1968
CHARLES K. HERSH, GERALDM. PLATZ AND RAYMOND J. SWEHLA
Vol. 63
Estimated Amount of Branching.-Several branching indices calculated from them should be theories17-19 relate the ratio of the intrinsic viscosi- considered relative measures of the amount of ties of branched and linear polymers to the weight branching rather than representative of the true average number of branch points per molecule. weight average number of branch Points Per The theories are only approximate; however, in molecule. Table I1 lists long chain branching indices calto polymer systems* Long chain culated by the relations of Stockmayer and Fix(17) B. H. Zimm and W. H. Stockmayer, J . Chem. Phys., 17, 1301 man18 and Zimm and E(ilb.19 The ionic poly(1949). styrenes prepared to conversions above 74% con(18) W. H. Stockmayer and M. Fixman, Ann. N . Y . Acad. Sci., 67, tain of the order of two long chain branches per 334 (1953). molecule On this basis. (19) B. H. Zimm and R. W. Kilb, J . PoEymer Sci., 37, 19 (1959).
DIELECTRIC CONSTANT OF LIQUID OZONE AND LIQUID OZONE-OXYGEN MIXTURES1 BY CHARLES K. HERSH,GERALDM. PLATZ AND RAYMOND J. SWEHLA Chemistry and Chemical Engineering Research Division, Armour Research Foundation of Illinois Institute of Technology, Technology Center, Chicago 16, Illinois Received June 89,1969
The objective of this study was to investigate the dielectric constant of liquid ozone-oxygen mixtures as a physical property t h a t might be useful in the analysis of these mixtures. This study was based on some preliminary measurements t h a t showed the dielectric constants of liquid ozone and liquid oxygen a t 90°K. to be 4.75 and 1.46, respectively. The data presented include the dielectric constants of liquid ozone-oxygen mixtures containing 0 to 29.8 wt. % ozone a t 90°K. and of pure liquid ozone from 90 to 185°K.
Auuaratus and Procedure --
The dielectric constants of the liquids were determined by the conventional capacitance method. Since ozone and its solutions were the dielectrics being studied, only materials compatible with both liquid and gaseous ozone were used in the construction of the apparatus. The capacitance cell consisted of two concentric stainless steel cylinders sealed in a glass tube. Small Teflon spacers were used to maintain a 0.1-mm. gap between the cylinders. The diameter of the outer cylinder was about 2.0 cm., and the height 7.3 cm. The capacitance of this cell when empty (in oacuo) at 90’K. was 365 micromicrofarads (ppf.). Later the cell was modified so that the gap was about 3 mm., the height about 4.0 em. and the empty capacitance 110
4.
A General Radio impedance bridge, Model 650-P1,. was used to measure the capacitance (within 1%). Associated
with this impedance bridge was a 1-kilocycle (kc.) oscillatoramplifier and the bridge balance was obtained by minimizing the oscillator hum. The apparatus used to prepare the calibrating liquid ozone-oxygen mixtures was similar to the apparatus which has been used to determine various physical properties during the past several years in the Foundation laboratories, and is described in detail in the literature.* The only change was t o replace the magnetic susceptibility unit with the capacitor unit. From the appropriate capacitance measurements, the dielectric constant of liquid ox gen a t 90°K. was determined to be 1.46 & 0.01, whicg agrees with the reported value of 1.46.8 These measurements indicate that corrections for dimensional changes in the cell are negligible between 90 and 298°K. A similar technique was used to obtain the dielectric constant of pure 100% li uid ozone in the temperature range of 90 t o 185°K. %he major change was t o place the concentric cylinder capacitor in a steel pressure vessel. (1) Presented before the Division of Physical Chemistry at the 135th meeting of the American Chemical Society, Boston, Mass., 1959. (2) C. Brown, A. W. Berger and C. K. Hersh, J . Chem. Phys., 2 3 , 103 (1955). (3) “International Critical Tables,” Vol. VI, E. W. Washburn, editor, McGraw-Hill Book Co., New York, N. Y., 1929.
Results and Discussion Liquid Ozone-Oxygen Mixtures.-The dielectric constants of ozone-oxygen mixtures at 90°K. are given in Table I. The measurements were confined to t,he single phase region of 0 to 29.8 wt. % ’ ozone. The dielectric constant of pure liquid ozone is given in Table 11, which also includes the density of liquid ozone.4 The densities of the ozoneoxygen liquid mixtures were taken from reference 5. TABLEI DIELECTRIC CONSTANTOF
LIQUIDOZONE-OXYGENMIX-
TURES AT -Ozone Wt. %
in oxygenMole %
0 14.9 17.6 19.2 29.8 100.0
0 10.5 12.5 13.7 22.1 100.0
90°K. Dielectric constant
(4
1.46 f0 . 0 1 1.82 1.90 1.93 2.20 4 . 7 5 f0 . 0 2
Molar
polarization (PI), CQ.
