Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure

Hossein Iloukhani; Zahra B. Mohammadlou

doi:10.1016/j.arabjc.2016.12.004

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Original article

12 (

); 5079-5085

doi:

10.1016/j.arabjc.2016.12.004

Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure

Hossein Iloukhani^⁎, Zahra B. Mohammadlou

Department of Physical Chemistry, Faculty of Chemistry, Bu-Ali Sina University, Hamedan, Iran

⁎Corresponding author. Fax: +98 8118282807. iloukhani@basu.ac.ir (Hossein Iloukhani)

Received: 2012-3-17, Accepted: 2014-10-8, Published: 2016-12-01

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

This article reports experimental densities ρ, viscosities η, and refractive indices n_D, of the ternary systems of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) and the binary systems of formamide (1) + N,N-dimethylacetamide (2), formamide (1) + 2-methyl-1-butanol (3), and N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) over the entire range of composition at T = 298.15 K for the liquid region and at ambient pressure. Excess molar volumes $V_{m}^{E}$ , deviations in the viscosity Δη, and deviations in the refractive index Δn_D, for the mixtures were derived from the experimental data. The binary and ternary data of $V_{m}^{E}$ , Δη, and Δn_D, were correlated as a function of the mole fraction by using the Redlich–Kister and the Cibulka equations, respectively. The results are consistent with the self-association of alcohol and the polar characters of used amide. McAlister’s multibody interaction model is used for correlating the kinematic viscosity of binary mixtures, with mole fraction. The experimental and the constituted binary and ternary systems are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.

Keywords

Excess molar volume

Deviation in the viscosity and Refractive index

Formamide

N,N-dimethylacetamide

2-Methyl-1-butanol

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1 Introduction

This paper is a part of an ongoing research program in which we study thermodynamic, and transport properties of binary and ternary mixtures (Iloukhani and Zarei, 2004; Iloukhani et al., 2000; Iloukhani and Rakhshi, 2009; Zarei and Iloukhani, 2003; Khanlarzadeh and Iloukhani, 2011; Fattahi and Iloukhani, 2010 ). Experimental data of properties such as density $ρ$ , and viscosity $η$ , and refractive index n_D, at over the whole composition range for binary and ternary liquid mixtures are useful for a full understanding of their thermodynamic and transport properties, as well as for practical chemical engineering purposes (Matthew and Koga, 2002; Zhang et al., 2008). On the other hand, excess thermodynamic properties and deviations of non-thermodynamic ones of binary liquid mixtures are fundamental for the design of industrial equipment and for the interpretation of the liquid state, particularly when polar components are involved. These properties have also been used as a qualitative and quantitative guide to predict the extent of complex formation in this kind of mixtures (Gomez Marigliano and Solimo, 2002). Here, we have measured densities $ρ$ , viscosities $η$ , and refractive indices n_D, for the binary and ternary systems formed by formamide, N,N-dimethylacetamide, and 2-methyl-1-butanol at T = 298.15 K for the liquid region and at ambient pressure for the whole composition range. The data obtained are used to calculate excess molar volumes, deviations in the viscosity, deviations in the refractive index, and excess Gibbs energies of activation of viscous flow of the binary and ternary mixtures. The excess and deviation quantities of binary mixtures have been fitted to the Redlich–Kister equation to determine the coefficients. For correlating the ternary data, the Cibulka equation was used. The kinematic viscosity data for the binary mixtures were fitted to McAllister’s interaction model and their parameters have been calculated.

2 Experimental

2.1

2.1 Materials

The mole fraction purity of the components from Merck were as follows: formamide (w ⩾ 99), N,N-dimethylacetamide (w ⩾ 99), and 2-methyl-1-butanol (w ⩾ 99), where w is mass fraction. All chemical substances were used without any further purification. Purity of each compound was checked by measuring the densities and refractive index and found to be in good agreement with values found in the literature (Nain, 2007; Cases et al., 2001; Gimenez et al., 2008; Iloukhani and Khanlarzadeh, 2006; Resa et al., 2005 ), reported in Table 1.

Table 1 Comparison of measured densities and refractive indices of the pure components with literature values at 298.15 K.

Component	$ρ (g / {cm}^{3})$		$n_{D}$
	Experimental	Literature	Experimental	Literature
Formamide	1.12904	1.12908^a	1.4455	1.4468^b
N,N-dimethylacetamide	0.93624	0.93634^c	1.4357	1.4356^d
2-Methyl-1-butanol	0.81537	0.8150^e	1.4087	1.4086^e

^a Nain (2007).

