speeds of sound in and isentropic compressibilities of (n-heptanol+n-pentane, orn-hexane,...

J. Chem. Thermodynamics 1998, 30, 1385]1392Article No. ct980406

Speeds of sound in and isentropic(compressibilities of n-heptanol H

n-pentane, or n-hexane, or n-heptane,)or n-octane at T s 293.15 K

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

Measurements of speeds of sound u have been made in binary mixtures of n-heptanolŽ . Ž . Ž . Ž .n-C H OH with n-pentane n-C H , or n-hexane n-C H , or n-heptane n-C H ,7 15 5 12 6 14 7 16

Ž .or n-octane n-C H at T s 293.15 K. Values of u have been used to calculate the8 18apparent excess speeds of sound Du and the isentropic compressibilities k for theseS

mixtures. The excess isentropic compressibilities k E have also been calculated from theS

values of k . The k E has been found to be negative throughout the entire composition rangeS S

for the present mixtures. Values of Du and k E have been fitted with smoothing equations. qS

1998 Academic Press

ŽKEYWORDS: experimental; speeds of sound; isentropic compressibilities; n-heptanol q.n-alkane

1. Introduction

Ž .This work continues studies devoted to mixtures of an alkanol q an alkane . Thebinary mixtures of this kind are of particular interest from the theoretical viewpointof a model of hydrogen-bonded systems. In previous papersŽ1 ] 3. studies of excess

E Ž .molar volumes V of binary liquid mixtures of n-butanol n-C H OH andm 4 9Ž . Ž . Ž .n-heptanol n-C H OH with n-pentane n-C H , or n-hexane n-C H , or7 15 5 12 6 14Ž . Ž . �n-heptane n-C H , or n-octane n-C H , or 2,2,4-trimethylpentane 2,2,4-7 16 8 18

Ž . 4CH C H have been reported at two temperatures. Speeds of sound u and3 3 5 9isentropic compressibilities k for binary mixtures of n-C H OH with n-C H , orS 4 9 5 12

� Ž . 4n-C H , or n-C H , or n-C H , or 2,2,4- CH C H have also been6 14 7 16 8 18 3 3 5 9reportedŽ4,5. at two temperatures. In this work, the measurements of u have beenmade in binary liquid mixtures of n-C H OH with n-C H , or n-C H , or7 15 5 12 6 14n-C H , or n-C H at T s 293.15 K, and the results obtained are reported and7 16 8 18interpreted in this paper.

2. Experimental

Liquid n-C H OH, n-C H , n-C H , n-C H , and n-C H were of the same7 15 5 12 6 14 7 16 8 18quality and were purified in a similar manner as described earlier.Ž3,4. The densities

0021]9614r98r111385 q 08 $30.00r0 q 1998 Academic Press

J. Nath1386

r* of the liquid samples of n-C H , n-C H , n-C H , and n-C H used in the5 12 6 14 7 16 8 18present work were measured very recently Ž4. by using a single-capillary pyknometer.

. y3The density r* of n-C H OH determined in this work is 0.82198 g cm at7 15T s 293.15 K. The uncertainty in r* is estimated to be of the order of

. y5 . y3"2 10 g cm . The speed of sound u in pure liquids and their binary mixturesŽ .were measured at T s 293.15 " 0.01 K and at a frequency of 3 MHz with a

quartz-crystal interferometer in the same manner as described earlier.Ž4 ] 8. Thespeeds of sounds u* in pure samples of liquid n-C H , n-C H , n-C H , and5 12 6 14 7 16

. y1Ž .n-C H used in this work are 1030.2, 1099.8, 1152.0, and 1188.6 m s ,8 18respectively, at T s 293.15 K, as measured recently.Ž4. The u* in pure liquid

. y1n-C H OH determined in this work is 1345.8 m s at T s 293.15 K. The7 15. y1uncertainty in u is of the order of "0.5 m s .

3. Results and discussion

The values of speeds of sound u in binary mixtures of n-C H OH with n-C H ,7 15 5 12or n-C H , or n-C H , or n-C H at T s 293.15 K are given in table 1, where x6 14 7 16 8 18refers to the mole fraction of n-C H OH in the mixture. The x has an uncertainty7 15of "0.0001. From thermodynamic considerations, the speed of sound u at zero0frequency is given by:Ž9.

