Ind. Eng. Chem. Res. 1993,32, 931-936
931
Volumetric, Acoustic, Optical, and Viscometric Properties of Binary Mixtures of 2-Methoxyethanol with Aliphatic Alcohols (Cl-C# Tejraj M. Aminabhavi,' Shrinivas K. Raikar, and Ramachandra H. Balundgi Department of Chemistry, Karnatak University, Dharwad, 580 003 India
Densities, refractive indexes, speed of sound data, and viscosities of 2-methoxyethanol+ alcohol mixtures are determined at 298.15,303.15, and 308.15 K. Density results are used to calculate excess molar volume. The results of speed of sound data, refractive index, and viscosity are used to calculate the changes in isentropic compressibility, molar refractivity, and viscosity. These properties are fitted to the Redlich-Kister type equation. Intermolecular interactions in mixtures of 2-methoxyethanol with alcohols have led to rather widely varying excess molar volumes from negative to large positive values, depending on the size of the alcohols. McAllister's three-body interaction model is used to correlate the binary kinematic viscosities, and results are compared with those from Lobe's relation. Furthermore, speed of sound data for mixtures are calculated from the theoretical relation of Auerbach. Table I. Comparison of Literature Data for Pure Solvents at 298.15 K
Introduction 2-Methoxyethanol, commonly known as methyl Cellosolve, is a widely used industrial solvent which possesses unique solvating properties associated with its quasiaprotic character (Garst, 1969). It is an ether alcohol showing physicochemicalcharacteristics midway between protic and dipolar aprotic solvents. As a result, it has attracted much attention as a solvent in electrochemical studies (Nandi et al., 1989; Franchini et al., 1986, 1989, 1990). Excess thermodynamic properties of the binary mixtures of 2-methoxyethanol have been reported earlier (Chandak et al., 1977; Marchetti et al., 1991). However, an extensive data base on the volumetric,acoustic,optical, and viscometric properties of mixtures of 2-methoxyethan01 with aliphatic alcohols is not available. Such data are required in many engineering design processes including liquid-liquid extraction, distillation, and separation, and in the petrochemical and pharmaceutical industries. On the other hand, theoretical knowledge about the mixing properties of 2-methoxyethanol with alcoholscontaining carbons c1-C~has a tremendous value toward understanding the nature of interactions. In the present paper we report the experimental densities p, refractive indexes nD, speeds of sound u, and viscosities q for the binary mixtures of 2-methoxyethanol with methanol, ethanol, 1-propanol, 1-butanol, 2-methyl-lpropanol, 1-pentanol,3-methyl-1-butanol,1-hexanol,l-heptanol, and 2-octanol in the temperature interval of 298.15308.15 K over the entire mixture composition. The experimental results are used to calculate excess molar volume VE in addition to changes in refractivity AR, isentropic compressibility AB, and viscosity, Aq. These results are used to qualitatively discuss the nature of interactions from mixing the components in terms of hydrogen-bond effects, dipole-dipole interactions, weak van der Waals type dispersion forces, etc. The calculated quantities have been fitted to the Redlich-Kister equation (Redlich and Kister, 1948)to estimate the coefficients. In view of the current interest (Reid et al., 1977) in knowing to what accuracy the approaches of McAllister (1960) and that of Lobe (1973) can predict the viscosities of binary liquid mixtures containing components of varying com~~
~
* To whom correspondence should be addressed. + T h i s paper is dedicated t o Professor Petr Munk of the University of Texas a t Austin on the occasion of his 60th birthday.
P, g c m 3
solvent
lit.
2-methoxyethanol methanol ethanol 1-propanol I-butanol 2-methyl-1-propanol 1-pentanol 3-methyl-1-butanol 1-hexanol 1-heptanol 2-octanol
0.9602 0.7864 0.7849 0.7996 0.8058 0.7978 0.8108 0.8018" 0.8153 0.8190b 0.8171
a
obsd 0.9591 0.7870 0.7858 0.8000 0.8067 0.7979 0.8111 0.8030' 0.8156 0.8199 0.8171
nD lit. 1.4002 1.3265 1.3594 1.3837 1.3974 1.3939 1.4080 1.4085b 1.4157 1.4226b 1.4241
obsd 1.4002 1.3256 1.3583 1.3825 1.3973 1.3933 1.4065 1.4048 1.4149 1.4211 1.4233
At 303.15 K. Sarmiento et al., 1985.
plexity, attempts have also been made to compute the binary viscosities from these equations.
