Indian Journal of Chemistry

Vol. 40A, January 200 I, pp. 53-64

Thermodynamic interactions in binary mixtures of 1-chloronaphthalene with n-alkanes

Tejraj M Aminabhav i' & Kamalika Banerj ee

Department of Chemist ry, Karnatak Un iversit y, Dharwad 580 003 , India

Received 6 March 2000; revised 12 July 2000

Thermodynamic interacti ons in binary mi xtures of 1-chl oronaphthalene with hexane, heptane, octane, nonane, decane, or dodecane have been studied using the experimental resu lts of density and viscosity at 298. 15, 303. 15, and 308 .15 K as well as speed of sound measurements at 298 .1 5 K over the ent ire mole fraction range. From the densi ty data, excess molar volumes have been calcul ated and compared with those calcul ated fro m Prigogine-Fiory-Patterson (PFP) and Flory theories. Deviations in logari thmic viscosity are calcu lated and compared with those obtained usi ng the Bloomfi eld and Dewan equation. From the speed of sound data, isentropic compressibilities have been calcul ated and co mpared with those calculated from the Benson and Ki yohara equation. The isothermal compressibi liti es calcul ated fro m the Benson and Ki yohara eq uation have been compared with those calcul ated fro m the Flory equati on of state. The excess volume, deviations in logarit hmic viscosity, the deviat ions in internal pressure, deviati ons in free energy of acti vati on, and isentropic compressibil ity have been fi tted to the Red lich and Ki ster equation to deri ve the coerticients and standard errors.

In an earlie r paper1, we have presented ex tensive

database on the thermodynamic interactions in binary mi xtures of styrene w ith n-a lkanes. In thi s paper, we will present the results of a s imil ar study on the thermodynamic interacti ons tn bin ary mi xtures conta ining 1-ch loronaphtha lene ( 1-CNP) with n-a lkanes. The n-a lkanes and aro matics have been studied ex tensive ly in vie w of the ir importance in the petrochemical industries, parti cularl y in the light of present-day trend s toward heavie r feedstocks2

J. 1-CNP be longs to an important c lass of persistent o rgani c pollutants with s ignificant toxic itl. Us ing the experimenta l data on density, p, and viscos ity, 17 at 298. 15, 303. 15, and 308. 15 K, as we ll as speed of sound , u at 298. 15 K fo r the binary mi xtures o f 1-C NP w ith hexane, heptane, octane, nonane, decane, or dodecane, we have ca lcul ated the excess mo lar vo lume, VO, devi ati on in logarithmi c viscos ity, L1ln7J, isentropic compress ibi I ity, L1ks, deviati ons in inte rna l pressure, L1Pi, dev iati ons in free energy of acti vati on, L1G#, and isothe rmal

compress ibility, L1kT. These results a re furthe r compared with the theoreti ca l ca lcul ati ons from the

theories of F lor/ ·6, Prigogine-Fiory-Patterson (PFPf ·8, Bloomfie ld and Dewan9

, and Benson and

Ki yohara10

. These results have been fitted to the Redlich and Ki ste r equati on 11 to de rive the bina ry coeffi c ients and the standard e rro rs.

Materials and Methods

Hexane, heptane, octane, nonane, decane, and dodecane were a ll ana lytical reagent grade samples procured from S.D. F ine Che mica ls, Mumba i, Ind ia

w ith purities> 99.5 mo l %. 1-C hl oronaphth alene was purchased from E. M erck, Germany with a mo l % purity of 90.06 as studied by GC (HP 6890) using an F ID detecto r. The ques tion regarding its purit y has been di scussed in our earli e r papers 12

. Dens ity and viscosity of the pure liquids are compared with the lite rature va lues in T abl e I .

Binary mi xtures were prepared by mass tn speciall y des igned g lass-s toppered bo ttl es 13

.15

. A set of nine compos iti ons was prepared fo r each sys tem and the ir phys ica l prope rti es were measured on the same day. T he poss ible error in mo le fract ion was estimated to be less than 10-4 in a ll cases.

54 IND IAN J CHEM, SEC. A, JANUARY 2001

Table I -Comparison or experimental densit ies (p) and viscosities ( TJ) of pure liquids with literature values at 298.15, 303.15 and

308. 15 K

Liquid

1-CNP

11-Hcxanc

11-Heptane

11-0ctanc

11-Nonane

11-Decane

11-Dodecane

(Mol% Temp.

puri ty) (K)

(>90.6)

(>99.6)

(>99.8)

(>99.6)

(>99.4)

(>99.8)

(>99.6)

298 .15

298.15

03. 15

308. 15

98 .1 5

03.15

308. 15

98.15

303.1 5

308. 15

98. 15

303.15

308.1 5

298 .1 5

303. 15

308. 15

298. 15

303. 15

308.1 5

Ex pt.

