High Pressure Thermodynamic and Acoustic Properties of Decan-1-ol

J. Phys. Chem. B 2009, 113, 11649–11661

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High Pressure Thermodynamic and Acoustic Properties of Decan-1-ol + Heptane Mixtures. A Theoretical and Experimental Study Marzena Dzida* Institute of Chemistry, UniVersity of Silesia, Szkolna 9, 40-006 Katowice, Poland ReceiVed: April 23, 2009; ReVised Manuscript ReceiVed: June 29, 2009

This paper reports a theoretical study of decan-1-ol + heptane and ethanol + heptane systems and experimental data of decan-1-ol + heptane mixtures as a function of temperature and pressure over the whole composition range. The ability of the modifications introduced into the original ERAS model in determining thermodynamic excess properties of decan-1-ol + heptane and ethanol + heptane mixtures at high pressures is tested. This model was found to be sufficient for describing semiquantitatively excess volumes and excess enthalpies and qualitatively excess heat capacities under high pressure. The densities and speeds of sound in decan-1-ol + heptane mixtures were measured over the whole concentration range within the temperature interval from 293 to 318 K at atmospheric pressure and at pressures up to 101 MPa, respectively. The densities, heat capacities and appropriate excesses of these binaries were calculated for the same temperatures and pressures up to 100 MPa. In the calculations the acoustic method was applied. The effects of pressure and temperature on the excess volume, excess enthalpy, and the excess heat capacity of decan-1-ol + heptane mixtures are analyzed and compared with those of ethanol + heptane and dodecane + heptane mixtures. Properties of the alkan-1-ol + alkane mixtures are explained in terms of the self-asssociation of the alkanols, free volume effect and the nonspecific interactions between the alcohol and heptane basing on the results obtained from the modified ERAS model. 1. Introduction Knowledge of thermodynamic properties of both pure organic liquids and their mixtures is of practical interest to the industry in very different fields ranging from the chemical industry to petrochemistry, pharmaceutical industries, and food technology, because applied procedures relate to temperature and pressure dependences of used liquids. In the petrochemical and automotive industries, an important point of interest is the influence of “biocomponent” additives, such as alcohols, ethers or esters, on the properties of fuels and greases. Therefore, the interest increases in the mixtures of hydrocarbons with alcohols, ethers or esters. Macroscopic properties are related to molecular level structure and intermolecular interactions. Alcohols + alkanes are convenient model systems for studying association phenomena, nonspecific physical interactions between the real species present in the mixture and the interstitial accommodation of the alkane molecules in the alkan-1-ol multimer structure in the liquid phase. Therefore, systematic studies of thermodynamic properties of binary alkan-1-ol + alkane mixtures are essential to the creation and testing of theoretical models. Experimental data of the thermodynamic and mainly acoustic properties of alkan1-ol + alkanes mixtures at high pressures are still rather scarce.1 The system investigated the most intensively under high pressures was hexan-1-ol + hexane. Randzio et al.2 measured thermal expansion coefficient of the above mixtures within the temperature range 302.6-503.1 K and from just above saturation pressures to 350 MPa. Coxam et al.3 reported experimental excess enthalpies of hexan-1-ol + hexane mixtures at temperatures from 323 to 513 K and pressures from 3.5 to 15 MPa. They compared measured excess enthalpies with UNIFAC calculations. Troncoso et al.4 measured densities of hexan-1-ol * E-mail: [email protected].

+ hexane mixtures in the temperature range from 278.15 to 333.13 K and at pressures up to 40 MPa. Recently, Navia et al.5 measured the thermal expansion coefficient of hexan-1-ol + hexane within the temperature and pressure intervals 278.15-348.15 K and 0.5-50 MPa, respectively. Lafitte et al.1 applied SAFT-VR Mie EOS for prediction of the temperature and pressure dependence of the thermal expansion and excess enthalpy of hexan-1-ol + hexane mixtures. They also described the excess enthalpy of this system and the speed of sound in ethanol + heptane mixtures under high pressures. To the best of my knowledge the speeds of sound in alkanol + alkane mixtures have been measured only in my laboratory. This work is a part of systematic studies of thermodynamic and acoustic properties of alkan-1-ol + heptane mixtures under elevated pressures. The ethanol + heptane and propan-1-ol + heptane mixtures have been investigated previously.6-9 In this paper, the experimental densities and speeds of sound in the decan-1-ol + heptane mixtures are reported for the temperature range from 293 to 318 K at atmospheric and at pressures up to 101 MPa, respectively. Additionally, the densities and heat capacities of the system under test calculated for the pressures up to 100 MPa and in the temperature range from 293.15 to 318.15 K, by the acoustic method, are presented. To the best of my knowledge, the acoustic and thermodynamic properties of this system have never been investigated under high pressures. Thus, the first objective of this work is to study the influence of the temperature and pressure on the excess volumes, excess enthalpies, and excess heat capacities of decan-1-ol + heptane mixtures. The results from the ERAS model calculations for decan-1ol + heptane mixtures under atmospheric pressure show that the chemical contribution to excess molar volumesarising from H-bonding disruptionsis small and positive, while the physical contributionswhich arises from nonpolar van der Waals interactions including the free volume effects on mixingsis

10.1021/jp903763c CCC: $40.75  2009 American Chemical Society Published on Web 07/28/2009

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J. Phys. Chem. B, Vol. 113, No. 34, 2009

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TABLE 1: Speeds of Sound in {Decan-1-ol (1) + Heptane (2)} Mixtures within the Temperature Range 293 to 318 K at Atmospheric Pressure x1

T, K

u, m · s-1

x1

T, K

u, m · s-1

x1

T, K

u, m · s-1

0.0127 0.0499 0.0892 0.2101 0.3046 0.4159 0.5219 0.6197 0.6837 0.8158 0.9093 0.0127 0.0499 0.0892 0.2101 0.3046 0.4159 0.5219 0.6197 0.6837 0.8158 0.9093

293.10 293.09 293.10 293.04 293.13 293.09 293.11 293.12 293.10 293.13 293.14 298.10 298.08 298.10 298.12 298.09 298.07 298.07 298.11 298.08 298.10 298.10

1153.78 1162.10 1172.20 1201.88 1225.41 1254.29 1281.71 1306.95 1323.41 1355.90 1377.30 1132.13 1140.68 1150.80 1180.82 1205.21 1234.64 1262.56 1288.20 1304.92 1337.95 1359.74

0.0127 0.0499 0.0892 0.2101 0.3046 0.4159 0.5219 0.6197 0.6837 0.8158 0.9093 0.0127 0.0499 0.0892 0.2101 0.3046 0.4159 0.5219 0.6197 0.6837 0.8158 0.9093

303.08 303.05 303.09 303.10 303.08 303.05 303.05 303.09 303.07 303.08 303.11 308.07 308.06 308.06 308.08 308.07 308.04 308.04 308.08 308.04 308.06 308.07

1110.71 1119.48 1129.75 1160.37 1185.20 1215.20 1243.61 1269.66 1286.59 1320.12 1342.20 1089.38 1098.26 1108.90 1140.10 1165.36 1195.91 1224.79 1251.22 1268.51 1302.51 1324.96

0.0127 0.0499 0.0892 0.2101 0.3046 0.4159 0.5219 0.6197 0.6837 0.8158 0.9093 0.0127 0.0499 0.0892 0.2101 0.3046 0.4159 0.5219 0.6197 0.6837 0.8158 0.9093

313.02 313.04 313.04 313.06 313.05 313.02 313.02 313.06 313.02 313.04 313.05 318.23 318.24 318.23 318.25 318.24 318.19 318.19 318.23 318.21 318.23 318.24