^b Cases et al. (2001).

^c Gimenez et al. (2008).

^d Iloukhani and Khanlarzadeh (2006).

^e Resa et al. (2005).

2.2

2.2 Apparatus and procedure

Densities of the pure liquids and their mixture were measured with an Anton Paar DMA 4500 oscillating U-tube densimeter, operated in the static mode and the uncertainties were estimated to be within ±1 × 10⁻² kg m⁻³. The temperature in the cell was regulated to ±0.01 K with a solid-state thermostat. The apparatus was calibrated once a day with dry air and double-distilled freshly degassed water. The mixtures were prepared by weighing amounts of the pure liquids by syringing into stoppered bottles to prevent evaporation and reducing possible errors in mole fraction calculations. Ternary mixtures were prepared by mixing the three components. Each mixture was immediately used after it was well-mixed by shaking. All the weightings were performed on an electronic balance (AB 204-N Mettler) accurate to 0.1 mg. The uncertainty in the mole fraction is estimated to be lower than ±2 × 10⁻⁴.

Dynamic viscosities at 298.15 K were measured with an Ubbelohde viscometer. The equation for viscosity, according to Poiseuille’s law, is

(1)

η = ρ υ = ρ (kt - c / t)

where k and c are the viscometer constants and t,

η

, and

ν

, are the efflux time, dynamic viscosity, and kinematic viscosity, respectively. The uncertainty of the viscosity measurements was estimated to be less than ±2 × 10⁻³ mPa s. The viscometer was suspended in a thermostated water bath maintained to ±0.01 K. An electronic digital stopwatch with uncertainty to ±0.01 s was used for flow time measurements. At least three repetitions of each data point obtained were reproducible to ±0.05 s, and the results were averaged.

Refractive indices were measured using a digital Abbe-type refractometer. Water was circulated into the prism of the refractometer by a circulation pump connected to an external thermostated water bath. The uncertainty of the refractive index is on the order of 0.0002 units.

3 Results and discussion

Table 2 lists the experimental densities, viscosities, refractive indices, excess molar volumes, deviations in viscosity, deviations in refractive index and excess Gibbs energy of activation for three binary systems formamide (1) + N,N-dimethylacetamide (2), formamide (1) + 2-methyl-1-butanol (3), and N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K. The excess molar volumes $V_{m}^{E}$ , were calculated from density data according to

(2)

V_{m}^{E} = \sum_{i = 1}^{n} x_{i} M_{i} (ρ^{- 1} - ρ_{i}^{- 1})

where x_i, M_i, and

ρ_{i}

are the mole fraction, molar mass, and density of the pure component i, respectively.

ρ

is the density of mixture, and n is the number of components. In the system studied, excess molar volumes are negative for the system formamide (1) + N,N-dimethylacetamide (2) over the whole composition range. For the system formamide (1) + 2-methyl-1-butanol (3), and N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) an inversion of sign of

V_{m}^{E}

, is observed over part of the concentration range. In first system values

V_{m}^{E}

, are positive at lower concentrations of alcohol and negative at higher concentrations of it. Fig. 1 shows the excess molar volumes for the three binary systems at T = 298.15 K. A plausible qualitative interpretation of the behavior of these mixtures with composition has been suggested. In the systems considered here, we can recognize four different effects as being important, (i) hydrogen bond rupture, (ii) dispersive interactions between unlike molecules, (iii) intermolecular dipolar interactions, and (iv) geometrical fitting between components. The positive contribution to

V_{m}^{E}

, is expected from first two effects while opposite contribution from remaining two. The volumetric behavior of the formamide + N,N-dimethylacetamide mixture shows that effect (iii) and (iv) which leads to packing in volumes, predominates over the two (i) and (ii), which contribute to expansion. For the system of formamide (1) + 2-methyl-1-butanol (3), positive values of

V_{m}^{E}

, were observed in the region of x₁ below 0.56 while negative values of

V_{m}^{E}

, were found for the other composition ranges. Mixing of formamide with alkanols would induce mutual dissociation of the hydrogen bonded structures present in pure liquids with subsequent formation of (new) H-bonds (C⚌⋯OH—O) between proton acceptor oxygen atom (with two lone pair of electrons) of C⚌O group of formamide and hydrogen atom of ⚌OH group(s) of alkanol molecules. Therefore at high concentration of alcohol dissociation is dominate while at low concentration opposite contribution (associated through hydrogen bonding and leading to a contraction in volume) is dominate. For the system of N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3), negative values of

