Density, Speed of Sound, and Refractive Index Measurements for the

Jun 25, 2015 - Density, speed of sound, and refractive index for the binary mixture (1,4-dioxane (1) + isobutyric acid (2)) were measured over the who...
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Density, Speed of Sound, and Refractive Index Measurements for the Binary Mixture (1, 4‑Dioxane + Isobutyric Acid) at T = (295.15, 298.15, 301.15, 304.15, 307.15, 310.15, and 313.15) K Taoufik Kouissi,*,† Adel Toumi,‡ and Moncef Bouanz†,‡ †

Unité de Recherche de Physique des Liquides et d’Optique Non Linéaire, Département de Physique, Faculté des Sciences de Tunis, Campus Universitaire, 2092 El Manar, Tunisia ‡ Laboratoire de Physique des Liquides Critiques, Département de Physique, Faculté des Sciences de Bizerte, Université de Carthage, 7021 Zarzouna, Tunisia ABSTRACT: Density, speed of sound, and refractive index for the binary mixture (1,4-dioxane (1) + isobutyric acid (2)) were measured over the whole composition range at temperatures T = (295.15, 298.15, 301.15, 304.15, 307.15, 310.15, and 313.15) K and at the atmospheric pressure. From the experimental data, excess molar volume VE, excess isentropic compressibility κES , excess speed of sound cE, excess refractive index nE, molar refraction R, and deviation in molar refraction ΔR were calculated. These results have been fitted to the Redlich−Kister polynomial equation. The excess molar volume, excess isentropic compressibility, and deviation in molar refraction were found to be negative, whereas excess speed of sound and excess refractive index were found to be positive for all temperatures. The thermodynamic properties have been discussed in terms of nature of molecular interactions between the components of the mixture.

1. INTRODUCTION 1,4-Dioxane and isobutyric acid have the same molecular formula, C4H8O2. They are important organic solvents that can be used in industrial applications. The determination and prediction of excess thermodynamic properties of liquid mixtures have a great interest for the convenient design of industrial processes like distillation and fluid phase separation.1 Moreover, they provide useful information on molecular interactions required for optimizing thermodynamic model development as well as their applications in some branches of science. Considerable progress has been made in the theoretical understanding of liquid−liquid mixtures.2−5 It is important to know the volumetric and ultrasonic properties together with the refractive index. In this work, the densities, the speed of sound, and refractive indices for the binary mixture (1,4-dioxane (1) + isobutyric acid (2)) have been measured over the entire composition range and in the temperatures range (295.15 to 313.15) K at 3 K intervals. In addition, to our knowledge, there are no other published data that are available in the literature. From these experimental data, excess molar volume, isentropic compressibility, excess isentropic compressibility, refractive index deviation, excess refractive index, molar refraction, and molar refraction deviation have been calculated over the entire composition range and at each temperature. Excess molar volume, excess isentropic compressibility, excess speed of sound, excess refractive index, and molar refraction deviation data have been correlated using the Redlich−Kister equation. The thermodynamic properties have been discussed in terms of © XXXX American Chemical Society

the nature of molecular interactions between the components of the mixture. This work is a continuation of our research group‘s studies on thermodynamic, transport, and critical properties of liquid−liquid mixtures.6−16

2. EXPERIMENTAL PROCEDURE 2.1. Chemicals. 1,4-Dioxane and isobutyric acid were obtained from Merck with mass purity >99%. All liquids were used without further purification as indicated in Table 1. The experimental values of density, speed of sound, and refractive index of pure liquids at temperature T = 298.15 K were compared with values available in the literature17−25 and are listed in Table 2, which leads to a satisfactory agreement. 2.2. Apparatus and Procedure. All mixtures of 1,4dioxane and isobutyric acid have been prepared by mixing known masses of the pure components. The mass is performed by using a digital electronic balance (Sartorius BP 221S) with a resolution of 10−4 g. The experimental uncertainty in mole fractions did not exceed ±0.0005. Some care was taken into consideration to avoid moisture and dust in the final sample, namely, baking the cells overnight under vacuum and preparing the mixtures in a dust-free area. The cell, in which the isobutyric acid and 1,4-dioxane were mixed together, was immersed in a thermally stabilized water bath with thermal Received: November 23, 2014 Accepted: June 10, 2015

A

DOI: 10.1021/je5010643 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Detailed Description of Chemical Compounds Used

Table 2. Comparison of Experimental and Literature Density (ρ), Refractive Index (n), and Speed of Sound (c) of Pure Components with Available Literature Values at T = 298.15 K and Atmospheric Pressure p = 101.32 kPaa ρ/(g·cm−3)

a

c /m·s−1

n

compd

exptl

lit.

exptl

lit.

exptl

lit.

