Excess properties of diethyl carbonate + ketone binary mixtures at variable temperatures: Application of PFP theory to excess volumes

Journal of Molecular Liquids 177 (2013) 229–236

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Excess properties of diethyl carbonate + ketone binary mixtures at variable temperatures: Application of PFP theory to excess volumes M.V. Rathnam a,⁎, Sudhir Mohite a, M. Nandini b a b

Physical Chemistry Research Laboratory, B.N. Bandodkar College of Science, Thane 400 601, India Department of Chemistry, Dr. P. R. Ghogrey Science College, Deopur, Dhule 424005, India

a r t i c l e

i n f o

Article history: Received 23 May 2012 Received in revised form 17 October 2012 Accepted 29 October 2012 Available online 13 November 2012 Keywords: Excess volume Viscosity Refractive index Diethyl carbonate Ketones

a b s t r a c t Measurements of densities ρ, viscosities η, and refractive indices nD have been carried out for binary mixtures of diethyl carbonate (DEC) with acetophenone, cyclopentanone, cyclohexanone, and 3-pentanone over the entire composition range at the temperatures (303.15, 308.15 and 313.15) K and at atmospheric pressure. From these experimental data, the excess volumes VE, deviation in viscosity Δη and deviation in molar refraction ΔR have been calculated. The Redlich–Kister polynomial equation has been used to estimate the binary fitting parameters and the standard errors. The Prigogine–Flory–Patterson (PFP) theory and its applicability in predicting VE at (303.15, 308.15 and 313.15) K has been tested. The experimental viscosities were analyzed on the basis of Lobe and Auslaender models. Further different mixing rules have been applied to predict the refractive index values of the studied mixtures. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The molecular interaction studies of esters of carbonic acid hold considerable interest due to their applications in industries for the synthesis of many chemicals, in pharmaceutical and in agricultural chemistry. Diethyl carbonate (DEC) is a solvent of both extraction and reaction used in many industries: pharmaceuticals, agrochemicals, and hydrocarbon refinery. It can make dyeing uniformity and increase fading against sunshine. DEC is used as paint remover in the paint industry. In the plastic process it is the solvent used as solvent of plasticizer directly. In the pharmaceutical industry it is the basic ingredient used to synthesize intermediate phenobarbital. Thus DEC has an extensive market developing prospect. Mixtures containing DEC + alcohols, and alkanes have been studied by Rodriguez et al. [1–4] for investigating density, viscosity, refractive index, and speed of sound at several temperatures. Pal et al. [5–7] have studied excess molar volumes, viscosities, and refractive indices of DEC with diethylene glycol dimethyl ether and triethylene glycol dimethyl ether. Pardo et al. [8–10] studied excess molar volumes, excess molar heat capacities and speed of sound for DEC + n-heptane, DEC + n-dodecane, or n-tetradecane and DEC + cyclohexane mixtures. Francesconi and Comelli [11] studied excess enthalpies and excess molar volumes for DEC+ n-alkanol mixtures at 298.15 K. Ottani et al. [12] studied densities, viscosities, and refractive indices of poly (ethylene glycols)+ DEC mixtures at 313.15 K. Likewise Rivas et al. [13] studied permittivity and density of DEC+ dodecane at (298.15 to ⁎ Corresponding author. Tel.: +91 8976545095; fax: +91 22 25337672. E-mail address: [email protected] (M.V. Rathnam). 0167-7322/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2012.10.038

328.15) K. Yang et al. [14] have determined density and viscosity for mixtures of DEC+ alcohols at (293.15 to 363.15) K. However there are only a few studies on binary mixtures of DEC + ketones [15–18] reported in literature. In view of the increasing importance of DEC, and the lack of extensive knowledge about its behavior with ketones, it has created in us an interest to undertake this present research. In continuation of our earlier work [19–22], in this paper we report density, viscosity, and refractive index data for the binary mixtures of DEC with acetophenone, cyclopentanone, cyclohexanone, or 3-pentanone at (303.15, 308.15 and 313.15) K over the entire composition range. From the experimental data, the excess volume, deviation in viscosity and deviation in molar refraction have been calculated. The main aim of this present investigation is to i) test the applicability of Prigogine–Flory–Patterson (PFP) theory [26–30] to the binary mixtures reported in this work, ii) study the correlating ability of the viscosity models proposed by Lobe [31], and Auslaender [32] and iii) study the predictive ability of various mixing rules of refractive indices. 2. Experimental 2.1. Materials Diethyl carbonate, acetophenone (Sigma-Aldrich), cyclopentanone, cyclohexanone and 3-pentanone (all Merck) with mass fraction purities greater than 99.0% were used. These chemicals were stored over 0.4 nm molecular sieves to reduce water content, and distilled just before use. The purity of these chemicals was ascertained by gas chromatographic analysis (GC-8610) and the analysis of purity was found to be >99.8%.

