densities, viscosities and refractive indexes

$: Densities, Viscosities And Refractive Indexes$
Densities, viscosities, and refractive indexes

for {C2H5CO2(CH2)2CH3+C6H13OH+C6H6}

at T ¼ 308:15K

Herminio Casas, Sandra Garc�ııa-Garabal, Luisa Segade,Oscar Cabeza *, Carlos Franjo, Eulogio Jim�eenez

Departamento de F�ıısica, Facultade de Ciencias, Universidade da Coru~nna, Campus da Zapateira,

15071 A Coru~nna, Spain

Received 22 November 2002; accepted 10 March 2003

Abstract

In this work we present densities, kinematic viscosities, and refractive indexes of the ternary

system {C2H5CO2ðCH2Þ2CH3 þ C6H13OHþ C6H6} and the corresponding binary mixtures

{C2H5CO2ðCH2Þ2CH3þC6H6}, {C2H5CO2ðCH2Þ2CH3þC6H13OH}, and {C6H13OHþC6H6}.

All data have beenmeasured at T ¼ 308:15K and atmospheric pressure over the whole composi-

tion range. The excess molar volumes, dynamic viscosity deviations, and changes of the refractive

index onmixingwere calculated fromexperimentalmeasurements.The results for binarymixtures

were fitted to a polynomial relationship to estimate the coefficients and standard deviations. The

Cibulka equation has been used to correlate the experimental values of ternarymixtures.Also, the

experimental values obtained for the ternary mixture were used to test the empirical methods of

Kohler, Jacob and Fitzner, Colinet, Tsao and Smith, Toop, Scatchard et al., and Hillert. These

methods predict excess properties of the ternary mixtures from those of the involved binary mix-

tures.The results obtained fordynamicviscosities of thebinarymixtureswereused to test the semi-

empirical relations of Grunberg–Nissan, McAllister, Ausl€aander, and Teja–Rice. Finally, the

experimental refractive indexes were comparedwith the predicted results for the Lorentz–Lorenz,

Gladstone–Dale, Wiener, Heller, and Arago–Biot equations. In all cases, we give the standard

deviation between the experimental data and that calculated with the above named relations.

Ó 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Density; Refractive index; Viscosity; Excess properties; Ternary mixture

J. Chem. Thermodynamics 35 (2003) 1129–1137

www.elsevier.com/locate/jct

*Corresponding author. Fax: +34-981-167065.

E-mail address: [email protected] (O. Cabeza).

0021-9614/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0021-9614(03)00081-8

1. Introduction

In a previous paper [1], we have reported experimental excess molar volumes,

dynamic viscosity deviations, and changes of refractive index on mixing of

{C2H5CO2ðCH2Þ2CH3 þ C6H13OHþ C6H6}, and of their corresponding binary

mixtures at T ¼ 298:15K. In the present paper, we continue with the investigation

of this ternary system but at T ¼ 308:15K. This paper and the previous one com-

plete the study of excess volumes of nonelectrolyte ternary mixtures with six car-

bon atoms started previously [2–4]. CibulkaÕs equation [5] has been used to

correlate the experimental values of ternary mixtures. Those experimental values

were used to test the empirical methods of Kohler [6], Jacob and Fitzner [7], Col-

inet [8], Tsao and Smith [9], Toop [10], Scatchard et al. [11], and Hillert [12]. These

methods predict excess properties of the ternary mixtures from those of the in-

volved binary mixtures. The results obtained for dynamic viscosities of the binary

mixtures were used to test the semiempirical relations of Grunberg–Nissan [13],

McAllister [14], Ausl€aander [15], and Teja–Rice [16]. Finally, the experimental re-

fractive indexes were compared with the predicted results for the Lorentz–Lorenz,

Gladstone–Dale, Wiener, Heller, and Arago–Biot equations, which were compiled

by Tasic et al. [17].

2. Experimental

The chemicals employed were supplied by Fluka. Their mole-fraction purities

were C2H5CO2ðCH2Þ2CH3 > 0:99, C6H13OH > 0:99, and C6H6 > 0:995. The sub-

stances were degassed by ultrasound and dried over molecular sieves (Sigma Union

Carbide, type 0.4 nm).

