixture Density
a b s t r a c t The densities ρ, viscosities η, and refractive indices nD of binary mixtures of dimethyl carbonate (DMC) with acetophenone, cyclopentanone, cyclohexanone, and 3-pentanone have been measured over the entire range of composition at the temperatures 303.15, 308.15 and 313.15 K and at atmospheric pressure. The density values were used to calculate excess molar volumes VE, and other excess functions of interest such as deviations in viscosity Δη, excess Gibb's free energies of activation of viscous flow ΔG E and deviations in molar refraction ΔR. The measured viscosities were compared with those predicted using the Grunberg–Nissan, Eyring–Margules, Soliman–Marshall, and McAllister four body models. Furthermore the refractive indices data have been correlated using Lorentz–Lorentz, Weiner, Newton, Gladstone–Dale, Eykman, and Eyring– John equations and a satisfactory agreement was found for all the binary systems studied in the present work. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The investigation of binary mixtures containing linear carbonates such as dimethyl carbonate (DMC) are of interest for the group contribution models [1] due to the presence of large and complicated carbonate groups. Excess properties of binary liquid mixtures are useful in the study of intermolecular interactions, since these properties reflect the interactions in solute–solvent species. Thermophysical properties such as density ρ, viscosity η, and refractive index nD are used for the design of industrial equipments for commercial applications. DMC is a unique molecule, in many aspects it is environmentally mild new building block. DMC is a flammable and synthetic organic chemical used as an intermediate for fruit trees and vegetables. Its main benefit over other methylating reagents such as iodomethane and dimethyl sulfate is its lesser toxicity and its biodegradability. DMC is also used in many industries such as pharmaceuticals, agrochemicals, hydrocarbon refinery, paint coatings and fragrances. It is used as an oxygenate for fuel additives [2]. In view of these numerous importance of the dimethyl carbonate, it is of interest to know the molecular interactions of binary mixtures of DMC with various solvents. There have been a few studies available in literature on thermodynamic and thermophysical properties of binary liquid mixtures consisting of carbonates with ethers [3–6], alcohols [7–9], alkanes [10,11], and hydrocarbons [12–14]. Wisniak et al. [15] have measured the density of dimethyl carbonate with butyl methacrylate, alkyl
⁎ Corresponding author. E-mail address: [email protected] (M.V. Rathnam). 0167-7322/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2011.09.002
methacrylate, styrene and vinyl acetate at T=(293.15, 303.15 and 313.15)K. However there are no reports in the literature except Pereiro [16] and Comelli [17] on the molecular interactions of carbonates with ketones based on density, viscosity and refractive index. Therefore in continuation of our earlier studies [18] on the determination of excess properties, in this paper we report density, viscosity and refractive index of binary systems (DMC+acetophenone), (DMC+cyclopentanone), (DMC+cyclohexanone) and (DMC+3-pentanone) at T=(303.15, 308.15 and 313.15) K, over the entire composition range. From the experimental data the values of excess molar volume VE, deviation in viscosity Δη, excess Gibb's free energy of activation of viscous flow ΔGE and deviation in molar refraction ΔR were calculated. Further the mixture viscosities and refractive indices of these binary mixtures were calculated theoretically from the pure component data by using various empirical and semi-empirical relations and the results were compared with the experimental data.
2. Experimental 2.1. Materials Dimethyl carbonate, acetophenone (Sigma-Aldrich), cyclopentanone, cyclohexanone and 3-pentanone (all Merck) with mass fraction purities greater than 99.0% were used without further purification. The purity of these solvents was verified by measuring their density, viscosity, and refractive index. Table 1 lists these values for the pure liquids at (303.15, 308.15 and 313.15) K together with the literature values. Comparison of these results reveals that experimental values show good agreement with literature values.
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
171
Table 1 Comparison of experimental densities (ρ), viscosities (η), and refractive indices (nD) of pure components with available literature values at (303.15, 308.15 and 313.15) K. Liquid
Dimethyl carbonate
Acetophenone
Cyclopentanone
Cyclohexanone
3-Pentanone
T/K
303.15 308.15 313.15 303.15 308.15 313.15 303.15 308.15 313.15 303.15 308.15 313.15 303.15 308.15 313.15
ρ/(g·cm−3)
η/(mPa·s) Literature
Experimental
Literature
Experimental
Literature
1.0571 1.0502 1.0435 1.0199 1.0169 1.0135 0.9385 0.9339 0.9290 0.9377 0.9328 0.9282 0.8057 0.8017 0.7977
1.0565 [7] 1.0508 [4] 1.0432 [6] 1.0194 [37] 1.0172 [38] 1.0139 [38] 0.9390 [38]
0.545 0.523 0.495 1.518 1.378 1.291 0.999 0.927 0.865 1.816 1.657 1.542 0.429 0.397 0.388
0.548 0.520 0.494 1.511
1.3647 1.3624 1.3600 1.5294 1.5270 1.5250 1.4335 1.4310 1.4290 1.4465 1.4440 1.4420 1.3879 1.3857 1.3835
1.3648 [13] 1.3628 [13] 1.3593 [7] 1.5297 [38]
0.9376 [38]
0.8054 [38]
2.2. Apparatus and procedures The binary solutions were prepared by mass in airtight glass bottles. Mass measurements accurate to ±0.01 mg were made on a digital electronic balance (Mettler, AE 240 Switzerland). To prevent the samples from undergoing preferential evaporation, the mixtures were prepared by transferring aliquots via syringe into the stoppered bottles. A set of nine compositions of mole fraction varying from 0.1 to 0.9 in steps of 0.1 was prepared. The mixtures were completely miscible over the whole composition range. The possible uncertainty in the mole fraction was estimated to be less than ±1 × 10 −4. The densities of the pure and their binary mixtures were determined with a portable density meter (DMA 35 Anton Paar). The instrument was calibrated frequently before the start of the actual experiments using deionized water and dry air according to the established standard procedures. The instrument has a temperature sensor which measures the sample temperature right at the measuring cell. The density of all the binary mixtures was measured after achieving thermal equilibrium with successive increments of 5 K for a temperature range from 303.15 to 313.15 K. All measurements for each sample were made in triplicate, the average values are reported and considered for further analysis. The reproducibility of the density measurements was ±0.0005 g·cm −3 and the experimental uncertainty in the density measurements was approximately ±4 × 10 −4. The viscosities of pure liquids and their mixtures were determined at atmospheric pressure and at temperatures 303.15, 308.15 and 313.15 K by using an Ubbelohode viscometer. The viscometer bulb has a capacity of about 15 ml and the capillary tube with a length of about 90 mm and 0.5 mm internal diameter. The viscometer thoroughly cleaned and perfectly dried, is filled with the sample liquid by fitting the viscometer to about 30° from the vertical and its limbs are closed with Teflon caps to avoid the evaporation. The viscometer is kept in a transparent walled bath with a thermal stability of ±0.01 K for about 20 min to obtain thermal equilibrium. An electronic digital stopwatch with an uncertainty of ±0.01 s was used for flow time measurements. At least three repetitions of each mixture reproducible to ±0.05 s were obtained, and the results were averaged. The viscosity was calculated from measured efflux time ‘t’, using the following relation η ¼ ρðAt–B=tÞ
nD
Experimental
ð1Þ
where ρ is the density and A and B are the characteristic constants of the viscometer, which were determined by taking water and benzene as the calibrating liquids. The uncertainty in viscosity thus estimated was found to be± 0.007 mPa·s. Refractive indices were measured using a refractometer (RM40, Mettler Toledo, Switzerland) with an uncertainty of ±0.0001. The
[9] [4] [10] [38]
0.995 [38]
1.810 [38] 1.635 [39] 0.424 [38] 0.380 [38]
1.4463 [39] 1.4439 [39] 1.3878 [38]
instrument has built-in solid state thermostat within temperature range (5 to 100 °C) with an uncertainty of ±0.1 °C. The instrument calibration was carried out with doubly distilled water. An average of three measurements was taken for each sample. 3. Results and discussion: The experimental results of densities ρ, viscosities η, and refractive indices nD for binary mixtures at 303.15, 308.15 and 313.15 K are listed in Table 2. The excess molar volumes VE of the binary mixtures were calculated from the densities of the pure liquids and their mixtures using the equation E
V ¼ ðx1 M1 þ x2 M2 Þ=ρ–ðx1 M1 =ρ1 þ x2 M2 =ρ2 Þ
ð2Þ
where ρ is the density of the mixture and (x1, M1 and ρ1) and (x2, M2 and ρ2) are the mole fraction, molar mass, and density of pure components 1 and 2 respectively. The calculated results of V E for binary liquid mixtures are listed in Table 2. From the results of viscosities the deviations in the viscosity, Δη were calculated using the relation Δη ¼ η–ðx1 η1 þ x2 η2 Þ
ð3Þ
