The study of partial and excess molar volumes for binary mixtures of nitrobenzene and benzaldehyde with xylene isomers from T = (298.15 to 318.15) K and P = 0.087 MPa

Journal of Advanced Research (2016) 7, 769–780

Cairo University

Journal of Advanced Research

ORIGINAL ARTICLE

The study of partial and excess molar volumes for
binary mixtures of nitrobenzene and benzaldehyde
with xylene isomers from T = (298.15 to 318.15) K
and P = 0.087 MPa
Hamid R. Rafiee *, Farshid Frouzesh
Department of Physical Chemistry, Faculty of Chemistry, Razi University, Kermanshah 67149, Iran

A R T I C L E

I N F O

Article history:
Received 14 August 2015
Received in revised form 9 November 2015
Accepted 16 November 2015
Available online 28 November 2015
Keywords:
Density
Redlich–Kister
Volumetric
Excess molar volume
Xylenes

A B S T R A C T
Based on density measurements, partial and excess molar volumes for binary mixtures of
nitrobenzene and benzaldehyde with three isomers of xylene have been measured. The whole
range of composition and temperatures from T = (298.15 to 318.15) K at ambient pressure
0.087 MPa, has been considered. The excess molar volumes were negative and decreased by
increasing temperature for all mixtures which are explained based on intermolecular interactions. Excess molar volumes for solutions including nitrobenzene were absolutely larger than
benzaldehyde binary mixtures. The partial and excess molar volumes for each component have
been appraised and reported. The excess molar volumes have been successfully fitted to
Redlich–Kister equation.
Ó 2015 Production and hosting by Elsevier B.V. on behalf of Cairo University. This is an open
access article under the CC BY-NC-ND license ( />4.0/).

Introduction
Liquid mixtures are important from both theoretical and practical points of view. From theoretical viewpoint, developing
the knowledge of molecular interactions could help to predict
thermodynamics and transport properties of components. In
* Corresponding author. Tel./fax: +98 833 4274559.
E-mail address: (H.R. Rafiee).
Peer review under responsibility of Cairo University.

Production and hosting by Elsevier

the other hand, mixtures are encountered more in practice,
in laboratory and in processes thereby attracting more attention. Volumetric properties of binary mixtures are complicated
properties since they depend not only on solvent–solvent,
solute–solute and solute–solvent interactions, but also on the
structural effects arising from differences in molar volume
and free volume between solution components. Benzaldehyde
is used chiefly as a precursor to other organic compounds,
ranging from pharmaceuticals to plastic additives while the

most application of nitrobenzene is in the production of aniline
which is a precursor to rubber chemicals, pesticide, dyes (particularly azo-dyes), explosives, and pharmaceuticals. Xylenes
are important in organic synthesis and their volumetric behavior in their mixtures with nitrobenzene and benzaldehyde may

/>2090-1232 Ó 2015 Production and hosting by Elsevier B.V. on behalf of Cairo University.
This is an open access article under the CC BY-NC-ND license ( />

770

H.R. Rafiee and F. Frouzesh

be useful in process design, modeling and synthesis reactions
which involve these binary systems. There are several reports
about the experimental data of volumetric and viscometric
behaviors for binary and ternary liquid mixtures including
benzene and its derivatives [1–5]. There are also some semiempirical relations that have been proposed to evaluate excess
properties from experimental data for binary [6–11] and
ternary mixtures [12–19]. In our previous work [20] we
reported volumetric properties of binary and ternary mixtures
of 1,4-dioxane, cyclohexanone and isooctane. In this work we
focused on volumetric properties of six binary mixtures of
nitrobenzene and benzaldehyde with three isomers of xylene
for whole range of composition at ambient pressure and
temperatures from T = 298.15 to 318.15 K. By measuring
densities we evaluated both excess molar and partial molar
volumes of components. Moreover their behaviors are
discussed in detail based on intermolecular interactions.
Experimental

Results and discussion

Table 2 includes measured and reported values for density of
pure components. Fig. 1 demonstrates a deviation plot to compare reported and measured densities at different temperatures. Deviations have been calculated as follows:
Dev % ¼ ½ðqexp À qreport Þ=qexp Š  100

ð1Þ

where qexp and qreport stand for measured and reported densities, respectively. As can be seen the agreement between our
data with literature reports is good.
Using the measured densities q, excess molar volumes are
calculated by the following equation:
X1 1 
À
VEm ¼
xi Mi
ð2Þ
q qi
i
in which q is density of mixture and qi, xi and Mi are density,
mole fraction and molar mass of pure component i, respec-

Material
Benzaldehyde and m-xylene with minimum mass fraction
purity >0.99, were obtained from the Merck. Nitrobenzene,
o-xylene and p-xylene with minimum mass fraction purity
>0.99, were obtained from the BDH. All materials were used
without further purification. Properties of used materials are
tabulated in Table 1.

Table 2 Measured and reported density values for pure
components.a

Components

Table 1

q (g cmÀ3)

q (g cmÀ3)

This work

Literature

Nitrobenzene

298.15
303.15
308.15
313.15

1.1977
1.1927
1.1877
1.1827

1.19818 [3]
1.193481 [21]
1.188222 [21]
1.183263 [21]

o-Xylene

298.15
303.15
308.15
313.15

0.8752
0.8710
0.8668
0.8625

0.87573 [3]
0.8711 [22]
0.867540 [21]
0.8626 [22]

m-Xylene

298.15
303.15
308.15
313.15

0.8599
0.8556
0.8513
0.8469

0.859901 [21]
0.85576 [3]

