1 Introduction

The thermodynamic and transport properties of binary liquid mixtures help to identify the nature of interactions in the constituent binaries. The compound tert-butyl acetate (t-BAc) is used as a solvent in the manufacture of many industrially many important chemicals such as adhesives and thinners. It is a very effective degreasing agent. Fluorobenzene (FB) is useful solvent for highly reactive species and chlorobenzene (CB) is mainly used as an intermediate in the production of commodities such as herbicides. bromobenzene (BB) is used to introduce a phenyl group via palladium-catalyzed coupling reactions such as the Suzuki reaction. Also it can be used to prepare the Grignard reagent, phenylmagnesium bromide, and as an ingredient in the manufacture of phencyclidine. A literature survey showed that very little work has been done on the mentioned properties for binary mixtures of halogen substituted benzene with branched esters. The interactions between esters and hydrocarbons were reported [1] for the binary mixtures of butyl acetate with some aromatic hydrocarbons. We have previously reported [2, 3] density, viscosity and speed of sound studies of binary mixtures of t-BAc with methanol and hydrocarbons. Herein I present the density, viscosity and speed of sound of t-BAc with FB, CB and BB at 298.15 and 308.15 K.

2 Experimental

2.1 Materials

The FB, CB (Sisco Research Lab Pvt. Ltd., purity > 99.5%), BB, acetone (S.D. Fine Chemicals, purity > 99%) and t-BAc (Spectrochem Pvt. Ltd., purity > 99%), were used after a single distillation. The purity of the solvents, after purification, was ascertained by comparing their densities, viscosities and speed of sound with the corresponding literature values at 298.15 and 308.15 K (Table 1). Binary mixtures were prepared by mass in air-tight stoppered glass bottles. The masses were recorded on an Adairdutt balance to an accuracy of ± 1 × 10−4 kg. Care was taken to avoid evaporation and contamination during mixing. The estimated uncertainty in mole fractions are < 1 × 10−4.

Table 1 Comparison of experimental density (ρ), viscosity (η) and speed of sound (u) of pure liquids with literature values at 298.15 and 308.15 K
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2.2 Apparatus

Densities were determined by using a bicapillary pycnometer as described earlier [4]. The calibration of the pycnometer was done by using conductivity water with 0.99705 kg·m−3 as its density [5] at 298.15 K. The estimated uncertainty of density measurements of solvent and binary mixtures is 0.1 kg·m−3. At least four measurements were made which had an average deviation of ± 0.1 kg·m−3.

The dynamic viscosities were measured using an Ubbelohde suspended level viscometer [4], having a flow time of approximately 300 s at 298.15 K. It was first thoroughly cleaned with warm chromic acid so that there were no obstructions in the capillary and the liquid ran cleanly without leaving drops behind. It was then thoroughly washed by drawing distilled water through it followed by distilled acetone and finally dried by aspirating clean hot air through it. The temperature of the thermostat was controlled within 0.02 K. A mechanical stirrer was used to maintain a uniform temperature. A suitable quantity of the liquid under investigation, usually measured exactly, was introduced into the viscometer with a pipette and allowed 10–15 min to reach the temperature of the thermostat. The liquid was then sucked up and released and the time of out flow between the two marks was determined with an electronic stopwatch reading to 0.01 s. The flow time measurement was repeated a number of times (usually 5 or 6). The different readings did not deviate from the mean by more than 0.2 s. To determine the influence of temperature on viscosity, the time of out flow was measured at 298.15 and 308.15 K. The viscometer was calibrated separately at each temperature with exactly the same volume of a liquid of known viscosity and density, usually water, the density and viscosity of which were taken from the literature [5]. From the densities and times of flow, absolute viscosities of the liquid mixtures were calculated with the help of the equation

$$ \eta = \rho \left( {\frac{at - b}{t}} \right), $$

where η is the viscosity, ρ is density of the liquid, t is flow time, and a and b are the constants for a given viscometer.

To evaluate the viscometer’s constants, the length of the capillary of the viscometer (ι) term is to be corrected as ι′ = ι + 0.05 r, where r being the radius of the viscometer capillary. Since ι is much larger (150–160 mm) as compared to r (0.5 mm), i.e., ι = ι′ and hence the end effect on the viscometer was negligible. Accuracy of the viscosity measurements was ± 0.001 mPa·s.