where η is the absolute viscosity of the mixture, and η1 and η2 are the viscosities of the pure components. The excess Gibb's free energies of activation ΔG E for viscous flow have been calculated using the relation E
ΔG ¼ RT ½lnðηV Þ–ðx1 lnðη1 V1 Þ þ x2 lnðη2 V2 ÞÞ
ð4Þ
where η1, V1, η and V denote the viscosity and molar volume of the pure components and their mixtures respectively. The refractive index values in Table 2 have been used to calculate the Lorentz–Lorentz molar refraction [19] and deviation in the molar refraction ΔR have been calculated using the equation ΔR ¼ Rm –ðx1 R1 þ x2 R2 Þ
ð5Þ
where Rm is the molar refractivity of mixtures, R1 and R2 are the molar refractivities of pure components 1 and 2 respectively. The results of V E, Δη, ΔG E and ΔR have been fitted to the Redlich– Kister [20] polynomial equation n
i
Δy ¼ x1 ð1−x1 Þ ∑ Ai ð2x1 −1Þ i¼0
ð6Þ
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M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
Table 2 Mole fraction (x1), densities (ρ), excess volumes (VE), dynamic viscosities (η), refractive index (nD) for the binary mixtures. x1
ρ/g·cm−3
VE/cm3·mol−1
Dimethyl carbonate (1) + acetophenone (2) T = 303.15 K 0.0000 1.0199 0.0802 1.0223 − 0.022 0.1338 1.0240 − 0.040 0.2501 1.0279 − 0.082 0.3589 1.0317 − 0.111 0.4569 1.0352 − 0.122 0.5789 1.0397 − 0.119 0.6612 1.0429 − 0.113 0.7589 1.0469 − 0.102 0.8523 1.0508 − 0.076 0.9249 1.0538 − 0.038 1.0000 1.0571 Dimethyl carbonate (1) + acetophenone (2) T = 308.15 K 0.0000 1.0169 0.0802 1.0190 − 0.013 0.1338 1.0205 − 0.027 0.2501 1.0239 − 0.055 0.3589 1.0272 − 0.070 0.4569 1.0303 − 0.078 0.5789 1.0343 − 0.074 0.6612 1.0372 − 0.073 0.7589 1.0407 − 0.057 0.8523 1.0442 − 0.036 0.9249 1.0471 − 0.021 1.0000 1.0502 Dimethyl carbonate (1) + acetophenone (2) T = 313.15 K 0.0000 1.0135 0.0802 1.0154 − 0.012 0.1338 1.0167 − 0.019 0.2501 1.0197 − 0.037 0.3589 1.0226 − 0.043 0.4569 1.0254 − 0.051 0.5789 1.0290 − 0.048 0.6612 1.0316 − 0.046 0.7589 1.0348 − 0.038 0.8523 1.0380 − 0.023 0.9249 1.0406 − 0.009 1.0000 1.0435 Dimethyl carbonate (1) + cyclopentanone (2) T = 303.15 K 0.0000 0.9385 0.0656 0.9458 0.011 0.1060 0.9502 0.030 0.2015 0.9607 0.069 0.3125 0.9733 0.089 0.4129 0.9849 0.100 0.5109 0.9965 0.096 0.6233 1.0100 0.087 0.7184 1.0217 0.066 0.8257 1.0351 0.037 0.9156 1.0464 0.018 1.0000 1.0571 Dimethyl carbonate (1) + cyclopentanone (2) T = 308.15 K 0.0000 0.9339 0.0656 0.9409 0.027 0.1060 0.9452 0.047 0.2015 0.9555 0.087 0.3125 0.9679 0.104 0.4129 0.9793 0.112 0.5109 0.9906 0.115 0.6233 1.0038 0.109 0.7184 1.0153 0.085 0.8257 1.0285 0.050 0.9156 1.0396 0.028 1.0000 1.0502
η/mPa·s
1.518 1.425 1.362 1.230 1.114 1.013 0.895 0.822 0.740 0.664 0.605 0.545
1.378 1.292 1.237 1.113 1.005 0.915 0.811 0.748 0.677 0.615 0.569 0.523
1.291 1.209 1.154 1.039 0.936 0.851 0.755 0.695 0.631 0.574 0.534 0.495
0.999 0.950 0.918 0.853 0.787 0.736 0.690 0.644 0.615 0.589 0.568 0.545
0.927 0.875 0.844 0.781 0.718 0.670 0.630 0.590 0.565 0.543 0.535 0.523
nD
1.5294 1.5195 1.5131 1.4986 1.4836 1.4690 1.4491 1.4346 1.4159 1.3969 1.3813 1.3647
1.5270 1.5176 1.5113 1.4969 1.4822 1.4677 1.4479 1.4333 1.4143 1.3949 1.3792 1.3624
1.5250 1.5157 1.5095 1.4959 1.4816 1.4670 1.4472 1.4325 1.4133 1.3937 1.3775 1.3600
1.4335 1.4286 1.4255 1.4183 1.4103 1.4032 1.3965 1.3890 1.3829 1.3760 1.3702 1.3647
1.4310 1.4262 1.4232 1.4162 1.4082 1.4012 1.3945 1.3869 1.3807 1.3738 1.3680 1.3624
Table 2 (continued) ρ/g·cm−3
VE/cm3·mol−1
η/mPa·s
nD
Dimethyl carbonate (1) + cyclopentanone (2) T = 313.15 K 0.0000 0.9290 0.0656 0.9359 0.027 0.1060 0.9401 0.051 0.2015 0.9500 0.114 0.3125 0.9620 0.150 0.4129 0.9731 0.169 0.5109 0.9843 0.164 0.6233 0.9974 0.148 0.7184 1.0088 0.116 0.8257 1.0219 0.072 0.9156 1.0330 0.034 1.0000 1.0435
0.865 0.811 0.779 0.715 0.654 0.607 0.572 0.536 0.517 0.504 0.501 0.495
1.4290 1.4243 1.4214 1.4145 1.4066 1.3996 1.3929 1.3853 1.3790 1.3718 1.3657 1.3600
Dimethyl carbonate (1) + cyclohexanone (2) T = 303.15 K 0.0000 0.9377 0.0814 0.9455 0.026 0.1180 0.9490 0.046 0.2351 0.9603 0.135 0.3356 0.9706 0.191 0.4428 0.9822 0.235 0.5480 0.9945 0.237 0.6510 1.0076 0.191 0.7489 1.0207 0.139 0.8359 1.0329 0.086 0.9556 1.0504 0.021 1.0000 1.0571
1.816 1.618 1.526 1.274 1.088 0.930 0.806 0.710 0.639 0.604 0.561 0.545
1.4465 1.4409 1.4383 1.4296 1.4219 1.4134 1.4049 1.3964 1.3880 1.3802 1.3690 1.3647
Dimethyl carbonate (1) + cyclohexanone (2) T = 308.15 K 0.0000 0.9328 0.0814 0.9404 0.034 0.1180 0.9438 0.059 0.2351 0.9549 0.150 0.3356 0.9650 0.209 0.4428 0.9765 0.243 0.5480 0.9886 0.244 0.6510 1.0014 0.206 0.7489 1.0144 0.142 0.8359 1.0264 0.088 0.9556 1.0437 0.014 1.0000 1.0502
1.657 1.474 1.393 1.162 1.008 0.862 0.749 0.664 0.602 0.571 0.536 0.523
1.4440 1.4385 1.4359 1.4273 1.4197 1.4113 1.4028 1.3942 1.3858 1.3780 1.3668 1.3624
Dimethyl carbonate (1)+cyclohexanone (2) T = 313.15 K 0.0000 0.9282 0.0814 0.9357 0.031 0.1180 0.9390 0.061 0.2351 0.9498 0.163 0.3356 0.9597 0.224 0.4428 0.9710 0.257 0.5480 0.9829 0.257 0.6510 0.9953 0.234 0.7489 1.0081 0.166 0.8359 1.0200 0.101 0.9556 1.0371 0.016 1.0000 1.0435
1.542 1.368 1.290 1.077 0.934 0.803 0.701 0.622 0.565 0.533 0.505 0.495
1.4420 1.4365 1.4339 1.4254 1.4179 1.4095 1.4010 1.3922 1.3837 1.3759 1.3645 1.3600
Dimethyl carbonate (1) + 3-pentanone (2) T = 303.15 K 0.0000 0.8057 0.0755 0.8207 0.047 0.1241 0.8304 0.102 0.2256 0.8515 0.189 0.3342 0.8753 0.256 0.4356 0.8989 0.277 0.5579 0.9290 0.283 0.6435 0.9513 0.266 0.7501 0.9807 0.212 0.8419 1.0075 0.147 0.9425 1.0385 0.061 1.0000 1.0571
0.429 0.435 0.439 0.447 0.456 0.466 0.480 0.491 0.506 0.520 0.536 0.545
1.3879 1.3865 1.3855 1.3835 1.3813 1.3791 1.3763 1.3742 1.3714 1.3690 1.3663 1.3647
x1
(continued on next page)
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177 Table 2 (continued) ρ/g·cm−3
VE/cm3·mol−1
Table 3 Derived parameters of Eq. (6) for various functions and standard deviation of the binary mixtures at (303.15, 308.15 and 313.15) K.
η/mPa·s
nD
Dimethyl carbonate (1) + 3-pentanone (2) T = 308.15 K 0.0000 0.8017 0.0755 0.8163 0.079 0.1241 0.8258 0.146 0.2256 0.8466 0.241 0.3342 0.8702 0.299 0.4356 0.8935 0.323 0.5579 0.9233 0.322 0.6435 0.9454 0.297 0.7501 0.9744 0.247 0.8419 1.0007 0.194 0.9425 1.0317 0.072 1.0000 1.0502
0.397 0.404 0.407 0.413 0.421 0.431 0.446 0.460 0.479 0.495 0.513 0.523
1.3857 1.3842 1.3832 1.3812 1.3790 1.3768 1.3740 1.3719 1.3691 1.3666 1.3640 1.3624
Dimethyl carbonate (1) + 3-pentanone (2) T = 313.15 K 0.0000 0.7977 0.0755 0.8120 0.100 0.1241 0.8213 0.181 0.2256 0.8417 0.298 0.3342 0.8647 0.395 0.4356 0.8876 0.432 0.5579 0.9170 0.434 0.6435 0.9390 0.390 0.7501 0.9680 0.303 0.8419 0.9944 0.212 0.9425 1.0251 0.083 1.0000 1.0435
0.388 0.391 0.392 0.396 0.401 0.408 0.421 0.432 0.448 0.465 0.484 0.495
1.3835 1.3820 1.3810 1.3790 1.3767 1.3745 1.3717 1.3697 1.3670 1.3645 1.3618 1.3600
x1
A2
A3
σ
Dimethyl carbonate (1) + acetophenone (2) 303.15 − 0.4946 − 0.0425 VE 308.15 − 0.3173 − 0.0055 313.15 − 0.2036 − 0.0239 Δη 303.15 − 0.2450 0.0066 308.15 − 0.2945 − 0.0098 313.15 − 0.3080 − 0.0178 ΔR 303.15 0.7854 − 0.0022 308.15 1.1005 0.0689 313.15 1.4975 − 0.0109 E ΔG 303.15 768.2434 133.5301 308.15 453.2249 − 45.1722 313.15 337.3072 − 126.0409
0.0425 0.09447 0.0528 0.0659 0.0735 0.0474 − 0.5204 − 0.5639 − 0.6298 237.5263 174.8317 87.6031
− 0.2183 − 0.0762 0.0408 0.0186 − 0.0183 − 0.0278 0.1195 − 0.1486 0.3623 153.8004 21.4384 − 33.3652
0.004 0.002 0.002 0.001 0.001 0.000 0.008 0.003 0.007 2.176 1.395 1.306
Dimethyl carbonate (1) + cyclopentanone (2) 303.15 0.4011 − 0.1411 VE 308.15 0.4670 − 0.0730 313.15 0.6774 − 0.1935 Δη 303.15 − 0.3143 0.0322 308.15 − 0.3690 0.0247 313.15 − 0.4247 0.0312 ΔR 303.15 − 0.3402 0.0826 308.15 − 0.2547 0.0293 313.15 − 0.0815 0.0422 E ΔG 303.15 − 614.3243 − 142.1283 308.15 − 981.9006 − 254.6284 313.15 − 1347.9801 − 318.8614
− 0.1884 − 0.0659 − 0.2497 0.0566 − 0.0028 0.0034 0.0848 0.1172 0.0390 264.5217 54.5684 136.4593
0.1504 − 0.0542 0.2136 0.0823 0.0647 0.0951 − 0.0005 0.0172 − 0.0245 394.6361 301.6100 469.9623
0.004 0.004 0.005 0.002 0.002 0.001 0.001 0.002 0.002 5.750 6.959 6.338
Dimethyl carbonate VE 303.15 308.15 313.15 Δη 303.15 308.15 313.15 ΔR 303.15 308.15 313.15 E ΔG 303.15 308.15 313.15
(1) + cyclohexanone (2) 0.9407 − 0.0846 0.9947 − 0.1003 1.0718 − 0.0361 − 1.2966 0.1826 − 1.1767 0.1391 − 1.1007 0.1748 0.1580 0.0022 0.2278 − 0.0308 0.3268 − 0.0534 − 1437.6098 − 900.8069 − 1530.6604 − 955.7912 − 1604.8611 − 852.4626
− 0.7659 − 0.7577 − 0.7622 0.1610 0.0971 0.0089 − 0.0363 − 0.0430 − 0.0948 405.3065 286.8745 57.0811
0.2605 0.1258 0.1177 − 0.0227 0.0678 0.0030 − 0.0176 0.0160 0.1379 429.7768 572.0501 300.8771
0.004 0.003 0.007 0.004 0.004 0.003 0.001 0.001 0.002 12.150 11.736 10.271
Dimethyl carbonate (1) + 3-pentanone (2) VE 303.15 1.1612 − 0.0382 308.15 1.3127 − 0.1101 313.15 1.7624 − 0.1494 Δη 303.15 − 0.0573 − 0.0052 308.15 − 0.0852 0.0074 313.15 − 0.1102 − 0.0077 ΔR 303.15 0.2826 − 0.0376 308.15 0.3102 − 0.0472 313.15 0.4115 − 0.0049 ΔGE 303.15 − 133.5051 14.6382 308.15 − 289.7984 106.0174 313.15 − 481.336 34.6523
− 0.2516 0.1006 − 0.3189 0.0238 0.0536 0.0384 − 0.1338 − 0.1049 − 0.0763 121.5469 316.2936 246.8420
0.3274 0.3403 0.2150 0.0004 − 0.0176 − 0.0055 0.0656 0.0755 0.0800 − 10.3467 − 131.4989 − 57.3802
0.007 0.008 0.005 0.000 0.001 0.001 0.002 0.001 0.002 1.243 1.589 1.855
Function
where ‘i’ is the number of estimated parameters and Ai the polynomial coefficients obtained by fitting the equation to the experimental results by least-squares regression method. The standard deviations σ for VE, Δη, ΔGE and ΔR were calculated using the equation h i1=2 2 σ ðyÞ ¼ ∑ðyobs –ycal Þ =ðn−mÞ