I. I t\82

0.6549

0.650 1

0.6447

0.68 13

0.6756

0.6700

0.6997

0.6953

0.69 11

0.7150

0.7108

0.7062

0.7267

0.7228

0.7182

0.7466

0.7433

0.738 1

Densities of liquids and liquid mi xtures were measured with a capillary pycnometer of about 10 cm3 vo lume as per the experimental deta il s given earli er 16

·17

• Standard deviations tn densities of the liquids and mi xtures were less than 0.0 I%.

Lit.

1880912.11

1878412 11

0.654H9 12.t1

0.65484b 1221

0.65033 1241

0.65018 1221

0.64562 1251

0.6795 12"11

0.67946 1121

0.67528 12-1 1

0.67519 1221

0.67107 1251

0.69862 1221

0.69854 12 -1 1

0.69470 12 -1 1

0.69010 12-11]

0.71375 1221

0.71002 1241

0.70596 ll.ll

0.72635 1221

0.72257 1241

0.71780 12(>1

0.745 18 122 1

0.74164 12·11

0.73760 12('1

Ex pt.

3.075

0.270

0.263

0.25 1

0.393

0.372

0.353

0.5 13

0.484

0.457

0.665

0.623

0.584

0.855

0.799

0.743

1.246

1.175

1.090

T) /(m.Pa.s)

Lit.

2.940 1211

0.2968 12-11

0.2942 1221

0.283 1 12-1 1

0.2703 12 -11

0.3906 12 -1 1

0.3967 1221

0.3707 1241

0.3525 12 -11

0.3592 1221

0.5 15 1 1221

0.5 128 1241

0.4835 12 -11

0.4568 1241

0.6696 1221

0.66 12 12-1 1

0.6194 12-1 1

0.581 8 1241

0.86 14 1221

0.8406 12 -1 1

0.7820 1241

0.7296 1241

1.3780 1221"

1.5556 1271

Viscosities were measured using a Schott-Gerate viscometer (Model A VS 350, Germany). This instrume nt automat ically measures n ow-th rough times in capill a ry viscometers. Efflux time on the digital display was determined with an accuracy o f

AMINABHA VIet al.: THERMODYNAMIC INTERACTIONS IN BINARY MIXTURES . 55

Table 2- Values of molar volume (V), thermal expansion coefficient (a), heat capacity (Cp), isothermal compressibility (kT),

isentropic compressibility (k5) and characteristic parameters(?', Vand r' ) for pure n-alkanes at 298. 15 K

Liquid v • v Tc

V (cm3mol" 1) (cm3mol" 1

) (K)

1-CNP 136.9 116.7 1.173 785

Hexane 131.6 98.6 1.335 507.5

Heptane 147.1 107.2 1.372 540.3

Octane 163.3 125.6 1.300 568.8

Nonane 179.4 140.0 1.281 594.6

Decane 195.8 155.0 1.263 617.9

Dodecane 228.2 186.5 1.223 658.2

O.Ols. Ten independent measurements in one measuring sequence were stored in the memory of the instrument and the liquid meniscus was sensed optoelectronically at the measuring levels. A measuring stand (A VS/S anodized with aluminium/ stainless steel material) was used for optoelectronic sensing of the meniscus . LED in the upper part of the measuring stand generates light in the near infrared range, which is transmitted through a glass fiber cable to the measuring level s. The estimated error in viscosity was ± 0.001 mPa.s . Approximately 5 cm3

volume of the liquid was taken into the viscometer. The liquid was allowed to equilibrate for 7 to 10 min . Viscosity was calculated using the relation T] = t. k. p , where k is the viscometer constant (0.0 I 035 mm2/sec2

), p is the density of liquid/mixture and t is the efflux time in sec.

Speed of sound was measured using a variable path single-crystal interferometer (Mittal Enterprises, New Delhi , Model M-84). A crystal-controlled high­frequency generator was used to excite the transducer at a frequency of 4 MHz. The freq uency was measured within an accuracy of l in I 04 using a digital frequency meter. The current variat ions across the transducer were observed on a 0-30 pA range microammeter (Lektrolab Equipment Co., Mumbai). The interferometer cell was filled with the test liquid and water was then circulated around the measuring cell from a thermostat maintained at 298.15 ± 0.0 I K.

