April, 1%iO
CONDENSATION COEFFICIENTS O F
H,
hiiD
Dz
ON
ALUMINA
433
POTESTIA4LEXERGY BARRIER FOR ROTATIOS AKD THE CONDENSATION COEFFICIENTS OF Hz AND Dz O K AT,Ui\TIXA BY GAS CHROMATOGRAPHY BY EARL31. MORT ENS EX^
AND
HENRYEYRING
Department of Chemistry, U n i v e r s z t y of Utah, Salt Lake Czty, Ctah Received September IO, 1969
From the retention times of ortho- and parahydrogen and deuterium on a chromatographic column the potential energy barrier hindering rotation and condensation coefficients were determined. The height of the barrier u a s found to he 460 cal./mole and the condensation coefficients, cy, were calculated to be CC~-H( = 1.0, (YO-H~ = 0.53, 0.55, and O[O-D~ = 0.97 on an alumina surface a t 77.4”K.
where f ’ ~ , ~ ( Xf’odxd d, f’~,~(xd, Srp,&G) are the rotational partition functions for the surface and vapor, and Ko’(X2) and K p ’ ( X 2 ) that part of the equilibrium constant containing the traiislational and vibrational degrees of freedom for the ortho and para species, respectively. In equatioii 2 we are not completely justified in separating the rotational motion from that of translation becaupe we know that the molar volume* for liquid parahydrogen is greater than for the ortho species indicating that the rotational motion of orthohydrogen in the liquid is more restricted which results in greater orientation and, hence, a tighter packing due to van der Waal forces. We might expect a similar situation to exist for the adsorbed hydrogen or deuterium and the alumina surface. Kow if the rotational and translational degrees of freedom t’O-Dz = 418 SeC. t’o-nz = 317 see. were seperable, then we would expect that Ko’(X?) t’,-n2 = 454 sec. ~ ’ , - I I ~= 259 sec. From the dimensions of their column and the flow would equal KP’(X?). Instead a better approxirate of the helium carrier gas, the average length mation would be to put of time t H e for the helium to pass through the (3) column is approximately three seconds. This is the same average time that the ortho- and para- In equation 3 the configuration integral for Ko‘(H,) hydrogen and deuterium spend in the vapor phase. which includes both the contributions of the poThe time, t , which the hydrogen and deuterium tential energy associated with translation and that spend on the surface is, therefore due to the coupling of the rotational and transla~o-D= ~ 415 sec. ~ o - H=~ 314 sec. tional motions should equal the configuration int,-H, = 256 SCC. t , - ~ ? = 451 sec. tegral of Kp’(D2). Likewise the configuration If we assume that the experiments were carried integrals of Kp’(H2)and Ko’(D2)should be equal. out on the linear portion of the isotherm, which is Upon combining equation 1 and 2 using equation 3 likely considering the small amounts of hydrogen or we obtain deuterium used, and if we assume that there is equilibrium between the vapor and the adsorbed molecules on the Purface, then the ratio of the conOn the alumina surface we &hall :mume that centratioiis of ortho and para species on the surface to the concentration iii the vapor phaPe is just there is some preferential direction of orielitation and that the potential energy V may be approxiproportional to t,’tHe. Hence mated by an equation of the form [O-x?(a)l ato-x? [P-x?(s)]- nfp-s*
In studying the evaporation and condensation from solids and liquids much attention has been given to determining the condensation coefficient2 which is the ratio of the number of molecules that strike the surface and stick to the total number which strike. From the retention times on a chromatographic column we are able to calculate condensation coefficients of H2 and Dz on alumina. Recently Moore and Ward3 have shown that ortho- and parahydrogen could be separated by means of chromatography at 77.4”K. using an alumina column. Similarly they also showed that ortho and paradeuterium could be separated. By taking measurements off their graph the retention times t‘ for the ortho- and parahydrogen and deuterium to pass through the column are
_-
[O-x’?(g)]
=
_tHe
’
.~
[P-xl(g)]
tHe
(1)
where a is the constant of proportionality and X represents either H or D. In addition we may write
(1) Supported by t h e Standard Oil Company of California through a predoctoral research felloiveliip. ( 2 ) 0. Knrrcke a n d I. S. Staneki. “Progress in klet,al Physics,” Vol. 6, Perg:inion Press Ltcl., London. 19.56, pp. 181-235: E. M , iMortenseii and Henry Eyrine, Tms J O ~ R X A L 64, , in press (1960). (3) W. R. LIoore a n d H. R. Ward. J. A m . Chem. Soc., 80, 2909
(1958).
v = ‘/*T’”(l- cos 23)
(5)
Wilson5 solved the wave equation for the linear rotator using equation 5 for the potential energy. SternGcalculated the energy levels of the hindered rotation for a few of the lowest levels in terms of the two parameters p and X defined by7
(4) R. B. Scott and f. G. Bricbvedde, J . Ciima. Phga., 5, 7 3 6 (1937). ( 5 ) A . H. Wilson. Proc. Rou. Soc. ( L o n d o n ) , A118, 62s (1‘32s). (6) T. E. Stern, ibzd., A130, 551 (1931). (7) We are using a definition of Vo which is twice as large as Stern’s.