173
ð7Þ
where ‘n’ represents the number of data points and ‘m’ is the number of coefficients. The calculated values of the polynomial coefficients along with their standard deviations σ are given in Table 3. The variation of VE with mole fraction x1, at (303.15, 308.15 and 313.15) K over the entire composition range are graphically represented in Fig. 1. A negative deviation from ideal behavior occurs for the system involving acetophenone, whereas DMC + cyclopentanone, DMC + cyclohexanone and DMC + 3-pentanone exhibit positive deviation. As previously reported [21–23] several effects may contribute to the values of V E. The positive V E may be due to the breaking of molecular order on mixing and the difference in molecular size between two mixing solvents, while the negative contribution of VE may be due to packing of larger sized molecules leading to interstitial void space that can be filled by smaller molecules. The molar volumes of DMC, acetophenone, cyclopentanone, cyclohexanone and 3-pentanone are 85.214, 117.806, 89.632, 104.671 and 106.901 cm3·mol−1 respectively at 303.15 K. The deviations in viscosity Δη, (Fig. 2) are negative for all the four binary systems (DMC + acetophenone, cyclopentanone, cyclohexanone and 3-pentanone) under study over the whole composition range at each investigated temperature. The negative Δη values are indicative of weak or strong dipole interactions [22–24] within the mixtures. This suggests that in these binary mixtures the forces between pairs of unlike molecules are less than the forces between like molecules. The isotherms are symmetric at x1 ≈ 0.5. The negative values of Δη for cyclohexanone with DMC decrease with increase in temperature while for systems acetophenone, cyclopentanone and 3-pentanone these values increase with increase in temperature. The values of Δη are less negative for DMC + cyclohexanone. The
T/K
A0
A1
negative Δη values of dimethyl carbonate and ketones follow the order
cyclohexanone N cyclopentanone N acetophenone N 3 pentanone: The values of ΔGE, calculated using Eq. (4) are positive for binary mixtures of DMC+ acetophenone and for the remaining systems DMC + cyclopentanone, DMC+ cyclohexanone, and DMC+ 3-pentanone the ΔGE is negative over the entire range of composition. Fig. 3 shows the variation of ΔGE values as a function of mole fraction. The positive ΔGE values indicate specific interactions while negative values indicate the dominance of dispersion forces. Like Δη, the ΔGE values at x1 ≈0.5 indicate that there is an effect of temperature on ΔGE. It is observed that for the binary mixtures of dimethyl carbonate+ acetophenone the positive values of ΔGE decrease with increase in temperature, while for the
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0.5
300
0.4
200 100
GE / J.mol -1
VE / cm3.mol -1
0.3
0.2
0.1
0 -100 -200
0 -300 -0.1
-400
-0.2 0
0.2
0.4
0.6
0.8
-500
1
x1
0
0.2
0.4
0.6
0.8
1
x1
Fig. 1. Excess volume, VE as a function of dimethyl carbonate mole fraction, x1 (Dimethyl Carbonate+ acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Dimethyl Carbonate + cyclopentanone): ( ), at 303.15 K; ( ), at 308.15 K; ( ), at 313.15 K. (Dimethyl Carbonate + cyclohexanone): (○), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Dimethyl Carbonate + 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.
Fig. 3. Excess Gibb's energy, ΔGE as a function of dimethyl carbonate mole fraction, x1 (Dimethyl Carbonate+ acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Dimethyl Carbonate+ cyclopentanone): ( ), at 303.15 K; ( ), at 308.15 K; ( ), at 313.15 K. (Dimethyl Carbonate + cyclohexanone): (O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Dimethyl Carbonate + 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.
remaining studied mixtures negative values of ΔGE increase with increase in temperature. The variations of ΔR versus mole fraction of dimethyl carbonate for all binary mixtures are graphically represented in Fig. 4. It is observed that the ΔR values are positive for the binary mixtures of DMC + acetophenone, DMC + cyclohexanone and DMC + 3-pentanone. Whereas for DMC + cyclopentanone the ΔR values are negative over the entire composition range. The magnitude of positive values increases and that of negative values diminishes with the rise in
temperature. A comparison of the values of η and nD (Table 2) shows that there is a systematic decrease in η and nD with a rise in temperature for all the mixtures. At any particular temperature as mole fraction of DMC increases the η and nD decrease. 3.1. Viscosity models In this report we have used some of the semi-empirical equations to correlate the experimental viscosity data. The evaluated equations
0
0.4 0.35
-0.05
0.3 -0.1
R / cm3.mol -1
mPa.s
0.25 -0.15 -0.2 -0.25
0.2 0.15 0.1 0.05
-0.3 0 -0.35 -0.4
-0.05 0
0.2
0.4
0.6
0.8
1
x1 Fig. 2. Deviations in viscosity, Δη as a function of dimethyl carbonate mole fraction, x1 (Dimethyl Carbonate + acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Dimethyl Carbonate+ cyclopentanone): ( ), at 303.15 K; ( ), at 308.15 K; ( ), at 313.15 K. (Dimethyl Carbonate + cyclohexanone): (O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Dimethyl Carbonate + 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.
-0.1
0
0.2
0.4
0.6
0.8
1
x1 Fig. 4. Deviation in molar refraction, ΔR as a function of dimethyl carbonate mole fraction, x1 (Dimethyl Carbonate + acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Dimethyl Carbonate + cyclopentanone): ( ), at 303.15 K; ( ), at 308.15 K; ( ), at 313.15 K. (Dimethyl Carbonate + cyclohexanone): (O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Dimethyl Carbonate 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
175
Table 4 Adjustable parameters and percentage standard deviation σ (%) of several correlations for the viscosities of binary mixtures. T/K
Grunberg–Nissan
Soliman and Marshall
McAllister four-body
σ (%)
A12
B12
σ (%)
ν1112
ν1122
ν2221
σ (%)
0.2440 0.1848 0.1726
0.36 0.53 0.31
1.0579 1.1224 1.1603
− 0.6820 − 0.9614 − 1.1343
0.61 0.31 0.39
0.7492 0.6721 0.6200
0.9311 0.8429 0.7935
1.1435 1.0400 0.9703
0.13 0.05 0.05
(2) − 0.2309 − 0.4308 − 0.5690
− 0.2258 − 0.3178 − 0.4519
0.48 0.31 0.40
0.1287 0.0885 0.0735
5.2883 6.2799 6.6562
0.41 0.31 0.39
0.5947 0.5326 0.4920
0.6617 0.6174 0.5507
0.8707 0.7861 0.7210
0.34 0.33 0.41
Dimethyl carbonate (1) + cyclohexanone (2) 303.15 − 0.5769 2.37 − 0.8343 308.15 − 0.6119 2.31 − 0.9304 313.15 − 0.6392 2.15 − 0.6132
− 0.1492 − 0.1684 − 0.3210
0.91 1.29 2.31
7.0053 7.1465 7.2582
− 6.7948 − 6.9285 − 7.0767
0.84 0.75 0.48
0.5979 0.5602 0.5198
0.7878 0.7466 0.7183
1.3179 1.2011 1.0985
0.52 0.57 0.43
Dimethyl carbonate (1) + 3-pentanone (2) 303.15 − 0.0829 0.17 − 0.0329 308.15 − 0.1328 0.44 − 0.0747 313.15 − 0.2128 0.34 − 0.0203
− 0.0516 − 0.1129 − 0.2026
0.29 0.46 0.21
0.0596 0.0586 0.0414
7.7696 7.7135 8.6530
0.13 0.41 0.32
0.5191 0.5018 0.4752
0.5064 0.4581 0.4285
0.5335 0.5005 0.4839
0.05 0.11 0.13
A21
Dimethyl carbonate (1) + acetophenone (2) 303.15 0.2730 0.64 0.3943 308.15 0.1389 0.27 0.2147 313.15 0.0855 0.45 0.0393 Dimethyl carbonate (1) + cyclopentanone 303.15 − 0.2338 0.46 308.15 − 0.3804 0.51 313.15 − 0.5183 0.57
include the Grunberg–Nissan [25], Eyring–Margules [26], Soliman– Marshall [27] and McAllister three-parameter model [28]. The Grunberg–Nissan parameter d12 was determined using the following equation ln η ¼ x1 ln η1 þ x2 ln η2 þ x1 x2 d12
ð8Þ
where d12 an interaction parameter has been interpreted as an appropriate measure of the strength of the interaction between the molecules [29,30]. Eyring–Margules equation for the binary viscosity is defined as lnðηV Þ ¼ x1 ln ðη1 V1 Þ þ x1 ln ðη2 V2 Þ þ x1 x2 ½A21 x1 þ A12 x1
ð9Þ
where A21 and A12 are the interaction parameters characterizing the binary mixture. Soliman and Marshall equation for kinematic viscosity is defined as h i 2 3 3 lnðνÞ ¼ x1 lnðν1 Þ þ x2 lnðν2 Þ þ 3x1 x2 ln ðA12 Þþ B12 x1 x2 =ðM1 =M2 Þ x1 þ x2
ð10Þ where ν is the kinematic viscosity of binary mixture and A12, B12 are the adjustable parameters determined from experimental data using a nonlinear least square fit. McAllister four-body equation is a quadratic equation having three interaction parameters. This model approaches more nearly a three dimensional treatment, and the molecular diameter is greater than 1.5. The equation of this model applied to binary mixtures is given by
The correlating ability of Eqs. (8)–(11) was tested by calculating the standard deviation σ (%) between the experimental and calculated viscosities as 0
92 11 8 2 <100 ηexpt −ηcal = 1 B C ∑ σ ð%Þ ¼ @ A ; n−k : ηexpt
3.2. Mixing rules of refractive index The refractive indices of the binary mixtures (DMC +acetophenone), (DMC + cyclopentanone), (DMC + cyclohexanone) and (DMC + 3pentanone) have been theoretically predicted in literature [31–36]. The following mixing rules have been employed in the present study. Lorentz–Lorentz [31, 32] h
þx2 4 ln ν2 −ln½x1 þ ðx2 M2 =M1 Þ þ 4x1 3 x2 ln ½f3 þ ðM2 =M1 Þg=4 4
þx2 ln ðM2 =M1 Þ
ð11Þ
where ν, ν1, ν2 are the kinematic viscosities of binary mixtures and those of the pure components 1 and 2 respectively. ν1112, ν1122 and ν2221 are the model parameters which are obtained by non-linear regression.
