speeds of sound in and isentropic compressibilities of (n-butanol + n-pentane, or n-hexane, or...

Speeds of sound in and isentropiccompressibilities of (n-butanol+ n-pentane,or n-hexane, or n-heptane, or2,2,4-trimethylpentane) at T = 288:15K,(n-hexanol+ n-pentane or n-hexane)at T = 298:15K, and(n-hexanol+ n-heptane or n-octane)at T = 298:15K and T = 303:15K

Jagan NathChemistry Department, DDU Gorakhpur University,Gorakhpur 273009, India

Measurement of speeds of sound u have been made in binary mixtures of n-butanol (n-C4H9OH) with n-pentane (n-C5H12), or n-hexane (n-C6H14), or n-heptane (n-C7H16), or2,2,4-trimethylpentane {2,2,4-(CH3Þ3C5H9} at temperature T ¼ 288:15K, in binarymixtures of n-hexanol (n-C6H13OH) with n-C5H12, or n-C6H14 at T ¼ 298:15K, and inbinary mixtures of n-C6H13OH with n-C7H16 or n-octane (n-C8H18) at T ¼ 298:15K andT ¼ 303:15K. Values of u have been used to calculate the apparent excess speeds ofsound Du and the isentropic compressibilities jS for these mixtures. The excess isentropiccompressibilities jE

S have also been calculated from the values of jS. Throughout theentire range of mole fraction x of n-C4H9OH or n-C6H13OH, the jE

S has been found to benegative for fð1� xÞ n-C5H12 þ x n-C4H9OHg and fð1� xÞ2; 2; 4-ðCH3Þ3C5H9þx n-C4H9OHg at T ¼ 288:15K, and for fð1� xÞ n-C5H12 þ x n-C6H13OHg atT ¼ 298:15K. The jE

S has been found to be positive at lower values of x, and negative athigher values of x for fð1� xÞ n-C6H14 þ x n-C4H9OH} and fð1� xÞ n-C7H16þx n-C4H9OHg at T ¼ 288:15K. The inversion of sign of jE

S occurs at x � 0:20and x � 0:45, respectively, for these mixtures of n-C4H9OH. The jE

S has been found to bepositive at lower x values and negative at higher x values for fð1� xÞ n-C6H14þx n-C6H13OHg; fð1� xÞ n-C7H16 þ x n� C6H13OHg, and fð1� xÞ n-C8H18 þ xn-C6H13OHg at T ¼ 298:15K and T ¼ 303:15K. At T ¼ 298:15K, the inversion of signof jE

S occurs at x � 0:12; x � 0:18, and x � 0:15, respectively, for these mixtures ofn-C6H13OH. The Du and jE

S have been fitted with smoothing equations. � 2002 ElsevierScience Ltd. All rights reserved.

KEYWORDS: speeds of sound in and isentropic compressibilities of (alkanolsþalkanes)

J. Chem. Thermodynamics 2002, 34, 1857–1872doi:10.1016/S0021-9614(02)00255-0Available online at http://www.idealibrary.com on

0021-9614/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

1. Introduction

This work continues studies devoted to mixtures of (an alkanol+an alkane). The binaryliquid mixtures of this kind are of considerable interest from the theoretical viewpoint ofa model of hydrogen-bonded systems. In previous papers,ð1–3Þ studies of excess molarvolumes of binary liquid mixtures of n-butanol (n-C4H9OHÞ and n-heptanol (n-C7H15OHÞ with n-pentane (n-C5H12Þ, or n-hexane (n-C6H14Þ, or n-heptane (n-C7H16Þ, orn-octane (n-C8H18Þ, or 2,2,4-trimethylpentane {2,2,4-ðCH3Þ3C5H9} have been reported attwo temperatures. Speeds of sound u and isentropic compressibilities jS for binary liquidmixtures of n-C4H9OH with n-C5H12, or n-C6H14, or n-C7H16, or n-C8H18, or 2,2,4-ðCH3Þ3C5H9 have also been reportedð4;5Þ at two temperatures. The results of measure-ments of u and jS for binary liquid mixtures of n-C7H15OH with n-C5H12, or n-C6H14, orn-C7H16, or n-C8H18, or 2,2,4-ðCH3Þ3C5H9 have been reportedð6;7Þ at T ¼ 293:15K andT ¼ 303:15K. In this work, the measurements of u were made in binary liquid mixturesof n-C4H9OH with n-C5H12, or n-C6H14, or n-C7H16, or 2,2,4-ðCH3Þ3C5H9 atT ¼ 288:15K, and in binary mixtures of n-hexanol (n-C6H13OHÞ with n-C5H12, or n-C6H14, at T ¼ 298:15K, and in ðn-hexanol+ n-heptane, or n-octane) at T ¼ 298:15Kand T ¼ 303:15K, and the results obtained are reported and interpreted in this paper.