Experimental Section 2-Methoxyethanol (Thomas Baker, Bombay) was purified by the recommended procedures (Riddick et al., 1986;Vogel, 1989). Other solvents,namely, methanol (S.D. fine, Bombay), ethanol (Riedel de Haen, Frankfurt, Germany), 1-propanol (Thomas Baker), 1-butanol (Sisco, fine), 1-pentanol (E. Bombay), 2-methyl-1-propanol(S.D. Merck, Darmstadt), 1-hexanol (Fluka A.G., Switzerland), 3-methyl-1-butanol (Thomas Baker), 1-heptanol, and 2-octanol (both BDH, London, England) were double distilled and purified as per the published procedures (Riddick et al., 1986; Vogel, 1989). The purity of all the solvents was ascertained by the constancy of their boiling points during final distillations and also by literature comparisons of their densities and refractive indexes at 298.15 K; these agreed well within the precision of experimentalerror. See Table I. Further test of the purity up to 99+ mol 96 for all the solvents was ascertained by gas chromatographic (GC)determinations. Binary mixtures were prepared by mass in specially designed glass ampules. All the weighing5 were made in a Mettler balance (Switzerland)with an accuracy of f0.05 mg. The possible error in the calculation of mole fractions was estimated to be around f0.0002. The evaporation losses of solvents were not significant as evidenced by a repeated measurement of the physical properties over an extended period (usually 2-3 days) during which time no changes in physical properties were observed.
OSSS-5885/93/2632-0931$04.00/00 1993 American Chemical Society
932 Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993
Densities of pure liquids and their binary mixtures were measured by using a pycnometer having a bulb volume of about 10 cm3 and a capillary with an internal diameter of 1mm. For each measurement, sufficient time was allowed to attain thermal equilibrium in a INSREF (Model 016 AP) precision thermostat, the bath temperature of which was monitored to f O . O 1 K using a mercury calibrated thermometer. The fluctuations in bath temperatures did not exceed f0.1 K. The reported densities at all temperatures are accurate to fO.OOO1 g/cm3. Viscosities were measured by using Cannon Fenske viscometers (sizes 75, 100, and 150 depending on liquid efflux times), ASTM D445, supplied by Industrial Research Glassware Ltd., Roselle, NJ. An electronic stopwatch with a precision of fO.O1 s was used for efflux time measurements. Triplicate measurements of flow times were reproducible within f0.02 % . The kinematic viscosity v is given by: v = q/p = At - B / t ,where 9 is absolute viscosity, p is density, A and B are the viscometric constants, and t is efflux time. The term Blt represents the kinetic energy correction, and these are calculated for the viscometers used. For instance, for viscometer size 75, the values of constants A and B for water in the temperature interval of 298.15-308.15 K are 0.007 67 and -0.706 05,respectively. Similarly, for size 100, the corresponding values are 0.014 61 and-1.264 25, respectively, and for size 150,these values are 0.0318 48 and -1.450 06, respectively. Using these values, the kinematic viscosities have been calculated. Comparisons of these data with literature are satisfactory. Absolute viscosities q , in units of mPa s, were calculated by using the relation q up. The accuracy in viscosity measurement is around fO.OO1 mPa s. The viscosities of pure liquids are of acceptable accuracy as evidenced by a comparison of the data with literature (Riddick et al., 1986). For instance, the observed data at 298.15 K (77 in mPa s) of 2-methoxyethanol (1.6951, methanol (0.5421, ethanol (1.080), l-butanol(2.442), and 2-methyl-l-propanol(3.256) are in agreement, respectively, with 1.600, 0.551, 1.083, 2.571, and 3.333 from the literature (Riddick et al., 1986). Refractive indexes for the sodium D line were measured with a thermostated Abbe refractometer (Bellingham and Stanley Ltd., London) with an accuracy of f0.0001 unit. Calibration checks of the refractometer were done routinely with the help of the test glass piece of known refractive index supplied with the instrument. Speeds of sound were measured by using a variablepath 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 1MHz. The frequency was measured with an accuracy of 1in lo6by using a digital frequency meter. The current variations across the transducer were observed on a microammeter. The interferometer cell was filled with the test liquid and was connected to the output terminal of the high-frequency generator through a shielded cable. Water was then circulated around the measuring cell from a thermostat maintained at the desired temperature. The experimental details are given earlier (Aralaguppi et al., 1991, 1992a,b). The speeds of sound data are accurate to f 2 m s-l. For instance, the speeds of sound in methanol (1098 m s-l), ethanol (1145 m s-l) and l-propanol (1207 m s-l) are in agreement with the published results (Kumar et al., 1981) for the respective liquids of 1112,1160, and 1213 m s-1 within about 1.5%. The results of isentropic compressibility @ were calculated as @ = 1/u2p. Tabulated values of experimental densities, refractive indexes, and viscosities at 298.15, 303.15, and 308.15 K,
and speeds of sound at 298.15 K for all the mixtures are available as supplementary material (see paragraph at end of paper regarding supplementary material).