ð12Þ
where ‘n’ represents the number of data points in each set and ‘k’ the number of numerical coefficients in the equations. Table 4 summarizes the model parameters along with standard percentage deviations σ (%). On examination of these values, it is found that the values of σ (%) for single-parameter equation of Grunberg–Nissan are in the range 0.27 to 2.37. For the two-parameter equation of Eyring–Margules and Soliman–Marshall the σ (%) are in the range 0.21–2.31, and 0.13–0.84 respectively. For the threeparameter equation of McAllister the σ (%) are in the range 0.05– 0.57. From the analysis of our present study it is evident that the McAllister model predicts very low σ (%) values as compared to others. Therefore it can be concluded that the predicting ability of these correlating equations improves satisfactorily as the number of adjustable parameters increases.
ln ν ¼ x1 4 ln ν1 þ 4x1 3 x2 lnν1112 þ 6x1 2 x2 2 ln ν1122 þ 4x1 x2 3 ln ν2221 þ6x1 2 x2 2 ln ½f1 þ ðM2 =M1 Þg=2 þ 4x1 x2 3 ln ½f1 þ ð3 M2 =M1 Þg=4
=
σ (%)
Eyring–Margules A12
d12
i h i h i 2 2 2 2 2 2 n12 −1=n12 þ 2 ¼ n1 −1=n1 þ 2 Φ1 þ n2 −1=n2 þ 2 Φ2 ð13Þ Weiner [31, 32]
h
2
2
2
n12 −n1 =n12 þ 2 n1
2
i
h i 2 2 2 2 ¼ n2 −n1 =n2 þ 2 n1 Φ2
ð14Þ
Newton [33] 2 2 2 n12 −1 ¼ n1 −1 Φ1 þ n2 −1 Φ2
ð15Þ
176
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
Table 5 Average deviation (AD) in the refractive index from different mixing relations. Mixing rule
100 AD 303.15 K
Dimethyl carbonate (1) + acetophenone (2) Lorentz–Lorentz 0.135 Weiner 0.054 Newton 0.063 Gladstone–Dale 0.098 Eykman 0.180 Heller 0.303 Eyring and John 0.175
308.15 K
313.15 K
0.178 0.081 0.055 0.179 0.284 0.387 0.258
0.237 0.119 0.132 0.291 0.396 0.501 0.425
Dimethyl carbonate (1) + cyclopentanone (2) Lorentz–Lorentz 0.079 Weiner 0.057 Newton 0.204 Gladstone–Dale 0.175 Eykman 0.209 Heller 0.142 Eyring and John 0.161
0.065 0.048 0.177 0.148 0.176 0.117 0.134
0.042 0.033 0.135 0.107 0.123 0.077 0.092
Dimethyl carbonate (1) + cyclohexanone (2) Lorentz–Lorentz 0.009 Weiner 0.013 Newton 0.093 Gladstone–Dale 0.053 Eykman 0.051 Heller 0.037 Eyring and John 0.034
0.004 0.007 0.073 0.034 0.029 0.028 0.017
0.015 0.002 0.051 0.014 0.019 0.036 0.008
Dimethyl carbonate (1) + 3-pentanone (2) Lorentz–Lorentz 0.003 Weiner 0.002 Newton 0.006 Gladstone–Dale 0.005 Eykman 0.006 Heller 0.006 Eyring and John 0.005
0.004 0.003 0.012 0.009 0.010 0.006 0.007
0.004 0.002 0.007 0.007 0.022 0.005 0.009
A comparison of AD values reveals that all the studied mixing rules produced very low AD values for the systems (DMC + 3-pentanone) followed by (DMC + cyclohexanone), (DMC + cyclopentanone) and (DMC+acetophenone). While for the systems (DMC+cyclopentanone) and (DMC + 3-pentanone) the variation in AD values with temperature is not systematic. From the analysis of our present study, it can be concluded that the predicting ability of the various studied mixing rules is satisfactory. 4. Conclusion It is realized that these binary data will have some relevance in industries because the ester studied is an important solvent with various applications in biochemistry, pharmaceuticals, agrochemicals, hydrocarbon refinery, paint coatings and fragrances, while the ketones are important intermediate in synthesis of many organic compounds. In this paper densities, viscosities and refractive indices at (303.15, 308.15 and 313.15) K were measured over entire range of mixture composition of dimethyl carbonate with acetophenone, cyclopentanone, cyclohexanone and 3-pentanone. Out of these measured data the excess molar volume, deviation in viscosity, excess Gibb's free energies of activation of viscous flow and molar refraction have been calculated and correlated by a Redlich–Kister type polynomial equation to derive the coefficients and standard deviation. Both negative and positive deviations were observed in case of excess molar volume, V E, excess Gibb's free energies of activation of viscous flow ΔG E and molar refraction, ΔR. Whereas only negative deviations were observed for Δη. Viscosity results were also analyzed by using Grunberg–Nissan, Eyring–Margules, Soliman–Marshall and McAllister three-parameter model. Further the refractive indices of binary mixtures were correlated theoretically from pure component data by using the various empirical and semi-empirical relations. Acknowledgment
Dale–Gladstone [34] n12 −1 ¼ ðn1 −1ÞΦ1 þ ðn2 −1ÞΦ2
ð16Þ
References
Eykman [35] h
i
i h i 2 2 2 n12 −1=n12 þ 0:4 ¼ n1 −1=n1 þ 0:4 Φ1 þ n2 −1=n2 þ 0:4 Φ2
h
ð17Þ Heller [31, 32] h i 2 2 ½n12 −n1 =n1 ¼ 3=2 ðn2 =n1 Þ −1=ðn2 =n1 Þ þ 2 Φ2
ð18Þ
Eyring–John [36] 2
Financial support from the University Grants Commission, New Delhi-India through Major Research Project (No. 38-24/2009SR) to one of the authors (MVR) is gratefully acknowledged.
1=2
n12 ¼ n1 Φ1 þ 2ðn1 n2 Þ
Φ1 Φ2 þ n2 Φ2
2
ð19Þ
In all of the above relations Φ1 and Φ2 are the volume fractions, and n1, n2 are the refractive index of pure components 1 and 2 respectively. n12 is the refractive index of the binary mixture. The results of Eqs. (13)–(19) have been analyzed in terms of average deviation (AD) between the experimental and the calculated values obtained by using relation n
Average deviation ¼ ∑ jnD –nDcal j=n
ð20Þ
i¼1
where ‘n’ is the number of data points and nD is refractive index of binary mixture. The results of Eq. (20) are summarized in Table 5.
[1] J. Garcia, M.J.R. Lugo, E. Comunas, J.F. Lopez, Journal of the Chemical Society, Faraday Transactions 94 (1998) 1707. [2] A.M. Pacheco, L.C. Marshall, Energy Fuels 11 (1997) 2. [3] A. Pal, G. Dass, Journal of Chemical and Engineering Data 45 (2000) 487. [4] A. Pal, A. Kumar, Journal of Chemical and Engineering Data 43 (1998) 143. [5] A. Pal, G. Dass, A. Kumar, Journal of Chemical and Engineering Data 43 (1998) 738. [6] S. Ottani, D. Vitalini, F. Comelli, C. Castellari, Journal of Chemical and Engineering Data 49 (2004) 148. [7] A. Rodriguez, J. Canosa, J. Tojo, Journal of Chemical and Engineering Data 46 (2001) 1476. [8] A. Rodriguez, J. Canosa, A. Dominugez, J. Tojo, Fluid Phase Equilibria 216 (2004) 167. [9] E. Romano, J.L. Trenzado, E. Gonzalez, J.S. Matos, L. Segade, E. Jimenez, Fluid Phase Equilibria 211 (2003) 219. [10] A. Rodriguez, J. Canosa, A. Dominugez, J. Tojo, Journal of Chemical and Engineering Data 48 (2003) 146. [11] C. Yang, W. Xu, P. Ma, Journal of Chemical and Engineering Data 49 (2004) 1802. [12] M.A. Rivas, S.M. Pereira, N. Benerji, T.P. Iglesias, The Journal of Chemical Thermodynamics 36 (2004) 183. [13] T.M. Aminabhavi, K. Banerjee, Journal of Chemical and Engineering Data 43 (1998) 1096. [14] A. Rodriguez, J. Canosa, J. Tojo, The Journal of Chemical Thermodynamics 33 (2001) 1383. [15] J. Wisniak, G. Cortez, R.D. Peralta, R. Infante, L.E. Elizalde, T.A. Amaro, O. Garcia, H. Soto, The Journal of Chemical Thermodynamics 40 (2008) 1671. [16] A.B. Pereiro, A. Rodriguez, J. Canosa, J. Tojo, Journal of Chemical and Engineering Data 50 (2005) 481. [17] F. Comelli, R. Francesconi, Journal of Chemical and Engineering Data 39 (1994) 108. [18] M.V. Rathnam, S. Mohite, M.S.S. Kumar, Journal of Chemical and Engineering Data 55 (2010) 5946.