2. Experimental

Liquid n-C5H12; n-C6H14; n-C7H16, and n-C8H18, 2,2,4-ðCH3Þ3C5H9, and n-C4H9OH wereof the same quality and were purified in a similar manner as described earlier.ð4;5Þ Liquidn-C6H13OH of AR quality was obtained from Sisco Research Laboratories Pvt. Ltd.,Mumbai, and was subjected to fractional distillations, and the middle third cut was usedfor the measurements. The densities q of the purified liquid components were deter-mined by using a single-capillary pyknometer as described earlier.ð4Þ The uncertainty inq is estimated to be of the order of 2 � 10�5 g � cm�3. The values of q for the variousliquids are given in table 1. The speeds of sound u in pure liquids and their binarymixtures were measured at various temperatures (controlled with an accuracy of0:01K) and at a frequency of 2MHz with a quartz-crystal ultrasonic interferometer(supplied by Mittal Enterprises, New Delhi, India) in the same manner as describedearlier.ð8;9Þ The uncertainty in u is about 0:5m � s�1.

3. Results and discussion

The values of the speeds of sound u (which refers to the speed of sound in pure liquids) inthe various pure liquids are given in table 1. The values of u in fn-butanol+ n-pentane orn-hexane, or n-heptane, or 2,2,4-(CH3Þ3C5H9g at T ¼ 288:15K are given in table 2,whereas the values of u in ðn-hexanol+ n-pentane, or n-hexane) at T ¼ 298:15K, and inðn-hexanol+ n-heptane, or n-octane) at T ¼ 298:15K and T ¼ 303:15K, are given intable 3, where x refers to the mole fraction of the alkanol (n-C4H9OH or n-C6H13OHÞ inthe mixture. The present values of u in n-C7H16 and n-C6H13OH at T ¼ 298:15K are(1129.8 and 1302.2)m � s�1, respectively, as compared with the availableð13Þ values(1130.18 and 1302.45)m � s�1, respectively, for the above liquids at T ¼ 298:15K. The

1858 J. Nath

TABLE 1. Values of densities q, cubic expansion coefficient a, molar isobaric heat capacities Cp;m;, speeds of sound u, isentropic com-

pressibilities jS, isothermal compressibilities j

T, and molar volumes Vm of the various pure liquids

Liquid T q=ðg � cm�3Þ 103 � a Cp;m; u j

S jT V

m

K Expt Lit K�1 J � K�1 �mol�1 m � s�1 TPa�1 TPa�1 cm3 �mol�1

n-C5H12 288.15 0.63112 0.63114a 1. 544f 162.58g 1056.0 1420.9 1903.9 114.322

298.15 0.62134b 0.62139c 1.565f 165.15g 1006.1b 1590.0 2103.9 116.216

n-C6H14 288.15 0.66383 0.66380a 1.348f 192.21g 1123.2 1194.1 1547.7 129.819

298.15 0.65488 0.65487d 1.373f 195.48g 1077.0 1316.5 1694.9 131.594

n-C7H16 288.15 0.68784 0.68785a 1.225f 219.21g 1173.4 1055.9 1343.3 145.682

298.15 0.67954 0.67960e 1.244f 221.94g 1129.8 1152.9 1459.5 147.462

303.15 0.67525b 0.67522a 1.254f 223.19g 1110.6b 1200.7 1517.7 148.398

n-C8H18 298.15 0.69865 0.69867d 1.151f 251.36g 1169.6 1046.3 1303.2 163.505

303.15 0.69445b 0.69440a 1.157f 253.20g 1150.2b 1088.5 1352.1 164.494

2,2,4-TMP i 288.15 0.69605 1.166f 230.63g 1123.0 1139.2 1418.0 164.116

n-C4H9OH 288.15 0.81338 0.81337a 0.931f 172.69h 1280.8 749.5 881.3 91.131

n-C6H13OH 298.15 0.81532 0.81537e 0.873f 242.9e 1302.2 723.3 840.5 125.323

303.15 0.81172 0.81201a 0.891f 248.3e 1285.6 745.4 867.4 125.878

aReference 10.bReference 5.cReference 11.dReference 12.eReference 13.fDerived from densities in references 10 and 11.gComputed by analytical treatment of the values of C

p;m; given in reference 10.hObtained by extrapolation of C

p;m from reference 5.i 2,2,4-TMP refers to 2,2,4-ðCH3Þ3C5H9.

Speedsof

soundand

isentropiccom

pressibilities1859

TABLE 2. Speeds of sound u, densities q, isentropic compressibilites jS, and the excess isentropiccompressibilities jE

