NOTES
374
Vol. 62
the bulb was taken off the high vacuum apparatus and smashed. Its contents were analyzed for unreacted decaborane by extraction with ethyl acetate, and then ultraviolet spectrophotometric analysis gf the ethyl acetate solution, using the wave length, 2650 A. Since it was difficult to separate the non-volatile boron hydride solids from bits of glass, the compositions df these solids were calculated from the decaborane and hydrogen data.
175
200 225 250 Temp., 'C. Fig. 1.-Decomposition of decaborane 175-250': comparison of hydrogen evolutions adter one hour.
of decaborane,l Stock reported that the latter was not appreciably decomposed after long heating at 200' but that it did decompose extensively, to hydrogen and non-volatile solids of approximate composition BHo., after long heating at 250'. We were therefore surprised to find, during experiments on the preparation of non-volatile boron hydride solids, that decaborane is far less thermally stable than was implied by Stock's observations. This led to the present study, in which decaborane samples were decomposed in evacuated glass bulbs over a wide temperature range, taking quantitative data on the disappearance of decaborane and the formation of products. Experimental Puritication of Decaborane.-Since small amounts of impurities might possibly affect the rates of decaborane pyrolysis, the latter (obtained from the American Potash Corporation) was very carefully purified. It was recrystallized from methylene chloride, followed by two successive vacuum sublimations. The purified decaborane melted sharply at 99.5', Mass spectrometric analysis indicated the absence of even traces of volatile impurities. Infrared analysis failed to detect impurities. An ultimate method of elemental analysis%gave a value of 11.53% hydrogen compared to a theoretical value of 11.54%. Pyrolyses.-The decaborane samples, in Pyrex bulbs fitted with break seals, were sealed onto a high vacuum apparatus and thoroughly evacuated. They were subsequently sealed and placed in a thermostated oven kept within 10.2'. Zero time for the pyrolysis was after a short period to allow the oven to rereach the reaction temperature after inserting the reactor, usually about ten minutes. Upon removal from the oven the reactions were quenched by immersal of the reactors in cold water. Analyses.-The hydrogen evolved was determined by resealing the bulb to a high vacuum apparatus, freezing the bulb with liquid nitrogen, and transferring the hydrogen, with a Toepler pump, to a calibrated volume whose pressure could be measured. After removal of the evolved hydrogen, the liquid nitrogen-bath was removed and the condensable contents of the bulb were transferred to another bulb for mass spectrometric analysis. I n some runs, the entire reaction contents were examined mass spectrometrically without prior removal of the hydrogen. After removal of the hydrogen and condensable material, ( 1 ) A. Stook and E.
(2) E. L. Simona, 36, 635 (1953).
Pohland, Be?., 62, 90 (1929).
E.W. Balis and H. A. Liebhafsky, Anal. Chem.,
Results The results are summarized in Table I. They show that decaborane is far more susceptible to thermal decomposition than is implied by the few semi-quantitative observations made previously.l Most of the present pyrolyses were carried out under conditions chosen so that the entire sample was in the gas phase within minutes after exposure t o the reaction temperature. These resulted in the formation of amorphous polymers evenly coated on the walls of the reactors. In one case conditions were chosen for a liquid phase reaction in which an appreciable hydrogen atmosphere would form (5.9 atm. after 15 hours). This reaction was faster than the corresponding gas phase reaction and resulted in a glassy polymer, formed in a lump where the decaborane was introduced. TABLE I Time, hr.
Moles H; evolved per mole Temp., decaborane OC. a t start
Decomposition,
%
Empirical formula of polymer
175 o 0 No polymer formed 200 0.0625 3.13b . . ,,.... . ..... 208 .lo6 5.30b . . . . , , . . . . . .... 1" 217 .432 21 .6b .............. .901 45.4 (BHl.w)z 1" 225 3.10 100 (BH.78)Z la 250 0.687 30.7 (BH.I)Z 8" 200 1.65 200 66.1 (BH.so)z 19" 1.826 89.6 (BH.es)z 200 15" 1.000 gram of B10HI4in 1 liter bulbs; gas phase reactions. 2Hz. c0.125 gram Based on B10H14 -+ lO/?(BH), BlOHl4 in 12.5-cc. bulb; a liquid phase reaction. 1"
.
la 1'
+
In every pyrolysis, hydrogen and non-volatile boron hydrides were the principal products. However trace quantities of pentaborane-9 were also products, even in the pyrolysis at 225'. The latter was the only other product found by mass spectrometric analysis. Acknowledgment.-The authors wish to acknowledge the helpful advice of Dr. Sol Skolnik. Dr. George Wilmot performed the infrared analyses. The mass spectrometric analyses were performed by Mrs. Mary Joslyn of the National Bureau of Standards under the direction of Dr. Fred Mohler. EQUILIBRIUM DISTRIBUTION OF MASS IN CENTRIFUGAL FIELDS BY MARSHALL FIXMAN Department
oj
Chemistry, Narvard University, Cambridge, Massuchusetts Received September 67, 1967
The equations governing the distribution of mass* may be given a particularly simple and (1)
R.J. Goldberg, THISJOURNAL,57, 194 (1953).
