speeds of sound in and isentropic compressibilities of (n-butanol + n-pentane) att=298.15 k, and...

J. Chem. Thermodynamics 1998, 30, 885]895Article No. ct980358

Speeds of sound in and isentropic( )compressibilities of n-butanol H n-pentane

(at T s 298.15 K, and n-butanol H n-hexane,or n-heptane, or n-octane, or

)2,2,4-trimethylpentane at T s 303.15 K

Jagan NathChemistry Department, Gorakhpur Uni ersity, Gorakhpur 273009, India

Measurements of speeds of sound u have been made in binary mixtures of n-butanolŽ . Ž .n-C H OH with n-pentane n-C H at T s 298.15 K, and in the mixtures of n-C H OH4 9 5 12 4 9

Ž . Ž . Ž .with n-hexane n-C H , or n-heptane n-C H , or n-octane n-C H , or 2,2,4-trimethyl6 14 7 16 8 18� Ž . 4pentane 2,2,4- CH C H at T s 303.15 K. Values of u have been used to calculate the3 3 5 9

apparent excess speeds of sound Du and the isentropic compressibilities k for theseSmixtures. The excess isentropic compressibilities k E have also been calculated from theS

E � Žvalues of k . The k values have been found to be highly negative for xn-C H OH q 1 yS S 4 9. 4 Ex n-C H . The values of k have been found to be positive at lower mole fractions of5 12 S

� Ž . 4n-C H OH and negative at its higher mole fractions for xn-C H OH q 1 y x n-C H ,4 9 4 9 6 14� Ž . 4 � Ž . 4 �xn-C H OH q 1 y x n-C H , xn-C H OH q 1 y x n-C H , and xn-C H OH q4 9 7 16 4 9 8 18 4 9Ž . Ž . 4 E1 y x 2,2,4- CH C H . The inversion of sign in k occurs at x f 0.11, x f 0.60, x f 0.89,3 3 5 9 Sand x f 0.26, respectively, for these mixtures. The Du and k E have been fitted withSsmoothing equations. Q 1998 Academic Press

ŽKEYWORDS: experimental; speeds of sound; isentropic compressibilities; n-butanol q.alkanes

1. Introduction

Mixtures of alkanes with alkanols are of particular interest from the theoreticalviewpoint of models of hydrogen-bonded systems. Systematic studies of thethermodynamic excess properties provide important information concerning thedeeper understanding of the molecular liquid structure and the intermolecularinteractions predominated by the self-association of the alkanol molecules throughhydrogen bonding. These studies are also important from the viewpoint of the

Ž .prediction of the thermodynamic properties of alkane q alkanol mixtures ofcomponents having varying numbers of CH units in the alkyl chain or2varying numbers of CH substituents attached to the alkyl chain in the alkane3or alkanol molecules. The temperature dependence of the thermodynamicproperties of these mixtures is also important from the viewpoint of understandingthe extent of self-association of the alkanol molecules. Accordingly, Wagner and

0021]9614r98r070885 q 11 $30.00r0 Q 1998 Academic Press

J. Nath886

Heintz Ž1. and Heintz et al.Ž2. have determined excess molar volumes V E ofmmixtures of nonane and hexane with five different n-alkanols at various

Ž3. E Žtemperatures. Fuente et al. determined V of nonan-1-ol q n-decane, or n-m. Ž . Ž4,5.tetradecane at the temperatures T s 298.15, 308.15, and 318.15 K. Zielkiewicz

E Žhas measured total vapour pressures and V of heptane q propan-2-ol, or butan-m.1-ol, or 2-methylpropan-1-ol, or 2-methylpropan-2-ol, or pentan-1-ol at T s

Ž6. E � Ž . Ž313.15 K. Franjo et al. have determined V of xCH CH OH q 1 ym 3 2 5. Ž . 4 Ž7. Ex CH CH CH at T s 298.15 K. Lemon et al. have determined V and3 2 4 3 m

E Ž . Žexcess molar enthalpies H of butane q propan-1-ol at T s 298.15, 323.15, andm. Ž . Ž8.348.15 K and at pressures 5, 10, and 15 MPa. Morrone and Francesconi have

