914
HENRYE. WIRTFI AND EMIELD. PALMER
Vol. 60
DIELECTRIC CONSTANT AND VAPOR PRESSURE OF PENTABORANE' BY HENRY E. WIRTHAND EMIELD. PALMER Department of Chemistry, Syracuse University, Syracuse, N. Y. Received December 7 , 1816
The melting point of pentaborane is 226.41 f 0.02"K. Li uid pentaborane has a high dielectric constant ranging from 21 at room temperature to 53.1 a t the melting point. Pent&orane is a highly polar substance, with an apparent dipole moment varying between 3.37 debyes at room temperature to 4.54 debyes a t the melting point. I n the temperature range 130-140°K. there is a sluggish solid-solid transition which may be accompanied by the onset of free rotation in the solid. The vapor pressure of pentaborane is given by the equation logto pmmi= 9.96491 (1951.14)jT 0.0036884T in the temperature range 226-298°K.
-
Introduction Dulmage and Lipscomb2 estimated the dipole moment of pentaborane to be 0.6 debye unit. Later calculations by Eberhardt, Crawford and Lipscomb3 gave 5.23 debyes as the maximum value, and 1.72.0 debyes as the more probable value of the dipole moment. An experimental value of 2.13 debyes in the gas phase was reported by Hrostowski, Myers and Pimenta14 from measurements in the microwave region. These results indicated that liquid pentaborane would have a high dielectric constant. The apparatus previously developed6 was therefore used to investigate this substance. Experimental Apparatus.-The apparatus described previously6 was used without modification, except that in some cases it was necessary to place a standard capacitance in series with the experimental cell in order to bring the measured capacitance within the range of the bridge. This reduced the precision of the dielectric constant measurements to &2%. Purification of Pentaborme.-Pentaborane waa frozen in a trap cooled with Dry Ice-acetone mixture and was maintained under vacuum for 18 hours to remove volatile impurities. A middle fraction of 6.5 ml. from a total sample of 15 ml. was used for the measurements reported.
Results Melting Point of Pentaborane.-The melting point was found to be 226.41 0.02"K., and the purity as determined from fraction melted us. temperature curves was 99.9+ mole per cent. Johnston, Kerr, Clarke and Hallett6 found the melting point to be 226.34"K., and Rossjni' quotes a value of 226.3"K. Dielectric Constant of Liquid Pentaborane.The observed values of the dielectric constant for pentaborane are given in Table I. The dielectric constant at room temperature is 21 (compared to 25 for ethyl alcohol, 34 for methyl alcohol, and 81 for water) and increases rapidly with decreasing temperature to a maximum value of 53.1 a t the melting point. The values reported are the averages of observations made at 200, 100 and 50 kc. The individual values did not differ by more
*
(1) Presented in part a t the New York meeting of the American Chemical Society, September, 1954. (2) W. J. Dulmage and W. N. Lipscomb, J. A m . Chem. Soc., 73, 3539 (1951). (3) W. H. Eberhardt, B. Crawford, Jr., and W. N. Lipscomb, J . Chem. Phvt., as, 989 (1954). (4) H. J. Hrostowski, R. J. Myers and G. C. Pimental, ibid., 20, 518 (1952). (5) H . E. Wirth and E. D.Palmer, THIBJOURNAL, 60,911 (1956). (6) H. L. Johnston, E. C. Kerr, J. T. Clarke and N. C. Hallett. ibid., 60, in press (1956). (An advance copy of this publication was supplied tlie authors through the courtesy of Prof. H. L. ,Johnston). (7) F. D. Rossini, Natl. Bureau of Standards Cirriilar 500, p. 7 2 1 .
-
than 2%. The specific resistance, as calculated from the observed dissipation factor at 50 kc., varied from 2 X 106 ohm em. at 297°K. to 4 X lo6 ohm em. at 226.4"K. The Onsager8 equation
(where B is the dielectric constant, n is the "internal refractive index," N is the number of molecules per cc., po is the permanent electric moment, k is BoltaTABLE I DIELECTRIC CONSTANT OF LIQUIDPENTABORANE Temp.,
e . 1
OK.
Series
(obsd.)
Density,n g./oc.
