Experimental Study and Modeling of the RefractiveIndices in Binary and Ternary Mixtures of Waterwith Methanol, Ethanol and Propan-1-ol at 293.15 K

Marlon Martnez-Reina Eliseo Amado-Gonzalez Wilfred Gomez-Jaramillo

Received: 9 August 2014 / Accepted: 1 November 2014 / Published online: 24 February 2015 Springer Science+Business Media New York 2015

Abstract Refractive indices of ternary mixtures of water ? methanol ? (ethanol orpropan-1-ol), (water or methanol) ? ethanol ? propan-1-ol and their binary mixtures have

been measured at 293.15 K and at atmospheric pressure over the whole composition range.

The refractive index deviations were calculated and fitted to the RedlichKister equation

for binary mixtures, and the Cibulka equation for ternary mixtures. Furthermore, we

demonstrate that the refractive index of the associated ternary mixtures can be estimated

with relative errors from 0.036 to 0.861 % by using the several mixing rules and the

refractive indices of the corresponding pure components. The behavior of refractive indices

is associated with solventsolvent interactions and the formation of clusters.

Keywords Refractive index Ternary mixtures Refractive index deviations Mixingrules Clusters

1 Introduction

The refractive indices of pure components and their mixtures are an optical property of

matter that allows control of processes in the chemical, petrochemical and pharmaceutical

industries, and its importance is well known. For some specific scientific applications, the

required accuracy is very high and requires precise measurements [1]. Since the refractive

index of a liquid at the sodium D line light, nD, is a property easy to measure with good

accuracy, it has been connected with other thermo physical properties, such as surface

tension and density, by empirical and theoretical equations [2, 3]. A structureproperty

model has been found to have great potential for predicting the physicochemical properties

of substances [4]. It is known that refractive index mixing rules allow estimation of the

M. Martnez-Reina E. Amado-Gonzalez (&) W. Gomez-JaramilloIbear L-307 Biofuels Laboratory, Department of Chemistry, University of Pamplona, CiudadUniversitaria, Pamplona, Colombiae-mail: eamado@unipamplona.edu.co

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J Solution Chem (2015) 44:206222DOI 10.1007/s10953-015-0305-5

refractive index of a mixture from the refractive indices of the pure components. Hellers

work [5] shows that these mixing rules can be used to predict the density or excess volumes

of a mixture from its refractive index or vice versa.

In recent years some workers have studied the refractive indices of (binary or ternary)

liquid mixtures and analyzed the applicability of the refractive index mixing rules: 19

binary mixtures of various polarities [6], 73 binary mixtures containing various groups of

organic compounds [7, 8], (water ? ethanol ? k-ethylene glycol) (when k is mono, di or

tri) [1], isomers of butanol with n-hexane, and 1-chlorobutane [9], isomers of chlorobu-

tanes and butanols [10], diethyl malonate ? (dimethylformamide, hexane, tetrahydrofuran

or 1,4-dioxane) [11], tetrahydrofuran ? (methanol or o-cresol) [12], eucalyptol ? hydro-

carbons [13], ethanol ? n-alkane mixtures [14], chlorobenzene ? n-hexane ? (n-heptane

or n-octane) [15], cyclohexane ? toluene ? methanol [16], and tetralin ? isobutylben-

zene ? dodecane [17]. Alcohols are polar molecules, self-associated by hydrogen bonding

of their hydroxyl groups [18]. The hydrogen bonding gives the alcohols the possibility of

interacting with other substances to change their structure. The applications of alcohols in

the food industry, and pharmaceutical uses as co-surfactants in micro emulsions, are still

under development [19].

Among the thermo physical properties, refractive indices of water with alcohols in

binary and ternary systems are expected to show complex behavior, due to the inter-

molecular interactions [20]. Therefore, the binary systems of water with methanol, ethanol

or propan-1-ol, and their ternary systems are of great interest.

In the present paper, refractive indices at 293.15 K are reported for six binary mixtures:

water ? (methanol, ethanol or propan-1-ol), methanol ? (ethanol or propan-1-ol), etha-

nol ? propan-1-ol, and for four ternary mixtures: water ? methanol ? (ethanol or pro-

pan-1-ol), water ? ethanol ? propan-1-ol and methanol ? ethanol ? propan-1-ol. These

data were used to calculate the refractive index deviations, DnD, which were correlatedusing a 5-parameter RedlichKister equation [21] for binary mixtures and the Cibulka

equation [22] for ternary mixtures. Finally, we have used several mixing rules, those of

LorentzLorenz [23, 24], GladstoneDale [25], Eykman [26], Newton [27] and Oster [28],

to predict refractive indices. The accuracy of the mixing rules for determination of re-

fractive indices is analyzed and cluster formation is predicted for the ternary mixtures.

