Densities and volumetric properties of (formamide + ethanol, or 1-propanol, or 1,2-ethanediol, or 1,2-propanediol) mixtures at temperatures between 293.15 K and 318.15 K

J. Chem. Thermodynamics 39 (2007) 462–473 www.elsevier.com/locate/jct

Densities and volumetric properties of (formamide + ethanol, or 1-propanol, or 1,2-ethanediol, or 1,2-propanediol) mixtures at temperatures between 293.15 K and 318.15 K Anil Kumar Nain

*

Department of Chemistry, Dyal Singh College, University of Delhi, New Delhi 110 003, India Received 20 May 2006; accepted 19 July 2006 Available online 11 August 2006

Abstract The densities of binary mixtures of formamide (FA) with ethanol, 1-propanol, 1,2-ethanediol, and 1,2-propanediol, including those of pure liquids, over the entire composition range were measured at temperatures (293.15, 298.15, 303.15, 308.15, 313.15, and 318.15) K and atmospheric pressure. From the experimental data, the excess molar volume, V Em , partial molar volumes, V m;1 and V m;2 , over the whole composition range and V m;1 and V m;2 at infinite dilution, and excess partial molar volumes, V Em;1 and V Em;2 , over the whole composition E range and V E m;1 and V m;2 at infinite dilution were calculated. The variation of these parameters with composition and temperature of the mixtures have been discussed in terms of molecular interaction in these mixtures. The observed trends in V Em values indicate the presence of specific interactions between FA and alkanol molecules. The V Em values follows the order: ethanol < 1-propanol < 1,2-ethanediol < 1,2-propanediol. It is observed that the V Em values depend upon the number of hydroxyl groups and alkyl chain length in these alkanol molecules.  2006 Elsevier Ltd. All rights reserved. Keywords: Density; Formamide; Alkanols; Excess molar volume; Partial molar volume; Molecular interactions

1. Introduction The multi-component solvent systems containing amides are interesting liquid systems for the study of molecular interactions as amides are the most common solvents used in chemical reactions and in many industrial processes. Moreover, amides are convenient model systems for the investigation of peptide and protein interactions in biological systems [1]. In previous papers [2–10] we have reported the studies on volumetric, acoustic and transport properties of binary mixtures containing amides and alkanols. The present work is focused on the study of molecular interactions in binary mixtures of formamide (FA) with ethanol, 1-propanol, 1,2-ethanediol, and 1,2-propanediol, over the entire composition range at various temperatures. FA molecules are highly polar (l = 3.37 D at 298.15 K) *

Tel.: +91 11 24365948; fax: +91 11 24365606. E-mail address: [email protected].

0021-9614/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.07.021

[11] and are strongly self-associated through extensive three-dimensional network of hydrogen bonds, through its three hydrogen bond donors (3 H-atoms) and three acceptors (two lone pairs of electrons at oxygen and one at nitrogen atom) [12,13]. Alkanol molecules are polar and self-associated through hydrogen bonding of their hydroxyl groups [13], whereas alkanediol molecules are self-associated through inter- and intra-hydrogen bonding. Since the components of these binary mixtures (FA + alkanols) have both proton-donating as well as proton-accepting abilities, significant interaction through hydrogen bonding between unlike molecules in these binary systems is expected. A survey of the literature indicates that there has been no temperature-dependent study on these systems from the point of view of their volumetric behaviour. However, Garcia et al. [14] have studied the volumetric behaviour of (FA + ethanol/1-propanol) mixtures at 298.15 K. In the present paper, we report densities, q of (FA + ethanol, or 1-propanol, or 1,2-ethanediol, or 1,2-propanediol)

A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

mixtures, including those of pure liquids at atmospheric pressure and temperatures (293.15, 298.15, 303.15, 308.15, 313.15, and 318.15) K, covering the entire composition range, expressed by the mole fraction x of FA. The experimental values of q were used to calculate the excess molar volume, V Em , partial molar volumes, V m;1 and V m;2 , over the whole composition range and V m;1 and V m;2 at infinite dilution, and excess partial molar volumes, V Em;1 and V Em;2 , over the whole composition range and E V E m;1 and V m;2 at infinite dilution. The variation of these parameters with composition and temperature of the mixtures have been discussed in terms of molecular interaction in these mixtures.

TABLE 1 Experimental values of density, q of pure liquids along with the corresponding values available in the literature at T = (293.15 to 318.15) K Liquid

T/K

q/(g Æ cm3) Experimental

Literature

FA

293.15 298.15

1.13300 1.12900

303.15 308.15 313.15 318.15

1.12500 1.12100 1.11700 1.11300

1.1330 1.12908 1.1290 1.1250 1.1210 1.1170 1.1130

[4] [18] [4] [4] [3,4] [4] [4]

Ethanol

293.15 298.15 303.15 308.15 313.15 318.15

0.78946 0.78520 0.78075 0.77642 0.77181 0.76738

0.7894 0.7852 0.7807 0.7763 0.7718 0.7673

[19] [19] [19] [19] [19] [19]

1-Propanol

293.15

0.80371

298.15

0.79974

303.15

0.79577

308.15

0.79180

313.15 318.15

0.78783 0.78386

0.80362 0.80375 0.79975 0.7996 0.79558 0.79586 0.79185 0.7918 0.7875 0.78359

[20] [19] [19] [16,20] [20] [22] [19] [21] [23] [19]