1068.36 1077.28 1088.20 1120.07 1145.68 1176.87 1206.22 1233.01 1250.54 1285.05 1307.84 1046.33 1055.54 1066.82 1099.30 1125.50 1157.19 1187.14 1214.28 1232.04 1267.01 1290.18

negative and predominated.10 Therefore, the next objective of this work is to compare the effects of temperature and pressure on excess volumes, excess enthalpies, and excess isobaric heat capacities of mixtures under test with systems, which characterized, on one hand, a weak association between molecules such as long linear alkanes termed orientational order or correlation of molecular orientations and, on the other hand, systems with strong associated alcohol molecules. Thus, high pressure thermodynamic and acoustic properties of decan-1-ol + heptane mixtures are compared with those of dodecane + heptane and ethanol + heptane mixtures. For description of high pressure excess functions of alcohol + heptane mixtures modified model ERAS11 was applied. 2. Experimental Section 2.1. Materials. The following chemicals have been used: heptane (POCh [Polish Chemicals], analytically pure, minimum 0.99 mass fraction purity C7H16) and decan-1-ol from Aldrich, minimum 0.99 mass fraction purity C10H21OH. The purities of these chemicals were tested by comparison of the densities, speeds of sound, and molar heat capacities with literature values in the previous paper.10 2.2. Measurements and Instrumentation. The mixtures were prepared by weighing. The balance accuracy was (6 × 10-4 g. Each sample was degassed in an ultrasonic cleaner just before the measurement. The speed of sound was measured at atmospheric and higher pressures using two measuring sets designed and constructed in our laboratory.12,13 The pressure was provided by a hand operated hydraulic press and was measured with a strain gauge measuring system (Hottinger Baldwin System P3MD) with an accuracy better than 0.15%. A stability of (0.03 MPa during the measurement was achieved. The temperature was measured using an Ertco Hart 850 platinum resistance thermometer with an accuracy of ( 0.05 K and resolution of 0.001 K. During the measurements, the stability of temperature was (0.005 K and (0.01 K at atmospheric and high pressures, respectively. All temperatures reported in this work are expressed in the International Temperature Scale of 1990 (ITS-90). Redistilled water was used as

standard for the calibration of the ultrasonic apparatus. Its electrolytic conductivity was 1 × 10-4 Ω-1 · m-1. The speeds of sound in water calculated from the polynomial of Marczak14 at atmospheric pressure and from the Kell and Whalley15 polynomial at higher pressures were taken as true values. The reproducibility of the measured speeds of sound was better than (0.02% at atmospheric pressure and (0.04% under elevated pressures. The uncertainties under atmospheric and elevated pressures were estimated to be better than (0.5 m · s-1 and (1 m · s-1, respectively. Other details of the highpressure device and the method of the speed of sound measurements can be found in the previous papers.12,13 The density was measured with a bicapillary pycnometer. The bicapillary pycnometer was calibrated with redistilled water of electrolytic conductivity as above and degassed by boiling just before each measurement. The uncertainty of the density measurements was 0.05 kg · m-3, whereas the reproducibility was estimated to be better than 0.003 kg · m-3. 3. Measurement Results The speeds of sound were measured for the whole concentration range within the temperature limits from 293 to 318 K and under pressures varying from atmospheric pressuer up to 101 MPa. The measured speeds of sound at atmospheric pressure and under higher pressures are listed in Tables 1 and 2, respectively. The experimental speeds of sound in pure heptane and decan-1-ol have been reported in the previous papers.10,16,17 Since the speeds under the atmospheric pressure and the elevated pressures were measured separately, it was necessary to determine the temperature and concentration dependences of the speeds of sound in order to calculate the speeds at atmospheric pressure for concentrations and temperatures at which they have been measured under elevated pressures. The best description of the dependences of the speed of sound on temperature and concentration was obtained using the following formula:

u0 ) u0,1x1 + u0,2(1 - x1) + ∆u0

(1)

Properties of Decan-1-ol + Heptane Mixtures

J. Phys. Chem. B, Vol. 113, No. 34, 2009 11651

TABLE 2: Speeds of Sound in {Decan-1-ol (1) + Heptane (2)} Mixtures at Pressures up to 101 MPa within the Temperature Range 293 to 318 K T, K

p, MPa

u, m · s-1

T, K

p, MPa

u, m · s-1

p, MPa

u, m · s-1

T, K

p, MPa

u, m · s-1

292.80 292.80 292.76 292.80 292.87 293.03 293.02 292.97 297.88 297.82 297.84 297.83

15.20 30.39 45.59 45.59 60.79 75.99 91.18 101.32 15.20 30.39 45.59 60.79

1259.02 1344.12 1419.18 1418.98 1486.33 1547.58 1605.20 1641.36 1239.48 1326.21 1402.29 1471.04

297.96 298.07 297.98 302.89 302.98 303.04 303.00 303.03 303.06 303.07 308.00 308.00

75.99 91.18 101.32 15.20 30.39 45.59 60.79 75.99 91.18 101.32 15.20 30.39

x1 ) 0.0111 1533.09 308.00 1590.61 308.01 1627.45 308.07 1220.65 308.02 1308.43 308.02 1385.37 307.96 1455.07 313.03 1518.18 313.07 1576.62 313.07 1613.54 313.05 1201.85 313.07 1291.48 313.08

45.59 60.79 75.99 91.18 101.32 15.20 15.20 30.39 45.59 60.79 75.99 91.18

1369.66 1440.00 1503.88 1562.62 1600.17 1202.16 1183.91 1274.66 1354.20 1425.44 1489.91 1549.16

313.14 313.04 318.23 318.23 318.23 318.24 318.24 318.23 318.22

101.32 45.59 15.20 30.39 45.59 60.79 75.99 91.18 101.32

1586.61 1354.15 1164.70 1257.71 1338.48 1410.50 1475.96 1535.63 1573.62

292.80 292.80 292.81 292.85 292.92 292.95 292.94 293.15 297.98 297.97 297.96

15.20 30.40 45.59 60.79 75.99 91.19 101.32 101.32 15.20 30.39 45.59

1258.78 1343.83 1418.57 1486.06 1547.40 1604.98 1641.10 1640.99 1238.90 1325.41 1401.57

297.97 297.97 297.97 297.98 302.91 302.90 302.91 302.92 302.96 302.95 302.95

60.79 75.99 91.18 101.32 15.20 30.39 45.59 60.79 75.99 91.18 101.32

x1 ) 0.0147 1470.18 307.98 1532.59 307.98 1590.40 307.98 1626.86 307.98 1220.39 307.98 1308.42 307.98 1385.47 307.99 1454.86 312.90 1517.89 312.92 1576.47 312.93 1613.43 312.96

15.20 30.39 45.59 60.79 75.99 91.18 101.32 15.20 30.40 45.59 60.79

1201.75 1291.34 1369.52 1439.79 1503.68 1562.30 1599.84 1183.70 1274.96 1354.31 1425.42

312.97 312.97 312.95 318.37 318.36 318.34 318.33 318.45 318.45 318.45

75.99 91.18 101.32 15.20 30.39 45.59 60.79 75.99 91.18 101.32

1489.83 1549.05 1586.66 1164.10 1257.17 1337.82 1409.94 1474.93 1534.59 1572.58

292.90 292.90 292.86 292.88 292.90 292.93 292.91 292.91 297.90 297.96 297.92

15.20 30.39 45.59 60.79 60.79 75.99 91.18 101.32 15.20 30.39 45.59

1265.20 1349.35 1423.72 1490.55 1490.56 1551.68 1608.96 1644.59 1245.92 1331.43 1407.00

297.90 297.95 298.00 298.00 302.96 302.98 302.99 302.99 302.98 302.96 302.99

60.79 75.99 91.18 101.32 15.20 30.39 45.59 60.79 75.99 91.18 101.32

x1 ) 0.0508 1475.04 307.95 1536.74 307.95 1594.23 307.97 1630.46 307.99 1226.59 307.98 1313.66 307.99 1390.07 308.00 1459.16 312.96 1521.78 312.95 1579.90 312.95 1616.68 312.96

15.20 30.39 45.59 60.79 75.99 91.18 101.32 15.20 30.39 45.59 60.79

1208.01 1296.71 1374.27 1443.90 1507.43 1565.78 1602.96 1189.65 1279.89 1358.71 1429.35