W. G. WITTEMAN, A. L. GIORGIAND D. T. VIER
434
Vol. 64
where I is the moment of inertia and W is the energy of the state. In order for the left-hand side of equation 4 to agree with the ratio of experimental t’s on the right-hand side it was necessary to take Vu
=
460 cal./mole
The rotational energy levels W J , ~ then I were deS‘O.g(H2) termined using Stern’s paper where the subscript so that J is the total angular momentum quantum number of the state when the hindering potential vanishes a p - H H Z = 1.0 and RI is the quantum number which specifies ao-liz = 0.53 the component of angular momentum along the Similarly we find Z-axis. -4 few of the lowest rotational energy CW-D~ = 0.55 levels for both hydrogen and deuterium are found CYO-D? = 0.97 to be We note that the condensation coefficients of h ydrogcn deuterium both parahydrogen and orthodeuterium are at or IB,,, = 260 cnl./molc It’c,~ = 260 cal./mole q = 480 T I 1 c = 340 near their maximum value. This is not surprising W’l 1 520 W1,] = 670 since neither species is rotating (except a few in TV,., = 1230 W;.a = 760 excited states) in the vapor phase, and so all of T P 2 . 1 = 1200 W?,, = 750 these molecules which evaporate from the surface T t i ? , p .= 1350 TV, 2 = 910 have essentially the gas phase distribution of rowhere IT‘I 11= J I 7 , , - ~ ~ . S o w , if we assume that there is no activation tational states giving rise to the maximum rate of energy needed for condensation, the condensation evaporation. The molecules of orthohydrogen coefficient a is the ratio of the internal partition and paradeuterium do not have the same distrifunction for the surface molecules to the internal bution of rotational states on the surface as in the partition function for the molecules in the vapor vapor phase, and so upon evaporation these molephase.? Since the vibrational partition function cules do not go over into the same distribution as for the molecules on the surface and in the vapor found in the vapor phase. As a result these moleis expected to be the same, the ratio of the inter- cules do not evaporate a t the maximum rate. nal partition functions just becomes the ratio of The reason that the condensation coefficient of orthodeuterium is not unity is because there are rotation3 1 partition functions. Since the energies of the rotational partition an appreciable number of molecules in excited function- for the burface are referred to a state rotational states and these behave in a similar having no rotation rather than to the zero point manner to the molecules in the rotational states of energy, the abow rotational partition functions orthohydrogen and paradeuterium. I n parahymust be buitably corrected. The zero point energy drogen the number of molecules in excited rofor the para qttLte of hydrogen is just Woo, and tational states is negligible. Acknowledgment.-The authors wish to exfor the ortho state T V l o - E , where El is the rotational energy for a molecule in the vapor phase press their appreciation to Dr. George Stewart with J = 1. The condenwtion Coefficients for for discussions on certain phases of this work and to Professor Paul Harteck for helpful suggestions. hydrogei~then are given by FT’j
THE I’KEPA€UTIO?; ASD IDENTIFICATIOI.\; OF SOME INTERMETALLIC COllPOUKD S OF POLOSIUM1 BY IT. G. WITTEMAS,A. L. GIORGI.4ND D. T. T’IER C‘ontrzbiition f r o m the Cniverszty of California, Los Alamos Scientific Laboratory, Los Alamos, Sex Mexzco Receaoed September 1 I 1,969 ~
A micro technique for the preparation of intermetallic polonium compounds is descrihed. Several compounds were prepared by this technique, and their composition and crystal structure were investigated by X-ray powder diffraction. The diffraction results obtained are summarized in Table 11. Similar investigations indicated that (1) nickel and polonium apparently farm compounds with a composition and a crystal structure which vary continuously between S i P o and S i P o r structures, respectively; ( 2 ) gold and polonium form solid solutions over a wide range of and between S i A s and C t l ( 0 H ) ~ composition; (3) tantalum, tungsten, molybdenum and carbon do not react with polonium; and (4) copper and silver formed coinpoiinds with polonium, but good X-ray data were not obtained.
Introduction Little is knolvrl collcerlling high temperature reaction? of poloniunl metal \vith other metals. The early literature on this phase of polonium (1) Work performed under t h e auspices of the .4tomic Energy Cornmission.
chemistry contains only fragmentary information of doubtful significance. More recently, in an inr.estigation of the action of molten polonium on gold, platinum, nickel and tantalum surfaces, Or formation the first three metals was evident. but no reaction with tan-