V_{m}^{E}

, were observed in the region of x₁ below 0.32 while positive values of

V_{m}^{E}

, were found for the other composition ranges. A sigmoid shape observed may be attributed to the hydrogen bond effect that occurred between amide and alcohol. At low concentration of amide, hydrogen bonding is dominant resulting in negative values of

V_{m}^{E}

, whereas at higher mole fraction of amide, dispersive forces are dominant resulting in positive values of

V_{m}^{E}

. The other reason for this observation is steric hindrance of the two methyl groups of N,N-dimethylacetamide.

Table 2 Experimental densities

ρ

, viscosities

η

, refractive indices

n_{D}

, excess molar volumes

V_{m}^{E}

, deviations in the viscosity

Δ η

, deviations in the Refractive Index

Δ n_{D}

, and excess Gibbs energy of activation

Δ G^{*^{E}}

, of viscous flow for the binary systems at 298.15 K.

$x$	$ρ (g / {cm}^{3})$	$η (mPa s)$	$n_{D}$	$V_{m}^{E} ({cm}^{3} / mol)$	$Δ η (mP s)$	$Δ G^{*^{E}}$ (J/mol)	$Δ n_{D}$
Formamide (1) + N,N-dimethylacetamide (2)
0.0811	0.94490	1.049	1.4370	−0.153	−0.027	192.719	0.0005
0.1596	0.95381	1.242	1.4381	−0.271	−0.010	409.411	0.0008
0.2403	0.96353	1.469	1.4391	−0.355	0.034	609.464	0.0010
0.3204	0.97372	1.740	1.4401	−0.395	0.125	811.345	0.0013
0.3978	0.98431	2.045	1.4410	−0.403	0.256	993.374	0.0014
0.4799	0.99664	2.402	1.4418	−0.390	0.427	1152.539	0.0014
0.5591	1.00974	2.735	1.4424	−0.351	0.583	1235.356	0.0012
0.6407	1.02512	3.080	1.4430	−0.308	0.743	1271.056	0.0010
0.7204	1.04190	3.340	1.4436	−0.235	0.824	1208.165	0.0008
0.7995	1.06156	3.464	1.4441	−0.175	0.770	1022.015	0.0006
0.8793	1.08485	3.485	1.4446	−0.110	0.612	741.455	0.0003
0.9607	1.11319	3.319	1.4452	−0.036	0.262	297.445	0.0001

N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3)
0.0803	0.82341	3.357	1.4106	−0.071	−0.804	−378.556	−0.0003
0.1600	0.83174	2.661	1.4125	−0.041	−1.216	−633.888	−0.0005
0.2397	0.84036	2.218	1.4145	−0.001	−1.375	−764.390	−0.0007
0.3207	0.84932	1.915	1.4164	0.020	−1.390	−804.579	−0.0009
0.3987	0.85820	1.685	1.4184	0.040	−1.343	−810.324	−0.0010
0.4801	0.86769	1.510	1.4206	0.071	−1.229	−757.163	−0.0011
0.5598	0.87731	1.367	1.4228	0.080	−1.089	−687.375	−0.0010
0.6402	0.88735	1.262	1.4249	0.079	−0.909	−566.148	−0.0010
0.7200	0.89768	1.157	1.4272	0.065	−0.731	−465.563	−0.0009
0.7996	0.90826	1.073	1.4295	0.050	−0.532	−338.052	−0.0008
0.8800	0.91934	0.999	1.4315	0.023	−0.321	−197.646	−0.0006
0.9588	0.93037	0.927	1.4344	0.007	−0.112	−70.095	−0.0002