E Ž .determined V of n-hexane, or cyclohexane q propan-2-ol, or butan-2-ol atmŽ . Ž9. ET s 288.15 and 298.15 K. Although Nath and Pandey have measured V form

Ž . Ž . Žmixtures of n-butanol n-C H OH with n-pentane n-C H , or n-hexane n-4 9 5 12. Ž . Ž .C H , or n-heptane n-C H , or n-octane n-C H , or 2,2,4-trimethylpentane6 14 7 16 8 18

� Ž . 4 Ž . Ž10.2,2,4- CH C H at the temperatures 288.15 and 298.15 K, and Nath has3 3 5 9Žmeasured speeds of sound u in, and isentropic compressibilities k for, n-butanolS

.q n-pentane, or n-hexane, or n-heptane, or n-octane, or 2,2,4-trimethylpentane atT s 293.15 K, u and k of these mixtures with n-butanol at other temperaturesShave not been determined. In this work, measurements of u have been made inŽ . Žn-butanol q n-pentane at T s 298.15 K, and n-butanol q n-hexane, or n-

.heptane, or n-octane, or 2,2,4-trimethylpentane at T s 303.15 K, and the resultsobtained are reported and interpreted in this paper.

2. Experimental

Ž .Liquid n-C H OH, n-C H , n-C H , n-C H , n-C H , and 2,2,4- CH C H4 9 5 12 6 14 7 16 8 18 3 3 5 9were of the same quality and were purified in a similar manner as describedearlier.Ž10. The densities r* of the pure liquid components were determined by

Ž 3.using a single-capillary pyknometer capacity about 25 cm made of Pyrex glass.The capillary had a 1 mm bore and an etched mark around it near the top endwhich could be closed with an outside cap. All apparent masses were determined

. y5 Ž .with an accuracy of 1 10 g using a K. Roy model no. K-15 super balance, andcorrection for the buoyancy of air was made. The uncertainty in r* is estimated to

. y5 . y3be of the order of "2 10 g cm . The values of r* are given in table 1. Thespeeds of sound u in pure liquids and their binary mixtures were measured at a

Žfrequency of 3 MHz with a quartz-crystal ultrasonic interferometer supplied by. Ž10 ] 13.Mittal Enterprises, New Delhi, India in the same manner as described earlier.

3. Results and discussion

Ž .The values of u* which refer to the speed of sound in pure liquids in liquidŽ .n-C H , n-C H , n-C H , n-C H , 2,2,4- CH C H , and n-C H OH are5 12 6 14 7 16 8 18 3 3 5 9 4 9

given in table 1, whereas the values of u in binary mixtures of n-C H OH with4 9Ž .n-C H , or n-C H , or n-C H , or n-C H , or 2,2,4- CH C H are given in5 12 6 14 7 16 8 18 3 3 5 9

table 2, where x refers to the mole fraction of n-C H OH. The present values of4 9

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TABLE 2. Speeds of sound u, densities r, isentropic compressibilities k , and the excess isentropicSE Ž . �compressibilities k of n-C H OH q n-C H at T s 298.15 K, and of n-C H OH q n-C H , orS 4 9 5 12 4 9 6 14