312.97 312.96 312.96 318.41 318.44 318.44 318.46 318.46 318.48 318.55

75.99 91.18 101.32 15.20 30.39 45.59 60.79 75.99 91.18 101.32

1493.50 1552.20 1589.70 1170.32 1262.23 1342.22 1413.67 1478.54 1537.78 1575.39

293.00 293.00 293.00 293.00 293.00 293.01 293.01 297.99 298.00 297.94 297.93

15.20 30.40 45.60 60.79 75.99 91.19 101.32 15.20 30.40 45.60 60.79

1285.21 1366.73 1439.18 1504.56 1564.36 1620.72 1655.59 1266.36 1349.41 1423.10 1489.14

297.94 297.99 297.99 302.96 303.03 303.08 303.11 303.11 303.11 303.13 303.15

75.99 91.18 101.32 15.20 30.40 45.60 60.79 75.99 91.18 101.32 101.32

x1 ) 0.1530 1549.68 307.99 1606.17 308.00 1641.56 308.00 1247.86 308.05 1332.09 308.03 1406.46 308.02 1473.53 308.03 1534.68 313.06 1591.79 313.04 1627.53 313.05 1627.49 313.04

15.20 30.40 45.59 60.79 75.99 91.18 101.32 15.20 30.40 45.59 60.79

1229.24 1315.17 1390.59 1458.69 1520.55 1578.06 1614.51 1210.94 1298.33 1374.89 1443.75

313.04 313.05 313.05 318.42 318.51 318.51 318.48 318.55 318.46 318.51 318.76

75.99 91.18 101.32 15.20 30.40 45.60 60.79 75.99 75.99 91.18 101.32

1506.61 1564.33 1601.19 1191.63 1280.56 1358.44 1428.33 1491.61 1491.78 1549.99 1587.02

292.97 293.02 292.97 293.01 293.00 293.02 292.95 297.98 297.96 297.96 297.97

15.20 30.40 45.60 60.79 75.99 91.18 101.32 15.20 30.39 45.59 60.79

1316.96 1394.50 1464.56 1527.64 1585.92 1640.41 1674.40 1298.61 1377.97 1448.73 1512.92

297.98 297.97 297.99 302.89 302.89 302.89 302.87 302.91 302.93 302.93 308.03

91.18 75.99 101.32 15.20 30.40 45.60 60.79 75.99 91.18 101.32 15.20

x1 ) 0.2911 1626.53 307.98 1571.60 308.01 1660.81 308.02 1280.97 308.03 1361.82 308.03 1433.44 308.04 1498.32 312.99 1557.47 312.96 1613.11 312.98 1647.76 312.99 1262.68 312.99

30.39 45.59 60.79 75.99 91.18 101.32 15.20 30.39 45.59 60.79 75.99

1345.08 1417.73 1483.19 1542.91 1599.05 1634.21 1245.20 1328.70 1402.30 1468.85 1529.37

312.98 313.04 318.49 318.52 318.51 318.52 318.52 318.46 318.66 318.90

91.18 101.32 15.20 15.20 30.39 45.59 60.79 75.99 91.18 101.32

1585.62 1621.19 1225.85 1225.78 1310.71 1385.47 1452.62 1514.20 1570.73 1606.72

292.71 292.71 292.72 292.70 292.70 292.97 292.72 298.02 298.00 297.99

15.20 30.41 45.60 60.80 75.99 91.19 101.32 15.20 30.40 45.59

1367.43 1440.71 1506.36 1566.20 1622.08 1673.55 1706.28 1349.18 1423.72 1490.15

298.05 298.03 298.03 298.03 302.94 302.93 302.90 302.92 302.92 302.92

76.00 91.18 91.18 101.32 15.20 30.41 45.59 60.79 75.99 91.18

x1 ) 0.5159 1607.14 308.05 1659.45 308.10 1659.19 308.10 1692.06 308.11 1332.40 308.11 1407.77 308.14 1475.08 308.18 1536.25 312.99 1593.31 312.98 1646.04 313.02

15.20 30.41 45.59 60.80 75.99 91.18 101.32 15.20 30.40 45.60

1314.82 1391.12 1459.53 1521.52 1578.82 1632.44 1665.75 1298.07 1375.72 1444.84

313.01 313.04 313.05 318.35 318.37 318.36 318.37 318.37 318.43 318.44

75.99 91.19 101.32 15.20 30.40 30.40 45.59 60.79 75.99 91.19

1565.60 1619.81 1653.55 1280.20 1359.23 1359.29 1429.55 1493.13 1551.34 1606.28

T, K

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TABLE 2: Continued T, K

p, MPa

u, m · s-1

T, K

p, MPa

u, m · s-1

T, K

p, MPa

u, m · s-1

T, K

p, MPa

u, m · s-1

297.99

60.79

1550.67

302.96

101.32

1678.80

313.03

60.79

1507.81

318.64

101.33

1640.50

15.20 30.39 45.59 60.79 75.99 91.18 101.32 15.20 30.39 45.59 60.79

1354.27 1426.92 1492.09 1551.58 1607.21 1658.66 1690.95 1337.81 1411.55 1477.60 1537.64

312.91 312.90 312.93 318.31 318.31 318.31 318.34 318.35 318.35 318.35

75.99 91.18 101.32 15.20 30.39 45.59 60.79 75.99 91.18 101.32

1593.94 1646.07 1678.94 1320.24 1395.07 1462.32 1523.12 1579.62 1632.61 1665.59

15.20 30.41 45.60 60.79 75.99 15.21 30.39 45.60 60.80 76.00

1375.80 1445.84 1509.14 1567.08 1621.28 1359.37 1430.34 1494.51 1553.06 1608.04

292.73 292.74 292.88 292.88 292.89 292.93 293.00 298.07 298.05 298.00 298.00

15.20 30.39 45.59 60.79 75.99 91.18 101.32 15.20 30.39 30.39 45.59

1407.02 1476.20 1538.17 1596.01 1649.29 1699.18 1730.93 1387.90 1458.42 1458.48 1521.78

298.03 298.02 298.06 298.05 302.85 302.83 302.83 302.83 302.92 302.85 302.84

60.79 75.99 91.18 101.32 15.20 30.39 45.59 60.79 75.99 91.18 101.32

x1 ) 0.6924 1580.05 307.85 1634.45 307.87 1684.78 307.89 1716.71 307.89 1371.00 307.91 1442.57 307.95 1507.05 307.95 1565.87 312.88 1620.86 312.89 1671.74 312.92 1704.13 312.91

292.82 292.82 292.82 292.81 292.83 297.94 297.93 297.94 297.92 297.90

15.20 30.40 45.61 60.79 76.00 15.21 30.41 45.59 60.79 75.99

1442.59 1508.61 1568.58 1624.48 1675.79 1425.73 1492.58 1553.05 1609.73 1661.80

302.96 302.95 302.93 302.97 302.96 307.95 307.93 307.93 307.96 307.96

15.20 30.41 45.59 60.79 75.99 15.20 30.41 45.60 60.79 75.99

x1 ) 0.8616 1408.99 313.10 1476.78 313.11 1538.03 313.10 1595.22 313.11 1647.97 313.16 1392.53 318.31 1461.61 318.33 1523.74 318.39 1581.15 318.33 1634.82 318.37

TABLE 3: Coefficients uij of Eq 2 and Mean Deviation from the Regression Line δ∆u0 -1

ui1, m · s · K

0 – 1 –30.4135 2 4.4221 3 –2.5234 4 –

–0.1749197 – – – –

i ui0, m · s

-1

-1

-1

ui2 × 10 , m · s · K 5

-2

-1

δ∆u0, m · s

65.8819 – – – –10.8883

0.07

where n

∆u0 ) x1(1 - x1)

m

∑ ∑ uij(1 - 2x1)iT j

(2)

i)0 j)0

and u0,1 is the speed of sound in decan-1-ol, u0,2 is the speed of sound in heptane, and uij are the regression coefficients found by the least-squares method. The coefficients uij are listed in Table 3, coefficients of the polynomial describing the temperature dependence of the speed of sound in pure liquids under atmospheric pressure have been reported in the previous paper.10 For the description of the temperature and pressure dependences of the ultrasonic speed, the following equation was chosen:

For pressures close to atmospheric pressure, the speed of sound in heptane (and mixtures rich in heptane) depends more significantly on pressure than those in decan-1-ol (and mixtures rich in decan-1-ol). With increasing pressure this effect decreases gradually and becomes comparable for all mixtures (Figure 1a). Similar dependence was observed for dodecane + heptane mixtures (Figure 1b), while, in the case of ethanol + heptane mixtures, the speeds of sound in pure heptane (and mixtures rich in heptane) are increasing with increasing pressure more rapidly than in pure ethanol over the whole pressure range under investigations. Finally the speed of sound in pure heptane became higher than in ethanol (and mixtures rich in ethanol) (Figure 1c). The densities of decan1-ol + heptane mixtures were measured within the whole concentration range at temperatures from 293 to 318 K in about 5 K steps under atmospheric pressure. The experimental results are listed in Table 5. The speeds of sound under high pressures and densities at atmospheric pressure were measured separately. It was therefore necessary to determine the temperature and concentration dependence of the densities in order to calculate the densities at atmospheric pressure for concentrations and temperatures for which the speed of sound had been measured under higher pressures. For the mixtures, the following formula satisfactorily approximates the dependence of density on temperature and mole fraction xi:

F ) x1F1 + x2F2 + ∆F m

p - p0 )

(4)

n

∑ ∑ bij(u - u0)iT j

(3)

where

i)1 j)0

3

where bij are coefficients calculated by the least-squares method, u0 is the speed of sound at atmospheric pressure p0, and u is the speed of sound at pressure p > 0.1 MPa. The stepwise rejection procedure was used to reduce the number of nonzero coefficients. The bij coefficients and the mean deviations from the regression lines are given in Table 4. A comparison of the speeds of sound in pure heptane and decan-1-ol measured in our laboratory with those reported in the literature is given in refs 10, 16, 17.

∆F ) x1x2

3

Tj ∑ ∑ dijx(i-2)/2 1

(5)

i)0 j)0

and F1 is the speed of sound in decan-1-ol, F2 is the speed of sound in heptane, and dij are the regression coefficients. The regression coefficients dij found by the least-squares method are given in Table 6. The temperature dependencies of the experimental densities of the pure liquids under atmospheric pressure have been reported in the previous paper.10



TABLE 4: Coefficients of Eq 3 and Mean Deviations from the Regression Line δu x1 0.0111 0.0147 0.0508 0.1530 0.2911 0.5159 0.6924 0.8616

b1j, K-j · MPa · s · m-1

j 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2

0.3623634779 -7.90562270 × 0.3680227625 -8.05063404 × 0.2400002003 -1.23363985 × 0.3444835145 -6.98458715 × 0.3753790924 -7.89521551 × 0. 3692091694 -7.14890072 × 0.2611195958 -9.91261828 × 0.2747517473 -1.02568912 ×

b2j, K-j · MPa · s2 · m-2 -4

2.09086927 × 10 -1.71475406 × 10-7 1.97587792 × 10-4 -1.37517211 × 10-7 2.15005662 × 10-4 -1.93462198 × 10-7 2.56502589 × 10-4 -3.17497428 × 10-7 1.86172709 × 10-4 2.24962438 × 10-4 -3.95285602 × 10-10 2.52534863 × 10-4 -8.10558895 × 10-10 3.43660218 × 10-4 -4.80451446 × 10-7 -

10-4 10-4

10-6 10-4 10-4 10-4

10-7 10-6

4. Correlation of Heat Capacities at Atmospheric Pressure The heat capacities of binary mixtures, Cp, were calculated from the thermodynamic relationship: o o Cp ) x1Cp,1 + x2Cp,2 + CEp

o Cp,1

∆F )

is the molar heat capacity of decan-1-ol, is the where molar heat capacity of heptane, and CpE is the excess molar heat capacity. The temperature dependencies of heat capacities of pure decan-1-ol and heptane at atmospheric pressure have been published in the previous paper.10 The excesses also reported in the previous paper10 were correlated by the following equation: 3

CEp ) x1x2

3

Tj ∑ ∑ kijx(i-2)/2 1

(7)

δu, m · s-1

-2.75026116 × 10-13 -1.96434459 × 10-13 -3.47621207 × 10-8 -

0.38

∫p

p2 1

(

5. Densities and Heat Capacities under High Pressures The densities and heat capacities of decan-1-ol + heptane mixtures were calculated for pressures up to 100 MPa and at temperatures from 293 to 318 K. To this end, a slightly modified method of Sun et al.,18 based on the earlier suggestion of Davis and Gordon,19 was applied. The pressure dependence of the density is given by the following thermodynamic relationship:

∂F ∂p

( )

T

)

TRp2 1 + Cp u2

(8)

)

Rp2T 1 + dp ≈ Cp u2

0.28 0.22 0.37 0.35 0.31 0.21

∫p

p2 1

Rp2T 1 dp + ∆p Cp u2

(9)

The approximate relationship (eq 9) is sufficiently accurate, provided ∆p is small enough, because the heat capacity depends rather slightly on pressure. Moreover, the first term on the righthand side of eq 9 is significantly larger than the second one since the latter results from the difference between the isentropic and isothermal compressibility that is small in comparison with both the compressibilities. The change of the heat capacity within the pressure limits ∆p is given by

i)0 j)0

where kij are constants, calculated by the least-squares method and given in Table 6. As results from substitution of eq 7 into eq 6, the heat capacity isobar for binary mixture of any concentration can be approximated by the third order polynomial of temperature.

0.26

where Rp is the isobaric thermal expansion calculated from definition: Rp ) -(1/F)(∂F/∂T)p. The change of the density of the liquid ∆F, caused by a pressure increase from p1 to p2 at constant temperature, can be calculated by integration:

(6) o Cp,2

b3j, K-j · MPa · s3 · m-3

∆Cp ≈ -

[

( )]

∂Rp T 2 Rp + F ∂T

p

∆p

(10)

The details of the algorithm were discussed in a previous work.9 In the calculations, the experimental speeds of sound were used, together with the densities and heat capacities at atmospheric pressure. The calculated densities and isobaric molar heat capacities can be found as Supporting Information. A comparison of the calculated high pressure densities and heat capacities of pure decan-1-ol and heptane, using speed of sound obtained in our laboratory, with those reported in the literature was given in the previous papers.16,17 Recently, Zuń˜iga-Moreno and Galicia-Luna reported densities of decan-1-ol at temperatures ranging from 313 to 363 K and at pressures up to 22 MPa.20 They compared densities of decan1-ol calculated from the correlation equation with densities of this liquid reported in my previous work.16 They found very good agreement with densities under atmospheric pressure, while the absolute average deviation AAD was found to be 0.56%

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Dzida increases in the heptane rich region and decreases in the decan1-ol rich region. Thus, the excess volume isotherms intersect each other at a common point at which the temperature dependence of the excess volumes is inverted (Figure 2). As pressure increases the crossing point moves toward higher mole fraction of decan-1-ol (Figure 3). Moreover, the negative excess volume values, in the region of low alcohol concentration, become positive at increasingly high alcohol concentrations as the pressure increases (Figure 4). The excess heat capacities of the decan-1-ol + heptane mixtures are positive over the whole composition range at the temperatures and pressures under test. The excess heat capacities increase with increasing temperatures10 and decrease with increasing pressure, but the effect of temperature on the excess molar heat capacities of investigated mixtures is more pronounced than the pressure one. At given temperature variation of excess enthalpies with pressure for each mixture can be calculated indirectly from dependence of excess volumes on pressure and temperature according to the exact thermodynamic relation:

( ) ∂HE ∂p

T

( )

) VE(p) - T

∂VE ∂T

p

(11)