Formamide (1) + 2-methyl-1-butanol (3)
0.0801	0.82461	4.092	1.4096	0.066	−0.252	−67.299	−0.0020
0.1609	0.83532	3.983	1.4108	0.091	−0.257	−1.657	−0.0038
0.2398	0.84723	3.999	1.4121	0.092	−0.137	130.185	−0.0054
0.3199	0.86110	4.064	1.4139	0.066	0.032	284.186	−0.0066
0.4005	0.87688	4.147	1.4159	0.049	0.220	439.098	−0.0075
0.4808	0.89504	4.229	1.4181	0.018	0.406	579.834	−0.0083
0.5609	0.91594	4.301	1.4206	−0.007	0.583	701.292	−0.0087
0.6401	0.94020	4.331	1.4236	−0.037	0.716	781.568	−0.0087
0.7200	0.96901	4.317	1.4274	−0.057	0.807	819.646	−0.0078
0.7997	1.00348	4.146	1.4313	−0.067	0.739	744.175	−0.0068
0.8809	1.04647	3.792	1.4364	−0.071	0.491	522.241	−0.0047
0.9601	1.09837	3.347	1.4417	−0.043	0.149	181.922	−0.0023

Variation of excess molar volume V m E with mole fraction x1 for the binary systems at T = 298.15 K: ♦, Formamide (1) + N,N-dimethylacetamide (2); ▴, N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3); ●, Formamide (1) + 2-methyl-1-butanol (3). Solid curves were calculated from the Redlich–Kister equation.

The viscosity deviations $Δ η$ , and excess Gibbs energies of activation of viscous flow $Δ G^{*^{E}}$ , for binary mixtures can be calculated as

(3)

Δ η = η - \sum_{i}^{N} x_{i} η_{i}

(4)

Δ G^{*^{E}} = RT [\ln (ν M) - \sum_{i = 1}^{c} x_{i} \ln (ν_{i} M_{i})]

where M is the molecular weight, x_i is the mole fraction and c refers to the number of components in the mixture

η

, is the absolute viscosity of the mixtures and

η_{i}

, is the absolute viscosity of pure component i. The

Δ η

, values are also graphically represented as a function of mole fraction at 298.15 K in Fig. 2. It is observed that the

Δ η

, values for system formamide (1) + N,N-dimethylacetamide (2) and formamide (1) + 2-methyl-1-butanol (3), an inversion of sign of

Δ η

, are observed over part of the concentration range. This reveals that the strength of specific interaction is not the only factor influencing the viscosity deviation of liquid mixtures. The molecular size and shape of the components also play an equally important role. According to Meyer et al. the observed negative values of

Δ G^{*^{E}}

correspond to the existence of solute–solute association.

Variation of deviation in the viscosity Δ η with mole fraction x1 for the binary systems at T = 298.15 K: ♦, Formamide (1) + N,N-dimethylacetamide (2); ▴, N,N-dimethylacetamide (2) + 2-methyl-2-methyl-1-butanol (3); ●, Formamide (1) + 2-methyl-1-butanol (3). Solid curves were calculated from the Redlich–Kister equation.

The deviation in the refractive index from the mole fraction average $Δ n_{D}$ , is given by

(5)

Δ n_{D} = n_{D} - \sum_{i}^{n} x_{i} n_{D, i}

where

n_{D}

and

n_{D, i}

are the refractive index of the mixture and the refractive index of pure component i, respectively. For the whole composition range, the

Δ n_{D}

, values are negative for systems formamide (1) + 2-methyl-1-butanol (3) and N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3). The

Δ n_{D}

, values for system formamide (1) + N,N-dimethylacetamide (2) are positive. Figs. 3 and 4 show the results of

Δ n_{D}

, and

Δ G^{*^{E}}

for the three binary mixtures at T = 298.15 K respectively. The mixing functions

V_{m}^{E}

Δ η

, and

Δ n_{D}

were represented mathematically by the Redlich–Kister equation for correlating the experimental data (Redlich and Kister, 1948):

(6)

Δ Q_{ij} = x_{i} x_{j} \sum_{k = 0}^{m} A_{k} {(x_{j} - x_{i})}^{k}

where

Δ Q_{ij}

refers to

V_{m}^{E} / {cm}^{3} {mol}^{- 1}

Δ η / mPa s

, and

Δ n_{D}

for each i–j binary pair; x_i is the mole fraction of component i; and A_k values are the coefficients. The values of coefficients A_k were determined by a multiple regression analysis based on the least squares method and are summarized along with the standard deviations between the experimental and the fitted values of the respective functions in Table 3. The standard deviation is defined by

(7)

σ = {[\sum_{i = 1}^{n} (Δ Q_{\exp, i} + Δ Q_{cal, i}) / (n - p)]}^{\frac{1}{2}}

where n is the number of experimental points and p is the number of adjustable parameters. The experimental densities, viscosities, excess molar volumes, deviations in the viscosity, deviations in refractive index and excess Gibbs energy of activation of the ternary mixtures system formamide (1) + N,N-dimethylacetamide (2) + 2-methy1-butanol (3) at 298.15 K are listed in Table 4. The derived data (