The speeds of sound (u) in the solutions were measured at a frequency of 2 MHz through the interferometric method (using Mittal’s F-81 model) at (298.15 and 308.15) K (± 0.02 K). The performance of the interferometer was checked by measurements of the speed of sound of pure liquids such as water, benzene, methylbenzene, isopropylbenzene, and FB and comparing the results with the precise literature values. The uncertainty in speed of sound measurements is ± 0.1%.

2.3 Results and Discussion

The experimental values of ρ, η and u of mixtures at (298.15 and 308.15) K as a function of mole fraction are listed in supplemental material. The density values have been used to calculate excess molar volumes VE using the equation

$$ \mathop V\nolimits^{\text{E}} = \sum\limits_{i} {\left( {\left. {\frac{1}{\rho } - \frac{1}{{\mathop \rho \nolimits_{1} }}} \right)} \right.x_{i} M_{i} }, $$
(1)

where ρ denotes the density of solution and x i , ρ i and M i are the mole fraction, density and molar mass of component i, respectively. The viscosity deviations ∆η were calculated using the equation

$$ \Delta \eta \;({\text{mPa}}{\cdot}{\text{s)}} = \eta_{12} - {{x}}_{1} \eta_{1} - {{x}}_{2} \eta_{2} , $$
(2)

where η12 is the viscosity of the mixture and x1, x2 and η1, η2 are the mole fraction and the viscosity of pure components 1 and 2, respectively.

The isentropic compressibility κ S was calculated using the Laplace relation,

$$ \kappa_{S} = \left( {\frac{1}{{u^{2} \rho }}} \right), $$
(3)

and the deviation from isentropic compressibility, ∆κ S , was obtained by the relation,

$$ \Delta \kappa_{S} = \kappa_{S12} { - }\phi_{1} \kappa_{S1} { - }\phi_{2} \kappa_{S2} , $$
(4)

where κS12 is the experimental isentropic compressibility of the mixture, ϕ1, ϕ2 and κS1, κS2 are the volume fraction and isentropic compressibility of the pure components. The volume fraction ϕ i , i = 1, 2, was calculated using the equation

$$ \phi_{i} = \frac{{x_{i} v_{i}^{0} }}{{x_{1} v_{1}^{0} + x_{2} v_{2}^{0} }},\quad i = 1,\; 2 , $$
(5)

where \( v_{i}^{0} \) are the molar volumes of pure components, 1 and 2.

The excess molar volumes and deviations in viscosity and isentropic compressibility were fitted with the Redlich–Kister [6] equation of the type

$$ Y = f_{1} f_{2} \sum\limits_{i = 0}^{n} {a_{i} \left( {f_{1} - f_{2} } \right)^{i} } , $$
(6)

where Y is either VE, or ∆η, or Δκ S , and n is the degree of polynomial, the f1 and f2 are mole fractions for VE and ∆η and volume fraction for Δκ S . Coefficients a i were obtained by fitting Eq. 6 to the experimental results using a least-squares regression method. In each case, the optimum number of coefficients was ascertained from an examination of the variation in standard deviation σ.

σ was calculated using the relation

$$ \sigma (Y) = \left[ {\frac{{\sum {(Y_{\exp {\text {t}}} - Y_{\text{calc}} )^{2} } }}{N - n}} \right]^{1/2} , $$
(7)

where ‘N’ is the number of data points and ‘n’ is the number of coefficients. The calculated values of the coefficients a i along with the standard deviations σ are given in Table 2.

Table 2 Parameters and standard deviations (σ) of Eq. 6 for t-BAc + FB, + CB, and + BB, at 298.15 and 308.15 K and p = 0.089 MPa
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The variation of VE with the mole fraction x1 of t-BAc for FB, CB and BB at 298.15 K is represented in Fig. 1. The values of VE are negative for all the three binary mixtures studied. The negative values of VE fall in the order BB > CB > FB. The negative values of VE indicate that there is a contraction in volume during the mixing process. This signifies the presence of weak specific interactions and geometrical fitting of one component into the empty space or voids of the other component. The excess molar volumes show dependences on the temperature.

Fig. 1
figure 1

Excess molar volumes VE at 298.15 K for (x1) t-BAc + (1 − x1) benzenes: ● fluorobenzene, ■ chlorobenzene, ▲ bromobenzene

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Figure 2 depicts the variation of Δη with the mole fraction x1 of t-BAc. The Δη values are very small and positive for all the three binary mixtures. The Δη values of many organic liquids with aromatic hydrocarbons are characterised by very low (almost ideal nature) values [7,8,9,10,11,12]. The positive Δη values show that there are only weak specific interactions present in the binary mixtures studied. The Δη values show little or no effect of temperature.

