Title Dielectric constant and density of cyclohexane ...repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/47080/1/... · uncertainty of 0.0490' at t ... perature of the sample
Post on 20-Mar-2018
213 Views
Preview:
Transcript
Title Dielectric constant and density of cyclohexane-benzenemixtures 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): 70-84
Issue Date 1980-02-20
URL http://hdl.handle.net/2433/47080
Right
Type Departmental Bulletin Paper
Textversion publisher
Kyoto University
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
70 THE REVIEW nP PHYSICAL CHEASISTRV qP JAPAN, VOL. 49, NO. 2, 1979
DIELECTRIC CONSTANT AND DENSITY OF
CYCLOHEXANE-BENZENE MIXTURES UNDER HIGH PRESSURE
BY HiROSHI KA$xlwACl, TU3IIASI FcsUNAnA, YnSHIYUlr2 TANAHA~
HIRONOHV KreorA AND TAnnsx2 3insuA
Few experimental data on the dielectric constant and the density of rycloheaane•
benzene mixtures are presented as functions of temperature, pressure and composition.
The dielectric constant bas bcen measnred by a frequenry counting method with the
uncertainty of 0.0490' at t[mperatures from 2"a'C to 7SC and pressures up to 190 MYa.
The density measurements have been performed at the same temperature range under
pressures up to I00 MPa with an estimated uncertainty of 0.069', using a new bigb
pressure burette. The isotherms of the dielectric constant and the density increase 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 between the Owen.Brinkley equa•
Lion and the Tait equation is also discussed.
InTroduc}ion
The dielectric constant of fluids is one of the important physical properties representing the
behavior of molecules in an electrostatic field. The effect of pressure on the dielectric constant is
also of chemical importance because it relates to the volume change of reacting species which deter-
mines the effect on the equilibrium or the rate of a reaction. The study on the pressure and tem-
pernture dependence of the dielectric constant provided some valuable information on the molecular
interactionll, and the measurements were applied to determined the density 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 for binary liquid mirtures.
This paper provides the new experimental data of the dielectric constant and the density of
cyclohexane-benzene mixtures under high pies<_ures. The measurements 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 Constant and Density of Cyclohexane-Benzene Mixtures at
temperatures, 25`C, SO°C and 75°C and under pressures up to 190 MPa for the dielectric constant
and 100 bfPa for the density. From the experimental results, the behavior of dielectric constant with
temperature, pressure, density and composition is described empirically and theoretically. The
molar polarization defined by the Clausius-Mossotti equation is also discussed as functions of den-
sity, temperature 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 con-
denser. 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 oscilla-
ting circuit including a high pressure capacitance cell filled with a sample Auid. The resonant fre-
quency 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, respec-
tively. Substitution of Eq. (1) into Eq. (1) and rearrangement yield
_ 1 1 LC, (3) a 4rr'LC, J' LC,
Assuming that L, C, and C, are independent of temperature and pressure, the equation is reduced
to
The dielectric constant of the fluid can be calculated by the measured frequency when the instru-
ment 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)
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 con-
nected with the circuit by a coaxial switch, in order to confirm the stability of the circuit. The varia-
ble 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
a
(NIGN MfSSViE ST51EN) Irr_'[iaOarS NF.~S{/MNa SRrEN1
Fig. 1 Schematic diagram of apparatus for
constant measuremanls
Fig.2 Cross 9,
B, C, D, E, F, G, H, I, J , >;.
a,
b,
c,
dielectric
section of high presssure capacitance cell
High Pressure Vessel ;
Flange;
0-ring Closure;
Electrode Connector;
Support Rod ;
Inner Electrode;
Outer Electrode
Tedon Spacers;
Pyre: Glass Spacers;
to Electronic Measuring System ;
Sample Outlet;
Sample Inlet ;1
c
D J
B
C
b K
H
E
F
G
A
I
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric. Constant and Density of Cydohexane-Benzene htix[ures 73
is detected by a differential linear transformer so as to prevent an eacess compression. Pressure is
measured with a Bourdon gauge calibrated against a standard pressure balance with an accuracy of
0.1 percent.
