Redlich-kister Equation 11373c

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ISSN 2278 -134X Original Article Correlation of excess molar volumes with Redlich-Kister polynomial and evaluation of partial molar volumes, excess partial molar volumes in some binary mixtures at 308.15 K M. Kondaiaha, and D Krishna Raob* a. NM Govt. Degree College, Jogipet, Medak Dt, A.P., India b. Department of Physics, Acharya Nagarjuna University, Nagarjuna Nagar – 522 510, A.P., India * Corresponding Author: [email protected] Phone: +91-863-2354395 (R), +91-9440712142 Received 17 November 2013; accepted 02 December 2013 Abstract Excess molar volumes,

E , partial molar volumes, V Vm m,1 , V m,2 , excess partial molar volumes, V m ,1 , V m , 2 and E

E,

E

E,

partial molar volumes, excess partial molar volumes at infinite dilution, V m,1 , V m , 2 , V m,1 , V m, 2 have been calculated using the experimentally measured density data for the prepared binary mixtures of 1,2-Dichloroethane(DE) + N,NDimethyl formamide (DMF), 1,2-Dichloroethane(DE) + Dimethyl sulphoxide(DMSO), Dichloromethane(DM) + N,NDimethyl formamide (DMF) and Dichloromethane(DM) +Dimethyl sulphoxide(DMSO) at 308.15 K. Positive suggesting dispersion forces exist in DE+DMF and DM+DMF binary systems and negative

VmE data

VmE data in DE+DMSO and

DM+DMSO binary systems s strong interactions exist between the liquid molecules. Redlich-Kister type polynomial gives better fitting of

VmE data with calculated data.

© 2013 Universal Research Publications. All rights reserved Keywords: Density, Molecular interactions, Redlich–Kister type polynomial, Excess molar volume, Partial molar volume, Excess partial molar volume Introduction The study of properties of liquid mixtures and solutions finds direct applications in chemical and biochemical industry. Knowledge of the temperature dependence of excess volumetric and transport properties of liquid mixtures provides valuable information on the nature of inter molecular interactions existing among the component molecules [1–3]. Many engineering and technological problems require quantitative data on the density and viscosity of liquid mixtures. Volumetric properties of liquid binary mixtures enable the important information for the characterization of the interactions between components. N,N-Dimethyl formamide is used as a solvent in peptide coupling for pharmaceuticals, in the development and production of pesticides, in the manufacture of adhesives, synthetic leathers, fibers, films, and surface coatings and other applications of pure solvents. It has a large dipole

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moment μ= 3.82D [4] and, in view of this, dipole–dipole interactions are expected to play an important role in molecular interactions present in the liquid mixtures. Dimethyl sulfoxide having highly polar S=O group and two hydrophobic CH3 groups. It is a typical aprotic highly polar (μ=4.06D) self-associated solvent, is an important solvent in chemistry, biotechnology, and medicine and it is able to participate in hydrogen bonding [5]. Dichloromethane used as a cleaning agent, paint remover and in extraction technology; paraffin extraction, recovery of specialty pharmaceuticals [6]. 1,2-Dichloroethane mostly used in the production of vinyl chloride which is used to make a variety of plastic and vinyl products including polyvinyl chloride. A survey of literature indicates that Radhamma et al. reported the excess molar volumes of binary mixtures of Dimethyl sulfoxide with Chloroethanes and Chloroethenes

International Journal of Research in Pure and Applied Physics 2013; 3(4):43-49

at 303.15K [7], Oana Cioclirlan and Olga Iulian [8] Harish Kumar and Deepika [9] Vijayakumar Naidu et al. [10], Fabio Comelli et al. [11] and others [12-16] reported the various excess properties of the liquid mixtures containing Dichloromethane, 1,2-Dichloroethane, Dimethyl sulfoxide as one component. In the present paper, densities, ρ of binary mixtures of N,N-Dimethyl formamide (DMF)+Dichloromethane (DM), N,N-Dimethyl formamide (DMF)+1,2-Dichloroethane (DE), Dimethyl sulfoxide (DMSO)+Dichloromethane (DM) and Dimethyl sulfoxide (DMSO)+1,2-Dichloroethane (DE) besides those of pure liquids at temperature 308.15K covering the entire composition range have been reported. The excess molar E , partial molar volumes, V m ,1 , V m,2 , excess volume, Vm partial molar volumes, at infinite dilution,

E

E

V m,1 , V m,2 , partial molar volumes

V m,1 , V m , 2 and excess partial molar E,

E,

volumesatinfinitedilution, V m,1 , V m, 2 havebeen calculated.