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177 [19] S. Glasstone, Textbook of Physical Chemistry, 2nd ed. D. van Nostrand Company, London, 1949. [20] O. Redlich, A.T. Kister, Industrial and Engineering Chemistry 40 (1948) 345. [21] T.S. Jyostna, N. Satyanarayana, Indian Journal of Chemistry 44A (2005) 1365. [22] M.A. Postigo, J.L. Zurita, M.L.G. De Soria, M. Katz, Canadian Journal of Chemistry 64 (1986) 1966. [23] W.A.L. Izonfuo, A.J. Kemeakegha, Indian Journal of Chemistry 48A (2009) 1242. [24] G. Moumouzias, K. Panopoulous, G. Ritzoulis, Journal of Chemical and Engineering Data 36 (1991) 20. [25] L. Grunberg, A.H. Nissan, Nature 164 (1949) 799. [26] S. Fang, Y.Y. Fu, Q. Wang, G.Y. Zhang, Journal of Molecular Liquids 154 (2010) 111. [27] X. Esteve, D. Boer, K.R. Patil, S.K. Chaudhari, Journal of Chemical and Engineering Data 39 (1984) 767. [28] R.A. McAllister, AICHE Journal 6 (1960) 427. [29] R.J. Fort, W.R. Moore, Transactions of the Faraday Society 62 (1966) 1112. [30] R. Ahluwalla, R.K. Wanchoo, J.L. Vashisht, Physics and Chemistry of Liquids 29 (1995) 87.
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[31] T.M. Aminabhavi, H.T.S. Phayade, R.S. Khinnavar, B. Gopalkrishna, K.C. Hansen, Journal of Chemical and Engineering Data 39 (1994) 251. [32] A.Z. Tasic, B.D. Djordjevic, D.K. Grozanic, N. Radojkovic, Journal of Chemical and Engineering Data 37 (1992) 310. [33] S. Kurtz Jr., A.L. Ward, Journal of the Franklin Institute 222 (1936) 563. [34] T.P. Dale, J.H. Gladstone, Philosophical Transactions of the Royal Society of London 148 (1858) 887. [35] C.J.F. Bottcher, Theory of Electric Polarization, Elsevier, Amsterdam, 1952. [36] H. Eyring, M.S. John, Significant Liquid Structures, Wiley, New York, 1969. [37] J. Timmermans, The Physico-Chemical Constants of Pure Organic Compounds, 2, Elsevier, New York, 1965. [38] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents, Physical Properties and Methods of Purifications, 2, Wiley-Interscience, New York, 1986. [39] M.I. Arralaguppi, C.V. Jadar, T.M. Aminabhavi, Journal of Chemical and Engineering Data 44 (1999) 435.
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Thermophysical properties of binary mixtures (dimethyl carbonate + ketones) at T = (303.15, 308.15 and 313.15) K M.V. Rathnam a,⁎, Sudhir Mohite a, M.S.S. Kumar b a b
Physical Chemistry Research Laboratory, B.N. Bandodkar College of Science; Thane, 400 601, India Zulal Bhilajirao Patil College, Deopur, Dhule, 424 002, India
a r t i c l e
i n f o
Article history: Received 29 June 2011 Received in revised form 8 August 2011 Accepted 1 September 2011 Available online 17 September 2011 Keywords: Dimethyl carbonate Ketones Binary mixture Density
a b s t r a c t The densities ρ, viscosities η, and refractive indices nD of binary mixtures of dimethyl carbonate (DMC) with acetophenone, cyclopentanone, cyclohexanone, and 3-pentanone have been measured over the entire range of composition at the temperatures 303.15, 308.15 and 313.15 K and at atmospheric pressure. The density values were used to calculate excess molar volumes VE, and other excess functions of interest such as deviations in viscosity Δη, excess Gibb's free energies of activation of viscous flow ΔG E and deviations in molar refraction ΔR. The measured viscosities were compared with those predicted using the Grunberg–Nissan, Eyring–Margules, Soliman–Marshall, and McAllister four body models. Furthermore the refractive indices data have been correlated using Lorentz–Lorentz, Weiner, Newton, Gladstone–Dale, Eykman, and Eyring– John equations and a satisfactory agreement was found for all the binary systems studied in the present work. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The investigation of binary mixtures containing linear carbonates such as dimethyl carbonate (DMC) are of interest for the group contribution models [1] due to the presence of large and complicated carbonate groups. Excess properties of binary liquid mixtures are useful in the study of intermolecular interactions, since these properties reflect the interactions in solute–solvent species. Thermophysical properties such as density ρ, viscosity η, and refractive index nD are used for the design of industrial equipments for commercial applications. DMC is a unique molecule, in many aspects it is environmentally mild new building block. DMC is a flammable and synthetic organic chemical used as an intermediate for fruit trees and vegetables. Its main benefit over other methylating reagents such as iodomethane and dimethyl sulfate is its lesser toxicity and its biodegradability. DMC is also used in many industries such as pharmaceuticals, agrochemicals, hydrocarbon refinery, paint coatings and fragrances. It is used as an oxygenate for fuel additives [2]. In view of these numerous importance of the dimethyl carbonate, it is of interest to know the molecular interactions of binary mixtures of DMC with various solvents. There have been a few studies available in literature on thermodynamic and thermophysical properties of binary liquid mixtures consisting of carbonates with ethers [3–6], alcohols [7–9], alkanes [10,11], and hydrocarbons [12–14]. Wisniak et al. [15] have measured the density of dimethyl carbonate with butyl methacrylate, alkyl
⁎ Corresponding author. E-mail address: [email protected] (M.V. Rathnam). 0167-7322/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2011.09.002
methacrylate, styrene and vinyl acetate at T=(293.15, 303.15 and 313.15)K. However there are no reports in the literature except Pereiro [16] and Comelli [17] on the molecular interactions of carbonates with ketones based on density, viscosity and refractive index. Therefore in continuation of our earlier studies [18] on the determination of excess properties, in this paper we report density, viscosity and refractive index of binary systems (DMC+acetophenone), (DMC+cyclopentanone), (DMC+cyclohexanone) and (DMC+3-pentanone) at T=(303.15, 308.15 and 313.15) K, over the entire composition range. From the experimental data the values of excess molar volume VE, deviation in viscosity Δη, excess Gibb's free energy of activation of viscous flow ΔGE and deviation in molar refraction ΔR were calculated. Further the mixture viscosities and refractive indices of these binary mixtures were calculated theoretically from the pure component data by using various empirical and semi-empirical relations and the results were compared with the experimental data.
2. Experimental 2.1. Materials Dimethyl carbonate, acetophenone (Sigma-Aldrich), cyclopentanone, cyclohexanone and 3-pentanone (all Merck) with mass fraction purities greater than 99.0% were used without further purification. The purity of these solvents was verified by measuring their density, viscosity, and refractive index. Table 1 lists these values for the pure liquids at (303.15, 308.15 and 313.15) K together with the literature values. Comparison of these results reveals that experimental values show good agreement with literature values.
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
171
Table 1 Comparison of experimental densities (ρ), viscosities (η), and refractive indices (nD) of pure components with available literature values at (303.15, 308.15 and 313.15) K. Liquid
Dimethyl carbonate
Acetophenone
Cyclopentanone
Cyclohexanone
3-Pentanone
T/K
303.15 308.15 313.15 303.15 308.15 313.15 303.15 308.15 313.15 303.15 308.15 313.15 303.15 308.15 313.15
ρ/(g·cm−3)
η/(mPa·s) Literature
Experimental
Literature
Experimental
Literature
1.0571 1.0502 1.0435 1.0199 1.0169 1.0135 0.9385 0.9339 0.9290 0.9377 0.9328 0.9282 0.8057 0.8017 0.7977
1.0565 [7] 1.0508 [4] 1.0432 [6] 1.0194 [37] 1.0172 [38] 1.0139 [38] 0.9390 [38]
0.545 0.523 0.495 1.518 1.378 1.291 0.999 0.927 0.865 1.816 1.657 1.542 0.429 0.397 0.388
0.548 0.520 0.494 1.511
1.3647 1.3624 1.3600 1.5294 1.5270 1.5250 1.4335 1.4310 1.4290 1.4465 1.4440 1.4420 1.3879 1.3857 1.3835
1.3648 [13] 1.3628 [13] 1.3593 [7] 1.5297 [38]
0.9376 [38]
0.8054 [38]