Ž . 4n-C H , or n-C H , or 2,2,4- CH C H at T s 303.15 K7 16 8 18 3 3 5 9

Eu r k kS Sx y1 y3 y1 y1. .m s g cm TPa TPa

� Ž . 4xn-C H OH q 1 y x n-C H4 9 5 12

0.0230 1007.4 0.62411 1578.8 y0.800.0517 1009.3 0.62830 1562.4 y3.760.1170 1015.0 0.63823 1520.9 y12.940.1547 1019.4 0.64417 1493.9 y20.140.2169 1027.9 0.65425 1446.6 y32.910.2524 1033.6 0.66015 1417.9 y40.840.2802 1038.3 0.66484 1395.2 y46.720.3230 1046.3 0.67219 1358.2 y56.150.3639 1054.4 0.67935 1324.0 y64.250.3950 1061.0 0.68488 1297.0 y70.130.4320 1069.5 0.69155 1264.2 y76.940.4755 1079.6 0.69952 1226.5 y82.860.5019 1086.0 0.70442 1203.7 y85.720.5363 1094.8 0.71088 1173.6 y89.080.5775 1105.6 0.71872 1138.3 y91.190.6162 1115.5 0.72579 1107.3 y91.550.6314 1120.6 0.72914 1092.2 y91.930.6790 1134.3 0.73850 1052.4 y89.770.7019 1141.0 0.74305 1033.7 y87.630.7365 1151.7 0.75000 1005.2 y83.840.7572 1158.1 0.75419 988.6 y80.640.7962 1170.5 0.76217 957.6 y73.340.8162 1177.1 0.76630 941.8 y68.980.8552 1189.6 0.77445 912.4 y58.060.8858 1200.2 0.78092 889.0 y48.860.9159 1210.5 0.78736 866.8 y38.150.9378 1218.0 0.79209 851.0 y29.460.9678 1228.4 0.79866 829.8 y16.37

� Ž . 4xn-C H OH q 1 y x n-C H4 9 6 14

0.0668 1054.6 0.65705 1368.4 1.120.0721 1054.8 0.65761 1366.8 1.280.1150 1057.3 0.66226 1350.7 y0.220.1798 1062.1 0.66968 1323.7 y3.840.2187 1065.4 0.67435 1306.4 y6.300.2741 1071.0 0.68126 1279.7 y10.760.3161 1075.8 0.68671 1258.2 y14.480.3462 1079.7 0.69072 1241.9 y17.540.3922 1086.3 0.69703 1215.8 y22.540.4343 1092.4 0.70299 1192.0 y26.090.4737 1098.7 0.70873 1168.9 y29.380.5239 1107.6 0.71627 1138.0 y33.770.5612 1115.0 0.72204 1114.0 y37.110.5935 1121.2 0.72715 1094.0 y38.520.6362 1130.1 0.73408 1066.7 y40.210.6647 1135.8 0.73881 1049.2 y39.940.6981 1143.6 0.74447 1027.1 y40.470.7309 1151.2 0.75014 1005.9 y39.700.7706 1161.3 0.75718 979.3 y38.600.7956 1167.4 0.76172 963.3 y36.510.8258 1175.3 0.76729 943.5 y33.77


TABLE 2}continued


0.8590 1184.3 0.77357 921.7 y29.880.8921 1193.5 0.77997 900.1 y24.880.9190 1201.2 0.78530 882.5 y20.100.9417 1207.9 0.78988 867.7 y15.470.9701 1216.1 0.79573 849.8 y8.33

� Ž . 4xn-C H OH q 1 y x n-C H4 9 7 16

0.0844 1109.2 0.68133 1193.0 8.730.1323 1109.7 0.68527 1185.0 10.820.1691 1110.3 0.68844 1178.3 12.270.2217 1111.7 0.69319 1167.3 13.540.2623 1113.0 0.69702 1158.1 14.350.3142 1116.1 0.70215 1143.3 13.080.3619 1119.2 0.70710 1129.0 12.000.4053 1122.7 0.71181 1114.6 10.330.4409 1125.8 0.71582 1102.2 8.890.4728 1129.2 0.71953 1090.0 6.940.5190 1134.2 0.72511 1072.1 4.650.5546 1138.7 0.72959 1057.1 2.320.5835 1142.5 0.73334 1044.7 0.650.6188 1147.8 0.73807 1028.4 y1.970.6512 1152.7 0.74257 1013.5 y3.740.6843 1158.2 0.74732 997.5 y5.720.7143 1163.6 0.75176 982.5 y7.460.7429 1168.4 0.75613 968.8 y8.000.7704 1173.9 0.76046 954.2 y9.440.7968 1179.0 0.76473 940.7 y9.830.8287 1185.7 0.77006 923.7 y10.310.8550 1191.0 0.77459 910.1 y9.710.8812 1196.5 0.77923 896.4 y8.720.9027 1202.0 0.78315 883.8 y8.830.9293 1207.9 0.78811 869.7 y6.930.9497 1212.7 0.79202 858.5 y5.420.9679 1217.2 0.79558 848.4 y3.850.9708 1218.0 0.79616 846.7 y3.66

