Title
Dielectric constant and density of cyclohexane-benzene
mixtures under high pressure
Author(s)
Kashiwagi, Hiroshi; Fukunaga, Tomiaki; Tanaka, Yoshiyuki;
Kubota, Hironobu; Makita, Tadashi
Citation
The Review of Physical Chemistry of Japan (1980), 49(2): 7084
Issue Date
URL
1980-02-20
http://hdl.handle.net/2433/47080
Right
Type
Textversion
Departmental Bulletin Paper
publisher
Kyoto University
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
THE REVIEWnP PHYSICALCHEASISTRV
qP JAPAN,VOL.49, NO. 2, 1979
70
DIELECTRIC CONSTANT
CYCLOHEXANE-BENZENE
BY HiROSHI
KA$xlwACl,
MIXTURES UNDER HIGH PRESSURE
TU3IIASI
HIRONOHV KreorA
Few experimental
data
AND DENSITY OF
FcsUNAnA,
YnSHIYUlr2
AND TAnnsx2
on the dielectric
constant
and the density
benzene mixtures are presented as functions of temperature,
The dielectric constant bas bcen measnred by a frequenry
uncertainty
of 0.0490' at t[mperatures
from 2"a'C to 7SC and
The density
measurements
have been performed at the same
pressures
up to I00 MPa with an estimated
pressure burette.
The isotherms
of the dielectric
constant
TANAHA~
3insuA
uncertainty
of 0.069',
and the density
of rycloheaane•
pressure and composition.
counting method with the
pressures up to 190 MYa.
temperature
range under
using
increase
a new bigb
with increasing
pressure and their behavior are represented
by some empirical
equations.
The effect of
temperature
and pressure on the dielectric constant is found to be eapresscd by a simple
linear (unction of the density.
The molar polarization
is discussed as functions
of
density, temperaaure
and composition.
An analogy
Lion and the Tait equation is also discussed.
between
the Owen.Brinkley
equa•
InTroduc}ion
The dielectric
behavior
constant
of molecules
also of chemical
of fluids is one of the important
in an electrostatic
importance
pernture
dependence
The effect of pressure
because it relates to the volume
mines the effect on the equilibrium
interactionll,
field.
of the dielectric
and the measurements
or the rate of a reaction.
constant
physical
properties
representing
on the dielectric
change of reacting
provided some valuable
is
species which deter-
The study on the pressure
were applied to determined
constant
the
information
the density
and tem-
on the molecular
of fluids under
the
particucar conditions, such as in a critical regioaEl or for multiple mixtures at low temperaturesa-s),
So iar, however, the investigations
on the density dependence
of the dielectric constant ace quite
limited,
especially
This paper
for binary liquid mirtures.
provides
cyclohexane-benzene
the new experimental
mixtures
data of the dielectric
under high pies<_ures. The measurements
constant
and the density of
have been carried out at
(Received November 13, 1979)
1) P. Debye, "Polar molecules", Reinhold Publishing Co., New York (1929)
2) L. A. Weber, Phys. Rev. A, 2, 2379 (1970).
3) D. W. BurGeld, H. P. Richardsoa and R. A. Guerew, AICAE J. ]4„ 97 (1970)
4) W. P. Pan, M. H. ifady and R. C. diiller, AIChE J., 21, 2g3 (1975)
5) S. P. Singb and R. C, Miller, J. Chem. Therrnadynamfcs, 10, 747 (1978)
6) S. P. Singh and R. C. Miller, ibid., 1I, 39i (1979)
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric
temperatures,
25`C, SO°C and
and 100 bfPa for the density.
temperature,
Constant
pressure,
molar polarization
sity, temperature
and Density
of Cyclohexane-Benzene
75°C and under pressures
From the experimental
density
and composition
defined by the Clausius-Mossotti
at
Mixtures
up to 190 MPa for the dielectric
results,
is described
equation
the behavior
empirically
of dielectric
constant with
and theoretically.
is also discussed
constant
as functions
The
of den-
and composition.
Experimentals
Diefectrie constant
The dielectric constant of a fluid, e, is defined by the ratio of the capacitance between txo plates
filled with the fluid, C, to that in vacuum, C„
Therefore the measurement of the dielectric constant is reduced to that of the capacitance of a condenser. The bridge method and the heterodyne-beat
method are commonly known as accurate
[ethniques to measure the dielectric constant. However these need the tedious and time-consuming
procedures to adjust the precision variahle condenser. The present method employed is a "frequency
counting method" developed recentlyn, based on counting the resonant frequency of a L-C oscillating circuit including a high pressure capacitance cell filled with a sample Auid. The resonant frequency of the circuit, f, is expressed by
where L and C, are the inductance of a coil and the whole stray capacitance in the circuit, respectively. Substitution of Eq. (1) into Eq. (1) and rearrangement yield
a_
1
1
4rr'LC, J'
LC,
LC,
Assuming that L, C, and C, are independent
(3)
of temperature
and pressure, the equation is reduced
to
The dielectric constant of the fluid can be calculated by the measured frequency when the instrument constants, A~ and Br, have been determined by use of vacuum and a reference liquid, whose
dielectric constant was known accurately.
Benzene is selected as the reference in the present work
and its dielectric constant is 2.1740 at 25`C and atmospheric pressures>.
