Densities and viscosities of binary and ternary liquid mixtures at 2 5 " ~ '

TEJRAJ M. AMINABHAVI,~ SHRIKANT S. JOSHI, AND RAMACHANDRA H. BALUNDGI Department of Chemistry, Karnatak Universiv, Dharwad-580 003, India

AND

SHYAM S . SHUKLA Department of Chemistry, Lamar University, Beaumont, iT 77710, U.S.A.

Received February 7, 19903

TEJRAJ M. AMINABHAVI, SHRIKANT S. JOSHI, RAMACHANDRA H. BALUNDGI, and SHYAM S. SHUKLA. Can. J. Chem. 69, 1028 (1991).

Densities and viscosities of ten binary and four ternary mixtures containing bromoform, bromobenzene, chlorobenzene, toluene, mesitylene, and dimethylformamide at 25°C have been measured over the whole range of mixture compositions. Excess molar volumes, apparent values of excess molar viscosities, and Gibbs energy of activation of flow have been calculated for these mixtures. The calculated results have been fitted to a linear regression equation to estimate the parameters and the standard deviation between the calculated and the experimental data.

Key words: ternary systems, excess quantities, bromoform, density, viscosity.

TEJRAJ M. AMINABHAVI, SHRIKANT S. JOSHI, RAMACHANDRA H. BALUNDGI et SHYAM S. SHUKLA. Can. J . Chem. 69, 1028 (1991).

Operant ?i 25°C et sur l'ensemble des melanges de composition, on a mesurt les densitCs et les viscositCs de dix mtlanges binaires et de quatre melanges ternaires contenant du bromoforme, du bromobenztne, du chlorobenztne, du toluitne, du mCsitylitne et du dimCthylformamide. Pour chacun de ces mtlanges, on a calcult les volumes molaires en excts, les valeurs apparentes des viscositts molaires en excits et l'enthalpie libre d'activation d'tcoulement. On a ajustC les rCsultats calculCs 2 une Cquation de rkgression lineaire afin d'tvaluer les paramttres et les tcarts types entre les donntes exptrimentales et calcultes.

Mots clis : systtmes ternaires, quantitts en exc.3, bromoforme, densitt, viscositC. [Traduit par la ridaction]

Introduction Experimental Theoretical predictions of excess molar volumes of nonideal

binary liquid mixtures have been satisfactory in explaining the sign and magnitude in terms of the extent of interactions between mixing components (1, 2). For ternary mixtures, the predictive approach is more complex and thus empirical methods based on experimental binary data have to be used (3, 4). However, if significant interactions among the liquids occur, considerable errors may be introduced if we attempt to express the excess molar volumes of ternary systems in terms of binary contributions. The study of transport properties of liquid mixtures, on the other hand, is also informative as it gives an insight into the intermolecular forces and the microscopic structure of liquids (5).

Previous work on binary systems has suggested that correla- tions of molecular order in addition to donor-acceptor type interactions play a significant role in studying the excess molar volumes of mixtures of bromoform with aromatic liquids (6-8). A search of the literature on ternary mixtures suggests the availability of several empirical relations used to calculate the excess volume (9-19). In this paper, we report the experimental densities and viscosities of ten binarv and four ternarv mixtures comprising bromofom, mesitylene, chlorobenzene, bromo- benzene, dimethylformamide (DMF), and toluene. The density data were used to calculate the binary and ternary excess molar volumes and these results were analyzed in terms of the empirical ternary relations. The viscosity data were also used to predict the apparent values of excess molar viscosity and excess molar Gibbs energy of activation of flow.

' ~ a k e n from Ph.D. thesis of S.S.J. submitted to Karnatak University, 1989.

2Author to whom correspondence may be addressed. 3~evision received December 20, 1990.

Printed in Canada i Imprim6 au Canada

Materials Bromoform (Thomas Baker, Bombay) was obtained in its highest

purity grade (>99 mol% as claimed by the manufacturer) and was thus not purified further. The reagent grade solvents, namely, chloro- benzene, bromobenzene, DMF, toluene, and mesitylene were purified before use (20, 21). The physical properties of the pure liquids are in close agreement with the literature results. The purity of the solvents as tested by gas chromatography exceeded more than 99 mol%. Mixtures were pre ared by weighing on a Mettler balance with a precision of i' I x 10- g.

Methods Densities were determined with a single stem pycnometer having a

bulb volume of about 10 cm3 and a capillary of 1 mm internal diameter. Viscosities were determined with a Cannon-Fenske viscometer, size 100, calibrated with double distilled water and benzene. The details of the procedures have been described earlier (6-8). The pycnometer and viscometer were suspended vertically for sufficient time in a constant temperature bath maintained within +O.Ol°C. The temperatures were read with certified thermometers. Densities and viscosities determined are accurate to k 0.0001 and ? 0.003 units respectively. Densities (p) and viscosities (q) of the binary and ternary mixtures, over the entire scale of mole fractions at 25OC, have been rneas~red .~

Results and discussion Following our earlier suggestions (22), the excess molar

volumes of binary mixtures, VE,B, have been calculated from density data as

4 ~ 1 1 numerical data may be purchased from the Depository of Unpublished Data, Document Delivery, CISTI, National Research Council Canada, Ottawa, Canada KIA OS2.