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Table 1 Mole fraction (x1), densities (ρ), excess volumes (VE), dynamic viscosities (η), refractive indices (nD) for the binary mixtures. x1

ρ/g cm−3

VE/cm3 mol−1

η/mPa s

nD

1.518 1.413 1.358 1.260 1.155 1.040 0.977 0.906 0.843 0.760 0.732 0.701

1.5294 1.5151 1.5072 1.4928 1.4766 1.4572 1.4455 1.4311 1.4169 1.3964 1.3890 1.3801

Diethyl carbonate (1) + acetophenone (2) T = 308.15 K 0.0000 1.0169 0.0972 1.0121 −0.138 0.1515 1.0092 −0.198 0.2512 1.0039 −0.285 0.3615 0.9977 −0.345 0.4921 0.9902 −0.385 0.5705 0.9855 −0.385 0.6654 0.9796 −0.343 0.7584 0.9737 −0.288 0.8932 0.9647 −0.136 0.9425 0.9614 −0.080 1.0000 0.9575

1.378 1.286 1.237 1.150 1.059 0.958 0.902 0.839 0.783 0.708 0.683 0.656

1.5270 1.5127 1.5049 1.4905 1.4743 1.4550 1.4434 1.4292 1.4151 1.3948 1.3874 1.3787

Diethyl carbonate (1) + cyclopentanone (2) T = 303.15 K 0.0000 0.9385 0.0876 0.9417 −0.030 0.1356 0.9433 −0.050 0.2458 0.9469 −0.090 0.3359 0.9497 −0.120 0.4228 0.9520 −0.134 0.5415 0.9548 −0.135 0.6475 0.9571 −0.127 0.7513 0.9590 −0.095 0.8664 0.9610 −0.055 0.9352 0.9620 −0.025 1.0000 0.9630 Diethyl carbonate (1) + cyclopentanone (2) T = 308.15 K 0.0000 0.9339 0.0876 0.9371 −0.050 0.1356 0.9389 −0.080 0.2458 0.9426 −0.151 0.3359 0.9454 −0.198 0.4228 0.9477 −0.218 0.5415 0.9504 −0.217 0.6475 0.9525 −0.200 0.7513 0.9542 −0.155 0.8664 0.9558 −0.090 0.9352 0.9567 −0.040 1.0000 0.9575

1.291 1.205 1.159 1.079 0.995 0.901 0.850 0.791 0.738 0.669 0.646 0.621

0.999 0.958 0.937 0.891 0.859 0.830 0.797 0.770 0.747 0.725 0.713 0.701

0.927 0.893 0.873 0.833 0.803 0.776 0.745 0.722 0.701 0.681 0.668 0.656

ρ/g cm−3

VE/cm3 mol−1

η/mPa s

nD

0.865 0.835 0.819 0.783 0.757 0.733 0.705 0.683 0.664 0.644 0.632 0.621

1.4290 1.4238 1.4211 1.4150 1.4102 1.4056 1.3994 1.3941 1.3890 1.3836 1.3804 1.3775

1.816 1.626 1.498 1.321 1.156 1.028 0.911 0.825 0.768 0.719 0.708 0.701

1.4465 1.4397 1.4353 1.4278 1.4207 1.4138 1.4069 1.4002 1.3945 1.3863 1.3831 1.3801

Diethyl carbonate (1) + cyclohexanone (2) T = 308.15 K 0.0000 0.9328 0.0898 0.9358 −0.050 0.1505 0.9377 −0.080 0.2556 0.9409 −0.120 0.3587 0.9439 −0.150 0.4619 0.9466 −0.169 0.5665 0.9492 −0.172 0.6701 0.9514 −0.148 0.7601 0.9531 −0.110 0.8945 0.9556 −0.045 0.9487 0.9566 −0.020 1.0000 0.9575

1.657 1.479 1.370 1.202 1.056 0.937 0.837 0.759 0.711 0.669 0.658 0.656

1.4440 1.4376 1.4334 1.4262 1.4193 1.4125 1.4057 1.3990 1.3933 1.3850 1.3817 1.3787

Diethyl carbonate (1) + cyclohexanone (2) T = 313.15 K 0.0000 0.9282 0.0898 0.9313 −0.075 0.1505 0.9334 −0.125 0.2556 0.9367 −0.195 0.3587 0.9397 −0.250 0.4619 0.9426 −0.298 0.5665 0.9450 −0.300 0.6701 0.9470 −0.255 0.7601 0.9484 −0.185 0.8945 0.9505 −0.082 0.9487 0.9513 −0.040 1.0000 0.9520

1.542 1.375 1.274 1.116 0.981 0.873 0.784 0.714 0.668 0.626 0.617 0.621

1.4420 1.4359 1.4319 1.4249 1.4182 1.4116 1.4049 1.3982 1.3923 1.3839 1.3806 1.3775

Diethyl carbonate (1) + 3-pentanone (2) T = 303.15 K 0.0000 0.8057 0.0893 0.8214 0.030 0.1498 0.8317 0.055 0.2601 0.8501 0.100 0.3555 0.8656 0.135 0.4667 0.8833 0.157 0.5689 0.8992 0.157 0.6701 0.9147 0.140 0.7565 0.9277 0.102 0.8858 0.9468 0.045 0.9501 0.9560 0.020 1.0000 0.9630

0.429 0.452 0.468 0.496 0.521 0.550 0.578 0.606 0.631 0.668 0.686 0.701

1.3879 1.3875 1.3872 1.3868 1.3864 1.3859 1.3851 1.3839 1.3828 1.3813 1.3807 1.3801

x1

Diethyl carbonate (1) + cyclopentanone (2)