Lichtenthaler24 found that ∆HE values are only accurate to within (25%, because temperature dependence of excess volumes is very small and hence relatively inaccurate. Moreover, it is important that in calculating ∆HE/∆T from eq 11, (∂VE/ ∂T)p is multiplied by T, i.e. by a relatively large number. 6. The ERAS model

Figure 1. Speeds of sound plotted against mole fraction at 298.15 K. (a) In decan-1-ol (1) + heptane (2) mixtures: (b) p ) 0.1 MPa; (+) 15.20 MPa; ([) 30.40 MPa; (O) 45.59 MPa; (2) 60.79 MPa; (9) 75.99 MPa. (b) In dodecane (1) + heptane (2) mixtures:17 (b) p ) 0.1 MPa; ([) 30.39 MPa; (2) 60.79 MPa; (9) 101.32 MPa. (c) In ethanol (1) + heptane (2) mixtures:6 (b) 0.1 MPa; ([) 30 MPa; (2) 60 MPa; (9) 90 MPa. Lines calculated from the empirical function: u ) ∑i3) 0aixi1.

for higher pressures. It is rather surprising because comparison of the raw densities obtained in both works shows excellent agreement: 822.38 kg · m-3 at 313.12 K, 9.994 MPa20 and 822.37 kg · m-3 at 313.15 K, 10 MPa;16 828.31 kg · m-3 at 313.12 K, 19.993 MPa20 and 828.24 kg · m-3 at 313.15 K, 20 MPa.16 From the densities and heat capacities, the excess functions were calculated. The densities and heat capacities of pure decan1-ol were determined for pressures up to 70 MPa.16 The upper pressure is limited by the freezing of decan-1-ol. Using the set for high pressure measurements of the speed of sound, it is not possible to obtain accurate enough pressure dependence of the melting temperature. Therefore speeds of sound in decan-1-ol have been measured at pressures up to 76 MPa.16 Thus, the excesses were calculated for pressures up to 70 MPa. Under atmospheric pressure, the composition dependence of the excess volume is S-shaped with small positive values in the heptane rich region. As temperature increases, the volume of mixing

The extended real associated solution (ERAS) model was originally developed by Heintz21,22 for describing simultaneously the excess molar Gibbs free energy, enthalpy, heat capacity, and excess volume of alcohol + alkane mixtures under atmospheric pressure. Heintz23 and Lichtenthaler24 have reported attempts to calculate the excess enthalpy and excess volume for alkane + alkane and alkanol + alkane mixtures under nonzero pressure using the Prigogine-Flory-Patterson theory and a modified real associated solution model taking into account the volume change related to the hydrogen-bonding formation, respectively. Moreover, the first attempt to apply the ERAS model to the description of the pressure dependence of excess volume and excess enthalpy for alkanol + alkane mixtures was made by Oswald et al.25 With this end in view, the ERAS model was modified taking account of the nonzero pressure (p * 0) and applied for description of the adiabatic and isothermal compressibility and speed of sound data at atmospheric pressure for the ethanol + heptane system.11 In the suggested modification, the reduction quantities of the pure alcohol, V1* and p1* are determined from Flory’s equation of state that contains terms arising from association effects and additional terms related to the nonzero pressure. The final equations for the reduction parameters are as follows:

p*1

)

(

Rp,1 - R*

κT,1 - R*

*

)

∆ν T ∆h*

˜ 12 - pV ˜ 12 TV

(12)



V* 1 ) V1

(

∆V* 3 - 6p κT,1 - R* T + 3(Rp,1 - R*)T ∆h* ∆V* - R*)T + 3 - 6p κT,1 - R* T + 3(Rp,1 - R*)T ∆h*

(

(Rp,1

)

)

(

)

3

(13)

with

(

HE(phys) ) (x1V*1 + x2V*2 )

The excess heat capacity is given by

CEp (chem) )

R* )

[

∆V* ∆h* (4K + 1)1/2 - 2K(4K + 1)-1/2 - 1 V*1 RT2 2K

]

(

E E XE ) Xchem + Xphys

(15)

The excess volume is given by

VE(chem) ) V˜Mx1K∆ν*(φ1 - φ01)

)

x1K∆h*2 φ1(1 - Kφ1) φ01(1 - Kφ01) +p 1 + Kφ1 RT2 1 + Kφ01

( ) E ∂Vchem

∂T

(14)

The above equations can be used as well for the alkanes putting ∆h* ) 0, ∆V* ) 0, and R* ) 0. The isobaric thermal expansion and isothermal compressibility, κT, of the pure liquids have been calculated from the experimental data reported in the previous papers.6,7,10,16,17 R* is the contribution to the isobaric thermal expansion due to the association. In this work the modified ERAS model has been applied for description of excess volumes, excess enthalpies, and excess isobaric heat capacities of decan-1-ol + heptane and ethanol + heptane mixtures. ∆h* is the enthalpy change accompanying the formation of one mole of hydrogen bonds. Heintz21 adopted ∆h* ) -25.1 kJ · mol-1 for all alkan-1-ol + alkane mixtures. Here ∆V* is the volume change associated with formation of one mole of hydrogen bonds. The average value of the association volume, ∆V* ) -5.6 × 10-6 m3 · mol-1, has been used to calculate the excess volumes, excess enthalpies, and excess heat capacities by the ERAS model for decan-1-ol + heptane mixtures over the whole temperature and pressure range. For ethanol + heptane mixtures ∆V* was fitted to the experimental excess volumes. Values of ∆V* are listed in Table 7. The thermodynamic excess functions, XE, of binary mixtures containing a self-associating component and an inert one is expressed, in this model, by the sum of two contributions: a physical which arises from nonpolar van der Waals interactions including the free volume effects on mixing and a chemical one due to the hydrogen bonding effect:

)

φ2p*2 p*M φ1p*1 E + + pVphys V˜1 V˜2 V˜M (19)

(

CEp (phys) ) (x1V*1 + x2V*2)

p

(20)

* R¯ MpM + φ1ϑ2(dX12 /dT) V˜M

) ( )

E R¯ 2φ2p*2 R¯ 1φ1p*1 ∂Vphys +p ∂T V˜1 V˜2

p

(21)

φ1 and φ01 are the volume fractions of the monomeric alkanol species in the mixture and pure alkanol, respectively. φi is the hard core volume fraction of the i-component in the mixture, V˜i is the reduced volume of the i-component. p*M is characteristic pressure and V˜M is reduced volume of the mixture. The surface to volume ratio for the pure components, s, was estimated using Bondi’s method26 and reported in refs 10, 11. K is the association constant. Values of K are equal 328 and 88 at 298.15 K for ethanol11 and decan-1-ol,10 respectively. Temperature dependence of K was calculated using the following equation:

( ∂ ∂Tln K )

) p

∆h* RT2

(22)

The values of K at high pressures are obtained using the relation:

( ∂ ∂pln K )

)T

∆V* RT

(23)

The second of the adjustable parameters is X12 which has the meaning of a measure for the difference in physical van der Waals intermolecular interactions of the components in the mixture.21 In this work, X12 was fitted to the excess enthalpies or to excess volumes if the excess enthalpies are not available. Values of the X12 parameter are listed in Table 7. For the calculation of CpE, the thermal expansion coefficient for mixture, R j M, and the temperature dependence of X12 are needed. R j M was calculated using the following equation:

(16) 3

VE(phys) ) (V*1x1 + V*2x2)(V˜M - φ1V˜1 - φ2V˜2)

(17)

√V˜M - 1 R¯ M ) 3 T(4/3 - √V˜M)

(24)

The parameter dX12/dT is defined as follows: The excess enthalpy is given by

HE(chem) ) K∆h*x1(φ1 - φ01) -

( ) E p*MVchem 2 ˜M V

(T0) dX12 X(T) 12 - X12 ) dT T - T0 E + pVchem

(18)

(25)

but the adjusted values of this parameter give a better agreement with the experimental CEp values. The values of parameters dX12/

