Excess molar volumes, excess viscosities and refractive indices of a quaternary liquid mixture at 298.15 K

ou real of

OLECULAR

LIQUIDS ELSEVIER

Journal of MolecularLiquids68 (1996) 107-125

EXCESS MOLAR VOLUMES, EXCESS VISCOSITIES AND REFRACTIVE INDICES OF A QUATERNARY LIQUID MIXTURE AT 298.15 K

Ernesto Caner, Graciela C. Pedrosa and Miguel Katz *

Catedra de Fisicoquimica, Instituto de Ingenieria Quimica, Facultad de Ciencias Exactas y Tecnologia, U. N. T. Av. Independencia 1800, S. M. de Tucuman (4000) R. Argentina.

Received 2 July 1994; accepted 11 October 1995

ABSTRACT Density, viscosity and refractive index values for the propan-2-ol + methylacetate + dichloromethane + n-pentane mixture have been measured at 298.15 K, over the whole concentration range. Excess molar volumes and viscosities have been calculated. Flory's statistical theory has been applied to predict the excess molar volumes and compare then to the experimental data. We have also applied Grunberg and Nissan's equation for calculating viscosities and Lorentz-Lorenz's equation for predicting refractive indices, by knowing the values of the pure components.

* To whom correspondence should be addressed. 0167-7322/96/$15.00 © 1996ElsevierScience B.V. All rights reserved PIl S0167-7322 (96) 00923-3

108 INTRODUCTION Theoretical predictions of excess molar volumes and excess viscosities o f non-ideal binary mixtures have been satisfactory in explaining their sign and magnitudes in terms of interactions between the pure components. For ternary systems the prediction are more complex, and thus empirical methods based on experimental binary data have to be used t6 . For quaternary liquid mixtures, there are less data of excess properties 79 . Recently ~°~1 a general equation for estimating excess properties o f multicomponents systems from the observed properties of the various contributory binary combination of the components has been developed and applied. In this work, we have determined the molar excess volumes (vE), excess viscosities (vlE) and the refractive indices for a quaternary liquid mixture formed by propan-2-ol (2-PR) + methylacetate (MA) ÷ dichloromethane (DCM) + n-pentane (P) at 298.15 K, and some correlations were found. Flory's statistical theory was extended to a quaternary mixture, following Shukla et.al. 7 Viscosity data have been analized in terms of the Grunberg and Nissan's method 8 and compared with experimental data. The knowledge of refractive indices of a quaternary liquid mixture is often desirable, and in this work the Lorentz-Lorenz equation was used to calculate the refractive indices of a quaternary mixture, by knowing the refractive indices of the pure components, following Pandey et.al. 9. EXPERIMENTAL The methods used in our laboratory have been described previously 6. Densities were determined with a digital densimeter AP, model DMA 45. All weighings were made on a H315 Mettler balance. A thermostatically controlled bath (constant to + 0.01 °C) was used. Temperatures were read from calibrated thermometers. Calibration o f the densimeter was done with air and doubly distilled water, with an appreciation of + 0.1 kg m 3. Viscosities of the pure liquids and o f the mixtures were determined with a Schott-Ger~ite AVS 300 viscosimeter. The Ubbelohde viscosimeter tubes were calibrated and the temperature were maintained to 0.02 °C with a Schott-Ger/ite CT 1450 temperature controller. The estimate error was + 0.005 mPa s. Refraction indices were measured with a Jena dipping refractometer with an estimated error of_+ 2x10 5. All the substances were purified following methods used in the original works. Mixtures were prepared by mixing weighed amounts of the pure liquids. Caution was taken to prevent evaporation. RESULTS AND DISCUSSION The experimental results for the pure components are reported in Table 1, together with literature values for comparison purposes.