Cp 103a ks kT P' .10" r' (J.K·1.mo1" 1

) (K.J) (TPa.1) (TPa. 1) (J.cm.3) (K)

211.37 0.658 384 468 577 6748

195.48 1.461 1293 1722 451 4333

224.98 1.681 1150 1701 555 4086

254.15 1.267 1051 1359 470 4629

284.55 1.168 958 1215 471 481 9

314.54 1.075 918 113.3 451 5030

375.97 0.883 812 953 413 5615

To increase the accuracy of the measurement , several such maxima were counted by changing the di stance between transducer and reflector. The total distance, d, moved by the reflector was used to calculate the wavelength, A by using the relation : d = nA./2. Knowing the frequency, v, of the crystal (4 MHz), the speed of sound, u in m.s·1 was calculated as: u = VA. The speed of sound values thus calculated are accurate to± 2 in l 000 m.s-1

•

The isentropic compressibilities were calculated using the relation : ks = llu2p. (where u is in m.s· 1

and p in kglm\ The isothermal compressibility, kT was computed from isentropic compressibility and heat capacity, Cr of liquids using the equation:

k,. ... ( I )

The values of a have been calculated from the experimental densities at different temperatures (see Table 2). The necessary Cp data of the mixtures were taken from Grolier et al. 18

, and Costas et al. 19.

In all of the above measurements, temperature was controlled within± 0.01 K using a Schott-Gerate (Model CT 050/2, made in Germany) constant temperature bath. At least three independent readings were taken for each composi tion and the average of these results are given in Table 3.

56 INDIAN J CHEM , SEC. A, JANUARY 2001

Table 3- Experimental density (p), viscosity (T/) and speed of sound (u) of binary mixtures at different temperatures

XJ p.1 o·' /(kg.m"3) TJ /(mPa.s) tt!(m.s-1)

(1-CNP) at temp (K) at temp (K) at298.15K

298.15 303. 15 308.15 298.15 303. 15 308. 15 Expt

I-Chloronaphtha1ene ( I)+ I!- Hexane (2)

0.0000 0.6549 0.6501 0.6447 0.270 0.263 0.251 1087

0.0966 0.7119 0.7073 0.7017 0.325 0.309 0.301 1125

0.1962 0.7695 0.7653 0.7597 0.392 0.383 0.363 1155

0.2929 0.8253 0.8207 0.8157 0.494 0.469 0.448 1179

0.4152 0.8932 0.8883 0.8829 0.645 0.612 0.579 1238

0.4944 0.9371 0.9321 0 9267 0.777 0.740 0.701 1281

0.5923 0.9901 0.9864 0.9797 0.979 0.93 1 0.878 131 8

0.6943 1.0421 1.0378 1.0323 1. 290 1.194 1.11 5 1360

0.8006 1.0952 1.0910 1.0856 1.652 1.530 1.422 1376

0.8997 1.1419 1.1374 1.1 3 17 2.147 1.965 1.797 1408

1.0000 1.1 882 1.1843 1.1789 3.075 2.757 2.51 9 1480

1-Chloronaphthalene ( I) + n-Heptane (2)

0.0000 0.681 3 0.6758 0.6700 0.393 0.372 0.353 11 30

0.0960 0.7290 0.7245 0.7193 0.453 0.430 0.407 1176

0.1941 0.7787 0.7742 0.7686 0.533 0.503 0.475 1200

0.2962 0.8301 0.8268 0.8208 0.635 0.598 0.563 1232

0.3883 0.8767 0.8743 0.8673 0.759 0.714 0.670 1256

0.4898 0.9282 0.9255 0.9191 0.916 0.855 0.799 1293

0.5871 0.9780 0.9746 0.9687 1.126 1.046 0.970 1336

0.6900 1.0310 1.0267 1.0216 1.404 1.295 1.1 99 13 80

0.7918 1.0836 1.0808 1.0748 1.713 1.623 1.504 1392

0.8650 1.1213 1. 1165 1.1134 2.163 1.962 1.797 1458

1.0000 1.1882 1.1843 1.1789 3.075 2.757 2.5 19 1480

1-Chloronaphth alene ( I) + /!-Octane (2)

0.0000 0.6997 0.6953 0.6911 0.513 0.484 0.456 1166

0.0972 0.7419 0.7373 0.7326 0.575 0.542 0.5 12 11 99

0. 1951 0.7856 0.7813 0.7756 0.658 0.619 0.583 1232

0.2939 0.8304 0.8266 0.8210 0.790 0.751 0.698 124 1

0.3911 0.8762 0.8713 0.8663 0.894 0.834 0.780 1272

0.490 I 0.9244 0.9199 0.9140 1.039 0.966 0.899 1299

0.5934 0.9757 0.9712 0.9658 1.239 1.1 46 1.062 1336

0.6979 1.0279 1.0236 1.01 82 1.52 1 1.395 1.288 1352

0.7967 1.0797 1.0756 1.0695 1.884 1.726 1.574 1380

0.8605 1. 1134 1.1095 1.1034 2.220 2.001 1.911 !443

1.0000 1. 1882 1.1 843 1.1789 3.075 2.757 2.519 1480

(con tel )