2 Experimental

Densities of the pure liquids were measured by using a pycnometer having bulb volume of

approximately 10 cm3 and capillary with internal diameter of 1 mm. First, the pycnometer

was calibrated with distilled water of known density, and then it was filled with pure liquid

and immersed in a thermostatic bath. The bath temperature was monitored to 0.01 K with

a calibrated thermometer. In addition, all of the measurements were conducted in a room

with controlled air temperature. About 120 min later, the sample was weighed. A cover

was used in order to prevent the samples from absorbing water or evaporating. The

uncertainly of the density measurements was estimated to be 0.05 %. Mixtures were

prepared by mixing the appropriate volumes of liquids in specially designed ground glass

air-tight ampules and weighed in single pan balance (Ohaus electronic balance) to an

accuracy of 0.0001 g. Preferential evaporation losses of solvent from the mixture were

kept to a minimum as evidenced by repeated measurements of thermo physical properties

over an interval of 23 days, during which time no change in physical properties were

observed. The composition of the mixtures were calculated in mole fraction with atomic

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weights recommended by IUPAC in 2000 [29]. The possible error in mole fraction is

estimated to be around 0.0001. Refractive indices for the sodium D line were measured

using Abbes refractometer (CARL ZEISS, Model A, Germany). Water was circulated into

the instrument from the thermostatically controlled bath. The current temperature of the

measurement prism of the refractometer was monitored using a built-in instrument with an

uncertainty 0.1 K. The refractometer was calibrated by measuring the refractive indices

of triply distilled water and ethanol at 293.15 K. The accuracy in the refractive index

measurements is 0.0001 U. The sample mixtures were directly injected into the prism

assembly of the instrument by means of an air-tight hypodermic syringe. An average of

three to five measurements was taken for a sample mixture. The source of our chemicals

and our measured values at 293.15 K of two physical properties of the pure compounds,

densities and refractive indices, are compared with literature [3034] values in Table 1.

The refractive indices of the binary systems water(1) ? propan-1-ol(2), water(1) ?

ethanol(2) and water(1) ? methanol(2) are compared with literature data in Fig. 1.

3 Results and Discussion

The experimental results of mole fraction, xi, refractive indices, nD, refractive index de-

viations, DnD, at 293.15 K for all binary mixtures are reported in Table 2. The refractiveindex deviations were evaluated for each composition point, using the following equation:

DnD nD Xn

i1xinD;i 1

where nD is the refractive index of the mixture and the corresponding quantity with

subscript i refers to the corresponding pure chemicals. The experimental DnD values werecorrelated using a 5-parameter RedlichKister equation:

DnD x1x2Xm

p0Apx1 x2p 2

where x is the molar fraction, A0, A1, A2, A3 and A4 are the RedlichKister parameters

obtained by least-squares method, and m = 4 is the degree of the polynomial expansion.

The parameters calculated using Eq. 2 are listed in Table 3. On Fig. 2, the refractive index

deviations are shown for the binary mixtures. The physical property values of these so-

lutions can be affected by two factors. The first factor is the concentration units (molar,

molalor mole fraction) of the solute in the mixture. The second factor is the strength of

Table 1 Experimental and literature values [3034] of densities, q, and refractive indices, nD, of the purecompounds at 293.15 K

Compound nD(experimental)

nD(literature)

q (experimental)gcm-3

q (literature)gcm-3

Water, deionized reagent grade 3 1.3330 1.3330 [30] 0.9981 0.9982 [33]

Methanol (Sigma-Aldrich, 99.9 %) 1.3299 1.32941 [31] 0.7912 0.79115 [31]

Ethanol (Carlo Erba, 99.8 %) 1.3618 1.3620 [30] 0.7895 0.78970 [34]

Propan-1-ol (Merck, 99.5 %) 1.3853 1.38512 [32] 0.8036 0.80360 [34]

208 J Solution Chem (2015) 44:206222

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bonds between solvent and solute molecules due to the values of polarity (dipoledipole

interaction and the H-bonds) and the electrical charge of solute molecules [35].

It can be observed from the experimental data in Table 2 and Fig. 2 that, over the whole

composition range for all aqueous solutions of this study at T = 293.15 K, the variation

of DnD is positive and follows this order: DnDCH3OH\DnDCH3CH2OH\DnDCH3CH2CH2OH for these solutions the values of DnD increase with the size of the(R) group. On Fig. 2, a maximum is observed at xM = xmethanol = 0.3961 for the mixture

water ? methanol. Takamuku et al. [37] found, from analysis of radial distribution

functions (RDF) for methanol ? water mixtures, three peaks at xM = 0.4 and 298.15 K

that were analyzed were the result of the intermolecular interactions of methanol chain

clusters and the second-neighbor interactions in the tetrahedral-like structure of water [38].

Positive deviations of the excess values of binary mixtures should be the result of dis-

persion forces and non-specific physical (weak) interactions [39]. Nagasaka et al. [40]

found that the total energy of the binary solution is stabilized by the network structure of

water with the methanol clusters. But, the effect of water molecules on the methyl group of

methanol may depend on whether water molecules are free or associated in the network.

For the mixture ethanol ? water, it is found on Fig. 2 that a maximum occurs at xE =

xEthanol = 0.2972. Matsumoto et al. found that both ethanol chain clusters and water

clusters are formed in ethanolwater mixture at xE = 0.3 and 298.15 from RDF analysis

[41]. For the mixture water ? propan-1-ol, the maximum is found at xp,1 = xpropan-1-

Fig. 1 Comparison between the experimental data and values from literature. Water(1) ? methanol(2):(filled circle) this work at 293.15 K, (circle) Ref. [35] at 292.15 K. Water(1) ? ethanol(2): (filled square)this work at 293.15 K, (square) Ref. [35] at 292.15 K, (cross) Ref. [36] at 293.15 K. Water(1) ? propan-1-ol(2): (filled diamond) this work at 293.15 K, (diamond) Ref. [35]

