Molecular interactions in binary mixtures of formamide with 1-butanol, 2-butanol, 1,3-butanediol and 1,4-butanediol at different temperatures: An ultrasonic and viscometric study

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Fluid Phase Equilibria 265 (2008) 46–56

Molecular interactions in binary mixtures of formamide with 1-butanol, 2-butanol, 1,3-butanediol and 1,4-butanediol at different temperatures: An ultrasonic and viscometric study Anil Kumar Nain ∗ Department of Chemistry, Dyal Singh College, University of Delhi, New Delhi 110003, India Received 6 November 2007; received in revised form 22 December 2007; accepted 22 December 2007 Available online 9 January 2008

Abstract The ultrasonic speeds, u and viscosities, η of binary mixtures of formamide (FA) with 1-butanol, 2-butanol, 1,3-butanediol and 1,4-butanediol, 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. From the experimental u and η data, the deviations in isentropic compressibility, ks , in ultrasonic speed, u, and in viscosity, η ◦ ¯ m,1 and K ¯ m,2 of FA and alkanol in the mixtures over the whole composition range and K ¯ m,1 were calculated. The partial molar compressibilities, K ◦E ◦E ◦ E E ¯ ¯ ¯ ¯ ¯ and Km,2 at infinite dilution and excess partial molar compressibilities, Km,1 and Km,2 , over the whole composition range and Km,1 and Km,2 at infinite dilution were calculated by using two different approaches. The variations of these parameters with composition and temperature of the mixtures are discussed in terms of molecular interaction in these mixtures. It is observed that the FA-alkanol interactions in these mixtures follows the order: 1-butanol < 2-butanol < 1,3-butanediol < 1,4-butanediol. The effect of the number and position of the hydroxyl groups in these alkanol molecules on the molecular interactions in these mixtures is discussed. Furthermore, the free energies, G* , enthalpies, H* , and entropies, S* of activation of viscous flow have also been obtained by using Eyring viscosity equation. The dependence of G* , H* and S* on composition of the mixtures have been discussed. © 2008 Elsevier B.V. All rights reserved. Keywords: Ultrasonic speed; Viscosity; Formamide; Alkanols; Alkanediols; Deviations in isentropic compressibility; Partial molar compressibility; Molecular interactions

1. Introduction Mixed solvents are frequently used as media for many chemical, industrial and biological processes, because they provide a wide range of desired properties [1]. The study of physicochemical properties of amide + alkanol mixed solvents is interesting because amides are convenient model systems for investigating peptide and protein–solvent interactions. Formamide (FA) is chosen for the study, as it is the simplest amide that contains a peptide linkage, the fundamental building block of proteins [2]. Alkanols are of interest in their own right and serve as simple examples of biologically and industrially important amphiphilic materials [3]. In previous papers [4–11] we have studied the volumetric, acoustic and transport properties of non-aqueous

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binary mixtures containing alkanols. Here we report the results of our studies on acoustic and transport properties of binary mixtures of FA with 1-butanol, 2-butanol, 1,3-butanediol, and 1,4-butanediol, over the entire composition range at various temperatures. FA molecules are highly polar (μ = 3.37 D at 298.15 K) [13] 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 on nitrogen atom) [13,14]. Alkanol molecules are polar and self-associated through hydrogen bonding of their hydroxyl groups [14], whereas alkanediol molecules are self-associated through inter- and intrahydrogen bonding. Since the components of these binary mixtures have both proton-donating/accepting abilities, significant interaction through hydrogen bonding between unlike molecules is expected. To the best of our knowledge, there has been no temperature-dependent study on these systems from the point of view of their acoustic and viscometric behaviour, except the

A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

work of Garcia et al. [15], who studied the viscometric behaviour of FA + 1-butanol mixtures at 298.15 K and Ali et al. [11], who studied ultrasonic and viscometric behaviour of FA + 1-butanol mixtures at 308.15 K. The present paper reports the ultrasonic speeds, u and viscosities, η of binary mixtures of FA with 1-butanol, 2-butanol, 1,3-butanediol, 1,4-butanediol and those of pure liquids at 293.15, 298.15, 303.15, 308.15, 313.15 and 318.15 K, covering the entire composition range, expressed by the mole fraction x1 of FA. The density, ρ data for the calculations was taken from our previous study [16]. The experimental values of ρ, u and η were used to calculate the deviations in isentropic compressibility, ks , deviations in ultrasonic speed, u, deviations in viscosity, η and excess molar compressibility, KsE . The partial ¯ m,1 and K ¯ m,2 of FA and alkanols in molar compressibilities, K ¯ ◦ and the mixture over the whole composition range and K m,1 ◦ ¯ Km,2 at infinite dilution, and excess partial molar compressibil¯ E and K ¯ E , over the whole composition range and ities, K m,1 m,2 ◦E ◦E ¯ ¯ K and K at infinite dilution were also calculated. The m,1 m,2 variation of these parameters with composition and temperature has been discussed in terms of molecular interaction in these mixtures. Furthermore, the free energies, G* , enthalpies, H* and entropies, S* of activation of viscous flow have also been obtained by using Eyring viscosity equation. The dependence of G* , H* and S* on composition of the mixtures have been discussed. 2. Experimental details Formamide, 1-butanol and 2-butanol (all AR grade products from s.d. fine chemicals, India), 1,3-butanediol and 1,4-butanediol (both products from E. Merck, Germany) used in the study were purified by using the methods described in the literature [17,18]; the mass fraction purities as determined by gas chromatography are: FA > 0.995, 1butanol > 0.995, 2-butanol > 0.994, 1,3-butanediol > 0.992 and 1,4-butanediol > 0.992. Before use, the chemicals were stored over 0.4 nm molecular sieves for 72 h to remove water content, if any, 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 weighings were done on electronic balance with a precision of ±0.1 mg. The probable error in the mole fraction was estimated to be less than ±1 × 10−4 . The ultrasonic speeds in pure liquids and in their binary mixtures were measured using a single-crystal variable-path multifrequency ultrasonic interferometer operating at 3 MHz by the method described elsewhere [4–11]. The ultrasonic speed data were reproducible within ±0.03%. The viscosities of pure liquids and their binary mixtures were measured by using Ubbelohde type suspended level viscometer. The viscometer was calibrated with triply distilled water. The viscometer containing the test liquid was allowed to stand for about 30 min in a thermostatic water bath so that the thermal fluctuations in viscometer were minimized. The time of flow was recorded in triplicate with a digital stopwatch with an accuracy of ±0.01 s. The viscosity data were reproducible within ±5 × 10−7 N s m−2 . The temper-