S at T ¼ 288:15K

x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

fð1� xÞ n-C5H12 þ x n-C4H9OHg0.0212 1056.6 0.63420 1412.4 )0.27

0.0982 1061.0 0.64544 1376.3 )4.76

0.1307 1064.4 0.65043 1357.0 )9.82

0.1716 1069.0 0.65687 1332.2 )15.93

0.2111 1074.2 0.66325 1306.6 )22.65

0.2474 1079.0 0.66923 1283.5 )27.66

0.2809 1084.8 0.67486 1259.2 )34.63

0.3254 1092.4 0.68248 1227.9 )41.94

0.3534 1098.0 0.68735 1206.8 )47.37

0.3900 1105.0 0.69381 1180.4 )52.61

0.4292 1113.6 0.70083 1150.6 )58.86

0.4589 1119.6 0.70621 1129.6 )61.40

0.4966 1129.2 0.71312 1099.8 )67.00

0.5298 1137.6 0.71926 1074.3 )70.44

0.5644 1146.2 0.72573 1048.8 )72.21

0.5932 1154.0 0.73117 1027.0 )73.66

0.6292 1164.0 0.73801 1000.1 )74.35

0.6576 1171.5 0.74346 980.1 )73.05

0.6906 1181.5 0.74983 955.4 )72.30

0.7209 1190.6 0.75574 933.5 )70.16

0.7521 1200.0 0.76187 911.5 )66.72

0.7777 1208.0 0.76694 893.5 )63.31

0.8094 1218.2 0.77328 871.4 )58.23

0.8366 1226.3 0.77877 853.9 )51.79

0.8630 1235.0 0.78416 836.1 )45.81

0.8953 1246.0 0.79084 814.5 )37.58

0.9243 1255.8 0.79694 795.7 )28.87

0.9535 1265.6 0.80318 777.3 )18.88

0.9837 1275.3 0.80976 759.3 )6.77

fð1� xÞ n-C6H14 þ x n-C4H9OHg0.0358 1123.6 0.66741 1186.8 1.67

0.1061 1126.0 0.67479 1168.8 2.26

0.1430 1127.6 0.67888 1158.5 2.31

0.1917 1131.2 0.68449 1141.7 )0.20

1860 J. Nath

TABLE 2—(Continued)

