Journal of Molecular Liquids 147 (2009) 191–197

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Journal of Molecular Liquids

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A study of dielectric properties and refractive indices of aniline+benzene, +toluene,+o-xylene, and +p-xylene at 298.15 K

Suman Lata ⁎, K.C. Singh, Suman AhlawatChemistry Department, Maharshi Dayanand University, Rohtak-124001, India

⁎ Corresponding author. Tel.: +91 9416259536 (mobE-mail address: jakhar.suman@rediffmail.com (S. La

0167-7322/$ – see front matter © 2009 Elsevier B.V. Adoi:10.1016/j.molliq.2009.04.002

a b s t r a c t

a r t i c l e i n f o

Article history:Received 4 December 2008Received in revised form 31 March 2009Accepted 2 April 2009Available online 16 April 2009

Keywords:Dielectric constantRefractive indexMolar polarizationApparent dipole moment

The present study describes interactions between aniline+benzene, +toluene, +o-xylene, and +p-xylenemixtures at 298.15 K. The experimental values of refractive indices (nD) and dielectric constants (∈) of pureaniline, benzene, toluene, o-xylene and p-xylene and their binary mixtures over the whole compositionrange at 298.15 K have been obtained. Using these experimental data, the values of deviations in dielectricproperties (∈E), refractive indices (nD

2E), molar polarization (PE) of aromatic hydrocarbons in aniline have also

been calculated and apparent molar polarization (PA), equilibrium constant (K), apparent dipole moment(µapp) and Kirkwood correlation parameter (g) for these mixtures have been evaluated further. The resultsindicate specific interactions between aniline and aromatic hydrocarbons, although more than onecompeting factors are responsible for these observed values of excess properties. The internal consistencyof these functions have been tested using Redlich-Kister type equation.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Studies on thermodynamic and transport properties of binaryliquid mixtures provide information on the nature of interactionsarising in the binary mixtures [1,2]. Such studies have tremendousacademic and industrial importance and are required in solvingmany engineering problems such as design calculation, heat transfer,mass transfer, fluid flow and energy transformations and so forth[3]. Aniline is predominantly used as [4,5] parent substance in themanufacture of several chemical products and intermediates. Inthe present study, the experimental values of refractive indices(nD

2) and dielectric constants (∈) of pure aniline, benzene, toluene,o-xylene, p-xylene and their binary mixtures over the whole com-position range have been presented. Excess molar polarization PE,excess molar refraction nD

2Eand excess dielectric constant (∈E) have

also been calculated from experimental data. Apparent molarpolarization (PA), apparent dipole moment (μapp) and Kirkwoodcorrelation parameter (g) were also calculated further for under-standing of interactions more precisely. Aniline molecules areknown to be associated in the pure state through hydrogen bonding.IR [6,7] and NMR [8,9] spectroscopic studies have proved that onlyone of the hydrogens in the −NH2 group forms a strong hydrogenbond, and that probably weak specific interactions of the secondhydrogen in −NH2 are present with the π-electrons of adjacent

ile).ta).

ll rights reserved.

aniline molecules [10]. While, Kreglewski and Wilhoit [11] haveinterpreted the thermodynamic data of aniline+benzene mixturesin terms of electron donor-acceptor interactions. These molecularinteractions between aniline and benzene were also studied byKharat et al [3] and discussed the deviations in thermodynamicproperties due to interstitial accommodation of benzene moleculesinto aggregates of aniline. So, in order to obtain more informationregarding the nature of interactions in aniline+aromatic hydro-carbon mixtures, the dielectric properties have been measured.Many investigators have obtained a lot of information regarding themolecular interactions in the components of mixtures by measuringtheir dielectric properties [12–22].

2. Experimental

Aniline, benzene, toluene, o-xylene and p-xylene (Aldrich, ARgrade) were purified by standard methods [23,24]. The purity offinally purified samples of each compound was checked by densitymeasurements at 298.15 K±0.01 K. The experimental values agreedwith the corresponding literature values [25–28] within ±5×10−5 gcm−3. The densities of the mixtures (ρ12) were evaluated from theexcess volume data [29] using the relation.

