Speed of sound and isentropic compressibility of benzonitrile, chlorobenzene, benzyl chloride and benzyl alcohol with benzene from various models at temperature range 298.15–313.15 K

R.K. Shukla; Atul Kumar; Naveen Awasthi; Urvashi Srivastava; Kirti Srivastava

doi:10.1016/j.arabjc.2014.07.013

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Original article

10 (

); 895-905

doi:

10.1016/j.arabjc.2014.07.013

Speed of sound and isentropic compressibility of benzonitrile, chlorobenzene, benzyl chloride and benzyl alcohol with benzene from various models at temperature range 298.15–313.15 K

R.K. Shukla^{^a,⁎}, Atul Kumar^{^b}, Naveen Awasthi^{^a}, Urvashi Srivastava^{^c}, Kirti Srivastava^{^d}

a Department of Chemistry, V.S.S.D. College, Kanpur 208002, India

b Department of Chemistry, PSIT, Kanpur, India

c Department of Physics, PSIT, Kanpur, India

d Department of Chemistry, JSS Academy of Technical Education, Noida, 201301, India

⁎Corresponding author. Address: Department of Chemistry, V.S.S.D. College, Nawabganj, Kanpur 208002, India. Tel.: +91 0512 2560070, mobile: +91 9838516217; fax: +91 2563842. rajeevshukla47@rediffmail.com (R.K. Shukla)

Received: 2012-10-27, Accepted: 2014-7-14, Published: 2014-11-01

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

Densities and speed of sound were measured for the binary liquid mixtures formed by benzonitrile, chlorobenzene, benzyl chloride and benzyl alcohol with benzene at 298.15, 303.15, 308.15 and 313.15 K and atmospheric pressure over the whole concentration range. Prigogine–Flory–Patterson model (PFP), Ramaswamy and Anbananthan (RS) model and model suggested by Glinski, were utilized to predict the associational behavior of weakly interacting liquids. The measured properties were fitted to Redlich–Kister polynomial relation to estimate the binary coefficients and standard errors. An attempt has also been made to study the molecular interactions involved in the liquid mixture from observed data. Furthermore, the McAllister multi body interaction model was also used to correlate the binary properties. These models were compared and tested for different systems showing that the associated processes yield fair agreement between theory and experiment as compared to non-associated processes.

Keywords

Speed of Sound

Prigogine–Flory–Patterson

McAllister

Ramaswamy and Anbananthan

Isentropic Compressibility

Redlich–Kister

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1 Introduction

Physicochemical behavior and molecular interactions occurring in a variety of liquid mixtures and solutions can be studied with the help of ultrasonic velocity (Shukla et al., 2010). Data on sound velocity offer a convenient method for determining certain thermo dynamical properties of liquids and liquid mixtures, which are not obtained by other methods. As a part of research concerning the thermo chemical studies on new working fluid pair, we present here some useful data on speed of sound and isentropic compressibility for the mixture of benzonitrile, chlorobenzene, benzyl chloride and benzyl alcohol with benzene at 298.15, 303.15, 308.15 and 313.15 K and atmospheric pressure over the whole concentration range. These data were analyzed in terms of Ramaswamy and Anbananthan (RS) model (Ramaswamy and Anbananthan, 1981), model suggested by Glinski (2003), Prigogine–Flory–Patterson (PFP) model Abe and Flory, 1965; Prigogine et al., 1957; Patterson and Rastogi, 1970 ., First two models, RS and model devised by Glinski are based on the association constant as adjustable parameters whereas PFP and others are based on the additivity of liquids. For such purposes, we selected the liquids containing poor ability to associate. From these results, deviations in ultrasonic velocity, Δu were calculated and fitted to the Redlich–Kister polynomial equation (Redlich and Kister, 1948) to derive the binary coefficients and the standard errors. An attempt has also been made to correlate the experimental data with the McAllister multi body interaction model (McAllister, 1960) which is based on Eyring’s theory of absolute reaction rates and for liquids the free energy of activation is additive on a number fraction and those interactions of like and unlike molecules. The associational behavior of liquids and their correlation with molecular interactions have also been made using different liquid state models. This is our first attempt to correlate all the models (associated and non-associated) simultaneously in predicting the associational behavior of binary liquid mixtures from sound velocity data.

Extensive work has been carried out by us (Shukla et al., 1989, 1993, 2008a,b, 2012 ) to investigate the liquid state through analysis of ultrasonic propagation parameters and to correlate ultrasonic velocity with other physical and thermodynamic parameters. Objective underlying in the present work is to find out the applicability of various models in binary liquid mixtures.

2 Experimental section

2.1

2.1 Materials

High purity and AR grade samples of benzonitrile, chlorobenzene, benzyl chloride and benzyl alcohol with benzene used in this experiment were obtained from Merck Co. Inc., Germany and purified by distillation in which the middle fraction was collected. The liquids were stored in dark bottles over 0.4 nm molecular sieves to reduce water content and were partially degassed with a vacuum pump. The purity of each compound was checked by gas chromatography and the results indicated that the mole fraction purity was higher than 0.99. The purity of chemicals used was confirmed by comparing the densities and ultrasonic speeds with those reported in the literature as shown in Table 1.

Table 1 Comparison of density and sound velocity with literature data for pure components at 293.15, 298.15, 303.15, 308.15 and 313.15 K.

Compound	α × 10³ (K)	β_T × 10¹² (Pa)	V/cm³ mol⁻¹	T	ρ_exp/g cm⁻³	ρ_lit/g cm⁻³	u_exp/ms⁻¹	u_lit/ms⁻¹
Benzene	1.218023	94.6097	89.3196	298.15	0.8732	0.8736^a	1310.8	1299.73^a
	1.21875	94.7791	89.9366	303.15	0.8686	0.8683^b	1271.8	1281.70^c
	1.228696	97.1185	90.7306	308.15	0.8653	–	1276.4	–
	1.24239	100.402	91.1329	313.15	0.8578	0.8576^b	1259.2	–
Benzonitrile	0.997994	52.0415	103.0787	298.15	1.0003	1.0006^b	1603.3	–
	1.008302	53.6709	103.5653	303.15	0.9980	0.9978^b	1592.6	1578.4^c
	1.010971	54.0982	104.8414	308.15	0.9941	–	1582.4	–
	1.016819	55.0424	105.2459	313.15	0.9919	–	1570.7	–
Chlorobenzene	0.99078	50.9211	102.2343	298.15	1.1004	1.1009^b	1273.4	–
	0.997456	51.9574	102.7476	303.15	1.0961	1.0955^b	1262.6	1249.41^a
	1.004295	53.0335	102.8414	308.15	1.0922	1.0926^d	1224.3	1235.6^d
	1.026654	56.6551	104.0132	313.15	1.0883	1.0878^d	1204.8	1214.8^d
Benzyl chloride	1.059322	62.2374	115.6495	298.15	1.0899	–	1343.6	–
	1.067131	63.6240	116.1589	303.15	1.0890	1.0897^e	1327.3	1312.3^c
	1.070387	64.2080	116.6620	308.15	1.0894	–	1314.2	–
	1.074842	65.0132	116.8921	313.15	1.0810	1.0806^b	1303.5	–
Benzyl alcohol	1.015504	54.8292	103.8210	298.15	1.0417	1.0413^b	1532.4	–
	1.021907	55.8729	104.2413	303.15	1.0370	1.0376^b	1501.5	1510.8^c
	1.033784	57.8437	105.4509	308.15	1.0372	–	1496.5	–
	1.063372	62.9539	107.9780	313.15	1.0366	–	1478.1	–

a Reference AL-Kandary et al. (2006).

b Reference Riddick et al. (1986).

c Reference Ali et al. (2005).

d Reference AL-Jimaz et al. (2007).

e Reference Askar and Ali (2012).

2.2

2.2 Apparatus and procedure

Before each series of experiments, we calibrated the instrument at atmospheric pressure with doubly distilled water. The uncertainty in the density measurement was within ±0.7 kg m⁻³ (about 0.06%). The densities of the pure components and their mixtures were measured with the bi-capillary. The liquid mixtures were prepared in terms of mass in an air tight stoppered bottle using an electronic balance model SHIMADZUAX-200 accurate up to ±0.1 mg. The average uncertainty in the composition of the mixtures was estimated to be less than ±0.0001. All molar quantities were based on the IUPAC relative atomic mass table.

Crystal controlled variable path ultrasonic interferometer supplied by M/s Mittal enterprises (model-05F), New Delhi (India), operating at a frequency of 2 MHz was used in the ultrasonic measurements with an accuracy of ±1.13% which are reproducible. Isentropic compressibility, β_s, was calculated from the relation,

(1)

β_{s} = u^{- 2} ρ^{- 1}

where ρ is the density and u is the ultrasonic velocity. The estimated error in the calculation of isentropic compressibility was found to be ±2.5 T Pa⁻¹.