x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

0.2384 1134.4 0.69009 1126.1 )1.36

0.2733 1138.0 0.69441 1112.0 )4.18

0.3131 1141.6 0.69949 1097.0 )5.79

0.3364 1144.2 0.70253 1087.3 )7.38

0.3911 1150.6 0.70988 1064.1 )10.71

0.4212 1154.6 0.71405 1050.5 )12.86

0.4516 1158.8 0.71835 1036.7 )14.71

0.4854 1164.0 0.72323 1020.5 )17.15

0.5214 1169.0 0.72856 1004.4 )18.02

0.5574 1175.6 0.73402 985.8 )20.78

0.5890 1181.2 0.73892 970.0 )22.14

0.6262 1188.0 0.74482 951.3 )23.20

0.6474 1192.0 0.74825 940.6 )23.51

0.6799 1199.0 0.75360 923.0 )24.71

0.7206 1207.9 0.76046 901.3 )25.01

0.7430 1212.4 0.76432 890.1 )24.01

0.7630 1217.5 0.76781 878.6 )24.35

0.7996 1226.4 0.77433 858.6 )23.28

0.8250 1232.4 0.77895 845.3 )21.43

0.8536 1239.7 0.78426 829.7 )19.45

0.8622 1242.4 0.78588 824.4 )19.34

0.8736 1244.8 0.78804 818.9 )17.60

0.9230 1258.8 0.79763 791.2 )12.80

0.9584 1268.8 0.80474 771.9 )7.65

0.9771 1274.4 0.80858 761.5 )4.72

fð1� xÞ n-C7H16 þ x n-C4H9OHg0.0188 1173.2 0.68914 1054.3 1.33

0.0807 1173.8 0.69383 1046.1 3.35

0.1624 1175.5 0.70056 1033.0 4.87

0.2085 1177.0 0.70462 1024.5 5.25

0.2574 1179.3 0.70914 1014.0 4.71

0.3001 1182.0 0.71327 1003.5 3.38

0.3366 1184.3 0.71695 994.5 2.60

0.3756 1186.8 0.72102 984.7 1.99

0.4195 1190.5 0.72579 972.1 0.28

0.4507 1193.0 0.72932 963.4 )0.32

Speeds of sound and isentropic compressibilities 1861


x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

0.4806 1195.3 0.73279 955.1 )0.56

0.5186 1199.0 0.73736 943.4 )1.56

0.5537 1202.5 0.74174 932.3 )2.31

0.5817 1206.2 0.74534 922.2 )3.81

0.6084 1209.0 0.74887 913.6 )3.91

0.6465 1213.8 0.75408 900.1 )4.76

0.6799 1217.6 0.75880 888.9 )4.33

0.7059 1221.2 0.76260 879.3 )4.51

0.7288 1225.0 0.76602 869.9 )5.34

0.7636 1230.4 0.77138 856.3 )5.38

0.7864 1234.0 0.77499 847.0 )5.44

0.8157 1239.0 0.77976 835.4 )4.73

0.8361 1242.8 0.78317 826.7 )4.55

0.8634 1248.0 0.78785 814.9 )4.05

0.8869 1252.8 0.79198 804.5 )3.47

0.9142 1259.0 0.79691 791.7 )3.04

0.9302 1262.5 0.79987 784.4 )2.34

0.9734 1273.2 0.80811 763.4 )0.75

0.9879 1277.2 0.81096 755.9 )0.34

fð1� xÞ2; 2; 4-ðCH3Þ3C5H9 þ x n-C4H9OHg0.0503 1125.2 0.69925 1129.6 )0.21

0.1240 1129.0 0.70425 1114.0 )0.95

0.1806 1132.8 0.70843 1100.0 )2.58

0.2180 1135.3 0.71135 1090.7 )3.22

0.2619 1138.5 0.71495 1079.1 )4.11

0.3084 1142.8 0.71897 1065.0 )6.18

0.3650 1148.0 0.72415 1047.8 )7.71

0.4024 1152.2 0.72776 1035.0 )9.48

0.4439 1157.0 0.73196 1020.6 )10.96

0.4763 1161.0 0.73537 1008.9 )12.03

0.5070 1165.2 0.73871 997.1 )13.17

0.5467 1171.0 0.74322 981.2 )14.89

0.5798 1176.4 0.74713 967.1 )16.40

0.6185 1183.0 0.75189 950.3 )17.67

0.6440 1187.2 0.75515 939.5 )17.74

0.6736 1193.0 0.75905 925.7 )18.53

1862 J. Nath

value of u in n-C5H12 at T ¼ 298:15K, and those of u in n-C7H16 and n-C8H18 atT ¼ 303:15K, included in table 1, are those reported earlier.ð5Þ From thermodynamicconsiderations, the speed of sound u0 at zero frequency is given by:ð14Þ

u0 ¼ Vm � f�M�1 � ðop=oVmÞSg1=2; ð1Þ

where Vm and M refer to the molar volume and molar mass of the material, respectively,and ðop=oVmÞS denotes the variation of pressure with molar volume at constant entropy.The speed of sound u0 defined by equation (1) is thus a thermodynamic quantity. Theexperimental speed of sound is equal to u0 over a wide range of frequencies and am-plitudes for most fluids, and so it may be treated as an equilibrium property.ð15Þ Hence,the experimental values of u for the various mixtures have been used to calculate theapparent excess speeds of sound Du (which refer to the deviations of the experimentalvalues of the speeds of sound u in the mixture from the values arising from the molefraction mixture law) from the relation:

Du ¼ u�XNi¼1

xiui ; ð2Þ

where ui refers to the speed of sound in pure component i; xi is the mole fraction of thecomponent i in the mixture, and N is the number of components. The Du for the variousmixtures has been fitted by a method of least-squares to the Redlich–Kisterð16Þ typeequation:

Du=ðm � s�1Þ ¼ xð1� xÞ �Xnj¼1

Ajð2x� 1Þj�1: ð3Þ


x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

0.7014 1198.7 0.76284 912.3 )19.16

0.7332 1205.2 0.76733 897.2 )18.94

0.7631 1212.0 0.77172 882.1 )18.91

0.7854 1217.8 0.77510 869.9 )19.33

0.8049 1222.2 0.77813 860.3 )18.27

0.8316 1229.4 0.78241 845.6 )17.80

0.8571 1236.0 0.78664 832.1 )16.15

0.8772 1241.8 0.79008 820.8 )15.04

0.8969 1247.5 0.79354 809.7 )13.54

0.9209 1254.4 0.79789 796.5 )10.78

0.9399 1260.8 0.80144 784.9 )9.26

0.9646 1268.3 0.80621 771.1 )5.30

0.9862 1276.0 0.81054 757.7 )2.50


TABLE 3. Speeds of sound u, densities q, isentropic compressibilites jS, and the excess isentropiccompressibilities jE