2.2. Apparatus and procedures The binary solutions were prepared by mass in airtight glass bottles. Mass measurements accurate to ±0.01 mg were made on a digital electronic balance (Mettler, AE 240 Switzerland). To prevent the samples from undergoing preferential evaporation, the mixtures were prepared by transferring aliquots via syringe into the stoppered bottles. A set of nine compositions of mole fraction varying from 0.1 to 0.9 in steps of 0.1 was prepared. The mixtures were completely miscible over the whole composition range. The possible uncertainty in the mole fraction was estimated to be less than ±1 × 10 −4. The densities of the pure and their binary mixtures were determined with a portable density meter (DMA 35 Anton Paar). The instrument was calibrated frequently before the start of the actual experiments using deionized water and dry air according to the established standard procedures. The instrument has a temperature sensor which measures the sample temperature right at the measuring cell. The density of all the binary mixtures was measured after achieving thermal equilibrium with successive increments of 5 K for a temperature range from 303.15 to 313.15 K. All measurements for each sample were made in triplicate, the average values are reported and considered for further analysis. The reproducibility of the density measurements was ±0.0005 g·cm −3 and the experimental uncertainty in the density measurements was approximately ±4 × 10 −4. The viscosities of pure liquids and their mixtures were determined at atmospheric pressure and at temperatures 303.15, 308.15 and 313.15 K by using an Ubbelohode viscometer. The viscometer bulb has a capacity of about 15 ml and the capillary tube with a length of about 90 mm and 0.5 mm internal diameter. The viscometer thoroughly cleaned and perfectly dried, is filled with the sample liquid by fitting the viscometer to about 30° from the vertical and its limbs are closed with Teflon caps to avoid the evaporation. The viscometer is kept in a transparent walled bath with a thermal stability of ±0.01 K for about 20 min to obtain thermal equilibrium. An electronic digital stopwatch with an uncertainty of ±0.01 s was used for flow time measurements. At least three repetitions of each mixture reproducible to ±0.05 s were obtained, and the results were averaged. The viscosity was calculated from measured efflux time ‘t’, using the following relation η ¼ ρðAt–B=tÞ
nD
Experimental
ð1Þ
where ρ is the density and A and B are the characteristic constants of the viscometer, which were determined by taking water and benzene as the calibrating liquids. The uncertainty in viscosity thus estimated was found to be± 0.007 mPa·s. Refractive indices were measured using a refractometer (RM40, Mettler Toledo, Switzerland) with an uncertainty of ±0.0001. The
[9] [4] [10] [38]
0.995 [38]
1.810 [38] 1.635 [39] 0.424 [38] 0.380 [38]
1.4463 [39] 1.4439 [39] 1.3878 [38]
instrument has built-in solid state thermostat within temperature range (5 to 100 °C) with an uncertainty of ±0.1 °C. The instrument calibration was carried out with doubly distilled water. An average of three measurements was taken for each sample. 3. Results and discussion: The experimental results of densities ρ, viscosities η, and refractive indices nD for binary mixtures at 303.15, 308.15 and 313.15 K are listed in Table 2. The excess molar volumes VE of the binary mixtures were calculated from the densities of the pure liquids and their mixtures using the equation E
V ¼ ðx1 M1 þ x2 M2 Þ=ρ–ðx1 M1 =ρ1 þ x2 M2 =ρ2 Þ
ð2Þ
where ρ is the density of the mixture and (x1, M1 and ρ1) and (x2, M2 and ρ2) are the mole fraction, molar mass, and density of pure components 1 and 2 respectively. The calculated results of V E for binary liquid mixtures are listed in Table 2. From the results of viscosities the deviations in the viscosity, Δη were calculated using the relation Δη ¼ η–ðx1 η1 þ x2 η2 Þ
ð3Þ
where η is the absolute viscosity of the mixture, and η1 and η2 are the viscosities of the pure components. The excess Gibb's free energies of activation ΔG E for viscous flow have been calculated using the relation E
ΔG ¼ RT ½lnðηV Þ–ðx1 lnðη1 V1 Þ þ x2 lnðη2 V2 ÞÞ
ð4Þ
where η1, V1, η and V denote the viscosity and molar volume of the pure components and their mixtures respectively. The refractive index values in Table 2 have been used to calculate the Lorentz–Lorentz molar refraction [19] and deviation in the molar refraction ΔR have been calculated using the equation ΔR ¼ Rm –ðx1 R1 þ x2 R2 Þ
ð5Þ
where Rm is the molar refractivity of mixtures, R1 and R2 are the molar refractivities of pure components 1 and 2 respectively. The results of V E, Δη, ΔG E and ΔR have been fitted to the Redlich– Kister [20] polynomial equation n
i
Δy ¼ x1 ð1−x1 Þ ∑ Ai ð2x1 −1Þ i¼0
ð6Þ
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M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
Table 2 Mole fraction (x1), densities (ρ), excess volumes (VE), dynamic viscosities (η), refractive index (nD) for the binary mixtures. x1
ρ/g·cm−3
VE/cm3·mol−1
Dimethyl carbonate (1) + acetophenone (2) T = 303.15 K 0.0000 1.0199 0.0802 1.0223 − 0.022 0.1338 1.0240 − 0.040 0.2501 1.0279 − 0.082 0.3589 1.0317 − 0.111 0.4569 1.0352 − 0.122 0.5789 1.0397 − 0.119 0.6612 1.0429 − 0.113 0.7589 1.0469 − 0.102 0.8523 1.0508 − 0.076 0.9249 1.0538 − 0.038 1.0000 1.0571 Dimethyl carbonate (1) + acetophenone (2) T = 308.15 K 0.0000 1.0169 0.0802 1.0190 − 0.013 0.1338 1.0205 − 0.027 0.2501 1.0239 − 0.055 0.3589 1.0272 − 0.070 0.4569 1.0303 − 0.078 0.5789 1.0343 − 0.074 0.6612 1.0372 − 0.073 0.7589 1.0407 − 0.057 0.8523 1.0442 − 0.036 0.9249 1.0471 − 0.021 1.0000 1.0502 Dimethyl carbonate (1) + acetophenone (2) T = 313.15 K 0.0000 1.0135 0.0802 1.0154 − 0.012 0.1338 1.0167 − 0.019 0.2501 1.0197 − 0.037 0.3589 1.0226 − 0.043 0.4569 1.0254 − 0.051 0.5789 1.0290 − 0.048 0.6612 1.0316 − 0.046 0.7589 1.0348 − 0.038 0.8523 1.0380 − 0.023 0.9249 1.0406 − 0.009 1.0000 1.0435 Dimethyl carbonate (1) + cyclopentanone (2) T = 303.15 K 0.0000 0.9385 0.0656 0.9458 0.011 0.1060 0.9502 0.030 0.2015 0.9607 0.069 0.3125 0.9733 0.089 0.4129 0.9849 0.100 0.5109 0.9965 0.096 0.6233 1.0100 0.087 0.7184 1.0217 0.066 0.8257 1.0351 0.037 0.9156 1.0464 0.018 1.0000 1.0571 Dimethyl carbonate (1) + cyclopentanone (2) T = 308.15 K 0.0000 0.9339 0.0656 0.9409 0.027 0.1060 0.9452 0.047 0.2015 0.9555 0.087 0.3125 0.9679 0.104 0.4129 0.9793 0.112 0.5109 0.9906 0.115 0.6233 1.0038 0.109 0.7184 1.0153 0.085 0.8257 1.0285 0.050 0.9156 1.0396 0.028 1.0000 1.0502
η/mPa·s
1.518 1.425 1.362 1.230 1.114 1.013 0.895 0.822 0.740 0.664 0.605 0.545
1.378 1.292 1.237 1.113 1.005 0.915 0.811 0.748 0.677 0.615 0.569 0.523
1.291 1.209 1.154 1.039 0.936 0.851 0.755 0.695 0.631 0.574 0.534 0.495
0.999 0.950 0.918 0.853 0.787 0.736 0.690 0.644 0.615 0.589 0.568 0.545
0.927 0.875 0.844 0.781 0.718 0.670 0.630 0.590 0.565 0.543 0.535 0.523
nD
1.5294 1.5195 1.5131 1.4986 1.4836 1.4690 1.4491 1.4346 1.4159 1.3969 1.3813 1.3647
1.5270 1.5176 1.5113 1.4969 1.4822 1.4677 1.4479 1.4333 1.4143 1.3949 1.3792 1.3624
1.5250 1.5157 1.5095 1.4959 1.4816 1.4670 1.4472 1.4325 1.4133 1.3937 1.3775 1.3600
1.4335 1.4286 1.4255 1.4183 1.4103 1.4032 1.3965 1.3890 1.3829 1.3760 1.3702 1.3647
1.4310 1.4262 1.4232 1.4162 1.4082 1.4012 1.3945 1.3869 1.3807 1.3738 1.3680 1.3624
Table 2 (continued) ρ/g·cm−3
VE/cm3·mol−1
η/mPa·s
nD
Dimethyl carbonate (1) + cyclopentanone (2) T = 313.15 K 0.0000 0.9290 0.0656 0.9359 0.027 0.1060 0.9401 0.051 0.2015 0.9500 0.114 0.3125 0.9620 0.150 0.4129 0.9731 0.169 0.5109 0.9843 0.164 0.6233 0.9974 0.148 0.7184 1.0088 0.116 0.8257 1.0219 0.072 0.9156 1.0330 0.034 1.0000 1.0435
0.865 0.811 0.779 0.715 0.654 0.607 0.572 0.536 0.517 0.504 0.501 0.495
1.4290 1.4243 1.4214 1.4145 1.4066 1.3996 1.3929 1.3853 1.3790 1.3718 1.3657 1.3600
Dimethyl carbonate (1) + cyclohexanone (2) T = 303.15 K 0.0000 0.9377 0.0814 0.9455 0.026 0.1180 0.9490 0.046 0.2351 0.9603 0.135 0.3356 0.9706 0.191 0.4428 0.9822 0.235 0.5480 0.9945 0.237 0.6510 1.0076 0.191 0.7489 1.0207 0.139 0.8359 1.0329 0.086 0.9556 1.0504 0.021 1.0000 1.0571
1.816 1.618 1.526 1.274 1.088 0.930 0.806 0.710 0.639 0.604 0.561 0.545
1.4465 1.4409 1.4383 1.4296 1.4219 1.4134 1.4049 1.3964 1.3880 1.3802 1.3690 1.3647
Dimethyl carbonate (1) + cyclohexanone (2) T = 308.15 K 0.0000 0.9328 0.0814 0.9404 0.034 0.1180 0.9438 0.059 0.2351 0.9549 0.150 0.3356 0.9650 0.209 0.4428 0.9765 0.243 0.5480 0.9886 0.244 0.6510 1.0014 0.206 0.7489 1.0144 0.142 0.8359 1.0264 0.088 0.9556 1.0437 0.014 1.0000 1.0502
1.657 1.474 1.393 1.162 1.008 0.862 0.749 0.664 0.602 0.571 0.536 0.523
1.4440 1.4385 1.4359 1.4273 1.4197 1.4113 1.4028 1.3942 1.3858 1.3780 1.3668 1.3624
Dimethyl carbonate (1)+cyclohexanone (2) T = 313.15 K 0.0000 0.9282 0.0814 0.9357 0.031 0.1180 0.9390 0.061 0.2351 0.9498 0.163 0.3356 0.9597 0.224 0.4428 0.9710 0.257 0.5480 0.9829 0.257 0.6510 0.9953 0.234 0.7489 1.0081 0.166 0.8359 1.0200 0.101 0.9556 1.0371 0.016 1.0000 1.0435
1.542 1.368 1.290 1.077 0.934 0.803 0.701 0.622 0.565 0.533 0.505 0.495
1.4420 1.4365 1.4339 1.4254 1.4179 1.4095 1.4010 1.3922 1.3837 1.3759 1.3645 1.3600
Dimethyl carbonate (1) + 3-pentanone (2) T = 303.15 K 0.0000 0.8057 0.0755 0.8207 0.047 0.1241 0.8304 0.102 0.2256 0.8515 0.189 0.3342 0.8753 0.256 0.4356 0.8989 0.277 0.5579 0.9290 0.283 0.6435 0.9513 0.266 0.7501 0.9807 0.212 0.8419 1.0075 0.147 0.9425 1.0385 0.061 1.0000 1.0571
0.429 0.435 0.439 0.447 0.456 0.466 0.480 0.491 0.506 0.520 0.536 0.545
1.3879 1.3865 1.3855 1.3835 1.3813 1.3791 1.3763 1.3742 1.3714 1.3690 1.3663 1.3647
x1
(continued on next page)
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177 Table 2 (continued) ρ/g·cm−3
VE/cm3·mol−1
Table 3 Derived parameters of Eq. (6) for various functions and standard deviation of the binary mixtures at (303.15, 308.15 and 313.15) K.