1,4-dioxane

1.03077

1.4197

134517 1344.418 134320

0.94222

1.420317 1.418119 1.420120 1.420524 1.41994840 1.3911521 1.391323

1344.8

isobutyric acid

1.028617 1.030518 1.0246319 1.0276020 1.0279224 0.9431921 0.943122

1086

1133.421

1.3907

Standard uncertainties (u) are u(ρ) = 0.00005 g.cm−3, u(n) = 0.0001, u(c) = 0.2 m.s−1, u(T) =0.01 K and u(p) = 0.05 kPa.

regulation in the order of 10−3 K over hours. The temperature was measured by using a quartz thermometer (HP 2804 A) giving a resolution of 10−3 K and was calibrated on an absolute scale within 0.01 K. For pure liquid isobutyric acid, the gap between the measured value of the speed of sound at temperature T = 298.15 K and that found in the literature is the order of 47 m·s−1. This may be due to the measuring instrument. It is interesting to note that to our knowledge there is no other value of literature for comparison. 2.3. Measurements. Density. Densities of the pure components and their compositions were measured with an Anton-Paar oscillating U-tube densimeter (DMA 4500 model). The U-cell of the apparatus was calibrated with dry air and twice-distilled water at atmospheric pressure. The estimated uncertainties are 0.00005 g·cm−3 for the density and 0.01 K for the temperature over a wide temperature range. Speed of Sound. Speeds of sound were determined by a multifrequency ultrasonic interferometer M-81 F (Mittal Enterprises, model M-81 F, New Delhi) working at 3 MHz, which was calibrated with water, methanol, and benzene at temperature T = 298.15 K. The precision of the speed of sound measurements was estimated to be better than ±0.1 m·s−1. The estimated uncertainty is better than 0.2 m·s−1. Refractive Index. Refractive indices of the pure liquids or mixtures were measured with a thermostatic digital Abbe refractometer (Atago, 3T, Tokyo, Japan) at the wavelength of the D-line of sodium, 589.3 nm, and atmospheric pressure. The precision of the measure is estimated to ±10−4. Temperature was controlled by circulating water into the refractometer through a thermostatically controlled bath with the digital temperature control unit in order to maintain the desired temperature within ±0.01 K.

3. RESULTS AND DISCUSSION The experimental values of density ρ for the binary mixture (1,4-dioxane (1) + isobutyric acid (2)) at temperatures T = (295.15, 298.15, 301.15, 304.15, 307.15, 310.15, and 313.15) K as a function of 1,4-dioxane mole fraction x1 have been reported in Table 3. The results for the density of the mixture show that it decreases with temperature and increases with 1,4dioxane mole fraction, but the determined isentropic compressibility increases with temperature and decreases with 1,4-dioxane mole fraction. 3.1. Volumetric Properties. The excess molar volumes VE have been calculated from the experimental density values using the following relation: VE =

(x1M1 + x 2M 2) xM xM − 1 1 − 2 2 ρ ρ1 ρ2

(1)

where x1, x2; M1, M2; ρ1 and ρ2 represent the mole fractions, molecular masses, and densities of components 1 and 2, respectively, ρ is the density of the binary mixture (1,4-dioxane (1) + isobutyric acid (2)). The values of excess molar volumes VE at each temperature from (295.15 to 313.15) K are listed in Table 3. The VE values at each studied temperature obtained from eq 1, have been correlated by the following type of Redlich−Kister polynomial equation at each temperature:26 Y E = x1x 2 ∑ Ak (x1 − x 2)k k=1

(2)

where YE represents an excess or deviation property, subscripts 1 and 2 represent the pure components, k is the number of fitted parameter and Ak represents the coefficients. Adjustable parameters of Ak were evaluated by least-squares method, and the values of standard deviation σ were obtained by the flowing equation: B