S for the various mixtures

x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

fð1� xÞ n-C5H12 þ x n-C6H13OHg; T ¼ 298:15K

0.0301 1008.5 0.62722 1567.6 )1.95

0.0688 1012.5 0.63565 1534.6 )7.76

0.0930 1016.6 0.64090 1509.8 )15.12

0.1258 1023.2 0.64797 1474.1 )26.64

0.1648 1032.7 0.65632 1428.7 )42.55

0.1970 1041.4 0.66316 1390.4 )55.93

0.2105 1045.3 0.66601 1374.2 )61.54

0.2581 1059.8 0.67601 1317.0 )80.75

0.2933 1071.3 0.68333 1275.1 )93.95

0.3315 1084.0 0.69121 1231.2 )106.15

0.3628 1094.5 0.69761 1196.6 )114.38

0.3810 1100.8 0.70131 1176.7 )118.80

0.4171 1113.0 0.70860 1139.2 )125.26

0.4228 1115.0 0.70974 1133.3 )126.22

0.4495 1124.2 0.71508 1106.5 )129.76

0.4923 1138.3 0.72356 1066.6 )131.95

0.5208 1147.6 0.72915 1041.4 )131.77

0.5567 1159.2 0.73613 1010.9 )130.00

0.5953 1171.2 0.74353 980.5 )125.37

0.6283 1181.4 0.74979 955.6 )120.07

0.6517 1188.4 0.75419 938.8 )115.32

0.6956 1202.0 0.76234 907.9 )105.50

0.7264 1212.0 0.76798 886.4 )98.23

0.7629 1223.0 0.77458 863.1 )87.23

0.7895 1231.4 0.77934 846.2 )79.01

0.8331 1246.0 0.78703 818.4 )65.41

0.8663 1256.5 0.79280 798.9 )53.22

0.8987 1268.0 0.79837 779.0 )42.07

0.9412 1282.2 0.80557 755.1 )25.06

0.9765 1294.2 0.81145 735.8 )10.24


0.0356 1077.2 0.66017 1305.4 4.80

0.0631 1079.0 0.66445 1292.7 4.71

0.1038 1083.0 0.67083 1271.0 2.13

1864 J. Nath


x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

0.1480 1089.5 0.67781 1242.9 )4.57

0.1811 1095.4 0.68307 1220.1 )10.93

0.2197 1103.4 0.68923 1191.7 )19.72

0.2480 1109.3 0.69376 1171.4 )25.34

0.2823 1117.2 0.69928 1145.7 )32.91

0.3142 1124.8 0.70443 1122.0 )39.43

0.3505 1133.0 0.71031 1096.7 )44.81

0.3838 1141.0 0.71573 1073.2 )49.68

0.4112 1147.8 0.72020 1053.9 )53.41

0.4481 1156.5 0.72624 1029.5 )56.50

0.4786 1163.8 0.73124 1009.7 )58.39

0.5110 1171.2 0.73657 989.7 )59.07

0.5427 1178.6 0.74178 970.5 )59.09

0.5744 1186.3 0.74700 951.2 )58.93

0.6055 1193.6 0.75211 933.3 )57.47

0.6408 1202.0 0.75792 913.2 )55.27

0.6793 1211.5 0.76423 891.5 )52.28

0.7114 1220.2 0.76948 872.9 )49.99

0.7358 1226.5 0.77345 859.5 )47.33

0.7719 1236.4 0.77931 839.4 )43.38

0.8011 1244.5 0.78403 823.5 )39.59

0.8359 1254.6 0.78962 804.6 )34.74

0.8713 1265.4 0.79526 785.3 )29.56

0.8923 1271.4 0.79859 774.7 )25.49

0.9372 1284.7 0.80563 752.1 )16.36

0.9694 1293.6 0.81063 737.2 )8.21


0.0419 1129.9 0.68417 1144.9 4.56

0.0849 1132.0 0.68911 1132.4 5.44

0.1320 1135.7 0.69470 1116.0 4.22

0.1697 1139.8 0.69928 1100.8 1.57

0.2211 1146.4 0.70563 1078.3 )3.25

0.2711 1153.4 0.71192 1055.9 )7.79

0.3355 1164.2 0.72018 1024.5 )15.24

0.3878 1173.3 0.72701 999.2 )20.27

0.4420 1183.2 0.73421 972.9 )24.78



x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

0.4889 1192.0 0.74054 950.4 )27.77

0.5328 1200.0 0.74656 930.2 )29.16

0.6291 1218.8 0.76007 885.7 )30.45

0.6779 1228.8 0.76707 863.4 )29.82

0.7235 1238.0 0.77369 843.3 )27.84

0.8077 1256.4 0.78609 805.9 )22.80

0.8363 1263.0 0.79035 793.2 )20.58

0.8957 1276.8 0.79928 767.5 )14.45

0.9115 1280.5 0.80167 760.8 )12.50

0.9793 1297.0 0.81208 732.0 )3.20


0.0274 1110.4 0.67836 1195.6 3.51

0.1750 1121.0 0.69583 1143.6 1.53

0.2306 1127.9 0.70270 1118.6 )3.11

0.2772 1134.6 0.70857 1096.3 )7.69

0.3441 1145.4 0.71719 1062.8 )14.68

0.3770 1151.0 0.72151 1046.2 )17.78

0.3800 1151.3 0.72191 1045.1 )17.64

0.4122 1157.0 0.72618 1028.7 )20.49

0.4458 1162.8 0.73069 1012.2 )22.54

0.4782 1168.7 0.73509 996.0 )24.49

0.5072 1174.2 0.73906 981.4 )26.07

0.5419 1180.7 0.74387 964.3 )27.26

0.5736 1186.6 0.74830 949.1 )27.60

0.6261 1197.2 075573 923.2 )28.22

0.6432 1201.0 0.75817 914.4 )28.59

0.6443 1200.8 0.75833 914.5 )27.95

0.6871 1210.2 0.76450 893.1 )27.85

0.7052 1214.3 0.76713 884.1 )27.59

0.7332 1220.4 0.77122 870.6 )26.54

0.7600 1226.8 0.77517 857.1 )25.89

0.7990 1236.0 0.78096 838.2 )23.76

0.8248 1242.0 0.78483 826.0 )21.78

0.8558 1249.4 0.78950 811.4 )19.03