The variations of excess properties with composition of the mixtures have been discussed in of molecular interactions in the mixtures. Experimental In the present investigation, chemicals were further purified by standard methods [17]. Binary mixtures of DMF with DM or DE and DMSO with DM or DE were prepared so that the entire composition range is covered (i.e. 0-100% of DE or DM). The mixtures were prepared by mass in airtight bottles. The mass measurements were performed with a METTLER TOLEDO (Switzerland) ABB5-S/FACT digital balance with an accuracy ±0.01mg. The uncertainty in the mole fraction is 10–4. The density of pure liquids and liquid mixture has been measured using a two stem doublewalled Parker & Parker type pyknometer [18]. The detailed description of measurements of density was presented in our previous papers [19-21]. The reproducibility in the measured parameters of density is 3 in 105parts. The experimental values of ρ of pure liquids at 308.15 K along with their literature [10,14,22,23] values are presented in Table 1.

Table 1: Comparison of densities, ρ (kg.m-3) of pure liquids with literature data at 308.15 K ρ (kg.m-3) Liquid In this work Literature Dichloromethane 1297.2 1297.2 [22] 1,2-Dichloroethane 1230.2 1230.8 [14] N,N-Dimethyl formamide 935.6 935.717 [23] Dimethyl sulphoxide 1085.2 1085.6 [10] n Results (3) YE x1x2 Ai ( x2 x1)i The experimental values of density have been used to i 0 calculate the molar volume and excess molar volume data E where Y = VmE ; the subscription ‘i’ in the eq 3 takes with the following equations. values from 0 to 4. Ai are the adjustable parameters of the x1M1 x2M 2 (1) Vm function and are determined using the least square method.

E Vm

Vm ( x1V1

x2V2 )

(2)

The corresponding standard deviations computed using the relation.

where ρ, and Vm are the density and molar volume of the mixture. M1, M2,

V1 and V2 are the molar masses and

molar volumes pure components1 (DE or DM) and 2 (DMF or DMSO) respectively and xi represents the mole fraction of the component ‘i’ in the mixture. The values of excess molar volume have been fitted to Redlich-Kister type polynomial [24] equation,

(Y E )

E Yexp m

E Ycal n

(Y E ) have been

2 1/2

(4)

where ‘m’ is the total number of experimental points and ‘n’ is the number of coefficients in eq 3. The coefficients Ai in eq 3 and the standard deviations of all the binary mixtures have been presented in Table 2.

Table 2 : Coefficients Ai of Redlich-Kister type polynomial equation eq 3 and the corresponding standard deviations (σ) of all the systems for VmE (x10-5) (m3.mol-1) A0 A1 DE+DMF 0.0813 0.0084 DE+DMSO -0.1623 0.0380 DM+DMF 0.1579 -0.0175 DM+DMSO -0.0872 0.0844 The molecular interactions in the systems are well reflected in the properties of partial molar volumes. The partial molar volumes

V m,1

A3 0.0492 -0.0153 0.0571 -0.0625

VmE

V1*

x2

V m,1 of component 1(DE or DM) and

V m,2 of component 2 (DMF or DMSO) in the mixtures over the entire composition range have been calculated by using the following relations.