47

ature of the test liquids during the measurements was maintained to an accuracy of ±0.01 K in an electronically controlled thermostatic water bath (Model: ME-31A, JULABO, Germany). The reliability of experimental measurements of u and η was ascertained by comparing the experimental data of pure liquids with the corresponding values, which were available in the literature [6,15,18–32] 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 and discussion The experimental values of ultrasonic speeds and viscosities of binary mixtures of FA with 1-butanol, 2-butanol, 1,3-butanediol, and 1,4-butanediol, with FA as a common component, over the whole composition range expressed in mole fraction x1 of FA (0 ≤ x1 ≤ 1), at different temperatures are listed in Tables 2 and 3, respectively. The excess function such as ks , u, η and KsE have been calculated by using the following standard relations: ks = ks − (x1 ks,1 + x2 ks,2 )

(1)

u = u − (x1 u1 + x2 u2 )

(2)

η = η − (x1 η1 + x2 η2 )

(3)

KsE = Ks − (x1 Ks,1 + x2 Ks,2 )

(4)

where x is the mole fraction; subscripts 1 and 2 stand for the pure components, FA and alkanol, respectively; ks and Ks are the isentropic compressibility and molar isentropic compressibility, calculated by using the relations: 1 u2 ρ

(5)

Ks = ks V

(6)

ks =

where V is the molar volume, calculated using the relation: V =

x1 M1 + x2 M2 ρ

(7)

The excess functions ks , u, η and KsE were fitted to a Redlich–Kister type polynomial equation: Y E = x1 (1 − x1 )

n 

Ai (1 − 2x1 )i

(8)

i=0

where YE is ks or u or η or KsE . The values of coefficients, Ai evaluated by using least-squares method with all points weighted equally, and the corresponding standard deviations, σ (YE ) are listed in Table 4. The variations ks , u and η with composition of the mixtures, along with smoothed values using Eq. (8), at 298.15 and 318.15 K are presented graphically in Figs. 1–3. The results shown in Fig. 1 indicate that the ks values are negative for FA + 1-butanol/2-butanol and are positive for FA + 1,3-butanediol/1,4-butanediol mixtures over entire mole fraction range and at all temperatures investigated. The magnitude of ks values follows the sequence: 1-butanol < 2butanol < 1,3-butanediol < 1,4-butanediol. This suggests that

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A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

Table 1 Comparison of experimental values of ultrasonic speed, u and viscosity, η of pure liquids with the corresponding literature values at different temperatures Liquid

FA

1Butanol

2Butanol

1,3Butanediol

1,4Butanediol

T (K)

u (m s−1 )

η (×10−3 N s m−2 )

Expt.

Lit.

Expt.

293.15 298.15

1615.8 1601.0

303.15 308.15 313.15 318.15

1589.2 1577.2 1565.1 1553.1

1615.8 [6] 1599.05 [19] 1601.0 [6] 1589.2 [6] 1577.2 [6] 1565.1 [6] 1553.1 [6]

2.9663 2.6531 2.4039 2.2187

293.15 298.15

1262.4 1242.6

– 1241.0 [20]

2.9356 2.5416

303.15 308.15 313.15 318.15

1224.6 1207.6 1189.2 1170.0

1224.0 [22] 1208.8 [24] 1189.5 [20] 1172.13 [24]

2.2751 1.9978 1.7442 1.5712

293.15 298.15

1232.6 1212.6

4.2124 3.0342

303.15 308.15 313.15 318.15

1194.6 1174.5 1155.9 1138.6

– 1211.5 [24] 1212.4 [20] 1205.0 [26] 1174.8 [24] 1155.3 [20] 1138.1 [24]

293.15 298.15

1539.6 1523.4

303.15 308.15

1506.3 1492.5

313.15 318.15

1480.8 1470.3

293.15 298.15

1616.4 1605.6

303.15 308.15 313.15 318.15

3.6542 3.3220

2.4954 2.1058 1.7840 1.5242

1539.0 [29] 1522.1 [30] 1524.1 [31] – 1492.1 [30] 1495.6 [31] – 1469.0 [31] 1472.0 [30]

130.3250 97.2620

97.2620 72.7454

1595.9 1587.3

1616.0 [29] 1605.1 [30] 1601.3 [31] – 1588.0 [30]

1579.8 1570.2

– 1570.8 [30]

35.8106 29.0542

there is an increase in the compressibility of the mixtures as we move from 1-butanol to 1,4-butanediol. 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) [12–14,33] 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 proton-acceptor oxygen atom (with two lone pair of electrons) of C O group of FA and hydrogen atom of OH group(s) of alkanol molecules. Equally important is the formation of Hbond of the type (N H· · ·· · ·O H) between hydrogen atoms of NH2 groups of FA and oxygen atom of OH group(s) of alka-

69.8440 52.5420 39.4180 30.5050

56.8860 44.8850

Lit. 3.6542 [6] 3.340 [15] 3.332 [6] 2.9663 [6] 2.6531 [6] 2.4039 [6] 2.2187 [6] – 2.5439 [21] 2.530 [15] 2.274 [23] 1.991 [25] – 1.569, 1.5786 [25] 4.210 [18] 3.0338 [21] 3.035 [25] 2.495, 2.496 [27] 2.1019, 2.111 [25] 1.785, 1.7833 [27] 1.523 [25] 1.525 [28] 130.300 [30] 97.25 [30] 97.28 [32] – 52.50 [30] 52.55 [32] – 30.487 [30] 31.61 [32] 72.618 [30] 72.75 [32] – 44.871 [30] 44.890 [32] – 29.071 [30] 29.02 [32]

nol molecules, leading to a contraction in volume, which should result in negative ks values. The observed negative ks values for FA + 1-butanol/2butanol mixtures (Fig. 1) can be considered due to formation of hydrogen bonding between FA and 1-butanol/2-butanol molecules that leads to more closer packing of molecules resulting in a contraction in volume of the mixture, and hence, decreasing the compressibility of the mixture leading to negative ks values. But contrary to our expectation, the positive trends are observed in ks values for FA + 1,3-butanediol/1,4butanediol mixtures (Fig. 1) 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 intermolecular hydrogen bond-