109 D e n s i t i e s and viscosities o f the binary mixtures have been published as follows: 2-PR(1) + MA(2), Ref.(14); 2-PR(1) + D C M ( 2 ) , Ref.(15); 2-PR(1) + P(4), Ref.(16); MA(2) + DCM(3), Ref.(17); MA(2) + P(4), Ref.(18) and D C M ( 3 ) + P(4), Ref.(19). With these data we can c a l c u l a t e V E and 11E. Each set o f results have been fitted with a R e d l i c h - K i s t e r e q u a t i o n o f the type:

1)

X E = xi xj k~oak (xi - xj)k where X z represents V E o r 'FIE, x i and xj the m o l e fractions j, and ak the p o l y n o m i a l coefficients. The m e t h o d o f least d e t e r m i n e the values o f the coefficients. In each case, c o e f f i c i e n t s has been ascertained from an e x a m i n a t i o n standard error o f e s t i m a t e with n:

o=

Xobs - Xcal

o f the c o m p o n e n t s and squares has been used to the o p t i m u m n u m b e r o f o f the variation o f the

nob s - n

(2)

T A B L E 1. P R O P E R T I E S C H A R A C T E R I Z I N G THE P U R E C O M P O N E N T S A T 298.15 K Substance 2-PR MA DCM P

p(g cm 3) Exp. Lit. 0.7800 0.7804 a 0.9274 0.9274 b 1.3163 1.3168 b 0.6219 0.62139 a

rl(mPa Exp. 2.053 0.361 0.420 0.218

s) Lit. 2.036 ~ 0.360 a 0.412 b 0.2152 ~

nD Exp. 1.37491 1.35876 1.42119 1.35466

Lit. 1.3752 b 1.3589 b 1.42115 b 1.35472 b

aRef.(12); bRef.(13)

The values adopted for the c o e f f i c i e n t s and the standard error o f estimate associated with the use of eq.(2) are s u m m a r i z e d in Table 2 for the six binary systems. The e x p e r i m e n t a l values o f densities, viscosities and r e f r a c t i v e indices o f the quaternary system are obtained by adding the second binary mixture to the first, in such a way that the relation b e t w e e n m o l e fractions is m a i n t a i n e d constant. Figures 1 and 2 show the e x p e r i m e n t a l values o f V E and .qE for the six binary systems.

11o T A B L E 2.

C O E F F I C I E N T S a k F R O M E Q U A T I O N (2) A N D S T A N D A R D D E V I A T I O N S FOR T H E B I N A R Y S Y S T E M S A T 2 9 8 . 1 5 K.

Systems

ao

a]

a2

a3

a4

a5

V z (cm 3 mol 1 ) 2-PR(1)+MA(2)

1.83

-0.32

2.0

2.8

-6.7

-9.2

0.02

2-PR(1)+DCM(3)

1.99

-0.80

-3.33

-4.9

2.3

4.2

0.02

2-PR(1)+P(4)

1.484

-3.63

-1.34

2.0

1.16

-2.1

0.008

MA(2)+DCM(3)

1.67

-0.42

0.29

-1.27

-0.43

--

0.008

MA(2)+P(4)

3.68

-0.90

-1.10

1.6

. . . .

DCM(3)+P(4)

1.78

0.20

-1.00

0.1

1.0

--

0.009

2-PR(1)+MA(2)

-1.337

-2.000

-1.320

0.30

-0.13

-1.0

0.006

2-PR(1)+DCM(3)

-1.199

-1.010

-0.65

-035

2-PR(1)+P(4)

-0.90

-I.000

-0.20

0.059

-0.012

0.041

MA(2)+P(4)

-0.149

-0.025

DCM(3)+P(4)

-0.125

-0.021

0.01

rl z ( m P a s)

MA(2)+DCM(3)

VE(cm

0.5

. . . .

. . . . . . 0.143

-0.081

-0.06

-0.049

-0.051

-0.18

0.004

0.073

--

0.008

0.06

0.27

-

_

-

0.01 -0.18

tool I )

0.5 X I

0.009

~

0.01

111 Fig. 1.- Experimental values of V E at 298.15 K. The first substance is the component 1. Continuous curves are calculated with eq.(1) using coefficients of Table 2.

Io~E(m Pas)

0.2 MA* DCM

0.5 X 1

0

-o.2! -0.4 2-PR,~

Fig. 2.- Experimental values of 11E at 298.15 K. The first substance is the component 1. Continuous curves are calculated with eq,(1) using coefficients of Table 2. Molar excess volumes have been calculated with the following equation: 4 v E = ~~ xi Mi(p-1 - f~-1 ) i=l

(3)

where Mi are the molecular weights of the components, Pi are the densities of the pure components and p the density of the solution.