0.851577 [21]
0.846724 [21]

p-Xylene

298.15
303.15
308.15
313.15

0.8567
0.8524
0.8480
0.8436

0.856697
0.852261
0.847877
0.843640

Benzaldehyde

298.15
303.15
308.15
313.15
318.15

1.0414
1.0369

1.0324
1.0279
1.0234

1.04138
1.03653
1.03201
1.02749
1.02297

Apparatus and procedure
All solutions were prepared afresh by mass using an analytical
balance (Sartorius, CP224S, Germany) with precision (10À4 g).
The average uncertainty in the mole fraction of the mixtures
was estimated to be less than ±0.0002. Caution was taken
to prevent evaporation of the samples and measurements were
performed immediately after preparation of solutions. The
densities of solutions were measured by means of an Anton
Parr DMA 4100 U-tube densimeter. The apparatus was calibrated with double distilled deionized, and degassed water,
and dry air at atmospheric pressure. All injections to densimeter were done by using micro liter syringe for afresh prepared
solutions. Temperature was automatically kept constant
within ±0.05 K by instrument. Before injection, all samples
were degassed by using ultrasound instrument (Hielscher
UP100H, Germany). All measurements were performed at
least three times, and the reported values are the relevant averages. The experimental uncertainty of density measurements
was ±5 Â 10À4 g cmÀ3. The pressure in our laboratory was
constant at 0.087 MPa with standard uncertainty of 5 kPa.

T (K)

a

[21]
[21]
[21]
[21]

[23]
[24]
[24]
[24]
[24]

Uncertainty for measured densities q = ±5 Â 10À4 g cmÀ3.

Provenance and mass fraction purity of the compounds studied.

Compound

CAS number

Supplier

Mass fraction purity

Molar mass (g molÀ1)

Benzaldehyde
m-Xylene
o-Xylene

p-Xylene
Nitrobenzene

100-52-7
108-38-3
95-47-6
106-42-3
98-95-3

Merck (GC)
Merck (GC)
BDH (GLC)
BDH (GLC)
BDH (GLC)

>0.99
>0.99
>0.99
>0.99
>0.99

106.13
106.17
106.17
106.17
123.11


Volumetric properties of some binary mixtures

771

0.06
0.04

Deviations %

0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
295

300

305

T/K

310

315

320

Fig. 1 Deviation plot for pure component’s densities at studied
temperatures. e, Nitrobenzene, , o-xylene, , m-xylene, ,

p-xylene, , benzaldehyde.

tively. The partial molar volumes Vm,i are appraised based on
following equations [25,26]:
Vm;1 ¼ VÃ1 þ ð1 À xÞ2

j
X
Ai ð1 À 2xÞi
i¼0

À 2xð1 À xÞ2

j
X
Ai ið1 À 2xÞiÀ1

ð3Þ

i¼1

Vm;2 ¼ VÃ2 þ x2

j
j
X
X
Ai ð1 À 2xÞi þ 2x2 ð1 À xÞ Ai ið1 À 2xÞiÀ1
i¼0

i¼1

ð4Þ
where x stands for mole fraction, Ai is the coefficient which
comes from fitting by Redlich–Kister equation [27] and Vi* is
molar volume of pure component i. Excess partial molar
volumes VEm,1 and VEm,2 are then calculated as (Vm,1 À V*1)
and (Vm,2 À V*2).
The Redlich–Kister equation is as follows:
VEm ¼ x1 x2

j
X
Ai ð1 À 2xÞi

ð5Þ

i¼0

Tables 3–8 present the densities, excess volumes, partial molar
and excess partial molar volumes for six binary studied
systems.
Also the excess molar volumes are fitted to Redlich–Kister
equation using least square method (minimizing the sum of
squared of difference between the experimental data and the
calculated values from Eq. (5)). This is done by using the
MathCAD 11(2001i) software using conjugate gradient algorithm. This is the preferred algorithm by the MathCAD 11
(2001i) software for the minimizing. Standard deviations are
calculated using the following equation:
112

0PN 
E
E
i¼1 Vexp À Vcalc
A
r¼@
ð6Þ
NÀP
where P is the number of parameters and N is the number of
experimental data.

The Ai coefficients for the binary mixtures, at different temperatures along with their relevant standard deviations r, are
given in Table 9.
The values of standard deviations show that the fitting is
very good.
As can be seen from Tables 3–8 all six mixtures show negative excess volumes over entire range of composition which
are reduced by growing temperature. There are two important
factors that affect the excess volume behavior in binary mixtures:(a) the intermolecular interactions (including dipole–
dipole interactions, cohesive and dispersive forces and
hydrogen-bonding)and (b) the size, shape and packing ability
of component’s molecules (geometrical factors) in solution.
The negative excess volume comes from stronger intermolecular interactions in mixture compared to pure components.
That is, contraction takes place in volume by mixing. However, inverse trend would be expected when expansion in
volume occurs on mixing which implies that structural (repulsive) effects are govern and prevailing to attractive interactions
in solution. Tables 3–8 show that the values of excess molar
volumes are absolutely larger, in nitrobenzene mixtures, compared to benzaldehyde ones. These larger values can be attributed to more polarity of nitrobenzene which leads to stronger
attractive forces. Further considering the tables also reveals
that in both nitrobenzene and benzaldehyde solutions, for
meta and para-xylene mixtures, excess volumes are relatively
higher than those for ortho-xylene mixtures. This behavior

can be explained by noting to configurations of these molecules. In ortho-xylene two vicinal methyl groups extend the
steric restrain of molecule which in turn leads to weaker interactions with nitrobenzene or benzaldehyde. The effect is less in
meta or para isomer which shows relatively larger negative
values of excess volumes.
Figs. 2–4 illustrate the plot of excess volumes for binary
mixtures of nitrobenzene against mole fraction of xylene.
For comparison, the reported results of Wang et al. [3] are also
shown. Figures illustrate that by noting to the negative values
of excess volumes, there is agreement in the trend of data. The
figures show that by increasing temperature excess volumes
reduce and tend to more negative values. Valtz and his
coworkers haveobserved similar behavior for some (triethylene
glycol + alcohol) binary systems. They explained this observation by the packing effects which become more dominant by
increasing temperature [28]. The same behavior is also
observed for poly (ethylene glycol) + methoxybenzene or
ethoxybenzene binary solutions [29]; pyridine + polyols binary solutions [30] and methoxybenzene + xylenes binary mixtures [31]. This behavior may be justified based on growing
packing ability of components by raising their kinetic energy.
By referring to Figs. 2–7 it can be seen that the effect of temperature is to decrease the excess volume values in all binary
studied systems. This means that by increasing-xylene
(m-C8H10) + 1 À x benzaldehyde (C7H6O) at T = (298.15 to 318.15) K and ambient pressure.a
q (g cmÀ3)

