1 Introduction

The study of thermodynamic properties of binary mixtures contributes to an understanding of the behavior of different liquids and their functional groups. This information is very useful in the design of industrial process and in the development of theories for the liquid state and predictive methods. Excess thermodynamic parameters of different mixtures are useful in the study of molecular interactions and arrangements.

The knowledge of physicochemical properties of non-aqueous binary liquid mixtures has relevance in theoretical and applied areas of research, and such results are frequently used in design process (flow, mass transfer or heat transfer calculations) in many chemical and industrial processes [1]. The excess properties derived from these physical property data reflect the physicochemical behavior of the liquid mixtures with respect to the solution structure and intermolecular interactions between the component molecules of the mixture [2, 3].

Study of hydrogen-bonded systems is essential and helpful as hydrogen bond plays a vital role in chemical, physical and biological process. Organic compounds containing electronegative group can interact with compounds containing active hydrogen through hydrogen bond. This type of hydrogen bond takes part in role in the stability of biologically important molecules. Alkanols are polar and self-associated liquids and the dipolar association of alkanols decreases when they are mixed with polar compounds containing various functional groups due to formation of hydrogen bonds between 2-ethyl-1-hexanol and various functional groups in the mixtures over the rupture of hydrogen bonds present in pure 2-ethyl-1-hexanol.

We report here a study of excess/deviation functions in four non-component molecules with 2-ethyl-1-hexanol systems. This is in continuation of our earlier work [4,5,6] on excess/deviation functions of polar liquids with amines. However, in this work a systematic study is reported on excess/deviation functions of non-component molecules with 2-ethyl-1-hexanol over the entire composition range and at temperature (T) ranging from 303.15 to 313.15 K. The results are discussed in terms of intermolecular forces between the different components molecules in the binary mixture are more than the average intermolecular forces existing between the similar molecules of pure components.

2 Procedure

2.1 Materials

The 3-methoxyaniline, benzyl chloride and 3-methylaniline liquids were sigma Aldrich samples. Table 1 contains information regarding their source, purification method, final purity and analysis method. Values of density, speed of sound, and viscosity are presented in Table 2. These values are in good agreement with the data available in the literature [7,8,9,10,11,12,13,14].

Table 1 List of chemicals with details of source, CAS number, purity and water content
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Table 2 Densities, viscosity and speeds of sounds data of pure components at different temperatures and 0.1 MPa pressure
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2.2 Apparatus and procedure

All the binary liquid mixtures were prepared by weighing required amounts of pure liquids in an electric balance (ER-120A, Afoset) with a precision of ± 0.01 mg by syringing each component into air-tight stopper bottles to minimize evaporation losses. The uncertainty of the mole fraction was ± 1 × 10−4.

The details of the density, speed of sound and viscosity methods and their measurement techniques were described elsewhere [15]. The uncertainty of density measurement for liquid mixtures is ± 0.2 × 10−4 g cm3. The uncertainty in the measured speed of sound is ± 0.053 m s−1. The experimental uncertainty of viscosity estimated as ± 1.13%. The temperature of the liquids during the measurements was maintained within an uncertainty of ± 0.01 K in an electronically controlled thermostatic water bath.

2.3 Theory

The excess thermodynamic/deviation functions were calculated by using the following equations

$$V^{E} = V \, {-} \, (x_{1} V_{1} + \, x_{2} V_{2} )$$
(1)
$$\Delta h = h - (x_{1} h_{1} + x_{1} h_{1} )$$
(2)
$$G^{*E} = RT[\ln hV - \, (x_{1} \ln h_{1} V_{1} + x_{2} \ln h_{2} V_{2} )$$
(3)

where η, η1,η2, V, V1 and V2 are viscosities and mixture molar volumes and pure components respectively.

The isentropic compressibilities were calculated from the relation

$$\kappa_{s} = \left( {u^{2} \rho } \right)^{ - 1}$$
(4)

where \(\rho\) is the density and \(u\) is the speed of sound of the binary mixture.

Further, the excess isentropic compressibilities (\(k_{s}^{E}\)) are calculated from the following relations recommended by Benson and Kiyohara [16]

$$k_{s}^{E} = k_{s} - k_{s}^{id}$$
(5)
$$k_{s}^{id} = \sum\limits_{{\text{i} = \text{1}}}^{\text{2}} {\varphi_{\text{i}} \left[ {\kappa_{{\text{s,}i}} + \frac{{TV_{i} \left( {\alpha_{i}^{\text{2}} } \right)}}{{C_{{p\text{,}i}} }} } \right] - \left\{ {\frac{{T\left( {\sum\nolimits_{{i = \text{1}}}^{2} {x_{i} V_{i} } } \right)\left( {\sum\nolimits_{{i = \text{1}}}^{\text{2}} {\varphi_{i} \alpha_{i} } } \right)^{\text{2}} }}{{\sum\nolimits_{{i = \text{1}}}^{\text{2}} {x_{i} C_{p,i} } }} } \right\}}$$
(6)

where \(\varphi_{\text{i}}\), \(C_{{p\text{,}i}}\), \(V_{i}\), \(\kappa_{{\text{s,}i}}\) and \(\alpha_{i}\) are the volume fraction, molar heat capacity, molar volume, isentropic compressibility and coefficient of isobaric thermal expansion of pure components respectively.

