Title Dielectric constant and density of cyclohexane-benzene … · 2012. 7. 12. · Its principle...

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)


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)


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


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)


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


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


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


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)


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)


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


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)


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)


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


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)


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

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