0.8826 1256.5 0.79357 798.2 )16.98

0.9091 1263.0 0.79763 785.9 )13.95

1866 J. Nath


x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

0.9389 1270.4 0.80221 772.4 )9.92

0.9720 1278.5 0.80735 757.8 )4.68

fð1� xÞn-C8H18 þ x n-C6H13OHg; T ¼ 298:15K

0.0402 1171.2 0.70193 1038.6 0.84

0.1142 1175.0 0.70862 1022.1 0.77

0.1796 1180.0 0.71481 1004.7 )1.25

0.2385 1184.8 0.72059 988.6 )2.78

0.3118 1191.8 0.72807 967.0 )5.23

0.3630 1197.0 0.73349 951.5 )6.65

0.4026 1201.5 0.73779 938.9 )7.95

0.4651 1208.8 0.74477 918.9 )9.36

0.5082 1214.0 0.74974 905.0 )9.88

0.5641 1222.0 0.75637 885.4 )11.40

0.6005 1226.9 0.76079 873.2 )11.37

0.6489 1234.2 0.76682 856.1 )11.64

0.6998 1242.6 0.77332 837.5 )11.80

0.7405 1249.6 0.77865 822.5 )11.50

0.7933 1259.4 0.78573 802.4 )10.96

0.8318 1267.2 0.79101 787.3 )10.43

0.8983 1280.5 0.80038 762.0 )7.53

0.9254 1286.0 0.80429 751.8 )5.78

0.9702 1296.0 0.81086 734.3 )2.93


0.0422 1150.0 0.69798 1083.3 4.35

0.0781 1151.0 0.70111 1076.6 6.00

0.1466 1155.6 0.70737 1058.6 4.65

0.1872 1159.2 0.71125 1046.3 2.67

0.2249 1162.8 0.71495 1034.5 0.76

0.2685 1167.0 0.71935 1020.7 )1.20

0.2972 1170.8 0.72232 1010.0 )3.88

0.3436 1175.4 0.72722 995.3 )5.21

0.3991 1181.2 0.73327 977.4 )6.43

0.4365 1185.5 0.73746 964.8 )7.36

0.4766 1190.4 0.74205 951.0 )8.25

0.5084 1194.0 0.74575 940.6 )8.10

0.5427 1198.6 0.74983 928.3 )8.72


The resulting values of the coefficients Aj of equation (3), and the standard deviationsdðDuÞ of the fits for the various mixtures are given in table 4. The isentropic com-pressibility jS is defined by jS ¼ f�V�1

m ðoVm=opÞSg. The values of jS of the mixturesof n-C4H9OH and n-C5H12, or n-C6H14, or n-C7H16, or 2,2,4-(CH3Þ3C5H9, and of themixtures of n-C6H13OH and n-C5H12, or n-C6H14, or n-C7H16, or n-C8H18, were obtainedfrom the equation:

jS ¼ ðV Em þ V id

m Þ�

u2 �XNi¼1

xiMi

!; ð4Þ

by using the VEm for the mixtures of n-C4H9OH reported by Nath and Pandey,ð1Þ and the

VEm for mixtures of n-C6H13OH reported by Treszczanowicz and Benson,ð12Þ and Tres-

zczanowicz et al.ð17Þ In equation (4), Vidm ¼

PxiV

m;i is the ideal molar volume of the

mixture. The jS values of the mixtures of n-C4H9OH are given in table 2, whereas the jS

values of mixtures of n-C6H13OH are given in table 3. The imprecision in the values of jS

is of the order of 0:5TPa�1. Also given in tables 2 and 3 are the values of the quantityPxiMi=ðVE

m þ VidmÞ, which refers to the calculated densities q of the mixtures.

The excess isentropic compressibility jES given in tables 2 and 3 was estimated from

the isentropic compressibility jS of the mixture using the relation:

jES ¼ jS � jid

S ; ð5Þwhere jid

S was obtained as outlined in references 18 and 19 by using the values ofa;V

m; jS; j

T and C

p;m of the pure liquids given in table 1.


x u q jS jES

m � s�1 g � cm�3 TPa�1 TPa�1

0.5735 1202.8 0.75355 917.3 )8.94

0.5921 1205.2 0.75582 910.9 )8.70

0.6350 1211.8 0.76116 894.7 )9.20

0.6605 1216.0 0.76439 884.7 )9.61

0.6977 1222.2 0.76918 870.3 )9.64

0.7282 1228.0 0.77317 857.7 )10.14

0.7573 1234.2 0.77704 844.9 )11.10

0.7855 1240.2 0.78085 832.6 )11.66

0.8149 1246.6 0.78488 819.9 )11.82

0.8394 1252.2 0.78829 809.0 )12.04

0.8680 1258.6 0.79232 796.8 )11.49

0.8937 1264.8 0.79599 785.3 )11.28

0.9281 1272.0 0.80099 771.6 )8.91

0.9631 1279.0 0.80616 758.3 )5.38

0.9901 1284.0 0.81022 748.6 )1.75

1868 J. Nath

The jES values for the various mixtures obtained through equation (5) were fitted by the

method of least squares with the equation:

jES=TPa

�1 ¼ xð1� xÞ �Xnj¼1

Bjð2x� 1Þj�1: ð6Þ

The values of the coefficient Bj of equation (6), along with the standard deviations dðjESÞ

for the various mixtures are given in table 5. The values of jES for mixtures of n-C4H9OH

at T ¼ 288:15K are plotted against x in figure 1, and the values of jES for mixtures of n-

C6H13OH at T ¼ 298:15K are plotted against x in figure 2.