The schematic diagram of the apparatus is given in Fig. 1. The left part of this figure is the
high pressure system and the right one the electronics measuring system. The latter consists of a
frequency counter, a stabilized power supply and the L-C oscillating circuit which is set in an air
bath controlled at 400.1°C
and is covered with a wire gauze for electric shielding. The Hartley-
7) T. Mal-ita, H. Rubota, Y. Tanaka and H. Rashiwegi, ReJsigera(ion,52, 543 (1977)
8) A. A. hfaryett and E. R. Smith, "Table of Dielectric Constants of Pure Liquids", NBS Circ. 514,
National Bureau o[ Standards (1951)
ca
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
71
H. Kashiwagi, T. Fukunaga, 1'. Tanaka, H. Kubota and T. Jlakita
type oscillating circuit is composed of a fixed coil L, a variable condenser C, and a high pressure
capacitance cell filled with a sample liquid. The standard condenser (100.0 pF) Csa could be connected with the circuit by a coaxial switch, in order to confirm the stability of the circuit. The variable condenser is used for a fine adjustment of the resonant frequency. The frequency used ranges
between 3.7 and 4.4 nlHz with the precision of I Hz. The fluctuation of the frequency during one
measurement at an experimental condition was less than 10 Hz.
The high pressure capacitance tell is a concentric cylindrical capacitor of two-terminal type as
shown in Fig. 2. The outer diameter of inner electrode F is 8 mm and the inner diameter of outer
electrode G is 10 mm. The effective length is about 100 mm. The geometrical capacitance of Chis
cell is nearly 25 pF in vacuum. The electrodes are provided with two holes at each end so as to be
filled with a fluid. The spacers, H and I, made of glass-fiber reinforced PTFE (TeBon), are employed
to insulate between the electrodes and to support them coaxially. The high pressure vessel is made
of Ni-Cr-Bfo steel, SNCM-5, and is immersed in a thermostat controlled within±0.01'C.
The tem-
perature of the sample liquid is determined with a standard thermometer calibrated by the National
Research Laboratory of Dfetrology. The accuracy in temperature measurement is estimated to be
better than 0.05°C.
Pressure is generated by an oil pump and, if necessary, is raised by an intensifier, as shown in
Fig. 1. The pressure is transmitted to the sample liquid from the oil by bellows, whose displacement
D
J
B
C
b
K
H
(NIGN
MfSSViEST51EN) Irr_'[iaOarS NF.~S{/MNa
SRrEN1
Fig. 1
for dielectric
Schematic
diagram
of apparatus
constant measuremanls
E
F
G
Fig.2
Cross section of high presssure capacitance
9, High Pressure Vessel ;
B, Flange;
C,0-ring Closure;
D, Electrode Connector;
E, Support Rod ;
F, Inner Electrode;
G, Outer Electrode
H, I, Tedon Spacers;
J , >;. Pyre: Glass Spacers;
a,
to Electronic
Measuring
Outlet;
b, Sample
c,Sample
Inlet
;
System
cell
A
I
;
1
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric.
is detected
Constant
by a differential
measured
and Density
linear transformer
with a Bourdon gauge calibrated
of Cydohexane-Benzene
so as to prevent
an eacess
against a standard
73
htix[ures
pressure
compression.
balance
Pressure
is
with an accuracy
of
0.1 percent.
The measurements
um pressure
Lave been performed
and then with decreasing
isothermally
pressure
with increasing
down to atmospheric
obsera•ed between the results at increasing
and decreasing
ment constants
the dielectric
constants
up to 75°C under atmospheric
pressure.
temperatures
determined,
pressure up to the maxim-
pressure.
pressures.
No hysteresis
of cyclohexane
and benzene were measured
at
It was found that they agree well with litera-
ture valuesa> within the uncertainty
of the present v:ork and there is no trend of deviation
perature.
of the capacitance
The pressure dependence
was
With the values of the instru-
cell nuns examined
with tem-
by calculating
the com-
pression of the cells), This evaluation proved that tie effect of pressure on the geometric dimensions
of the electrodes was sufficiently small in comparison with the reproducibility
of the present measurement.
It was also confirmed
that
the difference
before and after apressure-temperature
Taking account
of the uncertainties
ment, the accuracy of the reference
and so on, the total uncertainty
between
[he instrument
constants
determined
cycle is insignificant.
due to the instruments,
dielectric
constant
of the dielectric
the reproducibility
of the measure-
values cited, the comparison
constant
obtained
is estimated
with literatures
[o be less than 0.04/.
Denstry
The density Las been measured
described
pressure
elsewheretol.
Its
principle
is applied to the system
by a new "high pressure
is similar
measured,
the compression
in a high pressure vessel causes the du-placement
position of a magnetic
linear transformer,
burette"
to [hat developed
of mercury
whose details were
et al.ttl R'hen high
of the sample liquid of a known weight
level in a high pressure
float on the surface of mercury is detected
whose height is measured
method,
by Doolittle
burette.
The
outside the burette by a differential
with a cathetometer.
The density of the liquid under high pressure,
p, is calculated
by
IV
where
[V is the wLole weight
atmospheric
of the liquid
pressure and dV is the volume
difference between the position
filled in the vessel,
p, is the density
of the liquid at
change of the liquid in the vessel. dV is obtained by the
of the mercury
surface at atmospheric
presssure
and tbat
at a high
pressure, compensated with the volume change of the burette, the vessel, mercury and tubing. The
density of cycloheaane-benzene
mixtures at atmospheric pressure was cited from the results of N'ood
et al.[zl
The density
et al.ls>
The measurement
9)
10)
11)
li)
13)
of mercury
under Ligh pressure
and controll
of pressure
was obtained
and temperature
from the values
by Grindley
were performed
in the same
B, A. Younglove and G. C. S[raty, Rev. Sci. Iattrunr„ 41, ID87 (1970)
H. Kubota, Y. Tanaka and T. \Iakita, Ragakakogaka Ronbunsku, t, 176 (1975)
A. K. Doolittle, I. Simon and R. M. Cornish, AICGE J., 6, 150 (t960)
5. E. Wood and A. E. Austin, J. Anr. Ckenr. Sa., 67, 480 (1945)
T. Grindley and J. E. Lind, Jr., J. Chem. Phys„ 54, 3983 (1971)
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
74
way
H. Kashiwagi,
as those
estimated
in the dielectric
[0 6e less than
T. Fukunaga,
constant
1'. Tanaka,
measurements.