293.15

1.11357

298.15

1.11004

303.15

1.10651

308.15 313.15 318.15

1.10298 1.09945 1.09592

1.11350 1.11347 1.1100 1.11009 1.10665 1.106512 1.10296 1.099747 1.096312

[16] [22] [16] [22] [22] [24] [22] [24] [24]

293.15 298.15

1.03638 1.03276

1.0362 1.0328 1.03277

[25] [16] [26]

303.15 308.15 313.15 318.15

1.02914 1.02552 1.02190 1.01828

1.02540

[26]

1.01732

[26]

2. Experimental Formamide, ethanol, 1-propanol, 1,2-ethanediol, and 1,2-propanediol, used in the study were the products from s.d. fine-chem Ltd., India and were purified by using the methods described in the literature [15,16]; the mass fraction purities as determined by gas chromatography are: FA > 0.996, ethanol > 0.995, 1-propanol > 0.995, 1,2ethanediol > 0.994, and 1,2-propanediol > 0.993. Before use, the chemicals were stored over 0.4 nm molecular sieves for 72 h to remove water content, as far as possible, and were degassed at low pressure. The mixtures were prepared by mass and were kept in special airtight stopper glass bottles to avoid evaporation. The weightings were done an electronic balance with a precision of ±0.1 mg. The average uncertainty in the mole fraction was estimated to be less than ±0.0001. The densities of pure liquids and their binary mixtures were measured by using a single-capillary pycnometer (made of Borosil glass) having a bulb capacity of 10 mL. The capillary, with graduated marks, had a uniform bore and could be closed by a well-fitting glass cap. The marks on the capillary were calibrated by using triply distilled water. The densities of pure water at required temperatures were taken from the literature [17]. The reproducibility of density measurements was within ±2 Æ 105 g Æ cm3. The temperature of the test liquids during the measurements was maintained to an accuracy of ±0.02 K in an electronically controlled thermostatic water bath (JULABO, Model-MD, Germany). The reliability of experimental measurements of q was ascertained by comparing the experimental data of pure liquids with the corresponding values, which were available in the literature [2,4,16,18–26] at the studied temperatures. This comparison is given in table 1 and the agreement between the experimental and the literature values is found good in general. 3. Results The experimental results of density, q measurements of binary mixtures of FA with ethanol, 1-propanol, 1,2ethanediol, and 1,2-propanediol, with FA as a common

463

1,2-Ethanediol

1,2-Propanediol

Reference

component, over the whole composition range, expressed in mole fraction x of FA (0 6 x 6 1), at different temperatures are listed in tables 2 to 5. The excess molar volumes, V Em were calculated by using the following relation: V Em ¼ xM 1 ð1=q  1=q1 Þ þ ð1  xÞM 2 ð1=q  1=q2 Þ;

ð1Þ

where M is the molar mass; subscripts 1 and 2 stand for pure components, FA and alkanol, respectively. The V Em values were fitted to a Redlich–Kister [27] type polynomial equation: V Em =ðcm3  mol1 Þ ¼ xð1  xÞ

j X

Ai ð1  2xÞi :

ð2Þ

i¼0

The values of coefficients, Ai were evaluated by using the method of least squares, with all points weighted equally.

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A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

TABLE 2 Densities and excess molar volumes of {xFA + (1  x)ethanol} mixtures at T = (293.15 to 318.15) K and atmospheric pressure x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.0000 0.0698 0.1412 0.2032 0.2680 0.3234 0.3874 0.4365 0.4962

0.78946 0.80747 0.82672 0.84413 0.86291 0.87965 0.89952 0.91529 0.93506

0.0000 0.0921 0.1792 0.2472 0.3014 0.3456 0.3767 0.3934 0.4023

0.0000 0.0698 0.1412 0.2032 0.2680 0.3234 0.3874 0.4365 0.4962

0.78520 0.80330 0.82260 0.84006 0.85891 0.87569 0.89558 0.91135 0.93119

0.0000 0.1007 0.1928 0.2648 0.3237 0.3702 0.4019 0.4178 0.4292

0.0000 0.0698 0.1412 0.2032 0.2680 0.3234 0.3874 0.4365 0.4962

0.78075 0.79914 0.81849 0.83599 0.85491 0.87168 0.89165 0.90745 0.92732

0.0000 0.1236 0.2197 0.2943 0.3571 0.4021 0.4369 0.4530 0.4639

0.0000 0.0698 0.1412 0.2032 0.2680 0.3234 0.3874 0.4365 0.4962

0.77642 0.79494 0.81441 0.83194 0.85086 0.86771 0.88770 0.90354 0.92340

0.0000 0.1356 0.2413 0.3185 0.3813 0.4308 0.4660 0.4832 0.4920

0.0000 0.0698 0.1412 0.2032 0.2680 0.3234 0.3874 0.4365 0.4962

0.77181 0.79075 0.81028 0.82787 0.84685 0.86374 0.88375 0.89961 0.91952

0.0000 0.1687 0.2786 0.3591 0.4244 0.4749 0.5089 0.5252 0.5338

0.0000 0.0698 0.1412 0.2032 0.2680 0.3234 0.3874 0.4365 0.4962

0.76738 0.78659 0.80617 0.82384 0.84282 0.85975 0.87980 0.89570 0.91562

0.0000 0.1917 0.3061 0.3922 0.4569 0.5092 0.5441 0.5612 0.5682

x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.5423 0.5958 0.6456 0.7080 0.7748 0.8532 0.9282 1.0000