DOI: 10.1021/je5010643 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Density (ρ), Excess Molar Volume (VE), Speed of Sound (c), Excess Speed of Sound (cE), Isentropic Compressibility (κS), and Excess Isentropic Compressibility (κES ) for Various 1,4-Dioxane Mole Fractions x1 of the Binary Mixture (1,4-Dioxane (1) + Isobutyric Acid (2)) at Temperatures T = (295.15, 298.15, 301.15, 304.15, 307.15, 310.15, and 313.15) K and Atmospheric Pressure p = 101.32 kPaa x1

ρ/g·cm−3

VE/(cm3·mol−1)

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.94528 0.95563 0.96546 0.97508 0.98420 0.99305 1.00152 1.00956 1.01723 1.02438 1.03086

0 −0.2357 −0.4006 −0.5272 −0.5907 −0.6147 −0.5913 −0.5181 −0.4024 −0.2335 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.94222 0.95265 0.96263 0.97212 0.98118 0.98997 0.99846 1.00650 1.01412 1.02130 1.02759

0 −0.2469 −0.4289 −0.5456 −0.6056 −0.6259 −0.6059 −0.5338 −0.4152 −0.2490 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.93916 0.94987 0.95966 0.96921 0.97818 0.98693 0.99531 1.00343 1.01108 1.01824 1.02432

0 −0.2778 −0.4446 −0.5688 −0.6225 −0.6412 −0.6131 −0.5494 −0.4337 −0.2666 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.93610 0.94687 0.95670 0.96621 0.97519 0.98397 0.99236 1.00047 1.00810 1.01519 1.02105

0 −0.2875 −0.4604 −0.5841 −0.6407 −0.6632 −0.6376 −0.5742 −0.4580 −0.2848 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000

0.93304 0.94394 0.95370 0.96319 0.97214 0.98102 0.98941 0.99753 1.00512

0 −0.3042 −0.4731 −0.5974 −0.6532 −0.6877 −0.6630 −0.6015 −0.4821

c/(m·s−1) T = 295.15 1100.20 1119.60 1140.00 1161.70 1184.50 1208.80 1234.70 1262.30 1291.80 1323.60 1357.70 T = 298.15 1086.00 1105.40 1125.90 1147.50 1170.50 1194.90 1220.80 1248.60 1278.30 1310.30 1344.80 T = 301.15 1072.10 1091.50 1111.90 1133.60 1156.60 1181.10 1207.20 1235.00 1264.90 1297.10 1331.90 T = 304.15 1058.20 1077.60 1098.00 1119.70 1142.80 1167.30 1193.40 1221.50 1251.50 1283.90 1319.00 T = 307.15 1043.40 1062.80 1083.40 1105.10 1128.30 1152.90 1179.30 1207.50 1237.90 C

cE/(m·s−1)

1010·κS /(Pa−1)

1010·κES /(Pa−1)

0 140.4949 241.6894 318.2238 375.3356 417.0557 442.6543 447.7030 421.2622 327.4653 0

8.7397 8.3480 7.9699 7.5993 7.2418 6.8916 6.5496 6.2164 5.8910 5.5722 5.2625

0 −2.5953 −4.9209 −6.8977 −8.3754 −9.2792 −9.4682 −8.7943 −7.1372 −4.2904 0

0 117.8016 208.7570 279.3945 333.7634 374.0642 399.6193 405.5811 381.2155 295.8569 0

8.9989 8.5907 8.1948 7.8122 7.4389 7.0748 6.7202 6.3729 6.0345 5.7030 5.3810

0 −2.2001 −4.2120 −5.9179 −7.2130 −8.0184 −8.2289 −7.6875 −6.2731 −3.8370 0

0 103.3727 185.9356 252.7012 304.4227 343.5928 368.3266 375.6204 353.9318 274.9503 0

9.2638 8.8367 8.4285 8.0290 7.6421 7.2634 6.8942 6.5340 6.1816 5.8372 5.5033

0 −1.9776 −3.7826 −5.3484 −6.5292 −7.2816 −7.4770 −7.0395 −5.7918 −3.5894 0

0 95.3919 173.6014 237.7226 288.2373 326.9898 351.9363 360.3312 340.6816 265.5399 0