Diethyl carbonate (1) + acetophenone (2) T = 303.15 K 0.0000 1.0199 0.0972 1.0153 −0.130 0.1515 1.0126 −0.190 0.2512 1.0075 −0.280 0.3615 1.0015 −0.328 0.4921 0.9943 −0.365 0.5705 0.9899 −0.364 0.6654 0.9842 −0.330 0.7584 0.9786 −0.281 0.8932 0.9699 −0.125 0.9425 0.9667 −0.075 1.0000 0.9630

Diethyl carbonate (1) + acetophenone (2) T = 313.15 K 0.0000 1.0135 0.0972 1.0085 −0.145 0.1515 1.0055 −0.205 0.2512 1.0000 −0.300 0.3615 0.9937 −0.375 0.4921 0.9858 −0.400 0.5705 0.9810 −0.400 0.6654 0.9749 −0.375 0.7584 0.9687 −0.302 0.8932 0.9594 −0.147 0.9425 0.9561 −0.093 1.0000 0.9520

Table 1 (continued)

1.5250 1.5107 1.5028 1.4884 1.4723 1.4530 1.4414 1.4274 1.4135 1.3934 1.3861 1.3775

1.4335 1.4275 1.4245 1.4178 1.4126 1.4078 1.4015 1.3962 1.3912 1.3858 1.3828 1.3801

1.4310 1.4255 1.4226 1.4162 1.4112 1.4065 1.4003 1.3950 1.3900 1.3846 1.3815 1.3787

T = 313.15 K 0.0000 0.0876 0.1356 0.2458 0.3359 0.4228 0.5415 0.6475 0.7513 0.8664 0.9352 1.0000

0.9290 0.9324 0.9343 0.9382 0.9411 0.9434 0.9460 0.9480 0.9495 0.9509 0.9515 0.9520

−0.075 −0.125 −0.225 −0.288 −0.320 −0.321 −0.295 −0.240 −0.150 −0.080

Diethyl carbonate (1) + cyclohexanone (2) T = 303.15 K 0.0000 0.0898 0.1505 0.2556 0.3587 0.4619 0.5665 0.6701 0.7601 0.8945 0.9487 1.0000

0.9377 0.9405 0.9423 0.9453 0.9482 0.9509 0.9535 0.9560 0.9580 0.9608 0.9619 0.9630

−0.020 −0.030 −0.045 −0.055 −0.061 −0.061 −0.054 −0.043 −0.019 −0.007

M.V. Rathnam et al. / Journal of Molecular Liquids 177 (2013) 229–236

From the results of viscosities the deviations in the viscosity, Δη were calculated by using the relation

Table 1 (continued) x1

ρ/g cm−3

VE/cm3 mol−1

η/mPa s

nD

  Δη ¼ η – x1 η1 þ x2 η2

Diethyl carbonate (1) + 3-pentanone (2) T = 308.15 K 0.0000 0.8017 0.0893 0.8171 0.050 0.1498 0.8272 0.100 0.2601 0.8451 0.185 0.3555 0.8602 0.250 0.4667 0.8775 0.300 0.5689 0.8933 0.299 0.6701 0.9089 0.245 0.7565 0.9220 0.175 0.8858 0.9412 0.080 0.9501 0.9505 0.030 1.0000 0.9575

0.397 0.417 0.431 0.457 0.481 0.509 0.535 0.563 0.586 0.622 0.641 0.656

1.3857 1.3856 1.3855 1.3854 1.3852 1.3847 1.3840 1.3830 1.3818 1.3802 1.3795 1.3787

Diethyl carbonate (1) + 3-pentanone (2) T = 313.15 K 0.0000 0.7977 0.0893 0.8128 0.075 0.1498 0.8226 0.145 0.2601 0.8400 0.285 0.3555 0.8547 0.385 0.4667 0.8717 0.446 0.5689 0.8873 0.445 0.6701 0.9028 0.390 0.7565 0.9160 0.300 0.8858 0.9353 0.150 0.9501 0.9448 0.065 1.0000 0.9520

0.388 0.405 0.417 0.439 0.459 0.484 0.508 0.532 0.554 0.589 0.607 0.621

1.3835 1.3836 1.3835 1.3834 1.3832 1.3829 1.3822 1.3814 1.3804 1.3790 1.3784 1.3775

2.2. Apparatus and procedures The binary solutions were prepared by mass in airtight glass bottles. To prevent the samples from undergoing preferential evaporation, the mixtures were prepared by transferring aliquots via syringe into the stoppered bottles and weighed on a digital electronic balance (Mettler, AE 240 Switzerland). The uncertainty in the mole fraction was estimated to be less than ±1 × 10−4. The densities of the pure liquids and their binary mixtures were measured by using a DMA 35 Anton Paar digital density meter with an uncertainty of ±0.1%. Viscosities were determined by using an Ubbelhode viscometer. The average uncertainty in dynamic viscosity was established to be better than ± 0.7% and it has been obtained by using the following relation h i Uncertainty ¼ jη exp –ηlit j=η exp  100 Refractive indices were measured by using a refractometer (RM40, Metteler Toledo, Switzerland) with an uncertainty of ±0.0001. All the instrument calibrations and the detailed procedure for measurements have been described earlier [20]. 3. Results and discussion The experimental densities ρ, excess volumes V E, viscosities η, refractive indices nD of the studied binary mixtures as a function of the mole fraction of diethyl carbonate at (303.15, 308.15 and 313.15) K are given in Table 1. The excess volumes V E have been evaluated from the density data by using the relation E

V ¼ ðx1 M1 þ x2 M 2 Þ=ρ−ðx1 M1 =ρ1 þ x2 M 2 =ρ2 Þ

231

ð1Þ

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.