March, 1958
NOTES
rigorous form by a suitable selection of variables. We hope also t o illuminate the significance of the buoyant force on a macromolecule in solution. The equilibrium distribution of n components in an external field of acceleration g is determined by v p i = g, i = 1, 2, ..., n, where p i is the chemical potential (in units of energy/mass). Let the concentrations (in mass/volume), of the n components be pi. Then
moved explicitly from eq. 5 by setting Z(l &flk)Pk = 0, where the sum goes over solvent components. Thus Q = PJQ. (6) where ps is the total density of solvent components, and vS is the total volume fraction of solvent components. The equation Q = l / f l nfor the single solvent case forms an example of eq. 6.
375
n VPi =
(1)
(aPi)laPk)l*g
k=l
where we suppress a subscript indicating constant temperature. I n the derivative all p except p k are held constant. We introduce the partial specific volumes fli by means of the equation Dh(bPi/aPUk)p
(2)
= KPi
k=l
where is the compressibility. Equation 2 is derived readily from the Gibbs-Duhem equation and fli = K(bP/dpi)p, where P is the pressure. We multiply eq. 2 by an arbitrary constant Q and subtract the result from eq. 1
v
In
Pi
(1
=g
- & ~ (ad
+
~ i / d ~ ) p QK
[kIl
1
(3)
We will select a convenient value of Q later. Now we use an expression from Kirkwood and Buff R T ( 3 In
pi/&m)fi =
M k h f NpkGik
(4)
where M k is the molecular weight of component k, R is the gas constant, N is Avogadro’s number, 6 is the Kronecker 6, and Giro is a cluster integral
.f [gik(R) - 11 dR
THE SOLUBILITY OF XENON IN SOME HYDROCARBONS1 BY H. LAWRENCE CLEVER^ Contribution from lhe Department of Chemislry, Duke Universily, Durham, N . C. Received October 1. 1967
The solubility of xenon has been determined a t a total pressure of one atmosphere and temperatures of about 16, 25, 34.5 and 43” in benzene, cyclohexane, n-hexane, isooctane and n-dodecane. Experimental The solubility apparatus, procedure and solvents were those used and described before.8 The pure xenon was furnished by the Linde Air Products Co., Tonawanda, N. Y.
Results and Discussion The solubilities of xenon in the hydrocarbons corrected to one atmosphere of xenon by Henry’s law are given in Table I expressed as the Ostwald coefficient and mole fraction. Included are least square constants for the equation log solubility =
T
+b
in both solubility units. The slope intercept equations reproduce the experimental solubilities with where g i k is a radial distribution function. Equation 4 is valid for non-electrolytes, or for electro- an average deviation of 2.8% in benzene, 2.270 in lytes if applied to individual ion species. If i and k cyclohexane, 1.1% in n-hexane, 1.0% in isooctane refer t o macromolecules, G i k reduces to an osmotic and 0.7% in n-dodecane. Much of the departure second virial coefficient Gibo in the limit of low from linearity is in the low temperature determinamacromolecule concentration. Thus ?T = RT. tion where temperature control was difficult. [Z(pi/kfi)- 2 Z ( p i p k / 2 M i M k ) G 0 i k . . .], where Entropy of Solution.-Entropies for the transfer the sums go over macromolecular components i, k , of one mole of xenon from the gas phase t o the hypothetical unit mole fraction (Fig. l a , curve 1) ... are slightly more negative than values found beI n terms of the G i k , eq. 3 becomes fore for the other rare gases in the same soln v e n t ~ . However, ~ they are not as negative as the RTvln pi = g (1 - QUi)Mi N entropy calculated from either compressing and k=l condensing the xenon (Fig. la, curve 2 ) or the cor(1 - QZik)PkGik RTQK] (5) entropy of condensation of the solvent I n the subsequent discussion we take i to be a responding (Fig. la, curve 3). macromolecule. In the particular case where there Solubility and Surface. Tension.-The is only one solvent component, say n, all macro- Uhlig plot4 of theSolvent logarithm of the Ostwald coefmolecule-solvent interactions may be made to ficient against the solvent surface tension (Fig. 1b) vanish identically from eq. 5 by taking Q = l/fln. shows more scattering of the points than the same If several solvent components are present, macrofor the other rare gases in the same solvent^.^ molecule-solvent interactions cannot be rigorously plot Hildebrand critical temeliminated from eq. 5. If, however, the solvent perature 16.7”, Equation.-Xenon, is a gas with physically conmolecules are much smaller than the macro- stants from which t o evaluate solubilityreal parammolecules, and do not interact with macromolecules (1) Presented before the Division of Physical and Inorganic Chemisstrongly or specifically, we may assume that G i k 127th National Meeting of the American Chemical Society, Cinis independent of which solvent component k is try, cinnati, Ohio, April, 1955. chosen. (Under these Circumstances, G i k will (2) Department of Chemistry, Emory University, Emory Univerequal the “volumie” of macromolecule i). Then sity, Georgia. (3) H. L. Clever, R. Battino, J. H. Saylor and P. M . Gross, THIB macromolecule-solvent interactions may be re- JOURNAL, 61, 1078 (1957). Gik =
+
[
+
+
(2) J. G. Kirkwood and F. Buff, J . Chem. Phys., 19,774 (1951).
(4) H.H. Uhlig, ibid., 41, 1215 (1937).