V_{m}^{E}

Δ η

, and

Δ n_{D}

) as defined in Eqs. (2)–(5) for the ternary system were correlated respectively using the equation

(8)

Δ Q_{123} = Δ Q_{bin} + x_{1} x_{2} x_{3} Δ_{123}

(9)

Δ Q_{bin} = \sum_{i = 1}^{3} \sum_{j . i}^{3} Δ Q_{ij}

where

Δ Q_{123}

refers to

V_{m}^{E}

Δ η

, and

Δ n_{D}

, for the ternary system formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3).

Δ Q_{ij}

in Eq. (9) is the binary contribution of each i–j pair to the

V_{m}^{E}

Δ η

, and

Δ n_{D}

, given by Eq. (6) with the parameters shown in Table 3. The ternary contribution term

Δ_{123}

was correlated using the expression suggested by Cibulka (1982):

(10)

Δ_{123} = B_{0} + B_{1} x_{1} + B_{2} x_{2}

where the ternary parameters B₀, B₁, and B₂ were determined with the optimization algorithm similar to that for the binary parameters. The fitting parameters and the corresponding standard deviations are given in Table 3. As can be expected, the ternary system shows the same change in binary systems. McAllister’s multibody-interaction model (McAllister, 1960) is widely used for correlating the kinematic viscosity of binary mixtures with mole fraction. The three-body model is defined as

(11)

\ln ν = x_{1}^{3} \ln ν_{1} + 3 x_{1}^{2} x_{2} \ln v_{12} + 3 x_{1} x_{2}^{2} \ln v_{21} + x_{2}^{3} \ln ν_{2} - \ln (x_{1} + \frac{x_{2} M_{2}}{M_{1}}) + 3 x_{1}^{2} x_{2} \ln (2 / 3 + \frac{M_{2}}{3 M_{1}}) + 3 x_{1} x_{2}^{2} \ln (1 / 3 + \frac{2 M_{2}}{3 M_{1}}) + x_{2}^{3} \ln (M_{2} / M_{1})

and the four-body model is given by

(12)

\ln ν = x_{1}^{4} \ln ν_{1} + 4 x_{1}^{3} x_{2} \ln ν_{1112} + 6 x_{1}^{2} x_{2}^{2} \ln ν_{1122} + 4 x_{1} x_{2}^{3} \ln ν_{2221} + x_{2}^{4} \ln ν_{2} - \ln (x_{1} + \frac{x_{2} M_{2}}{M_{1}}) + 4 x_{1} x_{2}^{3} \ln (\frac{1 + 3 M_{2} / M_{1}}{4}) + x_{2}^{4} \ln (M_{2} / M_{1}) + 4 x_{1}^{3} x_{2} \ln (\frac{3 + M_{2} / M_{1}}{4}) + 6 x_{1}^{2} x_{2}^{2} \ln (\frac{1 + M_{2} / M_{1}}{2})

where

ν

ν_{1}

, and

ν_{2}

are the kinematic viscosities of the mixture and the viscosities of pure components 1 and 2, respectively.

ν_{12}

ν_{21}

ν_{1112}

ν_{1122}

and

ν_{2221}

are the model parameters. Table 5 records the calculated results with the standard deviation defined as in Eq. (7). It is shown that McAllister’s four-body equation gave a better result for those three systems.

Variation of deviation in the refractive index Δ n D with mole fraction x1 for the binary systems at T = 298.15 K: ♦, Formamide (1) + N,N-dimethylacetamide (2); ▴, N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3); ●, Formamide (1) + 2-methyl-1-butanol (3). Solid curves were calculated from the Redlich–Kister equation.

Excess Gibs energies of the binary mixtures vs. mole fraction x1 for the binary systems at T = 298.15 K: ♦, Formamide (1) + N,N-dimethylacetamide (2); ▴, N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3); ●, Formamide (1) + 2-methyl-1-butanol (3).

Table 3 Binary coefficients of the Redlich−Kister equation A_k, at 298.15 K and ternary coefficients of the Cibulka equation for

V_{m}^{E}

Δ η

, and

Δ n_{D}

at 298.15 K.