TABLE 4. Values of the coefficients Aj of equation (3) and the standard deviations dðDuÞ for thevarious mixtures

Mixture T A1 A2 A3 A4 dðDuÞ

K m � s�1

fð1� xÞ n-C5H12 þ x n-C4H9OHg 288.15 )153.695 35.429 )1.798 13.153 0.26

fð1� xÞn-C6H14 þ x n-C4H9OHg 288.15 )144.378 )6.679 1.447 19.829 0.28

fð1� xÞ n-C7H16 þ x n-C4H9OHg 288.15 )117.665 )19.165 )33.691 )17.053 0.35

fð1� xÞ2; 2; 4-ðCH3Þ3C5H9 þ x n-C4H9OHg 288.15 )150.248 )38.541 )6.673 )2.048 0.19




303.15 )101.389 23.103 )33.588 39.593 0.18

fð1� xÞ n-C8H18 þ x n-C6H13OHg 298.15 )91.750 )9.973 0.512 21.666 0.20

303.15 )100.598 )27.617 4.111 100.646 0.29

TABLE 5. Values of the coefficients Bj of equation (6) and the standard deviations dðjESÞ for the

various mixtures

Mixture T B1 B2 B3 B4 dðjES Þ

K TPa�1

fð1� xÞ n-C5H12 þ x n-C4H9OHg 288.15 )269.010 )198.483 55.550 )20.287 0.49

fð1� xÞ n-C6H14 þ x n-C4H9OHg 288.15 )70.039 )108.970 )4.926 )27.376 0.42

fð1� xÞ n-C7H16 þ x n-C4H9OHg 288.15 )7.081 )53.385 23.987 2.695 0.42

fð1� xÞ2; 2; 4-ðCH3Þ3C5H9 þ x n-C4H9OHg 288.15 )52.654 )77.978 )37.994 )12.266 0.28




303.15 )103.633 )92.560 86.799 )79.609 0.38


303.15 )33.674 )18.403 12.919 )148.377 0.39


The values of jES have been found to be negative throughout the entire range of x for

fð1� xÞ n-C5H12 þ x n-C4H9OH and ð1� xÞ2; 2; 4-ðCH3Þ3C5H9g at T ¼ 288:15K, andfor fð1� xÞ n-C5H12 þ x n-C6H13OHg at T ¼ 298:15K. The jE

S has been found to bepositive at lower values of x, and negative at higher values of x for fð1� xÞn-C6H14þx n-C4H9OHg and fð1� xÞ n-C7H16 þ x n-C4H9OHg at T ¼ 288:15K, with inversionof the sign of jE

S occurring at x � 0:20 and x � 0:45, respectively, for these mixtures.The jE

S has been found to be positive at lower values of x and negative at higher valuesof x for fð1� xÞ n-C6H14 þ x n-C6H13OHg; fð1� xÞ n-C7H16 þ x n-C6H13OHg, andfð1� xÞ n-C8H18 þ x n-C6H13OHg at T ¼ 298:15K and T ¼ 303:15K. At T ¼298:15K, the inversion of the sign of the jE

S occurs at x � 0:12; x � 0:18, and x � 0:15,respectively, for these mixtures. At x ¼ 0:5, the jE

S for the various mixtures of alkaneswith n-C4H9OH at T ¼ 288:15K, follows the sequence: n-C7H16 > 2; 2; 4-ðCH3Þ3C5H9 > n-C6H14 > n-C5H12.At T ¼ 298:15K, and x ¼ 0:5, the jE

S for the various mixtures of alkanes with n-C6H13OH follows the sequence: n-C8H18 > n-C7H16 > n-C6H14 > n-C5H12.The above sequence in the value of jE

S at x ¼ 0:5, for mixtures of n-C4H9OH withalkanes at T ¼ 288:15K, and for mixtures of n-C6H13OH with alkanes at T ¼ 298:15K,is the same as found in the values of the excess molar volumesð1Þ (at T ¼ 288:15K and

FIGURE 1. Plot of isentropic compressibility jES against the mole fraction x of n-C4H9OH for the

various systems at T ¼ 288:15K: �; fð1� xÞn-C5H12 þ x n-C4H9OHg;d; fð1� xÞn-C6H14 þ xn-C4H9OHg; ; fð1� xÞ n-C7H16 þ xC4H9OHg; ; fð1� xÞ2; 2;4-ðCH3Þ3C5H9 þ x n-C4H9OHg.

1870 J. Nath

T ¼ 298:15K), and excess isentropic compressibilitiesð4;5Þ at x ¼ 0:5, for binary mix-tures of n-C4H9OH with n-C5H12, or n-C6H14, or n-C7H16, or n-C8H18. The same se-quence is also foundð2;3Þ in the values of VE

m at x ¼ 0:5 for mixtures of n-C7H15OH withn-C5H12, or n-C6H14, or n-C7H16, or n-C8H18. Also, the same sequence is observedð6;7Þ inthe values of jE

S at x ¼ 0:5 for mixtures of n-C7H15OH with n-C5H12, or n-C6H14, or n-C7H16, or n-C8H18.