Excess molar volumes were determined from the densities of the pure liquids and

mixtures. Densities were measured with an Anton–Paar DMA 60/602 densimeter

thermostated at T ¼ ð308:15� 0:01ÞK in a Haake F3 circulating-water bath. The ac-

curacy of the measured densities is around 10ÿ2 kg �mÿ3. Immediately prior to each

series of measurements, distilled water and heptane were used to calibrate the densi-

meter. Kinematic viscosities were measured by means of Schott–Ger€aate automatic

viscometer with an accuracy of �5 � 10ÿ10m2 � sÿ1. The refractive indexes were mea-

sured with a thermostated automatic refractometer Atago RX-1000 with reproduc-

ibility in the refractive index data of 10ÿ4. Finally, mixtures were prepared in all cases

by mass using a Mettler AT 201 balance. The precision of the mole fraction is esti-

mated to be better than 10ÿ4.

3. Results and discussion

The measured densities, dynamic viscosities (obtained from the measured kine-

matic viscosities and densities), and refractive indexes of the pure liquids at

T ¼ 298:15K are listed in reference [1] together with published values when available.

1130 H. Casas et al. / J. Chem. Thermodynamics 35 (2003) 1129–1137

The agreement between both sets of data indicates that the compounds used were

pure and that our experimental equipment has a good accuracy.

The excess molar volumes V Em , dynamic viscosity deviations Dg, and changes

in the refractive index on mixing Dn were computed using equations (1) to (3),

respectively,

V Em ¼

X

N

i¼1

xiMiðqÿ1 ÿ q

ÿ1i Þ; ð1Þ

Dg ¼ gÿX

N

i¼1

xigi; ð2Þ

Dn ¼ gÿX

N

i¼1

xini: ð3Þ

In these equations q, g, and n are, respectively, the density, dynamic viscosity, and

refractive index in the mixture. The qi, gi, and ni are the properties of the pure

components, and N is the number of the components in the mixture (so N ¼ 2 in the

case of a binary mixture and N ¼ 3 for a ternary one). The derived excess functions

of the binary systems can be represented by a Redlich–Kister type equation [18],

QEij ¼ xixj

X

m

K¼0

AKðxi ÿ xjÞK; ð4Þ

TABLE 1

Coefficients AK and BK of equations (4) and (6) and standard deviations, s

A0 A1 A2 A3 A4 A5 A6 s

fx C2H5CO2ðCH2Þ2CH3 þ ð1ÿ xÞ C6H13OHg10ÿ6 � V E

m =ðm3 �molÿ1Þ 0.933 )0.052 0.153 0.0011

10ÿ3 � Dg=ðPa � sÞ )3.858 2.221 )1.776 0.9349 0.004

10ÿ3 � Dn )4.00 )0.58 0.23 0.03

fx C2H5CO2ðCH2Þ2CH3 þ ð1ÿ xÞ C6H6g

10ÿ6 � V Em =ðm3 �molÿ1Þ )0.217 )0.064 0.061 0.0012

10ÿ3 � Dg=ðPa � sÞ )0.0792 0.0209 )0.0429 0.0004

10ÿ3 � Dn )45.9 11.8 4.6 )16.7 )14.4 36.7 0.11

fx C6H13OHþ ð1ÿ xÞ C6H6g

10ÿ6 � V Em =ðm3 �molÿ1Þ 1.358 )0.669 0.186 0.132 )0.338 )0.474 0.865 0.0012

10ÿ3 � Dg=ðPa � sÞ )3.265 )0.7560 )0.1051 0.007

10ÿ3 � Dn )36.3 10.3 )2.7 0.15

B1 B2 B3 s

fx1 C2H5CO2ðCH2Þ2CH3 þ x2C6H13OHþ ð1ÿ x1 ÿ x2Þ C6H6g10ÿ6 � V E

m;123=ðm3 �molÿ1Þ )0.545 2.392 )2.642 0.005

10ÿ3 � Dg123=ðPa � sÞ 1.849 0.6731 2.113 0.011

10ÿ3 � Dn123 18.1 8.7 )13.5 0.15

H. Casas et al. / J. Chem. Thermodynamics 35 (2003) 1129–1137 1131

where QEij represents any of the following properties, V E

m , or Dg, or Dn; xi and xj are

the mole fractions of components i and j, respectively; and AK denotes the polyno-

mial coefficients. The degree of the polynomial Redlich–Kister equation was opti-

mised by applying the F test [19]. In table 1, we give the fitted coefficients AK for

equation (4) and the standard deviation, s, defined by,

s ¼X

M

i¼1

Ycalÿ

(

ÿ Yexp�2.

M ÿ 1

)1=2

; ð5Þ

where M is the number of data points, Ycal is the calculated value, and Yexp is the

experimental value.