The measurements Lave been performed isothermally with increasing pressure up to the maxim-
um pressure and then with decreasing pressure down to atmospheric pressure. No hysteresis was
obsera•ed between the results at increasing and decreasing pressures. With the values of the instru-
ment constants determined, the dielectric constants of cyclohexane and benzene were measured at
temperatures up to 75°C under atmospheric pressure. 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 with tem-
perature. The pressure dependence of the capacitance cell nuns examined 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 mea-
surement. It was also confirmed that the difference between [he instrument constants determined
before and after apressure-temperature cycle is insignificant.
Taking account of the uncertainties due to the instruments, the reproducibility of the measure-
ment, the accuracy of the reference dielectric constant values cited, the comparison with literatures
and so on, the total uncertainty of the dielectric constant obtained is estimated [o be less than 0.04/.
Denstry
The density Las been measured by a new "high pressure burette" method, whose details were
described elsewheretol. Its principle is similar to [hat developed by Doolittle et al.ttl R'hen high
pressure is applied to the system measured, the compression of the sample liquid of a known weight
in a high pressure vessel causes the du-placement of mercury level in a high pressure burette. The
position of a magnetic float on the surface of mercury is detected outside the burette by a differential
linear transformer, whose height is measured with a cathetometer.
The density of the liquid under high pressure, p, is calculated by
IV
where [V is the wLole weight of the liquid filled in the vessel, p, is the density of the liquid at
atmospheric pressure and dV is the volume change of the liquid in the vessel. dV is obtained by the
difference between the position 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 of mercury under Ligh pressure was obtained from the values by Grindley
et al.ls> The measurement and controll of pressure and temperature were performed in the same
9) B, A. Younglove and G. C. S[raty, Rev. Sci. Iattrunr„ 41, ID87 (1970) 10) H. Kubota, Y. Tanaka and T. \Iakita, Ragakakogaka Ronbunsku, t, 176 (1975)
11) A. K. Doolittle, I. Simon and R. M. Cornish, AICGE J., 6, 150 (t960) li) 5. E. Wood and A. E. Austin, J. Anr. Ckenr. Sa., 67, 480 (1945)
13) 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 H. Kashiwagi, T. Fukunaga, 1'. Tanaka, H. Kubota and T. blakita
way as those in the dielectric constant measurements. The uncertainty of the density obtained is
estimated [0 6e less than 0.06%.
Meteriuls
Pure cyclohexane and benzene used were "super-special grades" supplied by Wako Pure Chemi-
cal Industries, Ltd. and their reported parities are more than 99.g% in volume. They were purified
twice by the fractional crystallization.
The mixtures were prepared by the weighing method. The uncertainty of the composition is
estimated 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 tem-
perature 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 mono-
tonously with increasing pressure and is represented 6y the following polynomials:
e=a+LP+cPE+dP°+eP' (6)
z.zs
zao
2.15
2.10
e U
V
Y u
u A
2.03
Xe-0.4996
p 25'C ~ 30 ~ ~ ~ 50 ~ ~ p ~s
0 100 Pressure/MPu
200
Fig. 3 Pressure dependence of dielectric con-
stant of cyclohexnne•benzene mixture of
Xe-0.4996
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric Constant and Density of Cyclohexane-Benzene hfistures
Table 1 Dielectric Constant. of Cyclbhexane-Benzene 94ixtures
(%u: mole fraction ofbenzenG. P: pressure in hfPa)
75
Temp,
•C
xfi•
P
0.0000 •~D'
I'
0.2500 Xy.
P
o.assc ~h
P
0.3{52 Yb
I•
l.aeoD
o.lD z.ol sD 0.10 z.o59s n.lG 2.1109 0.10 2_]906 0.16 '.2:x0
6.96 2.oza1 6.96 2.afi89 2.1902 .24 z2m7 sss 2.289.
11.86 a.o335 I x.00 2.0]82 13 ~s 2.139fi 13.93 ?21]1 u.ei ?.2931
2a.iz z.Di1s zo.es z.oase v .Dz ?.1486 zess !os ?ose _̂.x824
..z i z.Da9i 29.4 x.as6o ?7.92 2.1573 27.99 _ 2su-
.3a 2.Tm
33.91 2.0570 34.41
41.44
2.10?i
2.1099
93.3..