η/mPa·s
nD
Dimethyl carbonate (1) + 3-pentanone (2) T = 308.15 K 0.0000 0.8017 0.0755 0.8163 0.079 0.1241 0.8258 0.146 0.2256 0.8466 0.241 0.3342 0.8702 0.299 0.4356 0.8935 0.323 0.5579 0.9233 0.322 0.6435 0.9454 0.297 0.7501 0.9744 0.247 0.8419 1.0007 0.194 0.9425 1.0317 0.072 1.0000 1.0502
0.397 0.404 0.407 0.413 0.421 0.431 0.446 0.460 0.479 0.495 0.513 0.523
1.3857 1.3842 1.3832 1.3812 1.3790 1.3768 1.3740 1.3719 1.3691 1.3666 1.3640 1.3624
Dimethyl carbonate (1) + 3-pentanone (2) T = 313.15 K 0.0000 0.7977 0.0755 0.8120 0.100 0.1241 0.8213 0.181 0.2256 0.8417 0.298 0.3342 0.8647 0.395 0.4356 0.8876 0.432 0.5579 0.9170 0.434 0.6435 0.9390 0.390 0.7501 0.9680 0.303 0.8419 0.9944 0.212 0.9425 1.0251 0.083 1.0000 1.0435
0.388 0.391 0.392 0.396 0.401 0.408 0.421 0.432 0.448 0.465 0.484 0.495
1.3835 1.3820 1.3810 1.3790 1.3767 1.3745 1.3717 1.3697 1.3670 1.3645 1.3618 1.3600
x1
A2
A3
σ
Dimethyl carbonate (1) + acetophenone (2) 303.15 − 0.4946 − 0.0425 VE 308.15 − 0.3173 − 0.0055 313.15 − 0.2036 − 0.0239 Δη 303.15 − 0.2450 0.0066 308.15 − 0.2945 − 0.0098 313.15 − 0.3080 − 0.0178 ΔR 303.15 0.7854 − 0.0022 308.15 1.1005 0.0689 313.15 1.4975 − 0.0109 E ΔG 303.15 768.2434 133.5301 308.15 453.2249 − 45.1722 313.15 337.3072 − 126.0409
0.0425 0.09447 0.0528 0.0659 0.0735 0.0474 − 0.5204 − 0.5639 − 0.6298 237.5263 174.8317 87.6031
− 0.2183 − 0.0762 0.0408 0.0186 − 0.0183 − 0.0278 0.1195 − 0.1486 0.3623 153.8004 21.4384 − 33.3652
0.004 0.002 0.002 0.001 0.001 0.000 0.008 0.003 0.007 2.176 1.395 1.306
Dimethyl carbonate (1) + cyclopentanone (2) 303.15 0.4011 − 0.1411 VE 308.15 0.4670 − 0.0730 313.15 0.6774 − 0.1935 Δη 303.15 − 0.3143 0.0322 308.15 − 0.3690 0.0247 313.15 − 0.4247 0.0312 ΔR 303.15 − 0.3402 0.0826 308.15 − 0.2547 0.0293 313.15 − 0.0815 0.0422 E ΔG 303.15 − 614.3243 − 142.1283 308.15 − 981.9006 − 254.6284 313.15 − 1347.9801 − 318.8614
− 0.1884 − 0.0659 − 0.2497 0.0566 − 0.0028 0.0034 0.0848 0.1172 0.0390 264.5217 54.5684 136.4593
0.1504 − 0.0542 0.2136 0.0823 0.0647 0.0951 − 0.0005 0.0172 − 0.0245 394.6361 301.6100 469.9623
0.004 0.004 0.005 0.002 0.002 0.001 0.001 0.002 0.002 5.750 6.959 6.338
Dimethyl carbonate VE 303.15 308.15 313.15 Δη 303.15 308.15 313.15 ΔR 303.15 308.15 313.15 E ΔG 303.15 308.15 313.15
(1) + cyclohexanone (2) 0.9407 − 0.0846 0.9947 − 0.1003 1.0718 − 0.0361 − 1.2966 0.1826 − 1.1767 0.1391 − 1.1007 0.1748 0.1580 0.0022 0.2278 − 0.0308 0.3268 − 0.0534 − 1437.6098 − 900.8069 − 1530.6604 − 955.7912 − 1604.8611 − 852.4626
− 0.7659 − 0.7577 − 0.7622 0.1610 0.0971 0.0089 − 0.0363 − 0.0430 − 0.0948 405.3065 286.8745 57.0811
0.2605 0.1258 0.1177 − 0.0227 0.0678 0.0030 − 0.0176 0.0160 0.1379 429.7768 572.0501 300.8771
0.004 0.003 0.007 0.004 0.004 0.003 0.001 0.001 0.002 12.150 11.736 10.271
Dimethyl carbonate (1) + 3-pentanone (2) VE 303.15 1.1612 − 0.0382 308.15 1.3127 − 0.1101 313.15 1.7624 − 0.1494 Δη 303.15 − 0.0573 − 0.0052 308.15 − 0.0852 0.0074 313.15 − 0.1102 − 0.0077 ΔR 303.15 0.2826 − 0.0376 308.15 0.3102 − 0.0472 313.15 0.4115 − 0.0049 ΔGE 303.15 − 133.5051 14.6382 308.15 − 289.7984 106.0174 313.15 − 481.336 34.6523
− 0.2516 0.1006 − 0.3189 0.0238 0.0536 0.0384 − 0.1338 − 0.1049 − 0.0763 121.5469 316.2936 246.8420
0.3274 0.3403 0.2150 0.0004 − 0.0176 − 0.0055 0.0656 0.0755 0.0800 − 10.3467 − 131.4989 − 57.3802
0.007 0.008 0.005 0.000 0.001 0.001 0.002 0.001 0.002 1.243 1.589 1.855
Function
where ‘i’ is the number of estimated parameters and Ai the polynomial coefficients obtained by fitting the equation to the experimental results by least-squares regression method. The standard deviations σ for VE, Δη, ΔGE and ΔR were calculated using the equation h i1=2 2 σ ðyÞ ¼ ∑ðyobs –ycal Þ =ðn−mÞ
173
ð7Þ
where ‘n’ represents the number of data points and ‘m’ is the number of coefficients. The calculated values of the polynomial coefficients along with their standard deviations σ are given in Table 3. The variation of VE with mole fraction x1, at (303.15, 308.15 and 313.15) K over the entire composition range are graphically represented in Fig. 1. A negative deviation from ideal behavior occurs for the system involving acetophenone, whereas DMC + cyclopentanone, DMC + cyclohexanone and DMC + 3-pentanone exhibit positive deviation. As previously reported [21–23] several effects may contribute to the values of V E. The positive V E may be due to the breaking of molecular order on mixing and the difference in molecular size between two mixing solvents, while the negative contribution of VE may be due to packing of larger sized molecules leading to interstitial void space that can be filled by smaller molecules. The molar volumes of DMC, acetophenone, cyclopentanone, cyclohexanone and 3-pentanone are 85.214, 117.806, 89.632, 104.671 and 106.901 cm3·mol−1 respectively at 303.15 K. The deviations in viscosity Δη, (Fig. 2) are negative for all the four binary systems (DMC + acetophenone, cyclopentanone, cyclohexanone and 3-pentanone) under study over the whole composition range at each investigated temperature. The negative Δη values are indicative of weak or strong dipole interactions [22–24] within the mixtures. This suggests that in these binary mixtures the forces between pairs of unlike molecules are less than the forces between like molecules. The isotherms are symmetric at x1 ≈ 0.5. The negative values of Δη for cyclohexanone with DMC decrease with increase in temperature while for systems acetophenone, cyclopentanone and 3-pentanone these values increase with increase in temperature. The values of Δη are less negative for DMC + cyclohexanone. The
T/K
A0
A1
negative Δη values of dimethyl carbonate and ketones follow the order
cyclohexanone N cyclopentanone N acetophenone N 3 pentanone: The values of ΔGE, calculated using Eq. (4) are positive for binary mixtures of DMC+ acetophenone and for the remaining systems DMC + cyclopentanone, DMC+ cyclohexanone, and DMC+ 3-pentanone the ΔGE is negative over the entire range of composition. Fig. 3 shows the variation of ΔGE values as a function of mole fraction. The positive ΔGE values indicate specific interactions while negative values indicate the dominance of dispersion forces. Like Δη, the ΔGE values at x1 ≈0.5 indicate that there is an effect of temperature on ΔGE. It is observed that for the binary mixtures of dimethyl carbonate+ acetophenone the positive values of ΔGE decrease with increase in temperature, while for the
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M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
0.5
300
0.4
200 100
GE / J.mol -1
VE / cm3.mol -1
0.3
0.2
0.1
0 -100 -200
0 -300 -0.1
-400
-0.2 0
0.2
0.4
0.6
0.8
-500
1
x1
0
0.2
0.4
0.6
0.8
1
x1
Fig. 1. Excess volume, VE as a function of dimethyl carbonate mole fraction, x1 (Dimethyl Carbonate+ acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Dimethyl Carbonate + cyclopentanone): ( ), at 303.15 K; ( ), at 308.15 K; ( ), at 313.15 K. (Dimethyl Carbonate + cyclohexanone): (○), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Dimethyl Carbonate + 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.
Fig. 3. Excess Gibb's energy, ΔGE as a function of dimethyl carbonate mole fraction, x1 (Dimethyl Carbonate+ acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Dimethyl Carbonate+ cyclopentanone): ( ), at 303.15 K; ( ), at 308.15 K; ( ), at 313.15 K. (Dimethyl Carbonate + cyclohexanone): (O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Dimethyl Carbonate + 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.
remaining studied mixtures negative values of ΔGE increase with increase in temperature. The variations of ΔR versus mole fraction of dimethyl carbonate for all binary mixtures are graphically represented in Fig. 4. It is observed that the ΔR values are positive for the binary mixtures of DMC + acetophenone, DMC + cyclohexanone and DMC + 3-pentanone. Whereas for DMC + cyclopentanone the ΔR values are negative over the entire composition range. The magnitude of positive values increases and that of negative values diminishes with the rise in
temperature. A comparison of the values of η and nD (Table 2) shows that there is a systematic decrease in η and nD with a rise in temperature for all the mixtures. At any particular temperature as mole fraction of DMC increases the η and nD decrease. 3.1. Viscosity models In this report we have used some of the semi-empirical equations to correlate the experimental viscosity data. The evaluated equations
0
0.4 0.35
-0.05
0.3 -0.1
R / cm3.mol -1
mPa.s
0.25 -0.15 -0.2 -0.25
0.2 0.15 0.1 0.05
-0.3 0 -0.35 -0.4
-0.05 0
0.2
0.4
0.6
0.8
1
x1 Fig. 2. Deviations in viscosity, Δη as a function of dimethyl carbonate mole fraction, x1 (Dimethyl Carbonate + acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Dimethyl Carbonate+ cyclopentanone): ( ), at 303.15 K; ( ), at 308.15 K; ( ), at 313.15 K. (Dimethyl Carbonate + cyclohexanone): (O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Dimethyl Carbonate + 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.