Excess/deviation functions (VE, ∆η and κ Es ) values are fitted to a Redlich–Kister polynomial equation [17]

$$Y^{\text{E}} = x_{1} x_{2} \sum\limits_{i = 0}^{j} {A_{i} \left( {1 - 2x_{1} } \right)^{i} }$$
(7)

where YE is the VE, ∆η and \(\kappa_{s}^{E}\). Coefficientsn values Ai are determined by using the method of least-squares. The standard deviation σ (YE) were calculated by the formula as follows

$$\sigma (Y^{E} ) = [ \, \varSigma (Y^{E}_{exp} - \, Y^{E}_{cal} )^{2} /(m - n)]^{1/2}$$
(8)

where m is the total number of experimental points and n is the number of parameters. The coefficients, Ai and corresponding standard deviation values (σ) are presented in Table 3.

Table 3 Coefficients of Redlich–Kister equation and standard deviation (σ) values for liquid mixtures of 2-ethyl-1-hexanol with various functional groups at T = (303.15–313.15) K
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3 Results and discussion

The experimental density, speed of sound and viscosity data and their excess/deviation values for the 2-ethyl-1-hexanol with various functional groups at various temperatures are given in Tables 2 and 4. All the excess/deviation values of these parameters VE, κ Es Δη and G*E at various temperatures are represented graphically in Figs. 1, 2, 3 and 4.

Table 4 Density (\(\rho\)), excess molar volumes (VE), speed of sound (u), excess isentropic compressibility (κ Es ), viscosity (η), deviation in viscosity (Δη) and excess Gibbs energy of activation of viscous flow (G*E) of binary liquid mixtures of 2-ethyl-1-hexanol with various functional groups at T = (303.15 to 313.15) K and 0.1 MPa pressure
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Fig. 1
figure 1

Curves of excess molar volume (VE) with mole fraction for the binary mixtures of 2-ethyl-1-hexanol with benzyl chloride (square); 3-methylaniline (circle):3-methoxyaniline (triangle) and 2,6-dimethylcyclohexanone (inverted triangle) at 303.15 K

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Fig. 2
figure 2

Curves of excess isentropic compressibility with mole fraction for the binary mixtures of 2-ethyl-1-hexanol with benzyl chloride (square); 3-methylaniline (circle):3-methoxyaniline (triangle) and 2,6-dimethylcyclohexanone (inverted triangle) at 303.15 K

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Fig. 3
figure 3

Variation of deviation in viscosity (Δη) with mole fraction for the binary mixtures of 2-ethyl-1-hexanol with benzyl chloride (square); 3-methylaniline (circle):3-methoxyaniline (triangle) and 2,6-dimethylcyclohexanone (inverted triangle) at 303.15 K

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Fig. 4
figure 4

Excess Gibbs energy of activation of viscous flow (G*E) with mole fraction (x1) of 2-ethyl-1-hexanol with benzyl chloride (square); 3-methylaniline (circle):3-methoxyaniline (triangle) and 2,6-dimethylcyclohexanone (inverted triangle) at 303.15 K

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All the excess/deviation values of these parameters may be explained qualitatively in terms of

  1. 1.

    molecular interactions between like/unlike molecules and the difference in size and shape of the unlike components

  2. 2.

    Possible H-bond interaction between 2-ethyl-1-hexanol and various functional groups in the mixtures having 2-ethyl-1-hexanol as a proton donor

  3. 3.

    Dipole–dipole interactions between polar–polar components

The magnitude of excess values of VE and κ Es from ideality of the systems that can be negative, positive, or zero may be explained as a balance between positive contributions (hydrogen bond rupture and dispersive interactions between unlike molecules) and negative contributions (intermolecular dipolar interactions, geometrical fitting between components, intermolecular association complexes between unlike molecules)

The experimental values indicate that the negative effects are dominant over positive ones in all the mixtures, since the excess values of VE and κ Es for all the binary systems is negative over the whole concentration range at various temperatures. In the present systems, negative sign of VE shows that the predominance of formation of hydrogen bonds between 2-ethyl-1-hexanol and various functional groups in the mixtures over the rupture of hydrogen bonds present in pure 2-ethyl-1-hexanol [18, 19].