9.5399 9.0948 8.6700 8.2551 7.8518 7.4585 7.0755 6.6990 6.3334 5.9757 5.6294

0 −1.8859 −3.6224 −5.1329 −6.2862 −7.0363 −7.2533 −6.8616 −5.6823 −3.5515 0

0 93.8659 170.9358 234.1617 284.1221 323.4818 348.9275 358.2099 339.9070

9.8446 9.3789 8.9333 8.5013 8.0802 7.6690 7.2673 6.8754 6.4925

0 −1.9417 −3.7239 −5.2730 −6.4549 −7.2571 −7.4944 −7.1119 −5.9086

K

K

K

K

K

DOI: 10.1021/je5010643 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. continued

a

x1

ρ/g·cm−3

VE/(cm3·mol−1)

0.9000 1.0000

1.01187 1.01778

−0.2806 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.92998 0.94103 0.95089 0.96024 0.96924 0.97807 0.98645 0.99454 1.00210 1.00886 1.01451

0 −0.3229 −0.5050 −0.6171 −0.6797 −0.7114 −0.6869 −0.6245 −0.5037 −0.3033 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

0.92692 0.93811 0.94793 0.95722 0.96621 0.97503 0.98345 0.99162 0.99914 1.00592 1.01124

0 −0.3416 −0.5217 −0.6314 −0.6954 −0.7272 −0.7081 −0.6542 −0.5296 −0.3315 0

c/(m·s−1) 1270.70 1306.20 T = 310.15 K 1030.80 1050.10 1070.60 1092.30 1115.40 1139.90 1166.30 1194.50 1224.90 1257.70 1293.30 T = 313.15 K 1015.20 1034.60 1055.10 1076.90 1100.20 1125.00 1151.60 1180.10 1210.90 1244.20 1280.40

cE/(m·s−1)

1010·κS /(Pa−1)

1010·κES /(Pa−1)

260.9875 0

6.1205 5.7587

−3.6018 0

0 98.6038 178.4429 242.4407 293.3085 332.7435 358.5580 368.1794 350.4529 273.3597 0

10.1199 9.6368 9.1752 8.7284 8.2929 7.8686 7.4525 7.0470 6.6510 6.2663 5.8931

0 −2.1410 −4.1081 −5.7848 −7.0836 −7.9434 −8.1984 −7.7765 −6.4690 −3.9965 0

0 108.0344 192.3067 258.4557 310.5789 350.6963 377.3253 388.2674 370.9913 295.4479 0

10.4678 9.9587 9.4762 9.0082 8.5504 8.1036 7.6673 7.2413 6.8259 6.4218 6.0319

0 −2.5024 −4.77326 −6.6919 −8.1712 −9.1347 −9.4212 −8.9539 −7.4413 −4.6610 0

Standard uncertainties (u) are u(x1) = 0.0005, u(ρ) = 0.00005 g·cm−3, u(c) = 0.2 m·s−1, u(T) = 0.01 K, and u(p) = 0.05 kPa. 2 ⎛ ⎞1/2 E E ⎜ ∑ (Yexp − Ycal )⎟ σ=⎜ ⎟ n−p ⎜ ⎟ ⎝ ⎠

due to branching of chains, geometrical mismatch of molecules, and formation of weaker solute−solvent bond than solute− solute and solvent−solvent bonds, solvent−solvent bonds.31 The studied system shows negative excess molar volumes that increase in magnitude with temperature and with minima displayed at the composition x1 = 0.5, as observed in Figure 1. This behavior is explained by the existence of chemical interaction (hydrogen bonding) between unlike molecules of mixture that makes the contraction of solution volume. 3.2. Acoustic Properties. The speed of sound c, excess speed of sound cE, isentropic compressibility κs, and excess isentropic compressibility κES for the mixture (1,4-dioxane (1) + isobutyric acid (2)) at temperatures T = (295.15, 298.15, 301.15, 304.15, 307.15, 310.15, and 313.15) K as a function of 1,4-dioxane mole fraction have been reported in Table 3. The analyses for the speed of sound of the mixture show that this parameter increases with a decrease in the temperature or with an increase of mole fraction of 1, 4-dioxane; nevertheless, the obtained isentropic compressibility increases with temperature and decreases with an increase of 1,4-dioxane mole fraction. Through, the use of the speed of sound and density data, the isentropic compressibilities (κS) have been calculated using the Laplace−Newton equation:34