ð2Þ

where η is the dynamic viscosity of the mixture and η1 and η2 are the viscosities of the pure components respectively. The computed data of Δη for the binary mixtures are graphically represented in Fig. 2. The refractive index values were used to calculate the Lorentz– Lorentz molar refraction [33] and deviation in the molar refraction ΔR have been calculated by using the equation ΔR ¼ Rm –ðx1 R1 þ x2 R2 Þ

ð3Þ

where R1 and R2 are the molar refractivities of pure components 1 and 2 respectively, Rm is the molar refractivity of the mixture obtained by the relation Rm ¼

h . i. 2 2 nD −1 nD þ 2 ½ðx1 M1 þ x2 M2 Þ=ρ

ð4Þ

All the quantities (V E, Δη and ΔR) were fitted to the Redlich–Kister [34] polynomial equation by the method of least squares to derive the binary coefficients n X Δy ¼ x1 ð1−x1 Þ

i

Ai ð2x1 −1Þ

ð5Þ

i¼0

where ‘i’ is the number of estimated parameters and Ai the polynomial coefficients. The variation in standard deviations (σ) was calculated by using the relation h i1=2 2 σ ðyÞ ¼ ∑ðyobs –ycal Þ =ðn−mÞ

ð6Þ

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 2. Fig. 1 shows plots of excess volumes VE as a function of diethyl carbonate mole fraction x1. It is observed that the excess volumes are positive for mixtures diethyl carbonate+3-pentanone, while for the remaining mixtures the VE is negative over the entire range of composition at all temperatures. The variation of VE with temperature is very systematic. The magnitude of VE is found to increase with an increase in temperature. The maxima or minima of isotherms in each binary system is found to occur at x1 =0.5, indicating the formation of 1:1 complexes in all the systems. The deviations in viscosity Δη for all the studied systems (Fig. 2) are negative over the whole composition range. Further it was observed that there is a significant change in magnitude of Δη values as temperature is increased. For the systems diethyl carbonate+ acetophenone, + cyclopentanone, + cyclohexanone the negative Δη values decrease with an increase in temperature. While for diethyl carbonate + 3-pentanone the negative Δη values increase with an increase in temperature. The values of Δη for diethyl carbonate + cyclohexanone are large while for diethyl carbonate + 3-pentanone are small and further follow the order Cyclohexanone > acetophenone > cyclopentanone > 3‐pentanone: The negative values of Δη in our present study may be due to the presence of dispersive interactions of electron donor–acceptor type [23–25]. A comparison of our present study of density and viscosity in terms of VE and Δη relative to the Redlich–Kister polynomial equation for diethyl carbonate+acetophenone with those reported by Iloukhnai and Rostami [17,18] has been made graphically in Figs. 3 and 4 respectively.

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0.5

Table 2 Derived parameters of Eq. (5) for various functions and standard deviations of the binary mixtures at (303.15, 308.15 and 313.15) K.

0.4

A3

σ

0.3

0.0157 0.0350 0.0059 0.0244 0.0060 −0.0080 −0.1829 −0.1485 −0.1138

0.3406 0.3114 0.1859 0.0326 0.0109 0.0052 0.3037 0.1914 0.1964

0.007 0.004 0.006 0.001 0.001 0.000 0.004 0.004 0.002

0.2

Diethyl carbonate (1) + cyclopentanone (2) VE 303.15 −0.5566 −0.0128 308.15 −0.8991 0.0332 313.15 −1.3107 0.0414 Δη 303.15 −0.1700 0.0373 308.15 −0.1437 0.0311 313.15 −0.1145 0.0232 ΔR 303.15 0.1600 0.0062 308.15 0.2191 −0.0046 313.15 0.2719 −0.0547

0.2099 0.3171 0.2493 0.0139 0.0457 0.0279 −0.0692 0.0184 −0.0101

−0.0355 −0.1507 −0.3878 −0.0090 −0.0094 −0.0098 −0.0240 −0.0363 0.0100

0.002 0.003 0.002 0.001 0.001 0.000 0.002 0.001 0.001

Diethyl carbonate (1) + cyclohexanone (2) VE 303.15 −0.2471 −0.0216 308.15 −0.6866 −0.0542 313.15 −1.1872 −0.1126 Δη 303.15 −1.1106 0.0099 308.15 −1.0369 0.0311 313.15 −0.9736 0.0866 ΔR 303.15 0.1734 −0.0016 308.15 0.2249 −0.0226 313.15 0.2755 −0.0003

0.0472 0.2322 0.5080 0.0112 0.0087 −0.0396 −0.0958 −0.0478 −0.0394

0.0830 0.2363 0.2615 0.0685 0.0253 −0.1141 0.0277 0.0335 −0.0452

0.001 0.002 0.007 0.004 0.001 0.002 0.001 0.001 0.002

Diethyl carbonate (1) + 3-pentanone VE 303.15 0.6382 308.15 1.1967 313.15 1.8065 Δη 303.15 −0.0240 308.15 −0.0358 313.15 −0.0534 ΔR 303.15 0.6119 308.15 0.9137 313.15 1.0084