A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

49

Table 2 Values of ultrasonic speeds, u (m s−1 ) as function of mole fraction, x1 of FA for the binary mixtures at different temperatures

Table 3 Values of viscosities, η (×10−3 N s m−2 ) as function of mole fraction, x1 of FA for the binary mixtures at different temperatures

X1

x1

298.15 K 308.15 K 318.15 K 298.15 K 308.15 K 318.15 K

298.15 K 308.15 K 318.15 K 298.15 K 308.15 K 318.15 K

FA + 1-butanol 0.1093 1302.3 0.2057 1337.7 0.3138 1377.0 0.4104 1412.0 0.5115 1448.4 0.6124 1484.4 0.7081 1518.0 0.8123 1554.0 0.9086 1586.4

1281.2 1315.3 1353.7 1388.3 1424.6 1461.0 1495.5 1533.1 1567.9

1261.5 1294.8 1332.6 1367.1 1403.4 1440.3 1475.4 1515.3 1552.5

1243.5 1275.6 1312.7 1347.0 1383.6 1420.5 1456.5 1497.9 1537.2

1223.7 1255.5 1292.1 1326.0 1362.6 1399.8 1437.0 1479.9 1521.9

1203.3 1234.5 1270.8 1305.0 1341.3 1379.1 1417.5 1461.9 1506.6

FA + 1-butanol 0.1093 3.2246 0.2057 3.4465 0.3138 3.5984 0.4104 3.6956 0.5115 3.7542 0.6124 3.7775 0.7081 3.7700 0.8123 3.7445 0.9086 3.7082

2.8101 3.0176 3.1810 3.2853 3.3518 3.3859 3.3894 3.3788 3.3551

2.5064 2.6928 2.8461 2.9468 3.0032 3.0316 3.0356 3.0194 2.9956

2.2024 2.3712 2.5161 2.6162 2.6757 2.7016 2.7046 2.6884 2.6713

1.9196 2.0814 2.2245 2.3236 2.3877 2.4177 2.4257 2.4225 2.4128

1.7248 1.8740 2.0076 2.1058 2.1675 2.2035 2.2171 2.2163 2.2155

FA + 2-butanol 0.1043 1264.1 0.2043 1295.8 0.3056 1329.1 0.4083 1364.5 0.5093 1401.3 0.6063 1438.8 0.7068 1480.1 0.8042 1522.5 0.9024 1568.0

1243.5 1274.8 1308.0 1343.4 1380.4 1418.1 1459.9 1503.4 1550.5

1225.0 1256.1 1289.2 1324.7 1361.9 1400.0 1442.6 1487.3 1536.0

1204.5 1235.7 1268.9 1304.5 1341.9 1380.6 1424.4 1470.5 1521.0

1185.6 1216.2 1249.3 1285.3 1323.1 1362.1 1406.8 1453.9 1506.1

1167.6 1197.6 1230.7 1266.9 1305.0 1344.2 1389.5 1437.6 1491.3

FA + 2-butanol 0.1043 4.1402 0.2043 4.0805 0.3056 4.0456 0.4083 4.0412 0.5093 4.0255 0.6063 3.9895 0.7068 3.9294 0.8042 3.8592 0.9024 3.7700

3.0435 3.0642 3.1127 3.1904 3.2611 3.3100 3.3380 3.3509 3.3475

2.5162 2.5515 2.6174 2.7131 2.7998 2.8687 2.9180 2.9485 2.9660

2.1264 2.1666 2.2388 2.3394 2.4351 2.5124 2.5714 2.6113 2.6395

1.8024 1.8484 1.9265 2.0347 2.1376 2.2240 2.2911 2.3378 2.3750

1.5426 1.5925 1.6775 1.7912 1.9034 1.9980 2.0717 2.1291 2.1751

FA + 1,3-butanediol 0.1061 1539.0 0.2004 1536.3 0.3068 1537.2 0.4026 1538.5 0.5033 1543.7 0.6046 1550.4 0.7013 1561.2 0.8073 1577.3 0.9058 1596.6

1521.7 1518.2 1518.3 1519.5 1524.6 1531.3 1542.5 1559.5 1580.2

1503.9 1499.8 1499.9 1501.1 1506.5 1513.8 1525.7 1543.8 1566.3

1488.7 1484.2 1483.6 1484.8 1490.1 1497.6 1509.9 1528.7 1552.5

1475.5 1470.2 1468.8 1469.6 1474.7 1482.1 1494.6 1513.9 1538.9

1463.3 1457.0 1454.8 1455.1 1459.9 1467.1 1479.7 1499.4 1525.5

FA + 1,3-butanediol 0.1061 99.9210 0.2004 78.2234 0.3068 59.7425 0.4026 46.1222 0.5033 34.6248 0.6046 25.0215 0.7013 17.5423 0.8073 10.4652 0.9058 6.5456

74.7246 57.5004 43.1023 32.2046 23.7426 17.0001 12.0003 7.5262 5.0012

53.0652 40.3090 28.9005 21.0949 15.0394 10.3316 7.0232 4.5434 3.5263

40.3644 30.9593 21.9759 15.6594 11.2474 7.4550 5.3292 3.5779 2.7019

31.0606 24.2294 17.4767 12.1365 8.4141 6.1810 4.5452 3.2294 2.6262

24.0363 18.6233 13.8208 9.9991 6.8027 4.6970 3.2993 2.4780 2.2571

FA + 1,4-butanediol 0.1052 1606.0 0.1988 1594.7 0.3041 1585.7 0.4002 1577.7 0.5009 1572.5 0.6022 1569.9 0.6992 1574.7 0.8051 1583.7 0.9050 1597.1