0.95083 0.96963 0.98765 1.01093 1.03690 1.06857 1.10066 1.13300

0.4027 0.3923 0.3731 0.3345 0.2815 0.1926 0.1005 0.0000

0.5423 0.5958 0.6456 0.7080 0.7748 0.8532 0.9282 1.0000

0.94693 0.96580 0.98382 1.00705 1.03301 1.06468 1.09671 1.12900

0.4269 0.4183 0.3973 0.3539 0.2975 0.2047 0.1063 0.0000

0.5423 0.5958 0.6456 0.7080 0.7748 0.8532 0.9282 1.0000

0.94306 0.96195 0.97998 1.00321 1.02913 1.06075 1.09276 1.12500

0.4596 0.4496 0.4266 0.3796 0.3175 0.2175 0.1133 0.0000

0.5423 0.5958 0.6456 0.7080 0.7748 0.8532 0.9282 1.0000

0.93920 0.95811 0.97618 0.99936 1.02526 1.05682 1.08883 1.12100

0.4894 0.4783 0.4550 0.4028 0.3362 0.2293 0.1205 0.0000

0.5423 0.5958 0.6456 0.7080 0.7748 0.8532 0.9282 1.0000

0.93530 0.95429 0.97235 0.99549 1.02135 1.05293 1.08487 1.11700

0.5276 0.5174 0.4903 0.4317 0.3585 0.2461 0.1283 0.0000

0.5423 0.5958 0.6456 0.7080 0.7748 0.8532 0.9282 1.0000

0.93142 0.95042 0.96854 0.99162 1.01744 1.04903 1.08095 1.11300

0.5612 0.5491 0.5223 0.4572 0.3780 0.2608 0.1367 0.0000

T = 293.15 K

T = 298.15 K

T = 303.15 K

T = 308.15 K

T = 313.15 K

T = 318.15 K

A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

465

TABLE 3 Densities and excess molar volumes of {xFA + (1  x)1-propanol} mixtures at T = (293.15 to 318.15) K and atmospheric pressure x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.0000 0.0557 0.1172 0.1854 0.2615 0.3469 0.3912 0.4434 0.4986

0.80371 0.81402 0.82605 0.84026 0.85742 0.87823 0.88989 0.90436 0.92067

0.0000 0.0267 0.0541 0.0820 0.1182 0.1435 0.1603 0.1759 0.1920

0.0000 0.0557 0.1172 0.1854 0.2615 0.3469 0.3912 0.4434 0.4986

0.79974 0.81006 0.82213 0.83635 0.85348 0.87430 0.88598 0.90047 0.91675

0.0000 0.0292 0.0616 0.0916 0.1267 0.1539 0.1726 0.1898 0.2040

0.0000 0.0557 0.1172 0.1854 0.2615 0.3469 0.3912 0.4434 0.4986

0.79577 0.80609 0.81820 0.83244 0.84954 0.87042 0.88206 0.89654 0.91283

0.0000 0.0308 0.0683 0.1015 0.1355 0.1682 0.1844 0.2013 0.2164

0.0000 0.0557 0.1172 0.1854 0.2615 0.3469 0.3912 0.4434 0.4986

0.79180 0.80216 0.81424 0.82851 0.84565 0.86650 0.87816 0.89262 0.90896

0.0000 0.0362 0.0726 0.1099 0.1484 0.1799 0.1979 0.2137 0.2322

0.0000 0.0557 0.1172 0.1854 0.2615 0.3469 0.3912 0.4434 0.4986

0.78783 0.79822 0.81033 0.82460 0.84172 0.86258 0.87426 0.88872 0.90505

0.0000 0.0407 0.0815 0.1201 0.1584 0.1918 0.2116 0.2278 0.2458

0.0000 0.0557 0.1172 0.1854 0.2615 0.3469 0.3912 0.4434 0.4986

0.78386 0.79425 0.80640 0.82065 0.83781 0.85868 0.87036 0.88480 0.90116

0.0000 0.0425 0.0887 0.1272 0.1703 0.2054 0.2257 0.2408 0.2609

x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.5534 0.6216 0.6800 0.7535 0.8270 0.8832 0.9328 1.0000

0.93791 0.96103 0.98232 1.01159 1.04370 1.07044 1.09556 1.13300

0.2025 0.2103 0.2044 0.1929 0.1618 0.1244 0.0714 0.0000

0.5534 0.6216 0.6800 0.7535 0.8270 0.8832 0.9328 1.0000

0.93403 0.95712 0.97844 1.00772 1.03983 1.06654 1.09165 1.12900

0.2169 0.2226 0.2177 0.2054 0.1726 0.1323 0.0772 0.0000

0.5534 0.6216 0.6800 0.7535 0.8270 0.8832 0.9328 1.0000

0.93012 0.95323 0.97457 1.00381 1.03595 1.06268 1.08774 1.12500

0.2299 0.2363 0.2318 0.2163 0.1831 0.1420 0.0830 0.0000

0.5534 0.6216 0.6800 0.7535 0.8270 0.8832 0.9328 1.0000

0.92620 0.94933 0.97066 0.99991 1.03206 1.05882 1.08381 1.12100

0.2425 0.2497 0.2440 0.2278 0.1934 0.1518 0.0882 0.0000

0.5534 0.6216 0.6800 0.7535 0.8270 0.8832 0.9328 1.0000

0.92232 0.94541 0.96678 0.99603 1.02821 1.05492 1.07991 1.11700

0.2578 0.2623 0.2581 0.2406 0.2057 0.1602 0.0947 0.0000

0.5534 0.6216 0.6800 0.7535 0.8270 0.8832 0.9328 1.0000

0.91842 0.94154 0.96288 0.99215 1.02436 1.05103 1.07597 1.11300

0.2722 0.2780 0.2714 0.2536 0.2183 0.1691 0.0997 0.0000

T = 293.15 K

T = 298.15 K

T = 303.15 K

T = 308.15 K

T = 313.15 K

T = 318.15 K

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TABLE 4 Densities and excess molar volumes of {xFA + (1  x)1,2-ethanediol} mixtures at T = (293.15 to 318.15) K and atmospheric pressure x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.0000 0.0612 0.1204 0.1859 0.2524 0.3302 0.3926 0.4517 0.5102