Figures 1(a) to (c) show, respectively, the experimental V Em , Dg, and Dn plotted

against x together with the fitted curves. The V Em is negative for {propylpropanoate +

FIGURE 1. (a) Excess molar volumes V Em , (b) dynamic viscosity deviations Dg, and (c) changes in the

refractive index on mixing Dn at T ¼ 308:15K plotted against mole fraction x of: s, {xC2H5CO2ðCH2Þ2CH3 þ ð1ÿ xÞ C6H6}; �, {xC2H5CO2ðCH2Þ2CH3 þ ð1ÿ xÞ C6H13OH}; D, {xC6H13OHþ ð1ÿ xÞ C6H6}.


benzene} and positive for the other systems, similar in shape and amplitude than for

T ¼ 298:15K [1]. The slightly negative value observed may be interpreted as proof of

some weak intermolecular interactions established between the carbonyl group of

propyl propanoate and the hydrogen atoms of the benzenic ring. This kind of inter-

action cannot be created between the OH group of 1-hexanol and benzene due to the

steric effect of the long hexanyl chain, which results in positive V Em . In a previous

work [20], there are reported V Em for {C6H6 þ C6H13OH} at T ¼ 298:15K and

T ¼ 308:15K. Their results are very similar to ours both in shape and absolute value.

Results for Dg, given in figure 1(b), show negative curves for the three binary mix-

tures. The absolute value of Dg is lower in around a 30% respecting those presented

before at T ¼ 298:15K for all binary mixtures [1]. Respecting Dn, presented in figure

1(c), the data present the same shape and nearly the same amplitude for all three bi-

nary mixtures than at T ¼ 298:15K. In conclusion, the effect of temperature is only

important for Dg, and not for Dn and V Em .

Table 2 shows the parameters calculated and the standard deviations between ex-

perimental values obtained for dynamic viscosity and the predicted results using the

semi-empirical relations of Grunberg–Nissan [13], McAllister [14], Ausl€aander [15],

and Teja–Rice [16]. The values of critical temperature and critical volume for pure

components, needed for the Teja–Rice relationship, were obtained from reference

[21]. As observed, the best accuracy is given for the Ausl€aander relationship.

Table 3 compares the experimental refractive indexes for binary mixtures with the

predicted results for the Lorentz–Lorenz, Gladstone–Dale, Arago–Biot, Heller, and

Wiener equations, which were compiled by Tasic et al. [17]. As in that paper, the

Lorentz–Lorenz relationship is the most suitable for our data.

TABLE 2

Parameters for the semiempirical relations of Grunberg–Nissan [13], McAllister [14], Ausl€aander [15], and

Teja–Rice [16] and standard deviations, s

System s=ðmPa � sÞ

fx C2H5CO2ðCH2Þ2CH3 þ ð1ÿ xÞ C6H13OHg

Grunberg–Nissan dw ¼ ÿ1:3855 0.03

McAllister g12 ¼ 0:7235 g21 ¼ 1:0903 0.018

Ausl€aander B12 ¼ 3:1844 B21 ¼ 0:0820 A21 ¼ 0:7186 0.012

Teja–Rice a12 ¼ ÿ0:0474 0.05

fx C2H5CO2ðCH2Þ2CH3 þ ð1ÿ xÞ C6H6g


McAllister g12 ¼ 0:5659 g21 ¼ 0:4818 0.016

Ausl€aander B12 ¼ ÿ1:1414 B21 ¼ 7:1632 A21 ¼ 0:1835 0.016

Teja–Rice a12 ¼ 0:8482 0.017

fx C6H13OHþ ð1ÿ xÞ C6H6g


McAllister g12 ¼ 1:7373 g21 ¼ 0:6530 0.012

Ausl€aander B12 ¼ 0:1523 B21 ¼ 1:4048 A21 ¼ 1:7648 0.009

Teja–Rice a12 ¼ 0:5029 0.04


The experimental excess molar volumes V Em;123, dynamic viscosity deviations Dg123,

and changes of refractive index on mixing Dn123 for ternary mixtures were obtained

using equations (1) to (3), respectively. The Cibulka equation [5] has been used to

correlate the experimental properties of the ternary mixtures.

QE123 ¼ QE

bin þ x1x2ð1ÿ x1 ÿ x2ÞðB1 þ B2x1 þ B3x2Þ; ð6Þ

FIGURE 2. Curves of constant (a) 10ÿ6 � V Em;123=ðm

3 �molÿ1), (b) 10ÿ3 � Dg123=ðPa � sÞ, and (c) Dn123, for

{x1 C2H5CO2ðCH2Þ2CH3 þ x2 C6H13OHþ ð1ÿ x1 ÿ x2Þ C6H6} at T ¼ 308:15K.