1592.6 1579.2 1568.5 1560.2 1553.9 1551.3 1556.0 1565.5 1580.5

1580.1 1565.3 1553.4 1544.2 1537.7 1534.5 1539.5 1550.0 1566.3

1568.8 1552.0 1539.2 1529.4 1522.1 1518.6 1524.0 1534.8 1552.1

1558.4 1539.9 1525.4 1514.6 1506.5 1503.0 1508.0 1519.6 1537.9

1546.2 1525.7 1510.2 1498.6 1490.6 1486.8 1491.7 1503.8 1524.0

FA + 1,4-butanediol 0.1052 64.5260 0.1988 44.0024 0.3041 30.1005 0.4002 21.2024 0.5009 15.1264 0.6022 11.3254 0.6992 7.9984 0.8051 5.5121 0.9050 4.0256

48.0757 31.1351 19.8171 12.4992 8.0213 6.2330 4.9708 3.9603 3.3719

38.0344 24.0346 13.4196 7.7145 4.7707 3.7223 3.0618 2.6575 2.7538

30.1164 18.5574 9.4984 4.6628 2.6965 2.1875 1.8700 1.9237 2.3663

23.7383 13.8131 6.5406 2.8712 1.6190 1.2725 1.0794 1.5250 1.9981

18.9497 10.7476 5.0937 2.0245 1.1667 1.0029 0.9823 1.2421 1.7059

ing with FA molecules in the mixture will be smaller in case of alkanediols than those available in alkanols. This leads to the formation of loosely packed hydrogen bonded aggregates between unlike molecules in FA + 1,3-butanediol/1,4-butanediol mixtures as compared to those in FA + 1-butanol/2-butanol mixtures, which results in an expansion in volume, i.e., increase in the compressibility of the mixture leading to positive ks values. The values of ks increase with increase in temperature of the mixture for all the four systems under study (Fig. 1). The increase in ks is attributed to the breaking of the H-bonded associates formed between unlike molecules with rise in temperature, leading to an expansion in volume, hence, resulting in an increase in ks values. As expected, the u values are negative (Fig. 2) for all the four binary systems over the entire mole fraction range and at all investigated temperatures and follow the order: 1-butanol > 2-

butanol > 1,3-butanediol > 1,4-butanediol. The magnitude of u values has been considered as an indicator of the strength of the intermolecular interaction between unlike molecules in the mixture [34,35]. In general, the strength of interactions decrease with increasingly negative u values. Thus, the observed trends of u versus x1 (Fig. 2) for the mixtures under study suggest that the order of FA-alkanol interaction follows the sequence: 1-butanol > 2-butanol > 1,3-butanediol > 1,4-butanediol, which further supports the behaviour of ks for these mixtures. The u values decrease (become more negative) with increase in temperature of the mixture (Fig. 2). As expected, these trends of u values with temperature are opposite to those exhibited by ks and these are due to similar reasons as for ks , which further supports the behaviour of ks with temperature. The curves in Fig. 3 indicate that η values are positive for FA + 1-butanol and negative for FA + 1,3-butanediol/1,4-

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A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

Table 4 Coefficients, Ai from Eq. (8) and standard deviations σ (YE ) for FA + alkanol binary mixtures at different temperatures T (K)

A0

A1

FA + 1-butanol ks (×10−10 m2 N−1 ) 293.15 −1.1588 −0.2649 298.15 −1.0714 −0.2390 303.15 −0.9827 −0.2307 308.15 −0.9017 −0.1946 313.15 −0.8170 −0.2125 318.15 −0.7477 −0.2098

A2

A3

A4

␴ (YE )

−0.0327 −0.0022 0.0511 0.1482 0.0980 0.1432

0.0249 −0.0241 0.0381 −0.0207 0.0750 0.1529

0.0065 −0.0301 −0.0309 −0.1770 −0.0316 −0.0238

0.0006 0.0002 0.0010 0.0013 0.0011 0.0016

u (×102 m s−1 ) 293.15 0.2073 298.15 −0.0530 303.15 −0.3054 308.15 −0.5260 313.15 −0.7586 318.15 −0.9796

−0.1032 −0.0294 0.0685 0.1183 0.2355 0.3338

0.0469 −0.0050 −0.0894 −0.1877 −0.1813 −0.2486

−0.0375 −0.0253 −0.0208 0.0704 −0.0087 −0.0524

0.0005 −0.0212 0.0264 0.1358 0.0411 0.0261

0.0006 0.0003 0.0002 0.0018 0.0014 0.0016

η (×10−3 N s m−2 ) 293.15 1.8125 298.15 1.6562 303.15 1.5146 308.15 1.3810 313.15 1.2286 318.15 1.0702

0.6365 0.5489 0.4781 0.3891 0.3386 0.2665

0.1595 −0.0164 −0.1268 −0.3698 −0.3986 −0.4046

−0.2194 −0.2278 −0.2763 −0.1933 −0.3177 −0.2534

−0.2424 −0.1676 −0.1859 0.0271 −0.0602 −0.1239

0.0052 0.0024 0.0018 0.0018 0.0017 0.0021

KsE (×10−14 m5 N−1 mol−1 ) 293.15 −3.0460 −0.4469 298.15 −3.1123 −0.4075 303.15 −3.1791 −0.3805 308.15 −3.2504 −0.3330 313.15 −3.3363 −0.3272 318.15 −3.4473 −0.3072

−0.0843 −0.0536 −0.0140 0.0643 0.0246 0.0630

0.0143 −0.0169 0.0398 −0.0011 0.0782 0.1453

0.0142 −0.0269 −0.0116 −0.1281 −0.0011 0.0166

0.0005 0.0002 0.0006 0.0008 0.0008 0.0012

FA + 2-butanol ks (×10−10 m2 N−1 ) 293.15 −0.4263 −0.0928 298.15 −0.4008 −0.0939 303.15 −0.3744 −0.0899 308.15 −0.3583 −0.1017 313.15 −0.3413 −0.0612 318.15 −0.3076 −0.0250