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Table 2 Experimental refractiveindices and their deviations fromideality at 293.15 K for the in-vestigated binary mixtures

x1 nD DnD x1 nD DnD

Water(1) ? methanol(2)

0.0000 1.3299 0.0000 0.6039 1.3436 0.0118

0.1007 1.3326 0.0023 0.6901 1.3432 0.0111

0.2044 1.3359 0.0054 0.7941 1.3412 0.0088

0.2910 1.3385 0.0076 0.8952 1.3376 0.0049

0.4034 1.3411 0.0099 1.0000 1.3330 0.0000

0.5003 1.3423 0.0108

Water(1) ? ethanol(2)

0.0000 1.3618 0.0000 0.5983 1.3645 0.0199

0.1037 1.3640 0.0052 0.7028 1.3626 0.0210

0.2064 1.3649 0.0090 0.7932 1.3584 0.0194

0.3047 1.3657 0.0127 0.8979 1.3488 0.0128

0.3939 1.3660 0.0156 1.0000 1.3330 0.0000

0.4937 1.3656 0.0180

Water(1) ? propan-1-ol(2)

0.0000 1.3853 0.0000 0.5979 1.3762 0.0221

0.1080 1.3843 0.0046 0.7225 1.3708 0.0233

0.2181 1.3834 0.0095 0.7939 1.3662 0.0224

0.2737 1.3828 0.0118 0.8999 1.3552 0.0169

0.4030 1.3809 0.0167 1.0000 1.3330 0.0000

0.4998 1.3789 0.0197

Methanol(1) ? ethanol(2)

0.0000 1.3618 0.0000 0.6108 1.3447 0.0024

0.1099 1.3591 0.0008 0.7062 1.3413 0.0020

0.1727 1.3576 0.0013 0.8078 1.3373 0.0012

0.3292 1.3535 0.0022 0.9010 1.3338 0.0007

0.4003 1.3514 0.0024 1.0000 1.3299 0.0000

0.5065 1.3481 0.0024

Methanol(1) ? propan-1-ol(2)

0.0000 1.3853 0.0000 0.6007 1.3596 0.0076

0.1177 1.3809 0.0021 0.7023 1.3534 0.0070

0.1798 1.3788 0.0035 0.7721 1.3485 0.0059

0.3147 1.3738 0.0059 0.8971 1.3387 0.0031

0.3760 1.3710 0.0065 1.0000 1.3299 0.0000

0.4801 1.3660 0.0073

Ethanol(1) ? propan-1-ol(2)

0.0000 1.3853 0.0000 0.6134 1.3720 0.0011

0.1077 1.3825 -0.0003 0.6879 1.3701 0.0010

0.2227 1.3803 0.0002 0.7961 1.3672 0.0006

0.2797 1.3792 0.0005 0.8930 1.3646 0.0003

0.3880 1.3771 0.0009 1.0000 1.3618 0.0000

0.5007 1.3747 0.0012

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ol = 0.2775 as seen in Fig. 2. It is found that the mixtures from C1 to C3 show that the

maximum moves to a more water-rich zone (xw = xwater = 0.6039 for methanol to

xw = 0.7225 for propan-1-ol). Thus cluster formation may be expected at these

concentrations.

In this work, the binary mixtures with alcohols show values of DnD lower than thosereported for aqueous mixtures. The variation of DnD in these mixtures is:DnDCH3CH2OH + CH3CH2CH2OH\DnDCH3OH + CH3CH2OH\DnDCH3OH +CH3CH2CH2OH; the mixture that deviates least from ideality is ethanol(1) ? propan-1-ol(2). Our results for this mixture, as a function of concentration at 298.15 K, coincide well

with those reported in the literature [32].

The experimental results of mole fraction, xi, refractive indices, nD, refractive index

deviations, DnD, at 293.15 K for all ternary mixtures are reported in Table 4. The re-fractive index deviations for the ternary mixtures have been fitted by the Cibulka equation:

DnD DnD;bin x1x21 x1 x2B1 B2x1 B3x2 3

DnD;bin x1x2Xm

p0Apx1 x2p x1x3

Xm

q0Aqx1 x3q x2x3

Xm

r0Arx2 x3r 4

where the Ai are binary solution parameters of a RedlichKister type equation for the

constituent binary mixtures, Bi are parameters of the Cibulka equation and xi is molar

fraction of component i at the ternary data composition. The parameters calculated using

Eq. 3 are listed in Table 5. The root-mean-square deviations (r) were computed usingEq. 5, where ncalc is the calculated value of refractive index, nexp is the measured value of

the refractive index, and NDAT is the number of experimental data values:

r PNDAT

i1 nexp ncalc2NDAT

!1=25

Figures 3, 4, 5, and 6 show that the refractive index deviations for all the ternary

mixtures are positive over the whole composition range. The results are consistent with

Table 3 RedlichKister parameters Ai (Eq. 2) and the standard deviations (r, Eq. 5)

A0 A1 A2 A3 A4 r

Water(1) ? methanol(2)

0.04414 0.01977 0.00840 -0.00547 -0.02717 0.00010

Water(1) ? ethanol(2)

0.07266 0.04826 0.04477 0.01016 -0.00877 0.00016

Water(1) ? propan-1-ol(2)

0.07904 0.05310 0.03719 0.05223 0.03536 0.00009

Methanol(1) ? ethanol(2)