112 TABLE 3. D E N S I T I E S , V I S C O S I T I E S AND R E F R A C T I V E I N D I CES FOR PROPAN-2-OL(1) +METHYLACETATE(2) + DICHLOROMETHANE(3) + PENTANE(4) SYSTEM AT 298.15 K

X1

X2

X3

X4

P (g cm -3)

q(mPa s)

nD

0.0228

0.2179

0.101 0.0694

0.6899

0.7001

0.248

1.35470

0.0387

0.3693

0.0541

0.5379

0.7347

0.253

1.35512

0.0547 0.0703 0.0831

0.5224 0.6713 0.7946

0.0386 0.0236 0.0112

0.3843 0.2348 0.1111

0.7761 0.8229 0.8671

0.271 0.303 0.336

1.35570 1.35664 1.35819

XI/X2 = 0.351;X3/X4 = 0.355 0.0600 0.1712 0.2013 0.1004 0.2862 0.1606

0.5675 0.4528

0.7691 0.7787

0.287 0.298

1.36131 1.36045 1.35999

X 1 / X2 = 0 . 1 0 5

; X3/X 4 =

0.1471 0.1897

0.4191 0.5405

0.1136 0.0706

0.3202 0.1992

0.8051 0.8330

0.319 0.346

0.2218

0.6319

0.0383

0.1080

0.8557

0.376

1.36035 1.35999

x l / x 2 = 0.988;X3/X4 =1.011 0.1000 0.1795

0.1012 0.1817

0.4017 0.3212

0.3972 0.3176

0.86i6 0.8580

0.318 0.346

1.37407 1.37143

0.2671 0.3480

0.2703 0.3521

0.2326 0.1508

0.2300 0.1491

0.8546 0.8520

0.397 0.443

0.4224

0.4275

0.0755

0.0746

0.8506

0.512

1.36970 1.36727 1.36607

xl/x2=2.961 ;x3/x4=3.079 0.1375 0.0464 0.6160 0.2517 0.0851 0.5006

0.2001 0.1626

1.0102 0.9728

0.350 0.407

1.38938 1.38501

0.3749

0.1266

0.3763

0.1222

0.9339

0.474

0.4962

0.1676

0.2538

0.0824

0.8962

0.581

1.38103 1.37708

0.6101

0.2060

0.1388

0.0451

0,8610

0.694

1.37363

0.0426 0.0361 0.0275 0.0190 0.0098

1.1614 1.0957 1.0168 0.9442 0.8682

0.418 0.467 0.572 0.748 1.070

1.40504 1.39851 1.39180 1.38571 1.37995

x~/x2 = 16.478; x3/x4 = 18.419 0.1604 0.2817 0.4400 0.5954 0.7634

0.0097 0.0171 0.0267 0.0362 0.0464

0.7873 0.6651 0.5058 0.3494 0.1804

113

xl/x3=O.385;x2/x4=0.329 0.0846

0.1724

0.2200

0.5230

0.7734

0.260

1.36358

0.1222

0.1389

0.3177

0.4212

0.8271

0.286

0.1696 0.2118

0.0966 0.0588

0.4410 0.5510

0.2928 0.1784

0.9054 0.9863

0.341 0.390

1.36904 1.37826

0.2480

0.0265

0.6450

0.0805

1.0660

0.437

x~/x3=O.976;x//x4=

1.38716 1.39580

1.061

0.1193

0.3904

0.1222

0.3681

0.7953

0.310

0.2016

0.3047

0.2065

0.2872

0.8357

0.359

0.2928

0.2097

0.2999

0.1976

0.8861

0.431

0.3654 0.4246

0.1340 0.0723

0.3743 0.4351

0.1263 0.0680

0.9312 0.9706

0.502 0.556

1.37413 1.38060 1.38649

0.331 0.384

1.35942 1.36386

1.36060 1.36673

x l / x 3 = 2 . 8 7 8 ; x 2 / x 4 = 2.982 0.1490 0.2849

0.5985 0.4614

0.0518 0.0990

0.2007 0.1547

0.8345 0.8472

0.3986

0.3467

0.1384

0.1163

0.8586

0.467

1.36817

0.5299 0.6243

0.2142 0.1189

0.1841 0.2169

0.0718 0.0399

0.8733 0.8846

0.602 0.758

1.37380 1.37807

xl/x3=20.879;x2/x4=

19.465

0.1710

0.7807

0.0082

0.0401

0.8842

0.376

1.35996

0.3320 0.5576 0.6509

0.6202 0.3954 0.3024

0.0159 0.0267 0.0312

0.0319 0.0203 0.0155