H. Kubota
The
and T. blakita
uncertainty
of the
density
obtained
is
0.06%.
Meteriuls
Pure cyclohexane
cal Industries,
twice by the fractional
The mixtures
estimated
and benzene used were "super-special
Ltd. and their reported
parities
grades" supplied by Wako Pure Chemi-
are more than 99.g% in volume.
They were purified
crystallization.
were prepared
by the weighing
method.
The uncertainty
of the composition
is
within 0.03 mole percent.
Results
Diefectrie Constant
The raw data obtained for pure components and three mixtures at 25°C, 50°C and 75°C are listed
in Table 1, where Xn, P and a denote the mole fraction of benzene, the pressure in MPa and the
dielectric constant, respectively.
9lthough the data at 20°C, 30-C, 40`C and 60-C are not included
in Table 1, they are also used in the analysis described below. The data at 75°C and 0.101 dl Pa are
determined by the extrapolation from both the pressure dependence at higher pressures and the temperature dependence at 0.101 MPa.
Pig. 3 exhibits typical curves for a mixture of Xe=0.50, as an instance [o show the relationship
between the dielectric constant and the pressure. Every isotherm for each mixture increases monotonously with increasing pressure and is represented 6y the following polynomials:
e=a+LP+cPE+dP°+eP'
z.zs
(6)
Xe-0.4996
zao
eU
V
2.15
Fig. 3
Yu
p
~
~
~
~
p
u
A
2.10
25'C
30
~
50
~
~s
2.03
0
100
Pressure/MPu
200
Pressure
dependence
of dielectric constant of cyclohexnne•benzene
mixture of
Xe-0.4996
The
Review
of Physical
Chemistry
Dielectric Constant and Density of Cyclohexane-Benzene
of Japan
75
hfistures
Table 1 Dielectric Constant. of Cyclbhexane-Benzene 94ixtures
(%u: mole fraction ofbenzenG. P: pressure in hfPa)
Temp,
xfi•
•C
P
o.lD
6.96
11.86
2a.iz
..z
i
33.91
0.0000
•~D'
Xy.
0.2500
z.ol sD
2.oza1
a.o335
z.Di1s
z.Da9i
2.0570
o.assc
P
I'
0.10
6.96
I x.00
zo.es
29.4
34.41
41.44
z.o59s
2.afi89
2.0]82
z.oase
x.as6o
2.10?i
46.34
55.30
2.1099
2.t 172
2.1229
6~
2.1309
39
69.29
2.13]3
n.lG
0.10
2_]906
2.1902
.24
z2m7
13.93
?21]1
?7.92
2.1573
2.163:
2.1726
?.1801
2.18]3
2.1925
x ~ma
2.201]
zess
27.99
_
2su
?;
3]G
7b_05
_281P
?.'_688
?29{fi
89.63
o.la
i _{
11.27
a LaD
za.9s
95.09
z.olce
x.425{
2.03:5]
D.la
T23
D. m
vla
13.58
2U.7-
2_D764
_iss
3{.GB
U.31
?.OBfi9
48,61
?.l]sD
" .1275
?.1381
2.H 50
S +. iO
2.u3n
7fi.?0
z.m i 2
x.0103
13.13
29.94
loan
2:.as
2osm
33
y0
2.0305
2ose9
46.54
55.99
52.x8
69.3fi
78.2fi
2.OJI6
2.0x95
x1.11
a 8.63
55.3:
2.o5ea
czin
2.OG29
z:9fis3
G9.zs
?.0998
z.mn
2 t096
15.93
L.1
92.81
?.U'I51
83.01
89.91
2.1215
B?.T!
a?.Ofi
s9
laisi
3.9816
l ssas
z.o9ae
2.0754
52.;3
in.o,
t}9
2.12:3
119.H3
96.80
303.5]
310.32
II 1.35
?.1334
2.1394
?.1152
95',4(1
103.;2
110.25
2.1510
ll
12924
3.1566
]91.35
21621
L'3.62
111.00
139.90.
i.l4
f q,79
15].9?
150.G5
1G5 5a
t :2.71
o.la
7.10
14.62
21.3]
27. Bfi
3{.68
2.0x]1
?.0989
308{
o.1a
:21
13.8?
21.03
r.as
3±.37
}3.85
38.88
S 0.83
.3a
?.2931
^_.x824
2.Tm
2.14 G7
2.1co3
2.I 103
D.IO
.l:
13.Bfi
22x]4
z.z356
2.2465
?.1809
20.75
:.afi
3a.T5
67D
x.2s72
i8.;i
5323
fi'!.19
69.2!
7fi.15
?2934
63.1'1
9958
96.53
2.3921
2.1396
2.3{6]
2.3131
2611
ra
?.ISa
3980
2.40 i 11
2:x159
a:/7
2.180?
2.19x7
?.?0x8
2.?a9D
221]9
?.?175
96.36
103.77
110.Bfi
117.Sfi
22238
2.2?6"0
131.00
]38.2}
2:23 i]
?.2390
22330
Hi.99
22667
?.2735
2.2797
z.aasc
2 .9H
2.2972
2.30?B
2.30G0
124.11
?ose
-
'.2:x0
2.289.
2.1182
2.3'_70
?2310
22393
2.?106
2 .530
2.2fi0?
.16 tl7
9.1753
z.1 513
l.aeoD
3:.ii
41.54
4e.{i
56.37
622fi
69.10
.?d i2
?s3i
2:!fi01
G?.95
69.63
78L05
a3.12
8554
z.lsue
'9
0.16
sss
u.ei
!os
91.75
41.30
B. BB
i3d]
6?.05
69.36
E32s
Yb
I•
2.1109
2.139fi
?.1486
6?.19
69.22
:6.13
0.3{52
P
13 ~s
v .Dz
93.3..
