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CHAPTER – 3
DENSITY AND VISCOSITY STUDIES OF BINARY LIQUID MIXTURES
3.1 GENERAL :
Due to recent developments made in the theories of liquid mixtures and
experimental techniques, the study of binary liquid mixtures, has attracted several
researchers in the field [1]. The prediction of the viscosity of liquid mixtures is a
goal of long standing, with both theoretical and practical importance. A truly
fundamental theory would predict the viscosity along with other thermodynamic
and transport properties from the knowledge of the intermolecular forces and
radial distribution function alone. Such a programme has had appreciable success
in application to pure simple liquids such as the liquefied rare gases [2], for
solutions however although the general theory has been formulated, It has not
been reduced successfully to numerical results.
One is thus forced to approximate approaches of which two general types
may distinguished. The first is that of continuous hydrodynamics, whose
application to molecular problem is identified with names of Einestein and stokes.
This approach, in which the discrete, molecular nature of solvent is
neglected, has been remarkably successful in explaining the viscosity o9f dilute
solutions of high polymers. It’s application to solutions in which both components
are of a comparable size is less appropriate.
The second general approach is to correlate the viscosity of liquid mixture
with the properties of pure components and the thermodynamic parameters
characteristic of the interactions, between components, since viscosity is a
property of liquid which depends on the intermolecular forces, the structural
aspects of liquids different concentrations and temperatures.
Viscosity date and excess thermodynamics functions of binary mixtures
have been widely used by various workers to know the nature of interactions
between their components. Relations between viscosity and excess
thermodynamic functions are also known and these functions can be determined
from the viscosity data of binary mixtures.
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3.2 LITERATURE SURVEY :
Brown and smith [3] measured volume changes on mixing of benzene
with methanol, ethanol, 1-propanol, 1-butanol, 2-methyl-2-propanol and hexanol
by using mixing cell, excess volume values increased with increases in
temperature and molecular weight of the alcohol.
Kinematic viscosities and densities were measured [4] experimentally in
the liquid system acetone-benzene-ethylene dichloride. Viscosities were obtained
between 25 and 55 oC. and densities between 25 and 45
oC.
Pardo and van Ness [5] determined excess molar volume at 25 and 45oC.
for binary mixture of ethanol with cyclohexane, toluene, o-xylene p-xylene and
molar volume were observed.
Kemal et al. [6] continuing a study of the effect of molecular structure on
refractive index-density relationships, mixtures of the three possible combinations
of the aromatics benzene, toluene, and xylene were investigated in the present
work The effect of composition and temperature on refractive index dispersion
and density measurement were presented for the mixture of benzene-toluene,
benzene-xylene and toluene-xylene at 20, 30 and 40 oC. Density measurement
provided a satisfactory means for analyzing for this system.
The excess volume of mixing of the binary system benzene-cyclohexane
were measured [7] as a function of composition at 25 and 40 oC. using a direct,
dilatometrictechnique. The results were compared with previous determinations,
and the comparison confirmed the superiority of the direct method of
measurement over the more usual indirect technique of calculating volume
changes from density measurements.
Nigam and Singh [8] determined excess volume for eight binary mixture
consisting of benzene, toluene, cyclohexane, CCl4 chloroform, bromobenzene and
chlorobenzene between 35-45 oC. They examined their results in terms of Apm
and Flory theory. They found Flory theory gave reasonable quantitative
agreement and correct sign of excess function.
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The density viscosity and molecular interaction in binary mixture of
benzene and toluene with chlorobenzene and bromobenzene were measured [9]
at 25 to 35 oC. The studies showed the existence of specific interaction between
the components of the system.
The densities in air of cycloheptane, n-nonanol, 2- methylcyclohexanol,
benzaldehyde, chlorobenzene, and bromobenzene were measured [10] from about
25 to 100 oC. with a modified Robertson pycnometer. The experimental data for
each compound were fitted to nth degree polynomials in temperature for
interpolation and limited extrapolation. The agreement with the literature values
was satisfactory.
The viscosity of 10 binary systems, including polar and nonpolar
components, was determined [11] at 20 and 25 oC. The viscosity of the ternary
system heptane-iso-octanetoluene was also determined at 25 oC. Experimental
data were correlated by means of the method of McAllister and that of Heric.
Densities and molar volumes of solutions of nitrobenzene in 18 week
electron solvents were measured [12] as functions of concentration at 25 oC The
data were fitted by a least-squares method to a polynomial. No obvious
relationship was observed between the electron donating ability of the solvents
and densities of the solutions.
Densities of mixtures of benzene with four n-alkanes C6, C7, C10 and C16
were determined [13] at 25 and 50 oC. using a pycnometric method. The density
measurements were used to extend the corresponding states method of Rowlinson
and coworkers to systems containing benzene and long chain hydrocarbons.
Measurements of excess enthalpies in a flow microcalorimeter and of
excess volumes in a successive dilution dilatometer were carried out [14] at
298.15 K. For binary mixtures of chlorobenzene with benzene, toluene,
ethylbenzene, and xylene, m-xylene, and p-xylene.
The relationship between the composition of the ternary mixtures of
benzene-toluene-xylene and the refractive index, as well as density, was
determined [15] at 25 oC.
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The viscosities for two systems, nitrobenzene-n-pentane and nitrobenzene-
n-heptane, were measured [16] for various concentrations and temperatures
between 20 and 40 oC. The viscosity in the neighborhood of critical point of
solution became anomalously large. The excess viscosity at the critical point lead
to a cusp rather than an infinity.
Ortega et al. [17] determined the excess volume of benzene with several
isomers of hexanol at 298.15 K. The results were fitted to a polynomial of
variable degree.
Rastogi et al. [18] measured excess molar volume for tetrachloro ethylene
+ toluene + p-xylene +CCl4 and + cyclohexane at 303.15 K. For some mixture an
inversion in sign in excess volume was observed.
Garrett and Pollock [19] measured the excess volume of benzene and
toluene with pyridine and methyl pyridine at 298.15 K. A linear correlation
between Pka and excess volume was found.
Nath and Singh [20] measured the excess molar volume at 293.15 K. for
mixture of tetrachloroethylene with benzene, toluene, p-xylene and CCl4. The
temperature coefficient of excess molar volume was determined.
Nath and Dubey [21] measured excess molar volume for trichloroethene
with benzene, toluene, p-xylene, tetrachloro methane and CHCl3 at 303.15 K. by
using dilatometer.
The volumes of mixing and dielectric constants of nitrobenzene-sulfolane
mixtures were measured, [22] at several temperatures ranging within 288.16-
333.16 K, over the entire composition range. The observed deflations from
ideality, decreasing with increasing temperature, were interpreted as not
indicative of significant interactions between unlike molecules.
Raman et al. [23] measured excess volume of n-alkanol with nitrobenzene
and chlorobenzene at 303. 15 K. Excess volumes were negative in mixture rich in
alkanol and positive else were. The results were attributed to the interaction
between unlike molecules.
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Excess volumes of nonelectrolyte solutions of n-heptane, n-octane, and n-
nonane with chlorobenzene, nitrobenzene and benzonitrile were measured [24] at
313.5 K. by using a dilatometer.
Karvo [25] measured the excess enthalpies of sulpholane + benzene,
toluene, p-xylene and + meistylene at 303.15, 313.15 and 323.15 K. The value
were positive and increased with increasing hydrocarbon alkylation.
Viscosities of three binaries, viz., n -hexane-toluene, n -hexane-
chlorobenzene, and n -hexane-1-hexanol, were determined [26] at 30, 40, 50, and
60 oC. over the complete composition range. Experimental viscosities were
compared with values calculated by using equations based on the concept of
significant liquid structures as well as McAllister type three-body interactions.
Energies of activation for viscous flow were obtained and their variations with
composition were discussed.
Iloukhani et al. [27] measured excess volume of binary mixture of
substituted benzene with ethyl acetate at 313.15 K. The excess volumes were
positive over the entire range of composition.
Excess volume for binary mixture of methyl ethyl ketone with benzene,
toluene, chlorobenzene, bromobenzene and nitrobenzene were determined by
Jayalakshmi and Reddy [28] at 303.15 K, and 313. 15 K. The excess volume were
negative over the entire range of composition for all the system and both the
temperature. The data were examined in terms of Flory’s original theory.
The excess molar enthalpies of halogenobenzene + benzene or toluene and
of some dihalogen benzene were measureed [29] at atmospheric pressure and
303.15 K. The results were fitted to Redlich-Kister equation.
Singh et al. [30] measured viscosity and density of ternary liquid mixture
of ethyl benzene, bromobenzene and toluene. Mixture viscosities and densities of
the partially miscible ternary systems of toluene, chlorobenzene, and 1-hexanol
with their partially miscible binary subsystem n-hexane-benzyl alcohol were
measured at 30, 40, 50, and 60 oC. Activation enthalpies and entropies for
viscous flow were obtained and their variations with composition were discussed.
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Rathnam [31] determined the excess volume of binary mixture at of ethyl
acetate with O-xylene. P-xylene at 303. 15 K, and 313. 15 K. Excess volume were
negative over the whole range of composition.
Viscosity coefficient measurements at saturated pressure were reported
[32] for ethyl acetate + o-xylene, ethyl acetate + p-xylene, ethyl acetate +p-
dioxane over the entire range of composition at 310.15 K. The value of mixture
viscosity were calculated for different composition by the application of Katti and
Chaudhri equation.
Marsh and Kim [33] reported the excess volume of binary system of 2-
methyl -2-propanol with water at 5 K interval from 303.15 to 323.15 K. The
partial molar volume of 2-methyl-2-propanol at infinite dilution in water was
extremely temperature dependent becoming more negative as temperature
increased.
Excess molar volumes for binary system of ethylbenzene with
chlorobenzene, nitrobenzene, aniline and benzene alcohol were measured [34] at
298. 15 K. using dilatometer. The excess volumes were negative for all systems
except for ethylbenzene + aniline. It was slightly positive at lower concentration
of aniline.
A number of excess functions were computed from the measured [35]
densities and viscosities of binary mixtures of bromoform with benzene, toluene,
p-xylene, acetonitrile, nitrobenzene and tetrahydrofuran at 298.15, 308.15
and318.15 K. Excess enthalpy and excess entropy of viscous flow were predicted
from the Arrhenius plots. Intermolecular interactions in the mixtures were
considered in the discussion of results.
Sinha et al. [36] measured the viscosity and density of ternary mixture for toluene,
ethylbenzene, bromobenzene and 1-Hexanol at 30, 40, 50, and 60 oC. the
nonidealities reflected in mixture viscosities were expressed and discussed in
terms of excess which were both positive and negative.
Aminabhavi et al. [37] measured excess volume, excess viscosity, excess
free energy of activation of flow, and contact interaction parameter were
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computed for binary liquid mixtures of nitrobenzene with cyclohexane or N,N-
dimethylformamide from density and viscosity measurements in the temperature
interval of 298.15-313.15 K. The calculated quantities were discussed in terms of
the nature of the molecular interactions between the components. Attempts were
also made to test the validity of the viscosity models of Heric, Auslaender, and
McAllister in predicting the binary viscosity data.
Experimental measurements of density and viscosity of three binary
systems, viz., p –xylene, m -xylene, p-xylene, o -xylene, and m -xylene/o -xylene,
were performed [38] over the complete concentration ranges, for temperatures
between 273.15 and 303.15 K. For the same temperature interval, densities and
viscosities of three ternary mixtures of the isomers were obtained. Experimental
densities were compared with those predicted by the Hankinson-Brobst-Thomson
method, showing average deviations of about 0.3 %. The viscosity data were
correlated by the McAllister equations, producing excellent representations of
both binary and ternary data.
Excess volume and isentropic compressibilities of binary mixture of p-
chloro toluene with 2-propanol, 2-methyl -1- propanol and 3- methyl –1-butanol
were measured [39] at 303.15 K. The excess volume exhibits inversion in sign in
three mixture. The results were compared with those of there corresponding 1-
alkanols was more + ve for 1-alkanols group.
Excess molar volumes were determined [40] as a function of composition
at 308.15 K. for cycloalkanol with cyclohexane, benzene, toluene and p-xylene.
The results were interpreted on the basis of the structure breaking effect of
aromatic hydrocardon and weak specific interaction of the type OH- electron
between unlike molecules.
