Density, Ultrasonic Velocity, Viscosity and their Excess Parameters of Some Binary Liquid Mixtures of Cumene with Aromatic Hydrocarbons at 298.15 K

Der Pharma Chemica
Journal for Medicinal Chemistry, Pharmaceutical Chemistry, Pharmaceutical Sciences and Computational Chemistry

ISSN: 0975-413X
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Research Article - Der Pharma Chemica ( 2024) Volume 16, Issue 2

Density, Ultrasonic Velocity, Viscosity and their Excess Parameters of Some Binary Liquid Mixtures of Cumene with Aromatic Hydrocarbons at 298.15 K

Dhirendra Kumar Sharma*, Chandra Pal Prajapati and Suneel Kumar
Department of Chemistry, Institute of Basic Science, Bundelkhand University, Jhansi (U.P.), India
*Corresponding Author:
Dhirendra Kumar Sharma, Department of Chemistry, Institute of Basic Science, Bundelkhand University, Jhansi (U.P.), India, Email:

Received: 26-Mar-2024, Manuscript No. DPC-24-132197; Editor assigned: 29-Mar-2024, Pre QC No. DPC-24-132197 (PQ); Reviewed: 12-Apr-2024, QC No. DPC-24-132197; Revised: 23-Apr-2024, Manuscript No. DPC-24-132197 (R); Published: 30-Apr-2024, DOI: 10.4172/0975-413X.16.2.301-306


Density (ρ), viscosity (η) and sound velocity (u) of binary mixtures of ethyl benzene, toluene, mesitylene with cumene have been measured over the entire range of composition at temperature 298.15 K. From the experimental density, viscosity and sound velocity, the excess sound velocity (uE) and deviation in viscosity (Δη) have been calculated. The excess sound velocity (uE) is positive and deviations in viscosities are negative for all the binary systems studies over the whole composition. The results have been used to discuss the nature and strength of intermolecular interactions in these mixtures. The excess properties are found to be either negative or positive depending on the molecular interactions and the nature of the liquid mixtures.


Density; Viscosity; Sound velocity; Cumene; Mesitylene; Viscosity deviation; Binary mixtures; Molecular interaction


Densities, viscosities and sound velocity of solution are very important properties especially for the chemical design and for the optimization of chemical processes. The study of these properties plays an important role in many industrially interesting systems such as organic synthesis, ion extraction systems, gas adsorption solvents and mass transfer phenomena. Furthermore, the study of excess thermodynamics and transport properties for binary mixtures gives important information concerning the deeper understanding of the molecular liquid structure and intermolecular interactions [1]. Aromatic hydrocarbons are also important organic solvents in organic synthesis and extraction systems. Aromatic hydrocarbons like ethyl benzene, toluene, mesitylene were frequently used as octane enhancer in vehicles [2].

The excess molar volume and viscosity deviations are properties sensitive to different kinds of association in the pure components and in the mixtures. These properties have been used to investigate the molecular packing, molecular motions and various types of intermolecular interactions and their strengths, but these properties are influenced by the size, shape and chemical nature of the component molecules [3-5]. In view of this significance, it was thought worthwhile to study the binary mixtures of cumene with ethyl benzene, toluene, mesitylene in order to understand the interactions between these components. The lack of information has motivated us to undertake the present investigations.

Materials and Methods


The chemicals used in the present work were high purity laboratory reagent grade samples of cumene, ethyl benzene, toluene, mesitylene were supplied by CDH Ltd. New Delhi, India with purity 99.5%. All chemicals was stored over sodium hydroxide pellets for several days and fractionally distilled twice. All the chemicals were stored in dark bottles over freshly activated molecular sieve to minimize adsorption of moisture. The purity of the solvent was ascertained by comparing the measured density, dynamic viscosities and sound velocity of the pure component at 298.15K with the available literature [6-10] as shown in Table 1. The reported experimental values of density (ρ), viscosity (η) and sound velocity conform closely to their corresponding literature values, with an average of the absolute value of deviation 3.6 × 10-3 kg m-3 and 3.3 × 10-3 m. Pa. s.

Name of  Liquid           Density Viscosity Sound Velocity
Obs. Lit. Obs. Lit. Obs. Lit.
Cumene 0.8532 0.8581 [6] 0.7337 0.7388 [6] 1326 1325 [6]
Toluene 0.8672 0.8621 [7] 0.5691 0.5525 [9] 1312 13.05 [7]
Ethyl benzene 0.863 0.8625 [7] 0.6345 0.628 [8] 1308 13.05 [7]
Mesityline 0.8616 0.8612 [7] 0.6049 0.667 [10] 1338 1336 [7]

Table 1: Experimental properties of pure liquid at 298.15 K.

Apparatus and procedure

Air tight stopper bottles were used for the preparation of the mixtures and were placed in the dark place. The losses in the mixtures were kept to minimum, as evidenced by repeated measurements of physical properties over an interval of 2-3 days during in which before use time no change in physical properties was observed. The mixtures were well mixed by shaking before use. Binary mixtures were prepared by mass, using an electronic analytical balance (Model K-15 Deluxe, K Roy Instruments Pvt. Ltd.) with an accuracy of ± 0.00001 × 10-3 kg as described elsewhere. The possible error in the mole fraction was estimated to be less than 1 × 10-4. Five samples were prepared for one system and their density and sound velocity were measured on the same day.