}1.31
48A9
53.94
~h
] 0342
110.8]
111.]2
1?3.u
]31.00
]35.10
]5t.{]
159.06
Vol. 49 No.
2.3350
2.342]
?.9499
?.3599
2:3962
2.30!0
2.3091
2.31'8
!.IZ3D
2,3603
2.3651
z:aTl i
2.3 iT6
2.3688
2.394]
?.3979
24 a{
_2a3fi
1.09 i0
1.95D2
L9630
1.9739
0.10
1.9i9fi
0.10
2.0331
0.30
2.0994
0.10
T.2T
13.79
lose
1.9912
2.0032
z.Dlis
z.D2sa
2.0351
9.38
H.DO
20.75
_..58
2.1137
2.1262
2.137fi
2.1485
2.1891
2.2013
z.z 121
2i'
31.31
2.0}59
2.05:9
2.0902
2.oe1D
7.59
]1.00
20.51
1.9836
1.9929
7.SB
13.93
20.96
2 i.5B
2.1 ii{
1.92
2.2253
2 (1979)
The
76
Review
of Physical
Chemistry
of Japan
Vol. 49 No.
2 (1979)
H. Rashiwagi, T. Fukunaga, 1'. Tanaka, A. Rubota and T. Makita
where P is the pressure in blPa. The coefficient; of Eq. (6), determined by means of the least squares
method, are given in Table 2 with the average and the maximum deviations.
Fig. 4 shows the temperature effect on the . dielectric constant for a mixture of Xa=0.50.
IC is
obvious that every isobar of the dielectric constant (or each mixture decreases with an inaease of
Table 2 Coefficientsof Polynomial (6) Eorthe Dielectric Constant of Cydohexane.Benzeae hlixtu res
uele
r~aeuaa
or
Temp.
4ve .Dove
25
50
.Yb = 0.008
- o.2sao
rb
1.40]5
1.8219
-0.4693
1.9264
-1.6975
s.al6
L4i40
L i 378
2.0188
-0555?
-O.i641
2525
2.135
_].3600
7.6916
-1.818
2.11883
2.07539
z.03 m9
L 1666
1.7+37
2.071}
-O.T433
3.041
3.0583
S ~Su
-0.5706
-1.0425
2.19078
2.1470}
2.05513
1.5160
].8147
z.03s3
-0.5693
-0.93]6
1.933
8.0;26
3.!026
-2.a I3
-0.+34 G
2.27973
2.22350
2.17+}6
1.49+]
t .577
2.0+46
-0.4aes
-0.8320
-9si?_
4.5882
4.049:
].875;1
1.93109
z.05as3
2.01755
1.97696
50
60
°0,999fi
so
Yy = 0.1462
ss
.rb
c x105
2.014]6
Ta
sh
8x103
•c
beneenc
~ ].0oa
60
d x108
-1.6361
C Y 1010
]8.}i]
-0.7711
-1 ~35B
-1.1499
11ax.Dev
0.005
0.m
-9.393
0.01
9.0}
.1
n.n6u
6.02
9.00;
0.01
9.m
0.03
0.01
0.03
0.004
9.91
0.01
0.0]
0.91
0 oa
O.OI
n_o2
0.01
0.01
0.03
0.04
u.90]
n.o^_
o.OI
0.03
0.03
ss4
La1s
-1.233
-0.7314
,0
S
S
O.OI
' TLe deviation percent is calculated by ~100(k, a-=~rJ/<<~t I
2.4
1.25
~
p
140 MPa
li0
100
Q
~
p
~
60
40
20
O.I01
X40
tl0
2.20
2.3
C
0
C Z.2
OU
~ 2.I5
c
0U
V
90
VY
Y
_
VY
Y_ 2.~0
Q
2.~
A,
O,r
O~~
Ad
zos
z.a
50'C
Xt-0.4996
25
FIR. 4
50
Temperature,
Temperature
dependence
of dielectricconstantofcydohexane-benzene
mixture
of .Ye-0.4996
0.00
75
'C
Fig.
5
1.00
0.50
'.Sole fraction
of Benzene
Dependence
of dielectric
hexane-benzene
mixtures
of benzene
at SO'C
constant
of cycloon mole (raction
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric Constant and Density of Cyclohezane-BenzeneMixtures
temperature
liquids[+-ts).
and its slope is linear over the whole temperature
77
range in this work like other
The composition dependence of the dielectric constant at 50°C is shown along isobars
in Fig. 5. All the isobars at each temperature behave as slightly concave curves, but they Gave no
anomalous minima.
The dielectric constant obtained for pure benzene are compared with the valuesin the recent
litera[ures. At 50`C the present results are in good agreement with those by Hartmann et alt?>.
under pressures up [0 180 MPa with the average deviation of 0.04%- On the other hand, most of the
smoothed values by Vij e[ al.tsf are higher than those of this work over the whole range of temperature and pressure. So far there exist ao data on [he pressure dependence of the dielectric constant
for cyclohexane-benzene mixtures in the literature.
Denzity
Table 3 lists the raw data obtained at temperatures
25°C, SO°Cand 75°C under pressures up Co
100 MPa, As an example, Fig. 6 shows the pressure dependence of the density [or a mixture of Xu
=0.50. All [he isotherms of the density- increase with increasing pressure like those of the dielectric
constant and are fitted to the polynomials:
p=n'+b'P+t'P'+d'Pa+e'I'c
(i)
where p is the density in 10'kgJm' and Pis the pressure in MPa. The above equations are found
to reproduce the experimental data satisfactorily at each temperature and compositfoa.
However,
they are often unsuitable to derive the thermodynamic properties, such as the isothermal compressibility.
