Fluid Phase Equilibria 203 (2002) 261–268

Speeds of sound in and isentropic compressibilities of (n-octanol+ n-hexane, orn-heptane, orn-octane) at T= 298.15 K

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

Received 23 April 2002; accepted 18 June 2002

Abstract

Speeds of soundu have been measured in binary liquid mixtures ofn-octanol (n-C8H17OH) andn-hexane(n-C6H14), or n-heptane (n-C7H16), or n-octane (n-C8H18) at T = 298.15 K. The values ofu have been used tocalculate the apparent excess speeds of sound�u and the isentropic compressibilitiesκS for these mixtures. Theexcess isentropic compressibilitiesκE

S have also been calculated from the values ofκS . TheκES property has been

found to be negative throughout the entire range of mole fractionx of n-C8H17OH for the present three mixtures.The values of�u andκE

S have been fitted to representative equations.© 2002 Elsevier Science B.V. All rights reserved.

Keywords: Speeds of sound; Isentropic compressibilities;n-Octanol+ n-alkanes

1. Introduction

This work continues studies devoted to mixtures of (an alkanol+ an alkane). The binary mixturesof this kind are of particular interest from the theoretical viewpoint of a model of hydrogen-bondedsystems. In previous paper[1–3], the measurements of excess molar volumesV E

m of binary mixtures ofn-butanol (n-C4H9OH) andn-heptanol (n-C7H15OH) with n-pentane (n-C5H12), or n-hexane (n-C6H14),or n-heptane (n-C7H16), or n-octane (n-C8H18), or 2,2,4-trimethylpentane (2,2,4-(CH3)3C5H9) havebeen reported at two temperatures. Speeds of soundu and isentropic compressibilitiesκS have beenreported[4,5] for binary mixtures ofn-C4H9OH with n-C5H12 at T = (293.15, 298.15) K, and forbinary mixtures ofn-C4H9OH with n-C6H14, or n-C7H16, or n-C8H18, or 2,2,4-(CH3)3C5H9 at T =(293.15, 303.15) K. Further,u andκS have been reported[6,7] for binary mixtures ofn-C7H15OH withn-C5H12, or n-C6H14, or n-C7H16, or n-C8H18, or 2,2,4-(CH3)3C5H9 at T = (293.15, 303.15) K. Inthis work, the measurementsu have been made in binary mixtures ofn-C8H17OH with n-C6H14, orn-C7H16, or n-C8H18 at T = 298.15 K, and the results obtained are reported and interpreted in thispaper.

0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S0378-3812(02)00185-1

262 J. Nath / Fluid Phase Equilibria 203 (2002) 261–268

2. Experimental

2.1. Materials

Liquid n-C6H14, n-C7H16 andn-C8H18 were of the same quality and were purified in a similar manner asdescribed earlier[4,5]. Liquid n-octanol of HPLC quality and of stated minimum purity (GC) of 99.5%was obtained from s.d. Fine-Chem Limited, Mumbai, and was used without further purification. Thedensitiesρ∗ of the pure liquid samples ofn-C6H14, n-C7H16, n-C8H18, andn-C8H17OH measured usinga single-capillary pyknometer are given inTable 1.

2.2. Method

The speeds of sound in pure liquids and their binary mixtures were measured at a frequency of 2 MHzusing a quartz-crystal interferometer in the same manner as described earlier[13,14]. The values ofu∗

for the various pure liquids are given inTable 1.

3. Results and discussion

The values of the speeds of soundu in binary liquid mixtures ofn-C8H17OH andn-C6H14, or n-C7H16,or n-C8H18 at T = 298.15 K are given inTable 2, wherex refers to the mole fraction ofn-C8H17OH inthe mixture. From thermodynamic considerations, the speed of soundu0 at zero frequency[16] is givenby

u0 = Vm

{−M−1

(∂p

∂Vm

)S

}1/2

, (1)

whereVm andM refer to the molar volume and the molar mass, respectively, of the material, and (∂p/∂Vm)Sdenotes the derivative of pressure with respect to molar volume at constant entropyS. The speed of soundu0 defined byEq. (1), is thus, a thermodynamic property. The experimental speed of sound is equal tou0

over a wide range of frequencies and amplitudes for most fluids, and so may be treated as an equilibriumproperty[17]. Hence, the experimental values ofu for the various mixtures have been used to calculatethe apparent excess speeds of sound�u from the relation:

�u = u −N∑

i=1

xiu∗i , (2)

wherexi is the mole fraction of the componenti in the mixture,u∗i refers to the speed of sound in the

pure componenti, andN is the number of components. The values of�u for the various mixtures havebeen fitted by the method of least-squares to the Redlich–Kister[18] type equation:

�u (m s−1) = x(1 − x)

4∑j=1

Aj(2x − 1)j−1. (3)

The resulting values of the coefficientsAj of Eq. (3), and the standard deviationsδ(�u) of the fits forthe various mixtures are given inTable 3. In Eq. (3), x refers to the mole fraction ofn-C8H17OH. The

J.Nath

/Fluid

Phase

Equilibria

203(2002)

261–268263

264 J. Nath / Fluid Phase Equilibria 203 (2002) 261–268

Table 2Speeds of soundu, densitiesa ρ, isentropic compressibilitiesκS , and excess isentropic compressibilitiesκE

S for the variousmixtures ofn-C8H17OH atT = 298.15 K

x u (m s−1) ρ (g cm−3) κS (TPa−1) κES (TPa−1)

{(x)n-C8H17OH + (1 − x)n-C6H14}0.0283 1081.6 0.66054 1294.1 −5.160.0571 1087.0 0.66644 1269.9 −11.570.0745 1090.7 0.66997 1254.7 −15.920.0968 1095.8 0.67447 1234.7 −21.930.1328 1104.0 0.68163 1203.7 −30.130.1794 1116.2 0.69073 1162.0 −42.000.2272 1129.4 0.69986 1120.2 −52.600.2767 1143.6 0.70910 1078.3 −62.550.3126 1153.8 0.71567 1049.6 −67.740.3568 1166.8 0.72361 1015.1 −73.190.4050 1181.0 0.73209 979.3 −77.230.4553 1195.5 0.74073 944.6 −78.740.4979 1207.8 0.74789 916.6 −78.630.5481 1222.0 0.75614 885.6 −76.530.5991 1236.0 0.76431 856.4 −72.180.6511 1250.8 0.77244 827.5 −66.970.7017 1264.7 0.78014 801.4 −60.020.7458 1277.0 0.78669 779.5 −53.230.8159 1296.6 0.79680 746.5 −40.910.8925 1318.6 0.80744 712.3 −26.030.9425 1332.2 0.81416 692.1 −14.46

{(x)n-C8H17OH + (1 − x)n-C7H16}0.0235 1132.6 0.68305 1141.3 −1.720.0625 1138.2 0.68896 1120.4 −5.910.1046 1144.4 0.69540 1098.0 −9.950.1291 1148.3 0.69915 1084.7 −12.430.1610 1153.6 0.70404 1067.3 −15.580.1703 1155.6 0.70546 1061.5 −17.190.1978 1160.6 0.70965 1046.1 −20.140.2509 1170.5 0.71770 1017.0 −24.870.2933 1179.2 0.72406 993.2 −28.940.3460 1190.5 0.73188 964.1 −33.200.3798 1197.8 0.73684 945.9 −35.300.4231 1207.6 0.74315 922.7 −37.690.4761 1220.0 0.75079 894.9 −39.770.5293 1232.6 0.75838 867.9 −40.700.5695 1242.8 0.76407 847.4 −41.350.6149 1253.8 0.77044 825.7 −40.480.6612 1265.2 0.77688 804.1 −38.920.7197 1279.6 0.78492 778.1 −35.480.7652 1291.0 0.79110 758.4 −32.140.8502 1312.0 0.80243 724.0 −23.260.9144 1327.6 0.81079 699.8 −14.570.9467 1335.0 0.81493 688.5 −9.27