Aralaguppi et al. [41] determined the molar volume excess isentropic
compressibility and excess molar refraction of binary mixture of methyl
acetoacetate with benzene, toluene, m-xylene, mesitylene and anisole in the
temperature range 298. 15- 308.15 K. The excess molar volumes were explained
on the basis of the presence of weak dispersion type molecular interaction.
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Excess molar volume VE of p-chlorotoluene with 1-propanol, 1-butanol, 1-
pentanol, 1-hexanol and heptanol were measured [42] at 303.15 K. VE were
negative in mixtures rich in alkanol and positive in those rich in p-chlorotoluene.
A comparison of these results with those for mixture of alkanols with toluene
showed that the algebraic value of VE were smaller in former group.
Kumar and Naidu [43] reported excess volume and isentropic
compressibilities of 1, 3 – dichlorobenzene + 2-propanol, + 2- methyl -1 propanol,
+ 3 methyl-1-butanol at 303.15 K. Both excess volume and deviation in isentropic
compressibilities were negative.
Yu and Tsai [44] determined the excess molar volume of binary mixture
or benzene and 1-alkonols ) at 298.15 K, and 308.15 K. The value of
molar volume were positive over the entire range of composition. The results
were compared with those predicted by the Hankinson-Brobst-Thomson
correlation (HBT) and the Spencer and Danner modified Rackett equation (SDR).
The HBT equation showed an average deviation of about 0.74% from the
experimental results while the SDR equation showed a 0.20% average absolute
deviation. The excess molar volumes, , calculated from the density values
were found to be positive for all the concentrations and temperatures considered.
Measurement of the densities for benzene + hexane using a high pressure
stainless steel pyconometer system at various temperatures between 298.15 and
473.15 K, were reported [45]. Excess molar volumes were found to be positive for
all concentrations and temperatures considered.
Excess volume for five ternary mixture of 2-methoxy ethanol + butyl
acetate + benzene + toluene, +chlorobenzene + bromobenzene and +nitrobenzene
measured [46] at 303.15 K. The excess volume exhibited positive deviation.
Jain et al. [47] determined excess molar volumes for the binary mixtures:
ethylbenzene + o-xylene, +m-xylene, + p-xylene; o-xylene + m-xylene, +p-xylene
and m-xylene +p-xylene were determined from density data obtained using
vibrating tube densimeter. The results were compared with literature values and
with Flory's theory.
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The density and viscosity of binary mixtures of propanoic acid + benzene,
+ toluene, and + 0-, + m-, and + p-xylenes were measured [48] at 298.15 K.
Excess volumes were calculated. The interactions existing between the
components were discussed. The results were used to theoretically justify the
validity of the viscosity models.
The volume of mixing, speed of sound, and viscosity of binary liquid
mixtures composed of butyl acetate + o-xylene, + m-xylene, and + p-xylene were
measured [49] at 303.15 K. The excess volumes and deviations in isentropic
compressibility and viscosity were discussed in terms of molecular interaction
between like and unlike components.
Excess volume for binary mixture of ethyl acetate with toluene,
chlorotoluene and p-chloro toluene derivative were determined from density
measurement [50]. Negative excess volume was observed due to the interaction
occurring between unlike molecules.
Densities and viscosities of mixture of nitrobenzene with methanol,
ethanol, propan-1-ol, propan-2-ol, butan-1-ol, 2-methyl propan-1-ol and 2-methyl
propan 2-ol were measured [51] at 298.15 and 303.15 K. From these
measurement excess volume (VE) and deviation in viscosity ( ) were calculated
and the results were fitted to the Redlich-Kister polynomial.
Densities and speed of sound were measured [52] at 298.15, 303.15,
308.15 and 313.15 K. for the binary mixture of aniline with methyl alcohol and
ethyl alcohol, from these, excess molar volume, excess intermolecular free length
and isentropic compressibility deviation were calculated. The experimental and
calculated quantities used to discusse the mixing behavior of the components.
Gupta et al. [53] measured the excess molar volume of 1-propanol or 2-
propanol + aromatic hydrocarbon at 303. 15 K. The excess volume data for these
binary systems were interpreted in terms of Mecke-Kempter type association
model with Flory contribution terms.
Excess molar volumes of binary mixed solvents containing tetraethylene
glycol and benzene, toluene, acetone and acetonitrile were measured [54] as a
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function of composition at 308.15K. The measurement were carried out with a
continuous-dilution dilatometer. The excess volumes were all negative over the
entire range of composition. The results were discussed in terms of the interaction
between components. The Flory model was used to calculate the excess volumes,
and were compared with experimental data for the four mixtures.
Gupta et al. measured [55] dielectric constants and refractive indices data
at 308.15 K. for 1-propanol with cyclohexane, benzene, toluene, o-, - and p-
xylene. The analysis of data showed the presence of strong specific interactions
between propanol and aromatic hydrocarbon. Frohlich equation was used to
calculate the apparent dipole moment of these binary mixtures
Densities, viscosities and refractive indices were measured [56] for 4-
chlorotoluene + methyl acetate, + ethyl acetate and + propyl acetate at 293.15,
298.15 and 303.15 K. The results were correlated by means of Redlich-Kister type
equation and discussed in terms of molecular interaction.
The excess volumes for 1-butanol or 2-butanol or 2-methylpropan-1-ol or
2-methylpropan-2-ol + o-xylene or m-xylene or p-xylene at 308.15 K. were
measured [57] overs the whole range of composition. The excess volumes vs
composition curves were skewed toward the low concentration of butanol. For
systems containing 1-butanol, curves were sigmoids and excess volumes values
changed sign in the 1-butanol (1) rich region (x1 > 0.8). For butanol + xylene
systems VE values varied in the order 2-methylpropan-2-ol > 2-butanol > 2-
methylpropan-1-ol > 1-butanol
Bhardwaj et al. [58] dilatometrically measured excess molar volume of
(butan-1-ol or butan-2-ol, or 2-methyl propan-1-ol or 2-methyl propan-2-ol
benzene + toluene) over the enter range of composition at the temperature 308.15
K. The results indicate the branching of an alkyl group of butanol near the
hydroxyl group make both the hydrogen bonding and electron donor accepter
interaction between butanol and benzene or toluene molecule less effective.
Excess molar volumes and excess molar heat capacities, were determined
[59] for mixtures of benzonitrile with chlorobenzene, or benzene, or toluene at the
temperatures 298.15 K, and 303.15 K. For all the systems the values of excess
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molar volumes were negative over the whole range of compositions and
(∂VmE/∂T) were negative. The values of excess molar heat capacities were all
positive for the mixtures of chlorobenzene and toluene, while the sign for the
mixture with benzene changed from positive to negative with increasing mole
fraction of benzonitrile. The magnitudes of (∂Cp,E/∂T) were small, and the sign
depended on the system.
Excess molar volume measured [60] in a vibrating tube densimeter and
excess molar heal capacity measured in a flow calorimeter, were made for binary
mixture of ( ethanol + benzene or toluene or xylene or chlorobenzene) at a temp
295.15 K. The experimental results were interpreted in terms of self association of
ethanol and hydrogen bonds formed between ethanol and aromatic compound.
Venkatesu and Rao [61] determined the molar excess volume of binary
mixture of triethylamine with ethyl benzene, chlorobenzene, nitrobenzene,
bromobenzene at 308.15 K. The molar excess volume values were negative in all
the system over the entire range of composition. The results were interpreted on
the basis of intermolecular interaction between unlike molecule.
Swain et al. [62] systematically determined viscosities and densities of
ternary mixtures of tri-n-butyl phosphate + benzene + o-xylene at (30, 35, 40, and
45) oC. The deviations in the viscosity from a mole fraction average were fitted in
a Redlich-Kister-type equation, which included the contribution of each
constituent binary system along with a ternary contribution term.
The excess molar Gibbs energies of mixing for (2-methyl propan-2-o1 +
benzene or toluene or o, or m, or p-xylene ) at T =308.15 K. were calculated [63]
by the Barker method from vapour pressure data measured by static method.
Bhardwaj et al. [64] measured excess molar enthalpies at 308.15 K. for 2-
methylpropan-1-ol with benzene, toluene, o-, m- and p-xylene over the entire
range of composition. The analysis in terms of an athermal associated mixture
model Mecke–Kempter type with a Flory contribution term and quasi-chemical
model by Barker was described. Association model predicted good agreement
with VE data, while the prediction of both association model and quasi-chemical
model were fairly good for HE data.
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Excess molar volume data on mixing for binary mixtures of sulfolane with
toluene, o-xylene, m-xylene, p-xylene, ethylbenzene and 1,2,4-trimethyl benzene
were measured [65] over the entire composition range at 298.15 K, and
atmospheric pressure in order to investigate interactions between molecules. A
vibrating tube density meter was used. All mixtures exhibited negative excess
volumes with a minimum which occurs approximately at = 0.5. The
experimental results were correlated using the Redlich–Kister equation.
Viscosities and densities of binary mixtures of tri-n-butyl phosphate (TBP)
with benzene, toluene and o-xylene were measured [66] at 30, 35, 40 and 45 oC.
The non-idealities reflected in mixture viscosities were expressed in terms of
excess viscosities. A Redlich-Kister-type equation was fitted to the binary -X-T
data for each system.
Excess molar enthalpies of (2-methyl propan 2- benzene or toluene or o,
m, or p-xylene ) were measured [67] in a flow micro calorimeter over entire
range of composition at 308.15 K. The results were analysed in terms of Mecke-
Kempter type association model with Flory contribution term.
Artigas et al. [68] measured densities and viscosities for mixture of some
hydrocarbon with 2-methyl -1-propanol at 298.15 and 313.15 K. The excess
molar volume and deviation in viscosity were found to be negative throughout the
entire range of composition.
The excess molar volume, excess molar enthalpies and excess molar heat
capacities were measured [69] as a function of mole traction at different
temperature for benzonitrile + benzene and benzonitrile + toluene. The results
were explained in terms of simple theory of complex formation.
Densities and refractive indices of the binary system ter butyl alcohol +
toluene +isooctane and + methyl cyclohexane and toluene + methyl cyclohexane
over entire range of composition were measured [70] at 298.15 K. Excess molar
volume and change of refractive indices were evaluated from empirical data. The
derived properties were fitted to variable degree polynomials.
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Densities and viscosities were measured [71] for anisole with 2-butanol, 2-
methyl 1-propanol and 2-methyl 2-propanol binary liquid mixture with vibrating-
tube densimeter and Cannon-Fenske routine viscometer over the temperature
range between 303.15 and 323.15 K, and atmospheric pressure. Excess moral
volume and viscosity deviation were calculated at various temperatures. Both
excess molar volume and the viscosity deviation were negative for investigated
system. The isothermal excess molar volume and viscosity deviation were fitted
to a Redlich-Kister type equation.
New experimental data on densities and viscosities [72] for the systems 4-
methylpyridine + methanol, + ethanol, + propan-1-ol, + propan-2-ol, + butan-2-ol,
and + 2-methylpropan-2-ol were presented at 298.15 K, and ambient pressure
using a vibrating tube densimeter and an Ubbelohde viscometer. The results were
discussed qualitatively in terms of the association of the mixture components
caused by chainlike self-association of the alcohol molecules and cross-
association between alcohol and 4-methylpyridine.
Prabhavati et al. [73] measured excess volume for binary mixture of N-
methyl cyclohexylamine with benzene, toluene, o-xylene, m-xylene, and p-
xylene, chlorobenzene, bromobenzene and nitrobenzene at 303. 15 K. The excess
volume values were positive in mixture of N-methyl cyclohexylamine with o. m.
p-xylene, bromobenzene and nitrobenzene and an inversion of sing from negative
to positive was observed in the mixture of N methyl cyclohexylamine with
benzene, toluene. p-xylene and chlorobenzene. The experimental VE
were
analysed on the basis of molecular interaction between unlike molecules.
The densities in the temperature range 288.15 K. To 308.15 K, and the
viscosities in the temperature range 293.15 K. To 308.15 K, of the binary systems
-butyrolactone + o-xylene and m-xylene were measured [74]. Viscosity data
were correlated by the Heric, McAllister, and Hind-McLaughlin-Ubbelohde
equations. Viscosity deviations from mole fraction linearity and excess volumes
were calculated and found to be negative. Excess volumes were also fitted to a
Redlich-Kister type equation.
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Molar excess volumes ) were evaluated for binary mixtures of
hexadecane and butanol in the temperature range of 303.15K to 318.15 K, at 5 K
intervals. values were computed [75] form density at various compositions.
negative over the entire range of composition and become less negative
at increasing temperatures. The results of excess molar volume were fitted to the
Redlich-Kister relation to estimate the adjustable parameters and standard
deviations. The results were discussed on the basis of intermolecular interactions
between unlike molecules.