Results and Discussion The excess molar volume VE of a binary mixture is a quantity which can be calculated traditionally from the difference between the measured property for the mixture and that for an ideal mixture. Thus,
VE = v, - (V1xl+ V g , ) where Vm represents the molar volume of the mixture + Mg2)/pm;the quantities which can be calculated as (MIXI V1 and V2 refer to the molar volumes of components 1and 2, respectively. The symbols Mi and xi are the molecular weights and mole fractions, respectively, of the ith component of the mixtures. However, in the case of other properties such as the speed of sound, molar refraction, and yiscosity, it is not common to use the term “excess quantity”,though, in some instances, such terminology is used. Therefore, in this work, we prefer to use the word “changes” as a prefix to the property instead of “excess”. Accordingly, the changes in isentropic compressibility, Ab, molar refractivity, AR, and viscosity, Aq, are expressed most generally as A Y = Y , - ( Y I C l+ Y2C2)
(2) where Y refers to pure component properties, namely, 8, R, or q as the case may be. The symbol Ci refers to mixture composition, (either mole fraction, xi or volume fraction, &). We have followed here the usual practice of using & for calculating AR and A@ and xi for Aq. However, the mole fraction, X i , and volume fraction, di, of the ith component are related as 2
f#Ji
=
xivi/cXivi
(3)
i=l
Molar refractivities of the mixture R , and those of the pure components Ri are obtained from the Lorentz-Lorenz and Eykman relations (Aralaguppi et al., 1991; AbdelAzim and Munk, 1987; Bottcher, 1952) for the densities of mixtures and of pure components in the usual way. The parameters VE,AR,A@,and Aq have been fitted to the Redlich-Kister relation (1948). 3
AY (or VE) = x 1 x 2 C a i ( ~ ,c1Y
(4)
1=0
By using the least-squares procedure the coefficients ai of eq 4 have been estimated. However, these coefficients have no interpretive value. The optimal values of ai together with the standard errors u between the calculated and experimental data are given in the supplementary material. The smooth curves of the Figures 1-4 are drawn from the computed results. The excess molar volume data are presented in Figure 1. Alcohols themselves are strongly self-associated with the degree of association depending on such variables as molecular size, position of OH group, and temperature (Franks and Ives, 1966;Petterson et al., 1986). Due to the electron-donating inductive effect of the alkyl group, the strength of bonding in alcohols is expected to decrease with an increase in the molecular size,implying that higher alcohols have smaller proton-donating capacity. Thus, increase in VE with the size of alcohols may not only be due to molecular size differences but are also attributed to the presence of hydrogen-bond effects. For mixtures
Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 933
15
-
0
a.
0
I-
-15 L
n
k
U
.L!
n
-
-30 -
L
C
VI
-
.= -45 Y
C m U c
-
-60
0
0.2
0.4 0.6 lrlole Fraction, x 1
0.8
1
Figure 1. Excess molar volume vs mole fraction at 298.15 K for mixtures of 2-methoxyethanol with (0)methanol, ( 0 )ethanol, (A) 1-propanol,(A)1-butanol, (0) 2-methyl-1-propanol,(v)1-penhol, (m) 3-methyl-1-butanol, (v)1-hexanol, ( 0 )1-heptanol, and (+) 2-octanol.