Therefore, the data are also expressed b}•the Tait equation:
p-p,
_
B+P`
where p° is the density in IOzkgJm' at P, which is taken as 0.101 MPa in the present work. It was
Xc-0.4997
0.85
em
a
r.a
Fig. 6
oso
p
Q
~
o"
0.75 o
so
Pressure/MPa
Pressure
benzene
dependence
of density
miature
of Xe-0.4997
of cydo6eaane•
2>'C
50
13
loo
14) R. G. Benaett,G.H. Hall and J. H. Calderwood,
J. Phyr.,D,6, i81 (1973)
13) W..G.S. Scaife,J. Phyr.,A,4, 413(1971)
Ib) J. K Vij and W. G.5. Sraife,J. Chem.Phyr.;64, 2226(1976)
V) H. Hartmann,A. Neumannand G. Rinck,Z. Pkyr.CGern.
(Frankfurt),44, 104(1965)
The
78
H. Kasbiwagi,
T. Fukunaga,
Ta61e 3
(.Yp :mole
'C
7.
P
0.10
8.87
13.86
21.10
2 7.93
39.]0
010
-
0.773 TB
O.iTD•1
0.7848
0.:901
0.7947
O.i999
0.:49 Bi
0
.7573
1+.21 o.7asn
50
21,111
3].96
35.15
0.769.1
0.7x8
O.i600
i ^_.O1
49.}3
6sSi
0.7851
O.T899
o.]s42
63.16
50.32
0.]983
0.8021
i 7.15
8?.03
O.R062
U.8100
ab'
TS
0.10
G.eo
13.87
21.21
29.09
3a 23
41. BT
{9.30
56.03
r,2.81
70.09
77.13
8416
91.17
98.28
101.12
0.10
5,32
14.13
21,16
3 7.99
30.18
02.17
0.53484
0.]337
O.i400
0.77 78
0.4640
0.759!
0.7609
O.7i05
0.7753
O.i598
o.7a45
0,7991
0.7930
0.7970
0.8007
D.eu9a
xb.
P
0,70164
0.7976
0,8032
0.8006
0.8141
0.0181
0.8223
0.8267
O.fl306
o.A3a4
u,8382
0.8419
0.8492
0.8986
0.8518
0.8547
0.70711
D.774G
0,7808
0.7889
0.7922
0.79 i8
48.66
0.8029
O.BOiO
ss.o6
63.07
70.2]
0.8115
0.8158
0.8199
i 7.93
64,20
91.26
0.0271
8.82]]
0.0313
0.8947
0.30
7.09
3+.38
20.79
27.87
37,02
42,08
99,19
56.03
63.05
sssi
7sse
89.32
91.06
97.99
109.83
0.8281
0.'4189
0.7504
0.]602
0.7048
0.7712
0,5772
O,T828
0,7880
0.7927
0.7975
o.ema
0.0063
0.8107
0.8112
0.0170
0.6214
known that the coefficient C is independent
sent analysis,
the coefficienu,
Band
0.10
732
14.00
21,06
2].99
35.19
42.28
49.25
56.20
03.25
70,33
7e.zs
84.33
91.18
98.31
]07.28
0.10
6,99
13,91
29,93
28,04
94.99
4L98
98.95
Si.24
63.09
73.13
11.13
84,22
91.1]
90.03
1 05.40
on the assumption
that C is a coestant
perimental
range, B and C are rede[ermined
closed equation
0 81352
0.8197
o.a25s
0.8311
0.8358
0.0702
0.8449
O. A492
0.8534
0.8573
0.8616
0.8661
0.8687
0.8723
0.8756
0.6]89
O.i497
Xb=
P
0.10
fi.96
14.11
21.19
28.07
33.10
41.]0
49.94
65.89
s33a
70:51
77.31
8?16
91.35
98.39
1A5.6a
0.84063
0.10
7.Ofi
0.81476
0.8222
0.78840
0.7963
0.8020
0.8086
0.8143
0.8196
0.8'_48
0.8298
0.8341
0.8385
0.8427
0.8472
0.8606
0.8541
0.8579
0.8615
91,95
98.07
107.15
0.46261
0.]722
o3RDo
0.7008
0,]930
0.7996
0.6063
0.8106
0.8160
0,8208
0.8254
0.8299
0,8341
0,8382
0.8921
0.8{6]
0,10
s,99
13sa
20,80
28,04
35.02
41.87
?9.23
65.]8
62.91
7013
7708
86,92
93,16
96,09
105.10
0.10
0,8802
0.8852
0.890]
0,8950
0,8997
0.8]21
0.8769
0.6607
o.eflso
o,8A89
0.8925
0.896E
0.9000
42.11
48,98
ss.es
52.94
70.01
0,9042
0.9086
o,elzs
Dslss
0.9203
0.8036
os671
0.10
6.94
1+.25
21.29
28.06
95.13
42.26
?8.92
0.8209
0.83{9
0.8{03
0.80 5T
14.07
20.75
27.83
35.02
0.8509
0.6555
4236
as.os
95.62
62.91
i 0,51
77.30
8;.60
x.8800
0.8648
0.8883
0.8733
0.8774
0.8811
56.03
63.05
70.23
77.16
84.11
9311
0.884fl
o.eeae
98.60
105.12
0.78814
0.]908
0.8043
0.8111
0.8170
0.8220
0.10
6,86
13,98
21,09
28,20
33.25
0.8290
0.8399
0.8401
0.8491
0.8300
0.8945
0.8988
4221
49.]3
56.19
63.03
70.35
77.50
81.41
0.8629
0.8070
0.8712
9 L 61
88.47
ms.13
for each composition
of temperature
expression.
to calculate the isothermal
So the Tait
IB) R. E. Gibson and 7• F. Rincaid, J. Am. Chem. Sa., 60, 51l (1938)
0.84689
0.8538
a.fisol
0.8857
0,8713
0,8768
0.8817
0.8864
0.8.908
0'.8951
0.8995
0.9034
0.9073
0.8111
0.9149
0.9186
0.81938
0.82]5
0.8349
0.8417
0.8401
D.fisao
0.8595
0.8662
0.8897
O.BT44
O.BT92
0.3838
0.8878
O.BBl9
0.8959
0.099!