$Δ Q_{ij}$	$A_{0}$	$A_{1}$	$A_{2}$	$A_{3}$	$A_{4}$	$σ$
Formamide (1) + N,N-dimethylacetamide (2)
$V_{m}^{E}$ (cm³/mol)	−1.5233	0.8383	−0.0966	−0.2925	0.1409	0.0039
$Δ η (mPa s)$	1.8886	4.1602	1.4651	−0.2627	0.1721	0.0114
$Δ n_{D}$	0.0054	−0.0018	−0.0028	−0.001	0.0024	0.000036

N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3)
$V_{m}^{E}$ (cm³/mol)	0.2899	0.1039	−0.2824	0.8259	−0.9068	0.0069
$Δ η (mPa s)$	−4.7762	3.3975	−2.4403	1.9729	−0.9216	0.00474
$Δ n_{D}$	−0.0042	−0.0008	−0.0017	0.0003	0.0027	0.000036

Formamide (1) + 2-methyl-1-butanol (3)
$V_{m}^{E}$ (cm³/mol)	0.0363	−0.6418	0.3016	−0.5868	−0.5001	0.0043
$Δ η (mPa s)$	1.7763	4.9465	1.3156	−0.3651	−4.5054	0.0143
$Δ n_{D}$	−0.0344	−0.0078	0.0072	−0.0097	−0.0228	0.000227

$Δ Q_{123}$	$B_{0}$	$B_{1}$	$B_{2}$	$σ$
$V_{m}^{E}$ (cm³/mol)	1.6013	−3.5073	−2.8107	0.0372
$Δ η / (mPa s)$	5.02495	−16.6239	−10.6946	0.0229
$Δ n_{D}$	0199.0	−0.0106	0.0007	0.0002

Table 4 Experimental densities

ρ

, viscosities

η

, refractive Indices

n_{D}

, excess molar volumes

V_{m}^{E}

, deviation in the viscosity

Δ η

, deviations in the refractive index

Δ n_{D}

, and excess Gibbs energy of activation

Δ G^{*^{E}}

, of viscous flow for the ternary for the system formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K.

$x_{1}$	$x_{2}$	$ρ (g / {cm}^{3})$	$η (mPa s)$	$n_{D}$	$V_{m}^{E} ({cm}^{3} / mol)$	$Δ η (mPa s)$	$Δ G^{*^{E}}$ (J/mol)	$Δ n_{D}$
0.1015	0.0834	0.8368	3.295	1.4123	0.066	−0.720	−236.041	−0.0024
0.1014	0.1867	0.8490	2.605	1.4153	0.061	−1.044	−408.908	−0.0022
0.1016	0.2894	0.8617	2.183	1.4181	0.039	−1.101	−439.286	−0.0022
0.1025	0.3915	0.8748	1.875	1.4211	0.025	−1.046	−411.146	−0.0019
0.1009	0.4918	0.8879	1.658	1.4243	−0.013	−0.909	−322.437	−0.0014
0.1013	0.5960	0.9023	1.472	1.4274	−0.051	−0.724	−205.464	−0.0011
0.1000	0.6974	0.9167	1.331	1.4306	−0.115	−0.507	−60.532	−0.0006
0.0999	0.7984	0.9315	1.201	1.434	−0.151	−0.278	82.433	0.0001
0.2067	0.0703	0.8510	3.463	1.4138	0.062	−0.463	0.500	−0.0044
0.2060	0.1752	0.8649	2.856	1.4174	0.013	−0.698	−65.313	−0.0036
0.2055	0.2801	0.8792	2.410	1.4207	−0.027	−0.772	−74.981	−0.0031
0.2048	0.3854	0.8942	2.102	1.4242	−0.079	−0.708	−2.705	−0.0024
0.2037	0.4901	0.9097	1.860	1.4277	−0.147	−0.579	102.201	−0.0017
0.2023	0.5952	0.9257	1.651	1.4314	−0.208	−0.417	214.427	−0.0008
0.2009	0.6989	0.9420	1.486	1.4351	−0.267	−0.216	354.827	0.0001
0.3128	0.0609	0.8686	3.665	1.4161	0.028	−0.156	256.269	−0.0058
0.3106	0.1720	0.8848	3.083	1.4200	−0.046	−0.347	256.998	−0.0048
0.3107	0.2765	0.9009	2.658	1.4239	−0.099	−0.401	295.196	−0.0037
0.3088	0.3830	0.9179	2.351	1.4280	−0.180	−0.332	401.388	−0.0024
0.3057	0.4898	0.9351	2.074	1.4319	−0.248	−0.234	499.750	−0.0013
0.3026	0.5964	0.9530	1.852	1.436	−0.327	−0.081	626.389	0.0001
0.4193	0.0561	0.8901	3.846	1.4187	−0.008	0.146	491.786	−0.0069
0.4170	0.1659	0.9082	3.328	1.4231	−0.095	0.015	552.277	−0.0054
0.4112	0.2743	0.9258	2.906	1.4274	−0.174	−0.029	626.429	−0.0038
0.4098	0.3851	0.9459	2.566	1.4323	−0.264	0.021	739.573	−0.0019
0.4048	0.4940	0.9652	2.280	1.4366	−0.338	0.116	857.658	−0.0003
0.5243	0.0560	0.9165	3.986	1.4221	−0.048	0.422	691.211	−0.0074
0.5196	0.1690	0.9371	3.498	1.4272	−0.148	0.329	791.397	−0.0052
0.5122	0.2813	0.9575	3.105	1.4321	−0.237	0.325	914.353	−0.0030
0.5068	0.3913	0.9788	2.764	1.4371	−0.321	0.367	1036.467	−0.0008
0.6262	0.0608	0.9487	4.058	1.4264	−0.085	0.643	837.740	−0.0070
0.6195	0.1749	0.9721	3.617	1.4319	−0.195	0.598	973.379	−0.0043
0.6091	0.2894	0.9913	3.189	1.4369	−0.068	0.563	1089.410	−0.0020
0.7231	0.0704	0.9875	4.002	1.4314	−0.101	0.746	892.271	−0.0058
0.7118	0.1866	1.0132	3.616	1.4376	−0.218	0.759	1061.625	−0.0023
0.8146	0.0835	1.0352	3.772	1.4378	−0.139	0.682	811.692	−0.0031