-0.1
0
0.2
0.4
0.6
0.8
1
x1 Fig. 4. Deviation in molar refraction, ΔR as a function of dimethyl carbonate mole fraction, x1 (Dimethyl Carbonate + acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Dimethyl Carbonate + cyclopentanone): ( ), at 303.15 K; ( ), at 308.15 K; ( ), at 313.15 K. (Dimethyl Carbonate + cyclohexanone): (O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Dimethyl Carbonate 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
175
Table 4 Adjustable parameters and percentage standard deviation σ (%) of several correlations for the viscosities of binary mixtures. T/K
Grunberg–Nissan
Soliman and Marshall
McAllister four-body
σ (%)
A12
B12
σ (%)
ν1112
ν1122
ν2221
σ (%)
0.2440 0.1848 0.1726
0.36 0.53 0.31
1.0579 1.1224 1.1603
− 0.6820 − 0.9614 − 1.1343
0.61 0.31 0.39
0.7492 0.6721 0.6200
0.9311 0.8429 0.7935
1.1435 1.0400 0.9703
0.13 0.05 0.05
(2) − 0.2309 − 0.4308 − 0.5690
− 0.2258 − 0.3178 − 0.4519
0.48 0.31 0.40
0.1287 0.0885 0.0735
5.2883 6.2799 6.6562
0.41 0.31 0.39
0.5947 0.5326 0.4920
0.6617 0.6174 0.5507
0.8707 0.7861 0.7210
0.34 0.33 0.41
Dimethyl carbonate (1) + cyclohexanone (2) 303.15 − 0.5769 2.37 − 0.8343 308.15 − 0.6119 2.31 − 0.9304 313.15 − 0.6392 2.15 − 0.6132
− 0.1492 − 0.1684 − 0.3210
0.91 1.29 2.31
7.0053 7.1465 7.2582
− 6.7948 − 6.9285 − 7.0767
0.84 0.75 0.48
0.5979 0.5602 0.5198
0.7878 0.7466 0.7183
1.3179 1.2011 1.0985
0.52 0.57 0.43
Dimethyl carbonate (1) + 3-pentanone (2) 303.15 − 0.0829 0.17 − 0.0329 308.15 − 0.1328 0.44 − 0.0747 313.15 − 0.2128 0.34 − 0.0203
− 0.0516 − 0.1129 − 0.2026
0.29 0.46 0.21
0.0596 0.0586 0.0414
7.7696 7.7135 8.6530
0.13 0.41 0.32
0.5191 0.5018 0.4752
0.5064 0.4581 0.4285
0.5335 0.5005 0.4839
0.05 0.11 0.13
A21
Dimethyl carbonate (1) + acetophenone (2) 303.15 0.2730 0.64 0.3943 308.15 0.1389 0.27 0.2147 313.15 0.0855 0.45 0.0393 Dimethyl carbonate (1) + cyclopentanone 303.15 − 0.2338 0.46 308.15 − 0.3804 0.51 313.15 − 0.5183 0.57
include the Grunberg–Nissan [25], Eyring–Margules [26], Soliman– Marshall [27] and McAllister three-parameter model [28]. The Grunberg–Nissan parameter d12 was determined using the following equation ln η ¼ x1 ln η1 þ x2 ln η2 þ x1 x2 d12
ð8Þ
where d12 an interaction parameter has been interpreted as an appropriate measure of the strength of the interaction between the molecules [29,30]. Eyring–Margules equation for the binary viscosity is defined as lnðηV Þ ¼ x1 ln ðη1 V1 Þ þ x1 ln ðη2 V2 Þ þ x1 x2 ½A21 x1 þ A12 x1
ð9Þ
where A21 and A12 are the interaction parameters characterizing the binary mixture. Soliman and Marshall equation for kinematic viscosity is defined as h i 2 3 3 lnðνÞ ¼ x1 lnðν1 Þ þ x2 lnðν2 Þ þ 3x1 x2 ln ðA12 Þþ B12 x1 x2 =ðM1 =M2 Þ x1 þ x2
ð10Þ where ν is the kinematic viscosity of binary mixture and A12, B12 are the adjustable parameters determined from experimental data using a nonlinear least square fit. McAllister four-body equation is a quadratic equation having three interaction parameters. This model approaches more nearly a three dimensional treatment, and the molecular diameter is greater than 1.5. The equation of this model applied to binary mixtures is given by
The correlating ability of Eqs. (8)–(11) was tested by calculating the standard deviation σ (%) between the experimental and calculated viscosities as 0
92 11 8 2 <100 ηexpt −ηcal = 1 B C ∑ σ ð%Þ ¼ @ A ; n−k : ηexpt
3.2. Mixing rules of refractive index The refractive indices of the binary mixtures (DMC +acetophenone), (DMC + cyclopentanone), (DMC + cyclohexanone) and (DMC + 3pentanone) have been theoretically predicted in literature [31–36]. The following mixing rules have been employed in the present study. Lorentz–Lorentz [31, 32] h
þx2 4 ln ν2 −ln½x1 þ ðx2 M2 =M1 Þ þ 4x1 3 x2 ln ½f3 þ ðM2 =M1 Þg=4 4
þx2 ln ðM2 =M1 Þ
ð11Þ
where ν, ν1, ν2 are the kinematic viscosities of binary mixtures and those of the pure components 1 and 2 respectively. ν1112, ν1122 and ν2221 are the model parameters which are obtained by non-linear regression.
ð12Þ
where ‘n’ represents the number of data points in each set and ‘k’ the number of numerical coefficients in the equations. Table 4 summarizes the model parameters along with standard percentage deviations σ (%). On examination of these values, it is found that the values of σ (%) for single-parameter equation of Grunberg–Nissan are in the range 0.27 to 2.37. For the two-parameter equation of Eyring–Margules and Soliman–Marshall the σ (%) are in the range 0.21–2.31, and 0.13–0.84 respectively. For the threeparameter equation of McAllister the σ (%) are in the range 0.05– 0.57. From the analysis of our present study it is evident that the McAllister model predicts very low σ (%) values as compared to others. Therefore it can be concluded that the predicting ability of these correlating equations improves satisfactorily as the number of adjustable parameters increases.
ln ν ¼ x1 4 ln ν1 þ 4x1 3 x2 lnν1112 þ 6x1 2 x2 2 ln ν1122 þ 4x1 x2 3 ln ν2221 þ6x1 2 x2 2 ln ½f1 þ ðM2 =M1 Þg=2 þ 4x1 x2 3 ln ½f1 þ ð3 M2 =M1 Þg=4
=
σ (%)
Eyring–Margules A12
d12
i h i h i 2 2 2 2 2 2 n12 −1=n12 þ 2 ¼ n1 −1=n1 þ 2 Φ1 þ n2 −1=n2 þ 2 Φ2 ð13Þ Weiner [31, 32]
h
2
2
2
n12 −n1 =n12 þ 2 n1
2
i
h i 2 2 2 2 ¼ n2 −n1 =n2 þ 2 n1 Φ2
ð14Þ
Newton [33] 2 2 2 n12 −1 ¼ n1 −1 Φ1 þ n2 −1 Φ2
ð15Þ
176
M.V. Rathnam et al. / Journal of Molecular Liquids 163 (2011) 170–177
Table 5 Average deviation (AD) in the refractive index from different mixing relations. Mixing rule
100 AD 303.15 K
Dimethyl carbonate (1) + acetophenone (2) Lorentz–Lorentz 0.135 Weiner 0.054 Newton 0.063 Gladstone–Dale 0.098 Eykman 0.180 Heller 0.303 Eyring and John 0.175
308.15 K
313.15 K
0.178 0.081 0.055 0.179 0.284 0.387 0.258
0.237 0.119 0.132 0.291 0.396 0.501 0.425
Dimethyl carbonate (1) + cyclopentanone (2) Lorentz–Lorentz 0.079 Weiner 0.057 Newton 0.204 Gladstone–Dale 0.175 Eykman 0.209 Heller 0.142 Eyring and John 0.161
0.065 0.048 0.177 0.148 0.176 0.117 0.134
0.042 0.033 0.135 0.107 0.123 0.077 0.092
Dimethyl carbonate (1) + cyclohexanone (2) Lorentz–Lorentz 0.009 Weiner 0.013 Newton 0.093 Gladstone–Dale 0.053 Eykman 0.051 Heller 0.037 Eyring and John 0.034
0.004 0.007 0.073 0.034 0.029 0.028 0.017
0.015 0.002 0.051 0.014 0.019 0.036 0.008
Dimethyl carbonate (1) + 3-pentanone (2) Lorentz–Lorentz 0.003 Weiner 0.002 Newton 0.006 Gladstone–Dale 0.005 Eykman 0.006 Heller 0.006 Eyring and John 0.005
0.004 0.003 0.012 0.009 0.010 0.006 0.007
0.004 0.002 0.007 0.007 0.022 0.005 0.009
A comparison of AD values reveals that all the studied mixing rules produced very low AD values for the systems (DMC + 3-pentanone) followed by (DMC + cyclohexanone), (DMC + cyclopentanone) and (DMC+acetophenone). While for the systems (DMC+cyclopentanone) and (DMC + 3-pentanone) the variation in AD values with temperature is not systematic. From the analysis of our present study, it can be concluded that the predicting ability of the various studied mixing rules is satisfactory. 4. Conclusion It is realized that these binary data will have some relevance in industries because the ester studied is an important solvent with various applications in biochemistry, pharmaceuticals, agrochemicals, hydrocarbon refinery, paint coatings and fragrances, while the ketones are important intermediate in synthesis of many organic compounds. In this paper densities, viscosities and refractive indices at (303.15, 308.15 and 313.15) K were measured over entire range of mixture composition of dimethyl carbonate with acetophenone, cyclopentanone, cyclohexanone and 3-pentanone. Out of these measured data the excess molar volume, deviation in viscosity, excess Gibb's free energies of activation of viscous flow and molar refraction have been calculated and correlated by a Redlich–Kister type polynomial equation to derive the coefficients and standard deviation. Both negative and positive deviations were observed in case of excess molar volume, V E, excess Gibb's free energies of activation of viscous flow ΔG E and molar refraction, ΔR. Whereas only negative deviations were observed for Δη. Viscosity results were also analyzed by using Grunberg–Nissan, Eyring–Margules, Soliman–Marshall and McAllister three-parameter model. Further the refractive indices of binary mixtures were correlated theoretically from pure component data by using the various empirical and semi-empirical relations. Acknowledgment
Dale–Gladstone [34] n12 −1 ¼ ðn1 −1ÞΦ1 þ ðn2 −1ÞΦ2
ð16Þ
References
Eykman [35] h
i
i h i 2 2 2 n12 −1=n12 þ 0:4 ¼ n1 −1=n1 þ 0:4 Φ1 þ n2 −1=n2 þ 0:4 Φ2
h
ð17Þ Heller [31, 32] h i 2 2 ½n12 −n1 =n1 ¼ 3=2 ðn2 =n1 Þ −1=ðn2 =n1 Þ þ 2 Φ2
ð18Þ
Eyring–John [36] 2
Financial support from the University Grants Commission, New Delhi-India through Major Research Project (No. 38-24/2009SR) to one of the authors (MVR) is gratefully acknowledged.
1=2
n12 ¼ n1 Φ1 þ 2ðn1 n2 Þ
Φ1 Φ2 þ n2 Φ2
2
ð19Þ
In all of the above relations Φ1 and Φ2 are the volume fractions, and n1, n2 are the refractive index of pure components 1 and 2 respectively. n12 is the refractive index of the binary mixture. The results of Eqs. (13)–(19) have been analyzed in terms of average deviation (AD) between the experimental and the calculated values obtained by using relation n
Average deviation ¼ ∑ jnD –nDcal j=n
ð20Þ
i¼1
where ‘n’ is the number of data points and nD is refractive index of binary mixture. The results of Eq. (20) are summarized in Table 5.
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