Densities and viscosities were measured [76] for the binary mixture of
butan-2-o1 and 2-methyl propanol-2-ol with nitroethane at temperature from
293.15 K, to 313.15 K, and atmospheric pressure. McAllister’s three body
interaction model was used to correlate the binary kinematic viscosities.
Densities and viscosities for the binary liquid mixtures of anisole or
methyl tert-butyl ether (MTBE) with benzene, chlorobenzene, benzonitrile, and
nitrobenzene were measured [77] at 288.15, 293.15, and 298.15 K. These were
used to compute the excess volumes (VE) and deviations in viscosity ( ). These
properties were discussed with reference to the nature of interactions between the
unlike molecules.
Densities and viscosities of butanenitrile + 1-butanol, + 2-methyl 1-
propanol, + 2-butanol or + methyl 2-propanol were measured [78] at several
temperatures between 288.15 K, and 318.15. At each temperature, the
experimental viscosity data were correlated by means of the McAllister bi
parametric equation.
Tu et al. measured [79] densities and viscosities for the binary mixture of
methanol, propan-1-ol, propan-2-ol, butan 2-ol and 2methyl propan-2-ol with
nitro methane at temperatures from 293.15 K, to 313.15 K, and atmospheric
pressure. The results were fitted to McAllister three body interaction model to
correlate the binary kinematic viscosities.
Densities and viscosities of binary mixture of benzonitrile with methanol
ethanol, propan-1-ol, butan-1-ol, pentan-1-ol, and 2-methyl 2-propanol were
measured by Nikam et al. [80] at 303.15, 308.15 and 313.15 K. From these data,
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excess molar volume and deviation in viscosity were computed. These quantities
were fitted to a Redlich-Kister type polynomial.
The density, viscosity and ultrasonic velocity in binary mixture of propan-
l-ol, butan-l-ol and pentan-l-ol with 1,2-dibromoethane were determined [81] at
different temperatures from 298.15 to 313.15 K, over the whole composition
range. Using these parameters the excess volume ) excess viscosity ),
excess compressibility ), inter molecular free length ) and Grunberg and
Nissan parameter were evaluated. The butan-1ol + 1,2-dibromoethane system
were found to be negative at all temperature whereas for pentan-1-ol + 1,2-
dibromoethane the ) value were observed to be negative at low concentration
of pentan-1-ol (up to 0.1 molefraction).
Ouyana G, et al. [82] measured density for binary mixture of (2-propanal +
o-xylene, +m-xylene, + p-xylene, + 2methyl–2 propanol + o-xylene, +m-xylene, +
P-xylene ) at 298.15 K, and the excess molar volumes were derived.
Bahadur and Sastry [83] measured the densities and speed of sound of ten
ternary mixture of methyl acrylate (1) + 1-propranol (2) or 1-butanol (2) + n-
hexane (3) + n-heptane (3), + cylohexane (3) + benzene (3) + toluene (3) at
308.15 K. The excess volume, VE, and excess isentropic compressibility, Ks
E,
were estimated.
Aminabhavi et al. [84] determined densities, viscosities, and refractive
indices at (298.15, 303.15, and 308.15) K, and the speed of sound at 298.15 K, as
a function of mixture composition for the binary mixtures of ethyl chloroacetate +
cyclohexanone, + chlorobenzene, + bromobenzene, or + benzyl alcohol. Using
these data, excess molar volume and deviations in viscosity, molar refraction, and
speed of sound was calculated. These results were correlated with the Redlich and
Kister polynomial equation to derive the coefficients and standard errors.
George and Sastry [85] measured densities, speeds of sound, viscosities,
and relative permittivities for 21 binary mixtures of alkoxyethanols (2-
methoxyethanol, 2-ethoxyethanol, and 2-butoxyethanol) + benzene, + toluene, +
(o-, m-, and p-) xylenes, + ethylbenzene, and + cyclohexane at different
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64
temperatures. The excess molar volumes, excess isentropic compressibilities,
deviations in dynamic viscosities, speeds of sound, and relative permittivities
were calculated across the mole compositions. The compositional variation of
excess and deviation functions has been expressed in terms of the Redlich-Kister
equation.
Densities and viscosities of ternary mixtures of N,N-dimethylformamide +
benzene + chlorobenzene and corresponding binary mixtures of N,N-
dimethylformamide + benzene, N,N-dimethylformamide + chlorobenzene, and
benzene + chlorobenzene were measured [86] at (298.15, 303.15, 308.15, and
313.15) K. From these data, excess molar volumes (VE) and deviations in
viscosity ( ) were calculated. Several empirical equations were used to predict
the excess molar volumes and deviations in viscosity of ternary mixtures. The
kinematic viscosities of binary and ternary liquid mixtures were also correlated
with mole fractions by McAllister’s equation.
George and Sastry [87] measured the densities, dynamic viscosities,
speeds of sound, and relative permittivities, for (dibutyl ether + benzene, or
toluene, or p-xylene) at different temperatures over the whole composition range
and at atmospheric pressure. The mixture viscosities were correlated with semi
empirical equations. Calculations of the speed of sound based on Nomoto’s
equation were found to be close to experimental values for the three mixtures and
at two temperatures. Excess functions such as excess molar volumes , excess
isentropic compressibilities , deviations in relative permittivities , and molar
polarizations were calculated and fitted to Redlich–Kister type equations.
Grunberg et al. [88] measured thermodynamic properties of non aqueous
binary mixture of benzene with corbon tetrachloride and chloroform at 298, 308,
318 K. The excess volume the excess viscosity, excess free energy of activation
of viscous flow and interaction parameter of Grunberg and Nissan were calculated
from experimental data as a function of composition and discussed.
The densities of (o-xylene, or m-xylene, or p-xylene + dimethyl sulfoxide)
were measured [89] at temperatures 293.15, 303.15, 313.15, 323.15, 333.15,
343.15, 353.15 K, and atmospheric pressure by means of a vibrating-tube
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densimeter. The excess molar volume, , calculated from the density data
provided the temperature dependence of in the temperature range of 293.15 to
353.15 K. The results were correlated using the fourth-order Redlich–Kister
equation, with the maximum likelihood principle being applied for the
determination of the adjustable parameters. It was found that the in the
systems studied increase with rising temperature.
Yang et al. [90] measured excess molar volume and viscosity of binary
mixture of sulfolane with benzene, toluene, ethyl benzene, p-xylene, o-xylene at
303.13 and 323.15 K, and atmospheric pressure. The computed quantities were
fitted to Redlich–Kister equation to drive the coefficient and estimate the standard
error. The results were discussed in terms of intermoleclulor interactions.
Densities and speeds of sound were reported [91] for the binary mixtures
of (1,3-dioxolane or 1,4-dioxane) with (2-methyl-1-propanol or 2-methyl-2-
propanol) at the temperatures (298.15 and 313.15) K. Excess volumes and excess
isentropic compressibility coefficients were calculated from experimental data
and fitted by means of a Redlich–Kister type equation. The ERAS model was
used to calculate the excess volumes of the four systems at both temperatures.
Tanaka and Yokayama [92] measured apparent dipole movement of 1-
butanol, 1-propanol and chlorobenzene in cyclohexane or benzene and excess
molar volume al. 298.15 K. using Rohlich equation. The dipole-dipole
interactions observed for chlorobenzene were rather weak.
The viscosities and densities of binary mixture of ethyl benzene with
ethanol, 1-propanol, 1-butanol were determined [93] at 298.15 and 308.15 K. The
deviation in viscosity for all 3 system, were negative and the values decresed with
an increase in temperature which may be due to the reduction in dispersion force.
Singh et al. [94] measured the viscosities, densities, and speeds of sound
of binary mixtures of 4-methylpentan-2-one with o-xylene, m-xylene, p-xylene,
and isopropylbenzene at 298.15 K, over the whole composition range. Excess
volume, excess compressibility, and deviations in viscosity were calculated.
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Singh et al. [95] measured viscosity and density of binary mixture of o-
xylene, m-xylene, and isopropyl benzene with 2- butanone at 298.15 K. The
deviation in viscosity were negative for the system containing o-xylene, m-xylene
and isopropyl benzene but for p-xylene, the deviation was positive.
Rathnam and Mohite measured [96] the viscosity density and refractive
indices of binary mixture of ethyl formate or ethyl benzoate with o-xylene, m-
xylene and ethyl benzene at 303.15 K, and 315.15 K, and atomsphric pressure for
the whole composition range. The experimental viscosities were fitted to an
empirical equation proposed by Frenkal.
Densities, viscosity and refractive indices of binary mixtures of anisole
with benzyl chloride, chlorobenzene and nitrobenzene were measured [97] al.
303.15 K. The variation of properties with composition suggested that the stegth
of intraction in these mixture followed the order, benzyl chloride > Nitrobenzene
> chlorobenzene.
The densities of binary mixtures formed by nitrobenzene with benzene or
toluene or ethyl benzene or styrene or o-xylene or m-xylene + nitrobenzene were
measure [98] in the temperature rang e of (298.15 to 353.15 K) and ambient
pressure using a vibrating tube densimeter. The results were correlated using
the fourth order Redlich-Kister equation. It was found that the in these system
studied, increases with rising temperature.
Densities and viscosities of 1-brombutane + 1-butanol, +2-methyl 1-
propanol, +2 butanol or + 2-methy-2 propanol were measured [99] at several
temperature. The experimental viscosities data were correlated by means of
McAllister bi parametric equation.
Density, viscosity, and refractive index, values for (tetradecane + benzene,
+ toluene, + chlorobenzene, + bromobenzene, + anisole) binary mixtures over the
entire range of mole fraction were measured [100] at temperatures 298.15,
303.15, and 308.15 K at atmospheric pressure. The speed of sound was measured
at 298.15 K, only. Using these data, excess molar volume deviations in viscosity,
Lorentz–Lorenz molar refraction, speed of sound, and isentropic compressibility
were calculated. These results were fitted to the Redlich and Kister polynomial
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equation to estimate the binary interaction parameters and standard deviations.
Excess molar volumes exhibited both positive and negative trends in many
mixtures, depending upon the nature of the second component of the mixture. For
the (tetradecane + chlorobenzene) binary mixture, an incipient inversion was
observed. Calculated thermodynamic quantities were discussed in terms of
intermolecular interactions between mixing components.
Excess volumes, ultrasonic sound velocity, isentropic compressibilities
and viscosities ( ) were measured [101] for the binary mixture of DMSO with
1,2-dichlorobenze, 1,3-dichlorobenzene, 1,2,4 trichloro benzene, o-chlorotoluene,
m-chlorotoluene, p-chlorotoluene, o-nitrotoluene and m-nitrotoluene at 303.15 K.
Hasan et al. [102] measured density, viscosity and speed of sound studies
of binary mixture of methyl benzene with heptan-1-ol, octan-1-ol and decan-1-ol
at 303.15 and 313.15 K. The excess molar volume and excess isentropic
compressibility were positive for all three binaries studied over whole
composition where as deviation in viscosities were negative, and excess isentropic
compressibility were fitted to the Redlich-Kister polynomial equation The
Joyaban Acree model was used to correlate the experimental values of density,
viscosity and ultrasonic velocity at different temperatures.
The viscosities, densities, and speeds of sound of binary mixtures of
anisole with benzene, toluene, o-xylene, m-xylene, p-xylene, and mesitylene over
the entire range of mole fraction were measured [103] at temperatures 288.15,
293.15, 298.15, and 303.15 K, and atmospheric pressure. Excess compressibility
and deviations in viscosity were calculated and fitted to the Redlich-Kister
polynomial relation to estimate the binary coefficients and standard errors. The
deviations in viscosities and excess compressibilities were negative for all binary
systems. The speeds of sound were analyzed in terms of collision factor theory
and free length theory. The viscosity data were correlated with equations of
Grunberg and Nissan, Tamura and Kurata, Heric and Brewer, and McAllister.
Densities and viscosities of binary mixtures of aniline with benzene were
measured [104] over the entire range of composition, at atmospheric pressure,
and at 298.15, 303.15, 308.15, and 313.15 K. Excess molar volumes and
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deviations in viscosity were calculated from the experimental data. Negative
excess molar volume and negative deviations in viscosity for aniline + benzene
systems were due to the interstitial accommodation of benzene molecules into
aggregates of aniline. The excess molar volumes and deviations in viscosity were
fitted to the Redlich–Kister polynomial equation. Furthermore, densities and
viscosities of ternary mixtures of aniline+benzene+N,N-dimethylformamide were
measured at atmospheric pressure, and at 298.15, 303.15, 308.15, and 313.15 K.