}1.31
2.163:
2.1726
91.75
41.30
?; 3]G
.?d i2
3:.ii
41.54
2.11822.3'_70
46.3455.30
2.t 172
2.1229
48A9
53.94
?.1801
2.18]3
B. BB
i3d]
?s3i
2:!fi01
4e.{i
56.37
2.3350
2.342]
6~ 39 2.1309 6?.19 2.1925 6?.05 2611 622fi ?.9499
69.29 2.13]3 69.22 x ~ma 69.36 ra 69.10 ?.3599
:6.13 2.201] 7b_05 _281P
E32s ?.'_688
89.63 ?29{fi
o.la laisi D.la z.m i 2 D. m 2.0754 o.1a 2.14 G7 D.IO 22x]4
i _{ 3.9816 T23 x.0103 vla 2.0x]1 :21 2.1co3 .l: z.z356
11.27 l ssas 13.13 loan 13.58 ?.0989 13.8? 2.I 103 13.Bfi 2.2465
a LaD z.o9ae 29.94 2.0305 2U.7- 308{ 21.03 ?.1809 20.75 67D
za.9s z.olce 2:.as 2osm _iss ?.l]sD r.as ?.ISa :.afi x.2s72
95.09 x.425{ 33 y0 2ose9 3{.GB " .1275 3±.37 3980 3a.T5 2:3962
a?.Ofi 2.03:5] x1.11 2_D764 U.31 ?.1381 }3.85 2.40 i 11 i8.;i ?2934
46.54 2.OJI6 a 8.63 ?.OBfi9 48,61 2.H 50 38.88 2:x159 5323 2.30!0
55.99 2.0x95 55.3: ?.0998 S +. iO 2.u3n S 0.83 a:/7 fi'!.19 2.3091
s9 52.x8 2.o5ea czin z.mn 52.;3 z.lsue G?.95 ?2310 69.2! 2.31'8
69.3fi 2.OG29 G9.zs 2 t096 in.o,'9
.16 tl7 69.63 22393 7fi.15 !.IZ3D
78.2fi z:9fis3 15.93 L.1 t}9 7fi.?0 9.1753 78L05 2.?106 63.1'1 2.3921
92.81 ?.U'I51 83.01 2.1215 B?.T! z.1 513 a3.12 2 .530 9958 2.1396
89.91 2.12:3 119.H3 2.180? 8554 2.2fi0? 96.53 2.3{6]
96.80 ?.1334 95',4(1 2.19x7 96.36 22667 ] 0342 2.3131
303.5]
310.32
2.1394
?.1152
103.;2110.25
?.?0x8
2.?a9D
103.77
110.Bfi
?.2735
2.2797
110.8]
111.]2
2,36032.3651
II 1.35 2.1510 ll i.l4 221]9 117.Sfi z.aasc 1?3.u z:aTl i
12924 3.1566 L'3.62 ?.?175 124.11 2 .9H ]31.00 2.3 iT6
]91.35 21621 111.00 22238 131.00 2.2972 ]35.10 2.3688
139.90. 2.2?6"0 ]38.2} 2.30?B ]5t.{] 2.394]
f q,79 2:23 i] Hi.99 2.30G0 159.06 ?.3979
15].9? ?.2390
150.G5 22330
1G5 5a 24 a{
t :2.71 _2a3fi
o.la 1.09 i0 0.10 1.9i9fi 0.10 2.0331 0.30 2.0994 0.10 2.1 ii{
7.10 1.95D2 T.2T 1.9912 7.SB 2.0}59 9.38 2.1137 7.59 2.1891
14.62 L9630 13.79 2.0032 13.93 2.05:9 H.DO 2.1262 ]1.00 2.2013
21.3] 1.9739 lose z.Dlis 20.96 2.0902 20.75 2.137fi 20.51 z.z 121
27. Bfi 1.9836 2i' z.D2sa 2 i.5B 2.oe1D _..58 2.1485 1.92 2.2253
3{.68 1.9929 31.31 2.0351
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
76 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 Coefficients of Polynomial (6) Eor the Dielectric Constant of Cydohexane.Benzeae hlixtu res
uele r~aeuaa Temp. 4ve .Dove 11ax.Dev ,0
or beneenc •c 8x103 c x105 d x108 C Y 1010 S S
25 2.014]6 1.40]5 -0.4693 0.005 0.m
.Yb = 0.008 50 ].875;1 1.8219 -1.6361 ]8.}i] -9.393 0.01 9.0}
Ta 1.93109 1.9264 -1.6975 s.al6 .1 ss4 n.n6u 6.02
z.05as3 L4i40 -0555? 2525 9.00; 9.m
sh - o.2sao 50 2.01755 L i 378 -O.i641 2.135 0.01 0.03
1.97696 2.0188 _].3600 7.6916 -1.818 0.01 0.03
2.11883 L 1666 -O.T433 3.041 0.004 9.91
rb °0,999fi 60 2.07539 1.7+37 -0.7711 3.0583 -0.5706 0.01 0.0]
z.03 m9 2.071} -1 ~35B S ~Su -1.0425 0.91 0 oa
2.19078 1.5160 -0.5693 1.933 O.OI n_o2