VEm (cmÀ3 molÀ1)

Vm,1 (cmÀ3 molÀ1)

Vm,2 (cmÀ3 molÀ1)

Vm,1E (cmÀ3 molÀ1)

Vm,2E (cmÀ3 molÀ1)

T = 298.15 K
0.0000
1.0414
0.1029
1.0206
0.1992
1.0011
0.3034
0.9807
0.3989
0.9627
0.5007
0.9441
0.6003
0.9264
0.6977
0.9094
0.7978
0.8925
0.8998
0.8759
1.0000
0.8599

0.0000
À0.1362
À0.1833
À0.2203

À0.2513
À0.2695
À0.2638
À0.2177
À0.1608
À0.0998
0.0000

122.6518
122.7133
122.8341
123.0261
123.2185
123.3437
123.4191
123.4722
123.4890

101.9060
101.8440
101.7589
101.7049
101.6602
101.5975
101.5121
101.3894
101.0192

À0.8160
À0.7545

À0.6337
À0.4417
À0.2493
À0.1241
À0.0487
0.0044
0.0212

À0.0049
À0.0669
À0.1520
À0.2060
À0.2507
À0.3134
À0.3988
À0.5215
À0.8917

T = 303.15 K
0.0000
1.0369
0.1029
1.0162
0.1992
0.9967
0.3034
0.9762
0.3989
0.9583
0.5007

0.9397
0.6003
0.9220
0.6977
0.9050
0.7978
0.8882
0.8998
0.8716
1.0000
0.8556

0.0000
À0.1554
À0.2010
À0.2246
À0.2644
À0.2794
À0.2701
À0.2198
À0.1714
À0.1055
0.0000

123.2505
123.3118
123.4218
123.6226
123.8277
123.9590

124.0384
124.0980
124.1165

102.3629
102.2949
102.1997
102.1436
102.1008
102.0371
101.9482
101.8182
101.3762

À0.8379
À0.7766
À0.6666
À0.4658
À0.2607
À0.1294
À0.0500
0.0096
0.0281

À0.0001
À0.0681
À0.1633
À0.2194
À0.2622
À0.3259

À0.4148
À0.5448
À0.9868

T = 308.15 K
0.0000
1.0324
0.1029
1.0117
0.1992
0.9922
0.3034
0.9718
0.3989
0.9538
0.5007
0.9352
0.6003
0.9175
0.6977
0.9006
0.7978
0.8838
0.8998
0.8672
1.0000
0.8513

0.0000
À0.1572

À0.2031
À0.2378
À0.2659
À0.2799
À0.2689
À0.2291
À0.1783
À0.1094
0.0000

123.8504
123.9705
124.1078
124.2897
124.4626
124.5730
124.6449
124.7070
124.7406

102.8078
102.7518
102.6689
102.6074
102.5405
102.4405
102.3034
102.1151
101.6741

À0.8794
À0.7593
À0.6220
À0.4401
À0.2672
À0.1568
À0.0849
À0.0228
0.0108

À0.0015
À0.0575
À0.1404
À0.2019
À0.2688
À0.3688
À0.5059
À0.6942
À1.1352

T = 313.15 K
0.0000
1.0279
0.1029
1.0072
0.1992
0.9877
0.3034
0.9673
0.3989

0.9494
0.5007
0.9308
0.6003
0.9131
0.6977
0.8963
0.7978
0.8795
0.8998
0.8629
1.0000
0.8469

0.0000
À0.1589
À0.2053
À0.2399
À0.2792
À0.2926
À0.2803
À0.2518
À0.1991
À0.1276
0.0000

124.4048
124.5953
124.7533
124.9401

125.1155
125.2285
125.3031
125.3659
125.3949

103.2639
103.2121
103.1286
103.0644
102.9954
102.8972
102.7699
102.6012
102.1713

À0.9731
À0.7826
À0.6246
À0.4378
À0.2624
À0.1494
À0.0748
À0.0120
0.0170

0.0045
À0.0473
À0.1308
À0.1950

À0.2640
À0.3622
À0.4895
À0.6582
À1.0881

T = 318.15
0.0000
1.0234
0.1029
1.0027
0.1992
0.9832
0.3034
0.9628
0.3989
0.9449
0.5007
0.9263
0.6003
0.9086
0.6977
0.8918
0.7978
0.8751
0.8998
0.8585
1.0000
0.8426

0.0000
À0.1608
À0.2076
À0.2420
À0.2810
À0.2932
À0.2791
À0.2484
À0.2065
À0.1317
0.0000

125.0541
125.2746
125.4243
125.5967
125.7627
125.8751
125.9545
126.0226
126.0522

103.7227
103.6749
103.5896
103.5192
103.4419
103.3381
103.2125
103.0544

102.6363

À0.9787
À0.7582
À0.6085
À0.4361
À0.2701
À0.1577
À0.0783
À0.0102
0.0194

0.0092
À0.0386
À0.1239
À0.1943
À0.2716
À0.3754
À0.5010
À0.6591
À1.0772

x

a

Uncertainties for x = 0.0002 q = ±5 Â 10À4 (g cmÀ3) and for VEm, Vm,i and Vm,iE = ±0.0005 (cmÀ3 molÀ1).