AMINABHAYI eta/.: THERMODYNAMIC INTERACTIONS IN BINARY MIXTURES 57

Table 3- Experimental density (p), viscosity ( I")) and speed of sound (u) of binary mixtures at different temperatures- Contd.

x, p.l o··1 /(kg.m"3) 17 /(mPa.s) u/(m.s-1)

(1-CNP) at temp (K) at temp (K) at298.15K

298.15 303.15 308. 15 298.15 303. 15 308. 15 Expt

1-Chloronaphthalene ( I) + n-Nonane (2)

0.0000 0.7150 0.7108 0.7062 0.665 0.623 0.584 1208

0.0952 0.7516 0.7477 0.7425 0.725 0.680 0.635 1217

0. 1958 0.7924 0.7878 0.7824 0.809 0.756 0.705 1232

0.2958 0.8340 0.8301 0.8246 0.909 0.847 0.790 1262

0.3926 0.8760 0.8724 0.8664 1.028 0.953 0.887 1282

0.4962 0.9232 0.9196 0.9137 1.175 1.088 1.010 13 14

0.5892 0.9676 0.9633 0.9580 1.367 1.259 1. 165 1342

0.6897 1.0179 1.0137 1.0087 1.616 1.483 1.365 1360

0.7952 1.0732 1.0693 1.0638 1.962 1.788 1.636 1400

0.8980 1.1297 1.1256 1.1199 2.428 2.195 1.993 1440

1.0000 1.1882 1.1843 1.1789 3.075 2.757 2.519 1480

1-Chloronaphthalene ( I) + n-Decane (2)

0.0000 0.7267 0.7228 0.7182 0.855 0.799 0.743 1224

0.0960 0.7593 0.7564 0.7506 0.860 0.806 0.764 1232

0.1972 0.7962 0.7924 0.7873 0.945 0.898 0.840 1248

0.2962 0.8343 0.8303 0.8252 1.080 1.004 0.923 1262

0.3923 0.8737 0.8696 0.8646 1.161 1.104 1.030 1280

0.4594 0.9027 0.8987 0.8934 1.293 1. 199 1.107 1299

0.5950 0.9650 0.9611 0.9557 1.534 1.411 1.298 1323

0.6943 1.0142 1.0 l 03 1.0047 1.760 1.608 1.479 1360

0.7960 1.0680 1.0639 1.0585 2.048 1.875 1.714 1384

0.8982 1.1263 1.1221 1.11 65 2.472 2.231 2.026 1424

1.0000 1.1 882 1.1843 1.1789 3.075 2.757 2.5 19 1480

1-Chloronaphthalene ( I) + n-Dodecane (2)

0.0000 0.7466 0.7433 0.7381 1.246 1.175 1.090 1284

0.0988 0.7742 0.7704 0.7657 1.306 1.236 1.132 1290

0.1953 0.8037 0.8003 0.7953 1.393 1.287 1.174 1296

0.2927 0.8361 0.8323 0.8272 1.445 1.342 1.232 1304

0.3910 0.8722 0.8680 0.8630 1.533 1.430 1.328 131 2

0.4954 0.9132 0.9094 0.9038 1.663 1.573 1.437 1322

0.5939 0.9560 0.9522 0.9471 1.770 1.674 1.532 1363

0.6916 1.0036 0.9997 0.9940 1.955 1.786 1.667 1377

0.8196 1.0723 1.0682 1.0626 2.265 2.077 1.910 1400

0.8992 1.1206 1.11 62 1.1105 2.537 2.300 2.095 1440

1.0000 1.1882 1.1843 1.1789 3.075 2.757 2.519 1480

58 INDIAN J CHEM, SEC. A, JANUARY 2001

Results and Discussion

Using the experimental values of density and speed of sound, the results of 0, Ilks, and MT have been calculated by a general type of equation 11

·14'16

0 (or ~Y) = Vm(or Ym) -x1 V1(or Y1) -xzVz(or Yz)

.. . (2)

Here, V m is molar volume of the mixture, and V1 and V2 are molar volumes of the individual components, I and 2 of the mixture. The symbol ~y refers to Ilks, MT, ~P;, and ~G#, while Y1 and Y2 refer to the respective individual properties of the pure components; Y m refers to a mixture property. To compute ~ks and MT, the volume fraction, <X>; was used16, but mole fraction, X; was used to calculate other quantities.

Thermodynamic behaviour in liquid mixtures has been studied using the Flory5

'6 and PFP7

'8 theories .