Fig. 2
figure 2

Deviations in viscosity (∆η) at 298.15 K for (x1) t-BAc + (1 − x1) benzenes: ● fluorobenzene, ■ chlorobenzene, ▲ bromobenzene

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The kinematic viscosities (v = η/ρ) of the binary mixtures of t-BAc with FB, CB and BB have been correlated with the help of McAllister’s multi body interaction models [13]. The three-body McAllister’s model is defined by

$$ \begin{aligned} \ln \nu & = x_{1}^{3} \ln \nu_{1} + x_{2}^{3} \ln \nu_{2} + 3x_{1}^{2} x_{2} \ln \nu_{12} + 3x_{1} x_{2}^{2} \ln \nu_{21} - \ln \left[ {x_{1} + \frac{{x_{2} M_{2} }}{{M_{1} }}} \right] + 3x_{1}^{2} x_{2} \ln \left[ {\frac{2}{3} + \frac{{M_{2} }}{{3M_{1} }}} \right] \\ & \quad + 3x_{1} x_{2}^{2} \ln \left[ {\frac{1}{3} + \frac{{2M_{2} }}{{3M_{1} }}} \right] + x_{2}^{3} \ln \left[ {\frac{{M_{2} }}{{M_{1} }}} \right], \\ \end{aligned} $$
(9)

where ν12 and ν21 are interaction parameters and M1 and M2 are the molecular weights of components 1 and 2.

The correlating ability of Eq. 9 was tested by calculating the percentage standard deviation (σ %) between the experimental and calculated viscosity as

$$ \, \sigma \;{\text{\% }} = \left[ {\frac{1}{{ (n - m )\sum {{\text{\{(100(}}\nu_{\text{exptl}} { - }\nu_{\text{calcd}} ) /\nu_{\text{exptl}} )^{2} \}^{1/2} } }}} \right], $$
(10)

where ‘n’ represents the number of experimental points and m represents the number of coefficients. Table 3 lists the parameters for McAllister equation and percentage standard deviations.

Table 3 Interaction parameters of McAllister model (v12, v21) and standard deviations (σ) at 298.15 and 308.15 K and p = 0.089 MPa
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The variation of ∆κ S with mole fraction of t-BAc, x1, is shown in Fig. 3. The values of ∆κ S for mixtures of t-BAc with mole fraction, x1, are also shown in Fig. 3. The values of ∆κ S for mixtures of t-BAc with FB, CB and BB are negative which indicates that the mixtures are less compressible than the individual components, an observation which is very well supported by the sign of VE.

Fig. 3
figure 3

Deviations in isentropic compressibility (ΔK S ) at 298.15 K for (ϕ1) t-BAc + (1 − ϕ1) benzenes: ● fluorobenzene, ■ chlorobenzene, ▲ bromobenzene

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The negative values are in the order FB > CB > BB. Both components of all the binary mixtures (t-BAc and halobenzenes) are polar in nature, therefore dipole–dipole interactions are present in the pure components. When a polar component t-BAc is added to another polar components (i.e., halobenzenes), then there is a possibility that the dipole–dipole interactions between the pure components (like molecules) may be disrupted and new dipole–dipole interactions may take place between unlike molecules. If this interaction is strong then the ∆κ S values should be negative. The negative Δκ S values indicate that these dipole–dipole interactions between unlike molecules are stronger than those between the like molecules.

3 Conclusions

In this work I studied the volumetric properties of binary mixtures of t-BAc with FB, CB and BB. Densities were measured over the temperature range at (298.15 and 308.15) K and at pressure 0.087 MPa.

The values of VE are negative for all the three binary mixtures, which indicates that there is a contraction in volume during the mixing process. The Δη values are very small and positive for all the three binary mixtures. These values show little or no effect of temperature, which means there are only weak specific interactions present in the binary mixtures. The values of ∆κ S are negative, which indicates that the mixtures are less compressible, an observation which is very well supported by the sign of the excess molar volumes. For binary mixtures parameters of the Redlich–Kister equation and McAllister’s model were fitted to the experimental VE, Δη and ∆κ S values.