The results are listed in Table 1 together with literature values (Riddick et al., 1986; Askar and Ali, 2012; Ali et al., 2005; AL-Kandary et al., 2006; AL-Jimaz et al., 2007; Timmermans, 1950 ) for comparison.

3 Modeling

3.1

3.1 Ramaswamy and Anbananthan model

Ramaswamy and Anbananthan (1981) proposed the model based on the assumption of linearity of acoustic impedance with the mole fraction of components. Further it is assumed, that an equilibrium physical property such as viscosity, refractive index, surface tension etc which are based on linearity can be predicted (Aralaguppi et al., 1999; Shukla et al., 2011; Ali and Tariq, 2008; Rodrignez et al., 2001 ). Glinski (2003) assumed that when solute is added to solvent the molecules interact according to the equilibrium as:

(2)

A + B \leftrightarrow AB

and the association constant K_as can be defined as;

(3)

K_{as} = \frac{[AB]}{[A] [B]}

where [A] is amount of solvent and [B] is amount of solute in the liquid mixture.

By applying the condition of linearity in speed of sound with composition

(4)

u_{cal} = x_{A} u_{A} + x_{AB} u_{AB}

where x_A, x_AB, u_A and u_AB and u_cal are the mole fraction of A, mole fraction of associate AB, ultrasonic velocity of A, ultrasonic velocity of associate AB and calculated ultrasonic velocity, respectively. The associate AB cannot be obtained in its pure form. Following simplifications have been made in Eq. (4), firstly, molar concentration term should be replaced by activities for concentrated solution and second, the equilibrium reaction is not complete by definition; i.e. there are also molecules of non associated component present in the liquid mixture even prevailing in the high solute content. Eq. (4) takes the form,

(5)

u_{cal} = [x_{A} u_{A} + x_{B} u_{B} + x_{AB} u_{AB}]

The general idea of this model can be, however, exploited as;

(6)

K_{as} = \frac{[AB]}{(C_{A} - [AB]) (C_{B} - [AB])}

where C_A and C_B are initial molar concentrations of the components. One can take any value of K_as and calculate the equilibrium value of [AB] for every composition of the mixture as well as [A] = C_A − [AB] and [B] = C_B − [AB]. Replacing molar concentration by activities for concentrated solution, Eq. (6) becomes,

(7)

K_{as} = \frac{a_{AB}}{(a_{A} - a_{AB}) (a_{B} - a_{AB})}

where a_A, a_B and a_AB are the activity of component A, component B and associate, AB, respectively. Taking equimolar activities which are equal to;

a_{A}^{'} = a_{A} - a_{AB} and a_{B}^{'} = a_{B} - a_{AB}

where a′_A and a′_B are the activities of [A] and [B] in equimolar quantities, respectively.

From Eq. (7) one can obtain the value of K_as as;

(8)

K_{as} = \frac{a_{AB}}{a_{A} a_{B} - a_{A} a_{AB} - a_{B} a_{AB} + a_{AB}^{2}} = \frac{a_{AB}}{a_{A}^{'} . a_{B}^{'}}

Similarly, assume any value of ultrasonic velocity for hypothetical pure component AB, and calculate the ultrasonic velocity of liquid mixture, u_cal by substituting the value of association constant obtained from Eq. (8) in Eq. (5). Now, it is possible to compare the ultrasonic velocity calculated using Eq. (5) with the experimental values. On changing both the adjustable parameters K_as and u_AB gradually, one can get different values of the sum of squares of deviations,

(9)

S = \sum {(u_{obs} - u_{cal})}^{2}

where u_obs and u_cal are the observed and calculated equilibrium properties, respectively.

The minimum value of S can be obtained theoretically by a pair of the fitted parameters. But we found that for some K_as and u_AB, the value of S is high and changes rapidly, and for others, it is low and changes slowly when changing the fitted parameters. The condition which is prevailing in the process of adjustment is that the value of u_AB should not be much lower than the lowest observed ultrasonic velocity of the system or much higher than the highest one. Quantitatively, it should be reasonable to accept the pair of adjustable parameters K_as and u_AB which has the physical sense and which reproduces the experimental physical property satisfactorily.

On inspecting the results obtained from Ramaswamy and Anbananthan model, Glinski (2003) suggested the equation assuming additivity with the volume fraction, ϕ of the components, the refined version of Natta and Baccaredda model (Natta and Baccaredda, 1948) as,

(10)

u_{cal} = \frac{u_{A} u_{B} u_{AB}}{ϕ_{A} u_{B} u_{AB} + ϕ_{B} u_{A} u_{AB} + ϕ_{AB} u_{A} u_{B}}

where u_cal is the theoretical ultrasonic velocity of binary liquid mixture, ϕ_A and ϕ_B are the volume fractions of components A and B and u_A, u_B and u_AB are the ultrasonic velocity of components A, B and AB. The numerical procedure and determination of association constant, K_as, were similar to those described before and the advantage of this method as compared with the earlier one was that the data on densities of liquid mixture are not necessary except those of pure components needed to calculate the volume fractions.

3.2

3.2 Prigogine–Flory–Patterson model

The original cell model of Prigogine (Prigogine and Saraga, 1952) for spherical chain molecules uses a dependence of the configurational energy on volume equivalent to the Lennard–Jones (6, 12) energy–distance relation i.e.

(11)

\tilde{U} (\tilde{V}) = - 2 {\tilde{V}}^{- 2} + {\tilde{V}}^{- 4}

More generally for an (m, n) potential,

(12)

\tilde{U} (\tilde{V}) = \frac{(- n {\tilde{V}}^{- m / 3} + m {\tilde{V}}^{- n / 3})}{(n - m)}

This leads to the following equation of state

(13)

\frac{\tilde{P} \tilde{V}}{\tilde{T}} = {(1 - b {\tilde{V}}^{1 / 3})}^{- 1} + \frac{mn}{3 (n - m)} ({\tilde{V}}^{- n / 3} - {\tilde{V}}^{- m / 3})

where b is a packing factor and equals (m/n)^1/(ⁿ⁻^m⁾.

Flory and collaborators (Abe and Flory, 1965) used the cell partition function of Hirschfelder and Eyring and a simple Van der Waals energy–volume relation, $\tilde{U} = - {\tilde{V}}^{- 1}$ , by putting m = 3, n → ∞ so that the Flory equations for the mixing functions and partial molar quantities may be obtained from the general corresponding state equations given by making this particular choice of (m, n).

Patterson and Rastogi (1970) have drawn attention to the close connection between the Flory theory and corresponding state theory of Prigogine employing a simple cell model of the liquid state. The equation of state for the materials conforming to the principle of corresponding states can be expressed in a universal form through the use of suitable characteristic values i.e. (reduction parameters) P^∗, V^∗, T^∗ for the pressure, volume and temperature, respectively.

In order to extend the corresponding state theory to deal with the surface tension, Patterson and Rastogi (1970) used the reduction parameters as,

(14)

σ^{*} = k^{1 / 3} P^{* 2 / 3} T^{* 1 / 3}

called the characteristic surface tension of the liquid. Here k is the Boltzmann constant. Paterson and Rastogi extended the simple cell model theory of the surface tension of spherical molecules by Prigogine and Saraga (1952) to the case of chain molecules. A segment experiences an increase in the configurational energy equal to

- M \tilde{U} (\tilde{V})

due to the loss of a fraction, M, of its nearest neighbors at the surface while moving from the bulk phase to the surface phase. Its most suitable value ranges from 0.25 to 0.29. In the present case the value of M is taken as 0.29 throughout the calculation. The cell partition function of a segment at the surface is increased due to the loss of constraining nearest neighbors in one direction, so that,

(15)

\frac{Φ_{surface}}{Φ_{bulk}} = \frac{({\tilde{V}}^{1 / 3} - 0.5 b)}{({\tilde{V}}^{1 / 3} - b)}

Here b is a packing fraction given by $b = {(\frac{m}{n})}^{1 / (n - m)}$ and tends to unity when n → ∞.