� Ž . 4xn-C H OH q 1 y x n-C H4 9 8 18

0.0709 1149.3 0.69804 1084.6 5.100.1396 1149.1 0.70231 1078.3 8.240.1972 1149.0 0.70620 1072.6 11.070.2508 1150.0 0.71007 1064.9 11.880.2861 1150.3 0.71277 1060.3 13.210.3438 1151.9 0.71741 1050.5 13.700.3776 1153.2 0.72028 1044.0 13.610.4297 1155.5 0.72493 1033.2 13.260.4556 1157.0 0.72735 1027.0 12.550.4984 1159.6 0.73152 1016.6 11.650.5418 1162.5 0.73596 1005.4 10.700.5752 1164.8 0.73955 996.6 10.240.6089 1167.6 0.74331 986.8 9.280.6426 1171.0 0.74724 975.9 7.670.6766 1174.3 0.75138 965.1 6.740.7032 1177.0 0.75475 956.4 6.140.7308 1180.4 0.75837 946.4 4.91

J. Nath890

TABLE 2}continued


0.7591 1184.1 0.76223 935.7 3.610.7918 1188.4 0.76687 923.3 2.620.8163 1192.2 0.77048 913.1 1.390.8388 1195.2 0.77391 904.5 1.350.8652 1199.7 0.77808 893.0 0.320.8895 1203.5 0.78206 882.8 0.200.9127 1207.8 0.78599 872.2 y0.380.9352 1212.0 0.78993 861.8 y0.650.9516 1215.3 0.79288 853.9 y0.910.9823 1221.2 0.79861 839.6 y0.27

� Ž . Ž . 4xn-C H OH q 1 y x 2,2,4- CH C H4 9 3 3 5 9

0.0831 1064.9 0.68874 1280.3 1.610.1195 1066.5 0.69124 1271.9 2.250.1962 1071.0 0.69692 1250.9 1.670.2321 1073.7 0.69977 1239.6 0.610.2894 1078.4 0.70458 1220.4 y1.250.3327 1082.5 0.70844 1204.6 y3.080.3729 1086.8 0.71220 1188.8 y5.180.4186 1091.9 0.71670 1170.3 y7.190.4555 1097.1 0.72051 1153.1 y10.300.4981 1102.7 0.72512 1134.2 y12.020.5293 1107.5 0.72865 1118.9 y14.070.5643 1113.3 0.73276 1101.1 y16.280.5927 1118.1 0.73622 1086.5 y17.640.6315 1125.2 0.74114 1065.7 y19.420.6638 1131.3 0.74542 1048.2 y20.220.6972 1138.7 0.75002 1028.3 y21.960.7197 1143.9 0.75322 1014.6 y22.880.7493 1150.2 0.75758 997.8 y22.160.7780 1157.7 0.76196 979.2 y22.960.8099 1165.6 0.76702 959.6 y21.780.8197 1167.9 0.76862 953.8 y20.970.8527 1177.3 0.77414 932.0 y19.700.8752 1183.7 0.77805 917.3 y17.910.8923 1188.7 0.78110 906.0 y16.250.9186 1197.2 0.78593 887.7 y13.840.9369 1203.1 0.78940 875.2 y11.350.9569 1209.7 0.79328 861.4 y8.190.9799 1217.5 0.79789 845.5 y3.80

. y1Ž .u* in n-C H and n-C H at T s 303.15 K are 1110.6 and 1150.2 m s ,7 16 8 18Ž19. . y1Ž .respectively, as compared with the available values 1112 and 1150 m s ,

respectively, for the above liquids at T s 303.15 K. The present u* in n-C H OH4 9. y1 . y1at T s 303.15 K is 1225.0 m s , compared with the corresponding value 1224 m s

reported by Reddy and Naidu.Ž20. The present u* in n-C H OH at T s 298.15 K is4 9. y1 . y11239.0 m s , compared with the corresponding value 1242 m s obtained by

extrapolation of the results reported by Reddy and Naidu.Ž20. From thermodynamic


considerations, the speed of sound u at zero frequency is given by:Ž21.0

1r2y1u s V yM pr V , 1Ž . Ž .� 40 m m S

where V and M refer to the molar volume and molar mass of the material,mŽ .respectively, and pr V denotes the variation of pressure with molar volumem S