−0.3654 −0.8311 −0.9651 0.0120 −0.0053 0.0066 −0.4255 −0.4462 −0.3040

−0.30625 −0.0016 0.2648 −0.0056 0.0012 0.0061 −0.0433 0.0451 0.1429

0.002 0.007 0.003 0.000 0.000 0.000 0.006 0.007 0.008

Function

T/K

A0

A1

(2) 0.0748 0.0477 0.1387 −0.0007 −0.0016 −0.0042 0.0469 0.0528 0.0836

VE/ cm3 .mol-1

A2

Diethyl carbonate (1) + acetophenone (2) 303.15 −1.4688 −0.1291 VE 308.15 −1.5391 −0.1265 313.15 −1.6268 −0.1038 Δη 303.15 −0.3020 −0.0256 308.15 −0.2584 −0.0155 313.15 −0.2384 −0.0134 ΔR 303.15 0.7981 −0.0203 308.15 0.7360 0.0117 313.15 0.6352 0.0062

0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5

0

0.2

0.4

0.6

0.8

1

x1 Fig. 1. Excess volume, VE as a function of diethyl carbonate mole fraction, x1(diethyl carbonate+acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Diethyl carbonate+cyclopentanone): (X), at 303.15 K; (✴), at 308.15 K;(__), at 313.15 K. (Diethyl carbonate+cyclohexanone):(O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Diethyl carbonate+3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.

The plots of ΔR with mole fraction x1 of diethyl carbonate are shown in Fig. 5. It is observed that the values of ΔR are positive for all the systems at (303.15, 308.15 and 313.15) K, over the entire range of composition. It is further observed that the variation of ΔR with temperature is not systematic. For mixtures of acetophenone the values of ΔR decrease with an increase in temperature, while for the remaining studied mixtures the ΔR values increase with an increase in temperature. However all the plots are parabolic in shape with well defined maxima occurring at x1 = 0.5.

0

-0.05

-0.1

Δ η / mPa.s

Wherein it is observed that the values of VE and Δη in both the studies closely match with each other confirming the good agreement. It is interesting to compare with the present results of diethyl carbonate + ketones with dimethyl carbonate + ketones reported earlier [20]. The VE values of diethyl carbonate are negative for acetophenone, cyclopentanone, cyclohexanone but positive for 3-pentanone binary systems. While for dimethyl carbonate the values are positive for cyclopentanone, cyclohexanone, 3-pentanone and negative for acetophenone binary systems. The values of deviation in viscosity for diethyl carbonate and dimethyl carbonate binary systems are found to be negative. However the variation in Δη values with temperature is different. The negative Δη values of diethyl carbonate with acetophenone, cyclopentanone, and cyclohexanone decrease with an increase in temperature and for 3-pentanone the negative Δη values increase with an increase in temperature. While for dimethyl carbonate + acetophenone, cyclopentanone, and 3-pentanone the negative Δη values increase with an increase in temperature but for cyclohexanone these values decrease with an increase in temperature. Likewise the ΔR values of diethyl carbonate exhibit positive deviations for all the studied mixtures but for dimethyl carbonate these ΔR values for cyclopentanone are negative while for acetophenone, cyclohexanone and 3-pentanone these values are positive.

-0.15

-0.2

-0.25

-0.3

0

0.2

0.4

0.6

0.8

1

x1 Fig. 2. Deviation in viscosity, Δη as a function of diethyl carbonate mole fraction, x1 (diethyl carbonate+acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Diethyl carbonate+cyclopentanone): (X), at 303.15 K; (✴), at 308.15 K;(__), at 313.15 K. (Diethyl carbonate+cyclohexanone):(O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Diethyl carbonate+3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.

M.V. Rathnam et al. / Journal of Molecular Liquids 177 (2013) 229–236

233

0.3 0 -0.05

0.25

0.2

Δ R / cm3.mol -1

VE / cm3.mol -1

-0.1 -0.15 -0.2 -0.25

0.15

0.1

-0.3 0.05

-0.35 -0.4

0 -0.45

0 0

0.2

0.4

0.6

0.8

0.2

0.4

1

x1 Fig. 3. Comparison plots of excess volume, VE of (diethyl carbonate + acetophenone): (□), for present work; (O), for Iloukhani et al. at 303.15 K and (Δ), for present work; (+), for Iloukhani et al. at 313.15 K by using Redlich–Kister polynomial equation.

These observed variations in the excess properties (VE, Δη, ΔR) as dimethyl carbonate are replaced by diethyl carbonate which may be explained due to the difference in the solvent effect arising from the different steric hindrances and flexibilities of \C2H5 and –CH3 groups. Usually the association trends on mixing depend on the intermolecular force when two components come into contact and the molecular packing because of the difference in size and shape of the molecules in the component. However in the present study it is believed that the cyclic configuration of diethyl carbonate with a longer chain makes it less flexible than the linear chain of dimethyl carbonate leading to the significant changes in the excess properties.