According to Prigogine and Saraga the reduced surface tension is given by

(16)

\tilde{σ} {(\tilde{V})}^{2 / 3} = - M \tilde{U} (\tilde{V}) - T \ln \frac{({\tilde{V}}^{1 / 3} - 0.5 b)}{({\tilde{V}}^{1 / 3} - b)}

The surface energy and entropy are given by

(17)

{\tilde{σ}}_{u} = - M \tilde{U} (\tilde{V}); {\tilde{σ}}_{S} = \ln \frac{({\tilde{V}}^{1 / 3} - 0.5 b)}{({\tilde{V}}^{1 / 3} - b)}

With the particular (3, ∞) choice of m, n potential or the Flory model, Eq. (17) takes the form as;

(18)

\tilde{σ} (\tilde{V}) = [M {\tilde{V}}^{- 5 / 3} - (\frac{{\tilde{V}}^{1 / 3} - 1.0}{\tilde{V^{2}}}) \ln (\frac{{\tilde{V}}^{1 / 3} - 0.5}{{\tilde{V}}^{1 / 3} - 1.0})]

Thus on the basis of the Flory theory, surface tension of liquid mixture is given by the expression,

(19)

σ = σ^{*} \tilde{σ} (\tilde{V})

(20)

u = {(\frac{σ}{6.3 \times 10^{- 4} ρ})}^{2 / 3}

All the notations used in the above equations have their usual significance as detailed out by Flory.

3.3

3.3 McAllister multi body interaction model

Multi body interaction model of McAllister (McAllister, 1960) is widely used for correlating the viscosity of liquid mixtures with mole fraction which is based on the assumption of additivity. The three body interaction model for ultrasonic velocity is defined as;

(21)

\ln u = x_{1}^{3} \ln u_{1} + 3 x_{1}^{2} u_{2} \ln a + 3 x_{1} x_{2}^{2} \ln b + x_{2}^{3} \ln u_{2} - [\ln (x_{1} + x_{2} M_{2} / M_{1})] + 3 x_{1}^{2} x_{2} [\ln (2 + M_{2} / M_{1}) / 3] + 3 x_{1} x_{2}^{2} \ln [(1 + 2 M_{2} / M_{1}) / 3] + x_{2}^{3} \ln (M_{2} / M_{1)}

and four body model is given by,

(22)

\ln u = x_{1}^{4} \ln u_{1} + 4 x_{1}^{3} x_{2} \ln a + 6 x_{1}^{2} x_{2}^{2} \ln b + 4 x_{1} x_{2}^{3} \ln c + x_{2}^{4} \ln u_{2} - \ln (x_{1} + x_{2} M_{2} / M_{1})] + 4 x_{1}^{3} x_{2} \ln [(3 + M_{2} / M_{1}) / 4] + 6 x_{1}^{2} x_{2}^{2} \ln [(1 + M_{2} / M_{1}) / 2 + 4 x_{1} x_{2}^{3} \ln [(1 + 3 M_{2} / M_{1}) / 4] + x_{2}^{4} \ln (M_{2} / M_{1})

where u, x₁, u₁, M₁, x₂, u₂ and M₂ are the ultrasonic velocity of mixture, mole fraction, ultrasonic velocity and molecular weight of pure component 1 and 2, respectively; a, b and c are adjustable parameters that are characteristic of the system. The coefficients a, b, and c were calculated using the least square procedure and the results of estimated parameters and standard deviation between the calculated and experimental values are presented in Table 3.

4 Results & discussion

The interferometer technique was used for all the reported results. Data were taken from 298.15 K up to 313.15 K in temperature intervals of 5 K. Pure component results and comparison with literature values (Riddick et al., 1986; Askar and Ali, 2012; Ali et al., 2005; AL-Kandary et al., 2006; AL-Jimaz et al., 2007; Timmermans, 1950 ) are provided in Table 1. The reported uncertainty ±1.36% is the highest uncertainty found from all the data points. The mixture data are presented in Tables 5 and 6.

Relations between association phenomena in liquids were analyzed earlier (Shukla et al., 2011) by considering Van der Waals equation of state which was based only on simple averaged geometrical deviations without analyzing the system in terms of equilibrium. The association phenomenon has been related usually to the deviation of different quantities from additivity. Ramaswamy and Anbananthan derived the model based on the assumption of linearity of acoustic impedance with the mole fraction of components which was corrected (Glinski, 2003) and tested to predict the associational behavior. The quantities analyzed were refractive index, molar volume, viscosity, intermolecular free length and many others (Ali and Tariq, 2008; Rodrignez et al., 2001; Shukla et al., 2007; Pandey et al., 2008; Pandey and Verma, 2001 ). The results of fittings obtained from the model were utilized properly. The basic doubt regarding this model except the assumption of linearity of ultrasonic velocity with mole fraction is that these liquids have poor affinity to form dimmers. The calculations were performed using a computer program which allows easy fittings of both the adjustable parameters simultaneously or the parameters were changed manually.

Values of thermal expansion coefficient (α) and isothermal compressibility needed in the PFP model were obtained from the equation which has already been tested in many cases by us (Shukla et al., 2011) and others (Shukla et al., 2007; Pandey et al., 2008; Dey et al., 2006 ).

The standard deviation Δσ can be represented mathematically by Redlich–Kister polynomial equation (Redlich and Kister, 1948) for correlating the experimental data as;

(23)

y = x_{i} (1 - x_{1}) \sum_{i = 0}^{p} A_{i} {(2 x_{1} - 1)}^{i}

where y refers to deviation in ultrasonic velocity (Δu), x₁ is the mole fraction and A_i is the coefficient. The values of coefficients were determined by a multiple regression analysis based on the least square method and are summarized along with the standard deviations between the experimental and fitted values of the respective function in Table 2. The standard deviation values for speed of sound and isentropic compressibility lie between 2.58 and 35.33 and 1.22 and 4.27 × 10², respectively with the largest value corresponding to benzene + benzyl alcohol mixture at 313.15 K for ultrasonic velocity and benzene + benzonitrile mixture for isentropic compressibility at 308.15 K.

Table 2 Coefficients of the Redlich–Kister equation and standard deviations (δ) for speed of sound and isentropic compressibility of binary liquid mixtures at various temperatures.

	Speed of sound (U/ms⁻¹)							Isentropic compressibility (β_s/TPa⁻¹)
	T	A₀	A₁	A₂	A₃	Std dev (δ)		A₀ × 10⁻³	A₁ × 10⁻³	A₂ × 10⁻³	A₃ × 10⁻³	Std dev (δ) × 10⁻²
Benzene + benzonitrile
Δu	298.15	368.27	−7.57	−29.26	583.75	13.54	Δβ_s	−1.66	2.29	−4.33	−9.30	1.22
	303.15	396.90	−31.44	20.54	338.40	10.95		−1.69	2.33	−4.43	−9.30	1.23
	308.15	396.87	−74.15	−58.11	664.38	14.51		−1.74	2.40	−4.54	−9.60	4.27
	313.15	418.93	279.76	−191.59	−650.15	15.18		−1.80	2.43	−4.67	−9.80	1.29

Benzene + chlorobenzene
Δu	298.15	243.13	136.06	349.47	424.82	10.21	Δβ_s	−1.78	2.92	−4.02	−11.00	1.37
	303.15	237.23	197.98	257.54	262.97	5.63		−1.81	2.95	−4.07	−11.00	1.37
	308.15	264.62	184.95	306.04	380.59	7.05		−1.88	3.05	−4.20	−11.00	3.49
	313.15	172.07	112.01	−7.072	−411.26	7.08		−1.97	3.21	−4.38	−12.00	1.50

Benzene + benzyl chloride
Δu	298.15	59.59	128.11	−173.32	−568.42	6.39	Δβ_s	−2.03	3.88	−3.22	−13.00	1.54
	303.15	54.86	168.02	−84.38	−816.62	9.74		−2.07	3.93	−3.26	−13.00	1.54
	308.15	81.31	279.66	−192.84	−1172.37	11.15		−2.12	4.09	−3.66	−14.00	1.70
	313.15	109.08	236.65	−200.54	−809.16	8.55		−2.19	4.22	−3.81	−14.00	1.71

Benzene + benzyl alcohol
Δu	298.15	222.34	39.88	64.15	13.01	5.91	Δβ_s	−1.75	2.65	−4.22	−10.00	1.30
	303.15	190.41	−7.40	−24.90	40.06	2.58		−1.90	2.78	−4.03	−10.00	1.25
	308.15	204.16	288.16	−53.98	−848.00	18.86		−1.84	2.72	−4.39	−10.00	1.30
	313.15	360.42	95.86	162.43	885.77	35.33		−1.95	2.88	−4.65	−11.00	1.44

Parameters of McAllister three and four body interaction models and standard deviations for speed of sound and isentropic compressibility are presented in Tables 3 and 4. The absolute average percent deviations (AAPD) in ultrasonic velocity and isentropic compressibility obtained from different models are provided in Table 5 which shows that co relational models provide fairly good results as compared to the PFP model. McAllister multi interactive model provides excellent agreement with the experimental findings. Higher deviation values in the PFP model can be explained as the model was developed for non-electrolyte γ-meric spherical chain molecules and the system under investigation has interacting and associating properties. Moreover, the expression used for the computation of α and β_T is also empirical in nature. With the increase of mole fraction, the values of ultrasonic velocity obtained from all the models decrease at all temperatures except at few places as evidenced by Table 6. Positive deviations in speed of sound are a result of molecular association and complex formation whereas negative deviations are due to molecular dissociation. The actual sign and magnitude of deviations depend upon relative strength of two opposite effects. The lack of smoothness in deviations is due to the interaction between the component molecules. Isentropic compressibility increases regularly with the increase of mole fraction while density and ultrasonic velocity show regular behavior. Results of ultrasonic velocity obtained from different models along with percent deviation are reported in Table 6. A careful perusal of the results clearly indicates the close proximity of our results with the experimental findings.