0.00998 -0.00036 -0.00199 -0.00053 -0.00259 0.00006

Methanol(1) ? propan-1-ol(2)

0.02971 0.00779 0.00436 0.00122 -0.01539 0.00005

Ethanol(1) ? propan-1-ol(2)

0.00467 0.00151 -0.00615 0.00373 -0.00237 0.00002

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those reported in binary mixtures; aqueous solutions show a greater deviation than the

mixtures composed of the three alcohols: methanol(1) ? ethanol(2) ? propan-1-ol(3). The

maximum refractive index deviation (DnD) for the ternary mixtures in Table 6 variesin the order: methanol ? ethanol ? propan-1-ol \ water ? methanol ? ethanol \ water ?methanol ? propan-1-ol = water ? ethanol ?propan-1-ol. The refractive index de-

viations of the aqueous mixtures are due to hydrogen bond interactions between the water

or methanol molecule, ethanol and propanol molecules.

Reiss et al. [42] considered that the increase of the refractive indices for the mixtures of

solvents is explained as the result of both energetic and structural effects where the en-

hancement of London disperse forces plays an important role. We may expect that these

maxima in the water-rich zone should reflect cluster structures. In the mixtures of solvents

with water, Fontao et al. considered that positive values of the refractive index deviation on

mixing may be due to two opposing factors: (a) the hydrogen-bond interaction between

solute and solvent for each mixture, and (b) the steric hindrance of aliphatic residues [32].

The positive refractive index deviation decrease in the following order for the binary

mixtures: water(1) ? propan-1-ol(2) [ water(1) ? ethanol(2)[ water(1) ? methanol(2) [methanol(1) ? propan-1-ol(2) [ methanol(1) ? ethanol(2) [ ethanol(1) ? propan-1-ol(2).This suggests that the steric hindrance of aliphatic residues affects the increase for alcohol

mixtures where hydrogen bonding is not strong. The isolines of DnD obtained from Cibulkaequation, for the four ternary systems, are plotted at the bottom of Figs. 3, 4, 5, and 6.

The following equations were used for quantitative determination of refractive indices

of ternary mixtures:

Fig. 2 Curves of refractive index deviations at 293.15 K for the systems: (filled circle) wa-ter(1) ? methanol(2), (filled square) water(1) ? ethanol(2), (filled diamond) water(1) ? propan-1-ol(2),(circle) methanol(1) ? ethanol(2), (square) methanol(1) ? propan-1-ol(2), and (diamond) ethanol(1) ?propan-1-ol(2). The experimental data were fitted with RedlichKister type polynomials (solid line)

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Table 4 Experimental refractive indices and their deviations from ideality at 293.15 K for the ternarymixtures

x1 x2 nD DnD x1 x2 nD DnD

Water(1) ? methanol(2) ? ethanol(3)

0.1047 0.7951 1.3363 0.0029 0.2865 0.3089 1.3548 0.0111

0.1076 0.6916 1.3407 0.0041 0.2865 0.2154 1.3581 0.0114

0.0956 0.6055 1.3442 0.0045 0.2854 0.1088 1.3613 0.0112

0.1107 0.5061 1.3479 0.0054 0.3941 0.4995 1.3453 0.0108

0.0997 0.4133 1.3512 0.0055 0.4357 0.3762 1.3504 0.0132

0.0906 0.3139 1.3542 0.0050 0.3976 0.3060 1.3540 0.0134

0.1112 0.2032 1.3576 0.0055 0.3745 0.2117 1.3580 0.0137

0.1060 0.0784 1.3608 0.0046 0.4103 0.1096 1.3613 0.0148

0.1873 0.7079 1.3399 0.0061 0.5118 0.3821 1.3479 0.0130

0.1896 0.6047 1.3444 0.0074 0.5146 0.2914 1.3526 0.0149

0.1659 0.5231 1.3478 0.0075 0.4912 0.1991 1.3573 0.0160

0.1847 0.4154 1.3517 0.0085 0.4746 0.1345 1.3601 0.0163

0.2151 0.3006 1.3558 0.0098 0.5879 0.2982 1.3497 0.0143

0.2217 0.2004 1.3590 0.0100 0.5995 0.2075 1.3543 0.0164

0.2302 0.1013 1.3618 0.0099 0.6175 0.0963 1.3594 0.0185

0.3283 0.5718 1.3431 0.0090 0.7211 0.1842 1.3498 0.0146

0.3045 0.4992 1.3470 0.0099 0.7007 0.1020 1.3541 0.0157

0.3069 0.3988 1.3513 0.0111 0.7960 0.0961 1.3506 0.0148

Water(1) ? methanol(2) ? propan-1-ol(3)