774

H.R. Rafiee and F. Frouzesh

Table 5 Densities q, excess molar volumes VEm, partial molar volumes Vm,i and excess partial molar volumes Vm,i of x p-xylene
(p-C8H10) + 1 À x benzaldehyde (C7H6O) at T = (298.15 to 318.15) K and ambient pressure.a
x

q (g cmÀ3)

VEm (cmÀ3 molÀ1)

Vm,1 (cmÀ3 molÀ1)

Vm,2 (cmÀ3 molÀ1)

Vm,1E (cmÀ3 molÀ1)

Vm,2E (cmÀ3 molÀ1)

T = 298.15 K
0.0000
0.0701
0.1032
0.2007
0.3038
0.4025
0.5013
0.5944
0.6974
0.7999

0.8992
1.0000

1.0414
1.0270
1.0204
1.0002
0.9796
0.9605
0.9419
0.9250
0.9069
0.8894
0.8730
0.8567

0.0000
À0.1119
À0.1707
À0.2128
À0.2475
À0.2614
À0.2499
À0.2377
À0.2112
À0.1596
À0.0998
0.0000

123.0228

123.1243
123.3062
123.4404
123.5485
123.6300
123.6883
123.7531
123.8311
123.9014

101.9113
101.9077
101.8759
101.8150
101.7323
101.6090
101.4386
101.1836
100.8627
100.4335

À0.9062
À0.8047
À0.6228
À0.4886
À0.3805
À0.2990
À0.2407
À0.1759
À0.0979

À0.0276

0.0004
À0.0032
À0.0350
À0.0959
À0.1786
À0.3019
À0.4723
À0.7273
À1.0482
À1.4774

T = 303.15 K
0.0000
0.0701
0.1032
0.2007
0.3038
0.4025
0.5013
0.5944
0.6974
0.7999
0.8992
1.0000

1.0369
1.0224
1.0160

0.9958
0.9752
0.9561
0.9375
0.9206
0.9025
0.8851
0.8687
0.8524

0.0000
À0.1112
À0.1903
À0.2308
À0.2633
À0.2746
À0.2599
À0.2442
À0.2133
À0.1702
À0.1056
0.0000

123.5968
123.7209
123.9424
124.0754
124.1624
124.2250
124.2766

124.3463
124.4359
124.5189

102.3646
102.3627
102.3364
102.2747
102.1786
102.0307
101.8306
101.5384
101.1794
100.7297

À0.9574
À0.8333
À0.6118
À0.4788
À0.3918
À0.3292
À0.2776
À0.2079
À0.1183
À0.0353

0.0016
À0.0003
À0.0266
À0.0883

À0.1844
À0.3323
À0.5324
À0.8246
À1.1836
À1.6333

T = 308.15 K
0.0000
0.0701
0.1032
0.2007
0.3038
0.4025
0.5013
0.5944
0.6974
0.7999
0.8992
1.0000

1.0324
1.0179
1.0115
0.9913
0.9707
0.9516
0.9331
0.9162
0.8981

0.8807
0.8643
0.8480

0.0000
À0.1125
À0.1924
À0.2334
À0.2657
À0.2764
À0.2724
À0.2556
À0.2227
À0.1772
À0.1095
0.0000

124.2055
124.3254
124.5438
124.6923
124.8005
124.8781
124.9345
125.0021
125.0877
125.1674

102.8102
102.8072

102.7768
102.7141
102.5795
102.5055
102.3882
102.1694
101.8029
101.3463

À0.9950
À0.8751
À0.6567
À0.5082
À0.4000
À0.3224
À0.2660
À0.1984
À0.1128
À0.0331

0.0009
À0.0021
À0.0325
À0.0952
À0.1863
À0.3255
À0.5181
À0.8052
À1.1646
À1.6313

T = 313.15 K
0.0000
0.0701
0.1032
0.2007
0.3038
0.4025
0.5013
0.5944
0.6974
0.7999
0.8992
1.0000

1.0279
1.0135
1.0070
0.9868
0.9662
0.9471
0.9286
0.9117
0.8936
0.8763
0.8599
0.8436

0.0000
À0.1253

À0.1961
À0.2389
À0.2728
À0.2842
À0.2805
À0.2633
À0.2295
À0.1963
À0.1270
0.0000

124.7505
124.9433
125.2237
125.3602
125.4589
125.5381
125.6021
125.6814
125.7757
125.8494

103.2679
103.2691
103.2412
103.1694
103.0693
102.9260
102.7374
102.4727

102.1561
101.6908

À1.1179
À0.9251
À0.6447
À0.5082
À0.4095
À0.3303
À0.2663
À0.1870
À0.0927
À0.0190

0.0085
0.0097
À0.0182
À0.0900
À0.1901
À0.3334
À0.5220
À0.7867
À1.1033
À1.5686

T = 318.15
0.0000
0.0701
0.1032
0.2007

0.3038
0.4025
0.5013
0.5944
0.6974
0.7999
0.8992
1.0000

1.0234
1.0089
1.0025
0.9823
0.9617
0.9427
0.9242
0.9073
0.8892
0.8718
0.8555
0.8393

0.0000
À0.1174
À0.1999
À0.2446
À0.2799
À0.3041
À0.3011
À0.2841

À0.2499
À0.2019
À0.1448
0.0000

125.3371
125.5682
125.8599
125.9797
126.0870
126.1927
126.2844
126.3868
126.4872
126.5449

103.7265
103.7294
103.6956
103.6080
103.4982
103.3593
103.1933
102.9826
102.7491
102.3343

À1.2064
À0.9753
À0.6836

À0.5638
À0.4565
À0.3508
À0.2591
À0.1567
À0.0563
0.0014

0.0130
0.0159
À0.0179
À0.1055
À0.2153
À0.3542
À0.5202
À0.7309
À0.9644
À1.3792

a

Uncertainties for x = 0.0002 q = ±5 Â 10À4 (g cmÀ3) and for VEm, Vm,i and Vm,iE = ±0.0005 (cmÀ3 molÀ1).