(3)

where YEexp, YEcal, n and p are, respectively, the experimental, the calculated data, the number of experimental points, and number of considered parameters. Adjustable parameters of Redlich− Kister equations Ak and standard deviation σ values are presented in Table 4. In this case, the optimum number of coefficients Ak was determined from an examination of the variation of standard deviation, the best fit was obtained by using only four adjustable fitting coefficients in eq 2. For the binary mixture (1,4-dioxane (1) + isobutyric acid (2)), the obtained excess molar volume VE values are negative over the whole composition range at the studied temperatures, as depicted in Figure 1. The sign of excess molar volume VE depends upon the relative magnitude of contractive and expansive effects that arise on mixing of the components.27,28 The factors that cause contraction on mixing can be analyzed qualitatively in terms of strong specific interaction, usually a kind of chemical interaction, strong physical interaction and geometrical contributions.28,29 The physical interactions comprise mainly dispersion forces giving a positive contribution30 such as dipole−dipole or dipole−induced dipole interaction between the mixing components.31 The geometrical contribution is due to the differences in free volumes and molar volumes between the components.29 The chemical interactions contribute negatively to the excess molar volume.32,33 The factors that causes expansion of volume on mixing of the components can be explained in the terms of dissociation of one component or both of the components, steric hindrance

κS =

1 ρc 2

(4)

The values of excess isentropic compressibility κES and excess speed of sound cE have been calculated using the following relations:34−36 κSE = κS − κSid D

(5) DOI: 10.1021/je5010643 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Coefficients Ai and Standard Deviations σ, Obtained for the Binary Mixture (1,4-Dioxane (1) + Isobutyric Acid (2)) at Temperatures T = (295.15, 298.15, 301.15, 304.15, 307.15, 310.15, and 313.15) K VE(cm3·mol−1)

cE/(m·s−1)

1010·κES /(Pa−1)

nE

ΔR/(cm3·mol−1)

T/K

A0

A1

A2

A3

σ

295.15 298.15 301.15 304.15 307.15 310.15 313.15 295.15 298.15 301.15 304.15 307.15 310.15 313.15 295.15 298.15 301.15 304.15 307.15 310.15 313.15 295.15 298.15 301.15 304.15 307.15 310.15 313.15 295.15 298.15 301.15 304.15 307.15 310.15 313.15

−2.4551 −2.5071 −2.5522 −2.6363 −2.7255 −2.8149 −2.8779 1640.5956 1473.0577 1352.4609 1286.6539 1273.8091 1308.4435 1376.2851 −37.1020 −32.0687 −29.0804 −28.0903 −28.9890 −31.7151 −36.4705 0.0085 0.0080 0.0076 0.0071 0.0069 0.0064 0.0063 −0.1844 −0.2167 −0.2458 −0.2854 −0.3143 −0.3577 −0.3799

0.0295 0.0764 0.1063 0.0511 −0.1270 −0.1061 −0.1834 600.1780 592.6079 581.1639 581.3487 602.1946 596.2466 597.1285 −11.2171 −10.3009 −9.7005 −9.8729 −10.816 −11.5205 −12.8750 −0.0002 −0.0003 −0.0001 0.0001 −0.0002 −0.0012 −0.0013 −0.0200 −0.0103 0.0073 0.0060 −0.0495 −0.0909 −0.1150

−0.1963 −0.3784 −0.6429 −0.7498 −0.7705 −0.9697 −1.2244 1321.6368 1136.9428 1030.2637 987.1178 974.5676 1049.2407 1184.9375 −1.6948 −2.1105 −2.6056 −3.0094 −2.9673 −3.6932 −4.9438 −0.0022 −0.0031 −0.0037 −0.0035 −0.0039 −0.0035 −0.0044 −0.1361 −0.2210 −0.3120 −0.3285 −0.3560 −0.3802 −0.4844

−0.0428 −0.0945 −0.0711 −0.0654 0.3848 0.3568 0.3913 1036.5724 953.0811 907.3161 892.3238 838.0429 919.9724 1042.4277 −0.8612 −1.5031 −2.2607 −2.5556 −1.2505 −2.1388 −3.1644 −0.0039 −0.0033 −0.0039 −0.0042 −0.0034 −0.0009 −0.0001 −0.1872 −0.1715 −0.1967 −0.2031 −0.0632 0.0534 0.0987