The procedures outlined in our earlier paper1 have been used to calculate all the quantities. The constants used in these calculations are given in Table 2. The contact interaction energy parameter, X1 2 needed in these calculations was computed using the Marquardt algorithm20 in an optimization procedure employing experimental HE data18'21 at 298.15 K and by minimizing the function, d (XJ2) using Eq . 3.

I

crif(XIz)= f (He:p -Hc~~~(XI z )Ydxl .. . (3) 0

Here H c and H c 1 (X 12), denote the ex peri-, exp c <~

mental and calculated (from PFP theory) excess enthalpies respectively. Due to the non-availability of HE data for 1-CNP + nonane mixture, the x l2 values for this mixture were calculated usmg the experimental 0 at 298.15 K (Eq.4),

... (4)

These results are given in Table 4.

From viscosity data, the deviation in logarithmic viscosity was calculated using Eq. 5,

". ( 5)

The ~ln7J values were also calculated from the equation of Bloomfield and Dewan9 using the constants given in Table 5 .

The Bloomfield and Dewan values of ~ln7J are also compared in Table 5 with the calculated ~ln7J values obtained from Eq. 5. The signs between the calculated ~ln7J values and the experimental results are in agreement.

The Ilks values have been calculated from Eq. 2 and the additive ideal isentropic term was calculated from the Benson and Kiyohara 10 equation:

The values of C P for the individual components of the mixtures taken 'from Riddick et al22 are taken from Table 2. In the absence of Cp data for 1-CNP + nonane mixture, the following additive relation was used:

... (7)

The MT value was calculated usmg Flory theor/·6 as:

v

... (8)

where the symbols have their usual meanings as given in our earlier paper1,

The mixing quantities, viz., 0, L1ln7J, L1P; , L1G#, and L1ks, have been fitted to Red lich and Kister equation 11 by the method of least-squares using the Marquardt20 algorithm to derive the binary coefficient, A; and standard error, a as :

AMINABHA VIet a/.: THERMODYNAMIC INTERACTIONS IN BINARY MIXTURES 59

Table 4- Comparison of near equimolar excess molar volume data with! literature findings and theoretical calculations at 298.15 K for 1-CNP + 11-alkane

mixtures

1-CNPwith (}2 x,2/(J.mol"1) from l/'-/10.6 (m]mol"1) PFP contribution

alkanes

HE yE Lit Expt Flory PFP yEint V'-rv !/'-;, c, 0.4775 5.96 6.87 - 1.745" -1.908 -2.089 -1.967(-1.951) 0.107(0 12)) 1.02 -1.05

c1 0.4961 12.66 32.94 -1.259''' -1.182 -1.878 -1.617(-1.213) 0.253(0.657) 1.651 -.21 9

c. 0.5222 10.61 21 .63 -1.047''' - 1.092 -1.435 -1.315( -1.099) 0.206(0.419) 0.731 -.787

c, 0.5342 19.46 -0.895 -1.287 - (-0.891) - (0379) 0564 -.706

CIO 0.5872 12.78 20.78 -0.737 -1.169 -0.893(-0.732) 0.258(0.419) 0.413 -.739

c,2 0.5821 12.51 8.55 -0.572" -0.595 -0.768 -05 16(-0.595) 0.246(0 193) 0.136 -.605

The bracketed values are obtained using X12 from 1/'- data calculated from Eq . 4.

Table 5- Experimental and computed values of Bloomfield-Dewan equation at 298 .15 K at about equimolar compositions or

1-CNP + n-alkane mixtures

1-CNP with In T/H

Hexane -0.269

Heptane -0.265

Octane -0.266

Decane -0.262

Dodecane -0.234

k

VE(~Y)=x1 x2 LAi (x 2 -x,)i-t j=l

In Tis In T/v

-0.167 -0.026

-0.208 -0.353

-0.085 -0.204

-0.030 -0.216

-0.010 -0. 128

... (9)

In each case, the optimum number of coefficients, Ai was ascertained from an examination of the variation of the standard deviation, a with n,

... (10)

where n represents the number of measurements and m, the number of coefficients. Estimated values of Ai and a for 0 and Ms are summarized in Table 6.

i".ln 17th l'.ln Tlcxp (t-.1 n Tlcxp· t-.1 11 IJ ,h)

-0.461 -0.145 0.316

-0.826 -0.162 0.665

-0.556 -0.172 0.385

-0.508 -0.174 0.334

-0.371 -0.159 0.213

The results of 0 at 298.15 K calculated from Eq. 2 are displayed in Fig. I. The points represent the 0 values calculated from Eq. 2, while the smooth curves are drawn from the best fitted values of 0 calculated from Eq. 9. For all mixtures, the values of 0 are negative and become more positive with increasing size of n-alkane. The 0 results at ot her temperatures are not displayed to avoid redundancy . For all the mixtures, except 1-CNP + octane, the negative 0 values become more negative with an increase in temperature. However, the values of 0 and are av E;aT comparable with those of Costas et al.