TABLE 3

Standard deviations of the experimental refractive index results from the predicted for the Lorentz–Lorenz

(L–L), Gladstone–Dale (G–D), Arago–Biot (A–B), Heller (H), and Wiener (W) equations

System L–L G–D A–B H W

fx C2H5CO2ðCH2Þ2CH3 þ ð1ÿ xÞ C6H13OHg 0.0002 0.0001 0.0014 0.0004 0.0004

fx C2H5CO2ðCH2Þ2CH3 þ ð1ÿ xÞ C6H6g 0.0003 0.0010 0.0013 0.0003 0.0006

fx C6H13OHþ ð1ÿ xÞ C6H6g 0.0003 0.0009 0.0017 0.0016 0.0018


where

QEbin ¼ QE

12 þ QE13 þ QE

23: ð7Þ

The symbol QE123 represents V

Em;123, Dg123 or Dn123, and QE

ij is given by equation (4).

The parameters BK for equation (6) and the corresponding standard deviations, s,

defined by equation (5), are given in table 1. The lines of constant ternary excess

properties, calculated by equations (6) and (7), are shown in figures 2(a) to (c) for

V Em;123, Dg123, or Dn123, respectively. Figures 3(a)–(c) shows lines of constant ‘‘ternary

contribution’’, which represent the difference between the experimental value and

that predicted from the binary mixtures (QE123 ÿ QE

bin). Inside the triangular diagrams

exist maxima and/or minima, whose coordinates are presented in table 4.

FIGURE 3. Curves of ternary contribution (a) 10ÿ6 � ðV Em;123 ÿ V E

m;binÞ=ðm3 �molÿ1), (b) 10ÿ3 � ðDg123 ÿ

Dgbin=ðPa � sÞ, and (c) (Dn123 ÿ Dnbin) for {x1 C2H5CO2ðCH2Þ2CH3 þ x2 C6H13OHþ ð1ÿ x1 ÿ x2Þ C6H6}

at T ¼ 308:15K.


Finally, values of V Em;123, Dg123, and Dn123 have been also calculated using the em-

pirical equations proposed by Kohler [6], Jacob and Fitzner [7], Colinet [8], Tsao–

Smith [9], Toop [10], Scatchard et al. [11], and Hillert [12], which take only the binary

contribution into account. For the asymmetric methods (Tsao–Smith, Toop, Scat-

chard, and Hillert), we must indicate the order of components in the mixtures. Table

5 shows the standard deviations, s, between experimental and predicted values. The

most accurate predictions correspond to those of Toop, Scatchard, and Hillert.

TABLE 5

Standard deviations s of different models for: (a) {x1 C2H5CO2(CH2)2CH3 + x2 C6H13OH+(1)x1 ) x2)

C6H6}; (b) {x1 C6H13OH+ x2 C6H6 + (1) x1 ) x2) C2H5CO2(CH2)2CH3}; (c) {x1 C6H6 + x2 C2H5CO2

(CH2)2CH3 + (1)x1 ) x2) C6H13OH}

a b c

10ÿ6 � V Em;123, s=ðm

3 �molÿ1ÞJacob and Fitzner 0.012

Kohler 0.018

Colinet 0.015

Tsao and Smith 0.057 0.024 0.033

Toop 0.021 0.028 0.007

Scatchard 0.016 0.027 0.008

Hillert 0.017 0.027 0.007

10ÿ3 � Dg123, s=ðPa � sÞ

Jacob and Fitzner 0.0620

Kohler 0.0790

Colinet 0.0758

Tsao and Smith 0.2484 0.0159 0.2432

Toop 0.1342 0.0158 0.0924

Scatchard 0.1339 0.0157 0.0782

Hillert 0.1339 0.0157 0.0916

Dn123, s

Jacob and Fitzner 0.0004

Kohler 0.0005

Colinet 0.0004

Tsao and Smith 0.0017 0.0020 0.0002

Toop 0.0007 0.0006 0.0002

Scatchard 0.0006 0.0005 0.0002

Hillert 0.0006 0.0006 0.0002

TABLE 4

Maxima and minima for ternary contributions of the mixture: {x1 C2H5CO2(CH2)2CH3 + x2

C6H13OH+(1)x1 ) x2) C6H6}

Value Coordinates

10ÿ6 � ðV Em;123 ÿ VE

binÞ=ðm3 �molÿ1Þ Maximum 0.0125 x1 ¼ 0:67 x2 ¼ 0:12

Minimum )0.0420 x1 ¼ 0:19 x2 ¼ 0:5310ÿ3 � ðDg123 ÿ DgbinÞ=ðPa � sÞ Maximum 0.105 x1 ¼ 0:32 x2 ¼ 0:38

Dn123 ÿ Dnbin Maximum 0.0006 x1 ¼ 0:40 x2 ¼ 0:27


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