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A2 0.1110 0.0787 0.0662 -0.0426

V m, 2

VmE

V2*

x1

A4 -0.1601 -0.0171 -0.0169 0.0845

VmE x

(5) T ,P

E m

V x

σ 0.0024 0.0011 0.0004 0.0006

(6) T ,P

International Journal of Research in Pure and Applied Physics 2013; 3(4):43-49

where

V1 and V2 are the molar volumes of pure

components of DE or DM and DMF or DMSO respectively. The derivates V E in eq.s (5) and (6) are m x

T ,P

obtained by differentiating Eq.(3) which lead to the following equations for V m,1 V m, 2

V1*

x22

V2*

x12

V m,1 and V m,2 .

j

Ai ( x2 i 0 j

Ai ( x2

2 x1 x22

x1 ) i

2 x2 x12

x1 ) i

i 0

j

Ai ( x2

x1 ) i

i 1 j

Ai ( x2

x1 ) i

1

1

(7) (8)

i 1

E

E

E

V m,1 V1*

E m, 2

V m, 2 V2*

E calculated from Comparison of excess molar volume, Vm equation (2) and (3) against mole fraction, x1 of DE/DM are plotted in fig. 2. The deviation of physical and chemical properties of the liquid mixture from the ideal behavior is a measure of the interaction between molecules of the components of liquid mixtures, and such a type of deviation is generally attributed to dipole−dipole interactions and hydrogen bond between unlike molecules [25] respectively. From this figure, a good correlation exist between experimentally calculated and RK polynomial excess molar E data volumes. This show, experimentally calculated Vm

better fits the RK polynomial.

V m,1 , V m,2 have been calculated using the relations, V m ,1

V

(9)

(10) The experimental values of densities, excess molar E

E

V m,1 , V m,2 , V m ,1 and V m , 2 are furnished in

volumes,

Table 3. Furthermore, the partial molar volumes and excess partial molar volumes of the components at infinite dilution E,

E,

respectively, V m ,1 , V m,2 , V m ,1 and V m ,2 were obtained by; putting x1 = 0 in eq. 7 and x1 =1 in eq. 8. E,

V m,1 E,

V m,2

A0

A1

A2

A3 ...... V m,1 V1 ,

(11)

A0

A1

A2

A3 ...... V m,2 V2 ,

(12)

Fig. 2 Comparison plots of excess molar volume,

E,

against mole fraction, x1 of DE/DM for binary mixtures of DE with DMF (O), DMSO (O) or DM with DMF ( ), DMSO ( ) (solid lines: calculated, dotted lines: R-K Polynomial) E is the resultant of several effects such as chemical, Vm

E,

The pertinent values of V m ,1 V m,2 V m ,1 and V m ,2 are shown in Table 4. Discussion The variation of density with mole fraction, x1 of DE or DM as shown in fig. 1. From this figure 1 and table 3 densities increased monotonically, non-linearly in all the binary systems with increase in concentration of DE or DM. This non-linear variation is a deviation from ideal behavior suggests that interactions between molecules of component liquids of the mixtures.

physical and structural. Physical contributions, which are non-specific interactions between the liquid molecules of E values. The the mixture [26,27], contribute to positive Vm E are contributed by the chemical or negative values to Vm specific intermolecular interactions [28] that result in the volume decrease. The structural contributions are mostly negative and arise from interstitial accommodation of the mixing components because of the difference in molar

volumes [29]. In the present investigation the

Fig.1 Plots of densities, ρ against mole fraction, x1 of DE/DM for the binary mixtures of DE with DMF/DMSO or DM with DMF/DMSO

46

VmE

VmE data are

positive in DE+DMF and DM+DMF binary systems indicates dispersion forces exist between unlike molecules of the liquid mixing components and negative in DE+DMSO and DM+DMSO binary systems s strong interactions exist between the liquid molecules. The strength of interaction follows the order DE+DMSO > DM+DMSO > DE+DMF > DM+DMF. The above mentioned order indicates the formation of transition complex with formation of new hydrogen bonds between the unlike molecules in the liquid mixtures. When DMSO mixed with DE (μ=1.86 D and ε=10.36) which is polar but practically unassociated, specific interaction could be donor-acceptor type between the

International Journal of Research in Pure and Applied Physics 2013; 3(4):43-49

oxygen atom of S=O group of DMSO with its unshared pairs of electrons, acts as electron-donor towards electronacceptor chlorine atoms of DE. This might be the reason

E for negative values of Vm . In case of DMF+DE a new

hydrogen bond between the chlorine atom of DE and hydrogen atom of DMF (C–Cl ---- H), hydrogen atom of DE and oxygen atom of carbonyl group of DMF (-H--C=O) may be formed. The strength of interaction in DMSO is predominant compared to DMF. DMSO (4.06D) has large dipole moment compared to DMF (3.82D and hence dipole-dipole interactions may be expected in the binary liquid mixtures, this might be possible reason for more negative

VmE values in the DMSO binary mixtures.