of 2-methoxyethanol with methanol, ethanol, or 1-propanol VE is negative over the whole range of mixture composition and in the investigated range of temperature. This suggests the presence of specific interactions. The values of VE are more negative for methanol than either ethanol- or 1-propanol-containing mixtures. However, the minimum of VE vs XI curve shifts at higher XI values for ethanol than for methanol in the mixture. For 2-methoxyethanol 1-butanol or 2-methyl-1-propanol mixtures, the positive values of VE are more or leea identical with no sharp maxima. This suggests that the structural differences between 1-butanol (linear) and 2-methyl-lpropanol (branched) show no effect on the VE results. The positive VE for these mixtures may be the result of weak dispersive-type interactions. Further, for higher alcohols, namely, 3-methyl-1-butanol,1-pentanol, 1-hexanol,l-heptanol, and 2-octanol,the VE resulta increase systematically suggesting further weak dispersion-type interactions. Due to the nonavailability of the VE data for the present mixtures, we cannot compare these results with the literature. However, the dependence of VE on the size of alcohols as observed here parallels some of the published results on a similar type of mixtures (Dewan et al., 1991; Pikkarainen, 1983a,b; Uosaki et al., 1992; Sandhu and Singh, 1992; Karunakar et al., 1982; Sandhu et al., 1986). However, the effect of temperature on VE for the binary mixtures of this study is not quite systematic. For instance, VE decreases with a rise in temperature for mixtures of 2-methoxyethanolwith methanolor 1-hexanol. In the case of mixtures of 2-methoxyethanol + ethanol, 1-heptanol, or 2-octanol, VE results do not show any systematic variation with temperature. However, for the remaining mixtures, VE results tend to increase slightly with a rise in temperature. Due to the limited range of the temperature interval (Le., 5 K) studied, we are presently not in a position to explain the temperature dependence of VE.
+
-75
-
0
a2
0.4 0.6 Volume Fraction, @
0.8
1
1
Figure 2. Changes in isentropic compressibility va volume fraction at 298.15 K for the binary mixtures given in Figure 1.
However, the observed inconsistency is in agreement with the published results (Asfour et al., 1990; Garcia et al., 1986). The acoustic data on liquids and liquid mixtures are of great interest in a variety of disciplines in addition to theoretical interest (Kumar et al., 1992). In view of this, we have attempted to calculate the speed of sound, u, in the binary mixtures from the Auerbachrelation (Auerbach, 1948) and by employing Flory’s equation of state (Flory and Abe, 1964; Flory, 1965) and that of the Patterson and Rastogi method (Patterson and Rastogi, 1970). The calculated values of u at 298.15 K are available as supplementary material. The average absolute error between theory and experiments is around 8-9 9%. The changes in isentropic compressibilitiee as calculated from eq 2 are displayed in Figure 2 as a function of $1 at 298.15 K. These results show the same trend as those of VE data; Le., they increase from a large negative value for methanol to a large positive value for 1-heptanol. This clearly indicates the influence of the size of alcohols on AS. For mixtures of 2-methoxyethanol with 1-propanol or 2-methyl-1-propanol, the Aj3 data are negative and vary identically. Similarly, for mixtures of 2-methoxyethanol with 1-butanol or 3-methyl-1-butanol, AB values are negative and are almost identical. For the latter mixtures, the values of Aj3 are not greatly affected by the structural variations of alcohols. Binary mixtures of 2-methoxyethanol with 1-pentanol, 1-hexanol, or 1-heptanol are positive and increase in the above sequence. However, in the case of the 2-methoxyethanol + 2-octanol mixture, the positive Aj3 values are somewhat smaller than those for the 2-methoxyethanol + 1-heptanol mixture. In general, the observed trend for the dependence of M on 41 resembles closely that of VE and, therefore, the same explanations hold good for the dependence of both Aj3 and VE on mixture composition. Changes in molar refractivity, AR,as calculated from eq 2 using the refractive index mixing rules (Bottcher,
Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 0.2
!-
I
I
Table 11. Values of Adjustment Parameters and Average Percent Absolute Error (A%) for McAllister and Lobe Models for Binary Mixtures
I
2-methoxyethanol with methanolb
0
-0.2
-0 4
-0.6
-
-0.8
-
-1.0
0
02
04 06 Voiume Fraction, @,
08
temp, K 298.15 303.15 308.15 298.15 ethanolb 303.15 308.15 298.15 1-propanol 303.15 308.15 1-butanol 298.15 303.15 308.15 2-methyl-1-propanol 298.15 303.15 308.15 1-pentanol 298.15 303.15 308.15 3-methyl-1-butanol 298.15 303.15 308.15 1-hexanol 298.15 303.15 308.15 1 heptanol 298.15 303.15 308.15 2-octanol 298.15 303.15 308.15 ~
Figure 3. Changes in refractivity vs volume fraction at 298.15 K for the binary mixtures given in Figure 1.