0.00732 0.00743 0.01205 0.01192 0.01424 0.01071 0.01561 8.4370 7.3444 6.7161 6.4959 5.5357 6.5290 8.0556 0.0065 0.8729 0.0134 0.0202 0.0121 0.0068 0.0148 0.00002 0.00003 0.00002 0.00001 0.00002 0.00009 0.00010 0.00285 0.00432 0.00347 0.00491 0.00485 0.00514 0.00526

c E = c − c id

(6)

the superscript “id” represents ideal mixture, the values of ideal isentropic compressibility κidS and ideal speed of sound cid are calculated using the following relations:34 κSid = ϕ1κS ,1 + ϕ2κS ,2 + ⎡ ϕ V (α )2 Vmid(αpid)2 ⎤ ϕ2Vm ,2(αp ,2)2 1 m ,1 p ,1 ⎥ T⎢ + − id ⎥⎦ ⎢⎣ Cpm ,1 Cpm ,2 Cpm c id = (ρ id κSid)−1/2

(7) (8)

ρ id = ϕ1ρ1 + ϕ2ρ2

(9)

Vidm,

where the values of the ideal molar volume the ideal molar isobaric heat Cidpm, the ideal isobaric expansivity αidp and the ideal density ρid of studied mixture have been calculated respectively by the following relations:34

E

Figure 1. Curves of excess molar volume V against the mole fraction of 1,4-dioxane x1, for the binary mixture (1,4-dioxane (1) + isobutyric acid (2)) at different temperatures (■, 295.15 K; red ●, 298.15 K; blue ▲, 301.15 K; blue ▼, 304.15 K; pink ◀, 307.15 K; green ▶, 310.15 K; blue ⧫, 313.15 K). The solid lines represent the values calculated from the Redlich−Kister equation.

E

Vmid = x1Vm ,1 + x 2Vm ,2

(10)

id Cpm = x1Cpm ,1 + x 2Cpm ,2

(11) DOI: 10.1021/je5010643 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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αpid = ϕ1αp ,1 + ϕ2αp ,2

(12)

ρ id = ϕ1ρ1 + ϕ2ρ2

(13)

where ϕ1, ρ1, c1, κS,1, Vm,1, Cpm,1 , and αp,1 are, respectively, the volume fraction, the density, the speed of sound the isentropic compressibility, the molar volume, the molar isobaric heat and the isobaric expansivity of pure 1,4-dioxane, ϕ2, ρ2, c2, κS,2, Vm,2, Cp m,2, and αp,2 are the corresponding quantities of pure isobutyric acid. The values of isobaric expansivity have been calculated from the temperature dependence of the density data of pure liquids using the relation ((−1/ρ)(∂ρ/∂T)p) and the molar isobaric heat of pure 1,4-dioxane and pure isobutyric acid at studied temperatures have been estimated by interpolation from the literature data.37−39 The volume fraction was calculated from the individual pure molar volume Vi and the corresponding mole fraction xi using the following relation: xV ϕi = i i ∑ xiVi

Figure 3. Curves of excess isentropic compressibility κES against the mole fraction of 1,4-dioxane x1, for the binary mixture (1,4-dioxane (1) + isobutyric acid (2)) at different temperatures (■, 295.15 K; red ●, 298.15 K; blue ▲, 301.15 K; blue ▼, 304.15 K; pink ◀, 307.15 K; green ▶, 310.15 K; blue ⧫, 313.15 K). The solid lines represent the values calculated from the Redlich−Kister equation.

(14) E

The results of excess speed of sound c versus mole fraction x1 exhibit positive deviations over the entire composition range of 1,4-dioxane and temperature as shown in Figure 2. The positive deviation in cE indicated the presence of significant interactions between the molecule of 1,4-dioxane and isobutyric acid.