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TABLE 5: Densities of {Decan-1-ol (1) + Heptane (2)} Mixtures Measured within the Temperature Range 293 to 318 K at Atmospheric Pressure with a Bicapillary Pycnometer x1

T, K

F, kg · m-3

x1

T, K

F, kg · m-3

x1

T, K

F, kg · m-3

0.0035 0.0117 0.0244 0.0402 0.0507 0.0630 0.0889 0.1460 0.2131 0.2498 0.3005 0.3608 0.4110 0.4641 0.5201 0.5390 0.5644 0.6145 0.6791 0.7299 0.8120 0.8640 0.9028 0.9506 0.0035 0.0117 0.0244 0.0402 0.0507 0.0630 0.0889 0.1460 0.2101 0.2498 0.3046 0.2498 0.3005 0.3651 0.4110 0.4641 0.5201 0.5390 0.5644 0.6145 0.6793 0.7299 0.8152 0.8640

293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15

684.46 685.99 688.38 691.39 693.44 695.72 700.60 711.01 722.83 729.02 737.40 746.98 754.83 762.78 770.80 773.47 776.99 783.74 792.18 798.66 808.70 814.74 819.14 824.44 680.23 681.77 684.18 687.21 689.24 691.55 696.46 706.91 718.25 725.09 734.19 712.92 721.60 732.19 739.42 747.49 755.79 758.52 762.12 769.06 777.78 784.34 794.94 800.78

0.3608 0.4159 0.4797 0.5219 0.5499 0.5644 0.6197 0.6837 0.7355 0.8158 0.8640 0.9093 0.9584 0.0035 0.0117 0.0244 0.0402 0.0507 0.0630 0.0889 0.1460 0.2131 0.2498 0.3005 0.3608 0.4110 0.4641 0.5201 0.5390 0.5644 0.6145 0.6793 0.7299 0.8120 0.8640 0.9028 0.9506 0.0035 0.0117 0.0244 0.0402 0.0507 0.0630 0.0889 0.1460 0.2101 0.2498 0.3046

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15

743.18 751.72 761.25 767.36 771.27 773.29 780.83 789.24 795.83 805.66 811.29 816.43 821.85 675.97 677.52 679.94 682.91 685.00 687.35 692.28 702.81 714.82 721.04 729.53 739.29 747.16 755.15 763.35 766.04 769.58 776.45 785.04 791.52 801.67 807.77 805.28 810.70 663.00 664.54 667.00 670.07 672.19 674.55 679.51 690.28 701.91 708.85 718.22

0.9028 0.9506 0.0035 0.0117 0.0244 0.0402 0.0507 0.0630 0.0889 0.1460 0.2101 0.2498 0.3046 0.3651 0.4159 0.4797 0.5219 0.5499 0.5644 0.6197 0.6793 0.7355 0.8158 0.8640 0.9093 0.9584 0.0035 0.0117 0.0244 0.0402 0.0507 0.0630 0.0889 0.1460 0.2131 0.3651 0.4159 0.4797 0.5219 0.5499 0.5644 0.6197 0.6837 0.7355 0.8152 0.8640 0.9093 0.9584

303.15 303.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 308.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15 318.15

812.20 817.56 671.68 673.22 675.63 678.72 680.75 683.15 688.03 698.66 710.17 716.96 726.27 736.09 743.99 753.69 759.87 763.84 765.89 773.53 781.46 788.70 798.61 804.28 809.50 814.98 667.38 668.91 671.32 674.38 676.48 678.85 683.85 694.50 706.61 728.19 736.23 746.00 752.27 756.27 758.33 766.04 774.65 781.38 791.36 797.23 802.43 808.02

dT obtained by adjusting to the excess molar heat capacities are listed in Table 7. The results of the ERAS model calculations are shown in Figures 2-4 and 6-11.

TABLE 6: Coefficients dij and kij of Eqs 5 and 7, Respectively, and Mean Deviations from the Regression Line δ∆G and δCpE

7. Discussion The modified ERAS model describes semiquantitatively the composition, temperature and pressure dependences of the excess volumes. In principle the characteristic parameters should not depend on temperature and pressure. Therefore, the test for the modified model was description of excess volume isotherms of decan-1-ol + heptane mixtures at 70 MPa i.e. reproduction of the crossing point, because the volume effects of mixing are small and its temperature dependence is weak. The obtained results show that the pressure dependence of characteristic pressure of both components, characteristic volume of alkane, and characteristic volume of alkan-1-ol in calculation of R* should be included. Without these modifications, the model is

i

di0, kg · m-3

di1 × 102, kg · m-3 · K-1

di2, kg · m-3 · K-2

δ∆F, kg · m-3

0 1 2 3

1.189 –4.391 66.181 –46.292

–0.34496 – – 8.183

– – – –

0.03

i

ki0, J · mol-1 · K-1

ki1, J · mol-1 · K-2

ki2 · 105, J · mol-1 · K-3

δCEp , J · mol-1 · K-1

0 1 2 3

– –22.8683 –112.8307 –

– – – 0.76851

–3.7949 106.5058 – –186.1068

0.14

not able to reproduce the crossing point. The excess enthalpies are also described semiquantitavely by the modified ERAS



TABLE 7: ERAS Parameters for the Mixtures T, K

298.15 318.15

298.15 318.15 a

(dX12/dT) × p, MPa ∆V* × 106, m3 · mol-1 X12×106, J · m-3 106, J · m-3 · K-1

0.1 90 0.1 90

Ethanol + Heptane -9.9 8.3 -5.9 2.6 -8.2 14.5 -5.9 5.6

0.29 0.16 0.58 0.48

0.1a 70 0.1a 70

Decan-1-ol + Heptane -5.6 4.5 -5.6 3.0 -5.6 7.3 -5.6 5.0

0.13 0.12 0.25 0.23

Taken from ref 10.

Figure 2. Excess volumes of decan-1-ol + heptane mixtures under atmospheric pressure: (9) 298.15 K; (b) 308.15 K; (2) 318.15 K. Points are the experimental data, and lines are the ERAS model; positive contribution, chemical; negative contribution, physical: ( · · · ) 298.15 K; (- - -) 318.15 K.

Figure 3. Excess volumes of decan-1-ol + heptane mixtures at 70 MPa: (0) 298.15 K; (∆) 318.15 K. Points are the experimental data, and lines are the ERAS model: ( · · · ) 298.15 K; (;;;) 318.15 K. Positive contribution, chemical; negative contribution, physical.

model. The excess enthalpies calculated from the relation 11 and from the ERAS model are in very good agreement (Figure 8a and Figure 9). The results of the ERAS model calculations show that for decan-1ol + heptane mixtures the ∆V* does not depend on temperature and pressure. Hence, the excess volumes and excess enthalpies of decan-1-ol + heptane mixtures were described using one adjustable parameter X12. For ethanol + heptane mixtures the ∆V* depends on temperature and pressure. Thus, two adjustable parameters, X12 and ∆V*, are required for simultaneous description excess volumes and excess enthalpies. However, the same value of ∆V* was obtained at 298.15 and

Figure 4. Excess volumes of decan-1-ol + heptane mixtures. (a) At 298.15 K: (9) 0.1 MPa; (0) 70 MPa. (b) At 318.15 K: (2) 0.1 MPa; (∆) 70 MPa. Points are the experimental data, and lines are the ERAS model: (;;;) 0.1 MPa; ( · · · ) 70 MPa. Positive contribution, chemical; negative contribution, physical.