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

where V and M refer to the molar volume and the 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 property. The experimental speed of sound is assumed to be equalto u over a wide range of frequencies and amplitudes for most fluids, so it may be0treated as an equilibrium property.Ž10. Hence, the experimental values of u for thevarious mixtures have been used to calculate the apparent excess speeds of soundDu from the relation:

Du s u y Ý x uU , 2Ž .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 2. The isentropic compressibility

y1Ž .k s yV V r p . The values of k of the mixtures of n-C H OH withS m m S S 7 15n-C H , or n-C H , or n-C H , or n-C H were obtained from the relation:5 12 6 14 7 16 8 18

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

Ž .u and k for n-heptanol q n-alkaneS 1387

TABLE 1. Speeds of sound u, densities r, isentropic compressibilities k , and the excess isentropicS

compressibilities k E at T s 293.15 KS

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 H7 15 5 12

0.0364 1039.1 0.63522 1458.0 y20.40.0771 1049.7 0.64526 1406.5 y41.80.1125 1059.0 0.65383 1363.8 y57.50.1536 1070.6 0.66359 1314.8 y74.50.1815 1078.8 0.67010 1282.3 y84.80.2119 1088.0 0.67709 1247.7 y95.00.2510 1100.5 0.68590 1203.8 y107.00.2848 1110.6 0.69337 1169.3 y113.60.3249 1123.8 0.70205 1127.9 y121.50.3545 1134.0 0.70833 1097.8 y126.70.4010 1149.4 0.71799 1054.2 y130.90.4356 1161.1 0.72501 1023.1 y132.50.4749 1174.7 0.73282 988.9 y133.00.5107 1187.0 0.73978 959.4 y131.70.5560 1202.5 0.74838 924.1 y128.00.5951 1215.9 0.75563 895.1 y123.20.6261 1226.0 0.76125 874.0 y117.50.6743 1242.4 0.76980 841.6 y108.30.7159 1257.0 0.77700 814.5 y99.50.7575 1270.8 0.78402 789.8 y88.30.8121 1288.1 0.79300 760.0 y71.30.8600 1303.8 0.80066 734.7 y55.60.9061 1317.6 0.80785 713.0 y38.10.9439 1329.6 0.81361 695.3 y23.7

� Ž . 4xn-C H OH q 1 y x n-C H7 15 6 14

0.0374 1104.7 0.66611 1230.2 y5.60.0811 1111.8 0.67391 1200.5 y13.70.1213 1118.6 0.68104 1173.5 y20.30.1602 1126.3 0.68791 1145.9 y27.80.1928 1132.5 0.69363 1124.1 y32.40.2299 1140.4 0.70010 1098.3 y38.30.2600 1147.2 0.70531 1077.3 y42.90.3102 1158.8 0.71395 1043.1 y49.30.3351 1164.7 0.71820 1026.4 y52.00.3711 1173.5 0.72430 1002.6 y55.40.4095 1183.0 0.73076 977.8 y58.10.4357 1189.7 0.73513 961.1 y59.60.4879 1203.0 0.74376 929.0 y61.10.5356 1215.6 0.75156 900.4 y61.30.5669 1224.5 0.75662 881.5 y61.40.5935 1230.9 0.76088 867.4 y59.40.6398 1244.3 0.76824 840.7 y57.90.6703 1253.0 0.77303 824.0 y55.90.7160 1265.5 0.78013 800.4 y51.20.7555 1276.6 0.78618 780.5 y46.50.7821 1284.9 0.79022 766.5 y43.90.8326 1299.6 0.79778 742.2 y36.40.8775 1311.6 0.80441 722.6 y27.50.9184 1323.5 0.81036 704.5 y19.60.9657 1337.0 0.81713 684.6 y9.2

J. Nath1388

TABLE 1}continued

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 H7 15 7 16


� Ž . 4xn-C H OH q 1 y x n-C H7 15 8 18



Ž . Ž .TABLE 2. Values of the coefficients A of equation 3 , and the standard deviations d Du for thejvarious mixtures at T s 293.15 K

y1.Ž . Ž .Mixture A A A A d Du r m s1 2 3 4

� Ž . 4xn-C H OH q 1 y x n-C H y19.8794 56.1013 y5.1740 y1.9077 0.267 15 5 12� Ž . 4xn-C H OH q 1 y x n-C H y66.6417 32.0469 y1.3561 26.2563 0.297 15 6 14� Ž . 4xn-C H OH q 1 y x n-C H y72.9990 19.1511 y9.2823 13.4587 0.247 15 7 16� Ž . 4xn-C H OH q 1 y x n-C H y68.8212 y3.7695 4.4261 y13.0402 0.307 15 8 18