Volumetric properties of some binary mixtures

775

Table 6 Densities q, excess molar volumes VEm, partial molar volumes Vm,i and excess partial molar volumes Vm,i of x o-xylene
(o-C8H10) + 1 À x nitro benzene (C6H5NO2) at T = (298.15 to 318.15) K and ambient pressure.a

q (g cmÀ3)

VEm (cmÀ3 molÀ1)

Vm,1 (cmÀ3 molÀ1)

Vm,2 (cmÀ3 molÀ1)

Vm,1E (cmÀ3 molÀ1)

Vm,2E (cmÀ3 molÀ1)

T = 298.15 K
0.0000
1.1977
0.1147
1.1557
0.2268
1.1162
0.3336
1.0797
0.4384
1.0450
0.5378
1.0130
0.6345
0.9827
0.7297
0.9537
0.8206

0.9268
0.9103
0.9008
1.0000
0.8752

0.0000
À0.0702
À0.1360
À0.1805
À0.2080
À0.2130
À0.1990
À0.1778
À0.1508
À0.0984
0.0000

120.6187
120.8705
120.9669
121.0504
121.1397
121.2269
121.2967
121.3314
121.3272

102.7466
102.7027

102.6692
102.6171
102.5312
102.4058
102.2448
102.0816
101.9907

À0.6907
À0.4389
À0.3425
À0.2590
À0.1697
À0.0825
À0.0127
0.0220
0.0178

À0.0421
À0.0860
À0.1195
À0.1716
À0.2575
À0.3829
À0.5439
À0.7071
À0.7980

T = 303.15 K
0.0000

1.1927
0.1147
1.1509
0.2268
1.1114
0.3336
1.0750
0.4384
1.0405
0.5378
1.0087
0.6345
0.9785
0.7297
0.9495
0.8206
0.9225
0.9103
0.8965
1.0000
0.8710

0.0000
À0.0815
À0.1404
À0.1872
À0.2277
À0.2470
À0.2368
À0.2074

À0.1588
À0.0961
0.0000

120.4764
120.6837
120.8740
121.0537
121.1842
121.2654
121.3105
121.3288
121.3235

103.1970
103.1620
103.0930
102.9817
102.8579
102.7420
102.6271
102.4886
102.3131

À0.8330
À0.6257
À0.4354
À0.2557
À0.1252
À0.0440

0.0011
0.0194
0.0141

À0.0226
À0.0576
À0.1266
À0.2379
À0.3617
À0.4776
À0.5925
À0.7310
À0.9065

T = 308.15 K
0.0000
1.1877
0.1147
1.146
0.2268
1.1067
0.3336
1.0704
0.4384
1.0359
0.5378
1.0041
0.6345
0.9740
0.7297

0.9451
0.8206
0.9182
0.9103
0.8923
1.0000
0.8668

0.0000
À0.0838
À0.1546
À0.2042
À0.2369
À0.2477
À0.2399
À0.2128
À0.1670
À0.1073
0.0000

121.6439
121.9162
122.0783
122.2102
122.3170
122.4008
122.4605
122.4916
122.4946

103.6203
103.5700
103.5102
103.4280
103.3261
103.2065
103.0689
102.9237
102.8009

À0.8411
À0.5688
À0.4067
À0.2748
À0.1680
À0.0842
À0.0245
0.0066
0.0096

À0.0338
À0.0841
À0.1439
À0.2261
À0.3280
À0.4476
À0.5852
À0.7304
À0.8532

T = 313.15 K
0.0000
1.1828
0.1147
1.1412
0.3336
1.0657
0.4384
1.0313
0.5378
0.9996
0.6345
0.9695
0.7297
0.9406
0.8206
0.9138
0.9103
0.8880
1.0000
0.8625

0.0000
À0.0893
À0.2101
À0.2477
À0.2635
À0.2488
À0.2139
À0.1725

À0.1173
0.0000

122.2597
122.4822
122.6189
122.7810
122.9287
123.0430
123.1199
123.1510

104.0390
104.0092
103.9653
103.8654
103.7243
103.5592
103.3613
103.1214

À0.8359
À0.6134
À0.4767
À0.3146
À0.1669
À0.0526
0.0243
0.0554

À0.0445
À0.0743
À0.1182
À0.2181
À0.3592
À0.5243
À0.7222
À0.9621

T = 318.15
0.0000
1.1778
0.1147
1.1363
0.2268
1.0972
0.3336
1.0611
0.4384
1.0267
0.5378
0.9951
0.6345
0.9650
0.7297
0.9361
0.8206
0.9093
0.9103
0.8836

1.0000
0.8583

0.0000
À0.0917
À0.1702
À0.2277
À0.2574
À0.2760
À0.2521
À0.2068
À0.1612
À0.1013
0.0000

122.8829
123.0464
123.1792
123.3432
123.4961
123.6173
123.6993
123.7347
123.7238

104.4963
104.4732
104.4275
104.3254
104.1792

104.0054
103.8071
103.5944
103.4160

À0.8151
À0.6516
À0.5188
À0.3548
À0.2019
À0.0807
0.0013
0.0367
0.0258

À0.0291
À0.0522
À0.0979
À0.2000
À0.3462
À0.5200
À0.7183
À0.9310
À1.1094

x

a

Uncertainties for x = 0.0002 q = ±5 Â 10–4 (g cmÀ3) and for VEm, Vm,i and Vm,iE = ±0.0005 (cmÀ3 molÀ1).