VE cm3mol−1� �

= x1M11ρ12

− 1ρ1

� �+ x2M2

1ρ12

− 1ρ2

� �ð1Þ

where x andM aremole fraction andmolecularmass and suffixes 12,1and 2 represent mixture, component 1 and component 2 respectively.

Table 1Experimental and Literature values of densities (ρ), permittivities (∈) and refractive indices (nD) of purified compounds at 298.15±0.01 K.

Compound Density (ρ)in g cm−3 ∈ nD

Experimental value Literature value Experimental value Literature value Experimental value Literature value

Aniline 1.01749 1.0174925 6.774 6.77425 1.5840 1.583031

Benzene 0.87373 0.8737226 2.274 2.27326 1.4980 1.498031

Toluene 0.86223 0.8622427 2.3760 2.376026 1.4940 1.494031

o-xylene 0.87581 0.8758328 2.5700 2.570530 1.5020 1.502831

p-xylene 0.85671 0.8567328 2.3520 2.352530 1.4930 1.493231

192 S. Lata et al. / Journal of Molecular Liquids 147 (2009) 191–197

Dielectric constants of the aniline (1) +aromatic hydrocarbons (2)mixtures at 298.15 K were determined from capacity measurementsusing a dipolemeter (type RL 09 Toshniwal, Scientific Instruments Co.,Indore). The sampleswere placed in a cell consistingof two coaxial brass

Table 2Values of dielectric constants (∈), excess dielectric constants (∈E), square of refractive indiceaniline (1)+aromatic hydrocarbon (2) mixtures at 298.15 K.

x1 ϕ1 ∈Aniline (1)+Benzene (2)0.0000 0.0000 2.27400.0652 0.0666 2.45080.1306 0.1333 2.69850.1963 0.2000 2.97060.3281 0.3333 3.54380.4608 0.4666 4.15620.5944 0.6000 4.79150.7287 0.7333 5.43880.8639 0.8666 6.09820.9318 0.9333 6.43131.0000 1.0000 6.7740

Aniline (1)+Toluene (2).0000 0.000 2.3760.0770 0.0666 2.5309.1523 0.1333 2.7613.2259 0.2000 2.9976.3686 0.3333 3.5277.5053 0.4666 4.0804.6365 0.6000 4.6708.7625 0.7333 5.3009.8836 0.8686 6.0179.9423 0.9333 6.37541.0000 0.000 6.7740

Aniline (1)+o-xylene (2)0.0000 0.0000 2.57050.0864 0.0666 2.77700.1693 0.1333 3.01240.2487 0.2000 3.26030.3384 0.3333 3.77320.5368 0.4666 4.30190.6652 0.6000 4.85080.7846 0.7333 5.42590.8959 0.8666 6.05080.9488 0.9333 6.38671.0000 0.0000 6.7740

Aniline (1)+p-xylene (2)0.0000 0.0000 2.35250.0882 0.0666 2.51180.1742 0.1333 2.73520.2529 0.2000 2.99130.4037 0.3333 3.508390.5423 0.4666 4.07020.6701 0.6000 4.67150.7883 0.7333 5.28910.8990 0.8666 6.20890.9499 0.9333 6.38381.0000 1.0000 6.7740

cylinders. The cell was immersed in awater bath at 298.15±0.01 K andwas calibrated with several pure liquids of known dielectric constant.The refractive index was measured with the help of an Abbe'srefractometer at 298.15±0.01K. The experimentally observeddielectric

s (nD2) and square of excess refractive indices (nD

2E) over the whole composition range for

∈E nD2 nD

2E×103

– 2.2440 –

−0.1209 2.2591 −2.71−0.1754 2.2741 −25.42−0.2033 2.2892 −7.75−0.2300 2.3251 −8.22−0.2175 2.3634 −4.31−0.1825 2.4023 −0.75−0.1350 2.4410 +2.70−0.0755 2.4775 +3.81−0.0425 2.4937 +2.38– 2.5090 –