1.11357 1.11413 1.11454 1.11504 1.11555 1.11611 1.11661 1.11720 1.11785

0.0000 0.0149 0.0366 0.0592 0.0830 0.1137 0.1369 0.1546 0.1703

0.0000 0.0612 0.1204 0.1859 0.2524 0.3302 0.3926 0.4517 0.5102

1.11004 1.11054 1.11093 1.11139 1.11184 1.11236 1.11286 1.11344 1.11401

0.0000 0.0169 0.0387 0.0622 0.0877 0.1189 0.1411 0.1582 0.1763

0.0000 0.0612 0.1204 0.1859 0.2524 0.3302 0.3926 0.4517 0.5102

1.10651 1.10694 1.10731 1.10774 1.10813 1.10866 1.10910 1.10964 1.11017

0.0000 0.0195 0.0414 0.0653 0.0925 0.1220 0.1458 0.1636 0.1823

0.0000 0.0612 0.1204 0.1859 0.2524 0.3302 0.3926 0.4517 0.5102

1.10298 1.10338 1.10366 1.10407 1.10447 1.10492 1.10536 1.10585 1.10638

0.0000 0.0201 0.0455 0.0693 0.0950 0.1269 0.1496 0.1686 0.1862

0.0000 0.0612 0.1204 0.1859 0.2524 0.3302 0.3926 0.4517 0.5102

1.09945 1.09981 1.10006 1.10042 1.10077 1.10118 1.10162 1.10208 1.10255

0.0000 0.0212 0.0472 0.0724 0.0994 0.1319 0.1535 0.1727 0.1919

0.0000 0.0612 0.1204 0.1859 0.2524 0.3302

1.09592 1.09621 1.09644 1.09673 1.09709 1.09746

0.0000 0.0239 0.0500 0.0775 0.1030 0.1360

x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.5643 0.6101 0.6596 0.7454 0.8195 0.8883 0.9491 1.0000

1.11848 1.11918 1.12009 1.12211 1.12435 1.12702 1.13003 1.13300

0.1846 0.1905 0.1918 0.1796 0.1542 0.1131 0.0578 0.0000

0.5643 0.6101 0.6596 0.7454 0.8195 0.8883 0.9491 1.0000

1.11466 1.11531 1.11622 1.11819 1.12037 1.12299 1.12599 1.12900

0.1886 0.1957 0.1959 0.1837 0.1588 0.1176 0.0609 0.0000

0.5643 0.6101 0.6596 0.7454 0.8195 0.8883 0.9491 1.0000

1.11081 1.11146 1.11236 1.11423 1.11638 1.11900 1.12195 1.12500

0.1940 0.2002 0.1997 0.1895 0.1638 0.1208 0.0640 0.0000

0.5643 0.6101 0.6596 0.7454 0.8195 0.8883 0.9491 1.0000

1.10695 1.10760 1.10846 1.11028 1.11238 1.11501 1.11789 1.12100

0.1998 0.2050 0.2051 0.1950 0.1693 0.1239 0.0679 0.0000

0.5643 0.6101 0.6596 0.7454 0.8195 0.8883 0.9491 1.0000

1.10313 1.10372 1.10459 1.10635 1.10842 1.11098 1.11386 1.11700

0.2040 0.2108 0.2094 0.1997 0.1733 0.1286 0.0707 0.0000

0.5643 0.6101 0.6596 0.7454 0.8195 0.8883

1.09929 1.09989 1.10070 1.10242 1.10446 1.10696

0.2091 0.2146 0.2146 0.2045 0.1774 0.1330

T = 293.15 K

T = 298.15 K

T = 303.15 K

T = 308.15 K

T = 313.15 K

T = 318.15 K

A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

467

TABLE 4 (continued) x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.3926 0.4517 0.5102

1.09788 1.09829 1.09874

0.1574 0.1778 0.1968

0.9491 1.0000

1.10979 1.11300

0.0751 0.0000

TABLE 5 Densities and excess molar volumes of {xFA + (1  x)1,2-propanediol} mixtures at T = (293.15 to 318.15) K and atmospheric pressure x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.0000 0.0567 0.1191 0.1881 0.2649 0.3409 0.3904 0.4478 0.4936