Ž .at constant entropy. The speed of sound u defined by equation 1 is thus a0thermodynamic quantity. The experimental speed of sound is equal to u over a0wide range of frequencies and amplitudes for most fluids, and so it may be treatedas an equilibrium property.Ž22. Hence, the experimental values of u for the variousmixtures have been used to calculate the apparent excess speeds of sound Du fromthe relation:

Du s u y x uU , 2Ž .Ý i i

where uU refers to the speed of sound in the pure component i and x is the molei ifraction of the component i in the mixture. The Du has been fitted by the methodof least-squares with the equation:

njy1y1. . .Dur m s s x 1 y x A 2 x y 1 . 3Ž . Ž . Ž . Ž .Ý j

js1

Ž .The values of the coefficients A of equation 3 , and the standard deviationsjŽ .d Du for the various mixtures are given in table 3. The isentropic compressibility

y1 .Ž .k s yV V r p . The values of k of the mixtures of n-C H OH withS m m S S 4 9Ž .n-C H , or n-C H , or n-C H , or n-C H , or 2,2,4- CH C H were obtained5 12 6 14 7 16 8 18 3 3 5 9

from the relation:

E id 2 .k s V q V r u x M , 4Ž .Ž . Ž .ÝS m m i i

using the data on excess molar volumes V E for the various mixtures reportedmŽ9. Ž . id Urecently. In equation 4 , x is the mole fraction of i in the mixture, V s Ý x Vi m i i

is the molar volume corresponding to the ideal mixture, and M is the molar massiof the component i. The values of V U of the pure components given in table 1i

id Ž .were used to obtain V for calculating k from equation 4 . The values ofm Sisentropic compressibilities kU of the pure liquids n-C H , n-C H , n-C H ,S 5 12 6 14 7 16

Ž . Ž .n-C H , 2,2,4- CH C H , and n-C H OH, obtained from equation 4 with r*,8 18 3 3 5 9 4 9are reported in table 1, whereas the k values of the present mixtures are given inStable 2. The imprecision in k is of the order of "0.5 TPay1. Also given in table 2S

Ž E id.are the values of the quantity Ý x M r V q V which refers to the calculatedi i m mdensities r of the mixtures. The imprecision in r is estimated to be approximately

. y5 . y3 UŽ ."2 10 g cm . The values see table 1 of the isothermal compressibilities kTof the pure liquids were calculated from the cubic expansion coefficient a and theisobaric molar heat capacity C by using the equation:p, m

k s k q a 2V TrC . 5Ž .T S m p , m

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93y

207.

4660

64.8

612

y48

.463

10.

344

95

12�

Ž.

4xn

-CH

OH

q1

yx

n-C

Hy

128.

1409

y15

9.29

37y

0.41

39y

13.0

725

0.33

49

614

�Ž

.4

xn-C

HO

Hq

1y

xn-

CH

21.4

885

y11

4.67

48y

27.0

112

y17

.433

30.

334

97

16�

Ž.

4xn

-CH

OH

q1

yx

n-C

H48

.146

3y

40.7

220

y19

.475

4y

11.6

981

0.30

49

818

�Ž

.Ž

.4

xn-C

HO

Hq

1y

x2,

2,4-

CH

CH

y49

.455

7y

123.

2829

y41

.593

03.

2008

0.36

49

33

59


The values of a and C used to calculated k of the pure liquids from equationp, m TŽ .5 are given in table 1, with references.

The excess isentropic compressibilities k E given in table 2 were estimated fromSthe isentropic compressibilities k of the mixtures by using the relation:S

k E s k y k id , 6Ž .S S S

id Ž . Ž .where k was obtained as outlined in references 23 and 24 , by using the valuesSof a*, V U , kU , kU , and CU of the pure liquid components given in table 1.m S T p, m

E Ž .The k values for the various mixtures obtained through equation 6 have beenSfitted by the method of least-squares with the equation:

njy1E y1 . .k rTPa s x 1 y x B 2 x y 1 . 7Ž . Ž . Ž .ÝS j

js1

Ž .The values of the coefficients B of equation 7 , along with the standard deviationsjŽ E . Ed k for the various systems are given in table 4. The values of k have beenS S