– 2.2320 –

−0.1287 2.2434 −7.11−0.1923 2.2579 −11.02−0.2500 2.2734 −14.21−0.3075 2.3074 −17.08−0.3423 2.3439 −17.33−0.3400 2.3832 −15.04−0.2975 2.4236 −11.60−0.1681 2.4656 −6.51−0.1045 2.4874 −3.22– 2.5090 –

– 2.2591 –

−0.0730 2.2675 −8.20−0.1180 2.2813 −11.00−0.1505 2.2972 −11.81−0.1980 2.3303 −12.00−0.2297 2.3645 −11.23−0.2416 2.3998 −9.21−0.2269 2.4358 −6.62−0.1624 2.4724 −3.31−0.1069 2.4906 −1.81– 2.5090 –

– 2.2290 –

−0.1347 2.2411 −6.60−0.2063 2.2577 −8.72−0.2450 2.2747 −10.31−0.3175 2.3099 −12.40−0.3451 2.3465 −13.22−0.3337 2.3841 −12.95−0.3055 2.4233 −11.12−0.1752 2.4636 −8.05−0.0952 2.4850 −5.42– 2.5090 –

Table 3Adjustable parameters a0, a1, a2, a3 and standard deviation σ(∈E) of excess permittivities or σ(nD

E2) square of excess refractive indices for aniline (1)+aromatic hydrocarbon (2)

mixtures at 298.15 K.

System a0 a1 a2 a3

Aniline (1)+Benzene (2) ∈E −0.7947 0.3580 −0.6366 0.5060 σ(∈E)=0.0677nD2E −14.9760 65.8812 13.7763 −23.0250 σ(nD

2E)=1.1251

Aniline (1)+Toluene (2) ∈E −1.2927 −0.2978 −0.7094 0.3817 σ(∈E)=0.0471nD2E −68.1996 −9.7629 −15.6310 17.4813 σ(nD

2E)=1.9175

Aniline (1)+o-Xylene (2) ∈E −0.8514 −0.3050 −0.8130 −0.4698 σ(∈E)=0.0652nD2E −43.7279 15.1401 −37.4792 35.2105 σ(nD

2E)=1.2519

Aniline (1)+p-Xylene (2) ∈E −1.3434 −0.4990 −0.6887 0.4819 σ(∈E)=0.0881nD2E −47.7365 −4.5998 −58.3518 −11.2812 σ(nD

2E)=1.6490

193S. Lata et al. / Journal of Molecular Liquids 147 (2009) 191–197

constants, refractive indices and densities of pure components agreewell with the corresponding literature values [25,26,30,31] and arecompared in Table 1.

3. Results and discussion

The experimental values of dielectric permittivities (∈) and squareof refractive indices (nD

2) for all the binary mixtures at 298.15 K overthe whole composition range are summarized in Table 2 along withtheir excess values which were calculated using the followingequations:

aE = a12 − /1a1 − /2a2 ð2Þ

n2E

D = n212 − /1n

2D1 − /2n

2D2 ð3Þ

where ϕ, ∈ and nD are volume fraction, permittivity and refractiveindex respectively. The subscripts 1, 2 and 12 correspond to thecomponent 1(aniline), the component 2 (aromatic hydrocarbon) and12 (solution) respectively. Frank and Ives [32] have shown thatcomparison on a volume fraction basis largely compensates for the“Dipole-dilution” effect. These experimental results for all the systems

Fig. 1. Excess dielectric constants of mixing of aniline (1)+(o) benzene (2); +(△)toluene (2); +(□) o-xylene (2) and +(●) p-xylene (2) at 298.15 K.

were fitted by the method of least squares with all points weightedequally to the Redlich-Kister polynomial equation [33] as:

YE = /1 1− /1ð Þ a0 + a1 2/1 − 1ð Þ + a2 2/1−1ð Þ2 + a3 2/1−1ð Þ3h

ð4Þ

where YE is the excess property (say ∈E or nD2E

and a0,a1,a2 and a3 areadjustable parameters which are given together with standarddeviations σ(YE) in Table 3.