776

H.R. Rafiee and F. Frouzesh

Table 7 Densities q, excess molar volumes VEm, partial molar volumes Vm,i and excess partial molar volumes Vm,i of x m-xylene
(m-C8H10) + 1 À x nitro benzene (C6H5NO2) at T = (298.15 to 318.15) K and ambient pressure.a
q (g cmÀ3)

VEm (cmÀ3 molÀ1)

Vm,1 (cmÀ3 molÀ1)

Vm,2 (cmÀ3 molÀ1)

Vm,1E (cmÀ3 molÀ1)

Vm,2E (cmÀ3 molÀ1)

T = 298.15 K
0.0000
1.1977
0.1139
1.1538
0.2240
1.1129
0.3337
1.0737
0.4342

1.0389
0.5383
1.0039
0.6334
0.9727
0.7297
0.9421
0.8197
0.9139
0.9125
0.8858
1.0000
0.8599

0.0000
À0.1172
À0.2105
À0.2951
À0.3483
À0.3723
À0.3537
À0.3217
À0.2236
À0.1273
0.0000

122.2076
122.5038
122.8159
123.0663

123.2582
123.3698
123.4328
123.4604
123.4688

102.7731
102.7138
102.5942
102.4389
102.2585
102.1015
101.9628
101.8479
101.7327

À1.2602
À0.9640
À0.6519
À0.4015
À0.2096
À0.0980
À0.0350
À0.0074
0.0010

À0.0156
À0.0749
À0.1945
À0.3498

À0.5302
À0.6872
À0.8259
À0.9408
À1.0560

T = 303.15 K
0.0000
1.1927
0.1139
1.1490
0.2240
1.1082
0.3337
1.0690
0.4342
1.0342
0.5383
0.9993
0.6334
0.9683
0.7297
0.9377
0.8197
0.9095
0.9125
0.8815
1.0000
0.8556

0.0000
À0.1309
À0.2292
À0.3083
À0.3552
À0.3826
À0.3797
À0.3394
À0.2317
À0.1371
0.0000

122.7338
123.0790
123.4382
123.6988
123.8767
123.9687
124.0183
124.0479
124.0743

103.2074
103.1353
102.9961
102.8346
102.6681
102.5396
102.4350
102.3343

102.1620

À1.3545
À1.0093
À0.6501
À0.3895
À0.2116
À0.1196
À0.0700
À0.0404
À0.0140

À0.0122
À0.0843
À0.2235
À0.3850
À0.5515
À0.6800
À0.7846
À0.8853
À1.0576

T = 308.15 K
0.0000
1.1877
0.1139
1.1441
0.2240
1.1034
0.3337

1.0643
0.4342
1.0296
0.5383
0.9947
0.6334
0.9637
0.7297
0.9332
0.8197
0.9052
0.9125
0.8772
1.0000
0.8513

0.0000
À0.1357
À0.2384
À0.3218
À0.3732
À0.3931
À0.3821
À0.3446
À0.2534
À0.1484
0.0000

123.3467
123.7364

124.0596
124.2942
124.4712
124.5804
124.6513
124.6911
124.7111

103.6247
103.5473
103.4239
103.2786
103.1121
102.9582
102.8030
102.6501
102.4723

À1.3684
À0.9787
À0.6555
À0.4209
À0.2439
À0.1347
À0.0638
À0.0240
À0.0040

À0.0294
À0.1068

À0.2302
À0.3755
À0.5420
À0.6959
À0.8511
À1.0040
À1.1818

T = 313.15 K
0.0000
1.1828
0.1139
1.1392
0.2240
1.0986
0.3337
1.0596
0.4342
1.0250
0.5383
0.9902
0.6334
0.9592
0.7297
0.9288
0.8197
0.9008
0.9125
0.8728
1.0000

0.8469

0.0000
À0.1344
À0.2443
À0.3346
À0.3929
À0.4194
À0.4028
À0.3713
À0.2725
À0.1586
0.0000

123.8955
124.3272
124.6795
124.9306
125.1189
125.2340
125.3063
125.3435
125.3601

104.0516
103.9649
103.8297
103.6740
103.4968
103.3348

103.1797
103.0455
102.9183

À1.4676
À1.0359
À0.6836
À0.4325
À0.2442
À0.1291
À0.0568
À0.0196
À0.0030

À0.0319
À0.1186
À0.2538
À0.4095
À0.5867
À0.7487
À0.9038
À1.0380
À1.1652

T = 318.15
0.0000
1.1778
0.1139
1.1344
0.2240

1.0939
0.3337
1.0550
0.4342
1.0204
0.5383
0.9856
0.6334
0.9547
0.7297
0.9243
0.8197
0.8965
0.9125
0.8684
1.0000
0.8426

0.0000
À0.1487
À0.2639
À0.3592
À0.4116
À0.4305
À0.4178
À0.3770
À0.2950
À0.1561
0.0000

124.4740
124.9617
125.3280
125.5566
125.7198
125.8243
125.8976
125.9452
125.9830

104.4945
104.3910
104.2470
104.1045
103.9509
103.8048
103.6610
103.5464
103.4432

À1.5288
À1.0411
À0.6748
À0.4462
À0.2830
À0.1785
À0.1052
À0.0576
À0.0198

À0.0309
À0.1344
À0.2784
À0.4209
À0.5745
À0.7206
À0.8644
À0.9790
À1.0822

x

a

Uncertainties for x = 0.0002 q = ±5 Â 10À4 (g cmÀ3) and for VEm, Vm,i and Vm,iE = ±0.0005 (cmÀ3 molÀ1).


Volumetric properties of some binary mixtures

777

Table 8 Densities q, excess molar volumes VEm, partial molar volumes Vm,i and excess partial molar volumes Vm,i of x p-xylene
(p-C8H10) + 1 À x nitro benzene (C6H5NO2) at T = (298.15 to 318.15) K and ambient pressure.a
q (g cmÀ3)

VEm (cmÀ3 molÀ1)

Vm,1 (cmÀ3 molÀ1)

Vm,2 (cmÀ3 molÀ1)

Vm,1E (cmÀ3 molÀ1)

Vm,2E (cmÀ3 molÀ1)

T = 298.15 K
0.0000
1.1977
0.1172
1.1514
0.2275
1.1103
0.3291
1.0737
0.4365
1.0360
0.5366
1.0020
0.6355
0.9693
0.7317
0.9385
0.8233
0.9099
0.9114
0.8831
1.0000
0.8567