−0.0858 −0.0375 −0.0385 −0.1181 −0.0040 0.1138

0.0220 0.0369 0.0519 0.1024 0.0496 0.0572

0.0809 0.0519 0.0904 0.2557 0.1053 0.0166

0.0004 0.0003 0.0003 0.0003 0.0012 0.0020

0.0689 −0.0340 −0.0334 0.0023 −0.1040 −0.2381

−0.0404 −0.0284 −0.0247 −0.0389 0.0461 0.0731

−0.0854 −0.0229 −0.1069 −0.2390 −0.1566 −0.0634

0.0006 0.0003 0.0005 0.0009 0.0017 0.0024

u (×102 m s−1 ) 293.15 −1.0557 298.15 −1.1970 303.15 −1.3435 308.15 −1.5026 313.15 −1.6443 318.15 −1.7840

0.2015 0.2703 0.3326 0.4115 0.4411 0.4890

FA + 2-butanol η (×10−3 N s m−2 ) 293.15 0.3744 298.15 0.3058 303.15 0.2473 308.15 0.1893 313.15 0.1400 318.15 0.0882

−0.6885 −0.7124 −0.7195 −0.7294 −0.7459 −0.7565

−0.7210 −0.6533 −0.6306 −0.6113 −0.6164 −0.6433

0.2511 0.3069 0.3224 0.3200 0.3371 0.3499

0.9027 0.7636 0.6528 0.5733 0.4577 0.4268

0.0022 0.0015 0.0013 0.0009 0.0011 0.0009

KsE (×10−14 m5 N−1 mol−1 ) 293.15 −2.7475 −0.1661 298.15 −2.8735 −0.1600 303.15 −3.0001 −0.1240 308.15 −3.1587 −0.1602 313.15 −3.3160 −0.1256 318.15 −3.4607 −0.0894

−0.0839 −0.0498 −0.0477 −0.1030 −0.0097 0.0884

0.0083 0.0246 0.0424 0.0883 0.0566 0.0787

0.0629 0.0254 0.0729 0.1983 0.0768 0.0077

0.0003 0.0002 0.0003 0.0003 0.0007 0.0012

Table 4 (Continued ) T (K)

A0

A1

FA + 1,3-butanediol ks (×10−10 m2 N−1 ) 293.15 1.0126 −0.2462 298.15 1.1225 −0.2580 303.15 1.2315 −0.2619 308.15 1.3461 −0.2694 313.15 1.4685 −0.2800 318.15 1.5979 −0.2909

A2

A3

A4

␴ (YE )

0.0485 0.0841 0.1198 0.1367 0.1707 0.2104

0.0420 0.0467 0.0406 0.0487 0.0568 0.0725

−0.3263 −0.4012 −0.4587 −0.4567 −0.4974 −0.5414

0.0022 0.0021 0.0024 0.0019 0.0019 0.0021

u (×102 m s−1 ) 293.15 −1.3795 298.15 −1.5233 303.15 −1.6672 308.15 −1.8060 313.15 −1.9467 318.15 −2.0904

0.3876 0.4183 0.4442 0.4712 0.4980 0.5288

−0.1131 −0.1945 −0.2578 −0.3220 −0.3803 −0.4330

−0.1329 −0.1334 −0.1179 −0.1304 −0.1269 −0.1656

0.6883 0.8035 0.8514 0.8597 0.8863 0.8970

0.0040 0.0037 0.0041 0.0032 0.0031 0.0031

η (×10−1 N s m−2 ) 293.15 −1.2774 298.15 −1.0503 303.15 −0.8489 308.15 −0.6579 313.15 −0.4932 318.15 −0.3752

−0.4429 −0.3658 −0.2687 −0.1851 −0.1158 −0.0346

−0.3771 −0.1587 −0.1202 0.0354 0.2005 0.0493

−0.0178 0.0906 0.0916 0.1218 0.1156 −0.0072

0.1929 0.1414 0.1890 0.0080 −0.1533 0.0064

0.0019 0.0021 0.0004 0.0013 0.0015 0.0009

KsE (×10−14 m5 N−1 mol−1 ) 293.15 0.2955 0.0914 298.15 0.3583 0.1155 303.15 0.4116 0.1446 308.15 0.4784 0.1707 313.15 0.5572 0.1981 318.15 0.6448 0.2291

−0.0297 −0.0041 0.0224 0.0308 0.0549 0.0781

−0.0158 −0.0213 −0.0284 −0.0207 −0.0162 −0.0073

−0.2024 −0.2596 −0.3030 −0.3003 −0.3315 −0.3569

0.0017 0.0017 0.0020 0.0016 0.0015 0.0016

FA + 1,4-butanediol ks (×10−10 m2 N−1 ) 293.15 1.2081 −0.4548 298.15 1.3553 −0.4727 303.15 1.5084 −0.5060 308.15 1.6583 −0.5235 313.15 1.8261 −0.5480 318.15 1.9923 −0.5641

−0.1086 −0.0408 −0.0228 0.0047 0.0141 0.1472

0.0539 0.0513 0.0804 0.0818 0.0767 0.0725

0.0449 −0.0499 −0.0291 −0.0043 0.0183 −0.1464

0.0036 0.0036 0.0038 0.0048 0.0043 0.0043

u (×102 m s−1 ) 293.15 −1.7555 298.15 −1.9760 303.15 −2.2026 308.15 −2.4106 313.15 −2.6378 318.15 −2.8465

0.6760 0.6857 0.7271 0.7261 0.7418 0.7274

0.2356 0.0640 −0.0003 −0.0618 −0.1046 −0.3459

−0.0890 −0.0839 −0.1351 −0.1034 −0.1008 −0.0795

−0.1012 0.1163 0.0752 −0.0019 −0.0502 0.2348

0.0071 0.0068 0.0073 0.0088 0.0077 0.0074

η (×10−1 N s m−2 ) 293.15 −1.3879 298.15 −1.1874 303.15 −1.0020 308.15 −0.8423 313.15 −0.7012 318.15 −0.5799