by using the data on V E for the various mixtures at T s 293.15 K determinedmŽ3. Ž .recently. In equation 4 , x is the mole fraction of the component i in thei

mixture, M is the molar mass of the component i, and V id s Ý x V U is the molari m i m, ivolume corresponding to the ideal mixture. The values of V U of pure componentsm, in-C H , n-C H , n-C H , and n-C H reported recently Ž4. were used to5 12 6 14 7 16 8 18

id Ž . Uobtain V for calculating k from equation 4 . The V of n-C H OH asm S m, i 7 153 . y1obtained from its present value of density is 141.372 cm mol . The isentropic

compressibilities kU of the pure component liquids n-C H , n-C H , n-C H ,S 5 12 6 14 7 16Ž . Ž4.and n-C H , obtained from equation 4 , have been reported recently, whereas8 18

the k of n-C H OH is 671.7 TPay1 at T s 293.15 K. The k values of theS 7 15 S

present mixtures are given in table 1. The imprecision in k is the order ofSy1 Ž E id."0.5 TPa . Also given in table 1 are the values of the quantity Ý x M r V q Vi i m m

which refers to the calculated densities r of the mixture. The imprecision in r is. y5 . y3estimated to be of the order of "2 10 g cm . The values of isothermal

compressibilities kU of the pure component liquids were estimated from the cubicTexpansion coefficient a , and the isobaric molar heat capacity C , by using thep, mrelation:

2 .k s k q a V TrC . 5Ž .T S m p , m

The values of a and C used to calculate k of the pure liquids n-C H ,p, m T 5 12Ž . Ž4.n-C H , n-C H , and n-C H from equation 5 were those reported earlier.6 14 7 16 8 18

The value of a of n-C H OH, as derived from densities given in reference 11, is7 15. y3 y10.750 10 K at T s 293.15 K, whereas C of n-C H OH as obtainedp, m 7 15

from the group-contribution method using table 5-10 of reference 12 is. y1 . y1 U262.0 J K mol at T s 293.15 K. The values of k of the pure liquids n-C H ,T 5 12

n-C H , n-C H , and n-C H have been reported earlier,Ž4. whereas kU of6 14 7 16 8 18 Tn-C H OH is 760.7 TPay1 at T s 293.15 K.7 15

The excess isentropic compressibilities k E reported in table 1 were calculatedS

from the isentropic compressibilities k of the mixtures by using the relation:S

k E s k y k id , 6Ž .S S S

where k id was obtained as outlined in references 13 and 14.S

J. Nath1390

Ž . Ž E .TABLE 3. Values of the coefficients B of equation 7 , and the standard deviations d k for thej S

various mixtures at T s 293.15 K

E y1Ž . Ž .Mixture B B B B d k r TPa1 2 3 4 S

� Ž . 4xn-C H OH q 1 y x n-C H y527.7135 87.6065 18.1183 y13.0023 0.417 15 5 12� Ž . 4xn-C H OH q 1 y x n-C H y245.5410 y20.4814 33.5610 y46.2711 0.447 15 6 14� Ž . 4xn-C H OH q 1 y x n-C H y137.7400 y39.9674 34.6215 y27.8697 0.427 15 7 16� Ž . 4xn-C H OH q 1 y x n-C H y86.0674 y21.1089 y7.2406 15.6127 0.397 15 8 18

E Ž .The values of k of the various mixtures obtained through equation 6 haveS

been fitted 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 are given in table 3. The k values of the various mixtures have beenS S

plotted against x in figure 1.The k E has been found to be negative throughout the entire range of x forS

� Ž . 4 � Ž . 4xn-C H OH q 1 y x n-C H , xn-C H OH q 1 y x n-C H ,7 15 5 12 7 15 6 14� Ž . 4 � Ž . 4xn-C H OH q 1 y x n-C H , and xn-C H OH q 1 y x n-C H . At x s7 15 7 16 7 15 8 180.5, the k E for the various mixtures of alkanes with n-C H OH at T s 293.15 KS 7 15has the sequence: n-C H ) n-C H ) n-C H ) n-C H . The same sequence8 18 7 16 6 14 5 12is also foundŽ2,3. in the values of V E at x s 0.5 for the mixtures of n-C H OHm 7 15with n-C H , or n-C H , or n-C H , or n-C H at various temperatures.5 12 6 14 7 16 8 18Again, the same sequence is foundŽ1. in the values of V E at x s 0.5 for binarymmixtures of n-C H OH with n-C H , or n-C H , or n-C H , or n-C H at4 9 5 12 6 14 7 16 8 18various temperatures.