0.6

0.8

1

x1 Fig. 5. Deviation in molar refraction, ΔR as a function of diethyl carbonate mole fraction, x1 (diethyl carbonate + acetophenone): (□), at 303.15 K; (◊), at 308.15 K; (Δ), at 313.15 K. (Diethyl carbonate + cyclopentanone): (X), at 303.15 K; (✴), at 308.15 K;( ), at 313.15 K. (Diethyl carbonate + cyclohexanone):(O), at 303.15 K; (+), at 308.15 K; (■), at 313.15 K. (Diethyl carbonate + 3-pentanone): (♦), at 303.15 K; (▲), at 308.15 K; (●), at 313.15 K.

3.1. Prigogine–Flory–Patterson theory The Prigogine–Flory–Patterson (PFP) theory [26–30] was used to correlate the V E results for the present mixtures. The PFP theory leads to the following expression for V E 

 i h  i.h V Em −1=3  ¼ v~ 1=3 –1 v~ 2=3 ψ1 θ2 χ 12 =P 1 −1 ð4=3Þv~  þ x2 V 2 h i.h   i 2 −1=3 −1=3 ð4=3Þ v~ ψ1 ψ2 −1 v~ − ðv~ 1 −v~ 2 Þ ð14=9Þ v~    .     P 1 ψ2 þ P 2 ψ1 þ ðv~ 1 −v~ 2 Þ P 1 −P 2 ψ1 ψ2

x1 V 1

ð7Þ

-0.02

In Eq. (7) the first term relates to the interactional contribution VE(int), the second term is the free volume contribution VE(fv), and the last term relates to the internal pressure contribution VE(ip). Where ψ, θ and P* are the molecular contact energy fraction, molecular surface fraction and characteristic pressure respectively are calculated by using the following relation

-0.03

    ψ1 ¼ 1−ψ2 ¼ ϕ1 P 1 = ϕ1 P 1 þ ϕ2 P 2

0

Δ η / mPa.s

-0.01

-0.04

θ2 ¼ 1−θ1 ¼ ϕ2

-0.05

i    −1=3 þ ϕ2 ϕ1 V 1 =V 2

ð9Þ

the volume fractions are defined by     ϕ1 ¼ 1−ϕ2 ¼ x1 V 1 = x1 V 1 þ x2 V 2

-0.06 -0.07 -0.08

.h

ð8Þ

ð10Þ

The v~ of the solution is approximated in Eq. (7) by

0

0.2

0.4

0.6

0.8

1

v~ ¼ ψ1 v~ 1 þ ψ2 v~ 2 :

ð11Þ

x1 Fig. 4. Comparison plots of deviations in viscosity, Δη of (diethyl carbonate+ acetophenone): (□), for present work; (O), for Iloukhani et al. at 303.15 K and (Δ), for present work; (+), for Iloukhani et al. at 313.15 K by using Redlich–Kister polynomial equation.

The thermal expansion coefficient αi is obtained from the numerical results of the density by using the equation α i ¼ −1=ρðdρ=dTÞ

ð12Þ

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M.V. Rathnam et al. / Journal of Molecular Liquids 177 (2013) 229–236

Table 3 Parameters of the pure components used in PFP theory calculations at (303.15, 308.15 and 313.15) K. Component

T/K

104 α/K−1

104 KT/MPa−1

v~

P*/J cm−3

V*/cm3 mol−1

Diethyl carbonate

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

11.42 11.49 11.55 5.81 5.83 5.85 10.83 10.89 10.95 9.45 9.49 9.54 9.93 9.98 10.03

57.7 59.6 62.1 22.4 23.0 23.6 38.6 39.8 41.0 37.9 39.0 40.1 46.3 47.7 49.3

1.2798 1.2849 1.2898 1.1574 1.1602 1.1630 1.2681 1.2729 1.2777 1.2396 1.2438 1.2481 1.2497 1.2541 1.2586

98.28 98.08 96.90 105.32 105.13 104.98 136.77 136.61 136.53 116.15 115.99 116.06 101.54 101.40 100.92

95.85 96.02 96.20 101.79 101.84 101.94 70.68 70.76 70.87 84.44 84.60 84.72 85.54 85.66 85.79

Acetophenone

Cyclopentanone

Cyclohexanone

3-Pentanone

which is used to compute the reduced volume by equation 3 v~ i ¼ ½ð1 þ ð4=3Þα i TÞ=ð1 þ α i TÞ

ð13Þ

3.2. Viscosity models

The characteristic volume is 

V i ¼ V i =v~ i

ð14Þ

and the characteristic pressure is given by 

While for the mixtures of diethyl carbonate+ acetophenone the predicted VE(PFP) values are larger and for diethyl carbonate+ 3-pentanone they are smaller in magnitude.

2

P i ¼ T v˜ i α i =ðK T Þi

ð15Þ

where KT is the isothermal compressibility for component ‘i’ in the mixtures. The contact interaction parameter χ12 required for the calculation of VE (PFP) has been obtained by fitting the VE expression to the experimental equimolar VE values for each of the systems investigated. The parameters involved in Eq. (7) for the pure components are obtained by the PFP theory and are given in Table 3. While the values of the three contributions of the PFP theory to VE and the calculated VE data at x1 = 0.5 along with experimental equimolar values of VE for each of the binary mixture at the studied temperatures are given in Table 4. A perusal of Table 4 reveals that the interactional contribution VE(int), and the free volume VE(fv) contribution are positive, while the internal pressure VE(ip) contribution values are negative for the liquid mixtures investigated. Moreover comparison between VE(expt) and VE(PFP) is made by calculating VE(PFP) values by using χ12 at equimolar composition. On the basis of the present analysis it may be concluded that PFP theory satisfactorily predicts VE values for the systems diethyl carbonate + cyclopentanone and diethyl carbonate+ cyclohexanone.