Excess permittivity (∈E) and refractive index (nD2E) as a function of

volume fraction (φ1) for all the systems are recorded showngraphically in Figs. 1 and 2 respectively. ∈E as well as nD

2Evalues for

all the systems are negative except nD2E

values for aniline+benzenesystem. For this system, nD

2Evalues are negative for benzene rich region

(up to 0.6 mole fraction) whereas these are positive for aniline richregion. The order of variation for ∈E at equimole fraction isbenzeneNo-xyleneN toluene≈p-xylene. The minima for benzene,toluene, p-xylene and o-xylene systems are at 0.3, 0.55, 0.55 and0.75 mole fraction of aniline respectively.

The sequence of variation of nD2E

values for equimole fraction isbenzeneNo-xyleneNp-xyleneN toluene. Generally, from earlier ther-modynamical studies of HE, VE and GE [29] of these binaries, it hasbeen observed that:

1. There is stretching or breaking of hydrogen network of anilinemolecules when aromatic hydrocarbons are added to it.

2. There are weak electron donor acceptor type interactions betweenaniline and aromatic hydrocarbons.

3. The orientational order of aromatic hydrocarbons is also disruptedby the addition of aniline.

Fig. 2. Square of excess refractive indices of mixing of aniline (1)+(o) benzene (2);+(△) toluene (2); +(□) o-xylene (2) and +(●) p-xylene (2) at 298.15 K.

Table 4Values of molar polarization (P), excess molar polarization (PE), molar volume (Vm) apparent dipole moment (μapp), apparentmolar polarization (PA), concentration (C), equilibriumconstants (K) and functions f(∈) at different compositions of aniline (1)+aromatic hydrocarbon (2) at 298.15 K.

x1 ϕ1 P (cm3mol−1) PE (cm3mol−1) Vm (cm3mol−1) μapp PA (cm3mol−1) C mol m3 K f(∈)

Aniline (1)+Benzene (2)0.0000 0.0000 26.6512 – 89.4091 – – – – –

0.0652 0.0666 29.1713 0.8302 89.4926 1.6887 72.9448 0.7283 1.4078 0.08500.1306 0.1333 32.3833 1.5512 89.5808 1.5786 72.0825 1.4567 0.3686 0.09400.1963 0.2000 35.5518 2.3121 89.6838 1.5823 71.9983 2.1851 0.3683 0.10290.3281 0.3333 41.2451 3.5988 89.8860 1.5222 71.1248 3.6418 0.3583 0.11940.4608 0.4666 46.2147 4.0943 90.1422 1.5108 69.1030 5.0986 0.3257 0.13430.5944 0.6000 50.4933 3.8908 90.4458 1.5036 66.7648 6.5553 0.2936 0.14710.7287 0.7333 54.1758 3.0631 90.7905 1.4979 64.4220 8.0121 0.2655 0.16010.8639 0.8666 57.3897 1.7384 91.1603 1.4939 62.2308 9.4688 0.2430 0.17110.9318 0.9333 58.8441 0.9127 91.3466 1.4923 61.1981 10.1972 0.2323 0.17611.0000 1.0000 60.2186 – 91.5282 – – – – –

Aniline (1)+Toluene (2).0000 0.000 33.4362 – 106.8685 – – – – –

.0770 0.0666 35.7064 0.7012 105.6790 1.2110 69.3120 0.2436 0.7280 0.0868

.1523 0.1333 38.6582 1.5203 104.5047 1.3535 70.208 0.2790 1.4567 0.0949

.2259 0.2000 41.3106 2.1421 103.3509 1.3709 69.6901 0.2719 2.1851 0.1025

.3686 0.3333 46.2399 3.0514 101.12 1.4134 68.4931 0.2629 3.6418 0.1176

.5053 0.4666 50.1559 3.1852 99.0023 1.4267 66.5216 0.2353 5.0985 0.1314

.6365 0.6000 53.3760 2.8915 96.9980 1.4380 64.7612 0.2182 6.5553 0.1443

.7625 0.7333 56.0201 2.16185 95.0964 1.4501 63.0538 0.2000 8.0120 0.1567

.8836 0.8686 58.3781 1.2776 93.2802 1.4721 61.6646 0.2048 2.4688 0.1690

.9423 0.9333 59.3017 0.6270 92.3976 1.4796 60.840 0.1868 10.200 0.17491.0000 0.000 60.2186 – 91.5282 – – – – –