1.03638 1.03829 1.04052 1.04347 1.04735 1.05167 1.05479 1.05892 1.06242

0.0000 0.0782 0.1634 0.2365 0.2958 0.3444 0.3695 0.3823 0.3922

0.0000 0.0567 0.1191 0.1881 0.2649 0.3409 0.3904 0.4478 0.4936

1.03276 1.03456 1.03678 1.03969 1.04350 1.04779 1.05091 1.05502 1.05849

0.0000 0.0855 0.1709 0.2458 0.3084 0.3574 0.3815 0.3942 0.4047

0.0000 0.0567 0.1191 0.1881 0.2649 0.3409 0.3904 0.4478 0.4936

1.02914 1.03082 1.03303 1.03591 1.03965 1.04396 1.04702 1.05108 1.05456

0.0000 0.0937 0.1792 0.2553 0.3211 0.3676 0.3943 0.4085 0.4174

0.0000 0.0567 0.1191 0.1881 0.2649 0.3409 0.3904 0.4478 0.4936

1.02552 1.02712 1.02925 1.03211 1.03585 1.04009 1.04315 1.04715 1.05068

0.0000 0.0992 0.1897 0.2662 0.3309 0.3804 0.4061 0.4225 0.4275

0.0000 0.0567 0.1191 0.1881 0.2649 0.3409 0.3904 0.4478 0.4936

1.02190 1.02341 1.02552 1.02833 1.03201 1.03622 1.03928 1.04324 1.04676

0.0000 0.1054 0.1968 0.2759 0.3434 0.3933 0.4180 0.4355 0.4399

x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.5578 0.6262 0.6838 0.7544 0.8295 0.8818 0.9392 1.0000

1.06801 1.07452 1.08096 1.08983 1.10075 1.10970 1.12057 1.13300

0.3877 0.3805 0.3511 0.3035 0.2340 0.1626 0.0787 0.0000

0.5578 0.6262 0.6838 0.7544 0.8295 0.8818 0.9392 1.0000

1.06407 1.07055 1.07695 1.08577 1.09663 1.10553 1.11644 1.12900

0.3991 0.3917 0.3624 0.3147 0.2451 0.1735 0.0857 0.0000

0.5578 0.6262 0.6838 0.7544 0.8295 0.8818 0.9392 1.0000

1.06010 1.06660 1.07295 1.08167 1.09250 1.10140 1.11231 1.12500

0.4122 0.4019 0.3734 0.3279 0.2567 0.1830 0.0928 0.0000

0.5578 0.6262 0.6838 0.7544 0.8295 0.8818 0.9392 1.0000

1.05612 1.06264 1.06891 1.07758 1.08836 1.09727 1.10816 1.12100

0.4260 0.4128 0.3864 0.3408 0.2690 0.1927 0.1008 0.0000

0.5578 0.6262 0.6838 0.7544 0.8295 0.8818 0.9392 1.0000

1.05218 1.05866 1.06490 1.07351 1.08426 1.09310 1.10404 1.11700

0.4379 0.4249 0.3982 0.3530 0.2797 0.2041 0.1077 0.0000

T = 293.15 K

T = 298.15 K

T = 303.15 K

T = 308.15 K

T = 313.15 K

(continued on next page)

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A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

TABLE 5 (continued) x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.0000 0.0567 0.1191 0.1881 0.2649 0.3409 0.3904 0.4478 0.4936

1.01828 1.01967 1.02177 1.02451 1.02819 1.03237 1.03544 1.03931 1.04286

0.0000 0.1139 0.2055 0.2885 0.3547 0.4052 0.4284 0.4498 0.4514

x

q/(g Æ cm3)

V Em =ðcm3  mol1 Þ

0.5578 0.6262 0.6838 0.7544 0.8295 0.8818 0.9392 1.0000

1.04822 1.05473 1.06087 1.06944 1.08016 1.08894 1.09988 1.11300

0.4511 0.4346 0.4111 0.3654 0.2906 0.2152 0.1163 0.0000

T = 318.15 K

The coefficients A0, A1, A2, A3, and A4 for all the mixtures are listed in table 6, along with standard deviation, r calculated by using the following relation: X  1=2 2  r=ðcm3  mol1 Þ ¼ V Em;Calc:  V Em;Expt: ; ðn  jÞ ð3Þ where n is the number of experimental data points and j is the number of Ai coefficients considered (j + 1 in the present study). The values of V Em;Calc: were obtained from equation (2) by using the best-fit values of Ai coefficients. The variations of V Em with mole fraction x of FA at various tem-

peratures, along with the smoothed V Em values by using equation (2) are presented graphically in figures 1 to 4. 4. Discussion The results presented in tables 2 to 5 and figures 1 to 4 indicate that V Em values are negative for (FA + ethanol/1propanol) and are positive for (FA + 1,2-ethanediol/1,2propanediol) mixtures over the entire mole fraction range and at all temperatures investigated for each binary system under study. The V Em values for (FA + ethanol/1-propanol) mixtures at 298.15 K obtained in this work compare well

TABLE 6 Coefficients, Ai from equation (2) for V Em =ðcm3  mol1 Þ and standard deviations r for {xFA + (1  x)alkanol} at T = (293.15 to 318.15) K T/K