Another important and considerable effect is geometrical fitting of smaller molecules into the voids created by the

E bigger molecules for interpreting negative Vm vales. Molar volumes of DM, DE, DMF and DMSO at 308.15K are 65.472 80.442, 48.14, 72 cm3.mol-1 respectively. Therefore, the large

VmE values are attributed to the

dipole-dipole interactions, favorable fitting of smaller molecules into bigger molecules and hydrogen bond formation between the unlike molecules in the liquid molecules. The similar results were also reported by several authors [7,9,10,12].

negative and positive values of

VmE in all the binary

systems. Fig. 3 shows excess partial molar volumes of E

E

DE/DM, V m ,1 and DMF/DMSO, V m , 2 .. Examination of figure 3 reveals that, indicating strong interactions exist between the unlike molecules in the DE+DMSO and DM+DMSO binary mixtures and weak forces between DE+DMF and DM+DMF. These figures the

VmE values. From table 4 the

conclusions drawn from E,

E,

values of V m ,1 V m,2 V m ,1 and V m ,2 values are negative and positive concluded that strong and weak interactions exist in the unlike molecules of the components. Table 4 Partial molar volumes, excess partial molar volumes at infinite dilutions, V m,1 , systems at 308.15 K Binary system DE+DMF DE+DMSO DM+DMF DM+DMSO

E,

E,

V m , 2 , V m,1 , V m, 2 for binary

V m,1

V m, 2

8.134 7.9662 6.794 6.5238

E,

E,

V m,1

V m, 2

(x10-5) ( m3.mol-1) 4.7886 0.0898 7.0766 -0.078 4.9816 0.2468 7.1328 -0.0234

-0.0254 -0.1234 0.1676 -0.0672

Fig. 3 Plots of excess partial molar volumes of DE/DM, E

E

V m ,1 and DMF/DMSO, V m , 2 for the binary mixtures of DE with DMF/DMSO or DM with DMF/DMSO (solid E

The existing molecular interactions in the systems are well reflected in the properties of partial molar volumes. From table 3, the values of V m ,1 and V m,2 for both the components in the DE+DMSO and DM+DMSO binary mixtures are less than their respective molar volumes in the pure state i.e contraction of volume takes place on mixing DE/DM with DMSO. In case of DE+DMF and DM+DMF binary mixtures V m ,1 and V m,2 for both the components are higher than their respective molar volumes in the pure state i.e expansion of volume takes place in the liquid mixtures. This data are also ing the observed

47

E

lines: V m ,1 , dotted lines: V m , 2 ) Conclusions The densities, ρ of binary mixtures of 1,2-Dichloroethane+ N,N-Dimethyl formamide, 1,2-Dichloroethane+Dimethyl sulphoxide, Dichloromethane+ N,N-Dimethyl formamide and Dichloromethane+Dimethyl sulphoxide at 308.15 K. From this experimental data, excess molar volume has been determined. A good correlation exist between experimentally calculated and RK polynomial excess molar volumes. This show, experimentally calculated

VmE data

better fits the RK polynomial. Hydrogen bond formation between the unlike molecules, dipole-dipole interactions and interstitial accommodation of unlike molecules are the

International Journal of Research in Pure and Applied Physics 2013; 3(4):43-49

favorable factors for the responsible of

VmE data in the E

E

present binary mixtures. The V m ,1 , V m,2 , V m ,1 , and V m,2 have been computed from the experimental results. The calculated values of partial molar volumes and excess partial molar volumes at infinite dilution data s the

E

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Source of : Nil; Conflict of interest: None declared

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International Journal of Research in Pure and Applied Physics 2013; 3(4):43-49