Table 5 Binary coefficients of McAlister^,s multibody-interaction equations and standard deviations

σ

, for kinematic viscosities at 298.15 K.

Three-body			Four-body
$ν_{12} ({mm}^{2} /s)$	$ν_{2, 1} ({mm}^{2} / s)$	$σ ({mm}^{2} / s)$	$ν_{1112} ({mm}^{2} / s)$	$ν_{1122} ({mm}^{2} / s)$	$ν_{2221} ({mm}^{2} / s)$	$σ ({mm}^{2} / s)$
Formamide (1) + N,N-dimethylacetamide (2)
5.0746	1.7067	0.0135	1.49633	1.02288	0.414879	0.0095

N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3)
1.4621	1.5566	0.0297	0.203471	0.535476	0.685996	0.0071

Formamide (1) + 2-methyl-1-butanol (3)
7.3493	3.6403	0.0355	1.72536	1.67282	1.37031	0.0349

4 Conclusions

Excess molar volumes, viscosities, and refractive index deviations for mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) were obtained from experimental results and fitted by the Redlich–Kister and Cibulka equations. Positive quantities show that dominant factors are physical interactions, and negative values suggested that the main factor in the interactional forces is chemical interactions. McAllister’s multibody-interaction model was used for correlating the kinematic viscosity of binary mixtures with mole fraction. Results showed that McAllister’s four-body equation gave a better result for those three systems.

Acknowledgment

The authors would like to thank the Bu-Ali Sina University for providing the necessary facilities to carry out the research.

References

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Introduction

Experimental

Materials
Apparatus and procedure

Results and discussion

Conclusions

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[1] Cases A.M., Gomez Marigliano A.C., Solimo H.N., . Density, viscosity and refractive index of formamide three carboxylic acids and formamide + carboxylic acid binary mixtures. J. Chem. Eng. Data. 2001;46:712-715.
[Google Scholar]

[2] Cibulka I., . Estimation of excess volume and density of ternary liquid mixtures of non electrolytes from binary data. Collect. Czech. Chem. Commun.. 1982;47:1414-1419.
[Google Scholar]

[3] Fattahi M., Iloukhani H., . Excess molar volume, viscosity, and refractive index study for the ternary mixture 2-methyl-2-butanol (1) + tetrahydrofuran (2) + propylamine (3) at different temperatures. Application of the ERAS-model and Peng–Robinson–Stryjek–Vera equation of state. J. Chem. Thermodyn.. 2010;42:1335-1345.
[Google Scholar]