A0

A1

A3

A4

r

{xFA + (1  x)ethanol} 0.1139 0.1191 0.1551 0.1503 0.1663 0.1909

A2

0.0776 0.0926 0.2335 0.3159 0.5147 0.6450

0.1451 0.1354 0.0537 0.0981 0.3568 0.5515

0.0015 0.0018 0.0019 0.0023 0.0033 0.0041

{xFA + (1  x)1-propanol} 0.2350 0.2550 0.3043 0.3133 0.3261 0.3653

0.0718 0.0798 0.0574 0.0267 0.0371 0.0148

0.1555 0.1313 0.1558 0.1202 0.0612 0.0928

0.0025 0.0023 0.0021 0.0026 0.0025 0.0030

0.0021 0.0279 0.0341 0.0378 0.0664 0.0793

0.0317 0.0020 0.0526 0.0682 0.0818 0.1546

0.0011 0.0012 0.0009 0.0012 0.0014 0.0015

0.2658 0.2269 0.2145 0.2076 0.1680 0.1603

0.4723 0.3892 0.2663 0.1899 0.1323 0.0008

0.0031 0.0029 0.0030 0.0029 0.0028 0.0029

293.15 298.15 303.15 308.15 313.15 318.15

1.6143 1.7186 1.8572 1.9769 2.1442 2.2851

0.0910 0.0811 0.0629 0.0588 0.0173 0.0057

293.15 298.15 303.15 308.15 313.15 318.15

0.7636 0.8158 0.8667 0.9218 0.9781 1.0360

0.4655 0.4815 0.4862 0.4837 0.4969 0.5046

293.15 298.15 303.15 308.15 313.15 318.15

0.6772 0.6962 0.7170 0.7358 0.7551 0.7745

0.5178 0.5124 0.5162 0.5240 0.5215 0.5217

{xFA + (1  x)1,2-ethanediol} 0.1034 0.1088 0.1029 0.1220 0.1329 0.1266

293.15 298.15 303.15 308.15 313.15 318.15

1.5623 1.6109 1.6625 1.7119 1.7619 1.8113

0.1728 0.1616 0.1602 0.1644 0.1564 0.1559

{xFA + (1  x)1,2-propanediol} 0.2463 0.2711 0.2723 0.3085 0.3421 0.3574

0.24

-0.1

0.20

-0.2

0.16

Vm/(cm3 .mol-1 )

0.0

-0.3

469

0.12

E

E

Vm/(cm3 .mol-1 )

A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

-0.4

0.08

-0.5

0.04

-0.6

0.00 0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

x

0.6

0.8

1.0

x E m,

FIGURE 1. Variation of excess molar volumes, V against mole fraction, x for {xFA + (1  x)ethanol} binary mixtures at different temperatures T: r, 293.15 K; j, 298.15 K; m, 303.15 K; d, 308.15 K; h, 318.15 K; and n, 313.15 K; solid lines, calculated with Redlich–Kister equation; symbols, experimental values.

FIGURE 3. Variation of excess molar volumes, V Em , against mole fraction, x for {xFA + (1  x)1,2-ethanediol} binary mixtures at different temperatures T: r, 293.15 K; j, 298.15 K; m, 303.15 K; d, 308.15 K; h, 318.15 K; and n, 313.15 K; solid lines, calculated with Redlich–Kister equation; symbols, experimental values.

0.00 0.5

-0.05 0.4

Vm/(cm3 .mol-1 )

-0.15

E

E

Vm/(cm3 .mol-1 )

-0.10 0.3

0.2

-0.20

0.1

-0.25

-0.30

0.0

0.0

0.2

0.4

0.6

0.8

1.0

x

0.0

0.2

0.4

0.6

0.8

1.0

x E m,

FIGURE 2. Variation of excess molar volumes, V against mole fraction, x for {xFA + (1  x)1-propanol} binary mixtures at different temperatures T: r, 293.15 K; j, 298.15 K; m, 303.15 K; d, 308.15 K; h, 318.15 K; and n, 313.15 K; solid lines, calculated with Redlich–Kister equation; symbols, experimental values.

FIGURE 4. Variation of excess molar volumes, V Em , against mole fraction, x for {xFA + (1  x)1,2-propanediol} binary mixtures at different temperatures T: r, 293.15 K; j, 298.15 K; m, 303.15 K; d, 308.15 K; h, 318.15 K; and n, 313.15 K; solid lines, calculated with Redlich–Kister equation; symbols, experimental values.

470

A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

with those reported by Garcia et al. [14] for these mixtures at 298.15 K (figure 5). The observed trends in V Em values for these (FA + alkanol/alkanediol) mixtures indicate the presence of specific interactions between unlike molecules. The magnitude of V Em values follows the sequence: ethanol < 1-propanol < 1,2-ethanediol < 1,2-propanediol (figure 5). This suggests that there is an expansion in volume of the mixtures as we move from ethanol to 1,2-propanediol. A plausible qualitative interpretation of the behaviour of these mixtures with composition has been suggested. As stated earlier, the molecules of both FA and alkanols are associated through hydrogen bonding due presence of a strong proton-acceptor as well as proton-donor group(s) [12–14,28] in their molecules. Mixing of FA with alkanols would induce mutual dissociation of the hydrogen bonded structures present in pure liquids with subsequent formation of (new) H-bonds (C@O  H–O) between protonacceptor oxygen atom (with two lone pair of electrons) of C@O group of FA and hydrogen atom of –OH group(s) of alkanol molecules, and equally important is the formation of H-bond of the type (N–H  O–H) between hydrogen atoms of –NH2 groups of FA and oxygen atom of –OH group(s) of alkanol molecules, leading to a contraction in volume [5,14,25,29], which should result in negative V Em values for all the four binary systems under study. The observed negative V Em values for (FA + ethanol/ 1-propanol) mixtures are due to formation of hydrogen

0.45

0.30

0.00

E

Vm/(cm3 .mol-1 )

0.15

-0.15

-0.30

-0.45 0.0

0.2

0.4

0.6

0.8

1.0

x FIGURE 5. Variation of excess molar volume, V Em , against mole fraction, x of FA for the binary mixtures at T = 298.15 K. xFA + (1  x)ethanol, r; xFA + (1  x)1-propanol, j; xFA + (1  x)1,2-ethanediol, m; xFA + (1  x)1,2-propanediol, }; xFA + (1  x)ethanol, + and xFA + (1  x)1propanol, · reported by Garcia et al.; solid lines, calculated with Redlich– Kister equation; symbols, experimental values.