Density: Densities of pure liquids and their binary mixtures were determined by using a R. D. Bottle with a 25 cm3 is used to measure the densities (ρ) of pure liquids and binary mixtures. The R. D. Bottle is calibrated by using conductivity water (having specific conductance less than 1 × 106 ohm-1) with 0.9970 and 0.9940 gcm-3 as its densities at T=298.15 K, respectively. The R. D. Bottle filled with air bubbles free liquids is kept in a thermostate water bath (MSI Goyal Scientific, Meerut, India) controlled with a thermal equilibrium. The precision of the density measurements was estimated to be ± 0.0002 g cm-3.

Sound velocity: The ultrasonic velocities were measured using a multi-frequency ultrasonic interferometer (Model F-80D, Mittal Enterprise, New Delhi, India) working at 3 MHz. The meter was calibrated with water and benzene at 298.15 K. The measured values of ultrasonic velocities of pure cumene, ethyl benzene, toluene and mesitylene at 298.15 K were 1326, 1308, 1312 and 1338 m.s-1 respectively, which compare well with the corresponding literature values.

Viscosity: The viscosity of pure liquids and their binary mixture were measured using suspended Ostwald viscometer having a capacity of about 15 ml and the capillary having a length of about 90 mm and 0.5 mm internal diameter has been used to measure the flow time of pure liquids and liquid mixtures and it was calibrated with triply distilled water, methanol and benzene at 298.15 K. The details of the methods and techniques have been described by researchers. The efflux time was measured with an electronic stop watch (Racer) with a time resolution (± 0.015) and an average of at least four flow time readings was taken. Glass stopper was placed at the opening of the viscometer to prevent the loss due to evaporation during measurements. The two bulbs reservoir, one at the top and other at the bottom of the viscometer linked to each other by U type facilitate the free full of liquid at atmospheric pressure.

Theoretical: The excess sound velocity (uE) is evaluated from the experimental values of ultrasound velocities for component liquid and their binary mixtures by:


Where u1,2 is ultrasound velocity in the mixture and u1, u2, X1, X2 are the sound velocities and mole fractions respectively of the component liquid 1 and 2. The ultrasonic velocity (u), density (ρ) and viscosity (η) in pure liquids and liquid mixtures of various concentrations have been measured at 298.15 K.

Viscosity deviations: The viscosity deviations (Δη) with mole fraction were calculated by the following:


Where, xi, ηi and η12 refer, respectively, to the mole fraction and viscosities of ith pure components and of the binary mixtures. The excess value of AE of these thermodynamic parameters have been obtained by subtracting the ideal value from the experimental value:


Where A represents the parameter such as intermolecular free length, molar volume, available volume, free volume and isentropic compressibility and X1 and X2 are the mole fractions of components whose parameters.

Result and Discussion

The experimental values of densities and viscosities of the hydrocarbons are compared with the literature values and are presented in Table 2. It was found that the experimental values are in proximity with the literature values. Insufficient data on densities, viscosities and sound velocity of pure cumene, ethyl benzene, toluene, mesitylene is available. The densities, ρ, viscosities, η and sound velocity, u, of binary mixtures were measured at 298.15 ± 0.01 K as a function of the composition of the corresponding binary mixtures. The results of the study are presented in Table 3.

 Mole fraction (x1)  Density (ρ)  Sound velocity (u)
 Viscosity  (η)
Cumene+ethyl benzene 
0 0.863 0.6345 1308
0.1193 0.8612 0.6472 1310
0.2209 0.8602 0.6633 1314
0.3312 0.8596 0.6715 1316
0.4397 0.8592 0.3882 1317
0.5319 0.8588 0.6931 1318
0.6395 0.858 0.7042 1320
0.7301 0.8572 0.7124 1321
0.8315 0.8564 0.7198 1322
0.9313 0.8554 0.7249 1324
1 0.8532 0.7337 1326
0 0.8672 0.5691 1312
0.1193 0.8628 0.5801 1314
0.2209 0.8612 0.6046 1315
0.3312 0.86 0.6293 1316
0.4397 0.8592 0.6457 1318
0.5319 0.8584 0.6706 1390
0.6395 0.8576 0.6869 1320
0.7301 0.8568 0.7032 1321
0.8315 0.8556 0.7191 1322
0.9313 0.8544 0.7266 1324
1 0.8532 0.7337 1326
0 0.8616 0.6049 1338
0.1193 0.8612 0.6216 1336
0.2209 0.8608 0.6384 1335
0.3312 0.8604 0.6551 1334
0.4397 0.8601 0.6718 1333
0.5319 0.8596 0.6885 1332
0.6395 0.8592 0.6967 1331
0.7301 0.8588 0.7048 1330
0.8315 0.8584 0.713 1329
0.9313 0.8576 0.7293 1328
1 0.8532 0.7337 1326

Table 2: Experimental results for the binary liquid mixtures at 298.15 K.