From these data, excess molar volumes and viscosity deviations were calculated.
McAllister's three-body interaction model has been used to correlate the
kinematic viscosities of binary and ternary liquid mixtures with mole fractions.
Several empirical equations were used to predict excess molar volumes and
deviations in viscosity of ternary mixtures.
Acoustical and excess properties of chlorobenzene + 1-hexanol or 1-
heptanol or 1-octanol or 1-nonanol or 1-decanol were studied by Adel et al. [105]
at 298.15, 303.15, 308.15, 313.15 K. The calculated excess and deviation
functions were fitted to polynomial relation to estimate the coefficient and
standard errors. The effect of n-alkan-1-ol chain length as well as temperature on
the excess molar volume were studies.
Ultrasonic speed, and viscosities of pure aniline, 1-propanol, 2-propanol,
2-methyl 2-propanol and their binary mixtures with aniline as a common
component over the entire composition range were measured [106] at 293.15,
298.15 303.15, 308.15, 313.15 and 318.15 K. From experiment data the deviation
in isentropic compressibility Ks and in viscosity, were calculated.
Densities and viscosities for N-formylmorpholine (NFM) with p-xylene,
m-xylene, and o-xylene were determined [107] over several temperatures at
atmospheric pressure. Density and viscosity data were used to compute the excess
molar volumes and viscosity deviations and they were fitted to the Redlich-Kister
equation
Excess volume of the binary liquid system of methyl formate, ethyl
formate, propyl formate, with bromo, chloro, and nitrobenzene were derived from
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experimental density measurement [108] at (303.15, 308.15 and 313.15) K. The
excess volume were fitted to Redlich-Kister polynomial equation.
Bhaskarn and Kubendran [109] measured densities, viscosities, refractive
index, surface tension and ultrasonic velocity for p-anisaldehyde +chlorobenzene
at 303.15, 313.15 and 323.15 K. The excess values were fitted to the Redlich-
Kister polynomial equation.
Densities and viscosities for binary mixture of vitamin K3 +benzene,
toluene, ethylbenzene, o-xylene, m-xylene, p-xylene respectively were
determined by Song et al. [110] at 303.15 to 313.15 K. Results were fitted to
obtain appropriate parameter and standard deviation between the measured and
fitted values.
The densities, of binary mixtures of methyl acrylate (MA) with benzene,
toluene, o-xylene, m-xylene, p-xylene, and mesitylene, including those of pure
liquids, over the entire composition range were measured [111] at temperatures
(293.15, 298.15, 303.15, 308.15, 313.15, and 318.15) K and atmospheric pressure.
From the experimental data, the excess molar volume, partial molar volumes, and
excess partial molar volumes, at infinite dilution were calculated. The values
were found negative over the whole composition range for all the mixtures and at
each temperature studied, except for MA + mesitylene which exhibit positive
values, indicating the presence of specific interactions between MA and
aromatic hydrocarbon molecules.
The experimental densities, dynamic viscosity and speed of sound of thirty
six binary mixture of ester + organic solvent (n-hexane, benzene, toluene, o, m, P-
xylene), + halogenated benzene (chloro bromobenzene), + nitrobenzene were
measured [112] over the complete composition range at atmospheric pressure and
temperature (295.15 to 313.15 K) excess molar volume, excess isentropic
compressibilities were calculated and fitted to Redlich-Kister type equation.
Densities for binary systems of (p-xylene or o-xylene + ethylene glycol
dimethyl ether) were measured [113] over the full mole fraction range at the
temperatures of (298.15, 303.15 and 308.15) K along with the densities of the
pure components. The excess molar volumes (VE) calculated from the density
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data show that the deviations from ideal behaviour in the two binary systems were
negative, and they become more negative with the temperature increasing. The VE
were fitted to the Redlich–Kister polynomial equation.
The experimental densities and viscosities of binary mixture of 2-
pyrrolidone with butanol isomers were measured [114] at 293.15, 298.15 and
303.15 K, and atmospheric pressure over the whole mole fraction range. The
experimental results were correlated using Redlich-Kister polynomial equation.
Densities and speeds of sound of 2-propanone + aniline, + N-
methylaniline, or + pyridine systems were measured [115] at 293.15, 298.15, and
303.15 K, and atmospheric pressure using a vibrating tube densimeter and sound
analyzer (Anton Paar model DSA-5000). The data were interpreted assuming
strong acetone-amine interactions and weak structural effects.
Densities and viscosities for the binary mixtures of hexan-1-ol with p-
xylene were measured at a number of mole fractions [116] at 303.15, 313.15, and
323.15 K. The excess molar volumes and viscosity deviations were calculated
from the experimental results and were fitted to the Redlich-Kister polynomial
equation.
Densities, speeds of sound, viscosities and refractive indices of binary
mixtures of octan-2-ol with benzene, chlorobenzene and bromobenzene were
measured over the entire range of composition [117] at 298.15 and 303.15 K, and
atmospheric pressure. From the experimental data, excess molar volumes VE,
isentropic compressibilities ΚS, excess isentropic compressibilities , and
deviations of speeds of sound D, were calculated at 298.15 and 303.15 K. These
excess functions were fitted to the Redlich–Kister polynomial equation. The
viscosity data were correlated using Kendall–Monroe, Grunberg–Nissan,
Tamura–Kurata, Hind–Mclaughlin Ubbelohde and Katti–Chaudhary viscosity
models, and McAllister's threebody interaction model at different temperatures.
The viscosities , densities , speeds of sound and refractive indices D
of binary mixtures of 1-decanol with o-xylene, m-xylene, p-xylene, ethylbenzene
and mesitylene were measured over the entire range of composition [118] at
298.15 and 308.15 K, and at atmospheric pressure. Excess molar volumes VE,
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deviations of isentropic compressibilities , deviations of the speeds of sound
, viscosity deviations , excess free energies of activation for viscous flow
G*E and deviations of refractive indices D were calculated from the density ρ,
speed of sound , viscosity and refractive index D data. The calculated excess
and deviation functions were fitted to the Redlich–Kister polynomial equations
and the results analyzed in terms of molecular interactions and structural effects.
The viscosity data were correlated using McAllister's three body interaction
model at different temperatures.
The viscosities and the densities of binary mixtures of methylcyclohexane
+ nitrobenzene, methylcyclohexane + 1-bromobutane, and 1-bromobutane +
nitrobenzene and those of the constituent ternaries were measured [119] at 293.15
to 308.15 K, with the whole entire composition range and atmospheric pressure.
The excess molar volumes for the binary mixtures were fitted to the Redlich-
Kister equation to determine the appropriate coefficients. The experimental
viscosity data were correlated with the Grunberg Nissan equation too.
Papari et al. [120] computed densities and speed of sound for three binary
mixture with 2-phenylethanol with 1-butanol, 2-butanol and 2-methyl-1-propanol
at six temperatures from 298.15 K. To 323.15 K. The results, were used to discuss
the nature and strength of intermolecular interaction in these mixtures.
Kumar et al. [121] presented densities, viscosities and speed of sound for
binary mixture of cyclopentane with 2-methyl-1- propanol, 3-methyl 1-butanol
and 2-methyl 2-butanol and triethylene glycol ether with 2-mtheyl 1-propanol
densities were calculated these value fitted to Redlich kister equation.
3.2 RESULTS AND DISCUSSION :
Densities and viscosities for all binary mixtures at 298.15, 303.15, 308.15
and 313.15 K, and compositions are listed in tables 3.1 to 3.10.
The experimental densities of binary liquid mixtures of t-butanol with
benzene and substituted benzenes are plotted in Figure 3.1 against mole fraction
x1 of t-butanol at 298.15 K. No attempt was made to find the best smoothing
function to represent these results.
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The excess molar volume values have been calculated using the density
values of the pure components and the binary mixture with the help of following
equation 3.1.
VE = (x1 M1 + x2 M2) /12 -(x1 M1/1) – (x2 M2 /2) ---(3.1)
where M1, x1, 1 and M2, x2, 2 are molecular weight, mole fraction and density of
components 1 and 2 respectively of binary mixtures, 12 is the mixture density.
The table 3.1 to 3.10 also include the excess molar volume values at four
temperature studied. At equimolar concentration (x1 = 0.5) the excess molar
volume value as 0.495 of t-butanol + benzene at 308.15 K, agree very
well with the reported values of 0.520 [58] similarly at 308.15 the
excess molar volume values as 0.418, 0.537 and 0.492 for o-xylene,
m-xylene and p-xylene agree very well with the reported values of 0.418, 0.537
and 0.493 [57] at (x1 = 0.5). The present 10 binary mixtures can be
classified into two groups, first electron donating groups attached to benzene ring
which consists of mixture of t-butanol with toluene, xylenes and aniline and
second mixtures of t-butanol with electron withdrawing group attached to benzene
which consists of o-chlorotoluene, p-chlorotoluene, chlorobenzene and
nitrobenzene.
The behaviour of excess molar volume values with the composition of (x1) of
t-butanol of all the binary mixture is depicted in Fig. 3.2 It is seen that excess
molar volume values for the mixture of t-butanol with benzene, toluene, o-xylene,
m-xylene, p-xylene, p-chlorotoluene and o-chlorotoluene are positive where as
the excess molar volume values for mixture of t-butanol with chlorobenzene,
nitrobenzene and aniline are negative. The positive excess molar volume values
follow the order m-xylene > p-xylene > benzene > toluene > o-xylene >
p-chlorotoluene > o-chlorotoluene where as the negative values of excess molar
volume follow the order aniline > nitrobenzene > chlorobenzene.
It has been shown that the excess molar volume values are determined by
three mains contributions namely physical, chemical and structural contributions.
Physical contributions include non polar intermolecular interactions for liquid
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mixture having non polar constituents, dipole-dipole interactions for liquid
mixtures with polar constituents and dipole induced dipole interaction for binary
liquid mixtures in which one component is polar and other non polar. Chemical
contribution are mainly through H-bonding and electron donar-acceptor
interactions. The structural contribution arises from the breaking of self associated
liquid molecules, interstitial accommodation of one component into the empty
spaces of another component due to difference in size, shape and free volume of
the components.
t-butanol is a polar liquid and is self associated while the aromatic
hydrocarbon have a large quadruple-moment which causes molecular order in
them in the pure state. Mixing of t-butanol with these aromatic hydrocarbons
leads to breaking of the self association in t-butanol and the decrease in the
molecular order of hydrocarbon resulting in an expansion in volume and hence
the positive excess molar volume values are observed. As the electron donating
power of toluene is more than that of benzene due to the introduction of methyl
group, the hydroxyl hydrogen should interact more strongly with the electron
cloud of toluene than that of benzene thus the excess values for toluene should be
smaller than those of benzene.
The molar volumes of xylenes do not differ very much but the different
positions of methyl group change the geometry of xylene molecule, the position
of the substituted group play an important role on the electron density in the
aromatic ring. Among the three isomer of xylene, o-xylene seems to offer
minimum steric hindrance, thus increasing the electron donor-acceptor interaction
and making excess molar volume minimum among the three isomers of xylene.
The trend in the excess volume values for the binary mixture of t-butanol
with o-chlorotoluene and p-chlorotoluene could be explained on the basis of
strong hydrogen bonding between the hydroxyl hydrogen of t-butanol and chloro
group of the o-chlorotoluene because the electron cloud on the chloro group of the
o-chlorotoluene is more as compared to p-chlorotoluene
The excess molar volume values for t-butanol with chlorobenzene show a
sigmoid nature with excess molar volume values being negative at low t-butanol
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mole fractions and becoming positive as the mole fraction of t-butanol in the
mixture increases. The excess moral volume values at equimolar mole fractions
go from negative to positive values. The excess molar volume values for t-butanol
with nitrobenzene and aniline are negative indicating a contraction in volume
when two components are mixed. It implies that the chemical contributions
predominate over the physical and structural contributions, this also implies that
the interactions between unlike molecule are stronger compared with the
intramolecular interactions.
The excess molar volume values show that the values for all the binary
mixture depend on the temperature of measurement.