The values of jES of the (alkanol+alkane) mixtures may be interpretedð6Þ as the result

of the contributions of the various types of intermolecular interactions operating betweenthe components of these mixtures. Three main types of contributions are important indetermining the thermodynamic excess properties of (alkanol+alkane) mixtures:physical, due to non-specific van der Waals type interactions; chemical, due to hydrogen-bonding; and structural, due to changes of interstitial accommodation and free volume.

FIGURE 2. Plot of isentropic compressibility jES against the mole fraction x of n-C6H13OH for the

various systems at T ¼ 298:15K: �; fð1� xÞn-C5H12 þ x n-C6H13OHg; ; fð1� xÞn-C6H14þx n-C6H13OHg; ; fð1� xÞn-C7H16 þ x n-C6H13OHg;d; fð1� xÞn-C8H18 þ x n-C6H13OHg.


The chemical contribution is relatively important a low values of x, where the breakingof the self-association of the alkanol molecules due to H-bonds makes a positive con-tribution to jE

S. At higher values of x, the dissociation of the alkanol is of less importance,and the balance is essentially between physical and structural contributions. The positivevalues of jE

S for fð1� xÞ n-C6H14 þ x n-C4H9OHg; fð1� xÞ n-C7H16 þ x n-C4H9OHg;fð1� xÞ n-C6H14 þ x n-C6H13OHg; fð1� xÞ n- C7H16 þ x n-C6H13OHg, and fð1� xÞn-C8H18 þ x n-C6H13OHg at low values of x may thus be attributed to the predominanceof the contributions to jE

S from the breaking of the self-association due to H-bonds inthe alkanol (butanol or hexanol) molecules in these mixtures. The negative values of jE

S

at low x values in the case of fð1� xÞ n-C5H12 þ x n-C4H9OHg; fð1� xÞ2; 2; 4-ðCH3Þ3C5H9 þ x n-C4H9OHg, and fð1� xÞ n-C5H12 þ x n-C6H13OHg may be thought of asbeing due to the predominance of contributions to jE

S from physical and structural effectsover those due to breaking of self-association via hydrogen bonding in the butanol orhexanol molecules.

The author greatly thanks the Head, Chemistry Department, DDU Gorakhpur Uni-versity, Gorakhpur, for providing laboratory facilities. Thanks are also due to the Councilof Scientific and Industrial Research, New Delhi, India, for financial support {schemenumber: 01(1585)/99-EMR-II}.

REFERENCES

1. Nath, J.; Pandey, J. G. J. Chem. Eng. Data 1997, 42, 128–131.2. Nath, J.; Pandey, J. G. J. Chem. Eng. Data 1997, 42, 514–516.3. Nath, J.; Pandey, J. G. J. Chem. Eng. Data 1997, 42, 1137–1139.4. Nath, J. J. Chem. Thermodyn. 1997, 29, 853–863.5. Nath, J. J. Chem. Thermodyn. 1998, 30, 885–895.6. Nath, J. J. Chem. Thermodyn. 1998, 30, 1385–1392.7. Nath, J. Fluid Phase Equilibr. 2000, 175, 63–73.8. Nath, J. J. Chem. Thermodyn. 1996, 28, 481–490.9. Nath, J. J. Chem. Thermodyn. 1996, 28, 1083–1092.10. Timmermans, J. Physico-Chemical Constants of Pure Organic Compounds. Elsevier:

Amsterdam. 1950.11. Riddick, J. A.; Bunger, W. B. Techniques of Chemistry, Vol. II. Organic solvents, physical

properties and methods of purification. Weissberger, A.: editor: third ed. Wiley-Interscience:New York. 1970.

12. Treszczanowicz, A. J.; Benson, G. C. J. Chem. Thermodyn. 1980, 12, 173–179.13. Kiyohara, O.; Benson, G. C. J. Chem. Thermodyn. 1979, 11, 861–873.14. Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids. Wiley:

New York. 1954.15. Rowlinson, J. S. Liquids and Liquid Mixtures. Butterworths: London. 1959.16. Redlich, O.; Kister, A. T. J. Am. Chem. Soc. 1949, 71, 505–507.17. Treszczanowicz, A. J.; Treszczanowicz, T.; Benson, G. C. Fluid Phase Equilibr. 1993, 89, 31–

56.18. Benson, G. C.; Kiyohara, O. J. Chem. Thermodyn. 1979, 11, 1061–1064.19. Handa, Y. P.; Halpin, C. J.; Benson, G. C. J. Chem. Thermodyn. 1981, 13, 875–886.

(Received 3 April 2002; in final form 25 June 2002)

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1872 J. Nath

speeds of sound in and isentropic compressibilities of (n-butanol + n-pentane, or n-hexane, or...

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