Table 3 Parameters of McAllister three body and four body interaction models and standard deviations (δ) for speed of sound of binary liquid mixtures at various temperatures.

		McAllister three body (u/ms⁻¹)			McAllister four body (u/ms⁻¹)
Component	Temp	a × 10⁻³	b × 10⁻³	(δ)	a × 10⁻³	b × 10⁻³	c × 10⁻³	(δ)
Benzene + benzonitrile	298.15	1.63	1.56	8.34	1.54	1.59	1.58	8.34
	303.15	1.60	1.57	7.36	1.51	1.60	1.56	7.22
	308.15	1.60	1.56	10.45	1.52	1.57	1.57	10.46
	313.15	1.53	1.59	13.21	1.42	1.64	1.54	11.98
Benzene + chlorobenzene	298.15	1.65	1.44	15.19	1.64	1.37	1.58	7.71
	303.15	1.64	1.43	11.42	1.61	1.39	1.54	5.00
	308.15	1.65	1.41	12.86	1.62	1.37	1.53	5.25
	313.15	1.42	1.47	8.26	1.36	1.46	1.44	8.14
Benzene + benzyl chloride	298.15	1.35	1.42	8.76	1.29	1.48	1.34	4.87
	303.15	1.33	1.43	8.85	1.28	1.45	1.35	6.61
	308.15	1.31	1.43	15.20	1.23	1.53	1.30	10.14
	313.15	1.33	1.40	23.21	1.25	1.50	1.29	7.31
Benzene + benzyl alcohol	298.15	1.56	1.53	3.43	1.49	1.50	1.54	2.68
	303.15	1.51	1.56	6.29	1.44	1.52	1.53	4.70
	308.15	1.49	1.52	10.39	1.42	1.51	1.50	10.37
	313.15	1.72	1.38	25.94	1.63	1.43	1.45	25.00

Table 4 Parameters of McAllister three body and four body interaction models and standard deviations (δ) for isentropic compressibility of binary liquid mixtures at various temperatures.

		McAllister three body (β_s/TPa⁻¹)			McAllister four body (β_s/TPa⁻¹)
Component	Temp	a	b	(δ)	a	b	c	(δ)
Benzene + benzonitrile	298.15	417.00	402.00	6.36	467.00	398.00	404.00	6.36
	303.15	433.00	404.00	6.15	496.00	382.00	423.00	5.55
	308.15	440.00	412.00	8.08	499.00	401.00	427.00	7.93
	313.15	484.00	398.00	12.80	569.00	373.00	446.00	10.70
Benzene + chlorobenzene	298.15	429.00	480.00	9.66	428.00	548.00	409.00	5.67
	303.15	443.00	493.00	6.13	455.00	523.00	441.00	3.06
	308.15	442.00	512.00	7.97	449.00	555.00	446.00	4.04
	313.15	599.00	482.00	10.00	642.00	489.00	512.00	9.48
Benzene + benzyl chloride	298.15	654.00	482.00	11.70	720.00	439.00	573.00	5.92
	303.15	677.00	483.00	11.70	732.00	460.00	568.00	7.91
	308.15	688.00	511.00	20.70	819.00	387.00	694.00	9.10
	313.15	675.00	543.00	19.10	809.00	404.00	721.00	6.76
Benzene + benzyl alcohol	298.15	536.00	419.00	2.91	572.00	443.00	435.00	2.50
	303.15	582.00	402.00	5.63	621.00	440.00	439.00	3.77
	308.15	606.00	428.00	10.80	654.00	446.00	467.00	9.48
	313.15	468.00	520.00	20.00	518.00	485.00	508.00	19.90

Table 5 Comparison of absolute average percent deviation (AAPD) values obtained from various liquid state models.

Temperature	K_as	u_ab/m.s⁻¹	u_/ms⁻¹ Eq. (20)	u_/ms⁻¹ Eq. (5)	u_/ms⁻¹ Eq. (10)	u_/ms⁻¹ Eq. (21)	u_/m.s⁻¹ Eq. (22)	β_s/TPa⁻¹ Eq. (20)	β_s/TPa⁻¹ Eq. (5)	β_s/TPa⁻¹ Eq. (10)	β_s/TPa⁻¹ Eq. (21)	β_s/TPa⁻¹ Eq. (22)
Benzene + benzonitrile
298.15	0.0009	1615.70	6.85	4.66	5.36	0.43	0.44	15.40	10.10	11.76	0.91	0.89
303.15	0.0002	1590.00	5.99	4.89	5.51	0.39	0.38	13.36	10.64	12.11	0.96	0.86
308.15	0.0011	1585.00	5.75	4.93	5.56	0.55	0.56	12.71	10.73	12.23	1.29	1.24
313.15	0.0004	1574.80	4.20	4.52	5.21	0.67	0.63	9.01	9.84	11.51	1.66	1.46

Benzene + chlorobenzene
298.15	0.0002	1532.30	4.11	4.37	4.77	0.86	0.44	8.93	9.41	10.33	1.57	0.66
303.15	0.0005	1516.40	3.13	4.08	4.42	0.70	0.31	6.66	8.75	9.52	1.00	0.46
308.15	0.0001	1495.90	3.57	1.33	1.35	0.81	0.31	6.66	8.75	9.52	1.29	0.58
313.15	0.0004	1452.00	2.08	2.08	2.32	0.49	0.53	3.98	4.32	4.84	1.11	1.35

Benzene + benzyl chloride
298.15	0.0008	1391.40	1.15	0.81	0.82	0.86	0.44	2.27	1.61	1.63	1.52	0.80
303.15	0.0003	1374.90	1.60	0.89	0.89	0.70	0.31	3.09	1.77	1.78	1.54	1.06
308.15	0.0004	1367.80	3.57	1.33	1.35	0.81	0.31	6.58	2.64	2.68	2.75	1.08
313.15	0.0013	1356.20	15.40	1.25	1.26	0.49	0.53	24.28	2.53	2.55	2.45	0.83

Benzene + benzyl alcohol
298.15	0.0014	1532.30	3.37	2.95	2.99	0.52	0.30	7.18	6.20	6.28	0.50	0.43
303.15	0.0015	1516.40	1.91	2.31	2.34	0.52	0.37	4.01	4.80	4.86	0.88	0.63
308.15	0.0016	1496.40	2.13	2.52	2.55	1.03	0.62	4.25	5.24	5.30	1.05	1.02
313.15	0.0002	1452.00	2.76	5.67	5.70	1.71	0.50	5.99	12.63	12.69	3.03	3.06

Table 6 Experimental density (ρ), experimental ultrasonic velocity (u_Exp), theoretical ultrasonic velocity (u_Theo), excess molar volume (V^E), percent deviations in ultrasonic velocity (%Δu) and PERCENT deviations in adiabatic compressibility (%Δβ) obtained from various models for binary liquid mixtures at various temperatures.