The excess molar volumes were fitted to Redlich-Kister equation of the
type
VE = x1 x2
n
1i
ai (x1- x2)i ---(3.2)
where n is the degree of polynomial. Coefficients ai were obtained by fitting eq
3.2 to experimental results using a least-squares regression method. In each case,
the optimum number of coefficients is ascertained from an examination of the
variation in standard deviation ().Where was calculated using the relation
σ (VE) = [
∑(
)
]
---(3.3)
where N is the number of data points and n is the number of coefficients. The
calculated values of the coefficients ai along with the standard deviations are
given in Table 3.11.
Recently Jouyban and Acree (122,123) proposed a model for correlating
the density and viscosity of liquid mixtures at various temperatures. The proposed
equation is
lnm,T = f1ln1,T +f2ln2,T+ f1f2 [Aj (f1-f2) j/T] ---(3.4)
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where m,T, 1,T and 2,T is density of the mixture and solvents 1 and 2 at
temperature T, respectively, f1and f2 are the volume fractions of solvents in case
of density, and mole fraction in case of viscosity, and Aj are the model constants.
The correlating ability of the Jouyban - Acree model was tested by
calculating the average percentage deviation (APD) between the experimental and
calculated density as
APD = (100/N) [(| exptl - calcd |) / exptl)] ---(3.5)
where N is the number of data points in each set. The optimum numbers of
constants Aj, in each case, were determined from the examination of the average
percentage deviation value. The calculated values of the coefficients Aj along with
the standard deviations () are given in table 3.12. It is seen that Jouyban and
Acree model represent the viscosity of binary mixtures to a very good extent.
The experimental viscosities of binary liquid mixtures of t-butanol with
benzene and substituted benzenes are plotted in Figure 3.3 at 298.15 K against
mole fraction x1 of t-butanol.
The viscosity deviations, , are obtained by means of;
= 12 - x11 -x22 ---(3.6)
where x1, 1 and x2, 2 are mole fractions and dynamic viscosities of constituents
1and 2 respectively of binary mixtures. 12 are viscosity of binary mixtures.
The values are listed in table 3.1 to 3. 10. Figure 3.4 depicts the
variation of with x1 at 298.15 K for binary mixtures of t-butanol with benzene
and substituted benzenes. Similar plots are obtained at other temperatures.
The values for all the binary mixtures of t-butanol with aromatic
hydrocarbons are negative, it is important to note here that values follow the
particular trends on the nature of the substituents on the benzene ring. The
values are large and close to each other for mixtures of t-butanol with benzene
and toluene but as one more methyl group is attached to toluene, the values
decreases sharply in absolute term for three isomers of xylene with nearly the
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same values, similar trends is observed when one methyl group is substituted by
the chloro group in p–chloro and o-chlorotoluenes. The values are negative
for mixture of t-butanol with chlorobenzene, nitrobenzene and aniline. The
negative values of are characteristics for system in which dispersive force
like rupture of the self association in t-butanol are predominant. It is known that
the strength of intermolecular electron donar acceptor interactions is not the only
factor which influences the viscosity deviation in liquid mixtures. The other
factors such as the molecular size and shape of component and average degree of
association of the mixture also play on important role.
The values generally decrease in absolute terms with increase in
temperature.
Grunberg-Nissan, Tamura-Kurata, Hind et al. and Katti-Choudhari equations
have been used to determine the interaction parameters d, T12, H12, and Wvis.
These parameter were evaluated using least-square method and they are listed in
table 3.15.
The Grunberg-Nissan parameter d is negative for binary mixtures of
t-butanol with benzene, toluene, chlorobenzene, nitrobenzene, o-chlorotoluene
and aniline where as positive for p-chlorotoluene, o-xylene, m-xylene, and p-
xylene.
The Katti-Choudhari parameter Wvis not only shows the same trend as that of
d but also the magnetitud is of the same order. The d and Wvis values are negative
and large for mixtures of benzene, toluene, nitrobenzene and aniline and increase
in absolute terms with increase in temperature. It has been reported by Nigam and
Mahal [124], that [i] if > 0, d > 0 with large values then there would be strong
specific interaction between the component of liquid mixtures, [ii] if < 0 but d
> 0 then there would be weak specific interaction and lastly [iii] if < 0 with d
< 0 with large magnitude then dispersion forces would be dominant in the liquid
mixture.
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The parameter T12 and H12 are negative for benzene and toluene and
positive for the other binary mixtures with almost similar magnitude, they also
increase in absolute term with increase in temperature.
The kinematic viscosities () of the binary liquid mixtures were obtained
from their dynamic viscosities and densities.
McAllister’s three-body and four body interaction models [125] have been
used to correlate the kinematic viscosities of binary liquid mixtures. The three-
body interaction model is given by
lnν = x13 ln ν1+ x2
3ln ν2 +3 x1
2 x2ln ν12 +3 x1 x2
2ln ν21- ln [x1+(x2M2/M1)] + 3 x1
2
x2 ln [(2/3) + (M2/3M1)] + 3x1x22 ln [(1/3) + (2M2/3M1)] + x2
3 ln (M2/M1). ---(3.7)
where ν12, ν21 are interaction parameters and M1 and M2 are molecular weights of
components1 and 2.
The four body interaction model is given by
ln x1ln + 4x1
3 x2 ln 1112 + 6x1
2x2
2 ln 1122 + 4x1x2
3 ln 2221+ x2
4 ln 2
- ln[x1+ x2M2/M1)] +4x13x2 ln[{3 + (M2/M1)}/4] + 6x1
2x2
2 ln[{1 + (M2/M1)}/2] +
4x1x23 ln[{(1 + 3M2/M1)}/4] + x
24 ln(M2/M1) ---(3.8)
where 12, 21, 1112, 1122, and 2221 are interaction parameters and M1 and M2 are
molecular weights of components 1 and 2.
The correlating ability of equations 3.7 and 3.8 was tested by calculating
the percent standard deviations ( %) between the experimental and calculated
viscosity as
σ % = [1/(n-m)∑ {(100(νexptl - νcalcd )/ νexptl)2)}
1/2 ] ---(3.9)
where n represents the number of experimental points and m represents the
number of coefficients.
Table 3.16 list the parameters for McAllister equation and percentage
standard deviations. From table 3.16, it is clear that McAllister’s four-body
Page 30
78
interaction model gives a better result than the three-body model for correlating
the kinematic viscosities of the binary mixtures studied.
Page 31
79
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Table 3.1 : Density (ρ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + Benzene.
Temp.
K
x1
ρ x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 0.8735 0.616 0.000 0.000
0.0923 0.8622 0.745 0.239 -0.224
0.2003 0.8503 0.842 0.402 -0.541
0.3009 0.8398 0.875 0.509 -0.893
0.4005 0.8300 0.931 0.566 -1.219
0.5011 0.8207 1.067 0.570 -1.468
0.6007 0.8119 1.320 0.539 -1.596
0.7011 0.8035 1.700 0.465 -1.601
0.8005 0.7956 2.329 0.353 -1.352
0.9008 0.7880 3.213 0.203 -0.852
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 0.8682 0.568 0.000 0.000
0.0923 0.8566 0.641 0.265 -0.186
0.2003 0.8446 0.644 0.432 -0.487
0.3009 0.8340 0.596 0.543 -0.818
0.4005 0.8242 0.558 0.593 -1.136
0.5011 0.8149 0.592 0.589 -1.385
0.6007 0.8061 0.741 0.551 -1.516
0.7011 0.7976 1.016 0.480 -1.523
0.8005 0.7896 1.551 0.371 -1.267
0.9008 0.7820 2.317 0.213 -0.783
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 0.8630 0.532 0.000 0.000
0.0923 0.8515 0.563 0.259 -0.164
0.2003 0.8397 0.573 0.408 -0.382
0.3009 0.8295 0.470 0.478 -0.697
0.4005 0.8200 0.382 0.484 -0.995
0.5011 0.8109 0.336 0.495 -1.253
0.6007 0.8023 0.417 0.406 -1.382
0.7011 0.7939 0.617 0.323 -1.394
0.8005 0.7858 1.039 0.225 -1.182
0.9008 0.7777 1.729 0.126 -0.704
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 0.8574 0.502 0.000 0.000
0.0923 0.8456 0.551 0.299 -0.099
0.2003 0.8336 0.525 0.478 -0.298
0.3009 0.8232 0.413 0.577 -0.572
0.4005 0.8135 0.293 0.624 -0.851
0.5011 0.8042 0.197 0.628 -1.109
0.6007 0.7955 0.186 0.584 -1.280
0.7011 0.7870 0.307 0.519 -1.320
0.8005 0.7790 0.659 0.415 -1.127
0.9008 0.7715 1.284 0.248 -0.663
1.0000 0.7648 2.106 0.000 0.000
Page 38
86
Table 3.2 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + Chlorobenzene.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 1.1005 0.757 0.000 0.000
0.0997 1.0718 0.780 -0.099 -0.345
0.2009 1.0413 0.877 -0.115 -0.621
0.2999 1.0107 1.057 -0.101 -0.806
0.4010 0.9789 1.334 -0.076 -0.902
0.5010 0.9469 1.701 -0.044 -0.904
0.6010 0.9145 2.152 -0.019 -0.821
0.7002 0.8817 2.672 0.027 -0.667
0.8009 0.8481 3.252 0.052 -0.459
0.9003 0.8146 3.851 0.058 -0.226
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 1.0956 0.721 0.000 0.000
0.0997 1.0666 0.735 -0.090 -0.251
0.2009 1.0359 0.754 -0.104 -0.501
0.2999 1.0052 0.855 -0.094 -0.663
0.4010 0.9732 1.016 -0.064 -0.771
0.5010 0.9410 1.290 -0.022 -0.763
0.6010 0.9085 1.616 0.003 -0.702
0.7002 0.8758 1.996 0.030 -0.586
0.8009 0.8421 2.449 0.060 -0.401
0.9003 0.8087 2.925 0.049 -0.189
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 1.0893 0.679 0.000 0.000
0.0997 1.0603 0.706 -0.081 -0.169
0.2009 1.0296 0.727 -0.084 -0.346
0.2999 0.9989 0.774 -0.062 -0.494
0.4010 0.9671 0.871 -0.039 -0.595
0.5010 0.9349 1.030 0.017 -0.632
0.6010 0.9026 1.259 0.037 -0.600
0.7002 0.8702 1.548 0.046 -0.505
0.8009 0.8367 1.894 0.071 -0.357
0.9003 0.8035 2.267 0.055 -0.179
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 1.0844 0.640 0.000 0.000
0.0997 1.0551 0.648 -0.061 -0.138
0.2009 1.0244 0.664 -0.072 -0.271
0.2999 0.9936 0.704 -0.046 -0.376
0.4010 0.9617 0.797 -0.017 -0.431
0.5010 0.9297 0.914 0.014 -0.460
0.6010 0.8972 1.061 0.054 -0.460
0.7002 0.8648 1.297 0.062 -0.369
0.8009 0.8314 1.516 0.077 -0.298
0.9003 0.7982 1.808 0.063 -0.152
1.0000 0.7648 2.106 0.000 0.000
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Table 3.3 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + Toluene.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 0.8618 0.555 0.000 0.000
0.1018 0.8524 0.561 0.250 -0.390
0.2034 0.8434 0.613 0.430 -0.733
0.3010 0.8353 0.737 0.514 -0.989
0.4022 0.8273 0.965 0.529 -1.155
0.5017 0.8195 1.301 0.513 -1.206
0.6006 0.8119 1.747 0.455 -1.144
0.7004 0.8040 2.308 0.401 -0.972
0.8007 0.7960 2.965 0.329 -0.705
0.9008 0.7882 3.691 0.209 -0.368
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 0.8576 0.527 0.000 0.000
0.1018 0.8479 0.553 0.267 -0.264
0.2034 0.8388 0.561 0.439 -0.546
0.3010 0.8305 0.601 0.527 -0.784
0.4022 0.8223 0.719 0.545 -0.955
0.5017 0.8144 0.933 0.519 -1.025
0.6006 0.8065 1.254 0.475 -0.986
0.7004 0.7985 1.685 0.411 -0.840