In the pre-
and temperature
with temperature.
over the whole exrepresents
As mentioned
compressibility
equation
0,87380
7.99
13.93
21,06
27.89
39.01
and listed in Table 4. The Tait equation
of state with only two parameters.
P
0.6070
o.asz7
0.8381
0.8630
0.86]]
C is found to vary scarcely
independent
1.0000
I'
for many organic liquidsl~.
worse than the polynomial
however, the Tait equation can be applied
Vol. 49 No.
in ]0'kg/m'J
P
C, are first determined
Therefore,
as well as or slightly
ab.
of temperature
of Japan
Miatures
P
o.l D
6.69
17.12
21.50
28.37
3i. i9
41.96
48.97
s6.ot
62.62
]0.46
57.19
67.3{
61.55
68.41
1[5.42
For each composition
results
Chemistry
and T. Makita
0.4997
Y
by the least squares method.
present
H. Kubota
of Cyrlobexane-Benzene
03904
P
98.26
105.13
0.10
5.13
19.98
21.01
25.98
96.30
?3.99
?9.17
56.11
62.92
sss5
i 7,91
85.04
sl.ai
99.17
]05.33
Y. Taoaka,
of Physical
Traction o! benzene, P: Dressure in MPe, p :density
"
y= 0.0000
Temp.
Density
Review
the
above,
and is a simple
is preferable
to the poly-
2 (1979)
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric
Constant
and Density
of Cyclohexane-Benzene
Mixtures
79
nomial for representing the PVT relations of the present mixtures. The density values at 50°C
smoothed by Eq. (8) are plotted against the composition of the mixtures in Fig. 7. Every isobar
exhibits the similar behavior to that of the dielectric constant.
There are many reports on the pressure dependence of the density of pure benzene. The measurement by Gibson et al.ta> is considered as an accurate and representative one of them at temperatures
25°C to 65`C under pressures up to 100 MPa. They fitted their data to the Tait equation and concluded that C was independent of temperature and that p, and B were expressed by the polynomials
of temperature. As they did not measure the density at 50'C and 75'C, the density has been calculated
with the coefficients interpolated to 50`C and extrapolated to 75`C. Their values agree well with the
present results at only 25°C. The pressure coefficient of the density, (rip/o^P)r, of Gibson et al. is
larger than the present one. The disuepancy increases with increasing pressure up to 0.2% at 75`C
Tahle
Coefficients of the Tait Equation (8) for Cyclohexane-Senzese Mixtures
4
Mole
fraction
e} benzene
X6
xb
• O.D00
= 0.2509
Xb = 0.4997
Sam
•C
Xh • 1.000
p
[]
O
•
O
~
0.90
E m0.95
x
0.0]
o.m
0.01
0.05
0.03
O.Ofi
0.0]
0.01
0.09
0.09
0.03
o.oz
0.04
D.os
0.03
0.1]
0.02
0.02
0.02
0.05
0.06
0.06
0.01
0.02
0.01
0.06
0.04
17.9
6a
O.M984
61.5
r
0.12484
49.3
25
0.79154
O. T6Ttt
74.9
fi 1.1
C
C
0.1988
0.1947
T6
094189
98.9
0.0]
25
so
0.31352
0.02
o.T66as
T6.T
sas
0.16267
48.0
25
0.84063
50
T8
0.91476
0.78819
86.2
702
56.8
zs
0.67360
0.84889
88:5
60
]s
0.91938
809
T2.T
o.ls]s
0.200]
0.2000
0.0]
Fig. 7
0.80
0
50'C
0.7i
D.00
Maz.DeT.
A
100 MPa
80
60
40
20
O.lOI ~
0
b
Dev.
B
MPa
0.]]3]0
SO
Ave
Pa
103 kg/m3
2s
TS
Xb = 0 .]997
P.
O,iO
Jlole fraction of Benzene
L00
Dependence
of density of cydohxanebenzene mixtures as mole fraction of
benzene at 50'C
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
H. Kashiwagi,
80
and 100 MPa.
T, Fukunaga,
It seems that
S'. Tanaka,
this inconsistency
H, Kubola
would
and T. Makita
came partly
from the inadequacy
of ex-
Crapolating their data to 75°C.
There are a few available
The values of Kerimov
under pressures
papent9-'-~
on [he density
up to 10 MPa.
to represent
can not be sufficiently
the data by the Hudleston
bility of the PVT data of liquids.
low pressure
ments.
Tait
for tytlohexane-benzene
Their data agree well with the present results
Since the present results
tempted
The reproducibility
under pressures
compared
up
ersor.
with the literature
values,
it is at-
equation241 which is often used to verify the relia-
The equation
of the Hudleston
It is, however,
mixtures
within the experimental
is found to represent
region below 20 MPa, where it would be sensitive
equation.
under high pressure.
with the present results at 50`C
Most of their data are found to be higher than those of this work.
Holder et al.iz 231carried out the measurement
to 10 MPa.
for pure cyclohexane
et x1.211are only ones that can be compared
[he data very well except the
to the uncertainty
equation is also found to be better
not easy to solve the Hudleston
equation
in the measurethan that
of the
for the density at a given
pressure.
Discussion
The compositions
for dielectric
of the mixtures
constant
measurements.
the density of mixtures
calculated
prepared
of the same
for density
measurements
slightly
In order to correlate
the dielectric
constant
used in the dielectric
constant
compositions
differ from those
with the density ,
measurements is
using the Tait equation.