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AMINABHAVI ET AL. 1029

TABLE 1. Estimated coefficients and standard errors of excess molar volumes (v:,~, rn3 rnol-', eq. [2]) of binary mixtures at 25'C

System AfP)x1o6 Ag 'x106 AF'x1o6 Ag)x106 a x 1 0 6

I. II. 111. IV. v. VI. VII. VIII. IX. X.

Mesitylene (1) + brornoform (2) 3.27 -0.97 Brornobenzene (1) + brornoform (2) -0.03 -0.12 Chlorobenzene (1) + brornoform (2) 0.11 0.08 Brornobenzene (1) + mesitylene (2) 0.33 -0.18 Mesitylene (1) + chlorobenzene (2) 0.41 -0.34 DMF (1) + chlorobenzene (2) -0.90 -0.20 Brornobenzene (1) + chlorobenzene (2) 0.17 0.72 Chlorobenzene (1) + toluene (2) -0.37 -0.07 Brornobenzene (1) + DMF (2) -0.87 -0.23 DMF (1) + toluene (2) -0.47 -0.13

where Mi, xi, and pi represent the molar mass, mole fraction, and density of the ith component of the mixture, respectively; p refers to density of binary mixture. These results are further fitted to a Redlich-Kister-type formula (23).

By using a nonlinear regression analysis (Marquardt algo- rithm) we have estimated the binary parameters A$) of eq. [2]. In each case, the optimum number of coefficients was ascer- tained from an examination of the variation of the standard error (u) of the estimate with:

where n is the total number of data points and P is the number of coefficients considered ( P = 4 in the present calculation). The estimated parameters and the standard deviations between the computed and observed values of v:,~ are given in Table 1.

The plots of v:,~ versus x l for all the systems at 25OC are shown in Fig. 1 together with the lines for the standard errors. The estimated error in v:,~ varies in the range (2-5) X

lo-' m3 mol-'. The magnitude of the various binary mixtures follow the sequence: DMF + toluene < DMF + chlorobenzene < bromobenzene + DMF < chlorobenzene + toluene < bromobenzene + bromoform < bromobenzene + chloroben- zene = bromobenzene + mesitylene < chlorobenzene + bromoform < mesitylene + chlorobenzene < mesitylene + bromoform.

To extend the discussion to ternary mixtures, it is legitimate to write the ternary excess molar volume, v:,~ as

Here, p refers to density of the ternary mixture. Analogously, v:,~ can also be measured directly from dilatometry (14). However, v:,~ has been calculated from consideration of v:,~ data of the binaries making up the ternary mixture. This approach has led to the development of several empirical relations to predict v:,~ data. The popular ones among these are as follows:

Rastogi et al. model (4)

FIG. 1. Dependence of excess molar volume (v:,~) on mole frac- tion (x,) of binary mixtures at 25OC. Symbols: (0) brornobenzene(1) + DMF(2); (0) DMF(1) + toluene(2); (A) chlorobenzene(1) + toluene(2); (a) DMF(1) + chlorobenzene(2); (0 ) rnesitylene(1) + brornoform(2); (A) rnesitylene(1) + chlorobenzene(2); ('8) brorno- benzene(1) + rnesitylene(2); (V) brornobenzene(1) + chloroben- zene(2); ( W ) chlorobenzene(1) + brornoform(2); (V) brornoben- zene(1) + bromoform(2).

[6] v:,,= v;+ v & + VE Kohler model (1 2)

[7] v 5 . T = (XI + ~ 2 ) ~ V f z + (XI + ~ 3 ) ~ v f 3 + ( ~ 2 + ~ 3 ) ~ ~ 5 3

Radojkovic et al. model (9) Jacob and Fitzner model (13)

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1030 CAN. 1. CHEM. VOL. 69, 1991

TABLE 2. Estimated coefficients and standard errors of excess molar volumes (V;,T, m3 mol-I, eq. [12]) of ternary mixtures at 25°C

System x lo6 A Y ) x lo6 A(;;) x lo6 AT) x lo6 u x lo6

A. Bromoform (1) + mesitylene (2) + chlorobenzene (3) 0.87 -6.58 7.92 18.31 0.08 B. Chlorobenzene (1) + DMF (2) + toluene (3) 0.16 -8.51 5.40 42.20 0.05 C. Bromoform (1) + mesitylene (2) + bromobenzene (3) 12.35 25.06 -0.29 - 16.57 0.01 D. Chlorobenzene (1) + DMF (2) + bromobenzene (3) 0.16 1.83 -0.82 3.73 0.03

Tsao and Smith model (11)

Sanchez and Lacombe (24, 25) also developed a theory to calculate excess quantities of ternary mixtures. Following this approach, we propose to compute v:,~ from binary interactions obtained from v:,~ data. The total volume v:,~ of a ternary mixture can be expressed as