 Mole fraction (x1) Excess sound velocity (uE) ms-1 Excess viscosity  (ηE) mPa.s 
Cumene+ethyl benzene
0 0 0
0.1024 0.805448391 0.003592714
0.2117 1.316815648 0.005614672
0.3214 1.68579313 0.006837461
0.4617 1.862323267 0.007159198
0.5001 1.869044887 0.006826376
0.6616 1.712750618 0.005826448
0.7088 1.445886092 0.00454673
0.8079 1.00261098 0.002721492
0.9026 0.419256162 0.000601783
1 0 0
0 0 0
0.1024 0.352395 0.002101
0.2117 0.481198 0.003442
0.3214 0.574776 0.00443
0.4617 0.619846 0.004927
0.5001 0.621524 0.00498
0.6616 0.580937 0.004611
0.7088 0.511226 0.003941
0.8079 0.394676 0.002802
0.9026 0.240228 0.00128
1 0 0
0 0 0
0.1024 0.404023349 0.003795502
0.2117 0.737973565 0.006802694
0.3214 1.041263206 0.008969213
0.4617 1.251599686 0.010007761
0.5001 1.340694954 0.010055889
0.6616 1.316287178 0.009162538
0.7088 1.169430526 0.007632876
0.8079 0.846797677 0.005095458
0.9026 0.344591461 0.00176434
1 0 0

Table 3: Excess properties for the binary liquid mixtures at 298.15 K.

The values of Δη are negative for all the selected binary mixtures and regularly decrease with an increase in -CH3 groups from benzene to mesitylene. The deviations in viscosity of binary mixtures are essentially due to two factors (in general).

• The depolymerization of the associated entities like hydrocarbons and formation of monomeric moieties on mixing make a negative contribution to Δη values.
• Replacement of like contents in pure components by unlike contents in mixture makes positive contributions to Δη values.

Negative values of Δη throughout the whole composition range and at all temperatures suggest that the intermolecular interaction becomes weaker on mixing of components, also indicating that the dispersion type of forces is predominant in these mixtures. The negative Δη values support the positive uE values and account for dispersive forces in these binaries. Δη values are also expected to be negative because of vast different in viscosities of pure components (Table 2). The negative values of Δη at equimolar concentrations of 1-iodobutane and hydrocarbons mixtures are in the following order: Benzene>toluene>ethyl benzene>mesitylene.

The deviation in ultrasonic velocity with the mole fraction of cumene for the three systems indicates that there is a non-linear decrease in velocity without having any minimum as shown in Figure 1. The non-existence of maxima or dip at any intermediate concentration of cumenet with ethyl benzene, toluene and mesityline indicate that there is no complex formation between components. These observations are in agreement with the general trends of the ultrasonic velocity variations in binary liquids. The existence of structure differences in species in solution is bound to have its effect in the other physical parameters.


Figure 1. Variation of deviation in sound velocity with mole fraction.

The diversity in viscosity (Δη) gives a quantitative estimate of intermolecular interactions. The Δη at each composition is obtained from the relation suggested by Fort and Moore. The diversity in viscosity becomes positive as the strength of interaction increases. The Δη values may be generally explained considering on the following factors:

• The differences in the size and shape of the component molecules and the loss in dipolar interactions in pure components may contribute to a decrease in viscosity.
• The specific interactions between unlike molecules in hydrogen bond formation and charge transfer complex may lead to increase in viscosity in combinations than in pure components.

The later effect introduces positive deviation while the former effect produces negative deviation in viscosity. The net deviation in viscosity is generally considered as a result of the two major effects. The deviations in viscosity for the three systems at the temperature (298.15 K) are negative indicating the dominance of nonspecific interactions between unlike molecules.

The experimental values of viscosities as a function of mole fraction of trichloroethylene for three systems are shown in Figure 2. The three systems exhibit a positive deviation of excess viscosity over entire mole fraction range with a maximum corresponding to a mole fraction of about 0.5 at the temperature studied. These deviations indicate specific molecular interactions between different molecules.


Figure 2. Variation of deviation in viscosity with mole fraction.


The excess sound velocity, uE and deviations in viscosity, Δη, have been calculated from the experimental values at 298.15K for cumene, ethyl benzene, toluene, mesitylene binary mixtures. the sign and magnitude of these quantities have been discussed in terms of the molecular interactions between the mixing components. The deviation in viscosity and sound velocity show positive behavior, for the systems under investigation indicating strong interactions between the components. However, the deviation in sound showed positive trend.


The authors are very much thankful to the Hon’ble Vice Chancellor, Prof. Mukesh Pandey, Bundelkhand University, Jhansi (U.P.) India. For proving the facilities for research work.

Declarations Conflict of Interest

The authors have no competing interests to declare that are relevant to the content of this article.


The author(s) reported there is no funding associated with the work featured in this article.

Data Availability Statement

All data generated or analyzed during this study are included in this published article.


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