−0.8950 −0.7924 −0.7095 −0.6048 −0.5255 −0.4435

−0.5780 −0.2342 −0.2017 −0.1322 −0.2020 −0.1705

0.0141 0.1459 0.3561 0.3836 0.3442 0.2873

0.1630 0.0367 0.2877 0.3143 0.4151 0.3003

0.0027 0.0033 0.0007 0.0011 0.0009 0.0011

KsE (×10−14 m5 N−1 mol−1 ) 293.15 0.6649 −0.0148 298.15 0.7727 0.0118 303.15 0.8820 0.0280 308.15 0.9927 0.0541 313.15 1.1199 0.0796 318.15 1.2419 0.1147

−0.1575 −0.1149 −0.1086 −0.0862 −0.0859 −0.0073

0.0127 0.0095 0.0355 0.0449 0.0469 0.0458

−0.0065 −0.0707 −0.0532 −0.0483 −0.0314 −0.1348

0.0026 0.0026 0.0027 0.0034 0.0031 0.0032

A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

Fig. 1. Plots of deviations in isentropic compressibility, ks , vs. mole fraction, x1 of formamide (FA) for the binary mixtures (a) at 298.15 K and (b) at 318.15 K. Points show experimental values and curves show smoothed values using Eq. (8).

butanediol mixtures over the entire mole fraction range and at each investigated temperature, whereas for FA + 2-butanol mixtures the η values exhibit sigmoid trend, wherein η changes sign from negative to positive as the concentration of FA in the mixture is increased. The η values for FA + 1butanol mixtures at 298.15 K obtained in this work compare well with those reported by Garcia et al. [15] for these mix-

51

Fig. 2. Plots of deviations in ultrasonic speed, u vs. mole fraction, x1 of formamide (FA) for the binary mixtures (a) at 298.15 K and (b) at 318.15 K. Points show experimental values and curves show smoothed values using Eq. (8).

tures at 298.15 K. The positive η values for FA + 1-butanol and small negative/positive η values for FA + 2-butanol mixtures indicate the presence of significant interactions between unlike molecules in these mixtures. The large negative η values for FA + 1,3-butanediol/1,4-butanediol mixtures suggest the presence of weak interactions between unlike molecules [36,37]. Also, large negative η values are observed for the mixtures having component molecules that have too different molecular sizes [36], as in case of FA + 1,3-butanediol/1,4-butanediol mixtures. It is observed for all the four binary systems under study, the η

52

A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

¯ E of FA vs. mole fracFig. 4. Plots of excess partial molar compressibility, K m,1 tion, x1 of formamide (FA) in the binary mixtures at 298.15 K.

Fig. 3. Plots of deviations in viscosity, η vs. mole fraction, x1 of formamide (FA) for the binary mixtures (a) at 298.15 K and (b) at 318.15 K. Scale units of η are (×10−3 N s m−2 ) for FA + 1-butanol/2-butanol and (×10−1 N s m−2 ) for FA + 1,3-butanediol/1,4-butanediol mixtures. Points show experimental values and curves show smoothed values using Eq. (8).

values tend to vary towards zero (Fig. 3) as the temperature of the mixture increases, suggesting that the systems tend to shift towards ideal behaviour with rise in temperature. The trends observed in ks , u, and η with composition and temperature indicate that the interactions in these mixtures follow the order: 1-butanol > 2-butanol > 1,3-butanediol > 1,4butanediol, which is in agreement with the conclusions drawn in our previous paper [16] from the variations of excess molar

volumes, VmE of these mixtures with composition and temperature. ¯ m,1 and K ¯ m,2 , excess The partial molar compressibilities, K E E ¯ ¯ partial molar compressibilities, Km,1 and Km,2 , of component 1 (FA) and component 2 (alkanol) in these mixtures over entire composition range at 298.15 K were calculated by using the procedure [8,38], presented in our earlier work ¯ E and K ¯ E with composition at [4]. The variations of K m,1 m,2 298.15 K are presented in Figs. 4 and 5, respectively. A close ¯E perusal of Figs. 4 and 5 indicates that the values of K m,1 E ¯ and Km,2 are negative for FA + 1-butanol/2-butanol and positive for FA + 1,3-butanediol/1,4-butanediol binary mixtures over the whole composition range. In general, the negative ¯ E and K ¯ E values indicate the presence of significant K m,1 m,2 solute-solvent interactions between unlike molecules [39], ¯ E and K ¯ E values indicate preswhereas the positive K m,1 m,2 ence of solute–solute/solvent–solvent interactions between like molecules [39] in the mixture. The values of partial molar ¯ ◦ and K ¯ ◦ , and excess partial molar comcompressibilities, K m,1 m,2 ◦E ◦E ¯ ¯ pressibilities, K m,1 and Km,2 , of FA and alkanols at infinite dilution were calculated by using the relations presented in our earlier work [4]. Furthermore, the apparent molar compressibilities, Kφ,1 and ¯◦ Kφ,2 , limiting apparent (partial) molar compressibilities, K φ,1 ◦ ¯ ◦ , and excess partial molar compressibilities, K ¯ E and and K φ,2 φ,1 ¯ ◦ E , of FA and alkanols at infinite dilution, respectively, in these K φ,2 mixtures at each investigated temperature, have been calculated ¯◦ ,K ¯◦ , by using another approach [4,36,40,41]. The values K φ,1 m,1 ◦E ◦E ◦E ◦E ∗ ◦ ◦ ∗ ¯ ,K ¯ ,K ¯ ,K ¯ ,K ¯ ,K ¯ ,K ¯ , and K ¯ K for all the s,1 m,2 φ,2 s,2 m,1 φ,1 m,2 φ,2 four binary systems at each investigated temperature are listed

Table 5 ¯ ◦ , K∗ , K ¯ ◦E , K ¯ ◦E , K ¯◦ ,K ¯ ◦ , K∗ , K ¯ ◦ E , and K ¯ ◦ E for the binary mixtures at different temperatures ¯◦ ,K The values of K m,1 φ,1 s,1 m,1 φ,1 m,2 φ,2 s,2 m,2 φ,2 T (K)