0.0000

À0.0690
À0.1889
À0.2783
À0.3225
À0.3397
À0.3221
À0.2853
À0.2191
À0.1315
0.0000

122.8231
123.1981
123.3906
123.5384
123.6803
123.8173
123.9119
123.9456
123.9387

102.7503
102.6675
102.5891
102.4955
102.3597
102.1671
101.9844
101.9509
102.2205

À1.1059
À0.7309
À0.5384
À0.3906
À0.2487
À0.1117
À0.0171
0.0166
0.0097

À0.0384
À0.1212
À0.1996
À0.2932
À0.4290
À0.6216
À0.8043
À0.8378
À0.5682

T = 303.15 K
0.0000
1.1927
0.1172
1.1466
0.2275
1.1056
0.3291
1.0691

0.4365
1.0314
0.5366
0.9974
0.6355
0.9648
0.7317
0.9340
0.8233
0.9054
0.9114
0.8787
1.0000
0.8524

0.0000
À0.0823
À0.2074
À0.3022
À0.3401
À0.3501
À0.3358
À0.2900
À0.2137
À0.1289
0.0000

123.4320
123.7824
123.9749

124.1249
124.2701
124.4119
124.5125
124.5539
124.5568

103.1884
103.1085
103.0288
102.9333
102.7944
102.5953
102.4038
102.3606
102.6110

À1.1222
À0.7718
À0.5793
À0.4293
À0.2841
À0.1423
À0.0417
À0.0003
0.0026

À0.0312
À0.1111
À0.1908

À0.2863
À0.4252
À0.6243
À0.8158
À0.8590
À0.6086

T = 308.15 K
0.0000
1.1877
0.1172
1.1419
0.2275
1.1008
0.3291
1.0644
0.4365
1.0268
0.5366
0.9929
0.6355
0.9603
0.7317
0.9296
0.8233
0.9010
0.9114
0.8743
1.0000
0.8480

0.0000
À0.1069
À0.2197
À0.3209
À0.3644
À0.3801
À0.3593
À0.3184
À0.2337
À0.1398
0.0000

123.9712
124.3234
124.5507
124.7507
124.9226
125.0688
125.1667
125.2078
125.2087

103.6201
103.5454
103.4562
103.3312
103.1677
102.9615
102.7593

102.6501
102.7357

À1.2293
À0.8771
À0.6498
À0.4498
À0.2779
À0.1317
À0.0338
0.0073
0.0082

À0.0340
À0.1087
À0.1979
À0.3229
À0.4864
À0.6926
À0.8948
À1.0040
À0.9184

T = 313.15 K
0.0000
1.1827
0.1172
1.1370
0.2275
1.0961

0.3291
1.0597
0.4365
1.0221
0.5366
0.9883
0.6355
0.9558
0.7317
0.9251
0.8233
0.8965
0.9114
0.8699
1.0000
0.8436

0.0000
À0.1131
À0.2423
À0.3401
À0.3782
À0.3991
À0.3832
À0.3344
À0.2406
À0.1508
0.0000

124.7117

124.7831
125.0241
125.2928
125.4892
125.6216
125.7089
125.7738
125.8266

104.0583
103.9731
103.8755
103.7511
103.5928
103.3900
103.1907
103.0907
103.1875

À1.1418
À1.0704
À0.8294
À0.5607
À0.3643
À0.2319
À0.1446
À0.0797
À0.0269

À0.0340

À0.1192
À0.2168
À0.3412
À0.4995
À0.7023
À0.9016
À1.0016
À0.9048

T = 318.15 K
0.0000
1.1778
0.1172
1.1320
0.2275
1.0913
0.3291
1.0550
0.4365
1.0175
0.5366
0.9838
0.6355
0.9513
0.7317
0.9206
0.8233
0.8921
0.9114
0.8655

1.0000
0.8393

0.0000
À0.1004
À0.2450
À0.3487
À0.3918
À0.4180
À0.3948
À0.3374
À0.2474
À0.1476
0.0000

125.1753
125.5531
125.7956
126.0004
126.1832
126.3461
126.4557
126.4999
126.5023

104.4948
104.4097
104.3113
104.1820
104.0078

103.7791
103.5653
103.5005
103.7208

À1.3230
À0.9452
À0.7027
À0.4979
À0.3151
À0.1522
À0.0426
0.0016
0.0040

À0.0306
À0.1157
À0.2141
À0.3434
À0.5176
À0.7463
À0.9601
À1.0249
À0.8046

x

a

Uncertainties for x = 0.0002 q = ±5 Â 10À4 (g cmÀ3) and for VEm, Vm,i and Vm,iE = ±0.0005 (cmÀ3 molÀ1).

778

H.R. Rafiee and F. Frouzesh

Table 9 Coefficients of the Redlich–Kister equation, Eq. (5) for excess molar volume of binary mixtures along with standard
deviations, r, at various temperatures.
T (K)

A0

A1

A2

A3

r

A4

Nitrobenzene + p-Xylene
298.15
À1.3472
303.15
À1.4103
308.15
À1.5192
313.15

À1.5925
318.15
À1.6552

À0.1404
À0.0562
À0.1632
À0.1500
À0.1301

0.0902
0.0613
0.1836
0.0553
0.1704

À0.7743
À0.7304
À0.4681
À0.4817
À0.6363

0.4917
0.6048
0.1854
0.3704
0.5254

0.002
0.005

0.005
0.007
0.006

Nitrobenzene + m-Xylene
298.15
À1.4699
303.15
À1.5177
308.15
À1.5628
313.15
À1.6521
318.15
À1.7067

À0.3841
À0.4519
À0.3570
À0.4307
À0.3618

0.2775
0.0692
0.0521
0.0644
À0.2225

0.2036
0.4036

0.0985
0.0617
0.0102

À0.1462
0.0115
À0.1128
À0.0507
0.3316

0.007
0.008
0.004
0.006
0.004

Nitrobenzene + o-Xylene
298.15
À0.8489
303.15
À0.9670
308.15
À0.9859
313.15
À1.0437
318.15
À1.0874