[4] Gimenez P.G., Lopez J.F., Velasco I., . Excess molar enthalpies and (vapour + liquid) equilibria for mixtures containing N,N-dialkylamides and α,ω-dichloroalkanes. J. Chem. Thermodyn.. 2008;40:212-219.
[Google Scholar]

[5] Gomez Marigliano A.C., Solimo H.N., . Density, viscosity, excess molar volume, viscosity deviation and their correlations for formamide + three alkane-1-ols binary systems. J. Chem. Eng. Data. 2002;47:796-800.
[Google Scholar]

[6] Iloukhani H., Parsa J.B., Saboury A.A., . Excess molar enthalpies of binary mixtures containing N,N-dimethylformamide + six 2-alkanols (c₃–c₈) at 300.15 K. J. Chem. Eng. Data. 2000;45:1016-1021.
[Google Scholar]

[7] Iloukhani H., Zarei H.A., . Excess molar enthalpies of amides + some alkan-2-ols at 298.15 K. Phys. Chem. Liq.. 2004;42:75-79.
[Google Scholar]

[8] Iloukhani H., Khanlarzadeh H., . Densities, viscosities, and refractive indices for binary and ternary mixtures of N,N-dimethylacetamide (1) + 2-methylbutan-2-ol (2) + ethyl acetate (3) at 298.15 K for the liquid region and at ambient pressure. J. Chem. Eng. Data. 2006;51:1226-1231.
[Google Scholar]

[9] Iloukhani H., Rakhshi M., . Excess molar volumes, viscosities, and refractive indices for binary and ternary mixtures of cyclohexanone (1) + N,N-dimethylacetamide (2) + N,N-diethylethanolamine (3) at 298.15, 308.15, and 318.15 K. J. Mol. Liq.. 2009;149:86-95.
[Google Scholar]

[10] Khanlarzadeh K., Iloukhani H., . Application of ERAS-model and Prigogine–Flory–Patterson theory to excess molar volumes for ternary mixtures of 2-chlorobutane (1) + butylacetate (2) + isobutanol (3) at T = 298.15 K. J. Chem. Thermodyn.. 2011;43:1583-1590.
[Google Scholar]

[11] Matthew T.P., Koga Y., . Interactions in 1-propanol-(1,2- and 1,3-)propanediol-H₂O: the effect of hydrophobic vs hydrophilic moiety on the molecular organization of H₂O. J. Phys. Chem. B. 2002;106:7090-7095.
[Google Scholar]

[12] McAllister R.A., . The viscosity of liquid mixtures. AIChE J.. 1960;6:427-431.
[Google Scholar]

[13] Nain A.K., . Densities and volumetric properties of (formamide + ethanol, or 1-propanol, or 1,2-ethanediol, or 1,2-propanediol) mixtures at temperatures between 293.15 K and 318.15 K. J. Chem. Eng. Data. 2007;46:712-715.
[Google Scholar]

[14] Redlich O.J., Kister A.T., . Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem.. 1948;40:345-348.
[Google Scholar]

[15] Resa J.M., Gonzalez C., Goenaga J.M., . Density, refractive index, speed of sound at 298.15 K and vapour-liquid equilibria at 101.3 kPa for binary mixtures of methanol + 2-methyl-1-butanol and ethanol + 2-methyl-1-butanol. J. Chem. Eng. Data. 2005;50:1570-1575.
[Google Scholar]

[16] Zarei H.A., Iloukhani H., . Excess molar enthalpies of formamide + some alkan-1-ols (c₁–c₆) and their correlation at 298.15 K. Thermochim. Acta. 2003;405:123-128.
[Google Scholar]

[17] Zhang R., Zheng D., Pan Y., Lou S., Wu W., Li H., . All-atom simulation and excess properties study on intermolecular interactions of amide-water system. J. Mol. Struct.. 2008;875:96-100.
[Google Scholar]

Densities, viscosities, and refractive indices for binary and ternary mixtures of formamide (1) + N,N-dimethylacetamide (2) + 2-methyl-1-butanol (3) at 298.15 K for the liquid region and at ambient pressure

Abstract

Keywords

Excess molar volume

Deviation in the viscosity and Refractive index

Formamide

N,N-dimethylacetamide

2-Methyl-1-butanol

1 Introduction

2 Experimental

2.1 Materials

2.2 Apparatus and procedure

3 Results and discussion

4 Conclusions

Acknowledgment

References

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