P'
e f 2 d
226.4 226.4 230.0 237.0 240.0 247.0 254.0 261.0 268.0 273.0 278.0 280.6 283.0 288.0 288.3 292.0 292.3 296.0 297.1 298.0
I I1 I1 I
53.1 53.1 50.0 45.5 42.6 39.2 35.7 32.6 29.7 28.0 26.4 25.1 24.9 23.6 22.9 22.6 22.0 21.6 20.9 21.1
0.682 .682 .678 .673 ,670 .665 ,659 ,653 .648 .644 .639 .637 .635 .631 .631 .628 .628 .625 .624 .623
9.33 9.33 8.85 8.13 7.61 7.11 6.55 6.06 5.57 5.30 5.04 4.82 4.80 4.59 4.46 4.42 4.31 4.25 4.13 4.17
1.386 1.386 1.390 1.393 1.393 1.394 1.397 1.399 1.396 1.398 1.400 1.396 1.309 1.399 1.394 1.397 1.392 1.397 1.392 1.397
e
I1 I I I I I I I1 I I I1 I I1 I I1 I
mann's constant, and T is the absolute temperature) permits the calculation of the dipole moment from measurements made on a liquid: Bottcher'o and Phadke, Gokhale, Phalnikar and Bhidell have shown that application of this equation t o unassociated liquids gives results in excellent agreement with measurements made with dilute solutions or ) used gases. The ordinary refractive index ( n ~was by these authors. With associated liquids (water and alcohols) the values obtained were uniformly higher than obtained by other methods. ( 8 ) L. Onsager, J. Ana. Chem. Soc., 58, 1486 (1936). (9) Calculated from the equation
d = 0.8674
- 0.00082T
(1)
given by 8. H. Smitli, J r . , and R. R. Miller, ibid., 72, 1452 (1950). (10) C. J. F. Bbttcher, Physica, 6 , 59 (1939). (11) 9. R. Pliadke, S. D. Gokhale, N. L. Phalnikar and B. V. Rhide. J . Indian Chem. Soc., a 2 , 235 (1946).
L
DIELECTRIC CONSTANT AND VAPORPRESSURE OF PENTABORANE
July, 1956
The apparent dipole moment of pentaborane, calculated from the measured dielectric constant and index of refraction a t 24" ( n =~ 1.4445) is 3.41 debye units. W.vman12 showed that if the polarization per gram, defined by the relation
.
p' =
+ 1)/8.5d
(E
(3)
is plotted against the reciprocal of the absolute temperature, ;1 straight line should be obtained. From the slope of this line the dipole moment may be obtained = 0.0127
I.(
.\iM
dP'
debyes
915
+
The Clausius-Mosotti function, ( e - l ) / ( e 2) (l/d), given in Table I is unexpectedly constant. The average value (1.395) gives a molecular polarization of 88.0 cc. for the liquid, as compared to a molar refraction of 26.9 cc. calculated from the index of refraction. Dielectric Constant of Solid Pentaborane, and the Solid Phases.-On freezing pentaborane the dielectric constant drops rapidly, and becomes approximately 3 a t 200°K. I n Fig. 2 the dielectric
(4)
where M is the molecular weight. The intercept on the ordinate axis is the sum of the atomic and electronic polarizations, which can also be obtained from the index of refraction. Values of p' are given in Table I and are plotted in Fig. 1 against the reciprocal of the absolute tem'
10
-
9-
2.5
8-
-Y
constant of solid pentaborane is given as a function of the frequency for several temperatures. Below 130°K. the dielectric constant is independent of frequency. The behavior in the temperature range 130140°K. is shown in Fig. 3. Curve I was obtained
1
4
I
3 2
" " 1
0.5 1 5 10 20 50 100 200 Frequency, kcycles. Fig, 2.-Dielectric constant of solid pentaborane a t various temperatures as a function of the frequency.
6 -
5
I
0.1
7 -
k
13OoK, -
I
/
0
/
2.5 u;
1
2.4 I
I
I
I
0.003 0.004 l/T. Fig. 1.-Polarization per gram of liquid pentaborane us. reciprocal of the absolute temperature.
0.001
0.002
perature. It is evident that p' is not a linear function of 1/T, and that a considerable curvature is required if the intersection on the ordinate axis is to equal the polarization as obtained from the index of refraction. The slope of the line A, drawn from p' corresponding to the highest temperature (298°K.) t o the intercept, gives a calculated value of 3.37 debyes for the dipole moment, which agrees, as it must, with the value calculated by use of the Onsager equation. The slope of line B, drawn through p' corresponding to the lowest temperature (226.4"K.), gives an apparent dipole moment of 4.54 debyes. Line C is drawn with a slope corresponding to the dipole moment of 2.13 debyes found in the gas phase. (12) J. Wgtnan, Jr., J . A m . Clwm. Soc., 68, 1482 (1936).
2.3 130
135 140 Temp., "K. Fig. 3.-Dielectric constant of solid pentaborane in the temperature range 130-140'K.