The negative values of VE for the four systems are in the following order:

  • 2-Ethyl-1-hexanol + 2, 6-dimethylcyclohexanone > 2-ethyl-1-hexanol + 3-methoxyaniline > 2-ethyl-1-hexanol +3-methylaniline > 2-ethyl-1-hexanol + benzyl chloride

The value at the minima for the system (2-ethyl-1-hexanol + 2,6-dimethylcyclohexanone) is slightly more negative than that of remaining various functional groups, and this may be due to the ability of 2,6-dimethylcyclohexanone to form stronger hydrogen bonds with 2-ethyl-1-hexanol than various functional groups with 2-ethyl-1-hexanol. Hence, above order was justified. In the present systems, negative values of excess isentropic compressibilities shows that the interaction between the unlike molecules exceed the structure breaking effect between the like molecules.

The negative values of κ Es for the four systems are in the following order:

  • 2-Ethyl-1-hexanol + 3-methoxyaniline > 2-ethyl-1-hexanol + 3-methylaniline > 2-ethyl-1-hexanol + benzyl chloride > 2-ethyl-1-hexanol + 2, 6-dimethylcyclohexanone

Specific interactions are strong (more effect that is inductive) between 2-ethyl-1-hexanol and 3-methoxyaniline molecules thereby showing the highest negative excess isentropic compressibilities value for their binary mixture.

The sign and magnitude of Δη and G*E depend on the combined effect of factors such as molecular size, shape, and intermolecular forces [20]. The positive values ofΔη and G*E indicates the presence of specific interactions such as the formation of hydrogen bond between unlike molecules and negative values indicates that mutual loss of specific interactions in like molecules outweigh the specific interactions between unlike molecules [18, 21].

In the present study, the positive values of Δη and G*E for these systems indicates that the strength of interaction between the components in binary mixtures and the formation of an association complex [22, 23]. This results in a liquid structure where the flow is rather difficult than would be expected on the basis of the viscosities of the pure components.

3.1 Partial molar properties

The interpretations of excess partial molar properties (\(\overline{V}_{\text{m,1}}^{\text{E}}\), \(\overline{V}_{\text{m,2}}^{\text{E}}\), \(\overline{K}_{\text{s,m,1}}^{\text{E}}\) and \(\overline{K}_{\text{s,m,2}}^{\text{E}}\)) and excess partial molar properties at infinite dilution(\(\overline{V}_{\text{m,1}}^{{^\circ {\text{E}}}}\), \(\overline{V}_{\text{m,2}}^{{^\circ {\text{E}}}}\), \(\overline{K}_{\text{s,m,1}}^{{^\circ {\text{E}}}}\) and \(\overline{K}_{\text{s,m,2}}^{{^\circ {\text{E}}}}\)) of components 2 have previously been described [24]. Tables 5 and 6 shows that the values of \(\overline{V}_{\text{m,1}}^{{^\circ {\text{E}}}}\), \(\overline{V}_{\text{m,2}}^{{^\circ {\text{E}}}}\), \(\overline{K}_{\text{s,m,1}}^{{^\circ {\text{E}}}}\) and \(\overline{K}_{\text{s,m,2}}^{{^\circ {\text{E}}}}\) are negative over the whole composition range at experimental temperatures. The observed negative values suggest that the hetero molecular association interactions are stronger than the self-association of molecular interactions of like molecules in the mixtures [25, 26].

Table 5 The values of \(\overline{V}_{\text{m,1}}^{^\circ }\), \(V_{\text{m,1}}^{ *}\), \(\overline{V}_{\text{m,1}}^{{^\circ {\text{E}}}}\), \(\overline{V}_{\text{m,2}}^{^\circ }\), \(V_{\text{m,2}}^{ *}\) and \(\overline{V}_{\text{m,2}}^{{^\circ {\text{E}}}}\) of the components for 2-ethyl-1-hexanol with various functional groups of binary mixtures at T = (303.15–313.15) K
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Table 6 The values of \(\overline{K}_{\text{s,m,1}}^{^\circ }\), \(K_{\text{s,m,1}}^{ *}\), \(\overline{K}_{\text{s,m,1}}^{{^\circ {\text{E}}}}\), \(\overline{K}_{\text{s,m,2}}^{^\circ }\), \(K_{\text{s,m,2}}^{ *}\) and \(\overline{K}_{\text{s,m,2}}^{{^\circ {\text{E}}}}\) of the components 2-ethyl-1-hexanol with various functional groups of binary mixtures at T = (303.15–313.15) K
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4 Conclusions

Densities, viscosities and speeds of sound of binary mixtures of 2-ethyl-1-hexanol with benzyl chloride,3-methylaniline,3-methoxyaniline and 2,6-dimethylcyclohexanone have been measured at different temperatures and derived parameters along with their excess/deviations values, and also excess partial molar properties at infinite dilution (\(\overline{V}_{\text{m,1}}^{{^\circ {\text{E}}}}\), \(\overline{V}_{\text{m,2}}^{{^\circ {\text{E}}}}\), \(\overline{K}_{\text{s,m,1}}^{{^\circ {\text{E}}}}\) and \(\overline{K}_{\text{s,m,2}}^{{^\circ {\text{E}}}}\)) were calculated. The results are analyzed in terms of the specific interactions through the hetero molecular association between the components of the mixtures, resulting in the formation of association complexes.