composition range are negative. As mentioned in the literature,34,35,40 the negative values of excess isentropic compressibility κES suggest the presence of the dispersion forces or weak interactions between the component molecules in the mixture. Strong molecular interactions occur through charge transfer, dipole−induced dipole, and dipole−dipole interactions, interstitial accommodation, and oriental ordering and all lead to a more compact structure, which makes κES negative.41,42 In the present studied binary system, the negative κES values may indicate clustering of isobutyric acid molecules in the presence of 1,4-dioxane. Furthermore, κES values decrease with in increase in temperature at fixed 1,4-dioxane composition. 3.3. Optic Properties. The experimental values of the refractive index n, their calculated deviation Δn, the excess refractive index values nE, for the binary mixture (1,4-dioxane (1) + isobutyric acid (2)) at temperatures T = (295.15, 298.15, 301.15, 304.15, 307.15, 310.15, and 313.15) K as a function of 1,4-dioxane composition have been reported in Table 5. The obtained refractive index of the studied binary mixture increase with the mole fraction of 1, 4-dioxane and decreases with the temperature. As mentioned in the literature, the increase of the refractive indices for the mixture of solvents is explained as the result of both energetic and structural effects in which the enhancement of London disperse forces play an important role, centered in the dissimilar molecules of the mixture.43,44 Refractive index deviation Δn of mixture has been calculated using the suggestions of Fialkov and Fernerly45,46 by means of the following equation:

Figure 2. Curves of excess speed of sound cE against the mole fraction of 1,4-dioxane x1, for the binary mixture (1,4-dioxane (1) + isobutyric acid (2)) at different temperatures (■, 295.15 K; red ●, 298.15 K; blue ▲, 301.15 K; blue ▼, 304.15 K; pink ◀, 307.15 K; green ▶, 310.15 K; blue ⧫, 313.15 K). The solid lines represent the values calculated from the Redlich−Kister equation.

At a fixed composition, the isentropic compressibility κS increases systematically with temperature. The mixture becomes more compressible due to an increase in thermal agitation.21 As shown in Table 3, at a fixed temperature, the isentropic compressibility values for the binary mixture (1,4-dioxane + isobutyric acid (2)) decrease with an increase 1,4-dioxane composition As depicted in Figure 3, for the studied binary system, the excess isentropic compressibility values over the entire

Δn = n − (ϕ1n1 + ϕ2n2)

(15)

where n is the refractive index of the mixture, n1 and n2 are, respectively, the refractive indices of 1,4-dioxane and isobutyric acid. The ideal refractive index nid, the ideal refractive index deviation Δnid of mixing and the excess refractive index nE, are respectively defined by43 F

DOI: 10.1021/je5010643 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. Refractive Index (n), Refractive Index Deviation (Δn), Excess Refractive Index (nE), Molar Refraction (R) and Molar Refraction Deviation (ΔR) for Various 1,4-Dioxane Mole Fractions x1 of the Binary Mixture (1,4-Dioxane (1) + Isobutyric acid (2)) at Temperatures T = (295.15, 298.15, 301.15, 304.15, 307.15, 310.15, and 313.15) K and Atmospheric Pressure p = 101.32 kPaa x1

n

Δn

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.3919 1.3955 1.3988 1.4021 1.4052 1.4082 1.4110 1.4137 1.4161 1.4185 1.4211

0 0.0009 0.0014 0.0019 0.0021 0.0022 0.0021 0.0018 0.0011 0.0005 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.3907 1.3942 1.3974 1.4007 1.4038 1.4068 1.4096 1.4122 1.4146 1.4171 1.4197

0 0.0008 0.0013 0.0018 0.0020 0.0021 0.0020 0.0016 0.0010 0.0005 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.3895 1.3929 1.3961 1.3993 1.4024 1.4054 1.4082 1.4107 1.4132 1.4156 1.4183

0 0.0007 0.0012 0.0016 0.0019 0.0020 0.0019 0.0014 0.0010 0.0003 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.3883 1.3916 1.3948 1.3979 1.401 1.4039 1.4067 1.4093 1.4117 1.4141 1.4168

0 0.0007 0.0012 0.0015 0.0018 0.0019 0.0018 0.0014 0.0009 0.0003 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000

1.3872 1.3904 1.3936 1.3967 1.3997 1.4026 1.4054 1.4079 1.4103

0 0.0006 0.0011 0.0015 0.0017 0.0018 0.0017 0.0013 0.0008

nE T = 295.15 K 0 0.0008 0.0013 0.0018 0.0020 0.0021 0.0020 0.0017 0.0011 0.0004 0 T = 298.15 K 0 0.0008 0.0012 0.0017 0.0019 0.0020 0.0019 0.0015 0.0009 0.0004 0 T = 301.15 K 0 0.0007 0.0011 0.0015 0.0018 0.0019 0.0018 0.0014 0.0009 0.0003 0 T = 304.15 K 0 0.0006 0.0011 0.0014 0.0017 0.0018 0.0019 0.0014 0.0008 0.0002 0 T = 307.15 K 0 0.0005 0.0010 0.0014 0.0016 0.0017 0.0016 0.0013 0.0007 G