IC was found in our previous
and the density
of a fluid.
work7l that a simple relation
exists between the dielectric
constant
In Fig. 8, a part of the , dielectric
density in the limited range.
constant obtained is plotted against the
It is found that [he difference between [he isotherms of the same com-
positions almost disappears and that [he linear relations exist over the whole range of the present
work. This fact suggests that the pressure and temperature
effect on the dielectric constant is reduced to the effect of the density
represented
by a linear function
.4 few equations
stant of liquids.
from the Tait equation
19)
20)
21)
22)
23)
24)
23)
26)
In each composition,
within the average
the dielectric
deviation
have been proposed to express the pressure
Representative
e
only.
of density
one of them is the Owen-Brinkley
and the electrostatic
=A to
constant
is found to he
of 0.06%.
dependence
of the dielectric
wn-
equationis•7b1, which was derived
theory.
D+P
e D+P,
H. H. Reamer and B. H. Sage, Chem. Eng. Darn Ser., 2, 9 (1957)
E. Kuss and M. Taslimi, Chern, ]ng. Tech., 42, 1073 (1970)
A. Sf. Kerimov and T. A. Apaev, Fluid 3fechanict-Sovier R¢s., 3, 100,(1974)
G. A. Holder and E. Whalley, Trans. Faraday Sa., 58,.2095 (1961)
G. A. Holder and E. Whalley, ibid., 58, 2108 (1962)
L. ]. Hudleston, Trans. Faraday Soc., 33, 97 (1937)
B. B. Owen and S. R. Brinkley, Jr., Phyt. Rev., 64, 32 (1943)
B. B. Owen, 1, Chem. Educ., 21, 59 (1944)
(9)
p0
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric
Constant
and Density
of Cyclohexaae-Beazeae
Mixtures
81
p
X6=1,0000
2.20
°
o
~
0
p
0
m
X6=0
2.15
op
.7462
0
p
V
V
a
z.la
p
~o~
e8
Qg
9fl
® $
m p8
Fig. a
p°~
p
X6=0.2500
Xb=0,49960 ~
° ®
° ~ ~pp88
p4
0
0
Density dependence
of dielectric
con•
stant of cyclohexane-benzene
mixtures
25'C
50
° ~~°° xb=o,oooo
p 75
z.os
o
p
°
0.75
°
0.80
0.84
Density/1Wkg/mt
where e, is the dielectric constant at P,. which is taken as 0.101 JIPa in the presem work. Owen et
al. pointed out that the coefficientD was identical wit4 B in-the Tait equationand A was practica4
ly independent of temperature. However the data used for their analysis are now out of date and
inaccurate. Althoughthere are several reports on the equation~-~l, the validity of the equation
was not discussed sufficiently. Therefore, using the present data, the coeBicients.of theequation
have been determined on the followingassumptions:
1) Both coe(hcients,A and D. are determined without restriction, that is. D is not identical
with B in the Tai[ equation, and A is dependent on temperature, Z (D; B, A(Tr)#A(Tz))
7) D is not identical with B and A is independent of T. (DrB, A(TE)=A(T,})
3) D is identical with B and A is dependent on T. (D=B. A(Tt)*A(Ta))
4) D is identical with B and A is independent of T. (D=B, A(Tr)=A(T,))
As representatives otthe mixtures, the coefficientsobtained for cyclohexane, mixture of Xo=o.50 and
benzene are listed in Table 5. There is a good agreement between the present raw data and the
dielectric constants calculated with the assumption (1). It is concluded that the Owen-Brinkley
equation without restriction represents the dielectric constants of liquids under high pressure satisfactorily, as described6y Hartmann et al.~> and Srinivasan et al.~> Nith We assumption (2), it is
found that Eq. (9) can also reproducethe data well. On the other hand, Eq. (9) with the assumption
(4) expresses the data worst because of the rigorousrestriction. The ability with the assumption (3)
27) E. Huckeland E. Ganssauge,Z. Phys,Chem.(Frankfurt),12, 110(1957)
28) H. Hartmann,A.Neumannand G. Rinck.,ihid.,44, Z18(1965)
29) M. Nakahara,Rev.Phys.Chem.Japan,44, 57(1974)
30) R. R. Srinivasanand R. L. Ray, J. Chem.Phys.,.60,
3645(1974)
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
H. Kasbiwagi, T. Fukunaga, ]'. Tanaka, H.Kubota and T. bfakita
81
Table 5
Coefficients of the Owen•Brinkley Equation (9) for Cyclohexane- benzene 1fiatures
mole
of
fncliov
Lenzene
Temp.
Ae.umptiov
n
•C
25
50
2.0 ] 50
U1
]5
h
]IV x.Dev.
X
D.1]Da
D.m
0.03
]sr:
]].k
D.1ds5
0.01
].93 i0
65.1
0.1539
0.01
0.05
0.03
92.9
7G.u
D.3 S17
121
75
X
A1x.I>QY.
ms.e
25
50
c
11118
0.0]
6A.4
0.02
0.01
0.02
0.0;
0.03
• 0.000
25
50
131
15
RS
SD
f4]
]s
(]~
TS
2,o7za
2.D317
0.01
0.128]
0.03
0.1311
O.OB
i 1.9
sls
o.l_^;s
87.3
81.0
]0.6
0.1x]5
0.1591
0.163]
121
75
0.03
O.OG
0.13
O.Ok
0.05
o.os
D.oe
D.la
0.01
0.01
0.02
0.01
O. D3
0.01
0.01
o.az
0.02
0.09
D.os
0.03
88.1
zs
50
0.1901
6LG
49.3
z.31 as
zs
sn
]7.9
49.]