bonding between unlike molecules [14,29], resulting in decrease in the volume of the mixture. Another negative contribution to V Em comes from the geometrical fitting of unlike molecules into each other’s structures due to difference in size and shape of the molecules. The molar volumes of FA, ethanol, and 1-propanol, at 298.15 K, are (39.8937, 58.6729, and 75.1494) cm3 Æ mol1, respectively, which might allow the fitting of component molecules into each other’s structures [29–31], hence, decreasing the volume of the mixture. The greater V Em values for (FA + 1-propanol) than those for (FA + ethanol) mixtures are in accordance with the fact that the strength of hydrogen bonds formed by the alkanols decreases with increase in the carbon chain length [13,14]. Contrary to our expectation, the positive trends are observed in V Em values for (FA + 1,2-ethanediol/1,2-propanediol) mixtures over whole composition range. It has been pointed [13] that intramolecular hydrogen bonding in multihydroxylic alkanols considerably influences the formation of intermolecular hydrogen bonding, i.e., the proportion of hydroxyl groups available for association with FA molecules in the mixture will be smaller in case of alkanediols than those available in n-alkanols. This would lead to less pronounced hydrogen bonding between unlike molecules (as compared to monohydroxylic alkanols) resulting in an unfavourable geometrical fitting of component molecules into each other’s structures. This results in an expansion in volume, and hence, positive V Em values for (FA + 1,2-ethanediol/1,2-propanediol) mixtures. It is worth mentioning that for (FA + ethanol/1-propanol) systems, the V Em values decrease (become more negative) whereas for (FA + 1,2-ethanediol/1,2-propanediol) systems, V Em values increase (become more positive) with increase in temperature of the mixture (figures 1 to 4). In case of (FA + ethanol/1-propanol) mixtures, the expansion in volume due to increase in temperature of the systems seems to be dominated by more favourable fitting of smaller FA molecules into the larger voids created by bigger ethanol/1-propanol molecules at higher temperatures, leading to a contraction in volume, hence, resulting in more negative V Em values with rise in temperature. On the other hand, in case of (FA + 1,2-ethanediol/1,2-propanediol) mixtures, the increase in V Em is attributed to the breaking of associates presents between unlike molecules with rise in temperature, leading to an expansion in volume, hence, resulting in an increase in V Em values. The partial molar volumes, V m;1 of component 1 (FA) and V m;2 of component 2 (alkanol) in these mixtures over entire composition range, were calculated by using the following relations:   V m;1 ¼ V Em þ V m;1 þ ð1  xÞ oV Em =ox T ;p ; ð4Þ   V m;2 ¼ V Em þ V m;2  x oV Em =ox T ;p ; ð5Þ where V m;1 and V m;2 are the molar volumes of pure components, FA and alkanol, respectively. The derivative, ðoV Em =oxÞT ;p in equations (4) and (5) was obtained by differ-

A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

entiation of equation (2), which leads to the following equations for V m;1 and V m;2 : V m;1 ¼ V m;1 þ ð1  xÞ2 2

V m;2 ¼ V m;2 þ x2

j X i¼1 j X

Ai ð1  2xÞi 

1.0

i¼0

Ai ð1  2xÞ

i1

ð6Þ

;

i

Ai ð1  2xÞ þ

i¼0

2

2x ð1  xÞ

j X

Ai ð1  2xÞ

i1

ð7Þ

:

The values of partial molar volumes, V m;1 and V m;2 at infinite dilution were obtained from equations (4) to (7), and E the excess partial molar volumes, V E m;1 and V m;2 at infinite dilution were calculated by using the following relations V V

¼ V m;1  V ¼ V m;2  V

 m;1 ;  m;2 :

0.0

-0.5

-1.0

ð8Þ ð9Þ E m;1

E m;2

The variation excess partial molar volumes V and V with composition at 298.15 K is presented in figures 6 and 7, respectively. A close perusal of figs. 6 and 7 indicates that the values of V Em;1 and V Em;2 are negative over whole composition range for (FA + ethanol/1-propanol) binary mixtures. This suggests that volumes of each component in the mixture are less than their respective molar volumes in the pure state, i.e., there is a contraction in volume on mixing FA with ethanol/1-propanol. The values of V Em;1 and V Em;2 are positive over whole composition range 1.6 1.2 0.8 0.4 0.0

E

Vm,1/(cm3 .mol-1 )

0.5

E

i¼1

E m;1 E m;2

1.5

Vm,2 /(cm3 .mol-1 )

2xð1  xÞ

j X

-0.4 -0.8

-1.5 0.0

-1.2 -1.6 0.2

0.4

0.6

0.8

1.0

x FIGURE 6. Variation of excess partial molar volumes, V Em;1 , against mole fraction x for the binary mixtures at T = 298.15 K. xFA + (1  x)ethanol, r; xFA + (1  x)1-propanol, j; xFA + (1  x)1,2-ethanediol, m; and xFA + (1  x)1,2-propanediol, }.