R/(cm3·mol−1)

ΔR/(cm3·mol−1)

22.1884 22.1266 22.0630 22.0049 21.9493 21.8956 21.8415 21.7927 21.7385 21.6960 21.6770

0 −0.0143 −0.0296 −0.0383 −0.0438 −0.0465 −0.0488 −0.0452 −0.0462 −0.0350 0

22.1999 22.1312 22.0591 22.0041 21.9498 21.8973 21.8427 21.7892 21.7361 21.6975 21.6826

0 −0.0208 −0.0439 −0.0491 −0.0526 −0.0534 −0.0556 −0.0560 −0.0554 −0.0396 0

22.2116 22.1311 22.0633 22.0020 21.9497 21.8981 21.8459 21.7859 21.7368 21.6940 21.6882

0 −0.0319 −0.0502 −0.0610 −0.0620 −0.0613 −0.0605 −0.0668 −0.0615 −0.0493 0

22.2232 22.1361 22.0672 22.0018 21.9493 21.8923 21.8399 21.7848 21.7314 21.6902 21.6892

0 −0.0376 −0.0559 −0.0698 −0.0699 −0.0736 −0.0719 −0.0721 −0.0699 −0.0551 0

22.2400 22.1444 22.0770 22.0120 21.9551 21.8957 21.8432 21.7832 21.7307

0 −0.0450 −0.0608 −0.0732 −0.0766 −0.0814 −0.0787 −0.0827 −0.0785 DOI: 10.1021/je5010643 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. continued

a

x1

n

Δn

0.9000 1.0000

1.4127 1.4154

0.0003 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.3860 1.3891 1.3923 1.3953 1.3983 1.4011 1.4038 1.4063 1.4087 1.4112 1.4138

0 0.0005 0.0010 0.0014 0.0017 0.0017 0.0016 0.0012 0.0007 0.0003 0

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

1.3849 1.3879 1.3910 1.3941 1.3970 1.3998 1.4025 1.4049 1.4073 1.4098 1.4124

0 0.0004 0.0009 0.0014 0.0016 0.0016 0.0015 0.0011 0.0007 0.0003 0

nE 0.0002 0 T = 310.15 K 0 0.0007 0.0010 0.0013 0.0016 0.0016 0.0015 0.0011 0.0006 0.0002 0 T = 313.15 K 0 0.0004 0.0008 0.0013 0.0015 0.0015 0.0015 0.0010 0.0006 0.0002 0

R/(cm3·mol−1)

ΔR/(cm3·mol−1)

21.6967 21.6947

−0.0554 0

22.2517 22.1472 22.0774 22.0105 21.9527 21.889 21.8325 21.7731 21.7213 21.6917 21.6909

0 −0.0524 −0.0691 −0.0819 −0.0849 −0.0919 −0.0920 −0.0938 −0.0873 −0.0579 0

22.2686 22.1553 22.0813 22.0206 21.9578 21.8948 21.8368 21.7707 21.7199 21.6900 21.6963

0 −0.0602 −0.0800 −0.0855 −0.0920 −0.0979 −0.0978 −0.1049 −0.0964 −0.0662 0

Standard uncertainties (u) are u(x1) = 0.0005, u(n) = 0.0001, u(T) =0.01 K and u(p) = 0.05 kPa.

n id = [ϕ1(n1)2 + ϕ2(n2)2 ]1/2

(16)

Δn id = n id − (ϕ1n1 + ϕ2n2) =

ϕ1ϕ2(n1 − n2)2 ϕ1n1 + ϕ2n2 + [ϕ1(n1)2 + ϕ2(n2)2 ]1/2

n E = n − n id

(17) (18)

In view of eqs 15 and 17, eq 18 leads to the following equation:

n E = Δn − Δn id

(19)

The excess refractive index nE versus mole fraction x1 are graphically represented in Figure 4. The corresponding curve has a maximum for all temperatures in composition region 0.3