0.8661 0.8420 0.8325

0.431 0.600 0.720

1.36241 1.36669 1.36882

0.7906

0.1632

0.0378

0.0084

0.8184

1.026

1.37232

x l / x 4 = 0 . 3 6 8 ; x 2 / x 3 = 0.314 0.0284

0.2136

0.6809

0.0771

1.1158

0.385

1.39422

0.0561 0.1067

0.1811 0.1442

0.5772 0.4595

0.1766 0.2896

1.0198 0.9211

0.357 0.334

1.38578 1.37774

0.1534 0.2130

0.1028 0.0499

0.3276 0.1591

0.4162 0.5780

0.8286 0.7293

0.312 0.289

1.37022 1.36284

1.37945

xl/x4=

1 . 0 4 8 ; x 2 / x 3 = 1.044

0.0627

0.4482

0.4293

0.0598

1.0260

0.391

0.1414

0.3696

0.3540

0.1350

0.9517

0.383

1.37521

0.2177

0.2934

0.2811

0.2078

0.8867

0.376

1.37143

0.3075

0.2038

0.1952

0.2935

0.8180

0.369

1.36783

114

0.3805

0.1309

0.1254

0.3632

0.7669

0.365

1.36538

xl / x4 = 2.920 " x2/x3 = 2.984 0.1098 0.6386 0.2140 0.2243 0.5235 0.1754 0.3968 0.3500 0.1173 0.4580 0.2885 0.0967

0.0376 0.0768 0.1359 0.1568

0.9579 0.9106 0.8444 0.8222

0.397 0.420 0.467 0.490

1.36933 1.36810 1.26711 1.36690

0.0486

0.2057

0.7734

0.594

1.36640

1.4443;x2/x3 = 8.948 0.7355 0.0822 0.6066 0.0678 0.4544 0.0508 0.3011 0.0336 0.1511 0.0169

0.0118 0.0211 0.0320 0.0431 0.0539

0.9202 0.8911 0.8576 0.8260 0.7971

0.390 0.434 0.521 0.680 0.797

1.36376 1.36457 1.36621 1.36793 1.37402

0.6006 X1/X4

=

0.1705 0.3045 0.4628 0.6222 0.7781

0.1451

The excess viscosities are defined by the following expression:

(4)

tiE = rl - exP(i~l xi ln'0i I

where the additive law in a logarithmic form has been considered for the ideal mixtures. Table 4 shows the excess properties defined by eq.(3) and (4). If interactions in a quaternary system i÷j+k+l is assumed to be closely dependent on the interaction of the constituents i+j, i+k, i+l, j+k, j+l and k+l mixtures, it should be possible to evaluate thermodynamic excess properties for quaternary systems of non-electrolytes, by knowing the corresponding functions for the six binary mixtures.

TABLE 4. EXCESS MOLAR VOLUMES AND EXCESS VISCOSITIES OF THE PROPAN-2-OL(1) + METHYLACETATE(2) + DICHLOROMETHANE (3) + n-PENTANE(4) SYSTEM AT 298.15 K.

xl 0.0000 0.0228 0.0387 0.0547

x2 0.0000 0.2179 0.3693 0.5224

x3 0.0917 0.0694 0.0541 0.0386

VE34 (cmS mol.1)

rlE(mPa s)

0.115 0.860 1.103 1.030

-0.010 -0.020 -0.044 -0.058

I15

0.0703 0.0831 0.0950 0.0000 0.0600 0.1004 0.1471 0.1897 0.2218 0.2598 0.0000 0.1000 0.1795 0.2671 0.3480 0.4224 0.4970 0.0000 0.1375 0.2517 0.3749 0.4962 0.6101 0.7475 0.0000 0.1604 0.2817 0.4400 0.5954 0.7634 0.9400 0.0000 0.0846 0.1222 0.1696 0.2118 0.2480 0.2780

0.6713 0.7946 0.9050 0.0000 0.1712 O.2862 0.4191 0.5405 0.6319 0.7402 0.0000 0.1012 0.1817 0.2703 0.3521 0.4275 0.5030 0.0000 0.0464 0.0851 0.1266 0.1676 0.2060 0.2525 0.0000 0.0097 0.0171 0.0267 0.0362 0.0464 0.0600 0.2476 0.1724 0.1389 0.0966 0.0588 0.0265 0.0000