The viscosity mole fraction pairs of the studied mixtures were used to test the semi-empirical models. Lobe [31] proposed a two parameter relation involving the volume fractions of components Φ1 and Φ2 for kinematic viscosities. ν ¼ Φ1 ν1 exp½Φ2 α 12 lnðν2 =ν 1 Þ þ Φ2 ν2 exp½Φ1 α 21 lnðν2 =ν 1 Þ

ð16Þ

where ν is the kinematic viscosity, α12 and α21 are the adjustable parameters. Auslaender [32] proposed a relation involving a less complicated three-parameter equation for the dynamic viscosities η ¼ η1 x1 ðx1 þ B12 x2 Þ þ η2 ðA21 x2 ðB21 x1 þ x2 ÞÞ=x1 ðx1 þ B12 x2 Þ þ ðA21 x2 ÞðB21 x1 þ x2 Þ

ð17Þ

The values of the parameters of Eqs. (16)–(17) were evaluated from the experimental data by nonlinear least square fitting. The correlating ability of these relations was tested by calculating the percentage standard deviation σ (%) between the experimental and calculated viscosities as 0

 92 11 = 8 2 <100 η expt −ηcal = 1 B C ∑ σ ð% Þ ¼ @ A ; n−k : η exp t

ð18Þ

Table 4 Calculated values of three contributions of the PFP theory to excess volume at (303.15, 308.15 and 313.15) K. System

Diethyl carbonate (1) + acetophenone (2)

Diethyl carbonate (1) + cyclopentanone (2)

Diethyl carbonate (1) + cyclohexanone (2)

Diethyl carbonate (1) + 3-pentanone (2)

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

χ12/J cm−3

18.9578 19.1495 19.1874 −1.4417 −2.3775 −3.5828 1.4464 0.3412 −0.8647 2.6103 3.8387 5.1964

VE/cm3 mol−1 at equimolar concentration

Calculated contributions/cm3 mol−1

Experimental

PFP

Interactional VE(int)

Free volume VE(fv)

P* effect VE(ip)

−0.365 −0.385 −0.400 −0.135 −0.217 −0.321 −0.061 −0.169 −0.298 0.157 0.300 0.446

−0.418 −0.437 −0.462 −0.132 −0.213 −0.318 −0.060 −0.161 −0.273 0.144 0.266 0.411

0.00074 0.00076 0.00078 0.00096 0.00098 0.00100 0.00094 0.00096 0.00099 0.00104 0.00107 0.00111

0.01791 0.01861 0.01924 0.00017 0.00018 0.00018 0.00195 0.00205 0.00210 0.00111 0.00116 0.00120

−0.00026 −0.00027 −0.00032 −0.00001 −0.00001 −0.00001 −0.00007 −0.00007 −0.00008 −0.00001 −0.00001 −0.00001

M.V. Rathnam et al. / Journal of Molecular Liquids 177 (2013) 229–236

Table 5 Adjustable parameters and percentage standard deviation σ (%) of correlations for the viscosities of binary mixtures. T/K

Lobe α12

α21

Auslaender σ (%)

B21

σ (%)

B12

A21

0.8401 0.9146 1.2658

0.6356 0.6920 0.9454

0.9931 0.9255 0.6691

0.10 0.06 0.05

Diethyl carbonate (1) + cyclopentanone (2) 303.15 −0.5324 0.1170 0.12 0.0775 308.15 −0.4787 0.1233 0.25 0.0311 313.15 −0.7528 0.3333 0.20 0.0494

0.0523 0.0279 0.0399

10.5525 20.8114 15.5540

0.07 0.20 0.15

Diethyl carbonate (1) + cyclohexanone (2) 303.15 −1.0645 −0.2342 0.31 308.15 −1.0594 −0.2590 0.18 313.15 −1.0403 −0.2827 0.36

1.8169 1.8663 2.4018

0.9008 0.9012 1.1133

0.0473 0.0106 −0.0548

0.30 0.15 0.32

Diethyl carbonate (1) + 3-pentanone (2) 303.15 0.7131 −0.7131 0.13 308.15 2.0188 −1.8191 0.08 313.15 1.3498 −1.1457 0.06

0.0770 0.0807 0.1030

0.0775 0.0972 0.1291

14.0806 11.8071 9.6763

0.07 0.04 0.07

Diethyl carbonate (1) + acetophenone (2) 303.15 −0.6252 0.0527 0.14 308.15 −0.6547 0.0785 0.08 313.15 −0.5755 0.0506 0.05

where ‘n’ represents the number of data points in each set and ‘k’ is the number of numerical coefficients in the equations. The analysis of the results (Table 5) reveals that σ (%) values obtained by Auslaender relation are very low for most of the studied systems as compared to the Lobe model, indicating that the predicting ability of the Auslaender model for the present binary mixtures is satisfactory.