Figure 5. Excess volumes of dodecane + heptane mixtures17 at 298.15 K [(9) 0.1 MPa; (0) 70 MPa] and at 318.15 K [(2) 0.1 MPa; (∆) 70 MPa].

at 318.15 K for 90 MPa. Additionally, the ERAS model described qualitatively the composition, temperature, and pressure dependence of the excess molar heat capacity of the systems under investigations. Description of the excess heat capacities is possible using additional adjustable parameter dX12/dT. The volume effects of mixing of alkan-1-ol with alkane arise from the competition between two opposite contributions. The positive contribution involves the rupture of both dispersive and hydrogen bond interactions during mixing. The other one, namely, the structural or packing contribution, is negative, and it comes from the fitting of the alkane molecules into the cavities or holes in the hydrogen-bonded structure of the alcohol. In the ERAS model the excess functions are split into two additive terms, chemical and physical. The first one arises from

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Figure 6. Excess volumes of ethanol + heptane mixtures. (a) At 298.15 K: ([) 0.1 MPa; (]) 90 MPa. (b) At 318.15 K: (b) 0.1 MPa; (O) 90 MPa. Points are the experimental data;7 lines are the ERAS model; chemical and physical contribution: (;;;) 0.1 MPa; ( · · · ) 90 MPa. The maximum of chemical contribution is shifted toward lower alcohol concentration.

Figure 8. Excess enthalpies of decan-1-ol + heptane mixtures. (a) At 298.15 K: 0.1 MPa (9),28 (2),29 (b);30 (0) 70 MPa. (b) Predicted values for 318.15 K. Points are the experimental data, and lines are the ERAS model; chemical and physical contribution: (;;;) 0.1 MPa; ( · · · ) 70 MPa. The maximum of chemical contribution is shifted toward lower alcohol concentration.

Figure 7. Excess volumes of ethanol + heptane mixtures at 90 MPa: (]) 298.15 K and (O) 318.15 K. Points are the experimental data;7 lines are the ERAS model; chemical and physical contribution: ( · · · ) 298.15 K; (;;;) 318.15 K. The maximum of chemical contribution is shifted toward lower alcohol concentration.

is shifted toward lower alcohol concentrations, while the minimum of the physical contribution appears at higher concentrations of the alcohol. As temperature increases, the excess volume increases in the heptane rich region and decreases in the decan-1-ol rich region. Thus, the excess volume isotherms intersect each other at a common point at which the temperature dependence of the excess volumes is inverted (Figure 2). As pressure increases the crossing point moves toward higher mole fraction of decan-1-ol (Figure 3). Moreover, the negative excess volume values, at low alcohol concentrations, become positive at increasingly high alcohol concentrations as the pressure increases (Figure 4). The ERAS model shows that the hydrogen bonding term is the most important at high mole fraction of alkane and is dependent on temperature and pressure, but the effect of pressure is rather slight. The packing term is the most important at lower mole fraction of alkane and is also dependent on the temperature and pressure. However, the effect of pressure on the physical part of VE is more pronounced than the temperature effect. At high pressure and at high mole fraction of decan-1-ol the VE is weakly dependent on temperature. It is an effect of proportional changes of chemical and physical contributions with temperature and compensation of these terms (Figure 3). Additionally, the pressure dependence of excess volumes of decan-1-ol + heptane mixtures shows some similarities to that of dodecane + heptane (Figures 4 and 5) in contrast to excess enthalpies and excess heat capacities for which pressure and temperature dependencies are opposite.17 The excess volumes of dodecane + heptane mixtures are negative over the whole concentration range under atmospheric pressure, and the deviations from the ideality

hydrogen bonding effects, and the other one comes from nonpolar van der Waals interactions including free volume effects on mixing.21,22 For decan-1-ol + heptane mixtures, the composition dependence of excess molar volume under atmospheric pressure is S-shaped with small positive values in the decan-1-ol rich region. As results from the ERAS model calculations, the chemical contribution to excess molar volume is small and positive, while the physical contribution is negative and predominated.10 Both the physical and the chemical contribution to VE are asymmetric: the maximum of the chemical contribution



Figure 9. Excess enthalpies of ethanol + heptane mixtures. (a) At 298.15 K: 0.1 MPa ([),31 (9);32 (]) 90 MPa.7 (b) At 318.15 K: (b) 0.1 MPa;33 (O) 90 MPa.7 Points are the experimental data; lines are the ERAS model; chemical and physical contribution: (;;;) 0.1 MPa; ( · · · ) 90 MPa. The maximum of chemical contribution is shifted toward lower alcohol concentration.

Figure 10. Excess heat capacities of decan-1-ol + heptane mixtures. (a) At 298.15 K: (9) 0.1 MPa;10 (0) 70 MPa. (b) At 318.15 K: (2) 0.1 MPa;10 (∆) 70 MPa. Points are the experimental data, and lines are the ERAS model; chemical and physical contribution: (;;;) 0.1 MPa; ( · · · ) 70 MPa. The maximum of chemical contribution is shifted toward lower alcohol concentration.

increase with increasing temperature (Figure 5). This dependence is similar to that of decan-1-ol + heptane in the region from the crossing point to the high concentration of decan-1ol. It is commonly assumed that the negative volume deviations result mainly from the fitting of the shorter alkane molecules into the structure of the longer-chain alkanes. This leads to a more compact and less compressible structure. The volume effect of mixing decreases with increasing pressure, and at 293.15 K under 50 MPa, the excess volumes become positive for mixtures rich in heptane.16 As it is known for alcohol + alkane mixtures positive volume effect of mixing is connected with disruption of hydrogen bonds. It seems that, in the case of dodecane + heptane mixtures, the positive volume effect of mixing probably connected with rupture of the orientational order i.e. weak association between dodecane molecules. It is interesting that the positive volume effect of mixing appears under high pressure. Probably it is connected with repulsive forces which increases under high pressures. Thus, at higher pressures the repulsive forces cause an unrolling of the bended chains of dodecane. The interstitial accommodation of dodecane molecules into compact structure of heptane at relatively low concentrations of dodecane becomes less effective. Consequently, this leads to a positive volume of mixing. Distinct from the decan-1-ol + heptane system, for ethanol + heptane mixtures, excess volumes are positive over the whole composition range (Figures 6 and 7). With increasing temperature the volume effect of mixing increases and the maximum of VE(x1) isotherms moves toward lower concentration of ethanol, while, with increasing pressure, the opposite effect is observed. The ERAS model shows that the chemical contribu-

tion is predominating at 298.15 K under atmospheric pressure and at high pressures as well (Figure 6a). The physical and chemical contributions are approximately comparable at 318.15 K and at atmospheric pressure, but under high pressures the chemical contribution becomes predominant (Figure 6b). It seems that, as temperature increases, the hydrogen bonds in pure ethanol are partially destroyed by thermal motion before mixing. Thus, under atmospheric pressure, the effect of breaking of the hydrogen bonds during mixing becomes less pronounced. As pressure increases the association equilibrium is shifted into making of hydgogen bonds in pure ethanol. Therefore the chemical contributionsrelated to the hydrogen bonding disrupturesbecomes higher than the physical one. The increase in the association with increasing pressure is indicated as well by the decrease in the excess enthalpy.23-25,27 However, for the mixtures under test the experimental excess enthalpies at high pressures are not available. In this work excess enthalpies were calculated indirectly using relation 11. The heats of mixing of decan-1-ol + heptane and ethanol + heptane mixtures are positive, i.e. the mixing process is endothermic; the curves of the excess heat of mixing vs mole fraction are asymmetric (Figures 8 and 9). It is generally believed that the major positive contribution to the heat of mixing is due to the breaking of hydrogen bonds. For mixtures of this type, the heat of mixing increases with temperature due to the disruption of some of the hydrogen bonds by imparting thermal energy to the molecules. The chemical contribution to excess enthalpy, obtained from the ERAS model, is predominated at all temperatures under investigations, but the percentage of the physical contribution to heat of mixing increases with

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Dzida chemical contribution to excess heat capacity is dominant, and its maximum is shifted toward lower alcohol concentration. The physical contribution is smaller than the chemical one, and its maximum is slightly shifted toward higher alcohol concentration. The excess heat capacity calculated from the ERAS model increases with increasing temperature, and the maximum of the model CEp moves toward higher alkan-1-ol concentrations as the experimental ones. The appropriate pressure dependence of excess heat capacities is also described qualitatively by the ERAS model. At low concentration of decan-1-ol isobars of excess heat capacities cross each other (Figure 10). Despite that the ERAS model describes only qualitatively the composition dependence of CpE, it is able to describe the crossing of CpE isobars. This effect is more pronounced at 318.15 K (Figure 10 b). Crossing of the CpE isobars has been observed also for 2-methyl-2-butanol + heptane mixtures.38 8. Concluding Remarks