x₁	ρ/g cm⁻³	u_{Exp /m.s}⁻¹	u_/m.s⁻¹ Eq.(20)	u_/m.s⁻¹ Eq.(5)	u_/m.s⁻¹ Eq.(10)	V^E/cc mol⁻¹	%Δu Eq. (20)	%Δu Eq. (5)	%Δu Eq. (10)	%Δβ_s Eq. (20)	%Δβ_s Eq. (5)	%Δβ_s Eq. (10)	%Δβ_s Eq. (21)	%Δβ_s Eq. (22)
Benzene + benzonitrile
298.15
0.1681	0.9987	1594.1	1509.8	1564.3	1555.2	−1.7213	5.28	1.87	2.44	−11.47	−3.84	−5.06	0.40	0.01
0.3126	0.9875	1585.4	1471.1	1520.2	1506.5	−2.2694	7.21	4.11	4.97	−16.14	−8.76	−10.74	−0.32	−0.37
0.4381	0.9765	1562.2	1437.3	1481.8	1466.6	−2.6698	7.99	5.14	6.11	−18.13	−11.13	−13.45	0.48	0.65
0.5481	0.9645	1545.8	1408.9	1448.3	1433.3	−2.8344	8.85	6.30	7.27	−20.37	−13.91	−16.30	−0.16	0.03
0.6453	0.9568	1525.6	1380.2	1418.7	1405.1	−3.2917	9.53	7.01	7.89	−22.18	−15.64	−17.88	−1.41	−1.38
0.7318	0.9423	1475.9	1361.3	1392.3	1380.9	−2.9985	7.76	5.66	6.43	−17.55	−12.36	−14.22	1.02	0.98
0.8093	0.9356	1445.9	1337.7	1368.7	1359.9	−3.3593	7.48	5.33	5.94	−16.82	−11.59	−13.04	−0.29	−0.47
0.8792	0.9156	1390.5	1329.4	1347.5	1341.5	−2.3718	4.39	3.09	3.52	−9.39	−6.48	−7.44	1.96	1.87
0.9423	0.8876	1375.5	1332.3	1328.3	1325.3	−0.4863	3.13	3.43	3.65	−6.58	−7.23	−7.72	−2.16	−2.12
303.15
0.1681	0.9825	1591.5	1514.9	1543.2	1535.2	−0.5967	4.81	3.03	3.54	−10.36	−6.36	−7.46	0.98	−0.20
0.3126	0.9758	1580.7	1473.8	1502.8	1490.9	−1.6396	6.76	4.93	5.68	−15.02	−10.63	−12.41	0.09	−0.09
0.4381	0.9678	1561.8	1439.2	1467.7	1454.4	−2.3651	7.85	6.02	6.87	−17.76	−13.23	−15.31	−0.20	0.40
0.5481	0.9587	1534.5	1409.9	1437.0	1423.9	−2.8316	8.12	6.35	7.21	−18.45	−14.03	−16.14	0.09	0.81
0.6453	0.9564	1522.8	1377.8	1409.8	1397.9	−3.8245	9.52	7.42	8.20	−22.16	−16.66	−18.66	−2.80	−2.53
0.7318	0.9356	1464.8	1366.6	1385.6	1375.6	−2.9360	6.70	5.40	6.08	−14.87	−11.74	−13.38	1.27	1.14
0.8093	0.9152	1434.2	1358.0	1364.0	1356.2	−1.9769	5.31	4.89	5.43	−11.53	−10.55	−11.82	0.92	0.46
0.8792	0.9056	1389.4	1341.1	1344.5	1339.2	−1.9947	3.47	3.23	3.61	−7.32	−6.79	−7.63	1.42	0.75
0.9423	0.8768	1364.8	1345.8	1326.9	1324.2	0.0081	1.39	2.78	2.97	−2.84	−5.79	−6.22	−0.96	−1.39
308.15
0.1681	0.9721	1571.5	1525.3	1537.0	1528.8	−0.2630	2.94	2.19	2.71	−6.14	−4.54	−5.65	1.00	0.18
0.3126	0.9678	1571.0	1480.2	1495.3	1483.2	−1.5845	5.77	4.82	5.59	−12.63	−10.38	−12.19	−0.58	−0.80
0.4381	0.9512	1551.8	1453.0	1459.1	1445.6	−1.4630	6.37	5.97	6.84	−14.06	−13.10	−15.23	0.25	0.63
0.5481	0.9486	1522.4	1416.0	1427.5	1414.1	−2.6052	6.99	6.23	7.11	−15.59	−13.74	−15.89	0.52	0.89
0.6453	0.9456	1518.7	1383.4	1399.5	1387.4	−3.5581	8.91	7.85	8.64	−20.51	−17.75	−19.81	−3.34	−3.30
0.7318	0.9265	1450.5	1369.9	1374.7	1364.5	−2.8232	5.56	5.23	5.93	−12.11	−11.33	−13.00	1.99	1.82
0.8093	0.9011	1424.9	1365.6	1352.4	1344.5	−1.3422	4.16	5.08	5.64	−8.87	−11.00	−12.31	1.11	0.86
0.8792	0.8965	1382.9	1343.0	1332.4	1327.0	−1.8719	2.88	3.65	4.04	−6.03	−7.72	−8.59	0.83	0.40
0.9423	0.8695	1359.8	1249.0	1314.3	1311.6	−0.0206	8.15	3.34	3.54	−18.53	−7.04	−7.48	−2.02	−2.25
313.15
0.1681	0.9642	1569.3	1527.2	1525.2	1515.9	−0.2851	2.68	2.81	3.40	−5.59	−5.86	−7.17	−7.17	−0.84
0.3126	0.9523	1562.7	1488.7	1481.8	1467.9	−0.7587	4.73	5.17	6.06	−10.18	−11.21	−13.33	−13.33	0.24
0.4381	0.9487	1542.8	1447.1	1444.1	1428.6	−1.9163	6.20	6.39	7.40	−13.66	−14.13	−16.62	−16.62	0.51
0.5481	0.9356	1500.9	1419.7	1411.1	1395.8	−1.9441	5.41	5.98	7.00	−11.76	−13.12	−15.61	−15.61	2.37
0.6453	0.9365	1501.0	1382.3	1381.9	1368.1	−3.2599	7.91	7.93	8.85	−17.91	−17.97	−20.36	−20.36	−4.07
0.7318	0.9136	1425.8	1371.8	1356.0	1344.3	−2.0790	3.78	4.89	5.71	−8.02	−10.56	−12.48	−12.48	1.15
0.8093	0.9	1389.5	1355.0	1332.7	1323.7	−1.7360	2.48	4.08	4.73	−5.14	−8.69	−10.18	−10.18	0.10
0.8792	0.8865	1355.5	1340.7	1311.8	1305.7	−1.3192	1.09	3.22	3.67	−2.21	−6.77	−7.77	−7.77	−1.06
0.9423	0.8658	1290.8	1336.1	1292.9	1289.8	−0.0633	−3.52	−0.16	0.08	6.68	0.32	−0.15	−0.15	3.10