0.0863 0.8045 1.3417 0.0055 0.3021 0.2980 1.3689 0.0159

0.0963 0.6945 1.3502 0.0084 0.3168 0.1699 1.3750 0.0157

0.1015 0.5736 1.3584 0.0102 0.2943 0.0959 1.3784 0.0138

0.0919 0.5028 1.3628 0.0102 0.4025 0.4686 1.3529 0.0146

0.0988 0.4011 1.3681 0.0102 0.3713 0.4096 1.3586 0.0154

0.0911 0.2987 1.3731 0.0091 0.3712 0.3088 1.3659 0.0171

0.0990 0.1948 1.3772 0.0079 0.3851 0.2037 1.3715 0.0176

0.0945 0.0990 1.3807 0.0058 0.3860 0.0919 1.3769 0.0169

0.1844 0.6978 1.3459 0.0089 0.5135 0.3737 1.3539 0.0162

0.1789 0.6108 1.3531 0.0110 0.4737 0.3105 1.3616 0.0183

0.1505 0.4964 1.3617 0.0118 0.4886 0.2065 1.3680 0.0197

0.2129 0.3967 1.3658 0.0136 0.5071 0.0956 1.3738 0.0203

0.1915 0.3185 1.3705 0.0129 0.5726 0.3211 1.3547 0.0171

0.1524 0.2349 1.3751 0.0108 0.5769 0.2244 1.3628 0.0201

0.1803 0.1467 1.3782 0.0105 0.5939 0.0980 1.3706 0.0218

0.2686 0.6308 1.3474 0.0111 0.6953 0.1982 1.3564 0.0184

0.2953 0.4885 1.3571 0.0143 0.7502 0.0774 1.3630 0.0212

0.2787 0.4089 1.3630 0.0149 0.7724 0.1326 1.3555 0.0179

Water(1) ? ethanol(2) ? propan-1-ol(3)

0.0843 0.8128 1.3663 0.0045 0.3232 0.2841 1.3758 0.0141

0.1028 0.6966 1.3692 0.0056 0.2865 0.1968 1.3783 0.0126

0.0962 0.6005 1.3718 0.0056 0.2760 0.1176 1.3801 0.0120

0.1086 0.4907 1.3744 0.0063 0.4219 0.4789 1.3681 0.0161

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Table 5 Parameters, Bi, of the Cibulka equation for the ternary mixtures together with the correspondingstandard deviations, r

System B1 B2 B3 r

Water(1) ? methanol(2) ? ethanol(3) -0.02015 -0.11273 -0.01606 0.00050

Water(1) ? methanol(2) ? propan-1-ol(3) -0.02098 -0.00227 0.01776 0.00025

Water(1) ? ethanol(2) ? propan-1-ol(3) 0.02870 -0.35314 -0.02009 0.00035

Methanol(1) ? ethanol(2) ? propan-1-ol(3) 0.01070 0.01264 0.00850 0.00032

Table 4 continued

x1 x2 nD DnD x1 x2 nD DnD

0.0920 0.4001 1.3766 0.0055 0.3748 0.4140 1.3712 0.0152

0.1044 0.2894 1.3787 0.0057 0.3941 0.3193 1.3732 0.0160

0.1149 0.1966 1.3806 0.0059 0.3910 0.2006 1.3762 0.0161

0.0814 0.1001 1.3827 0.0040 0.4006 0.1017 1.3782 0.0162

0.1890 0.6961 1.3679 0.0088 0.5059 0.3967 1.3679 0.0184

0.1866 0.6005 1.3704 0.0090 0.4828 0.2990 1.3713 0.0183

0.1846 0.4881 1.3733 0.0091 0.4783 0.2045 1.3739 0.0184

0.1893 0.3977 1.3754 0.0093 0.4958 0.1028 1.3759 0.0189

0.1892 0.2879 1.3777 0.0091 0.5740 0.3227 1.3672 0.0195

0.1791 0.1900 1.3798 0.0083 0.6029 0.1978 1.3698 0.0207

0.1875 0.1176 1.3812 0.0085 0.5694 0.1140 1.3735 0.0207

0.2835 0.5994 1.3684 0.0120 0.6878 0.2121 1.3654 0.0211

0.2642 0.4958 1.3716 0.0118 0.6975 0.1095 1.3680 0.0218

0.2915 0.3812 1.3741 0.0130 0.8089 0.0944 1.3610 0.0202

Methanol(1) ? ethanol(2) ? propan1-ol(3)

0.0947 0.7928 1.3634 0.0020 0.2811 0.2982 1.3679 0.0052

0.0822 0.7133 1.3662 0.0022 0.2681 0.2290 1.3702 0.0051

0.1009 0.5978 1.3685 0.0028 0.3126 0.1124 1.3712 0.0059

0.0738 0.5123 1.3720 0.0028 0.3948 0.4945 1.3556 0.0038

0.0988 0.3997 1.3736 0.0032 0.4061 0.3906 1.3584 0.0048

0.0900 0.3069 1.3761 0.0030 0.4027 0.2873 1.3618 0.0056

0.0948 0.2020 1.3780 0.0027 0.4085 0.1935 1.3641 0.0060

0.0885 0.1005 1.3803 0.0023 0.4061 0.1189 1.3664 0.0064

0.2027 0.6831 1.3608 0.0028 0.4794 0.4202 1.3535 0.0046

0.2020 0.5960 1.3634 0.0033 0.5060 0.3082 1.3556 0.0056

0.1832 0.5127 1.3667 0.0036 0.5185 0.1997 1.3583 0.0064

0.2141 0.3850 1.3688 0.0044 0.5048 0.0997 1.3622 0.0072

0.1881 0.3063 1.3718 0.0041 0.5823 0.2947 1.3509 0.0048

0.1891 0.2083 1.3742 0.0043 0.6050 0.1999 1.3532 0.0061

0.1766 0.1143 1.3767 0.0039 0.5941 0.1090 1.3568 0.0070

0.2862 0.5990 1.3590 0.0036 0.7066 0.1946 1.3459 0.0043

0.3023 0.5087 1.3607 0.0041 0.6997 0.0981 1.3505 0.0063

0.3015 0.4011 1.3639 0.0047 0.7724 0.1205 1.3440 0.0043

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LorentzLorenz (LL):

n2 1n2 2

Xk

i1

n2i 1n2i 2

/i 6

GladstoneDale (GD):

n 1 Xk

i1ni 1/i 7

Fig. 3 Refractive index deviations and isolines at 293.15 K for the ternary systemwater(1) ? methanol(2) ? ethanol(3)