Aniline (1)+o-xylene (2)0.0000 0.0000 41.6448 – 121.2210 – – – – –

0.0864 0.0666 44.1885 0.8803 118.7893 1.4262 71.0760 0.7284 0.2935 0.09600.1693 0.1333 46.7295 1.8268 116.3921 1.4541 71.6831 1.4568 0.2612 0.10350.2487 0.2000 49.0076 2.5753 114.0528 1.4651 71.2442 2.1851 0.2649 0.11080.3384 0.3333 52.6433 3.329 109.5962 1.4684 69.2567 3.6419 0.2467 0.12430.5368 0.4666 55.2662 3.2900 105.4791 1.4657 67.0199 5.0987 0.2220 0.13690.6652 0.6000 57.1289 2.6819 101.6352 1.4640 64.9228 6.5554 0.1943 0.14850.7846 0.7333 58.4519 1.7068 98.0724 1.4627 63.0664 8.0122 0.1573 0.15940.8959 0.8666 59.4347 0.5466 94.7367 1.4734 61.5011 9.4689 0.0860 0.17010.9488 0.9333 60.1711 0.2650 93.1080 1.4793 61.1702 10.200 0.0790 0.17531.0000 0.0000 60.2186 – 91.5282 – – – – –

Aniline (1)+p-xylene (2)0.0000 0.0000 38.5008 – 123.9293 – – – – –

0.0882 0.0666 40.5917 0.7513 121.1046 1.2334 62.2193 0.7283 0.2108 0.86100.1742 0.1333 43.3877 1.2830 118.4029 1.2852 66.8520 1.4567 0.1873 0.09410.2529 0.2000 46.1197 2.0372 115.7925 1.3908 68.9495 2.1851 0.2295 0.10240.4037 0.3333 50.5009 2.9618 110.8993 1.4163 68.2277 3.6418 0.2295 0.11740.5423 0.4666 53.8073 3.1651 106.3841 1.4313 66.7239 5.0986 0.2249 0.13140.6701 0.6000 56.2551 2.7515 102.2215 1.4431 64.9972 6.5553 0.2110 0.14440.7883 0.7333 57.8886 1.9102 98.3786 1.4503 63.0959 8.0121 0.1885 0.15650.8990 0.8666 59.8654 1.2590 95.7208 1.4886 62.2930 9.4688 0.2301 0.16870.9499 0.9333 60.0210 0.6520 94.0891 1.4930 61.5774 10.1972 0.2295 0.17471.0000 1.0000 60.2186 – 91.5282 – – – – –

194 S. Lata et al. / Journal of Molecular Liquids 147 (2009) 191–197

Generally, negative values of∈E are interpreted due to the decreasein the degree of alignment of the molecular dipoles with changingcomposition of mixtures [34–36] and positive values are due to thepresence of strong specific interactions between the components ofthe binary mixtures. In the present case, negative values of the excessdielectric properties show that electron donor-acceptor type interac-tion effects are predominated by the molecular disorder created bymixing aniline in aromatic hydrocarbons. Therefore, the overall valuesof excess permittivity are negative over whole composition range. Inorder to obtain evidence for the existence of various electron donoracceptor type interactions which may result into the formation ofassociated species of type AB, AB2, A2B2 in the mixture [37–39],apparent molar polarization “PA” of various components in binarymixtures were obtained. These studies give a conclusive evidence [36]concerning the formation of different molecular complexes betweenthe components. The apparent molar polarization can be obtainedfrom the values of molar polarization of pure components and those of

their binary mixtures. The molar polarizations are, in turn, calculatedfrom the relative permittivity and refractive index data on pure liquidsand, their binary mixtures. The important theoretical approaches forthe calculation of total molar polarization are due to Debye [40],Kirkwood and Kirkwood [41] and Frolich [42], out of these, Debyetheory has been used to calculate the total molar polarization, P of themixtures, using the relation:

P =a12 − 1a12 + 2

x1v1 + x2v2 + vE� �

ð5Þ

where∈12 is the relative permittivity of the mixture, x1 and x2 are themole fractions of components 1 and 2 in the mixtures, V1 and V2 arethe liquidmolar volumes of the components,1 and 2 respectively. VE isthe excess molar volume taken from literature [29]. P for the mixture

Fig. 3. Excess molar polarisabilities of mixing of aniline (1)+(o) benzene (2);+(△) toluene (2); +(□) o-xylene (2) and +(●) p-xylene (2) at 298.15 K. Fig. 4. Apparent polarization of mixing of aniline (1)+(o) benzene (2); +(△) toluene

(2); +(□) o-xylene (2) and +(●) p-xylene (2) at 298.15 K.

195S. Lata et al. / Journal of Molecular Liquids 147 (2009) 191–197

have been used to calculate excess molar polarization, PE, which refersto deviation of molar polarization of the mixtures from the valuesarising from mole fraction mixture law, using the relation.

PE = P − x1P1 − x2P2: ð6Þ

The calculated PE values for these set of mixtures are reported inTable 4 and shown graphically in Fig. 3 and the PE data were fitted tothe Redlich-Kister equation [33].

PE = x1 1− x1ð Þ a + b 2x1 − 1ð Þ + c 2x1−1ð Þ2 + d 2x1−1ð Þ3h i

: ð7Þ

The values of constants a,b,c and d were evaluated by method ofleast squares and these are reported alongwith the standard deviationσ(PE) in Table 5. The PE values are found to be positive over the wholecomposition range for all these mixtures. The order of variation ofthese values for equimole fraction is benzeneNp-xyleneNo-xyle-neN toluene. The positive values again indicate the existence ofspecific interactions between aniline and aromatic hydrocarbonmolecules. Though, PE values do not show the presence of differentassociated species in the solution, but the high positive values for allthe systems, indicate the presence of intermolecular complexesbetween aniline and aromatic hydrocarbon.

The total molar polarization (P) was then used to calculate theapparent molar polarization (PA) of aniline at various concentrationsin benzene, toluene, o-xylene and p-xylene. The results are recordedin Table 4 and shown graphically in Fig. 4. The values of PA are found toincrease with decrease of mole fraction of aniline but at x1b0.1, the PA

Table 5Adjustable parameters a,b,c,d and standard deviation σ(PE) of excess molar polarizationof aniline (1)+aromatic hydrocarbon (2) mixtures at 298.15 K.

System a b c d σ(PE)

Aniline (1)+Benzene (2) 13.9792 13.1412 9.9081 −32.2933 0.0413Aniline (1)+Toluene (2) 12.9790 −1.2360 −2.7757 3.2023 0.4092Aniline (1)+o-Xylene 13.7878 −3.3793 −7.3439 0.3311 0.5150Aniline (1)+p-Xylene 12.1282 0.7867 −1.6925 3.0242 0.2779

values for p-xylene and toluene systems are found to decrease. Thisbehaviour of PA again indicates the presence of specific interactionsbetween aniline and aromatic hydrocarbon and due to these specificinteractions considering that 1:1 molar complex AB is formed and themolar polarization (PAB) of the complex AB was calculated by usingthemethod described by Earp and Glasstone [43]. The values of PAB forthe AB complex for aniline+benzene, +toluene, +o-xylene, and +p-xylene are 103.3, 107.0, 116.6 and 111.7 respectively. The values ofequilibrium constant (K) were also calculated by using the methoddescribed by Earp and Glasstone [43] and the results are presented inTable 4. The values of K are found to vary with concentration. Rivailand Thiebant [34] for pyridine+chloroform system and Nath andTripathi [36] for 1,1,2,2,-tetrachloro-ethane+acetone system andfurther supported by quinoline [44] and aromatic hydrocarbonshave also observed the variation of K with concentration. It is furtherpointed out by Rivial and Thiebant [34], a theory based upon

Fig. 5. Plot of log K vs f(∈) for aniline (1)+(o) benzene (2); +(△) toluene (2);+(□) o-xylene (2) and +(●) p-xylene (2) at 298.15 K.