D.oa
81.4
68.1
0.160]
]6.]
sz.c
48.9
0.1334
0.1353
D.az
D.D4
0.08
0.15
0.1316
D.tS
0 '3
0.02
0.05
0.11
0.2G
O.lfi
0.28
0.01
0.02
o.oe
O.Ok
Xp = 0.499fi
2"a
Ss
(31
75
25
50
75
76.7
(•IJ
25
sD
LL1
7s
z.17k4
25
50
121
]5
xb-
2.2 ik0
z.zz49
62.6
48.9
0.3330
153.8
sls
i 9.5
0.2196
D.1]4s
0.17zfi
11].9
9T.G
BD.B
0.1145
68.5
]2.1
59.9
88.5
]P.]
D.D2
0.02
0.02
0.02
o.D2
0.05
0.139a
o.14ze
0.04
O.1k32
0.14
0.09
O.1k
0.22
o.14ze
O.OA
D.De
0.19
0.14
0.13
0.2fi
0.0]
o.os
l.ooo
25
60
1]1
75
25
50
]5
(kl
58.9
0.09
to represent the data is also not good. This fact does not necessarily mean the inadequacy of
assumption (3), because not only the dielectric constant data but also the density data are subject to
the errors of measurements. It one used the values of B given by Cibson et al., the reproducibility
of the equation is improved but still not good for the present work.
By combiningthe Tait equation (g) and the Owen-Brinkleyequation (9) with assumption (3), a
simple relation is deduced as follows:
that is, a linear relationship between the reciprocalsof [hc dielectric constant and the density exists.
However, the least squares reduction of the data shows slightly worse fit for equation (10) than for
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric
Constant
the simple a vs. p linear relations
B for the present
and Density
of Cyclohexane-Bcnzene
:iE
Mixtures
as shown in Fig. 8. This fact implies
that D is not identical
with
miatures.
The Clausius-iliossotti
equation
is theoretically
derived
for nonpolar
liquids in an electrostatic
field as follows:
Psf=e+2p =3 r,Ncz
where Pat is the molar polarization,
molecular
polsrizability.
molar polarization
(11)
M the molecular
weight,
N the Avogadro's
According to the theory, the temperature
is very small, and an additive
number
and pressure
and a the
dependence
of the
law
t
is held for a mixture
nonpolar
liquids,
of nonpolar
it is expected
liquids
as nn ideal solution.
that the present
mixtures
Since cyclohexane
exhibit such a behavior.
and benzene are
The density
de-
pendence of the molar polarization u shown in Fig. 9, where the molecular weights of the mixtures
were calculated by the mole fraction average of thepure component values. Then, the molar polarization of the mixtures
was obtained
by
P,tf=E+1
1 {(1-Xa)MrtXeMQ}
(13)
P where FYI,and M, are the molecular weights of cyclohexane and benzene, respectively. ICis found that
the variation of the molar polarization with density is very small and Chat the molar polarization is
sensitive to the inaccuracies in the dielectric constant and the density measurements.
The molar
polarization shows an approximately linear decrease with increasing density and is slightly dependent
on temperature. The same linear relationship has been reported for other liquidsts, st,az) and for a
polar liquid [he temperature effect is distinct due [o a dipole momentsv. In the present results, the
temperature wefficients of the molar polarization, (BP,trl87?o, are negative for mixtures of Xp=0.50 ,
0.75 and pure benzene. However they are too small to confirm the presence of a dipole moment. On
O
E
0
c
e.
p
.~
O Q.
A
O
~.
,.rm,,,,,
w
Xb=0.0000
ee au°veee
z ~.5
°°rrre
Yqe~
X6=0.2500
°.a:
,
Fig. 9
zzo
26.5
D
IS'C
Q
50
75
.75
_
~
X6=0.7462
pe.
epee
°°eama
Xb=1.0000
0.80
~'P°bpga °
0.85
p~r .
0.90
Density/1Wkg/ms
31) F. I. hfopsik, J. Rer. Nal. Bur. Sand., 71A, 287 (1967)
32) F. I. Mopsil•, J, Chem. Phys., 50, 2559 (1969)
Density
dependence
of molar
polarization
of cydoheaaae•
benzene mixtures
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
CLI
H. Kashiwagi,
T. Fukunaga,
]'. Tanata,
H Kubota
and T. Makita
Fig.
Dependence
27.6
5 0'C
O
E
27.2
0
e
.q
.q
e
N
0
Oa
10
O.I01 DfPa
of molar
polarization
of cydohesane-benzene
mixtures
on mole iraction of benzene at 50'C
10
26.8
40
A
O
s
0
60
e
100
80
26.4
0.00
0.50
31o1eFraction Benzen
1.00
the other band, those for cyclohesane and mixture of Xa=0.15 are positive contrary to the theory.
The similar temperature dependence was observed for carbon disulfide.
The isotherms of 0.50
mixture are close to those of 0.75 mixture, while those of other mixtures depart from each other.
For the mixture composed of simple fluids it was verified3-6> that an additive law of the molar
polazization was held at a given pressure and temperature. In the present results, however, as shown
in Fig, 10, every isobar deviates from the behavior of an ideal mixture and an inflexion is observed
at the composition between Xp=0.50 and Xe=0.75. This deviation reveals that the particular molecular interaction between unlike molecules exists. Since the Clausius-Mossotti relation was ideally
derived, it is not suitable to assume that the molecular polarizability does not change even in the
dense state. Other formulas derived for the compressed fluid should be necessary to discuss the
present results.
The autbocs wish to express their appreciation to Mr. Toshiharu Takagf, Kyoto Technical
University, for his advice and assistance in constructing the apparatus for the dielectric constant
measurements and are also indebted to Mr. ]unzo Kobo and Miss Ryoko Tanaka for their careful
measurements of the density.
Deparlmen0 of Chernital Engineering
Fatul6y of Engineering
Kobe Univesity
Kobe 657, Japan