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Eykman (Eyk):

n2 1n2 0:4

Xk

i1

n2i 1n2i 0:4

/i 8

Fig. 4 Refractive index deviations and isolines at 293.15 K for the ternary system water(1) ?methanol(2) ? propan-1-ol(3)

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Newton (Nw):

n2 1 Xk

i1n2i 1/i 9

Fig. 5 Refractive index deviations and isolines to 293.15 K for the ternary system water(1) ?ethanol(2) ? propan-1-ol(3)

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Oster (Os):

n2 12n2 1n2

Xk

i1

n2i 12n2i 1n2i

/i 10

Here n is the refractive index of the mixtures, ni is the refractive index of the corresponding

pure components i, k is the number of the mixture components, and /i is the volumefraction of component i:

Fig. 6 Refractive index deviations at isolines to 293.15 K for the ternary system methanol(1) ? etha-nol(2) ? propan-1-ol(3)

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/i xiViPki1 xiVi

11

where xi is the mole fraction of the component i, and Vi is the molar volume of the

component i. In order to estimate the ability of the mixing rule Eqs. 610 to predict

refractive indices, the following quantities were analyzed: average absolute deviations

(AAD) and maximal deviation (M Dev),

AAD 100NDAT

XM

i1

npred nexpnexp

12

MDev 100: max npred nexpnexp

13

where npred is the predicted value of the refractive index and nexp is the measured value.

The AAD and M Dev quantities can be also viewed as mean and maximal relative errors.

The values of AADand MDev are shown in Table 7. Average absolute deviations (AAD

values) for all mixtures do not exceed 0.50 %. From the analysis of AAD of the ex-

perimental refractive indices using the L-L, G-D, Eyk, Nw or Os equations, the following

sequence was found: water(1) ? methanol(2) ? ethanol(3) [ water(1) ? methanol(2) ?propan-1-ol(3) * water(1) ? ethanol(2) ? propan-1-ol(3) [ methanol(1) ? ethanol(2) ?propan1-ol(3). This behavior suggests that the hydrogen bonding interaction effect de-

creases for alcohol mixtures. The maximal deviation M Dev in all the mixtures is lower

than 0.9 %. The predictions obtained using these mixing rules are very similar. The values

predicted by the Newton mixing rule display better agreement with the experimental values

Table 6 The maximum refractive index deviations (DnD) for the ternary mixtures at 293.15 K

System DnDmax x1 x2 x3

Water(1) ? methanol(2) ? ethanol(3) 0.0185 0.6175 0.0963 0.2862

Water(1) ? methanol(2) ? propan-1-ol(3) 0.0218 0.5939 0.0980 0.3081

Water(1) ? ethanol(2) ? propan-1-ol(3) 0.0218 0.6975 0.1095 0.1930

Methanol(1) ? ethanol(2) ? propan-1-ol(3) 0.0072 0.5048 0.0997 0.3955

Table 7 Average absolute deviations (AAD) and maximal deviation (M Dev) of the experimental re-fractive indices from the estimated results using the LorentzLorenz (LL), GladstoneDale(GD), Eykman(Eyk), Newton (Nw) and Oster (Os) equations

System LL GD Eyk Nw Os

Water(1) ? methanol(2) ? ethanol(3) AAD 0.495 0.490 0.492 0.485 0.488

M Dev 0.861 0.857 0.858 0.852 0.855

Water(1) ? methanol(2) ? propan-1-ol(3) AAD 0.315 0.300 0.305 0.283 0.292

M Dev 0.730 0.716 0.721 0.701 0.709

Water(1) ? ethanol(2) ? propan-1-ol(3) AAD 0.306 0.299 0.302 0.292 0.296

M Dev 0.686 0.676 0.680 0.665 0.670

Methanol(1) ? ethanol(2) ? propan-1-ol(3) AAD 0.013 0.017 0.016 0.024 0.020

M Dev 0.036 0.050 0.045 0.065 0.057

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of the refractive indices for aqueous mixtures, whereas in the ternary mixture of alcohols

the best prediction is with LorentzLorenz mixing rule.

4 Conclusions

We reported measurements of refractive indices at 293.15 K for six binary mixtures

(water ? methanol, water ? ethanol, water ? propan-1-ol, methanol ? ethanol, metha-

nol ? propan-1-ol, ethanol ? propan-1-ol) and four ternary mixtures (water ?

methanol ? ethanol, water ? methanol ? propan-1-ol, water ? ethanol ? propan-1-ol,

methanol ? ethanol ? propan-1-ol); the refractive index deviations calculated from the

experimental data of refractive indices are appropriately represented with the RedlichKister

equation for binary mixtures and with the Cibulka equation in ternary mixtures. The de-

viations of refractive indices are higher in aqueous ? alcohol mixtures compared with the

alcohol ? alcohol mixtures.