Fig. 6. Apparent dipole moment of mixing of aniline (1)+(o) benzene (2); +(△) toluene(2); +(□) o-xylene (2) and +(●) p-xylene (2) at 298.15 K.

196 S. Lata et al. / Journal of Molecular Liquids 147 (2009) 191–197

electrostatic interactions of solute with liquid predicts a linearvariation of log K with the quantity f(∈) by using the equation:

f að Þ = a − 1ð Þ a∞ − 1ð Þ3 2a + a∞ð Þ ð8Þ

where∈∞ is the infinite frequency relative permittivity of themixture.The value of ∈∞ was taken equal to the square of refractive index (nD

2)of the mixture (shown in Table 2) and the quantity f(∈) wascalculated at all the mole fractions for these set of mixtures and theplots between log K and f(∈) for these systems are reasonably goodstraight lines as shown in Fig. 5, where K was calculated using thefollowing Eqs. (9) and (10):

Firstly, the x was calculated as:

x =P − P1x1 + P2x2ð ÞP − P1 − P2 + PAB

=PE

P − P1 − P2 + PABð9Þ

where PE=P−(P1x1+P2x2) that is excess molar polarization, (PE), P ismolar polarization of mixture over whole composition range, P1, P2 andPAB are the molar polarizations of components 1, 2 and their complex(AB), where A is aniline and B is aromatic hydrocarbon. Then, by usingthese values of x, the equilibrium constant (K) was calculated as:

K =x 1− xð Þ

x1 − xð Þ x2 − xð Þ ð10Þ

where x1 and x2 are the mole fractions of components one and two inthe binary mixture over whole composition range.

This suggests that the results of equilibrium constant calculatedfrom the permittivity data using the method of Earp and Glasstone[43] are in accordance with the theory of electrostatic interactions ofsolute with liquid proposed by Barrial and Weishecker [45].

Stokes and Marsh [46] as well as Comphell et al [47] have shownthat the values of the apparent dipole moment (μapp) of polar solutesin non-polar solvents furnish useful information about both self-association of the solute molecules and association of the solutemolecules with the solvent molecules. That's why, μapp of aniline at

various mole fractions in aromatic hydrocarbons were calculatedusing the equation:

Vm a − 1ð Þ3a

=x1V1 aV1 − 1ð ÞaV1 + 2að Þ +

1− x1ð ÞV2 a2 − 1ð Þa2 + 2að Þ

+4∧N0x1gμ

2s; o aV1 + 2ð Þ2 2a + 1ð Þ27kBT aV1 + 2að Þ2

ð11Þ

where x1 is the mole fraction of polar solute, ∈ is the dielectricconstant of the solution, ∈1′ is the internal dielectric constant of thesolute. Vm, V1 and V2 are the molar volumes of the solution, anilineand aromatic hydrocarbon respectively. N0 is the Avogadro's constant,kB is Boltzmann's constant, μs,o is the dipole moment of the isolatedpolar molecule and g is the Kirkwood correlation parameter asmentioned by Stokes and Marsh [46], (gμs,o2 ) to be equal to apparentdipole moment (μapp) of the solute. The values of ∈1′ were obtainedfrom the refractive index of aniline as described by Stokes and Marsh[46] and is found to be equal to 2.5090.

The variation of apparent dipole moment (μapp) with logconcentration (log C) has been shown in Fig. 6. For aniline+benzenesystem, (μapp) decreases with increase of concentration, while forother systems the values of (μapp) increase with increase ofconcentration. Decrease of (μapp) for benzene system clearly indicatesthat the monomers of aniline are destabilized by the addition ofbenzene. Therefore, the aniline remains more, less associated andbenzene molecules fit well in the associated network of aniline,whereas, the increase of (μapp) for other systems indicate the presenceof specific interactions between aromatic hydrocarbons and anilinemolecules.

Thus, dielectric studies suggest that in these binary mixtures, thedissociation of associated aniline and also, the presence of specificinteractions between the two components of the mixtures. Thestrength of interaction depends upon the electron-donating capacityof aromatic hydrocarbons and extent of interaction depends upon theshape and size of the aromatic hydrocarbons.

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