Benzene + chlorobenzene
298.15
0.1808	0.9957	1522.1	1520.6	1492.2	1487.0	4.7190	0.10	1.96	2.31	−0.20	−4.03	−4.78	−2.51	0.27
0.3318	0.9865	1501.4	1475.1	1458.8	1451.0	3.3810	1.75	2.84	3.35	−3.59	−5.92	−7.06	−0.64	−0.37
0.4598	0.9665	1489.2	1447.2	1430.4	1421.9	2.9367	2.81	3.95	4.52	−5.88	−8.38	−9.68	1.39	−0.06
0.5697	0.9655	1472.3	1406.2	1406.0	1397.8	1.4890	4.49	4.50	5.06	−9.61	−9.64	−10.94	2.05	0.22
0.6651	0.9558	1465.8	1378.5	1384.9	1377.5	0.7223	5.95	5.52	6.02	−13.06	−12.02	−13.22	1.06	0.06
0.7487	0.9413	1455.8	1359.4	1366.4	1360.2	0.3367	6.62	6.14	6.56	−14.68	−13.51	−14.54	−0.21	0.11
0.8225	0.9346	1445.9	1336.1	1350.0	1345.3	−0.3845	7.59	6.63	6.95	−17.11	−14.70	−15.50	−3.01	−1.60
0.8882	0.9156	1390.5	1327.5	1335.5	133.37	−0.3685	4.53	3.95	4.18	−9.72	−8.40	−8.92	0.33	2.23
0.947	0.8856	1375.5	1332.4	1322.5	1320.9	0.2987	3.13	3.85	3.97	−6.57	−8.17	−8.43	−2.94	−1.31
303.15
0.1808	0.9835	1501.5	1527.9	1479.2	1474.7	5.2258	−1.76	1.48	1.78	3.43	−3.04	−3.66	−1.58	0.20
0.3318	0.9748	1489.8	1483.2	1448.1	1441.6	3.8107	0.44	2.80	3.23	−0.89	−5.84	−6.80	−0.79	−0.52
0.4598	0.9578	1475.6	1453.7	1421.7	1414.6	3.1560	1.48	3.65	4.13	−3.03	−7.72	−8.81	1.44	0.64
0.5697	0.9577	1465.8	1412.9	1399.1	1392.2	1.6234	3.61	4.55	5.02	−7.63	−9.75	−10.85	1.25	0.11
0.6651	0.9554	1455.7	1379.1	1379.5	1373.3	0.4176	5.26	5.23	5.66	−11.42	−11.35	−12.35	0.43	−0.31
0.7487	0.9346	1445.8	1367.0	1362.3	1357.1	0.3841	5.44	5.77	6.13	−11.85	−12.62	−13.48	−0.14	0.04
0.8225	0.9142	1434.2	1358.0	1347.2	1343.2	0.4055	5.31	6.06	6.34	−11.52	−13.33	−14.00	−1.71	−0.72
0.8882	0.9055	1389.4	1340.3	1333.7	1331.0	−0.1501	3.53	4.01	4.20	−7.45	−8.52	−8.96	−0.09	1.16
0.947	0.8758	1364.8	1346.2	1321.6	1320.3	0.5141	1.36	3.16	3.26	−2.78	−6.63	−6.85	−1.64	−0.56
308.15
0.1808	0.9761	1487.5	1527.7	1460.5	1456.2	5.6192	−2.70	1.81	2.10	5.20	−3.72	−4.34	−2.20	0.08
0.3318	0.9668	1475.6	1483.2	1430.5	1424.2	4.1617	−0.52	3.05	3.48	1.03	−6.40	−7.35	−0.80	−0.56
0.4598	0.9412	1466.5	1462.4	1405.0	1398.1	4.0059	0.28	4.19	4.66	−0.52	−8.89	−9.97	1.97	0.90
0.5697	0.9486	1456.7	1413.5	1383.2	1376.4	1.9088	2.96	5.04	5.51	−6.20	−10.90	−11.99	1.53	−0.01
0.6651	0.9446	1450.7	1381.1	1364.3	1358.2	0.7394	4.79	5.96	6.37	−10.32	−13.07	−14.08	0.46	−0.46
0.7487	0.9255	1445.5	1367.5	1347.7	1342.6	0.5730	5.39	6.77	7.12	−11.72	−15.04	−15.91	−0.86	−0.60
0.8225	0.9001	1424.9	1363.6	1333.0	1329.1	0.8524	4.30	6.45	6.72	−9.18	−14.26	−14.93	−1.05	0.30
0.8882	0.8964	1382.9	1340.9	1320.0	1317.3	−0.0271	3.03	4.55	4.74	−6.36	−9.76	−10.20	−0.31	1.32
0.947	0.8695	1359.8	1344.1	1308.3	1307.0	0.4694	1.15	3.79	3.88	−2.34	−8.02	−8.24	−2.50	−1.13
313.15
0.1808	0.9632	1449.8	1507.1	1420.1	1416.7	5.9694	−3.96	2.05	2.28	7.47	−4.22	−4.72	0.00	−1.23
0.3318	0.9523	1430.5	1467.8	1393.4	1388.4	4.6389	−2.61	2.59	2.94	5.02	−5.39	−6.14	0.49	0.44
0.4598	0.9387	1409.8	1437.6	1370.8	1365.3	3.7211	−1.98	2.76	3.15	3.84	−5.77	−6.61	0.76	1.52
0.5697	0.9346	1390.1	1403.1	1351.4	1346.1	2.3733	−0.94	2.78	3.16	1.85	−5.80	−6.64	0.03	0.75
0.6651	0.9355	1379.8	1368.2	1334.6	1329.8	0.9133	0.84	3.28	3.62	−1.69	−6.89	−7.66	−2.33	−2.16
0.7487	0.9126	1355.8	1360.4	1319.8	1315.8	1.0005	−0.34	2.65	2.94	0.69	−5.52	−6.16	−0.82	−1.02
0.8225	0.8988	1335.7	1346.8	1306.8	1303.8	0.6377	−0.84	2.16	2.39	1.65	−4.46	−4.95	−0.52	−1.08
0.8882	0.8862	1290.5	1334.7	1295.2	1293.2	0.2852	−3.43	−0.37	−0.21	6.52	0.74	0.42	3.50	2.85
0.9470	0.8648	1285.8	1333.9	1284.9	1283.8	0.5018	−3.75	0.07	0.15	7.09	−0.14	−0.30	1.55	1.12

Benzene + benzyl chloride
298.15
0.1988	1.0001	1380.1	1405.6	1375.2	1374.8	3.8832	−1.85	0.35	0.38	3.61	−0.70	−0.76	2.55	−0.55
0.3583	0.9984	1376.9	1371.2	1362.3	1361.7	2.0414	0.41	1.06	1.10	−0.82	−2.15	−2.24	−0.04	0.10
0.489	0.9801	1364.8	1357.1	1351.7	1351.1	1.5130	0.56	0.95	1.00	−1.13	−1.94	−2.04	−0.72	1.32
0.5982	0.9753	1355.8	1334.6	1342.9	1342.3	0.3797	1.56	0.95	0.99	−3.19	−1.92	−2.02	−2.38	−0.60
0.6907	0.9546	1339.1	1330.0	1335.5	1334.9	0.3084	0.68	0.27	0.31	−1.37	−0.53	−0.62	−1.02	−0.43
0.7701	0.9345	1326.3	1327.7	1329.1	1328.7	0.3090	−0.11	−0.22	−0.18	0.22	0.43	0.36	0.13	−0.60
0.839	0.9198	1315.8	1322.8	1323.6	1323.3	0.1034	−0.54	−0.60	−0.57	1.07	1.18	1.13	0.92	−0.77
0.8993	0.8943	1301.1	1330.7	1318.8	1318.6	0.5714	−2.27	−1.36	−1.34	4.40	2.67	2.64	2.86	1.05
0.9526	0.8835	1294.9	1325.9	1314.5	1314.4	0.3007	−2.40	−1.52	−1.51	4.63	2.97	2.95	3.06	1.76
303.15
0.1988	0.9991	1375.5	1400.9	1362.3	1361.9	3.6498	−1.85	0.96	0.98	3.60	−1.94	−2.00	1.66	−1.79
0.3583	0.9828	1366.9	1381.7	1352.0	1351.5	2.7160	−1.09	1.09	1.13	2.14	−2.21	−2.29	0.91	−1.43
0.489	0.9705	1360.8	1363.6	1343.6	1343.0	1.7837	−0.21	1.26	1.30	0.42	−2.58	−2.66	−1.08	0.73
0.5982	0.9688	1345.2	1339.4	1336.5	1336.0	0.4384	0.43	0.64	0.68	−0.86	−1.29	−1.38	−2.04	−0.55
0.6907	0.9456	1330.2	1338.5	1330.6	1330.1	0.5015	−0.62	−0.03	0.00	1.24	0.06	−0.01	−0.73	−0.25
0.7701	0.9245	1324.5	1338.4	1325.5	1325.1	0.5521	−1.06	−0.08	−0.05	2.08	0.16	0.10	−0.50	−1.17
0.839	0.9045	1312.2	1339.9	1321.1	1320.8	0.6338	−2.11	−0.68	−0.66	4.09	1.34	1.30	0.95	−0.49
0.8993	0.8876	1299.9	1340.4	1317.2	1317.0	0.6239	−3.12	−1.33	−1.32	5.96	2.62	2.59	2.40	0.80
0.9526	0.8735	1288.9	1339.9	1313.8	1313.7	0.5295	−3.96	−1.93	−1.93	7.47	3.76	3.75	3.67	2.55
308.15
0.1988	0.8993	1366.4	1501.4	1353.8	1353.4	1.7451	−9.88	0.92	0.95	17.18	−1.86	−1.92	5.08	0.06
0.3583	0.9798	1356.9	1382.0	1342.6	1342.0	2.5720	−1.85	1.05	1.09	3.61	−2.13	−2.22	−0.59	−0.79
0.489	0.9587	1359.1	1371.1	1333.4	1332.8	2.1595	−0.89	1.88	1.93	1.75	−3.88	−3.98	−3.00	0.44
0.5982	0.9388	1339.7	1363.2	1325.8	1325.2	1.8508	−1.76	1.04	1.08	3.42	−2.10	−2.20	−1.71	1.66
0.6907	0.9295	1325.8	1348.4	1319.3	1318.8	1.0570	−1.71	0.49	0.53	3.33	−0.98	−1.06	−1.45	−0.23
0.7701	0.9199	1315.9	1336.7	1313.8	1313.3	0.4258	−1.58	0.16	0.19	3.10	−0.32	−0.39	−1.18	−2.50
0.839	0.8974	1290.8	1340.0	1309.0	1308.6	0.6411	−3.82	−1.41	−1.38	7.22	2.76	2.71	2.45	−0.47
0.8993	0.8799	1275.9	1340.7	1304.8	1304.5	0.6559	−5.08	−2.27	−2.25	9.44	4.38	4.35	4.31	0.99
0.9526	0.8699	1265.8	1335.6	1301.1	1300.9	−0.7493	−5.51	−2.79	−2.78	10.18	5.35	5.34	5.02	2.56
313.15
0.1988	0.8871	1349.6	1511.0	1340.3	1340.0	3.2115	−11.96	0.69	0.71	20.23	−1.39	−1.43	5.16	0.48
0.3583	0.9687	1344.5	1724.5	1327.2	1326.9	2.4271	−28.27	1.28	1.31	39.22	−2.61	−2.67	−0.82	−1.01
0.489	0.9488	1350.1	1649.8	1316.6	1316.2	2.3860	−22.20	2.48	2.51	33.03	−5.15	−5.21	−3.18	0.09
0.5982	0.9356	1329.4	1579.3	1307.7	1307.4	1.6970	−18.80	1.63	1.65	29.14	−3.33	−3.39	−1.73	1.38
0.6907	0.9169	1320.9	1525.0	1300.3	1300.0	1.9597	−15.46	1.56	1.58	24.98	−3.19	−3.24	−1.40	−0.20
0.7701	0.9055	1299.7	1471.1	1293.9	1293.6	2.2659	−13.19	0.44	0.46	21.95	−0.89	−0.93	0.57	−0.60
0.839	0.8897	1288.1	1429.2	1288.4	1288.2	1.2274	−10.96	−0.03	−0.01	18.78	0.05	0.02	1.43	−1.37
0.8993	0.8762	1266.4	1390.9	1283.6	1283.4	0.3790	−9.84	−1.36	−1.35	17.11	2.66	2.64	3.73	0.53
0.9526	0.8645	1256.8	1356.0	1279.3	1279.3	1.6954	−7.90	−1.80	−1.79	14.10	3.50	3.49	4.09	1.82