Table 6 Average deviation (AD) in the refractive index from different mixing relations. Mixing rule

100 AD 303.15 K

308.15 K

313.15 K

Diethyl carbonate (1) + acetophenone (2) Lorentz–Lorentz 0.162 Weiner 0.076 Newton 0.050 Gladstone–Dale 0.179 Eykman 0.272 Heller 0.323 Eyring and John 0.243

0.156 0.073 0.041 0.168 0.258 0.311 0.232

0.142 0.066 0.023 0.149 0.234 0.290 0.212

Diethyl carbonate (1) + cyclopentanone (2) Lorentz–Lorentz 0.043 Weiner 0.024 Newton 0.047 Gladstone–Dale 0.064 Eykman 0.087 Heller 0.080 Eyring and John 0.073

0.068 0.040 0.095 0.111 0.147 0.121 0.119

0.092 0.055 0.140 0.156 0.202 0.177 0.164

Diethyl carbonate (1) + cyclohexanone (2) Lorentz–Lorentz 0.031 Weiner 0.014 Newton 0.008 Gladstone–Dale 0.033 Eykman 0.134 Heller 0.059 Eyring and John 0.046

0.055 0.030 0.052 0.078 0.108 0.103 0.090

0.078 0.044 0.098 0.122 0.163 0.147 0.135

Diethyl carbonate (1) + 3-pentanone (2) Lorentz–Lorentz 0.058 Weiner 0.037 Newton 0.106 Gladstone–Dale 0.106 Eykman 0.134 Heller 0.106 Eyring and John 0.103

0.085 0.054 0.156 0.156 0.147 0.156 0.150

0.083 0.054 0.153 0.153 0.194 0.153 0.148

235

3.3. Mixing rules of refractive index The refractive indices of the binary mixtures have been theoretically calculated by using Lorentz–Lorentz, Weiner, Newton, Dale–Gladstone, Eykman, Heller and Eyring–John models. The equations pertaining to these models have been reported earlier [19]. The predicting ability of these models was tested by calculating and comparing the average deviation (AD) as shown in Table 6. The analysis of these results reveals that for the mixtures of cyclopentanone and cyclohexanone the AD values were found to increase with an increase in temperature, while for the mixtures of acetophenone these values decrease with an increase in temperature. However for the mixtures of 3-pentanone no systematic variation was observed for the AD values with an increase in temperature. Nevertheless it may be concluded that all the models tested, gave a satisfactory agreement with experimental values. 4. Conclusion The values of densities, viscosities and refractive indices at (303.15, 308.15 and 313.15) K have been determined over the entire composition range for the binary mixtures of diethyl carbonate with acetophenone, cyclopentanone, cyclohexanone and 3-pentanone. From the experimental data excess volume, the deviations in viscosity and in the molar refraction have been calculated. The Redlich–Kister equation has been used to estimate the binary fitting parameters and standard deviations from the regression lines are shown. Both positive and negative deviations are observed for excess volume and deviation in viscosity, while the deviations in the molar refraction values show completely positive deviations. The Prigogine–Flory– Patterson (PFP) theory applied to the excess volume data correctly predicts the sign of VE values for all the studied mixtures. The PFP theory predicts the VE values satisfactorily for the mixtures of cyclopentanone and cyclohexanone, while for acetophenone and 3-pentanone it predicts values with a large difference. The viscosity results were analyzed by using Lobe and Auslaender models. It was observed that the Auslaender model predicts the mixture viscosities with low percentage standard deviations as compared to Lobe. The refractive indices of the binary mixtures were correlated theoretically from pure component data by using the various mixing rules. It was observed that all the mixing rules predict the refractive indices reasonably well. Acknowledgment The authors are thankful to Dr (Mrs.) Madhuri K. Pejaver, Principal, B. N. Bandodkar College of Science, Thane (India), for providing the necessary facilities in the physical chemistry research laboratory. Appendix A. Supplementary data Supplementary data to this article can be found online at http:// dx.doi.org/10.1016/j.molliq.2012.10.038. References [1] A. Rodriguez, J. Canosa, J. Tojo, Journal of Chemical & Engineering Data 46 (2001) 1506–1515. [2] A. Rodriguez, J. Canosa, A. Dominguez, J. Tojo, Journal of Chemical & Engineering Data 49 (2004) 157–162. [3] A. Rodriguez, J. Canosa, A. Dominguez, J. Tojo, Journal of Chemical & Engineering Data 48 (2003) 146–151. [4] A. Rodriguez, J. Canosa, J. Tojo, Journal of Chemical Thermodynamics 35 (2003) 1321–1333. [5] A. Pal, A. Kumar, Journal of Chemical & Engineering Data 43 (1998) 143–147. [6] A. Pal, G. Dass, A. Kumar, Journal of Chemical & Engineering Data 43 (1998) 738–741. [7] A. Pal, G. Dass, Journal of Chemical & Engineering Data 45 (2000) 487–491. [8] J.M. Pardo, C.A. Tovar, C.A. Cerdeirina, E. Carballo, L. Romani, Journal of Chemical Thermodynamics 31 (1999) 787–796. [9] J.M. Pardo, C.A. Tovar, D. Gonzalez, E. Carballo, L. Romani, Journal of Chemical & Engineering Data 46 (2001) 212–216.

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