19• Presently, no data are available for mixtures

of 1-CNP + n-nonane with which we can compare the

60 INDIA N J CHEM , SEC. A, JANUARY 2001

present results. The negative av E/()T values for all the systems suggest that there is a short-range orientational order effect between the long-chain n­

alkanes in the pure state. When a plate-like rigid molecule like 1-CNP is mixed with n-alkane, the order is destroyed so that mixing involves a net destruction of order, because 1-CNP has an order

breaking ability. In a study by Comelli and Francescon?' on the vE of mixtures of 1-CNP with n­

alkyl ketones at 298.15 K, the negative vE va lues showed variations in the limit i.e., -0.9 ~ 0 111 ; 11 (c m1

mol" 1) ~ -0.7 and these increased with increasing size

of n-alkyl ketones.

Table 6- Estimated parameters of Eq . (9) for various functi ons for binary mixtures of 1-chloronaphthalene with 11-alkanes

Function TempiK An AI A2 (J

1-Chloronaphthalene ( I) + n-Hexane (2)

11"110.6(m3 .mo1" 1) 298.15 -7.680 0.270 0.371 0.059

303.15 -7.93 1 -0.008 -0.032 0. 11 3

308.15 -8 . 185 -0.352 -0.160 0.087 6G'I(J.mol ·1

) 298.15 - 1522 508 -1197 39.48

303.15 - 1399 332 -1 342 28.7 1

308 .15 - 1304 425 -1283 36.74

.:lksi(TPa- 1) 298.15 -714 -228 99.2 12.78

I 06.6?/(TPa) 298. 15 5.32 -0.504 -4 .202 0.210

L'. lnfl I (mPa.s) 298.15 -3 .482 2.262 -1.754 0.068 303.15 -3.202 1.480 -1.952 0.045

308.15 -2 .664 1.642 - 1.336 0.058 ilkTI(TPa·1

) 298.15 -8.609 -5.705 -2.785 69.6

1-Chloronaphth alene ( I) + 11-Heptane (2)

II" I I 0"6(n1"1 mol" 1) 298.15 -4.773 0.220 -1 .770 0.043

303.15 -6.453 -1.196 -1.093 0.105 308.15 -6. 154 -0.542 -3.902 0.073

6G.I(J.mol" 1) 298. 15 -1647 361.0 -474.0 38 .41

303.15 -1569 192.0 -143.0 14.85 308.15 -1559 240.0 -157.0 10.86

M 51(TPa.1) 298.15 -565 .0 -209.0 -294.0 10.49

I 06 6?/(TPa) 298.15 5.660 -0.606 3.79 .0 0. 184

.:ll nfl I (mPa.s) 298.15 -3. 186 1.795 -0.951 0.052

303.15 -2.757 1.41 8 -0.616 0.0 12

308. 15 -2.475 1. 268 -0.544 0.004

L'.k-ri(TPa-1) 298.15 -6.660 -3.886 -1.782 17.21

1-C hl oronaphthalene ( I) + 11-0ctane (2)

v"!I0"6(m3 mol" 1) 298.15 -4.221 0.264 -0.206 0.046

303. 15 -4 .3 15 0. 128 -0.7 12 0.069 308. 15 -4.0 12 0.633 0.951 0.036

LlG'I(J.mo l.1) 298.15 - 1700 453 100 42.91

303. 15 - 160 1 528 64 52.04

308.15 - 1650 429 562 65.47 M 51(TPa-1

) 298.15 -421 -2 11 -208 10.27

I 06 6?/(TPa) 298.15 4.94 0.97 1 1.89 0.199

.!'.11111 I (mPa.s) 298.15 -2.95 1 1.579 -0.51 3 0.012

303.15 -2.546 1.371 -0.450 0.014

308. 15 -2.319 1.133 -0.077 0.037

L'.kTI(TPa-1) 298.15 -5 .548 -3.000 - 1.38 1 27.53

Contd. ..

AMINABHA VIet a!. : THERMODYNAMIC INTERACTIONS IN BINARY MIXTURES 61

Table 6- Estimated parameters of Eq. (9) for various function s for binary mixtures of 1-chloronaphthalene with n-alkanes- Con rd.

Function TempiK A(/ A, A1 (J

1-Ch loronaphthalene ( I ) + n-Nonane (2)

V0/1 0'6(m3 mol" 1) 298.15 -3.585 -0.502 -1.167 0.01 8.