0.0236 0.0112 0.0000 0.2620 0.2013 0.1606 0.1136 0.0706 0.0383 0.0000 0.5027 0.4017 0.3212 0.2326 0.1508 0.0755 0.0000 0.7548 0.6160 0.5006 0.3763 0.2538 0.1388 0.0000 0.9485 0.7873 0.6651 0.5058 0.3494 0.1804 0.0000 0.0000 0.2200 0.3177 0.4410 0.5510 0.6450 0.7520

0.786 0.500 0.192 0.291 0.790 0.955 0.933 0.750 0.620 0.387 0.445 0.746 O. 845 0.885 0.854 0.722 0.458 0.316 0.400 0.440 0.375 0.260 0.130 0.344 0.095 0.265 0.366 0.291 0.103 -0.037 -0.218 0.680 0.877 0.815 0.655 0.555 0.482 0.451

-0.061 -0.059 -0.039 -0.021 -0.023 -0.052 -0.085 -0.113 -0.130 -0.134 -0.031 -0.056 -0.095 -0.133 -0.184 -0.221 -0.331 -0.030 -0.105 -0.149 -0.215 -0.272 -0.347 -0.500 -0.006 -0.108 -0.173 -0.254 -0.313 -0.322 -0.255 0.029 -0.072 -0.093 -0.106 -0.128 -0.151 -0.173

116 0.0000

0.5148

0.0000

0.912

0.037

0.1193

0.3904

0.1222

0.857

-0.066

0.2016

0.3047

0.2065

0.774

-0.098

0.2928

0.2097

0.2999

0.639

-0.138

0.3654

0.1340

0.3743

0.555

-0.175

0.4246

0.0723

0.4351

0.515

-0.223

0.4939

0.0000

0.5061

0.500

-0.297

0.0000

0.7492

0.0000

0.593

0.023

0.1490

0.5985

0.0518

0.570

-0.095

0.2849

0.4614

0.0990

0.515

-0.172

0.3986

0.3467

0.1384

0.445

-0.228

0.5299

0.2142

0.1841

0.330

-0.297

0.6243

0.1189

0.2169

0.230

-0.324

0.7421

0.0000

0.2579

0.096

-0.370

0.0000

0.9511

0.0000

0.146

0.004 -0.101

0.1710

0.7807

0.0082

0.373

0.3320

0.6202

0.0159

0.453

-0.203

0.5576

0.3954

0.O267

0.395

-0.346

0.6509

0.3024

0.0312

0.306

-0.396

0.7906

0.1632

0.0378

0.128

-0.403

0.9543

0.0000

0.0457

-0.043

-0.127

0.2390

0.7610

0.305

0.010 -0.019

0.0000 0.0284

0.2136

0.6809

0.412

0.0561

0.1811

0.5772

0.507

-0.044

0.1067

0.1442

0.4595

0.630

-0.069

0.1534

0.1028

0.3276

0.682

-0.080

0.2130

0.0499

0.1591

0.615

-0.111

0.2690

0.0000

0.0000

0.546

-0.095

0.5108

0.4892

0.420

0.014 -0.026

0.0000 0.0627

0.4482

0.4293

0.506

0.1414 0.2177

0.3696

0.3540

0.600

-0.072

0.2934

0.2811

0.645

-0.119

0.3075

0.2038

0.1952

0.586

-0.178

0.3805

0.1309

0.1254

0.520

0.5117

0.0000 0.7490

0.0000

0.336

-0.229 -0.231

0.2510

0.1098

0.6386

0.2140

0.332 0.441

-0.046

0.2243

0.5235

0.1754

0.510

-0.107

0.0000

0.013

117 0.3968 0.4580 0.6006 0.7449 0.0000 0.1705 0.3045 0.4628 0.6222 0.7781 0.9352

0.3500 0.2885 0.1451 0.0000 0.8995 0.7355 0.6066 0.4544 0.3011 0.1511 0.0000

0.1173 0.0967 0.0486 0.2551 0.1005 0.0822 0.0678 0.0508 0.0336 0.0169 0.0000

0.495 0.455 0.229 -0.071 0.124 0.300 0.397 0.461 0.334 0.023 -0.106

-0.217 -0.260 -0.337 -0.359 0.005 -0.099 -0.179 -0.279 -0.367 -0.565 -0.116

From the different expressions existing in the literature for predicting the excess molar volume or the viscosities for a ternary system, we have taken Radojkovic's et.al. 2° expression applied to a quaternary system:

vE34 = vE* + v E , + v E * + v E * + v2E4* + V3E4*

(5)

where VIE2,, VE,, v1E4., v E , , V ~ , and V3E4• represents the excess molar volumes with xt, x2, x3 and xa the mole fractions of the quaternary system, calculated with eq.(1) by using the coefficients of Table 2. Kohler 2°'21 proposed an equation for a ternary system, which when extended to a quaternary system, results:

V!~34--(x1 + x2) 2 v1E2+ (x 1 + x3) 2 VE +(x I + x4) 2 VI~4 + (x 2 + x3) 2 vE3 + (x: + x4) 2 V2E4+ (x3 + x4): v3E4

(6)

in which Vij represents the excess molar volumes of the binary mixtures at compositions x 0i ,x 0j, such that:

X0---1-X0 = Xi/(Xi +Xj)

(7)

for the six binary systems. Jacob and Fitzner 22 suggested an equation for estimating properties of a ternary systems based on binary data. For a quaternary systems, it takes the following form:

118

E

x1x2V1E2

xIx3 V1E3

x1x4 V1E4

V1234 (Xl +X3/2)( x2 + X%2/] + ( xl + X2/2/ )~.'~(x3+x4/2/ J~ Lz~l("+ X2/2//)()Lx4 +X3/;] +, X2X3VE

X2;J/24

/\ +

x3x4V3E4

(8)

where ViE of the mixture at compositions x oi ,xjo such that: xi- xj =x ° - x j0

(9)

Cibulka 23 proposed the following equation, which extended to a quaternary system is:

V1E234= vIE2* + vIE3* +Vi4* E +V~3* E +v2E4* +v3E4, + xIX2X3x4(A + BXl +Cx2 +Dx3)

(10)

Finally, Nagata and Tamura 24 proposed the following equation, which, for a quaternary system, can be expressed as:

V~234E= vIE2* + vE. + v1E4• + vE, + V2E4• + vE4, + XlX2X3x4A1234

(11)

These two equations introduce corrected parameters and modifications of the Radojkovic's et. al. equation. E Figures 3-16 shows V~234 vs X1 for every constant relation, between molar fractions together with Radojkovic et.al, and Cilbulka curves, obtained from eq.(5) and (I 1) including the binary mixtures.

vE234 (crn 3 tool q) 1.0

0.5

I

0

0.5 Xl

----~

119

1.0 i

vE234(cm3mo1-1) v, E234(cm3 mo[ 1) f

////Yx,

0.5

~

x

0.8C

:0.35

0.60

0.387

/

/J

"-o. ~ .

\

• 0.291

0.401 • 0 I

0

0./-,58

0.5

!

0.1 X 1 - - , -

0.2

v1E234 (c;m 3 tool -1)

V1E234(cm3mol 1 ) 0.5 ¸

0.6 ,~/o-""-° ~ o

0.4

I

0.25 X 1 __,..

//"

"\

~-x

0.3

L316

~x

~---29~1 X2 "

0.2

3.344

~o.~

0.1

\\ x / . /

I

I

0.2

0.4

0

0.5

×1 - - - "

~'\\ -..q

I

0.6 X

-0.210

, v1E234(cm 3 m o r 1)

"--%%

0.80

t v1E234[cm m o r t)

1-01

o.6a~oL~"

o

10.912

0.60

I

"-----~e

------

X,

~ o ~ x ~ e

I

0.40 0.20

I

I

0.05

0.15

I

0.25 X1 "1"

0

i

0.2 X 1

~

0.4

120 t,

V1E234(c m 3 mo1-1 ) , vE234 (cm 3 mo1-1 )

-/

0.6

o.5~ ~ . \

\

0.4

0.4 0.2

~0.146

e

0.2

,

0

o.ogE I

0

0.5 X1 ---.--. -0.043

I.

0.3 X1

,

",,,

02

0.9 t vlE234(Cm3mOj'l) ' vE234 (¢m3 m°l1)

t

i-~°~--_ 0.6

0.3

/~I

x, :o358

0.305

14

0

I

0.6 r ~ .

/

0.3 F

0546

/ 8 ~/"

I

0.1

0.2 Xl

.-'f

I

I

0.336

×4 "

0

X1

-'-

,V lE234(cm3 tool -1 )

.~:.~ x, =,0~8

J

1

.... o~.