Ž .plotted against x n-C H OH in figure 1.4 9The k E has been found to be negative throughout the entire range of x forS

� Ž . 4 Exn-C H OH q 1 y x n-C H . The values of k have been found to be4 9 5 12 S�positive at lower values of x, and negative at higher values of x for xn-

Ž . 4 � Ž . 4 �C H OH q 1 y x n-C H , xn-C H OH q 1 y x n-C H , xn-C H OH q4 9 6 14 4 9 7 16 4 9Ž . 4 � Ž . Ž . 41 y x n-C H , and xn-C H OH q 1 y x 2,2,4- CH C H . The inversion of8 18 4 9 3 3 5 9sign of k E from positive to negative values occurs at x f 0.11, x f 0.60, x f 0.89,Sand x s 0.26 for these mixtures, respectively. At x s 0.5, k E for the variousSmixtures of alkanes with n-C H OH follows the sequence:4 9

n-C H ) n-C H ) 2,2,4- CH C H ) n-C H ) n-C H .Ž .8 18 7 16 3 5 9 6 14 5 123

Ž9. ŽThe same sequence is also observed in the values of excess molar volumes at. Ž10. ŽT s 288.15 K and T s 298.15 K , and excess isentropic compressibilities at

.T s 293.15 K at x s 0.5, for binary mixtures of n-C H OH with n-C H , or4 9 5 12Ž .n-C H , or n-C H , or n-C H , or 2,2,4- CH C H . The same sequence is6 14 7 16 8 18 3 3 5 9

also foundŽ25, 26. in the values of V E at x s 0.5 for mixtures of n-heptanolmŽ .n-C H OH with n-C H , or n-C H , or n-C H , or n-C H , or 2,2,4-7 15 5 12 6 14 7 16 8 18Ž .CH C H .3 3 5 9

E Ž .The values of k of the alkanol q alkane mixtures may be interpreted as theSresult of the contributions of the various types of intermolecular interactionsoperating between the alkane and alkanol molecules. Three main types ofcontributions are important in determining the thermodynamic excess properties ofŽ .alkanol q alkane : physical, due to non-specific van der Waals type interactions;chemical, due to hydrogen bonding; and structural, due to changes of interstitialaccommodation and free volume. The chemical contribution is relatively importantat low values of x, where the breaking of the self-association of the alkanolmolecules due to H-bonds makes a positive contribution to k E. At higher values ofSx, the dissociation of the alkanol is of less importance and the balance is

J. Nath894

FIGURE 1. Plot of k E against the mole fraction x of n-C H OH for the various systems: (,S 4 9� Ž . 4 � Ž . 4xn-C H OH q 1 y x n-C H , T s 298.15 K; v, xn-C H OH q 1 y x n-C H , T s 303.15 K;4 9 5 12 4 9 6 14

� Ž . 4 � Ž . 4I? , xn-C H OH q 1 y x n-C H , T s 303.15 K; ^ , xn-C H OH q 1 y x n-C H , T s?4 9 7 16 4 9 8 18� Ž . Ž . 4303.15 K; ', xn-C H OH q 1 y x 2,2,4- CH C H , T s 303.15 K.4 9 3 3 5 9

essentially between physical and structural contribution. The positive values ofE � Ž . 4 � Ž . 4 �k for xn-C H OH q 1 y x n-C H , xn-C H OH q 1 y x n-C H , xn-S 4 9 6 14 4 9 7 16

Ž . .4 � Ž . Ž . 4C H OH q 1 y x n-C H , and xn-C H OH q 1 y x 2,2,4- CH C H at4 9 8 18 4 9 3 3 5 9low values of x may thus be attributed to the predominance of the contributions tok E from the breaking of the self-association due to H-bonds in the butanolSmolecules in these mixtures.


The author gratefully acknowledges the financial support received from theDepartment of Science & Technology, New Delhi, India.

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( )Recei ed 30 October 1997; in final form 9 February 1998

O-707

speeds of sound in and isentropic compressibilities of (n-butanol + n-pentane) att=298.15 k, and...

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