on slowly cooling the solid pentaborane. Dotted lines indicate that the sample was held a t constant temperature for the time shown on the graph. Curve I1 was obtained on warming the sample. At 137.0"K. there are indications of a slow change; a t 137.7"K. the change is much faster. Curve I11 was obtained on continuous heating- a t a rate of 3" per hour. Johnston, Kerr, Clarke and Hallette reported similar effects in the heat capacity of pentaborane in the temperature range 130-140". The cooling curve was normal down to 131°K. At this temperature, if the calorimeter was isolated, the temperature rose rapidly to 132", and reached 13234°K. aft8erI1 hours. The temperature could
HENRYE. WIRTHAND EMIEL D. PALMER
916
be then increased to 136.7" without evidence of any transition. At 136.7" a transition of the orderdisorder type occurred. This behavior is attributed to the onset of free rotation. Dulmage and Lip~comb'~ give the structure of the high temperature (140-226°K.) form of pentaborane as body centered tetragonal (CgdV- I4 mm.), a = 7.16 c = 5.38 A., with two molecules per unit cell and a calculated density of 0.761 g./cc. King and Russell14 of this Laboratory have found that below 130°K. the X-ray powder pattern agrees yith that of a simple tetragonal cell with a = 10.33 A., c = 10.11 A., having eight molecules per unit cell and a calculated density 'of 0.778 g./cc. They have observed that if one considers the high temperature form in its face centere$ tetragonal orientation (a = 10.13 8.)c = 5.38 A.) the c-axis of the low temperature form is slightly less than double that of the high temperature form, and the a-axis is slightly larger. This, they suggest, indicates that the transition may involve a decrease in rotation which imposes the observed change in the symmetry. From this it may be concluded that the observed behavior in the temperature range 130-140°K. can be explained on the basis of a sluggish first-order transition. In the low temperature form there is no free rotation, but in the high temperature form some free rotation is possible. The most convincing evidence for the onset of free rotation is the increase in dielectric constant on going from the low temperature form t o the high temperature form despite the density decrease which accompanies this transition. Since there is only a slight shift in molecular positions involved in the transition, it is possible that the heat of transition is small, and the heat effects observed by Johnston, Kerr, Clarke and Halletts are due primarily to the entropy increase associated with the onset of free rotation in the high temperature form. The dispersion in the dielectric constant of solid pentaborane above 140°K. is in agreement with the observations of Errera's who found that solids consisting of polar molecules show this anomalous dispersion. Wintschl6 determined the dielectric constant and angle of dielectric loss for ice in the temperature range -50 to -6". While the effects he found for the dielectric constant were much greater (i.e., at -6" and 1000 cycles the dielectric constant of ice is 90% of the liquid value), the general shape of his curves is the same as was found for pentaborane (Fig. 2). On the other hand, the loss angle is quite different in the two cases. Wintsch found an increase of loss angle with increasing frequency for ice at -6, - lOand 20")and a maximum around one kilocycle
w.,
-
(13) W.
J. Dulmage and W. N. Lipscomb, Acto
Cryst., 6, 260
(1052). (14) A. J. King and V. Russell, private communication. (15) J. Errera, J . p h y s . , [ 6 ] 5, 304 (1924). (16) H. Wintsch, HsEv. Phys. Acto., 8 , 126 (1932).
Vol. 60
at -40 and -50". In pentaborane a minimum in the dissipation factor (tangent of loss angle) at about one kilocycle was found at low temperatures; this minimum was displaced toward higher frequencies as the temperature was increased so that at temperatures just below the melting point the dissipation factor decreased with increasing frequency throughout the frequency range studied. An attempt was made to interpret the behavior of solid pentaborane by the method of Debyel7 in terms of a relaxation time ( T ) which would be much greater for a solid than for a liquid, but no value of T could be found which would represent the data at a single temperature, and its variation with temperature was not as great as would be expected. A key to an interpretation might be the observed abrupt changes in dissipation factor and dielectric constant observed in scanning the frequency spectrum. The dissipation factor varied by as much as a factor of two with small changes in frequency. These "blips" were observed a t all temperatures and at frequencies above fifteen kilocycles, but became increasingly evident as the melting point was approached. Since the frequency is much too low to affect molecules, the absorption might be due to large groups of molecules rotating under the influence of the applied field (domain structure). Vapor Pressure of Pentaborane.-The vapor pressure of pentaborane in the temperature range 226.4-298°K. is given in Table 11, and can be represented by the equation loglo p -
c
9.96491
1951 14 -- 0.0036884T T
(5)
The values are in excellent agreement with those reported by Johnston, Kerr, Clarke and Hallett.'j TABLEI1
VAPORPRESSURE OF LIQUID PENTABORANE Temp., 0 K.
Pobad
Obsd.
Pmm
3.26 226.41 (m.p.) 7.19 237.02 14.31 247.03 22.28 254.07 33.72 261.04 49.74 267.97 64.77 272.99 83.57 278.08 283.05, 106.39 287.98 134.10 288. 27b 135.77 292.00 160.68 292.16' 161.96 293.73 173.55 296.04 191.19 297.84 206.85 Calculated from equation 5. rate sample.
Ca1cd.a
3.25 7.22 14.30 22.37 33.70 49.58 64.67 83.71 106.57 134.11 135.90 160.66 161.80 173.34 191.51 206.72 b Check values
-
Poalnd
(mm.)
+o. 01 -0.03 $0.01 -0.09 $0.02 +O. 16 $0.10 -0. I6 -0.18 -0.01 -0.13 $0.02 +O. 16
+0.21 -0.32 +O. 13 on a sepa-
(17) P. Debye, "Polar Molecules," Dover Publications, New York, N. Y.,1045, p. 106.
*