Mixing rules including the LorentzLorenz, GladstoneDale, Eykman, Newton and

Oster formulas were used for predicting the refractive indices of ternary mixtures. We have

demonstrated that the refractive indices provided by all the mixing rules reproduce the

measured values with a maximal relative error of 0.861 %.

References

1. Sechenyh, V.V., Legros, J., Shevtsova, V.: Experimental and predicted refractive index properties internary mixtures of associated liquids. J. Chem. Thermodyn. 43, 17001707 (2011)

2. Nakata, M., Sakurai, M.: Refractive index and excess volume for binary liquid mixtures. Part 1.Analyses of new and old data for binary mixtures. J. Chem. Soc. Faraday Trans. 183, 24492457 (1987)

3. Tripathi, R.C.: Relation between index of refraction and surface tension. J. Indian Chem. Soc. 18,411427 (1941)

4. Zhelezny, V., Sechenyh, V., Nikulina, A.: A new scaling principlesquantitative structure propertyrelationship model (SP-QSPR) for predicting the physicochemical properties of substances at thesaturation line. J. Chem. Eng. Data 59, 485493 (2014)

5. Heller, W.: Remarks on refractive index mixture rules. J. Phys. Chem. 69, 11231129 (1965)6. Teodorescu, M., Secuianu, C.: Refractive indices measurement and correlation for selected binary

systems of various polarities at 25 & #xB0;C. J. Solution Chem. 42, 19121934 (2013)7. Vuksanovic, J.M., Bajic, D.M., Ivanis, G.R., Zivkovic, E.M., Radovic, I.R., Serbanovic, S.P., Ki-

jevcanin, M.L.: Prediction of excess molar volumes of selected binary mixtures from refractive indexdata. J. Serb. Chem. Soc. 79, 707718 (2014)

8. Radovic, I.R., Kijevcanin, M.L., Gabrijel, M.Z., Serbanovic, S.P., Djordjevic, B.D.: Prediction of excessmolar volumes of binary mixtures of organic compounds from refractive indices. Chem. Pap. 62,302312 (2008)

9. Perez-Navarro, M., Pera, G., Haro, M., Gascon, I., Lafuente, C.: Refractive indices of the ternarymixtures butanol ? n-hexane ? 1-chlorobutane. J. Solution Chem. 37, 14991510 (2008)

10. Giner, B., Villares, A., Lopez, M.C., Royo, F.M., Lafuente, C.: Refractive indices and molar refractionsfor isomeric chlorobutanes with isomeric butanols. Phys. Chem. Liq. 43, 1323 (2005)

11. Baluja, S., Pandaya, N., Kachhadia, N., Solanki, A.: Theoretical evaluation of refractive index in binaryliquid mixtures. E-J. Chem. 2, 157160 (2005)

12. Parveen, S., Singh, S., Shukla, D., Singh, K.P., Gupta, M., Shukla, J.P.: Molecular interaction study ofbinary mixtures of THF with methanol and o-cresolan optical and ultrasonic study. Act. Phys.Polonica A 116, 10111017 (2009)

13. Sharma, S., Patel, P.B., Patel, R.S., Vora, J.J.: Density and comparative refractive index study on mixingproperties of binary liquid mixtures of eucalyptol with hydrocarbons at 303.15, 308.15 and 313.15 K.E-J. Chem. 4, 343349 (2007)

220 J Solution Chem (2015) 44:206222

123

14. Gayol, A., Iglesias, M., Goenaga, J.M., Concha, R.G., Resa, J.M.: Temperature influence on solutionproperties of ethanol ? n-alkane mixtures. J. Mol. Liq. 135, 105114 (2007)

15. Tourino, A., Hervello, M., Moreno, V., Marino, G., Iglesias, M.: Changes of refractive indices in ternarymixtures containing chlorobenzene ? n-hexane ? (n-heptane or n-octane) at 298.15 K. J. Serb. Chem.Soc. 69, 461475 (2004)

16. Sechenyh, V., Legros, J.C., Shevtsova, V.: Measurements of optical properties in binary and ternarymixtures containing cyclohexane, toluene, and methanol. J. Chem. Eng. Data 57, 10361043 (2012)

17. Sechenyh, V.V., Legros, J.C., Shevtsova, V.: Optical properties of binary and ternary liquid mixturescontaining tetralin, isobutylbenzene and dodecane. J. Chem. Thermodyn. 62, 6468 (2013)

18. Sen, D., Kin, M.G.: Excess molar volumes and molar enthalpies in the binary mixtures of x1CH3CHClCH2Cl ? x2CH3(CH2)n1 OH (n = 1 to 4) at T = 298.15 K. Korean J. Chem. Eng. 26, 806811(2009)

19. Kogan, A., Garti, N.: Microemulsions as transdermal drug delivery vehicles. Adv. Colloid Interface Sci.123126, 369385 (2006)

20. Sanz, L.F., Gonzalez, J.A., De La Fuente, I.G., Cobos, J.C.: Thermodynamics of mixtures with stronglynegative deviations from Raoults law. XI. Densities, viscosities and refractives indices at(293.15303.15) K for cyclohexylamine ? 1-propanol, or ?1-butanol systems. J. Mol. Liq. 172, 2633(2012)

21. Redlich, O., Kister, A.T.: Algebraic representation of thermodynamic properties and the classification ofsolutions. Ind. Eng. Chem. 40, 345348 (1948)

22. Cibulka, I.: Estimation of excess volume and density of ternary liquid mixtures of non-electrolytes frombinary data. Collect. Czech. Chem. Commun. 47, 14141419 (1982)

23. Lorentz, H.A.: Ueber die Beziehungzwischen der Fortpflanzungsgeschwindigkeit des Lichtes und derKorperdichte. Wied. Ann. 9, 641665 (1880)

24. Lorenz, L.V.: Ueber die Refraktion Konstante. Wied. Ann. 11, 7075 (1880)25. Gladstone, J.F., Dale, T.P.: Researches on the refraction, dispersion, and sensitiveness of liquids. Philos.