Yy = 0.1462 so 2.1470} ].8147 -1.1499 8.0;26 -2.a I3 0.01 0.03
ss 2.05513 z.03s3 -0.93]6 3.!026 -0.+34 G 0.01 0.04
2.27973 1.49+] -0.4aes La1s u.90] n.o^_
.rb ~ ].0oa 60 2.22350 t .577 -0.8320 4.5882 -1.233 o.OI 0.03
2.17+}6 2.0+46 -9si?_ 4.049: -0.7314 O.OI 0.03
' TLe deviation percent is calculated by ~ 100(k, a-=~rJ/<<~t I
1.25
2.20
~ 2.I5 c
0 U V
V Y
Y_ 2.~0 Q
zos
X40
tl0
90
A,
O,r O~~ Ad
Xt-0.4996
25 50 75 Temperature, 'C
Temperature dependence of dielec-
tricconstantofcydohexane-benzene
mixture of .Ye-0.4996
2.4
2.3
Z.2
2.~
C 0
C O U
V Y
Y_
z.a
FIR. 4
140 MPa ~ li0 p 100
Q 60 ~ 40 p 20 ~ O.I01
50'C
Fig. 5
0.00 0.50
'.Sole fraction of Benzene
Dependence of dielectric constant
hexane-benzene mixtures on mole
of benzene at SO'C
1.00
of cyclo-
(raction
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric Constant and Density of Cyclohezane-Benzene Mixtures 77
temperature and its slope is linear over the whole temperature range in this work like other
liquids[+-ts). 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 tempera-
ture 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°C and 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 compres-
sibility. 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
0.85
oso
e m
a
r .a
o"
Xc-0.4997
p 2>'C Q 50 ~ 13
Fig. 6 Pressure dependence of density of cydo6eaane•
benzene miature of Xe-0.4997
0.75 o so loo
Pressure/MPa
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. Neumann and G. Rinck, Z. Pkyr. CGern. (Frankfurt), 44, 104 (1965)
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
78 H. Kasbiwagi, T. Fukunaga, Y. Taoaka, H. Kubota and T. Makita
Ta61e 3 Density of Cyrlobexane-Benzene Miatures
(.Yp :mole Traction o! benzene, P: Dressure in MPe, p :density in ]0'kg/m'J
Temp.
'C
"y= 0.0000
7. P
ab'
P
03904
P
xb.
Y
0.4997
P
ab.
P
O.i497
P
Xb=
I'
1.0000
P
0.10 0.773 TB8.87 O.iTD•1
13.86 0.784821.10 0.:9012 7.93 0.794739.]0 O.i999
0.10G. eo
13.8721.2129.093a 2341. BT{9.3056.03r,2.8170.0977.13841691.1798.28
101.12
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
o.l D6.69
17.1221.5028.373 i. i941.9648.97s6.ot62.62]0.4657.1967.3{61.5568.41
1[5.42
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
0.87560.6]89
0.10fi.96
14.1121.1928.0733.1041.]049.9465.89s33a70:5177.318?1691.3598.39
1A5.6a
0.84063
0.6070
o.asz7
0.8381
0.8630
0.86]]
0.8]21
0.8769
0.6607
o.eflso
o,8A89
0.8925
0.896E
0.9000
0.8036
os671
0.10
7.99
13.93
21,06
27.89
39.01
42.11
48,98
ss.es
52.94
70.01
0,87380
0,8802
0.8852
0.890]
0,8950
0,8997
0,9042
0.9086
o,elzs
Dslss
0.9203
50
010 0.:49 Bi- 0
.7573
1+.21 o.7asn21,111 0.769.1
3].96 0.7x8
35.15 O.i600
i ^_.O1 0.785149.}3 O.T899
6sSi o.]s42
63.16 0.]983
50.32 0.8021
i 7.15 O.R0628?.03 U.8100
0.10
5,32
14.13
21,16
3 7.99
30.1802.17
48.66
ss.o6
63.07
70.2]
i 7.93