¯ ◦ (×10−14 m5 K ¯ ◦ (×10−14 m5 K m,1 φ,1 −1 −1 N mol ) N−1 mol−1 )

∗ (×10−14 m5 Ks,1 −1 N mol−1 )

¯ ◦ E (×10−14 m5 K ¯ ◦ E (×10−14 m5 K m,1 φ,1 N−1 mol−1 ) N−1 mol−1 )

¯ ◦ (×10−14 m5 K ¯ ◦ (×10−14 m5 K m,2 φ,2 −1 −1 N mol ) N−1 mol−1 )

∗ (×10−14 m5 Ks,2 −1 N mol−1 )

¯ ◦ E (×10−14 m5 K ¯ ◦ E (×10−14 m5 K m,2 φ,2 N−1 mol−1 ) N−1 mol−1 )

−2.201 −2.265 −2.134 −2.194 −2.090 −2.031

1.344 1.379 1.409 1.441 1.474 1.508

−3.549 −3.617 −3.545 −3.648 −3.562 −3.530

−3.545 −3.644 −3.543 −3.635 −3.564 −3.539

4.420 4.629 4.822 4.996 5.237 5.449

4.418 4.330 4.823 5.003 5.239 5.452

7.103 7.398 7.686 7.976 8.301 8.655

−2.684 −2.768 −2.864 −2.980 −3.064 −3.206

−2.685 −3.068 −2.863 −2.973 −3.062 −3.203

FA + 2-butanol 293.15 −1.582 298.15 −1.655 303.15 −1.647 308.15 −1.694 318.15 −1.844 318.15 −1.868

−1.585 −1.655 −1.655 −1.714 −1.853 −1.875

1.344 1.379 1.409 1.441 1.474 1.508

−2.926 −3.033 −3.057 −3.135 −3.318 −3.375

−2.929 −3.034 −3.064 −3.155 −3.327 −3.383

4.888 5.069 5.263 5.537 5.722 5.920

4.884 5.069 5.259 5.526 5.717 5.921

7.499 7.832 8.156 8.529 8.902 9.274

−2.611 −2.763 −2.893 −2.992 −3.180 −3.354

−2.615 −2.763 −2.897 −3.003 −3.185 −3.353

FA + 1,3-butanediol 293.15 1.483 298.15 1.567 303.15 1.656 308.15 1.800 318.15 1.936 318.15 2.095

1.503 1.593 1.685 1.827 1.966 2.126

1.344 1.379 1.409 1.441 1.474 1.508

0.139 0.189 0.247 0.359 0.463 0.588

0.159 0.214 0.276 0.386 0.492 0.618

3.767 3.883 4.009 4.152 4.281 4.411

3.787 3.908 4.037 4.180 4.311 4.444

3.779 3.883 3.995 4.093 4.182 4.267

−0.012 0.000 0.015 0.059 0.099 0.144

0.008 0.025 0.042 0.087 0.129 0.177

FA + 1,4-butanediol 293.15 1.843 298.15 1.987 303.15 2.193 308.15 2.398 318.15 2.603 318.15 2.768

1.848 1.997 2.199 2.402 2.605 2.778

1.344 1.379 1.409 1.441 1.474 1.508

0.499 0.608 0.784 0.957 1.129 1.260

0.504 0.618 0.790 0.961 1.131 1.270

3.847 3.975 4.128 4.289 4.460 4.589

3.853 3.986 4.138 4.299 4.469 4.606

3.344 3.409 3.471 3.529 3.584 3.650

0.503 0.566 0.657 0.759 0.876 0.939

0.509 0.577 0.667 0.770 0.885 0.956

A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

FA + 1-butanol 293.15 −2.205 298.15 −2.239 303.15 −2.136 308.15 −2.207 318.15 −2.088 318.15 −2.022

53

54

A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

¯ E of alkanol vs. mole Fig. 5. Plots of excess partial molar compressibility, K m,2 fraction, x1 of formamide (FA) in the binary mixtures at 298.15 K.

Fig. 6. Plots of free energy of activation of viscous flow, G* vs. mole fraction, x1 , of formamide (FA) for FA + alkanol binary mixtures.

in Table 5. A close perusal of Table 5 indicates that the val¯ ◦ E and K ¯ ◦ E , and K ¯ ◦ E and K ¯ ◦ E are nearly same ues of K m,1 m,2 φ,1 φ,2 in magnitudes for both the components in each mixture and ¯ ◦ E and K ¯ ◦ E , and K ¯ ◦E exhibit similar trends. The values of K m,1 m,2 φ,1 ¯ ◦ E are negative (Table 5) for FA + 1-butanol/2-butanol and K φ,2 and positive for FA + 1,3-butanediol/1,4-butanediol mixtures. ¯E , K ¯E , K ¯ ◦E , K ¯ ◦E , K ¯ ◦ E and K ¯ ◦E The magnitude of K m,1 m,2 m,1 m,2 φ,1 φ,2 values for these mixtures follow the order: 1-butanol < 2butanol < 1,3-butanediol < 1,4-butanediol, which indicates that the order of solute–solvent interactions between FA and alkanol molecules in the mixture follows the sequence: 1butanol > 2-butanol > 1,3-butanediol > 1,4-butanediol.which is also the order of solute-solvent interactions between FA and alkanol molecules in the mixture. ¯ ◦E , K ¯ ◦E , K ¯ ◦ E , and K ¯ ◦ E values have been anaThe K m,1 m,2 φ,1 φ,2 lyzed in terms of structural and geometrical compressibility as suggested by Hall [42] and others [40,41]. The structural compressibility results from the breakdown of associated structure (on addition of FA in alkanols) while geometrical compressibility is due to simultaneous compression of the molecules (due to formation of hydrogen-bond between FA and alkanol molecules) leading to contraction in volume and decrease in the ¯ ◦E , average intermolecular distance. The observed values of K m,1 ¯ ◦E , K ¯ ◦ E , and K ¯ ◦ E indicate that the structural compressibility K m,2 φ,1 φ,2 factor dominates in case of FA + 1,3-butanediol/1,4-butanediol, whereas geometrical compressibility factor dominates in FA + 1¯ ◦E , K ¯ ◦E , K ¯ ◦ E , and butanol/2-butanol mixtures. Also, the K m,1 m,2 φ,1 ¯ ◦ E values increase with increase in temperature (Table 5) for K φ,2 each binary mixtures under study. These trends further supports ¯ E and K ¯ E values for the trends observed in ks , u, η, K m,1 m,2 the binary mixtures under study.