0.8007 0.7903 2.208 0.341 -0.603
0.9008 0.7823 2.789 0.222 -0.307
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 0.8532 0.492 0.000 0.000
0.1018 0.8434 0.498 0.274 -0.213
0.2034 0.8342 0.521 0.453 -0.408
0.3010 0.8259 0.618 0.534 -0.521
0.4022 0.8176 0.770 0.557 -0.587
0.5017 0.8097 0.878 0.523 -0.693
0.6006 0.8017 1.073 0.485 -0.710
0.7004 0.7936 1.361 0.425 -0.637
0.8007 0.7854 1.686 0.347 -0.528
0.9008 0.7773 2.176 0.232 -0.253
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 0.8484 0.486 0.000 0.000
0.1018 0.8388 0.489 0.246 -0.162
0.2034 0.8289 0.512 0.511 -0.304
0.3010 0.8195 0.613 0.730 -0.361
0.4022 0.8098 0.772 0.929 -0.366
0.5017 0.8005 0.949 1.070 -0.350
0.6006 0.7913 1.145 1.181 -0.314
0.7004 0.7829 1.376 1.153 -0.245
0.8007 0.7755 1.635 0.964 -0.148
0.9008 0.7694 1.898 0.584 -0.047
1.0000 0.7648 2.106 0.000 0.000
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Table 3.4 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + o-Chlorotoluene.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 1.0778 0.958 0.000 0.000
0.1005 1.0524 1.127 0.090 -0.181
0.1998 1.0266 1.348 0.151 -0.307
0.3024 0.9990 1.619 0.200 -0.393
0.3987 0.9722 1.909 0.230 -0.439
0.5001 0.9430 2.246 0.240 -0.456
0.6001 0.9131 2.618 0.233 -0.433
0.6999 0.8821 3.022 0.207 -0.377
0.7997 0.8499 3.459 0.156 -0.288
0.9011 0.8158 3.940 0.083 -0.160
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 1.0726 0.892 0.000 0.000
0.1005 1.0470 0.986 0.099 -0.156
0.1998 1.0210 1.122 0.169 -0.267
0.3024 0.9932 1.296 0.228 -0.348
0.3987 0.9663 1.488 0.258 -0.396
0.5001 0.9370 1.730 0.269 -0.406
0.6001 0.9070 1.997 0.265 -0.387
0.6999 0.8760 2.294 0.231 -0.339
0.7997 0.8438 2.627 0.174 -0.254
0.9011 0.8097 2.994 0.097 -0.139
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 1.0679 0.826 0.000 0.000
0.1005 1.0421 0.872 0.114 -0.137
0.1998 1.0160 0.945 0.189 -0.244
0.3024 0.9881 1.056 0.253 -0.319
0.3987 0.9611 1.188 0.290 -0.362
0.5001 0.9318 1.361 0.296 -0.373
0.6001 0.9018 1.563 0.289 -0.353
0.6999 0.8707 1.788 0.265 -0.309
0.7997 0.8386 2.048 0.195 -0.230
0.9011 0.8045 2.345 0.119 -0.117
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 1.0631 0.767 0.000 0.000
0.1005 1.0375 0.779 0.083 -0.123
0.1998 1.0116 0.814 0.127 -0.221
0.3024 0.9841 0.883 0.138 -0.289
0.3987 0.9574 0.974 0.132 -0.327
0.5001 0.9284 1.098 0.096 -0.339
0.6001 0.8987 1.251 0.046 -0.320
0.6999 0.8681 1.432 -0.044 -0.272
0.7997 0.8362 1.628 -0.146 -0.210
0.9011 0.8025 1.865 -0.278 -0.109
1.0000 0.7648 2.106 0.000 0.000
Page 41
89
Table 3.5 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + p-Chlorotoluene.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 1.0648 0.848 0.000 0.000
0.0953 1.0402 1.000 0.290 -0.191
0.1989 1.0148 1.251 0.344 -0.312
0.2901 0.9916 1.501 0.383 -0.390
0.3943 0.9643 1.832 0.392 -0.434
0.4902 0.9382 2.168 0.383 -0.443
0.5922 0.9094 2.561 0.349 -0.417
0.6981 0.8781 3.006 0.305 -0.353
0.7988 0.8472 3.458 0.220 -0.263
0.8997 0.8147 3.920 0.129 -0.164
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 1.0597 0.785 0.000 0.000
0.0953 1.0349 0.860 0.301 -0.172
0.1989 1.0093 1.015 0.363 -0.286
0.2901 0.9860 1.185 0.401 -0.353
0.3943 0.9585 1.414 0.420 -0.394
0.4902 0.9323 1.655 0.412 -0.402
0.5922 0.9034 1.944 0.379 -0.377
0.6981 0.8721 2.279 0.324 -0.317
0.7988 0.8411 2.619 0.243 -0.238
0.8997 0.8087 2.974 0.133 -0.145
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 1.0526 0.731 0.000 0.000
0.0953 1.0295 0.761 0.129 -0.152
0.1989 1.0038 0.849 0.224 -0.262
0.2901 0.9805 0.961 0.283 -0.324
0.3943 0.9531 1.129 0.313 -0.356
0.4902 0.9269 1.307 0.327 -0.361
0.5922 0.8980 1.524 0.318 -0.339
0.6981 0.8668 1.783 0.278 -0.282
0.7988 0.8359 2.049 0.211 -0.209
0.8997 0.8035 2.335 0.129 -0.115
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 1.0474 0.718 0.000 0.000
0.0953 1.0245 0.673 0.103 -0.177
0.1989 0.9992 0.724 0.149 -0.270
0.2901 0.9762 0.796 0.169 -0.325
0.3943 0.9490 0.914 0.173 -0.351
0.4902 0.9232 1.048 0.138 -0.350
0.5922 0.8947 1.223 0.079 -0.317
0.6981 0.8639 1.429 -0.011 -0.258
0.7988 0.8334 1.642 -0.128 -0.185
0.8997 0.8014 1.865 -0.261 -0.102
1.0000 0.7648 2.106 0.000 0.000
Page 42
90
Table 3.6 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + o-Xylene.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 0.8756 0.755 0.000 0.000
0.1003 0.8666 1.004 0.193 -0.121
0.2009 0.8576 1.297 0.331 -0.199
0.3016 0.8485 1.607 0.428 -0.261
0.3990 0.8396 1.925 0.482 -0.302
0.4999 0.8302 2.282 0.505 -0.318
0.5998 0.8208 2.659 0.480 -0.309
0.6988 0.8112 3.056 0.430 -0.278
0.7997 0.8013 3.493 0.329 -0.213
0.9003 0.7911 3.952 0.200 -0.125
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 0.8716 0.703 0.000 0.000
0.1003 0.8626 0.869 0.169 -0.102
0.2009 0.8536 1.067 0.283 -0.174
0.3016 0.8443 1.283 0.383 -0.227
0.3990 0.8353 1.509 0.427 -0.262
0.4999 0.8257 1.763 0.451 -0.278
0.5998 0.8161 2.035 0.426 -0.273
0.6988 0.8062 2.33 0.390 -0.243
0.7997 0.7961 2.657 0.287 -0.186
0.9003 0.7855 3.013 0.180 -0.099
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 0.8676 0.650 0.000 0.000
0.1003 0.8587 0.769 0.144 -0.081
0.2009 0.8496 0.903 0.260 -0.147
0.3016 0.8403 1.059 0.348 -0.192
0.3990 0.8312 1.226 0.393 -0.219
0.4999 0.8215 1.415 0.418 -0.231
0.5998 0.8118 1.622 0.393 -0.223
0.6988 0.8019 1.849 0.344 -0.193
0.7997 0.7916 2.094 0.253 -0.149
0.9003 0.7809 2.360 0.145 -0.083
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 0.8635 0.571 0.000 0.000
0.1003 0.8550 0.655 0.074 -0.070
0.2009 0.8461 0.757 0.150 -0.122
0.3016 0.8371 0.875 0.184 -0.159
0.3990 0.8283 1.001 0.176 -0.182
0.4999 0.8189 1.154 0.148 -0.184
0.5998 0.8094 1.318 0.086 -0.174
0.6988 0.7997 1.498 -0.001 -0.146
0.7997 0.7895 1.690 -0.116 -0.109
0.9003 0.7792 1.888 -0.286 -0.065
1.0000 0.7648 2.106 0.000 0.000
Page 43
91
Table 3.7 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + m-Xylene.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 0.8601 0.585 0.000 0.000
0.0957 0.8524 0.807 0.248 -0.147
0.1947 0.8447 1.079 0.419 -0.258
0.2956 0.8369 1.395 0.537 -0.331
0.4002 0.8287 1.757 0.619 -0.373
0.5001 0.8210 2.131 0.626 -0.384
0.6001 0.8131 2.539 0.605 -0.362
0.7003 0.8052 2.973 0.525 -0.315
0.7994 0.7972 3.437 0.412 -0.234
0.8995 0.7891 3.922 0.240 -0.135
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 0.8555 0.553 0.000 0.000
0.0957 0.8479 0.679 0.219 -0.144
0.1947 0.8402 0.853 0.375 -0.250
0.2956 0.8323 1.069 0.490 -0.319
0.4002 0.8240 1.326 0.570 -0.358
0.5001 0.8160 1.604 0.600 -0.362
0.6001 0.8081 1.905 0.560 -0.344
0.7003 0.8000 2.242 0.487 -0.290
0.7994 0.7918 2.597 0.381 -0.215
0.8995 0.7836 2.980 0.200 -0.115
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 0.8518 0.501 0.000 0.000
0.0957 0.8443 0.602 0.191 -0.104
0.1947 0.8365 0.717 0.346 -0.201
0.2956 0.8286 0.872 0.446 -0.262
0.4002 0.8202 1.067 0.523 -0.291
0.5001 0.8122 1.271 0.537 -0.301
0.6001 0.8041 1.507 0.507 -0.279
0.7003 0.7959 1.764 0.430 -0.236
0.7994 0.7876 2.038 0.319 -0.175
0.8995 0.7789 2.336 0.183 -0.091
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 0.8474 0.474 0.000 0.000
0.0957 0.8403 0.534 0.124 -0.096
0.1947 0.8329 0.611 0.214 -0.181
0.2956 0.8252 0.719 0.277 -0.237
0.4002 0.8172 0.862 0.290 -0.265
0.5001 0.8095 1.022 0.256 -0.268
0.6001 0.8017 1.204 0.179 -0.249
0.7003 0.7937 1.409 0.069 -0.208
0.7994 0.7856 1.627 -0.074 -0.152
0.8995 0.7771 1.859 -0.241 -0.083
1.0000 0.7648 2.106 0.000 0.000
Page 44
92
Table 3.8 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + p-Xylene.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 0.8562 0.602 0.000 0.000
0.0994 0.8487 0.835 0.234 -0.149
0.1972 0.8415 1.123 0.393 -0.237
0.2992 0.8340 1.443 0.509 -0.309
0.4004 0.8265 1.798 0.580 -0.343
0.4976 0.8193 2.162 0.598 -0.352
0.6002 0.8117 2.575 0.564 -0.334
0.6968 0.8044 2.991 0.497 -0.289
0.7993 0.7966 3.455 0.376 -0.219
0.8980 0.7889 3.924 0.226 -0.129
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 0.8522 0.564 0.000 0.000
0.0994 0.8447 0.716 0.212 -0.128
0.1972 0.8374 0.905 0.362 -0.214
0.2992 0.8298 1.133 0.467 -0.273
0.4004 0.8222 1.384 0.527 -0.307
0.4976 0.8148 1.650 0.548 -0.315
0.6002 0.8070 1.958 0.514 -0.296
0.6968 0.7995 2.267 0.448 -0.258
0.7993 0.7913 2.627 0.350 -0.187
0.8980 0.7834 2.982 0.195 -0.110
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 0.8473 0.527 0.000 0.000
0.0994 0.8400 0.624 0.183 -0.113
0.1972 0.8328 0.752 0.320 -0.192
0.2992 0.8252 0.915 0.425 -0.245
0.4004 0.8177 1.101 0.471 -0.273
0.4976 0.8103 1.301 0.492 -0.278
0.6002 0.8024 1.538 0.470 -0.258
0.6968 0.7949 1.783 0.403 -0.218
0.7993 0.7867 2.059 0.304 -0.159
0.8980 0.7787 2.339 0.160 -0.087
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 0.8437 0.489 0.000 0.000
0.0994 0.8367 0.553 0.120 -0.097
0.1972 0.8297 0.637 0.210 -0.171
0.2992 0.8224 0.756 0.253 -0.217
0.4004 0.8151 0.895 0.253 -0.241
0.4976 0.8080 1.057 0.215 -0.237
0.6002 0.8004 1.245 0.135 -0.215
0.6968 0.7930 1.436 0.038 -0.180
0.7993 0.7851 1.659 -0.118 -0.122
0.8980 0.7770 1.876 -0.265 -0.065
1.0000 0.7648 2.106 0.000 0.000
Page 45
93
Table 3.9 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + Nitrobenzene.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 1.1982 1.801 0.000 0.000
0.0929 1.1633 1.509 -0.101 -0.538
0.1964 1.1228 1.519 -0.129 -0.801
0.3000 1.0818 1.601 -0.178 -0.993
0.3940 1.0438 1.641 -0.204 -1.202
0.5000 1.0004 1.649 -0.249 -1.474
0.6008 0.9577 2.194 -0.220 -1.196
0.6998 0.9148 2.652 -0.158 -0.999
0.8009 0.8701 3.011 -0.070 -0.908
0.8995 0.8256 3.556 0.049 -0.623
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 1.1933 1.618 0.000 0.000
0.0929 1.1587 1.381 -0.148 -0.401
0.1964 1.1179 1.289 -0.170 -0.675
0.3000 1.0768 1.225 -0.228 -0.921
0.3940 1.0387 1.159 -0.261 -1.153
0.5000 0.9968 1.101 -0.472 -1.398
0.6008 0.9534 1.325 -0.389 -1.351
0.6998 0.9097 1.623 -0.255 -1.227
0.8009 0.8656 2.262 -0.241 -0.766
0.8995 0.8202 2.768 -0.024 -0.434
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 1.1883 1.430 0.000 0.000
0.0929 1.1533 1.118 -0.120 -0.425
0.1964 1.1129 0.984 -0.184 -0.684
0.3000 1.0719 0.924 -0.258 -0.870
0.3940 1.0339 0.927 -0.305 -0.981
0.5000 0.9901 1.017 -0.330 -1.019
0.6008 0.9474 1.193 -0.313 -0.965
0.6998 0.9047 1.460 -0.280 -0.818
0.8009 0.8602 1.788 -0.216 -0.613
0.8995 0.8160 2.201 -0.131 -0.319
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 1.1834 1.252 0.000 0.000
0.0929 1.1489 0.886 -0.176 -0.445
0.1964 1.1083 0.873 -0.234 -0.547
0.3000 1.0670 0.773 -0.290 -0.735
0.3940 1.0291 0.755 -0.354 -0.833
0.5000 0.9854 0.811 -0.396 -0.868
0.6008 0.9424 0.937 -0.353 -0.828
0.6998 0.9009 1.139 -0.453 -0.711
0.8009 0.8551 1.407 -0.244 -0.529
0.8995 0.8111 1.730 -0.177 -0.290
1.0000 0.7648 2.106 0.000 0.000
Page 46
94
Table 3.10 : Density ( ),Viscosity ( ),Excess Molar Volume (VE) and Deviations
in Viscosity (∆ ) for t-Butanol + Aniline.