Figure 11. Excess heat capacities of ethanol + heptane mixtures. (a) At 298.15 K: 0.1 MPa (b),34 ([),35 (9),36 (2);37 (]) 90 MPa.7 (b) At 318.15 K: (b) 0.1 MPa;34 (O) 90 MPa.7 Points are the experimental data; lines are the ERAS model; chemical and physical contribution: (;;;) 0.1 MPa; ( · · · ) 90 MPa. The maximum of chemical contribution is shifted toward lower alcohol concentration.

increasing temperature. The ERAS model shows that the hydrogen bonding term accounts for the main contribution to excess enthalpies also at high pressures (Figures 8 and 9). For decan-1-ol + heptane the effect of pressure on excess enthalpies is smaller than that for ethanol + heptane. Thus, for decan-1ol + heptane the impact of pressure on chemical and physical contribution is small and comparable. In the case of ethanol + heptane mixtures the effect of pressure on the physical part of excess enthalpies is predominant (Figure 9). The excess heat capacities of the decan-1-ol + heptane and ethanol + heptane mixtures are positive over the whole investigated concentration range (Figures 10 and 11). The excess heat capacities isotherms are asymmetric, and with increasing temperature the maximum is shifted toward higher alcohol concentration; with increasing pressure the opposite effect is observed. Moreover, the effect of pressure on the excess heat capacities of ethanol + heptane is more pronounced than that of decan-1-ol + heptane mixtures. The positive excess heat capacity indicates more structured solution, thus the fewer hydrogen bonds in solution corresponded to bringing together alcohol molecules over longer distances than in pure alcohol. In alkan-1-ol + alkane mixtures it is easier to break up hydrogen bonds because there is a greater entropic driving force toward the randomly dispersed alkan-1-ol molecules. The hydrogen bonds are broken as the temperature increases producing an increase in entropy and heat capacity higher in solutions than in the pure alcohol. The ERAS model described qualitatively the composition temperature, and pressure dependence of the excess heat capacity of both systems under investigation (Figures 10 and 11). The

In this work, the ability of the modifications introduced into the original ERAS model in determining the excess properties of decan-1-ol + heptane and ethanol + heptane mixtures at high pressures has been tested. This model was found to be sufficient for describing semiquantitatively excess volumes and excess enthalpies and qualitatively excess heat capacities under high pressure. Additionally, the experimental densities and speeds of sound in decan-1-ol + heptane mixtures have been reported for the temperature interval from 293 to 318 K at atmospheric pressure and for pressures up to 101 MPa, respectively. The densities and heat capacities as a function of pressure have been calculated from those speeds. Acknowledgment. The author is profoundly indebted to Prof. S. Ernst for critical reading of the manuscript and to Ms. E. Powolna and Mr. T. Fular for the participation in the speed of sound and density measurements under atmospheric pressure. Supporting Information Available: Tables showing (I) the calculated densities of decan-1-ol + heptane mixtures and (II) the calculated isobaric molar heat capacities of decan-1-ol + heptane mixtures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Lafitte, T.; Pin˜eiro, M. M.; Daridon, J.-L.; Bessie`res, D. J. Phys. Chem. B 2007, 111, 3447. (2) Randzio, S. L.; Grolier, J. - P. E.; Quint, J. R. Int. J. Thermophys. 1995, 110, 341. (3) Coxam, J.-Y.; Grolier, J.-P. E.; Ogawa, H. Fluid Phase Equilib. 2004, 226, 141. (4) Troncoso, J.; Bessie`res, D.; Cerdeirinã, C. A.; Carballo, E.; Romanı´, L. Fluid Phase Equilib. 2003, 208, 141. (5) Navia, P.; Troncoso, J.; Romanı´, L. Fluid Phase Equilib. 2009, 276, 1. (6) Dzida, M.; Z˙ak, A.; Ernst, S. J. Chem. Thermodyn. 2005, 37, 405. (7) Dzida, M.; Marczak, W. J. Chem. Thermodyn. 2005, 37, 826. (8) Dzida, M.; Ernst, S. J. Chem. Eng. Data 2003, 48, 1453. (9) Dzida, M. J. Sol. Chem. 2004, 33, 527. (10) Dzida, M.; Go´ralski, P. J. Chem. Thermodyn. 2006, 38, 962. (11) Ernst, S.; Dzida, M. Fluid Phase Equilib. 1998, 146, 25. (12) Z˙ak, A.; Dzida, M.; Zore¸bski, M.; Ernst, S. ReV. Sci. Instrum. 2000, 71, 1756. (13) Dzida, M.; Chora¸z˙ewski, M.; Zore¸bski, M.; Man´ka, R. J. Phys. IV 2006, 137, 203. (14) Marczak, W. J. Acoust. Soc. Am. 1997, 102, 2776. (15) Kell, G. S.; Whalley, E. J. Chem. Phys. 1975, 62, 3496. (16) Dzida, M. J. Chem. Eng. Data 2007, 52, 521. (17) Dzida, M.; Cempa, M. J. Chem. Thermodyn. 2008, 40, 1531. (18) Sun, T. F.; Ten Seldam, C. A.; Kortbeek, P. J.; Trappeniers, N. J.; Biswas, S. N. Phys. Chem. Liq. 1988, 18, 107.

Properties of Decan-1-ol + Heptane Mixtures (19) Davis, L. A.; Gordon, R. B. J. Chem. Phys. 1967, 46, 2650. (20) Zuń˜iga-Moreno, A.; Galicia-Luna, L. A. J. Chem. Eng. Data 2007, 52, 1773. (21) Heintz, A. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 172. (22) Bender, M.; Heintz, A. Fluid Phase Equilib. 1993, 89, 197. (23) Heintz, A. Ber. Bunsen-Ges. Phys. Chem. 1981, 85, 632. (24) Lichtenthaler, R. N. Fluid Phase Equilib. 1983, 13, 253. (25) Oswald, S.; Schmittecker, B.; Wagner, D.; Lichtenthaler, R. N. Fluid Phase Equilib. 1986, 27, 119. (26) Bondi, A. Physical Properties of Molecular Crystals, Liquids, and Glasses; John Wiley & Sons, Inc.: New York, London, Sidney, 1968; Tables 14.1-14.4. (27) Wang, X.; Liu, Y.; Sun, X. Thermochim. Acta 1995, 253, 51. (28) Ramalho, R. S.; Ruel, M. Can. J. Chem. Eng. 1968, 46, 456. (29) Amigo, A.; Bravo, R.; Paz Andrade, M. I. J. Chem. Thermodyn. 1991, 23, 679.

J. Phys. Chem. B, Vol. 113, No. 34, 2009 11661 (30) Kumaran, M. K.; Benson, G. C. J. Chem. Thermodyn. 1984, 16, 175. (31) Roux, A. H.; Roux-Desgranges, G.; Grolier, J.-P. E. Fluid Phase Equilib. 1993, 89, 57. (32) Rogaini, V.; Santi, R.; Carra, S. Atti. Accad. Naz. Lincei, Cl. Sci. Fis., Mat. 1968, 45, 540. (33) Van Ness, H. C.; Soczek, C. A.; Kochar, N. K. J. Chem. Eng. Data 1967, 12, 346. (34) Klesper, I. Z. Phys. Chem. N.F. 1966, 51, 1. (35) Fortier, J. L.; Benson, G. C. J. Chem. Thermodyn. 1976, 8, 411. (36) Brown, G. N.; Ziegler, W. T. J. Chem. Eng. Data 1979, 24, 319. (37) Tanaka, R.; Toyama, S.; Murakami, S. J. Chem. Thermodyn. 1986, 18, 63. (38) Dzida, M.; Waleczek, L. J. Chem. Thermodyn., submitted.

JP903763C

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