--,-

, V %34 (cm3 mol'l )

0.6

0.4

I

0.33

01

V

•

Y:,, X1 ~

0.5

0.2

)124 •

~ - 14,443 ~ Y x4

\~

\\

i

0.5

121 E Fig 3-16.-Excess molar volumes V~234 vs. Xl at every constant relation of mole fractions, xxxxx experimental values;eoeeoRadojkovic et. al. equation; ooooa Cibulka equation. Table 5 shows the average deviation calculated by using the following expression:

The results with these two last equations, not difer very much from the other equations, where Cibulka's equation gives the minimum AD. The same calculation was made to evaluate TIE . The parameters A, B, C and D from Cibuika's equation for vE34 are A = 136.88; B = -287.74; C = -112.44; D= -231.68 and A1234 from Nagata and Tamura equation is = -22.39 cm 3 mol 1. The parameters for rl E are A = -20.73; B = 176.89; C = 18.25 and D = 15.61 The value for A1234for thE234= 1 19 mPa s. TABLE 5. AVERAGE DEVIATIONS FOR THE PROPAN-2-OL(1) + METHYLACETATE(2) + DICHLOROMETHANE(3)+ n-PENTANE(4) SYSTEM AT 298.15 K. Equation (5) (6) (8) (10) (11)

AD E V1234 (cm 3 mol "l) 0.12 0.10 0.21 0.10 0.11

AD

1"1111234(mPa

s)

0.07 0.10 0.18 0.04 0.10

Following Shukla et.al. 7 we applied Flory's theory to a quaternary system. The values of reduced volumes, reduced temperatures and characteristic pressures for the pure components are obtained with the following equations: ( 4 ]3 [ t+~aiT [

(13)

T i - T'i* - ~ / 3 - 1 Ti ~i4/3

(14)

122 ,

Pi =

/Td

(15)

where cti is the thermal expansivity and Zi the isothermal compressibility for the pure components. Considering every possibility of two body interaction and the statistical mechanical concepts of Flory, we have:

~_ (~0) li'3

(16)

where To is the ideal reduced temperature corresponding to the ideal reduced volume ~o.

TqO) /3 - 1

~0 _

(vo)4,,3

(17)

90 = £ Wi Vi

(18)

where Wi is the segment fraction defined as:

~i1_4 -

Xil_ 4 j=4 . . Xi +.2~xj(V i /Vj )

(19)

1=1

is the reduced temperature of the mixture, defined as: T=

T ,,' 4 I

,~

/'

,

(20)

P /" i__~l~gtiPi )//Ti The characteristic pressure of the mixture, is given by:

p,

4

, = ~"[N/iPi - (~1/102X12 + kl/EO3X23 + W304X34 + q/401X41 + W204X24 + tl1301X31)

i=l

(21) Oi is the site fraction given by:

123 0il_ 4 =

'= :=._.

Wil-4 _

(22)

'jlvi'/vl .

.

..

where X12, X23, X34, X41, X24 and X3~ are the interchange parameters assuming two body collisions. Here Xij = Xji can be calculated by application of the PrigogineFlory-Patterson theory 2s to the binary systems. They are X12 = 2500 J m 3 • X13 = -12347 J m "3 " Xl4 = 16369 J m "3 " X23 = 39484 J m -3 • X24 = 49463 J m "3 and X34 = 36212 J m 3. Table 6 gives the parameters used in this theory for the pure components. The average deviation is 29%, which means that Flory's theory, for this system does not make good prediction. TABLE 6.- PARAMETERS FOR THE PURE COMPONENTS AT 298.15 K.

a(K "1)

zxlO 6 (kPa-i)

~¢

V*xlO 6 (m 3 tool-l)

P*lO -6 (j m-3)

2-PR(1) MA(2)

0.001064 a 0.00139 a

1.332 a 1.148 b

1.2607 1.3226

61.1138 60.3948

441.3 631.5

0.05895 0.06728

DCM(3) P(4)

0.001391 a 0.001610 a

1.026 a 2.180 a

1.3227 1.3607

48.7821 85.2616

707.2 407.7

0.06730 0.07171

Substance

aRef. (13); bRef. (26).