Benzene + benzyl alcohol
298.15
0.1749	1.0008	1526.8	1476.4	1493.3	1488.7	1.7773	3.30	2.19	2.49	−6.93	−4.53	−5.18	0.25	−0.49
0.3229	0.9935	1502.0	1437.6	1460.	1460.4	0.9264	4.29	2.77	2.77	−9.16	−5.77	−5.77	0.81	0.74
0.4498	0.9825	1489.8	1407.6	1432.2	1432.2	0.4472	5.51	3.86	3.86	−12.01	−8.19	−8.19	−0.83	−0.50
0.5598	0.9601	1465.8	1392.9	1407.9	1407.9	0.7826	4.97	3.95	3.95	−10.73	−8.39	−8.39	−0.20	0.19
0.6561	0.9445	1446.3	1375.4	1386.6	1386.6	0.6746	4.90	4.13	4.13	−10.57	−8.80	−8.80	−0.78	−0.69
0.741	0.9236	1416.5	1366.4	1367.8	1367.8	0.9185	3.54	3.44	3.44	−7.47	−7.24	−7.24	0.34	0.17
0.8166	0.9001	1390.	1362.8	1351.1	1351.1	1.3213	1.99	2.83	2.83	−4.10	−5.91	−5.91	0.84	0.53
0.8841	0.8935	1365.1	1344.9	1336.3	1336.3	0.7243	1.48	2.11	2.11	−3.02	−4.36	−4.36	0.29	−0.16
0.945	0.8801	1340.5	1335.9	1322.8	1322.8	0.5619	0.34	1.31	1.31	−0.69	−2.68	−2.68	−0.17	−0.48
303.15
0.1749	0.9998	1505.7	1473.0	1480.2	1476.3	1.5202	55.09	1.69	1.95	−4.48	−3.47	−4.02	2.77	0.96
0.3229	0.9874	1489.4	1440.5	1449.6	1449.6	1.0416	71.53	2.67	2.67	−6.90	−5.56	−5.56	−1.02	−0.78
0.4498	0.9754	1475.8	1412.6	1423.4	1423.4	0.6070	78.19	3.54	3.54	−9.14	−7.48	−7.48	−1.62	−0.85
0.5598	0.9564	1446.8	1395.9	1400.8	1400.8	0.6991	80.67	3.17	3.17	−7.43	−6.67	−6.67	−0.47	0.18
0.6561	0.9354	1420.5	1384.7	1381.1	1381.1	0.9313	80.00	2.77	2.77	−5.23	−5.79	−5.79	0.24	0.43
0.741	0.9002	1399.8	1391.3	1363.7	1363.7	2.0817	77.19	2.58	2.58	−1.22	−5.36	−5.36	1.04	0.90
0.8166	0.8897	1376.5	1375.7	1348.2	1348.2	1.6372	71.75	2.05	2.05	−0.11	−4.24	−4.24	0.60	−0.02
0.8841	0.8845	1355.8	1357.1	1334.4	1334.4	0.9266	51.96	1.58	1.58	0.20	−3.23	−3.23	−0.16	−1.00
0.945	0.8789	1331.5	1341.0	1322.0	1322.0	0.3044	29.17	0.71	0.71	1.41	−1.44	−1.44	0.01	−0.63
308.15
0.1749	0.9875	1489.2	1511.4	1461.4	1457.8	1.6282	56.00	1.86	2.11	2.92	−3.83	−4.35	1.49	−0.10
0.3229	0.9756	1476.2	1438.1	1431.8	1431.8	1.1320	69.23	3.00	3.00	−5.36	−6.29	−6.29	0.45	0.31
0.4498	0.9632	1465.3	1411.6	1406.6	1406.6	0.7453	78.88	4.01	4.01	−7.75	−8.52	−8.52	−1.94	−1.08
0.5598	0.9426	1426.5	1397.3	1384.7	1384.7	0.9754	75.95	2.93	2.93	−4.21	−6.12	−6.12	0.11	1.06
0.6561	0.9254	1401.5	1383.3	1365.6	1365.6	0.9797	80.90	2.56	2.56	−2.64	−5.32	−5.32	0.22	0.61
0.741	0.8992	1386.2	1381.6	1348.8	1348.8	1.5856	78.45	2.69	2.69	−0.67	−5.61	−5.61	−0.23	−0.44
0.8166	0.8745	1367.2	1381.4	1333.9	1333.9	2.0847	71.03	2.43	2.43	2.05	−5.05	−5.05	−0.28	−0.97
0.8841	0.8645	1345.2	1368.3	1320.6	1320.6	1.6581	55.18	1.83	1.83	3.36	−3.76	−3.76	−0.56	−1.53
0.945	0.8566	1290.5	1355.1	1308.6	1308.6	1.1475	25.28	−1.40	−1.40	9.31	2.75	2.75	4.25	3.52
313.15
0.1749	0.9745	1442.3	1440.4	1421.2	1417.8	0.9795	55.55	1.46	1.70	−0.25	−2.99	−3.48	0.03	0.23
0.3229	0.9683	1466.3	1407.9	1395.0	1395.0	0.2435	68.13	4.86	4.86	−8.46	−10.47	−10.47	−2.97	−2.79
0.4498	0.9512	1402.5	1390.3	1372.6	1372.6	0.3998	77.57	2.13	2.13	−1.76	−4.40	−4.40	6.82	6.87
0.5598	0.9354	1485.9	1375.1	1353.2	1353.2	0.4617	79.29	8.93	8.93	−16.75	−20.57	−20.57	−4.40	−4.57
0.6561	0.9102	1475.3	1372.5	1336.2	1336.2	1.1676	79.14	9.43	9.43	−15.54	−21.90	−21.90	−3.31	−3.52
0.741	0.8754	1425.8	1383.0	1321.2	1321.2	2.5036	78.18	7.33	7.33	−6.28	−16.45	−16.45	2.22	2.23
0.8166	0.8563	1390.5	1380.0	1307.9	1307.9	2.7418	70.82	5.94	5.94	−1.52	−13.02	−13.02	3.16	3.23
0.8841	0.8365	1375.8	1380.2	1296.0	1296.0	3.0315	56.35	5.80	5.80	0.64	−12.69	−12.69	−0.13	0.03
0.945	0.8236	1355.8	1374.8	1285.3	1285.3	2.8744	15.78	5.20	5.20	2.75	−11.27	−11.27	−4.29	−4.15

The excess molar volume, V^E was calculated from density data according to the following equation:

(24)

V^{E} = [(x_{1} M_{1} + x_{2} M_{2}) / ρ) - (x_{1} M_{1} / ρ_{1} + x_{1} M_{1} / ρ_{2})]

where x₁, x₂, M₁, M₂, ρ, ρ₁, ρ₂ are mole fractions, molecular weights and densities of pure components 1 and 2 and ρ is the density of mixture, respectively. The excess molar volumes calculated from Eq. (24) are also summarized in Table 6. The values of this excess property are positive except for benzene + benzonitrile which is negative at all temperatures. The maximum values reached are −3.8245 for benzene + benzonitrile at 303.15 K, 5.2258 for benzene + chlorobenzene at 303.15 K, 3.8832 for benzene + benzyl chloride at 308.15 K and 3.0315 for benzene + benzyl alcohol at 313.15 K, respectively and minimum values reached are 0.0081 for benzene + benzonitrile at 303.15 K, −0.0271 for benzene + chlorobenzene at 308.15 K, 0.1034 for benzene + benzyl chloride at 308.15 K and 0.2435 for benzene + benzyl alcohol at 313.15 K, respectively. Sign and magnitude of excess volume values are important to describe the molecular interactions involved in the liquid system. The negative values of V^E for benzene + benzonitrile show that strong molecular association is formed between components. Dispersion type interactions and structural effects arising from interstitial accommodation because of differences in molecular volumes and free volumes between liquid components contribute negative terms to V^E. The repulsive forces between the loan pairs of electrons on nitrogen atom lead to positive values of V^E suggesting the presence of weak interactions between the component molecules and the favoring packing of unlike molecules.