Temp.
K
x1
x10-3
kg.m-3
mPa.s
VEx106
m3.mol-1
∆
mPa.s
298.15
0.0000 1.0171 3.375 0.000 0.000
0.1007 0.9946 3.293 -0.190 -0.190
0.1985 0.9723 3.028 -0.325 -0.559
0.2962 0.9496 2.829 -0.410 -0.863
0.3979 0.9257 2.707 -0.459 -1.094
0.4986 0.9018 2.716 -0.469 -1.193
0.5998 0.8776 2.826 -0.441 -1.191
0.6998 0.8535 3.050 -0.373 -1.074
0.7992 0.8295 3.365 -0.277 -0.865
0.9003 0.8051 3.831 -0.154 -0.507
1.0000 0.7810 4.445 0.000 0.000
303.15
0.0000 1.0121 3.141 0.000 0.000
0.1007 0.9898 2.672 -0.226 -0.493
0.1985 0.9674 2.394 -0.368 -0.794
0.2962 0.9446 2.184 -0.458 -1.027
0.3979 0.9206 2.049 -0.512 -1.187
0.4986 0.8966 2.007 -0.524 -1.253
0.5998 0.8722 2.084 -0.486 -1.200
0.6998 0.8480 2.246 -0.416 -1.062
0.7992 0.8239 2.483 -0.316 -0.848
0.9003 0.7993 2.890 -0.175 -0.465
1.0000 0.7750 3.379 0.000 0.000
308.15
0.0000 1.0087 2.521 0.000 0.000
0.1007 0.9863 2.311 -0.240 -0.222
0.1985 0.9638 2.005 -0.395 -0.540
0.2962 0.9409 1.818 -0.496 -0.739
0.3979 0.9169 1.658 -0.571 -0.911
0.4986 0.8927 1.591 -0.581 -0.990
0.5998 0.8682 1.620 -0.551 -0.974
0.6998 0.8438 1.746 -0.475 -0.860
0.7992 0.8195 1.958 -0.367 -0.660
0.9003 0.7947 2.267 -0.215 -0.363
1.0000 0.7700 2.642 0.000 0.000
313.15
0.0000 1.0049 2.400 0.000 0.000
0.1007 0.9829 2.000 -0.300 -0.370
0.1985 0.9609 1.725 -0.525 -0.617
0.2962 0.9383 1.513 -0.678 -0.800
0.3979 0.9145 1.339 -0.797 -0.944
0.4986 0.8906 1.275 -0.862 -0.978
0.5998 0.8663 1.288 -0.877 -0.936
0.6998 0.8421 1.390 -0.847 -0.804
0.7992 0.8179 1.553 -0.774 -0.612
0.9003 0.7931 1.807 -0.646 -0.328
1.0000 0.7648 2.106 0.000 0.000
Page 47
95
Table 3.11 : Least Square Parameters of Redlich-Kister Equation and Standard
Deviations, σ (VE) for Binary System at Different Temperatures.
System
t-Butanol +
Temp.
K a0 a1 a2 a3 a4 σ
Benzene
298.15 2.2631 -0.3071 0.4112 - - 0.0067
303.15 2.3403 -0.4103 0.6166 - - 0.0075
308.15 1.8794 -0.8785 -0.0193 -0.2195 0.8736 0.0023
313.15 2.5023 -0.2658 0.5400 -0.2658 0.7290 0.0061
Chlorobenzene
298.15 -0.1892 0.6115 0.0524 0.7472 -0.1790 0.0039
303.15 -0.1096 0.6798 -0.1655 0.4527 - 0.0050
308.15 0.0229 0.6172 -0.2492 0.5122 - 0.0089
313.15 0.0621 0.6322 -0.0929 0.6322 - 0.0052
Toluene
298.15 2.0251 -0.8115 1.0493 0.8777 -0.3895 0.0047
303.15 2.0845 -0.7874 0.9268 0.8024 0.0591 0.0023
308.15 2.1145 -0.8074 1.0590 0.8536 - 0.0040
313.15 4.3154 2.5467 1.2013 2.5467 -1.1704 0.0090
o-Chlorotoluene
298.15 0.9639 0.0771 -0.0022 -0.1776 - 0.0017
303.15 1.0841 0.0500 0.0032 -0.0834 - 0.0024
308.15 1.1916 0.0433 0.1376 - - 0.0046
313.15 0.3639 -0.4667 -0.0075 -0.4667 -3.5108 0.0190
p-Chlorotoluene
298.15 1.5469 -0.2065 -0.0508 -1.4654 2.0533 0.0129
303.15 1.6571 -0.1560 0.0041 -1.6159 1.9177 0.0124
308.15 1.3009 -0.0515 0.2312 - - 0.0032
313.15 0.5248 -0.4768 -0.3248 -0.4768 -2.8452 0.0199
o-Xylene
298.15 2.0147 -0.0332 -0.0088 0.1307 0.4214 0.0036
303.15 1.7747 0.0566 0.2051 - - 0.0076
308.15 1.6496 -0.0064 -0.0842 - - 0.0033
313.15 0.5411 -0.4675 0.4090 -0.4675 -4.8168 0.0227
m-Xylene
298.15 2.5050 -0.1093 0.3694 - - 0.0052
303.15 2.3604 -0.1178 0.0187 - - 0.0082
308.15 2.1499 -0.1750 -0.3200 0.0848 0.4180 0.0045
313.15 1.0017 -0.6529 -0.4165 -0.6529 -3.2933 0.0201
p-Xylene
298.15 2.3913 -0.1259 -0.1439 0.0565 0.5905 0.0023
303.15 2.1694 -0.1275 0.1313 - - 0.0037
308.15 1.9602 -0.0661 0.1031 -0.1824 -0.3220 0.0045
313.15 0.8317 -0.7951 -0.2601 -0.7951 -3.5772 0.0144
Nitrobenzene
298.15 -0.9599 -0.3530 0.9962 2.1756
0.0127
303.15 -1.4858 -1.1743 0.7953 3.1325
0.0654
308.15 -1.3212 -0.1929 0.5352 0.2314 -1.0851 0.0065
313.15 -1.5058 -0.1016 -0.6507 - - 0.0461
Aniline
298.15 -1.8691 0.2446 -0.0530 - - 0.0020
303.15 -2.0823 0.2388 -0.0334 0.1571 -0.2966 0.0027
308.15 -2.3312 0.1635 0.0973 -0.0057 -0.6246 0.0036
313.15 -3.4711 -0.3198 -0.3245 -0.3198 -3.8321 0.0206
Page 48
96
Table 3.12 : Parameters of Jouyban-Acree Model and Average Percentage Deviation
for Density.
System t-Butanol + A0 A1 A2 A3 A4 APD
Benzene -7.5608 1.5463 -0.5970 0.9474 -2.4376 0.0114
Chlorobenzene 25.9583 1.7109 0.8384 -1.4711 0.1095 0.0040
Toluene -2.7871 -1.0295 -2.5249 - - 0.0449
o-Chlorotoluene 34.0164 7.0329 1.4839 3.0088 2.7111 0.0291
p-Chlorotoluene 32.1527 7.2830 1.6631 4.7510 -0.3101 0.0453
o-Xylene 6.5692 1.4566 0.2419 2.3019 2.8063 0.0424
m-Xylene 3.8135 1.2853 0.6602 2.6245 2.0321 0.0443
p-Xylene 3.9481 1.4487 0.2635 2.5147 2.7710 0.0439
Nitrobenzene 42.2353 8.4298 -1.3387 -4.8398 2.6946 0.0341
Aniline 15.6782 0.1823 0.2501 2.4894 3.9346 0.0479
Page 49
97
Table 3.13 : Least Square Parameters of Redlich-Kister Equation and Standard
Deviations, ) for Binary System at Different Temperatures.
System
t-Butanol +
Temp.
K a0 a1 a2 a3 a4 σ
Benzene
298.15 -5.8439 -4.2338 -0.3952 - - 0.0096
303.15 -5.5352 -4.0753 0.0402 - - 0.0087
308.15 -4.9618 -3.8944 0.0564 - - 0.0210
313.15 -4.4280 -4.7248 -0.4705 1.3127 0.9879 0.0099
Chlorobenzene
298.15 -3.6182 0.8260 0.6812 - - 0.0003
303.15 -3.0709 0.5561 0.3907 -0.1930 0.8976 0.0078
308.15 -2.5267 -0.0691 0.9174 -0.0020 - 0.0000
313.15 -1.8585 -0.1024 -0.0161 - - 0.0097
Toluene
298.15 -4.8250 0.0788 0.9916 0.0117 - 0.0000
303.15 -4.0982 -0.3546 1.4696 0.0054 - 0.0000
308.15 -2.6724 -1.0167 -1.3148 1.0832 2.2446 0.0226
313.15 -1.3997 0.6806 -0.5134 0.1662 1.4123 0.0062
o-Chlorotoluene
298.15 -1.8170 0.0680 -0.0831 0.0962 -0.0721 0.0012
303.15 -1.6275 0.0406 -0.0193 0.0954 - 0.0020
308.15 -1.4883 0.0358 -0.0871 0.1354 0.3142 0.0021
313.15 -1.3552 0.0786 -0.0161 - - 0.0024
p-Chlorotoluene
298.15 -1.7789 0.2758 0.2550 -0.0542 -0.9516 0.0038
303.15 -1.6075 0.2654 0.1582 -0.0442 -0.7019 0.0018
308.15 -1.4408 0.2630 -0.0479 0.0615 -0.1071 0.0018
313.15 -1.3944 0.3612 0.1651 0.3087 -0.7119 0.0025
o-Xylene
298.15 -1.2774 -0.1165 0.0916 0.1294 -0.3581 0.0022
303.15 -1.1121 -0.1421 -0.0484 0.2445 0.0634 0.0012
308.15 -0.9216 -0.0149 0.0132 - - 0.0010
313.15 -0.7430 0.0967 0.1546 -0.0985 -0.2579 0.0013
m-Xylene
298.15 -1.5277 0.1318 -0.0956 - - 0.0019
303.15 -1.4563 0.1602 -0.0172 0.1301 - 0.0014
308.15 -1.1892 0.1762 -0.1098 -0.0742 0.3702 0.0030
313.15 -1.0714 0.2076 0.0199 -0.1297 0.1064 0.0015
p-Xylene
298.15 -1.4145 0.0916 0.0972 0.0969 -0.4460 0.0028
303.15 -1.2620 0.1180 0.0986 0.0451 -0.2815 0.0024
308.15 -1.1086 0.1634 0.0543 0.0513 -0.0784 0.0007
313.15 -0.9528 0.2448 -0.0161 - - 0.0015
Nitrobenzene
298.15 -5.3655 -0.1167 3.9204 -0.5722 -9.1860 0.0885
303.15 -5.5182 -1.8616 4.0892 2.9173 -4.4262 0.0472
308.15 -4.0727 0.0044 0.3943 1.3718 -1.0699 0.0108
313.15 -3.5454 -0.5037 1.8979 2.5343 -4.4564 0.0354
Aniline
298.15 -4.7678 -0.8064 0.3176 -2.2000 1.6892 0.0082
303.15 -4.9488 -0.4032 -0.5443 0.8302 - 0.0162
308.15 -3.9266 -0.4184 0.0101 -0.8558 1.6231 0.0172
313.15 -3.9205 -0.0872 0.4880 0.5360 -0.6496 0.0088
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Table 3.14 : Parameters of Jouyban-Acree Model and Average Percentage Deviation
for Viscosity.