J. Nath / Fluid Phase Equilibria 203 (2002) 261–268 265

Table 2 (Continued )

x u (m s−1) ρ (g cm−3) κS (TPa−1) κES (TPa−1)

{(x)n-C8H17OH + (1 − x)n-C8H18}0.0663 1175.6 0.70658 1024.0 −1.600.1126 1182.0 0.71213 1005.1 −5.660.1687 1190.2 0.71890 982.0 −10.350.2154 1197.5 0.72455 962.5 −14.160.2732 1207.0 0.73159 938.2 −18.620.3183 1214.2 0.73710 920.2 −20.800.3583 1220.8 0.74200 904.3 −22.440.4167 1230.8 0.74915 881.2 −24.320.4564 1237.6 0.75406 865.8 −25.040.5083 1246.2 0.76046 846.7 −24.640.5538 1253.6 0.76607 830.6 −23.360.6027 1263.2 0.77210 811.7 −23.290.6400 1270.3 0.77671 797.9 −22.420.6856 1279.4 0.78234 780.9 −21.250.7362 1289.8 0.78861 762.2 −19.500.7942 1302.6 0.79582 740.6 −17.290.8466 1314.6 0.80235 721.2 −14.840.9352 1334.6 0.81348 690.2 −8.200.9719 1342.4 0.81812 678.3 −4.25

a The values of densitiesρ of the various mixtures given are those calculated by using the densities of the pure componentsgiven inTable 1and the excess molar volume data reported by Treszczanowicz et al.[19].

isentropic compressibility is defined byκS = (−V −1m )(∂Vm/∂p)S . The values ofκS of the mixtures of

n-C8H17OH with n-C6H14, or n-C7H16, or n-C8H18 were obtained from the equation:

κS = V Em + V id

m

u2∑N

i=1xiMi

, (4)

using theV Em data of the various mixtures reported by Treszczanowicz et al.[19]. In Eq. (4), Mi denotes

the molar mass of the componenti, andV idm = ∑

xiV∗m,i is the molar volume of the ideal mixture. Here,

V ∗m,i is the molar volume of the pure componenti. The values of the isentropic compressibilitiesκ∗

S of thepure components are given inTable 1, whereas the values of the isentropic compressibilitiesκS of themixtures are given inTable 2. The precision in the values ofκS is of the order of±0.5 TPa−1. Also givenin Table 2are the values of the quantity(

∑xiMi)/(V

Em + V id

m ) which refers to the calculated densitiesρ

of the mixtures.

Table 3Values of the coefficientsAj of Eq. (3), and the standard deviationsδ(�u) for the various mixtures atT = 298.15 K

Mixture A1 A2 A3 A4 δ(�u) (m s−1)

{(x)n-C8H17OH + (1 − x)n-C6H14} −16.8757 28.8681 −39.8797 38.7180 0.23{(x)n-C8H17OH + (1 − x)n-C7H16} −51.4012 41.2781 −3.9512 3.0959 0.16{(x)n-C8H17OH + (1 − x)n-C8H18} −55.7619 −15.6436 −0.4305 75.9159 0.26

266 J. Nath / Fluid Phase Equilibria 203 (2002) 261–268

Table 4Values of the coefficientsBj of Eq. (6), and the standard deviationsδ(κE

S ) for the various mixtures atT = 298.15 K

Mixture B1 B2 B3 B4 δ(κES ) (TPa−1)

{(x)n-C8H17OH + (1 − x)n-C6H14} −315.1839 53.6748 91.6300 −107.2886 0.31{(x)n-C8H17OH + (1 − x)n-C7H16} −162.7324 −38.9552 29.8254 −17.9300 0.29{(x)n-C8H17OH + (1 − x)n-C8H18} −99.5590 14.4276 19.4917 −101.3339 0.37

The excess isentropic compressibilityκES given inTable 2was estimated from the isentropic compress-

ibility κS of the mixture using the relation:

κES = κS − κ id

S , (5)

whereκ idS was obtained as outlined in[20,21], by using the values ofα∗, V ∗

m, κ∗S , κ∗

T , andC∗p,m of the pure

liquid components given inTable 1.The κE

S values for the various mixtures ofn-C8H17OH obtained throughEq. (5) were fitted by themethod of least-squares with the equation:

κES (TPa−1) = x(1 − x)

4∑j=1

Bj(2x − 1)j−1. (6)

The values of the coefficientsBj of Eq. (6), along with the standard deviationsδ(κES ) are given in

Table 4. The values ofκES have been plotted againstx in Fig. 1. The values ofκE

S have been found to benegative throughout the entire range ofx for {(x)n-C8H17OH+ (1−x)n-C6H14}, {(x)n-C8H17OH+ (1−x)n-C7H16}, and{(x)n-C8H17OH + (1 − x)n-C8H18}. At x = 0.5, theκE

S for these systems follows thesequence:

n-C8H18 > n-C7H16 > n-C6H14,

which is the same as observed in the values ofκES at x = 0.5 for the mixtures ofn-C4H9OH with

n-C6H14, or n-C7H16, or n-C8H18 reported earlier[4,5]. The same sequence is also observed in the valuesof the excess molar volumes[1] for mixtures ofn-C4H9OH with n-C6H14, or n-C7H16, or n-C8H18 atT = (288.15, 298.15) K. The same sequence is also observed[6,7] in the values ofκE

S at x = 0.5 formixtures ofn-C7H15OH with n-C6H14, or n-C7H16, or n-C8H18.

TheκES values of the (alkanol+alkane) mixtures may be interpreted[6] as the result of the contributions

of the various types of intermolecular interactions operating between the components of these mixtures.Three main types of contributions are important in determining 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.The chemical contribution is relatively important at low values of the alkanol mole fractionx, where thebreaking of the self-association of the alkanol molecules due to H-bonds makes a positive contributionto κE

S . At higher values ofx, the dissociation of the alkanol is of less importance and the balance isessentially between physical and structural contributions. The presentκE

S values are observed to benegative throughout the entire range ofx for {(x)n-C8H17OH+ (1−x)n-C6H14}, {(x)n-C8H17OH+ (1−x)n-C7H16}, and{(x)n-C8H17OH + (1 − x)n-C8H18}. The negative values ofκE

S at low values ofx forthese mixtures may be thought of as being due to the predominance of contributions toκE

S from physical

J. Nath / Fluid Phase Equilibria 203 (2002) 261–268 267

Fig. 1. Plot of κES against the mole fraction ofn-C8H17OH, for the various systems atT = 298.15 K: ( ) {(x)n-

C8H17OH + (1 − x)n-C6H14}; ( ) {(x)n-C8H17OH + (1 − x)n-C7H16}; (�) {(x)n-C8H17OH + (1 − x)n-C8H18}.

and structural effects over those due to breaking of self-association via hydrogen bonding in the octanolmolecules.

List of symbolsAj coefficients of the Redlich–Kister type equation fitting the values of�uBj coefficients of the Redlich–Kister type equation fitting the values ofκE

S

Cp,m isobaric molar heat capacityM molar massN number of components(∂p/∂Vm)S derivative of pressure with respect to molar volume at constant entropySu speed of soundu0 speed of sound at zero frequency�u apparent excess speed of soundVm molar volumeV E

m excess molar volumeV id

m molar volume corresponding to ideal mixturex mole fraction ofn-C8H17OH in the mixture

Greek symbolsα cubic expansion coefficient

268 J. Nath / Fluid Phase Equilibria 203 (2002) 261–268

δ(�u) standard deviation in�uδ(κE

S ) standard deviation inκES

κS isentropic compressibility of the mixtureκE

S excess isentropic compressibilityκ id

S isentropic compressibility corresponding to the ideal mixtureκT isothermal compressibilityρ density

Subscripti componenti

Superscript* pure component

Acknowledgements

The author is thankful to the Head, Chemistry Department, DDU Gorakhpur University, Gorakhpur, forproviding laboratory facilities. Thanks are also due to the Council of Scientific and Industrial Research,New Delhi, India, for financial support (Scheme No. 01 (1585)/99-EMR-II).

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