303.15 -3.811 -0.650 -0.899 0.053

308.15 -3.73 1 -0.543 -1.343 0.046

~G'I(J . mor 1 ) 298.15 -1782 339 -126 9.40

303 .15 -1726 333 -66 8.32

308.15 - 1712 420 -280 9.92

M si(TPa.1) 298.15 -333 -48 103 4.99

I 06.~P/(TPa) 298.15 3.99 -0.102 -0.8 11 0.064

t.lnTj I (mPa.s) 298.15 -2 .7 15 1.434 -0.684 0.010

303.15 -2.353 1.214 -0.561 0.008

308. 15 -2. 109 1. 140 -0.637 0.015

~kri(TPa· 1 ) 298.15 -4.808 -2.271 -0.869 54.67

1-Chloronaphthalene ( I ) + n-Decane (2)

V0/1 0'6(m3 mo1" 1) 298.15 -2.996 0.560 0.305 0.019

303.15 -3.045 0.057 -0.793 0 68

308. 15 -3 .122 0.484 0.742 0.015

t.G' I(J.mor 1) 298.15 - 1639 -1274 -1483 39.23

303. 15 - 151 7 8.40 -1404 32.69

308. 15 -1538 172 -1267 14.65

M 5 I(TPa. 1) 298.15 -242 -57.4 53.8 3.22

I 06~P/(TPa) 298.15 1.74 0.335 -1.1 39 0.050

t.lnTj I (mPa.s) 298.15 -2.430 1.104 -1.206 0.028

303.15 -2.07 1 0.974 -1.027 0.011

308. 15 -1.868 0.947 -0.967 0.016

Mrf(TPa. 1) 298.15 -4.3 16 -1.873 -0 .599 66.91

1-Chl oronaphthalene ( I ) + n-Dodecane (2)

II" II o·"(m3 mo1" 1) 298.15 -2.446 0.741 0.752 0.047

303.15 -2.292 1.030 1.366 0.057

308.15 -2.480 0.294 0.618 0.047

~G'I(J.mor 1 ) 298. 15 - 1372 937 -297 18.01

303.15 - 123 1 756 -741 29.81

308.15 -1193 577 -898 19.7R M 51(TPa.1) 298. 15 -159 -1.75 43.3 6.61

106 M/(TPa) 298. 15 - 1.81 -0.242 -0.739 0.099

L'.lnTj I (mPa. s) 298.15 -2.0 10 1.434 -0.823 0.020

303. 15 -1 .643 1. 127 -0.895 0.021

308. 15 -1.480 0.925 -0.920 0.026

MT/CrPa. 1) 298.15 -3.605 -1.303 -3.009 24.44

We also attempted to investigate the dependence in the alkane. The calculated curves at equimolar vE of equimolar vE on the number of carbon atoms data from the theories of Flory and PFP are also given

in n-alkanes at different temperatures 16• Thi s plot is for comparison. The vE curve computed from the PFP

shown in Fig. 2. In all cases, the equimolar values of theory is in good agreement with the experimental vE vE increase with increasing number of carbon atoms curve, but the vE curve calculated from Flory theory

62 INDIAN J CHEM, SEC. A, JANUARY 2001

·0.5 'o

E ,...,E -1.0 ~ w >

·1.5

-2.0

:0.2 0.4 0.6 0.8

x, Fig. I - Excess molar volume (0) vs mole fraction of 1-CNP

with (0) hexane, (~) heptane, ( • ) octane, ( • ) nonane, (.&)

decane and( . ) dodecane at 298.15 K.

0. 0 r---,----,~.....-~-.~--,--~----,,-----,

-::o.5 -' 0 E -1.0 -

~

E u -- -1.5 (.lJ

> -2.0

-2. 5 '-----'----'---'------'-----'----"----''-----' 5 6 7 8 9 10 11 12 13

No. of carbon atoms

Fig. 2- Near equimolar 0 vs number of carbon atoms in n­

alkanes as fitted to Eq.(ll), ( 12) and (13) for mixtures of 1-C NP with n-alkanes at (0) 298.15 K; (+)303.15 K; (• )308.15 K

along with (.&) 0 from Flory and ( . ) 0 from PFP at 298.15K

lies below both the experimental and the PFP curves. Experimentally calculated equimolar 0 data of the mixtures of n-alkanes from hexane to dodecane (i.e., carbon atoms, n = 6 to 12) have been fitted to obtain the following empirical relations at the three temperatures investigated :