64,20
91.26
98.26
105.13
0.70711
D.774G
0,7808
0.7889
0.7922
0.79 i8
0.8029O.BOiO
0.8115
0.8158
0.8199
0.0271
8.82]]
0.0313
0.8947
0.8281
0.10732
14.0021,062].9935.1942.2849.2556.2003.2570,337e.zs84.3391.1898.31
]07.28
0.788400.79630.80200.80860.81430.81960.8'_480.82980.83410.83850.84270.84720.86060.85410.85790.8615
0.10
7.Ofi
1+.2521.29
28.06
95.13
42.26
?8.92
95.62
62.91
i 0,51
77.30
8;.60
91,95
98.07
107.15
0.81476
0.8222
0.8209
0.83{90.8{03
0.80 5T
0.85090.6555
x.8800
0.8648
0.8883
0.8733
0.8774
0.8811
0.884fl
o.eeae
0.10
6.94
14.0720.75
27.83
35.02
4236as.os
56.03
63.05
70.23
77.16
84.11
9311
98.60
105.12
0.846890.8538a.fisol0.88570,87130,87680.88170.88640.8.9080'.89510.89950.90340.90730.81110.91490.9186
TS
0.10 0.534845.13 0.]337
19.98 O.i40021.01 0.77 7825.98 0.464096.30 0.759!?3.99 0.7609?9.17 O.7i0556.11 0.775362.92 O.i598sss5 o.7a45i 7,91 0,799185.04 0.7930sl.ai 0.797099.17 0.8007
]05.33 D.eu9a
0.307.09
3+.3820.7927.8737,0242,0899,1956.0363.05sssi7sse89.3291.0697.99
109.83
0.'41890.75040.]6020.70480.77120,5772O,T8280,78800.79270.7975o.ema0.00630.81070.81120.01700.6214
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
0.462610.]722o3RDo0.70080,]9300.79960.60630.81060.81600,82080.82540.82990,83410,83820.89210.8{6]
0,10s,99
13sa20,8028,0435.0241.87?9.2365.]862.917013770886,9293,1696,09
105.10
0.78814
0.]908
0.8043
0.8111
0.81700.8220
0.8290
0.8399
0.8401
0.8491
0.8300
0.8945
0.8988
0.8629
0.8070
0.8712
0.10
6,86
13,98
21,09
28,20
33.25
4221
49.]3
56.19
63.03
70.35
77.50
81.41
9 L 61
88.47
ms.13
0.819380.82]50.83490.84170.8401D.fisao0.85950.86620.8897O.BT44O. BT920.38380.8878O.BBl90.89590.099!
known that the coefficient C is independent of temperature for many organic liquidsl~. In the pre-
sent analysis, the coefficienu, Band C, are first determined for each composition and temperature
by the least squares method. For each composition C is found to vary scarcely with temperature.
Therefore, on the assumption that C is a coestant independent of temperature over the whole ex-
perimental range, B and C are rede[ermined and listed in Table 4. The Tait equation represents the
present results as well as or slightly worse than the polynomial expression. As mentioned above,
however, the Tait equation can be applied to calculate the isothermal compressibility and is a simple
closed equation of state with only two parameters. So the Tait equation is preferable to the poly-
IB) R. E. Gibson and 7• F. Rincaid, J. Am. Chem. Sa., 60, 51l (1938)
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 measure-
ment 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 con-
cluded 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 4 Coefficients of the Tait Equation (8) for Cyclohexane-Senzese Mixtures
Mole fraction Sam P. Pa B C Ave Dev. Maz.DeT.