System
t-Butanol + A0 A1 A2 A3 A4 APD
Benzene -1226.6705 -824.8637 1213.6728 677.4755 - 8.4310
Chlorobenzene -248.0900 353.5325 49.1295 -159.5153 - 2.0817
Toluene -260.8114 449.5131 -256.1451 -149.1346 406.9507 2.4181
o-Chlorotoluene -46.4569 90.2659 -43.3004 16.4252 13.4101 2.5573
p-Chlorotoluene -4.7727 168.4881 -150.8322 - - 2.9115
o-Xylene 147.3911 -26.1343 -2.0584 - - 2.0186
m-Xylene 168.3289 21.4135 -23.2300 - - 2.6183
p-Xylene 187.0899 12.6179 -36.7927 - - 2.8323
Nitrobenzene -781.5835 178.2885 769.9588 303.9002 -1121.3646 3.6286
Aniline -576.7822 -47.5581 200.7802 -14.5218 -15.2652 2.2070
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Table 3.15 : Interaction Parameter for Binary System.
System
t-Butanol +
Temp.
K
d
σ
T12
mPa.s
σ
Wvisc/
RT
kj.mol-1
σ
H12
mPa.s
σ
Benzene
298.15 -1.4088 0.09 -0.4924 0.32 -1.4448 0.09 -0.4354 0.31
303.15 -2.7054 0.14 -0.8380 0.45 -2.6759 0.15 -0.7961 0.43
308.15 -3.7788 0.17 -0.9209 0.38 -3.7223 0.17 -0.8880 0.36
313.15 -4.9985 0.33 -0.9427 0.59 -4.9537 0.33 -0.9167 0.57
Chlorobenzene
298.15 -0.4225 0.11 0.9284 0.06 -0.6040 0.11 0.8576 0.04
303.15 -0.8192 0.11 0.6378 0.05 -0.8178 0.11 0.5867 0.04
308.15 -0.9335 0.04 0.5236 0.02 -0.9238 0.05 0.4837 0.02
313.15 -0.9267 0.03 0.5060 0.01 -0.9340 0.04 0.4759 0.01
Toluene
298.15 -0.8759 0.15 0.3006 0.04 -0.9011 0.14 0.1826 0.03
303.15 -1.2906 0.13 0.1309 0.07 -1.2615 0.13 0.0443 0.09
308.15 -1.0509 0.05 0.2573 0.04 -1.0318 0.05 0.1890 0.05
313.15 -0.4312 0.08 0.6511 0.06 -0.4091 0.08 0.6001 0.05
o-Chlorotoluene
298.15 0.3107 0.01 1.9805 0.02 0.1739 0.02 1.7824 0.06
303.15 -0.0472 0.02 1.4621 0.01 -0.0148 0.03 1.3202 0.04
308.15 -0.3485 0.02 1.0975 0.01 -0.3029 0.02 0.9923 0.03
313.15 -0.5923 0.03 0.8448 0.01 -0.5757 0.03 0.7668 0.03
p-Chlorotoluene
298.15 0.4602 0.01 1.9589 0.03 0.3382 0.03 1.7434 0.02
303.15 0.0590 0.04 1.4216 0.03 0.1006 0.04 1.2658 0.02
308.15 -0.2683 0.03 1.0779 0.02 -0.1225 0.03 0.9629 0.02
313.15 -0.6913 0.05 0.7917 0.04 -0.5738 0.05 0.7090 0.03
o-Xylene
298.15 0.9020 0.03 2.1984 0.07 0.8893 0.03 1.9565 0.04
303.15 0.5418 0.01 1.6590 0.06 0.5878 0.01 1.4829 0.04
308.15 0.3064 0.07 1.3187 0.05 0.3667 0.02 1.1865 0.01
313.15 0.1936 0.06 1.0742 0.08 0.2226 0.06 0.9718 0.03
m-Xylene
298.15 1.1365 0.03 2.0144 0.02 1.1418 0.03 1.7418 0.09
303.15 0.6005 0.01 1.4355 0.03 0.6559 0.01 1.2358 0.02
308.15 0.3742 0.02 1.1350 0.02 0.4764 0.06 0.9792 0.08
313.15 0.0468 0.02 0.8783 0.02 0.1178 0.02 0.7594 0.09
p-Xylene
298.15 1.1528 0.03 2.0858 0.02 1.1609 0.03 1.8087 0.01
303.15 0.7177 0.08 1.5425 0.02 0.7726 0.04 1.3390 0.01
308.15 0.3735 0.01 1.1863 0.02 0.4692 0.01 1.0338 0.01
313.15 0.1299 0.02 0.9483 0.03 0.1940 0.02 0.8313 0.02
Nitrobenzene
298.15 -1.7791 0.09 0.5151 0.06 -2.0107 0.09 0.4613 0.06
303.15 -2.4438 0.08 -0.0031 0.09 -2.4543 0.09 -0.0388 0.09
308.15 -2.4728 0.07 0.0280 0.03 -2.4318 0.06 0.0077 0.01
313.15 -2.6649 0.06 -0.0609 0.04 -2.6450 0.06 -0.0740 0.03
Aniline
298.15 -1.2979 0.04 1.6149 0.04 -1.4593 0.03 1.6237 0.04
303.15 -1.8587 0.02 0.7314 0.01 -1.8807 0.01 0.7330 0.01
308.15 -1.7518 0.03 0.6881 0.02 -1.7401 0.03 0.6907 0.02
313.15 -2.1090 0.02 0.3230 0.01 -2.1298 0.02 0.3227 0.06
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Table 3.16 : McAllister 3 and 4 Body Interaction Parameters for Binary Systems.
System
t-Butanol +
Temp.
K
3 Body 4 Body
ν12 ν21 σ% ν1112 ν1122 ν2221 σ%
Benzene
298.15 1.3652 1.2171 7.79 2.675 0.660 1.420 0.5364
303.15 0.7238 0.7759 16.00 2.000 0.203 1.275 0.7829
308.15 0.3721 0.5714 16.80 1.440 0.070 1.327 3.1524
313.15 0.1358 0.5996 29.63 0.977 0.016 2.082 7.4917
Chlorobenzene
298.15 3.2976 0.7306 3.80 3.698 1.638 0.677 0.1373
303.15 2.5692 0.6274 2.01 3.014 0.946 0.651 0.7859
308.15 1.7743 0.6426 2.06 2.356 0.645 0.716 0.6470
313.15 1.4470 0.5912 1.01 1.787 0.651 0.621 0.5165
Toluene
298.15 3.4625 0.5619 2.55 3.766 1.455 0.561 0.5580
303.15 2.2517 0.5339 5.67 3.211 0.637 0.670 1.2883
308.15 1.7528 0.5639 1.90 2.043 0.927 0.553 1.2878
313.15 2.2080 0.5374 2.04 2.165 1.168 0.502 0.8621
o-Chlorotoluene
298.15 3.1421 1.6497 2.30 3.785 1.928 1.402 0.1589
303.15 2.6493 1.2619 0.75 2.910 1.436 1.102 0.1296
308.15 2.0695 0.9708 0.28 2.324 1.068 0.905 0.1251
313.15 1.6256 0.7814 0.26 1.837 0.845 0.758 0.1438
p-Chlorotoluene
298.15 3.2294 1.5914 2.95 3.727 2.017 1.257 0.4148
303.15 2.7437 1.1566 1.93 2.836 1.538 0.938 0.3596
308.15 2.1970 0.8598 1.18 2.281 1.155 0.755 0.2843
313.15 1.8450 0.5944 1.93 1.785 1.008 0.544 0.5586
o-Xylene
298.15 3.5669 2.4119 0.35 4.147 2.379 1.922 0.1231
303.15 2.8691 1.7619 0.33 3.180 1.842 1.451 0.1372
308.15 2.2864 1.378 0.11 2.523 1.463 1.180 0.0606
313.15 1.8664 1.0944 0.29 2.015 1.224 0.946 0.1279
m-Xylene
298.15 3.563 2.2587 0.20 4.073 2.401 1.628 0.1004
303.15 2.9288 1.4322 1.03 3.072 1.905 1.081 0.2144
308.15 2.3034 1.1252 0.48 2.487 1.389 0.926 0.2574
313.15 1.8595 0.8397 0.74 1.962 1.127 0.727 0.2151
p-Xylene
298.15 3.6089 2.3282 0.49 4.083 2.419 1.731 0.1356
303.15 2.9046 1.6062 0.55 3.108 1.883 1.242 0.1701
308.15 2.3677 1.1551 0.61 2.464 1.492 0.947 0.1823
313.15 1.9321 0.8896 0.65 2.004 1.184 0.766 0.1350
Nitrobenzene
298.15 2.3016 0.8625 6.73 2.762 1.544 0.914 2.3132
303.15 1.5982 0.7255 9.51 2.600 0.460 1.091 1.9936
308.15 1.5811 0.4711 1.17 2.002 0.576 0.632 0.4796
313.15 1.2677 0.3499 3.27 1.421 0.581 0.443 2.2118
Aniline
298.15 2.5554 2.8182 2.37 3.737 1.858 3.451 0.4634
303.15 2.1265 1.8161 1.38 2.648 1.583 2.165 0.3094
308.15 1.5419 1.7551 2.56 2.220 0.994 2.258 0.2909
313.15 1.2578 1.2669 2.05 1.703 0.871 1.653 0.4808
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Figure 3.1 : Density at 298.15 K for (x1) t-Butanol + (1-x1) Benzene ( ),
Chlorobenzene ( ), Toluene ( ), o-Chlorotoluene (), p-Chlorotoluene (),
o- Xylene ( ), m-Xylene (), p-Xylene (-), Nitrobenzene (), Aniline ().
x1
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Figure 3.2 : VE values at 298.15 K for (x1) t-Butanol + (1-x1) Benzene ( ),
Chlorobenzene ( ), Toluene ( ), o-Chlorotoluene (), p-Chlorotoluene (),
o- Xylene ( ), m-Xylene (), p-Xylene (-), Nitrobenzene (), Aniline ().
x1
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Figure 3.3 : Viscosity at 298.15 K for (x1) t-Butanol + (1-x1) Benzene ( ),
Chlorobenzene ( ), Toluene ( ), o-Chlorotoluene (), p-Chlorotoluene (),
o- Xylene ( ), m-Xylene (), p-Xylene (-), Nitrobenzene (), Aniline ().
x1
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Figure 3.4 : ∆η values at 298.15 K for (x1) t-Butanol + (1-x1) Benzene ( ),
Chlorobenzene ( ), Toluene ( ), o-Chlorotoluene (), p-Chlorotoluene (),
o- Xylene ( ), m-Xylene (), p-Xylene (-), Nitrobenzene (), Aniline ().
x1