E Ž . Ž5.The values of k of the alkanol q alkane mixtures may be interpreted as theS

result of the contributions of the various types of intermolecular interactionsoperating between the alkane and alkanol molecules. Three main types ofcontribution are important in determining the thermodynamic excess properties ofŽ .alkanol q alkane mixtures: physical, due to non-specific van der Waals typeinteractions; chemical, due to hydrogen bonding; and structural, due to changes ofinterstitial accommodation and free volume. The dataŽ2,3. show that the values ofV E are positive at low values of x and negative at high values of x form� Ž . 4 � Ž . 4xn-C H OH q 1 y x n-C H and xn-C H OH q 1 y x n-C H at T s7 15 7 16 7 15 8 18Ž .293.15 and 308.15 K, and negative throughout the entire ranges of x for� Ž . 4 Ž . �xn-C H OH q 1 y x n-C H at T s 293.15 and 298.15 K, and xn-7 15 5 12

Ž . 4 Ž .C H OH q 1 y x n-C H at T s 293.15 and 308.15 K. The positive values of7 15 6 14V E at low values of x in the case of the two former systems of n-C H OH at bothm 7 15

Ž .the temperatures 293.15 and 308.15 K have been attributed to the predominanceof the contributions to the values of V E due to the breaking of self-association viamhydrogen bonding in the heptanol molecules in these mixtures.Ž2,3. The presentvalues of k E at T s 293.15 K are found to be negative throughout the entire rangeS


FIGURE 1. Plot of k E against the mole fraction x of n-C H OH for the various systemsS 7 15� Ž . 4 � Ž . 4at T s 293.15 K: ^ , xn-C H OH q 1 y x n-C H ; ? , xn-C H OH q 1 y x n-C H ;? 7 15 5 12 7 15 6 14

� Ž . 4 � Ž .v, xn-C H OH q 1 y x n-C H ; I? , xn-C H OH q 1 y x n-C H .7 15 7 16 7 15 8 18

� Ž . 4 � Ž . 4of x for xn-C H OH q 1 y x n-C H , xn-C H OH q 1 y x n-C H ,7 15 5 12 7 15 6 14� Ž . 4 � Ž . 4xn-C H OH q 1 y x n-C H , and xn-C H OH q 1 y x n-C H . The7 15 7 16 7 15 8 18negative values of k E at low values of x in the case of the systems of n-C H OHS 7 15with n-C H , or n-C H may be thought of as being due to the predominance of7 16 8 18

J. Nath1392

contributions to k E due to physical and structural effects over those dueS

to breaking of self-association via hydrogen bonding in the heptanol molecules.It is to be pointed out here that the values of k E are positiveŽ4. at lowS

� Ž . 4values of xn-C H OH in the case of xn-C H OH q 1 y x n-C H ,4 9 4 9 6 14� Ž . 4 � Ž . 4xn-C H OH q 1 y x n-C H , and xn-C H OH q 1 y x n-C H , which4 9 7 16 4 9 8 18may be attributed to the greater degree of self-association due to hydrogenbonding between the butanol molecules.

The author greatly thanks the Head, Chemistry Department, Gorakhpur University,Gorakhpur, for providing laboratory facilities. Thanks are also due to theDepartment of Science & Technology, New Delhi, India, for financial support.

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. Thermodynamics 1997, 29, 853]863.5. Nath, J. J. Chem. Thermodynamics 1998 7, 885]895.6. Nath, J. J. Chem. Thermodynamics 1996, 28, 167]170.7. Nath, J. J. Chem. Thermodynamics 1996, 28, 481]490.8. Nath, J. J. Chem. Thermodynamics 1996, 28, 1083]1092.9. Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids. John Wiley:

New York. 1954.10. Rowlinson, J. S. Liquids and Liquid Mixtures. Butterworths: London. 1959.11. Ortega, J. J. Chem. Eng. Data 1982, 27, 312]317.12. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases & Liquids: 4th edition.

McGraw-Hill: New York. 1988.13. Benson, G. C.; Kiyohara, O. J. Chem. Thermodynamic 1979, 11, 1061]1064.14. Handa, Y. P.; Halpin, C. J.; Benson, G. C. J. Chem. Thermodynamics 1981, 13, 875]886.

( )Recei ed 6 March 1998; in final form 15 June 1998

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speeds of sound in and isentropic compressibilities of (n-heptanol+n-pentane, orn-hexane,...

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