3

[lo] V m , ~ = C V l ~ , + AV12 + AV23 + AV13 + AVm,T r= l

where the various A V terms representing the changes in volume are given in terms of molar volumes of the respective binary mixtures. So eq. [ 101 becomes

3 3

[ I l l Vm,T = C Vixi + xlx2 1 A\;)(x~ - x2)11 i = 1 11 = 0

since the difference, 1 Vm,T - 2 vixi 1 , represents v;,~, i = l

which is obtained from the experimental density data and has been fitted to the following relationship:

where A?) represents the ternary interaction parameter. The various binary terms (as estimated from v:,~ data) given in Table 1 are used along with v:,~ estimated by eq. [4] to evaluate the ternary coefficients A(,") from eq. [12]. These data are included in Table 2. A detailed analysis of the various theoretical relations is summarized in Tables 2 and 3.

The apparent values of excess molar viscosity qE and excess molar Gibbs energy of activation of flow AGeE, for binary and

TABLE 3. Standard errors ( u ) in estimating excess molar volumes (v:,~, m3 mol-') of ternary mixtures at 25°C

0 x lo6

For systemsa Relation A B C D

Rastogi et al. (eq. [5]) 0.083 0.085 0.102 0.039 Radojkovic et al. (eq. [6]) 0.055 0.051 0.078 0.078 Kohler (eq. [7]) 0.054 0.080 0.067 0.036 Jacob and Fitzer (eq. [8]) 0.055 0.074 0.067 0.037 Tsao and Smith (eq. [9]) 0.057 0.067 0.077 0.035 Present work (eq. [12]) 0.077 0.051 0.012 0.029

"A, B, C, and D refer to ternary mixtures given in Table 2.

' - 1 2

FIG. 2. Dependence of excess molar viscosity (.rlE) on mole fraction (XI ) at 25°C. Symbols have the same meanings as in Fig. 1.

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AMINABHAVI ET AL

TABLE 4. Estimated coefficients and standard errors of excess molar viscosity (-qE, Pa s, eq. [13]) and excess molar Gibbs energy of activation of flow ( A G * ~ , J mol-', eq. [14])

for binary mixtures at 25OC

Systema Property A p A ~ I A p A p u

I

II

I11

IV

v

VI

VII

VIII

IX

X

"Systems I-X refer to binary mixtures given in Table 1.

TABLE 5. Estimated coefficients and standard errors of excess molar viscosity (-qF, Pa s, of eqs. [13] and [15]) and excess molar Gibbs energy of activation of flow ( A @ , J mol-', of eq. [14]) for

ternary mixtures at 25OC

Systema Property A$ A Y ) AY) AY' u

A -qF X lo3, eq. [13] A G * ~ , eq. [14] -qF X lo3, eq. [15]

B -qF x lo3, eq. [13] A G * ~ , eq. [14] -qF X lo3, eq. [15]

C -qF X lo3, eq. [13] A G * ~ , eq. [14] -qF X lo3, eq. [15]

D -qF x lo3, eq. [13] A G * ~ , eq. [14] -qF x lo3, eq. [15]

"A, B, C, and D refer to ternary mixtures given in Table 2.

ternary mixtures, were calculated (26-28) as:

Quite often an exponential relation was also used to calculate qE of the mixtures.

The computed values of qE and AGLE from eqs. [13] and [14] for binary mixtures have been fitted to eq. [2] to estimate the coefficients that are included in Table 4.

The results of -qE at 25°C calculated from eq. [13] along with the errors as indicated by the solid vertical lines are displayed in Fig. 2 for all the binary mixtures. The error analyses indicate that qE results vary in the range of (2-4) X lo7 Pas. The results for A G * ~ at 25°C are plotted in Fig. 3. The errors involved in the computation of A G * ~ are estimated to be, at the most, around + (2-3) J mol-'. The magnitude of A G * ~ for the various binary mixtures follows the sequence: bromobenzene + DMF > mesitylene + bromofom > DMF + chlorobenzene > bromo-

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1032 CAN. J. CHEM. VOL. 69, 1991

FIG. 3. Dependence of excess molar Gibbs energy of activation of flow ( A G * ~ ) on mole fraction ( x , ) at 25°C. Symbols have the same meanings as in Fig. 1.

benzene + bromoform > chlorobenzene + bromoform > D M F + toluene > chlorobenzene + toluene > bromobenzene + mesitylene > mesitylene + chlorobenzene > bromobenzene + chlorobenzene.

The ternary viscosity data have also been analysed in terms of eqs. [13]-[15] and these data are fitted to the following empirical relation:

where xE refers to rl as calculated from eqs. [ 131 and [ 151 and AG*E from eq. [14]. The estimated coefficients and the standard deviations are compiled in Table 5 . The rlE as calculated from eq. [13] appears to be better than that given by eq. [15].

Acknowledgements We thank the University Grants Commission (major grant:

F-12-55188-SR-111) New Delhi, India, and the Robert A. Welch Foundation, Houston, Texas, for the financial support of this study. We also thank Professor Keith C. Hansen, Chairman,

Chemistry Department, Lamar University, Beaumont, Texas, U.S.A. , for his interest in this research.

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