Conclusively, associated processes give more reliable results as compared to non-associated processes and are helpful in deducing the internal structure of associates through the fitted values of ultrasonic velocity and isentropic compressibility in a hypothetical pure associate and observed dependence of concentration on composition of a mixture.

Acknowledgments

Authors are very thankful to U.G.C., New Delhi for financial support (Grant-34-332/2008(SR), 15-57/12(SA-II)) and Department of Chemistry, V.S.S.D. College, for cooperation.

References

Abe A., Flory P.J., . J. Am. Chem. Soc.. 1965;82:1838-1845.
Ali A., Tariq M., . Phys. Chem. Liq.. 2008;46:47-58.
Ali A., Pandey J.D., Soni N.K., Nain A.K., Lal B., Chand D., . Chin. J. Chem.. 2005;23:377-385.
AL-Jimaz Adel S., AL-Kandary Jasem A., Haq Abdul, Latif M. Abdul, . J. Chem. Eng. Data. 2007;52:206-214.
AL-Kandary Jasem A., AL-Jimaz Adel S., Haq Abdul, Latif M. Abdul, . J. Chem. Eng. Data. 2006;51:2074-2082.
Aralaguppi M.L., Jadar C., Aminabhavi T.M., . J. Chem. Eng. Data. 1999;44:441.
Askar S.J., Ali A., . J. Chem. Pharm. Res.. 2012;4(1):617-632.
Dey R., Soni N.K., Mishra R.K., Dwivedi D.K., . J. Pure Appl. Ultrason.. 2006;28:20-28.
Glinski J., . J. Chem. Phys.. 2003;118:2301-2307.
McAllister R.A., . AIChE J.. 1960;6:427-431.
Natta G., Baccaredda M., . Atti Accad. Naz. Lincei. 1948;4:360.
Pandey J.D., Verma Richa, . Chem. Phys.. 2001;270:429-438.
Pandey J.D., Prakash Chandra, Srivastava Tanu, Soni N.K., Singh A.K., . Fluid Phase Equilib.. 2008;273:44-51.
Patterson D., Rastogi A.K., . J. Phys. Chem.. 1970;74:1067-1071.
Prigogine I., Saraga L., . J. Chem. Phys.. 1952;49:399-407.
Prigogine I., Bellemans A., Mathod A., . Molecular Theory of Solutions. Amsterdam: North-Holland; 1957.
Ramaswamy K., Anbananthan D., . Acustica. 1981;48:281-282.
Redlich O., Kister A.Y., . Ind. Eng. Chem.. 1948;40:345-348.
Riddick J.A., Bunger W.B., Sakano T.K., . Organic Solvents Techniques of Chemistry (forth ed.). New York: Willey; 1986.
Rodrignez A., Canosa J., Tojo J., . J. Chem. Eng. Data. 2001;46:1506.
Shukla R.K., Rai R.D., Shukla A.K., Pandey J.D., . J. Chem. Thermodyn.. 1989;21:125-129.
Shukla R.K., Rai R.D., Shukla A.K., Mishra N., Pandey J.D., . Indian J. Pure Appl. Phys.. 1993;31:54-59.
Shukla R.K., Kumar Atul, Srivastava Kirti, Singh Neetu, . J. Solution Chem.. 2007;36:1103-1116.
Shukla R.K., Kumar A., Srivastava K., Yadava S., . J. Mol. Liq.. 2008;140:25-32.
Shukla R.K., Kumar A., Singh N., Shukla A., . J. Mol. Liq.. 2008;140:117-122.
Shukla R.K., Dixit S.N., Jain Pratima, Mishra Preeti, Sharma Sweta, . Orbital Electron. J. Chem.. 2010;2:356-364.
Shukla R.K., Awasthi N., Kumar A., Shukla A., Pandey V.K., . J. Mol. Liq.. 2011;158:131-138.
Shukla R.K., Kumar Atul, Srivastava Urvashi, Awasthi Naveen, Pandey J.D., . J. Solution Chem.. 2012;41:1112-1132.
Timmermans J., . Physico Chemical Constants of Pure Organic Compounds. New York: Elsevier; 1950.

Introduction

Experimental section

Materials
Apparatus and procedure

Modeling

Ramaswamy and Anbananthan model
Prigogine–Flory–Patterson model
McAllister multi body interaction model

Results & discussion

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[1] Abe A., Flory P.J., . J. Am. Chem. Soc.. 1965;82:1838-1845.

[2] Ali A., Tariq M., . Phys. Chem. Liq.. 2008;46:47-58.

[3] Ali A., Pandey J.D., Soni N.K., Nain A.K., Lal B., Chand D., . Chin. J. Chem.. 2005;23:377-385.

[4] AL-Jimaz Adel S., AL-Kandary Jasem A., Haq Abdul, Latif M. Abdul, . J. Chem. Eng. Data. 2007;52:206-214.

[5] AL-Kandary Jasem A., AL-Jimaz Adel S., Haq Abdul, Latif M. Abdul, . J. Chem. Eng. Data. 2006;51:2074-2082.

[6] Aralaguppi M.L., Jadar C., Aminabhavi T.M., . J. Chem. Eng. Data. 1999;44:441.

[7] Askar S.J., Ali A., . J. Chem. Pharm. Res.. 2012;4(1):617-632.

[8] Dey R., Soni N.K., Mishra R.K., Dwivedi D.K., . J. Pure Appl. Ultrason.. 2006;28:20-28.

[9] Glinski J., . J. Chem. Phys.. 2003;118:2301-2307.

[10] McAllister R.A., . AIChE J.. 1960;6:427-431.

[11] Natta G., Baccaredda M., . Atti Accad. Naz. Lincei. 1948;4:360.

[12] Pandey J.D., Verma Richa, . Chem. Phys.. 2001;270:429-438.

[13] Pandey J.D., Prakash Chandra, Srivastava Tanu, Soni N.K., Singh A.K., . Fluid Phase Equilib.. 2008;273:44-51.

[14] Patterson D., Rastogi A.K., . J. Phys. Chem.. 1970;74:1067-1071.

[15] Prigogine I., Saraga L., . J. Chem. Phys.. 1952;49:399-407.

[16] Prigogine I., Bellemans A., Mathod A., . Molecular Theory of Solutions. Amsterdam: North-Holland; 1957.

[17] Ramaswamy K., Anbananthan D., . Acustica. 1981;48:281-282.

[18] Redlich O., Kister A.Y., . Ind. Eng. Chem.. 1948;40:345-348.

[19] Riddick J.A., Bunger W.B., Sakano T.K., . Organic Solvents Techniques of Chemistry (forth ed.). New York: Willey; 1986.

[20] Rodrignez A., Canosa J., Tojo J., . J. Chem. Eng. Data. 2001;46:1506.

[21] Shukla R.K., Rai R.D., Shukla A.K., Pandey J.D., . J. Chem. Thermodyn.. 1989;21:125-129.

[22] Shukla R.K., Rai R.D., Shukla A.K., Mishra N., Pandey J.D., . Indian J. Pure Appl. Phys.. 1993;31:54-59.

[23] Shukla R.K., Kumar Atul, Srivastava Kirti, Singh Neetu, . J. Solution Chem.. 2007;36:1103-1116.

[24] Shukla R.K., Kumar A., Srivastava K., Yadava S., . J. Mol. Liq.. 2008;140:25-32.

[25] Shukla R.K., Kumar A., Singh N., Shukla A., . J. Mol. Liq.. 2008;140:117-122.

[26] Shukla R.K., Dixit S.N., Jain Pratima, Mishra Preeti, Sharma Sweta, . Orbital Electron. J. Chem.. 2010;2:356-364.

[27] Shukla R.K., Awasthi N., Kumar A., Shukla A., Pandey V.K., . J. Mol. Liq.. 2011;158:131-138.

[28] Shukla R.K., Kumar Atul, Srivastava Urvashi, Awasthi Naveen, Pandey J.D., . J. Solution Chem.. 2012;41:1112-1132.

[29] Timmermans J., . Physico Chemical Constants of Pure Organic Compounds. New York: Elsevier; 1950.