À0.0309
À0.2905

À0.1606
À0.1626
À0.0567

0.0626
0.2901
0.0667
0.4233
0.4373

À0.4420
0.1332
À0.1786
À0.2077
À0.1789

À0.3103
À0.5108
À0.2644
À0.9062
À0.6260

0.001
0.001
0.002
0.002
0.004

Benzaldehyde + p-Xylene
298.15

À1.0159
303.15
À1.0486
308.15
À1.0859
313.15
À1.1179
318.15
À1.2064

0.1836
0.2711
0.2070
0.2069
0.2021

À0.3174
À0.4877
À0.4241
À0.4010
À0.1847

0.3209
0.2287
0.3167
0.1897
0.0407

À0.4596
À0.3538

À0.4386
À0.7732
À1.0641

0.007
0.011
0.011
0.009
0.012

Benzaldehyde + m-Xylene
298.15
À1.0862
303.15
À1.1223
308.15
À1.1217
313.15
À1.1724
318.15
À1.1707

À0.0846
À0.0747
À0.0488
À0.1188
À0.0866

0.5082
0.5668

0.2852
0.2576
0.2116

0.5373
0.6453
0.5561
0.4741
0.3728

À1.3113
À1.6937
À1.2928
À1.3928
À1.4258

0.003
0.004
0.001
0.003
0.004

Benzaldehyde + o-Xylene
298.15
À0.8209
303.15
À0.8709
308.15
À0.9185
313.15

À0.9744
318.15
À1.0217

À0.1126
À0.0016
0.0151
À0.0298
À0.1871

0.2511
0.3883
0.3549
0.1651
0.3445

0.6288
0.4354
0.0969
0.0343
0.1947

À0.3389
À0.6666
À0.8819
À0.6893
À1.2657

0.003
0.004

0.002
0.003
0.003

0.00

0

VmE / (cm3.mol-1)

VmE / (cm3.mol-1)

-0.10
-0.1

-0.2

-0.20
-0.30
-0.40

-0.3
0.00

0.20

0.40

x

0.60

0.80

1.00

Fig. 2 Excess molar volume for binary mixtures of o-(CH3)2
C6H4 + C6H5NO2 at T = 303.15 K and T = 313.15 K versus
o-xylene mole fraction. T = 303.15 K: , this work, , Wang et al.
[3], T = 313.15: , this work, , Wang et al. [3]; solid lines are
drawn based on Redlich–Kister equation.

-0.50
0.00

0.20

0.40

0.60

0.80

1.00

x
Fig. 3 Excess molar volume for binary mixtures of m-(CH3)2
C6H4 + C6H5NO2 at T = 303.15 K and T = 313.15 K versus
m-xylene mole fraction. T = 303.15 K: , this work, , Wang
et al. [3], T = 313.15: , this work, , Wang et al. [3]; solid lines

are drawn based on Redlich–Kister equation.


Volumetric properties of some binary mixtures

779

0.00

0.00

-0.10
VmE / (cm3.mol-1)

VmE / (cm3mol-1)

-0.10

-0.20

-0.30

-0.30

-0.40

-0.50
0.00

-0.20

0.20

0.40

x

0.60

0.80

-0.40
0.00

1.00

Fig. 4 Excess molar volume for binary mixtures of p-(CH3)2
C6H4 + C6H5NO2 at T = 303.15 K and T = 313.15 K versus
p-xylene mole fraction. T = 303.15 K: , this work, , Wang et al.
[3], T = 313.15: , this work, , Wang et al. [3]; solid lines are
drawn based on Redlich–Kister equation.

0.20

0.40

x

0.60

0.80

1.00

Fig. 6 Excess molar volume of x m-(CH3)2C6H4 + (1 À x)
C7H6O at ambient pressure plotted against mole fraction. At
; T = 308.15 K,
;
T = 298.15 K, e; T = 303.15 K,
T = 313.15 K, ; T = 318.15 K, ; solid lines are drawn based
on Redlich–Kister equation.

0.00
0.00

VmE / (cm3.mol-1)

VmE / (cm3.mol-1)

-0.10
-0.10

-0.20

-0.30
0.00

-0.20

-0.30

0.20

0.40

x

0.60

0.80

1.00

Fig. 5 Excess molar volume of x o-(CH3)2C6H4 + (1 À x)
C7H6O at ambient pressure plotted against mole fraction. At
; T = 308.15 K,
;
T = 298.15 K, e; T = 303.15 K,
T = 313.15 K, ; T = 318.15 K, ; solid lines are drawn based
on Redlich–Kister equation.

a result, better accommodation of solution components
between each other takes place at higher temperatures.
Conclusions

-0.40
0.00

0.20

0.40

0.60

0.80

1.00

x
Fig. 7 Excess molar volume of x p-(CH3)2C6H4 + (1 À x)
C7H6O at ambient pressure plotted against mole fraction. At
; T = 308.15 K,
;
T = 298.15 K, e; T = 303.15 K,
T = 313.15 K, ; T = 318.15 K, ; solid lines are drawn based
on Redlich–Kister equation.

observed behaviors of systems have been explained based on
variation of packing ability of components with structural factors and also formation of interaction complex between
components.
Conflict of interest

We studied volumetric properties of six binary mixtures
including three isomers of xylene with nitrobenzene and benzaldehyde from T = 298.15 to 318.15 K at ambient pressure
over the entire range of composition. The excess volumes for
all binary mixtures were negative and decreased by increasing
temperature. The excess molar volumes were fitted to Redlich–
Kister equation and the partial molar and excess partial molar
volumes are calculated and reported for components. The

The authors have declared no conflict of interest.
Compliance with Ethics Requirements
This article does not contain any studies with human or animal
subjects.


780
Acknowledgment
We are grateful to Razi University Research Council for the
financial support of this research.
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