Trans. R. Soc. Lond. 153, 317343 (1863)26. Eykman, J.F.: Recherchesrefractometriquesdefeu. Nat. Verh. VandeHoll. Maatsch. DerWet. TeHaarlem

8, 25255 (1919)27. Kurtz, S.S., Ward, A.L.: The refractive intercept and the specific refraction equation of Newton.

I. Development of the refractivity intercept and comparison with specific-refraction equations.J. Franklin Inst. 222, 563592 (1936)

28. Oster, G.: The scattering of light and its applications to chemistry. Chem. Rev. 43, 319365 (1948)29. Laeter, J.R., Bohlke, J.K., De Bie`vre, P., Hidaka, H., Peiser, H.S.: Atomic weights of the elements:

reviews 2000 (IUPAC Technical Report). Pure Appl. Chem. 75, 683800 (2003)30. Zaoui-Djelloul-Daouadji, M., Negadi, A., Mokbel, I., Negadi, L.: (Vaporliquid) equilibria and excess

Gibbs free energy functions of (ethanol ? glycerol), or (water ? glycerol) binary mixtures at severaltemperatures. J. Chem. Thermodyn. 69, 165171 (2014)

31. Kurnia, K.A., Taib, M.M., Mutalib, M.I.A., Murugesan, A.: Densities, refractive indices and excessmolar volumes for binary mixtures of protic ionic liquids with methanol at T = 293.15 to 313.15 K.J. Mol. Liq. 159, 211219 (2011)

32. Fontao, M.J., Iglesias, M.: Effect of temperature on the refractive index of aliphatic hydroxilicmixtures(C2C3). Int. J. Thermophys. 23, 513527 (2002)

33. Li, X., Xu, G., Wang, Y., Hu, Y.: Density, viscosity, and excess properties for binary mixture ofdiethylene glycol monoethyl ether ? water from 293.15 to 333.15 K at atmospheric pressure. Chin.J. Chem. Eng. 17, 10101013 (2009)

34. Almasi, M., Mousavi, M.: Excess molar volumes of binary mixtures of aliphatic alcohols (C1C5) withnitromethane over the temperature range 293.15 to 308.15 K: application of the ERAS model and cubicEOS. J. Mol. Liq. 163, 4652 (2011)

35. Koohya, F., Kiani, F., Sharifi, S., Sharifirad, M., Rahmanpour, S.H.: Study on the change of refractiveindex on mixing, excess molar volume and viscosity deviation for aqueous solution of methanol,ethanol, ethylene glycol, 1-propanol and 1,2,3-propantriol at T = 292.15 K and atmospheric pressure.Res. J. Appl. Scien. Engin. Technol. 4, 30953101 (2012)

36. Jimenez-Rioboo, R.J., Philipp, M., Ramos, M.A., Kruger, J.K.: Concentration and temperature de-pendence of the refractive index of ethanolwater mixtures: influence of intermolecular interactions.Eur. Phys. J. E 30, 1926 (2009)

37. Takamuku, T., Saisho, K., Nozawa, S., Yamaguchi, T.: X-ray diffraction studies on methanolwater,ethanolwater, and 2-propanolwater mixtures at low temperatures. J. Mol. Liq. 119, 133146 (2005)

J Solution Chem (2015) 44:206222 221

123

38. Takamuku, T., Yamaguchi, T., Asato, M., Matsumoto, M., Nishi, N.: Structure of clusters in methanolwater binary solutions studied by mass spectrometry and X-ray diffraction. Z. Naturforsch. 55a,513525 (2000)

39. Pandey, P.K., Pandey, V.K., Awasthi, A., Nain, A.K., Awasthi, A.: Study of intermolecular interactionsin binary mixtures of 2-(dimethylamino) ethanol withmethanol and ethanol at various temperatures.Thermochim. Acta 586, 5865 (2014)

40. Nagasaka, M., Mochizuki, K., Leloup, V., Kosugi, N.: Local structures of methanolwater binarysolutions studied by soft X-ray absorption spectroscopy. Phys. Chem. B118, 43884396 (2014)

41. Matsumoto, M., Nishi, N., Furusawa, T., Saita, M., Takamuku, T., Yamagami, M.: Structure of clustersin ethanolwater binary solutions studied by mass spectrometry and X-ray diffraction. Bull. Chem. Soc.Jpn 68, 17751783 (1995)

42. Reis, J.C.R., Lampreia, I.M.S., Santos, A.F.S., Moita, M.L.C.J., Douheret, G.: Refractive index of liquidmixtures: theory and experiment. ChemPhysChem 11, 37223733 (2010)

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Experimental Study and Modeling of the Refractive Indices in Binary and Ternary Mixtures of Water with Methanol, Ethanol and Propan-1-ol at 293.15 KAbstractIntroductionExperimentalResults and DiscussionConclusionsReferences