1952)represent the electronic perturbations due to orbital mixing of the two components. Moreover, AR represents the strength of interactions in mixtures and is a sensitive function of wavelength, temperature, and mixture composition (Aminabhavi, 1987; Aminabhavi et al., 1988a,b, Aralaguppi et al., 1992a,b;Aminabhavi and Munk, 1979; Aminabhavi, 1983). The dependence of AR on 41 is shown in Figure 3. As expected,the ARLL values calculated from the Lorentz-Lorenz rule follow a trend reverse from those of P or Ab data. A similar observation is found for the Eykman relation, i.e., ARE^^. These data are not displayed graphically to avoid redundancy. For instance, with mixtures of 2-methoxyethanol + 2-octanol, 1-heptanol, 1-hexanol, 3-methyl-1-butanol, 1-pentanol, 1-butanol, or 2-methyl-1-propanol, the AR values are negative and increase in the above order. However, for the mixtures containing 1-butanol or 2-methyl-1-propanol, AR values are almost identical and depend only slightly on the mixture composition. However, for mixtures of 2-methoxyethanol with methanol, ethanol or 1-propanol, AR values are positive. For 2-methoxyethanol+ methanol or 1-propanol, the dependence of AR on 41 is not very systematic. However, AR data for all the mixtures seem to support the explanations advanced for Por A@results. In view of the considerable interest in the study of viscosity of binary mixtures, attempts have been made to test the viscosity equations. However, the present knowledge in this area is not sufficiently developed due to the nonavailability of viscosity equations to accurately calculate the mixture viscosities from the pure component data. Yet, there is some interest in the literature (Garcia et al., 1991;Pikkarainen, 1983a,b)to study the changes in viscosity,Aq, which provides information about the nature and behavior of mixtures. In our earlier papers (Gokavi et al., 1986;Aminabhavi et al., 1987) viscosities have been fitted to theoretical relations to test their validities. In continuation of this program, we shall now analyze the viscosity data by using the McAllister (1960) three-bodyinteraction model and that of Lobe's approach (1973). According to McAllister, the kinematic viscosities have been calculated as
A%
rZ/r,a
a
0.801 1.507 1.364 1.255 0.904 1.658 1.493 1.370 0.981 1.778 1.600 1.455 1.050 1.872 1.671 1.517 1.053 1.975 1.750 1.560 1.110 2.110 1.873 1.676 1.112 2.163 1.920 1.705 1.164 2.293 2.015 1.788 1.213 2.576 2.262 1.983 1.261 2.990 2.598 2.239
b
1.235 1.140 1.052 1.350 1.248 1.123 1.655 1.504 1.359 2.106 1.924 1.742 2.164 1.970 1.809 2.491 2.251 2.053 2.433 2.218 2.013 2.919 2.588 2.288 3.688 3.221 2.845 4.141 3.536 3.090
McAllistar Lobe -0.11
-0.10 -0.10 0.09 0.00 0.06 0.03 -0.05 -0.07 -0.15 -0.22 -0.27 0.09 -0.08 -0.24 -0.07
-0.07 -0.16 0.33 0.21 0.55 0.24 0.23 0.09 0.36 0.63 0.44
1.48 1.31 -1.13
-11.44 -11.03 -10.67 -13.63 -12.90 -11.80 -17.95 -16.86 -15.20 -14.00 -13.44 -12.31 -16.34 -15.16 -14.12 -16.24 -16.26 -15.93 -15.26 -15.43 -15.19 -12.70 -12.60 -12.16
The values under the square-root term a r z h = (MzPI/MIP~S/~. are negative and hence A% for Lobe's method cannot be estimated.