e} benzene •C 103 kg/m3 MPa x A
2s 0.]]3]0 17.9 0.0] o.m
X6 • O.D00 6a O.M984 61.5 0.1988 0.01 0.05
r 0.12484 49.3 0.03 O.Ofi
25 0.79154 74.9 0.0] 0.09
xb = 0.2509 SO O. T6Ttt fi 1.1 0.1947 0.01 0.09
T6 094189 98.9 0.0] 0.03
25 0.31352 T 6.T 0.02 0.04
Xb = 0.4997 so o.T66as sas o.ls]s o.oz D.os
TS 0.16267 48.0 0.03 0.1]
25 0.84063 86.2 0.02 0.05
Xb = 0 .]997 50 0.91476 702 0.200] 0.02 0.06
T8 0.78819 56.8 0.02 0.06
zs 0.67360 88:5 0.01 0.02
Xh • 1.000 60 0.84889 T2.T 0.2000 0.01 0.06
]s 0.91938 809 0.0] 0.04
E m
0
C b 0
0.90
0.95
0.80
0.7i
p 100 MPa [] 80 O 60 • 40 O 20 ~ O.lOI ~
50'C
D.00 O,iO
Jlole fraction of Benzene
L00
Fig. 7 Dependence of density of cydohxane-
benzene mixtures as mole fraction of
benzene at 50'C
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
80 H. Kashiwagi, T, Fukunaga, S'. Tanaka, H, Kubola and T. Makita
and 100 MPa. It seems that this inconsistency would came partly from the inadequacy of ex-
Crapolating their data to 75°C.
There are a few available papent9-'-~ on [he density for pure cyclohexane under high pressure.
The values of Kerimov et x1.211 are only ones that can be compared with the present results at 50`C
under pressures up to 10 MPa. Most of their data are found to be higher than those of this work.
Holder et al.iz 231 carried out the measurement for tytlohexane-benzene mixtures under pressures up
to 10 MPa. Their data agree well with the present results within the experimental ersor.
Since the present results can not be sufficiently compared with the literature values, it is at-
tempted to represent the data by the Hudleston equation241 which is often used to verify the relia-
bility of the PVT data of liquids. The equation is found to represent [he data very well except the
low pressure region below 20 MPa, where it would be sensitive to the uncertainty in the measure-
ments. The reproducibility of the Hudleston equation is also found to be better than that of the
Tait equation. It is, however, not easy to solve the Hudleston equation for the density at a given
pressure.
Discussion
The compositions of the mixtures prepared for density measurements slightly differ from those
for dielectric constant measurements. In order to correlate the dielectric constant with the density ,
the density of mixtures of the same compositions used in the dielectric constant measurements is
calculated using the Tait equation.
IC was found in our previous work7l that a simple relation exists between the dielectric constant
and the density of a fluid. In Fig. 8, a part of the , dielectric constant obtained is plotted against the
density in the limited range. 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 re-
duced to the effect of the density only. In each composition, the dielectric constant is found to he
represented by a linear function of density within the average deviation of 0.06%.
.4 few equations have been proposed to express the pressure dependence of the dielectric wn-
stant of liquids. Representative one of them is the Owen-Brinkley equationis•7b1, which was derived
from the Tait equation and the electrostatic theory.
19) 20) 21) 22) 23) 24) 23) 26)
=A to D+P e 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)
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
Dielectric Constant and Density of Cyclohexaae-Beazeae Mixtures 81
0
V
V
2.20
2.15
z.la
z.os
p
X6=1,0000 ° o ~ 0
p 0 p
m ~o~
op e8 X6=0.7462 Q g
9fl
0
p ® $ m p8
p
°p
a p°~ p X6=0.2500
Xb=0,4996 0 ~ ° ®
~pp88 0 ° ~ p4 0 ° ~ ~°° xb=o,oooo p
o p
° °
'
D
o_ 0
e
m
25'C
50
75
0.75 0.80 0.84
Density/1Wkg/mt
Fig. a Density dependence of dielectric con•
stant of cyclohexane-benzene mixtures
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 coefficient D 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. Although there 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 following assumptions:
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 coefficients obtained 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 satis-factorily, as described 6y Hartmann et al.~> and Srinivasan et al.~> Nith We assumption (2), it is
found that Eq. (9) can also reproduce the data well. On the other hand, Eq. (9) with the assumption
(4) expresses the data worst because of the rigorous restriction. The ability with the assumption (3)
27) E. Huckel and E. Ganssauge, Z. Phys, Chem. (Frankfurt), 12, 110 (1957) 28) H. Hartmann, A. Neumann and G. Rinck., ihid., 44, Z18 (1965)
29) M. Nakahara, Rev. Phys. Chem. Japan, 44, 57 (1974) 30) R. R. Srinivasan and R. L. Ray, J. Chem. Phys.,.60, 3645 (1974)
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
81 H. Kasbiwagi, T. Fukunaga, ]'. Tanaka, H.Kubota and T. bfakita
Table 5 Coefficients of the Owen•Brinkley Equation (9) for Cyclohexane- benzene 1fiatures
mole fncliov Temp. Ae.umptiov n c A1x.I>QY. ]IV x.Dev.