Further, the thermodynamics parameters of viscous flow have been investigated by using the Eyring viscosity equation [43,44]:     hN G∗ η= exp (9) V RT where h is the Planck’s constant, N the Avogadro number and G* is the free energy of activation of viscous flow. Eq. (9) on combining with G* = H* − TS* gives the equation:     ηV H ∗ R ln = − S ∗ (10) hN T where H* and S* are the enthalpy and entropy of activation of viscous flow, respectively. The plots of the left hand side of Eq. (10), i.e., R ln (␩V/hN) versus 1/T for all the four binary systems were found to be almost linear for each composition. This indicates that H* is independent of temperature in the investigated temperature range. The values of H* and S* were obtained by using linear regression of R ln (␩V/hN) versus 1/T at each composition. The values of G* , H* , and S* are presented graphically in Figs. 6–8. Fig. 6 indicate that the values of G* decrease with increase in mole fraction, x1 of FA for all the mixtures except FA + 1-butanol for which G* values initially increase and then decrease as mole fraction of FA increases in the mixture. This suggests that the formation of an activated species that is necessary for viscous flow is easier in FA-rich region in comparison to that in alkanol-rich region. For FA + 1-butanol/2-butanol mixtures (Fig. 7), the H* values decrease with increase in x1 of FA. This suggests that the formation of an activated species that is necessary for viscous flow is easier in FA-rich region in comparison to that

A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

Fig. 7. Plots of enthalpy of activation of viscous flow, H* vs. mole fraction, x1 , of formamide (FA) for FA + alkanol binary mixtures.

in 1-butanol/2-butanol-rich region. For FA + 1,3-butanediol/1,4butanediol mixtures (Fig. 7), the H* values increase exhibit maximum then decrease with increase in x1 of FA. This suggests that the formation of an activated species that is necessary

Fig. 8. Plots of entropy of activation of viscous flow, S* vs. mole fraction, x1 , of formamide (FA) for FA + alkanol binary mixtures. Scale units of S* are (J mol−1 K−1 ) for FA + 1-butanol and (10 J mol−1 K−1 ) for FA + 2-butanol/1,3butanediol/1,4-butanediol mixtures.

55

for viscous flow is easier in near equimolar compositions as compared to FA/1,3-butanediol/1,4-butanediol-rich regions. The values of S* are found positive (Fig. 8) for all the four binary systems under study in the investigated temperature range. FA + 1-butanol/2-butanol mixtures, the S* values decrease with increase in the mole fraction, x1 of FA in the mixture. This suggests that during the viscous flow there is more structuredness in FA rich regions, as a result of the ease in which the activated species forms as compared to that in 1butanol/2-butanol-rich region, where S* values are large. For FA + 1,3-butanediol/1,4-butanediol mixtures, the values of S* increase to a maximum and then decrease as the mole fraction, x1 of FA increases in the mixture. The increase in S* values for FA + 1,3-butanediol/1,4-butanediol mixtures with increase in FA concentration indicates that, during the viscous flow, there is more structuredness in FA/1,3-butanediol/1,4-butanediol-rich regions, as a result of the ease in which the activated species forms as compared to that in near equimolar region where S* values are large. Similar results for G* , H* and S* values have also been observed for DMF + 1,2-ethanediol binary systems, wherein the H* and S* values were reported to increase as the amount of alkanol increases in the mixture [45], as in case of the mixtures under study, where the H* and S* values become large in alkanol-rich regions. 4. Conclusion The ultrasonic speeds and viscosities of the binary mixtures of FA with 1-butanol, 2-butanol, 1,3-butanediol and 1,4-butanediol have been measured and various derived parameters, viz., ks , ¯E ,K ¯E ,K ¯ ◦E , K ¯ ◦E , K ¯ ◦E , K ¯ ◦ E , G* , H* , and u, η, K m,1 m,2 m,1 m,2 φ,1 φ,2 S* were calculated. The variation of these properties with composition indicates that the interactions in these mixtures follow the order: 1-butanol > 2-butanol > 1,3-butanediol > 1,4butanediol, which decreases with rise in temperature. It is observed that the order of interactions in these mixtures depends upon the number and position of hydroxyl groups in these alkanol molecules. The FA–alkanol interaction decreases with increase in the number of hydroxyl groups and when hydroxyl group is attached to the ␤- or ␥-carbon atom in the alkanol molecule. List of symbols Ai adjustment parameters of Eq. (8) G* free energy of activation of viscous flow h Plancks constant (J s) H* enthalpy of activation of viscous flow ks isentropic compressibility (m2 N−1 ) ks deviations in isentropic compressibility molar compressibility (m5 N−1 mol−1 ) Ks Kφ apparent molar compressibility ¯m K partial molar compressibility ◦ ¯m K partial molar compressibility at infinite dilution ¯ φ◦ limiting apparent (partial) molar compressibility K KsE excess molar compressibility (m5 N−1 mol−1 )

56 E ¯m K ◦E ¯m K ◦E ¯φ K

M N R S* T u u V x

A.K. Nain / Fluid Phase Equilibria 265 (2008) 46–56

excess partial molar compressibility excess partial molar compressibility at infinite dilution excess apparent (partial) molar compressibility at infinite dilution molar mass (kg mol−1 ) Avogadro number universal gas constant (J K−1 mol−1 ) entropy of activation of viscous flow temperature (K) ultrasonic speed deviations in ultrasonic speed molar volume (m3 mol−1 ) mole fraction

Greek letters η viscosity η deviations in viscosity ρ density (kg m−3 ) σ

standard deviation σ(Y E ) =



E −Y E ) (YExpt cal m−n

2

1/2

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