+
~n v = x13 In v1 + 3xl2x2In a 3x1x22In b + x: In up ln[x, x$,/Ml1 + 3X12x2ln[(2 + M2/M,)/31
+
+
3x1x; M ( l + 2M2/Ml)/31 + x: 1n(M2/M1) (5) where a and b are the two undetermined parameters which are characteristics of the system; MI and MZ are the molecular weights of components 1 and 2, respectively. The values of a and b have been determined by the method of least squares from the binary viscosity data and are given in Table 11. In keeping with McAllister's analysis, there is a general downward trend in errors with decrease in molecular size ratio but the decrease is not so consistent. Errors for the 2-methoxyethanol + ethanol system are higher than those for the 1-propanol-containingmixture; for these systems, we observe a dependence on molar volume ratio and the molecular size ratio. The kinematic viscosity of binary mixtures was also calculated from Lobe's approach (Lobe, 1973). = 41v1e x ~ ( 4 ~ a+~ 42v2 * ) e x ~ ( 4 ~ a , * ) (6) Lobe has suggested that if the first component of the mixture has a smaller viscosity and if the kinematic viscosity of the mixture varies monotonically with composition, then the values of a ~ and * a2* are given by the following empirical equations. LJ
CY,*
= -1.7 h ( v , / v , )
(7)
+
(8)
a2*= 0.27 1n(v2/vl) 11.3 ln(v21vl)11/2
The values of the kinematic viscosities as estimated from eq 6 using the values of a1* and a2* given by eqs 7 and 8, respectively, are also included in Table 11. The average percent deviations A ?6 are calculated for both McAllister's
Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 936 ture. This negative contribution is attributed to the difference in the size and shape of the component molecules allowing them to fit into each other’s structure (Assarsson and Eirich, 1968). For mixtures of 2-methoxyethanol+ methanol, Aq values are almost zero but still are negative. Similarly, for other mixtures, Aq values are negative. However, sharp maxima are not observed for ethanol- or 1-propanol-containing mixtures. For mixtures containing 2-methyl-1-propanol or 3-methyl-1-butanol,the values of Aq are quite similar, suggesting their identical transport behavior. According to Fort and Moore (1966),Reed and Taylor (1959),and Oswal and Rathnam (1984),Aq values are negative in mixtures of unequal size in which dispersion forces are dominant. The decrease in Aq with an increase in the size of alcohols further supports the presence of dispersion forces. However, a reverse tendency should be true for VE, and this is indeed the case; i.e., molecular association decreases with an increase in the size of alcohols. This type of behavior was also observed by other alcohol-containing mixtures (Pikkarainen, 1983a,b).
0
-0.15
a
-0.30
E
e
a
d
-0.45
C
u c 2.
.-
L
3
-0.60
.->Io
- 0.75
\\ \
Acknowledgment
/
-0.90 4
0.2
I
1
0.4 0.6 Mole Fraction, x ,
I
J
0.8
1
Figure 4. Changes in viscosity vs mole fraction at 298.15 K for the binary mixtures given in Figure 1. Table 111. McAllister’s Three-Body Model Parameters and Average Percent Absolute Errors (A%) in Predicting Kinematic Viscosities Based on the Asfour et al. (1991) Procedure McAllister params 2-methoxyethanol with methanol ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol
a 1.355 1.641 1.865 2.131 2.402 2.709
b 0.990 1.509 1.968 2.550 3.172 3.912
We thank Mr. R. S. Khinnavar for his help in the computations and UGC [F.12-55/88(SR-III)],New Delhi, for major financial support of this study.
Supplementary Material Available: Tables listing values of experimental density, viscosity, refractive index, and speed of sound of the mixtures at different temperatures, values of the estimated parameters of eq 4, and the standard errors involved in the estimation of VE, A@,AR, and Aq for the mixtures a t different temperatures (23 pages). Ordering information is given on any current masthead page.
A%
8.71 2.87 6.31 9.30 10.78 13.68
and Lobe’s equations, and these values are presented in Table 11. It is observed that McAllister’s equation correlates the mixture viscosity to a significantly high degree of accuracy for all the systems as evidenced by smaller average deviations than those of Lobe’s approach, a fact that was established by Nath and Dixit (1984). Furthermore, the values of the McAllister parameters have shown a decreasing tendency with a rise in temperature, the same dependence was also observed by Vavanellos et al. (1991) and Asfour et al. (1991). Moreover, the A % values increase with the molecular size of alcohols. In all cases, the ratio of molecular radii (rdr1 < 1.5) remains within the limit of applicability of the McAllister relation. Following the recent approach suggested by Asfour et al. (1991) to predict the a and b parameters of the McAllister theory, we have attempted to estimate the McAllister three-body parameters on the basis of our experimental data. Unfortunately, this approach was not quite successful with the present systems as evidenced by the large differences between the predicted viscosities and those of the experimental data (see Table 111). Changes in viscosity, Aq, as calculated from eq 2 are displayed graphically in Figure 4. It is observed that, unlike VE, the results of Aq decrease systematically with an increase in the size of alcohols. A large negative value is observed for the 2-methoxyethanol+ 1-heptanol mix-
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Received for review August 4, 1992 Revised manuscript received October 27, 1992 Accepted December 11, 1992