of Lenzene •C11118 X
25 2.0 ] 50 ms.e D.1]Da D.m 0.03
50 U1 ]sr: ]].k D.1ds5 0.01 0.05]5 ].93 i0 65.1 0.1539 0.01 0.03
25 92.9 0.0] 0.0250 121 7G.u D.3 S17 0.02 0.0;75 6A.4 0.01 0.03
X • 0.000h
25 ]7.9 0.1901 0.01 0.03
50 131 6LG 0.128] 0.03 O.OG
15 49.] 0.1311 O.OB 0.13
RS i 1.9 0.03 0.05SD f4] sls o.l_^;s O.Ok o.os]s 49.3 D.oe D.la
zs z.31 as 87.3 0.1x]5 0.01 0.01sn (]~ 2,o7za 81.0 0.1591 0.01 O. D3
TS 2.D317 ]0.6 0.163] 0.02 D.oa
zs 88.1 0.01 0.0250 121 81.4 0.160] 0.01 0.0975 68.1 o.az D.os
Xp = 0.499fi
2"a ]6.] 0.1334 D.az D.D4
Ss (31 sz.c 0.1353 0.08 0.15
75 48.9 0.1316 D.tS 0 '3
25 76.7 0.02 0.05
50 (•IJ 62.6 0.3330 0.11 0.2G
75 48.9 O.lfi 0.28
25 2.2 ik0 153.8 0.2196 0.01 0.02sD LL1 z.zz49 sls D.1]4s D.D2 o.oe7s z.17k4 i 9.5 0.17zfi 0.02 O.Ok
25 11].9 0.02 0.0550 121 9T.G 0.1145 0.02 0.0]]5 BD.B o.D2 o.os
xb- l.ooo
25 68.5 0.139a 0.04 0.0960 1]1 ]2.1 o.14ze 0.09 O.1k75 59.9 O.1k32 0.14 0.22
25
50 (kl88.5]P.] o.14ze
O.OA
D.De0.190.14
]5 58.9 0.13 0.2fi
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 combining the Tait equation (g) and the Owen-Brinkley equation (9) with assumption (3), a
simple relation is deduced as follows:
that is, a linear relationship between the reciprocals of [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 and Density of Cyclohexane-Bcnzene Mixtures :iE
the simple a vs. p linear relations as shown in Fig. 8. This fact implies that D is not identical with
B for the present miatures.
The Clausius-iliossotti equation is theoretically derived for nonpolar liquids in an electrostatic
field as follows:
Psf=e+2 p = 3 r,Ncz (11) where Pat is the molar polarization, M the molecular weight, N the Avogadro's number and a the
molecular polsrizability. According to the theory, the temperature and pressure dependence of the
molar polarization is very small, and an additive law
t
is held for a mixture of nonpolar liquids as nn ideal solution. Since cyclohexane and benzene are
nonpolar liquids, it is expected that the present mixtures exhibit such a behavior. 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 polari-
zation 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. IC is 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 ~.
z ~.5
zzo
26.5
D
Q
,.rm,,,,, Xb=0.0000 wee au°veee
°°rrre X6=0.2500 Y qe~
°.a:,
IS'C _ ~ X6=0.7462 epeepe.
50 °°eama
75 Xb=1.0000 ~'P°bpga °p~r .
.75 0.80 0.85
Density/1Wkg/ms
0.90
Fig. 9 Density dependence of molar
polarization of cydoheaaae• benzene mixtures
31) F. I. hfopsik, J. Rer. Nal. Bur. Sand., 71A, 287 (1967) 32) F. I. Mopsil•, J, Chem. Phys., 50, 2559 (1969)
The Review of Physical Chemistry of Japan Vol. 49 No. 2 (1979)
CLI
27.6
H. Kashiwagi, T. Fukunaga, ]'. Tanata, H Kubota and T.
O E
0 e
e .q
N .q
O a
A O s
27.2
26.8
26.4
0
0
e
O.I01 DfPa
10
40
60
80
100
5 0'C
Fig. 10
Makita
Dependence of molar polarization
of cydohesane-benzene mixtures
on mole iraction of benzene at 50'C
0.00 0.50 1.00
31o1e Fraction Benzen
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 mole-
cular 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
top related