0.2

0.4

0.6

0.8

1.0

x FIGURE 7. Variation of excess partial molar volumes V Em;2 against mole fraction x for the binary mixtures at T = 298.15 K. xFA + (1  x)ethanol, r; xFA + (1  x)1-propanol, j; xFA + (1  x)1,2-ethanediol, m; and xFA + (1  x)1,2-propanediol, }.

for (FA + 1,2-ethanediol/1,2-propanediol) mixtures, suggesting that volumes of components are more than their respective molar volumes in the pure state, i.e., there is an expansion in volume on mixing FA with 1,2-ethanediol/1,2-propanediol. These trends further supports the trends observed in V Em values for these binary systems. The values of partial molar volumes, V m;1 and V m;2 at infinite dilution were also obtained from equations (4) to E (7), and the excess partial molar volumes, V E m;1 and V m;2 at infinite dilution were calculated by using equations (8) and (9) by substituting V m;1 and V m;2 values in place of V m;1 and V m;2 , respectively. Furthermore, the partial molar volumes at infinite dilution are also calculated by using another approach. This method makes use of the apparent molar volumes originally defined by Lewis and Randall as V /;1 ¼ ðV m  n2 V m;2 Þ=n1 ;

ð10Þ

 m;1 Þ=n2 ;

ð11Þ

V /;2 ¼ ðV m  n1 V

0.0

471

where V/,1 and V/,2 are the apparent molar volumes of the component 1 (FA) in component 2 (alkanol) and of the component 2 in component 1, respectively, n1 and n2 are the number of moles of components 1 and 2, respectively, and Vm is the molar volume of the mixture, can be written as V m ¼ V Em þ xV m;1 þ ð1  xÞV m;2 :

ð12Þ

The combination of equations (10) and (12) and (11) and (12) gives the following relations:

A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

1.4626 1.3443 1.3432 1.4374 1.4526 1.3412 1.3473 1.4275 58.6729 75.1494 55.9169 73.6860 57.2103 73.8051 57.2601 75.1234 1.4811 0.5399 0.2677 1.5665 1.4756 0.5378 0.2667 1.5581

57.2203 73.8082 57.2642 75.1135

V E/;1 =ðcm3  mol1 Þ V Em;1 =ðcm3  mol1 Þ

V m;2 =ðcm3  mol1 Þ

V /;1 ¼ V m;1 þ V Em =x; V /;2 ¼ V

 m;2

þV

E m =ð1

ð13Þ  xÞ:

ð14Þ

Equations (13) and (14) allow easy calculation of apparent molar volumes from experimental V Em values and corresponding mole fractions. Using the linear regression of V/,1 vs. x for dilute solutions of FA in alkanol, and of V/,2 vs. (1  x) for dilute solutions of alkanols in FA, gives the values of limiting apparent molar volumes, V /;1 and V /;2 at infinite dilution. These are also called as partial molar volumes at infinite dilution, represented as E V m;1 and V m;2 earlier. The values of V E /;1 and V /;2 have also been calculated by using equations (8) and (9).  E   The values V m;1 ; V /;1 ; V m;1 ; V E m;1 ; V /;1 ; V m;2 ; V /;2 ; V m;2 ; E E V m;2 ; and V /;2 for all the four binary systems at 298.15 K are listed in table 7. A close perusal of table 7 indicates that E E E the values of V E m;1 and V m;2 , and V /;1 and V /;2 calculated using equations (8) and (9) from both the approaches are nearly same in magnitude for each of the mixtures and found E to exhibit similar trends. The values of V E m;1 and V m;2 , and E E V /;1 and V /;2 are negative for (FA + ethanol/1-propanol) and are positive for (FA + 1,2-ethanediol/1,2-propanediol) (table 7) binary systems. The negative values suggest that the molar volumes of each component in the mixture are less than their respective molar volumes in the pure state, i.e., there is an contraction in volume on mixing FA with ethanol/1-propanol; and the positive values suggest that the molar volumes of each component in the mixture are greater than their respective molar volumes in the pure state, i.e., there is an expansion in volume on mixing FA with 1,2-ethanediol/1,2-propanediol. This further supports the trends observed in V Em values for these binary systems.

V m;1 =ðcm3  mol1 Þ

39.8937 39.8937 39.8937 39.8937

V /;1 =ðcm3  mol1 Þ

38.4186 39.3538 40.1614 41.4602

5. Conclusion The densities for (FA + ethanol, or 1-propanol, or 1, 2-ethanediol, or 1,2-propanediol) binary mixtures have been measured and the values of V Em ; V Em;1 and V Em;2 over E whole composition range, and V E m;1 and V m;2 at infinite E dilution were calculated. The V m values for these mixtures follow the order: ethanol < 1-propanol < 1,2-ethanediol < 1,2-propanediol. It is observed that the magnitude of V Em depends upon the number of hydroxyl groups and alkyl chain length in these alkanol molecules.

V m;1 =ðcm3  mol1 Þ

38.4181 39.3559 40.1604 41.4518 Ethanol 1-Propanol 1,2-Ethanediol 1,2-Propanediol

Acknowledgements

FA +

TABLE 7  E   E E The values of V m;1 ; V /;1 ; V m;1 ; V E m;1 ; V /;1 ; V m;2 ; V /;2 ; V m;2 ; V m;2 ; and V /;2 for (FA + alkanol) mixtures at T = 298.15 K

V /;2 =ðcm3  mol1 Þ

V m;2 =ðcm3  mol1 Þ

V Em;2 =ðcm3  mol1 Þ

V E/;2 =ðcm3  mol1 Þ

472

The author is thankful to Department of Science and Technology (DST), New Delhi, India for financial support in form of SERC Fast Track Young Scientist Scheme. Thanks are also due to Prof. Anwar Ali, Head, Department of Chemistry, JMI, New Delhi for providing laboratory facility for the experimental work and to Dr. D. Jagannathan, Principal, Dyal Singh College, New Delhi for encouragement and providing computation facilities.

A.K. Nain / J. Chem. Thermodynamics 39 (2007) 462–473

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JCT 06-134