(Pzo = 3.74) 26.352 26.296 25.642 23.774
The liquid mixture data were used to estimate the dipole moment of the ozone molecule. The treatment followed that of Danielss and LeF6v1-e’ on the infinite dilution technique and the interested (4) R . I. Brabets and J. M . McDonough, J. Chem. Phys., 27, 880 (1957). (5) C. K. Hersh, A. W. Berger and J, R. C. Brown, Physical Properties of Liquid Ozone-Oxygen Mixtures: Density, Viscosity and Surface Tension, “Ozone Chemistry and Technology,” Advances in Chemistry Series, No. 21, 1959, p . 22. (6) F. Daniels, J. H. Mathews and J. W. Williams, “Experimental Physiaal Chemistry,” 4th Ed., McGraw-Hill Book Co., Inc., New York, N . Y., 1949. (7) R. J. LeFBvre. “Dipole Moments,” 3rd Ed., Methuen and Co. Ltd., London, 1953.
NOTES
Nov., 1959 TABLE I1 DIELECTRIC CONSTANT A N D DENSITY OF 100% OZONEAS FUNCTION OF TEMPERATURE Dielectric constant
Temp., OK.
90 103 108 118 130 138 147 155 175 180 185 Reference 4 .
(8)
Density,~ g./cc.
4.75 f.0 . 0 2 4.33 4.15 3.85 3.64 3.46 3.33 3.20 2.91 2.84 2.78
1.571 1.533 1.517 1.486 1.449 1.425 1.397 1.372 1.310 1.295 1.279
A
1969
equation then was employed to obtain the dipole moment. The distortion polarization, Plo0,was estimated from the value of 7.6 cc. for the molar refraction calculated by Lewis and Smyth.* These two values then were used in eq. 2 p =
0.0127
E
reader is referred to these references for the derivation of the equations. After suitable assumptions have been made, the molar polarization can be calculated from PI
=
-
p fzPzQ -
fl
x
10-1
d(P10
- P1Do)TOK.
(2)
where p is the dipole moment. At 90°K. this dipole moment is 0.56 debye. The value for the dipole moment obtained from microwave spectroscopy data is 0.53 f 0.02 debye.g Lewis and Smyths give a value of 0.49 debye a t 80.8"K. Liquid Ozone.-The dielectric constant of 100% liquid ozone as a function of temperature is presented in Table I1 and may be represented by =
+ 0.9378
(3)
where e is the dielectric constant. The molar polarization of liquid ozone as a function of reciprocal temperature has been computed from these data and can be represented by
(1)
P =
+ 11.276
(4)
where P is the molar polarization, f is the mole fraction, subscript 1 indicates ozone (solute), subAcknowledgments.-The present work received script 2 indicates oxygen (solvent) and no sub- invaluable advice and assistance from K. Franson, script indicates the solution. As was expected, C. Brown, M. J. Klein and R. I . Brabets of the the molar polarization is a function of concentra- Armour Research Foundation. tion (compare Table I). By the method of least (8) G . L. Lewis and C. P. Smyth, J . A m . Chem. SOC.,6 1 , 3063 squares, the data of Table I were extrapolated to in- (1939). finite dilution to obtain a value of Plo = 28.94 cc. (9) R. Trambarulo, S. Ghosh, C. Burrus and W. Gordy, J . Chem. The Debye modification of the Clausius-Mossotti Phys., 21, 851 (1953).
NOTES THE FORMATION OF TETRACHLOROBORATE ION IN LIQUID SULFUR DIOXIDE SOLUTION'
rides strongly catalyzing the almost complete solvolysis of boron trichloride to thionyl chloride and boric oxide in a few days a t room temperature. I n experiments also designed to test for tetraBY D. E. BURGE, H. FREUND AND T. H. NORRIS chloroborate ion formation in sulfur dioxide solution, we have studied conductivities of solutions to Department of Chemistry, Oregon State College, CoTuallis, Oregon which boron trichloride and potassium chloride Received January $6,1969 mixtures been added in various proportions.6 The formation of salts containing the hitherto I n analogyhave to Gardner's observations we have found uncertain tetrachloroborate anion, BC14-, has been the initial low solubility7 of potassium chloride to indicated in recent reports. 2 , 8 Gardner4 adduced be greatly increased by boron trichloride. To a set the same complex in explanation of an observed liquid sulfur dioxide samples, each containing an great increase in the solubility of sodium chloride of initial excess, solubility-wise, of potassium in liquid sulfur dioxide on addition of boron tri- chloridelarge (50 mmoles and 0.1 mmole, respectively) chloride. However, in attempting further inves- successively larger amounts of boron trichloride tigation of this latter system, Burg and Birnbaum5 were added. The sealed tubes were kept a t 0" have reported lately an inability to obtain stable with occasional shaking, conductances being meassolutions, the presence of sodium or potassium chlo(1) Oregon State College, Research Paper No. 355, School of Sci. ence, Department of Chemistry. (2) M. F. Lappart, Proc. Chem. SOC.(London). 121 (1957). (3) E.L. Muetterties. J . Am. Chem. Soc.. 79, 6563 (1957). (4) D. M.Gardner, Ph.D. Thesis, University of Pennsylvania, 1955, p. 64. (5) A. B. Burg and E. R. Birnbaum, J . Inorg. NztcE. Chem., 7 , 146 (1958).
(6) A preliminary experiment showed the addition of boron trichloride to a sulfur dioxide solution of the soluble salt tetramethylammonium chloride to give only a small change in conductance. Such a result is inconclusive since, while conceivably implying the non-formation of complex, it might equally well simply indicate the molar conduotance of tetramethylammonium tetrachloroborate to be approximately the same as that of the chloride. (7) 0.013 g./100 g. solvent at 0". I . Lauder and E. Rossiter. Nature, 163,567 (1949).