0 (x, z0.5) = -2.07 + 45-345 (n+2) (n +2)2

0.0

-0.5 ....-<

' 0 E -1.0

~

E u --(.lJ -1.5 >

0.0 0.2 0.4 0.6 0.8 l.O

x1

Fig. 3 -Comparison of 0 data for mixtures of 1-CNP + hexane Symbols: (0) Expt; (+ )Flory theory; (• ) PFP theory

and for mixtures of 1-CNP +heptane, Symbols: { • ) Expt ; (.& ) Flory theory and( . )) PFP theory at 298.15 K.

~~~.-~~.-~--.------~~--

15

10

ro p.. b

5 p:.-<J

0

Fig. 4- Deviations in internal pressure (~P;) vs volume fraction of 1-CNP with (0) hexane, ( + ) heptane, ( • ) octane,

( e ) nonane, (.&)) decane and( . ) dodecane at 298.15 K.

cr = 0. II I at 298. 15 K ... ( I I )

0 (x,z0.5) = 0.004 + 3.28- 152 (n +2) (n +2) 2

cr = 0.093 at 303.15 K ... ( 12)

AMINABHA VIet al.: THERMODYNAMIC INTERACTIONS IN BINARY MIXTURES 63

Or-----.-----.-----.---~.----.

-100

• -sooL-----~-----L----~------~--~

0 0·2 o.4 o.G 0.8

x,

Fig. 5 -Excess molar Gibbs energy of activation of tlow ( c. G • E ) vs mole fraction at 298.15 K for the same mixtures

with the same symbols as given in Fig. l .

oor-1

m

-0.5

g: -1.0

--C/)

~·- -1.5

-2.0

0.0

0

0.2 . 0.4 0.6 0.8 1.0

¢1

Fi g. 6- Deviations in isentropic compressibility (Ms) vs volume fraction calculated from Benson-Kiyohara theory at 298 .15 K for

mixtures of 1-CNP with n- alkanes with the same symbols as given in Fig. 4.

-1.53 + 37-329 - --- ?

(n +2) (n +2t

cr = 0.112 at 308.15 K ... ( 13)

Experimental V: values for the mixtures of 1-CNP +hexane, and ICNP +heptane at 298.15K are compared in Fig. 3 with the calculated V: values from the Flory and PFP theories . In all cases, the

-1 -I (,j

p... f-

-2 --f-..:.: <l

_, I -4

0.4 0.6 0.8 0 0.2

¢1

Fig. 7- Comparison of experimental deviations in isothermal compressibility (t.kT) for 1-CNP with (0) hexane, (+)octane

and ( • )decane with Flory theory for 1-CNP with ( •) hexane, (.A.)octane and (.)decane at 298. 15 K.

experimental V: values are comparable to the calculated V: data from PFP theory. But, the V: values from the Flory theory are more negative than the experimental data and are different from PFP values.

Figure 4 shows the dependence of !:J.Pi on the mole fraction of 1-CNP. A negative deviation is observed for 1-CNP + dodecane while positive deviations are observed for all the remaining mixtures. The negative !:J.Pi values indicate that the repulsive forces between the interacting molecules have a predominant effect. The positive !:J.Pi values suggest that the attractive forces greater than the repulsive interactions. The results of !:J.G#E presented in Fig 5 are also negative for all the mixtures .

The results of Ilks calculated from the Benson and Kiyohara theory (Eq. 6) are presented in Fig. 6. The Benson and Kiyohara values of Ilks are more negative than those obtained from the experimental density values using Eq. 2. The Ms values exhibit a systematic dependence on the size of n-alkanes. The negative values of Ms suggest that the mixture is less compressible than the corresponding ideal mixture and the postttve values indicate an opposite behaviour. The values of !lkT have been calculated from Eqs, I and 2, and these are compared in Fig. 7 with MT values calculated from the Flory procedure . These values are also negative for 1-CNP + hexane, 1-CNP + octane, or 1-CNP + decane mixtures.

64 INDIAN J CHEM , SEC. A, JANUARY 2001

Conclusions

Experimental results on density, vi scosity, and speed of sound are presented for the binary mixtures of 1-CNP with hexane, heptane, octane, nonane, decane, and dodecane. From the density results, excess molar volumes have been calculated and these data when compared with the values calcu lated from the theoretical predictions of Flory and PFP agreed better with the PFP values than the Flory values . For all mixtures, 0 is negative at all temperatures, but becomes less negative with increasing length of then­alkanes. Bloomfield and Dewan ~ln7J values showed an agreement with the experimentally calculated ~ln7J values. The ~ks data calculated from experimental data and from the Benson and Kiyohara equat ion are negative, but the latter are more negative. Similarly, the isothermal compressibi lity values calculated from the Flory equation agree well with the experimental values.

Acknowledgement

This research was funded by the Department of Science and Technology, New Delhi, India (SP\S l\H-6\96(PRU)). Mrs. Kamalika Banerjee was appointed as a JRF to work in this project.

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