The empirical Orunberg and Nissan equation has been found to be useful for viscosities o f binary mixtures. Extended to a quaternary system, it takes the following expression: In rl = x l In rl~ + x2 In 'lq2 + x 3 In r13 + x4 In 114 + x~ x2 x3 x4 5

(23)

where 8 is the parameter which reflects the non-ideality of the system. The parameter 8 has usually been regarded as an appropiate measure of the strength o f the interaction between components. Wakefield 2v applied this equation also to quaternary mixtures at different temperatures. The values of 8 obtained for this system is -403.96, with an average deviation o f 18%. Finally, it is possible to predict refractive indices o f quaternary liquid mixtures 9. From the different expressions existing in the literature for predicting refractive indices for multicomponents system, we have taken the Lorentz-Lorenz relation, which has the following form:

(24)

124 where Wi =xi Mi / E xi Mi is the weight fraction. For our system at 298.15 K, the average deviation defined by eq. (12) is 0.3%, which means that the Lorentz-Lorenz equation predicts the refractive indices very well. ACKNOWLEDGMENTS The present work was financed by a CIUNT research grant.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16 17. 18. 19. 20.

N. Radojkovic, A. Tasic, D. Grozdanic, B. Diordievic and M. Malic. J. Chem. Thermodyn.,9,(1977) 349. R . P . Rastogi, J. Nath and S. S. Das. J. Chem. Eng. Data. 22, (1977) 249. I . C . Wei and R. L. Rowley. J. Chem. Eng. Data. 20, (1983) 336. P . P . Singh, R. K. Nigam, S. P. Sharma and S. Aggarwal. Fluid Phase Eq. 18, (1984) 333. H . P . Dahva, P. P. Singh and S. Dagar. Fluid Phase Eq. 43, (1988) 341. I . L . Acevedo, G. C. Pedrosa and M. Katz. Can. J. Chem., 69, (1991) 1006. R . S . Shukla, A. K. Shukla, R. D. Raid and J. D. Pandey. J. Phys. Chem., 93 (1989) 4627. D . L . Wakefield, K. N. Marsh and B. J. Zwolinsky. Intern. J. Thermophys., 9, (1988) 47. D. Pandey, A. K. Shukla, R. K. Shukla and R. D. Rai. Phys. Chem. Liq., 18, (1988) 337. G. L. Bertrand, W. E. Acree, Jr. And T. E. Bruchfield. J. Sol. Chem. 12, (1983) 327. W . E . Acree, Jr. T. E. Bruchfield, J. Sol. Chem. 12, (1983) 155. I. Wei Chien and R. L. Rowley. J. Chem. Eng. Data 29, (1984) 336. J. A. Riddick, N. B. Bunger, and T. Sakano, "Organic Solvents" 4 th ed. J. Wiley & Sons, New York 1986. G. C. Pedrosa. J. A. Salas and M. Katz. Actas Primer Simposio Latinoamericano de Equilibrio de Fases, Concepci6n, Chile, 1987. J . L . Zurita, M. L. G. de Soria, M. A. Postigo and M. Katz J. Sol. Chem., (1987) 163. J . L . Zurita, M. L. G. de Soria, M. A. Postigo and M. Katz. Lat. Am. Appl. Res., 1_2,7(1987) 93. J . A . Salas, G. C. Pedrosa, F. Davolio and M. Katz. Anal. Asoc. Quim. Arg., (1987) 191. M . L . G . de Soria, J. L. Zurita, M. A. Postigo and M. Katz. Thermochim. Acta, 130, (1988) 249. M . A . Postigo, J. L. Zurita, M. L. G. de Soria and M. Katz. Can. J. Chem., 64, (1986) 1966. F. Kohler, Monatsch. Chem., 91, (1960) 738.

125 21. 22. 23. 24. 25. 26. 27.

W. E. Acree, Jr. "Thermodynamic Properties of Nonelectrolyte Solutions", Academic Press, 1984. R.K. Jacob and K. Fitzner, Thermochim. Acta, 18, (1977) 197. I. Cibulka, Coll. Czech. Chem. Commun., 47, (1982) 1414. I. Nagata and K. Tamura, J. Chem. Eng. Data, 33, (1988) 283. T.M. Letcher and R. C. Baxter, J. Sol. Chem. 18, (1989) 65. ,1. A. Salas, B. O'Donell, L. Scida and M. Katz, Anal. Asoc. Quim. Arg., 76, (1988) 427. D.L. Wakerfield, Intern. J. Thermophys., 9, (1988) 365.