SEPARATION OF ISOTOPES BY DIFFUSIOS
1033
Analysis.-Weighed quantities of the crystals were decomposed with water in a LIeyer-Jannek a p p a r a t ~ s . ~ The free selenic acid was reduced to selenious acid by heating with conc. hydrochloric acid, after which it was reduced to elementary selenium hy hydrazine. Two analyses yielded 45.0 and 44.5O; of selenium, while SeOs(0H) (ONO) requires 4.5.35; of selenium. For the determination of nitrogen, weighed quantities of the crystals were shaken in a closed bottle with a solution of sodium hydroxide until the nitrogen oxide fumes which were evolved had again been absorbetj. The resulting solution was treated with a measured excess of potassium permanganate solution, and after oxidation of the nitrous to the nitric acid, the excess of permanganate was titrated back by means of oxalic acid. In two samples, 7 . 3 and 7.4% of nitrogen were found. Nitrosyl selenic acid requires Xc; nf nitrogen. Considering the methods of analysis used, the results are sufficiently accurate.
Kitrosyl selenic acid, SeOz(OI-I) (ONO), is decomposed by water. It is readilv soluble in conc. selenic and conc. sulfuric acids. Nitrosvl sulfuric acid is also soluble in these acids, and both compounds are soluble in absolute alcohol but not in ether. .It SO", nitrosyl selenic acid melts xith decomposition. This is also the melting point of nitrosyl sulfuric acid and is considerably higher than that of pure selenic acid, which is Nitrosyl selenic acid is very reactive and with certain of the organic amines readily forms compounds, which we are studying. RRESLAV,GERMAXY ~ ~ O N T R I B U T I O NFROM
LABORATORY OF (CHICAGO1
I H E K E N T CHEMICAL
THC I'SIVERSITY
Or
THE SEPARATION OF ISOTOPES BY THERMAL AND PRESSURE DIFFUSION B Y ROBERS T ~ILJLLIKEN~ Keceived March 1. 1922
Introduction R'ith the ultimate aim of obtaining extensive separations of isotopes, a careful preliminary study, both theoretical and experimental, is being made, in order to find the best practical method or methods. In a pre~-ious paper by hfulliken and Harkins2 the theory was developed and equations obtained for the change of composition and atomic weight for the fractions obtained when a mixtiire of isotopes is subjected to a praccib of irreversible evaporation, molecular effusion, molecular diffusion, 0 1 gaseous diffusion. A rather complete s u m m a n of the possible method5 for separating isotopes was also given (p. 62). In the present paper, the theory of the method of t h a m a l diffusion and that of the centrifugal Meyer and Jannek, %bid , 83,51 (1913). 2
National Research Fellow in Physical Chemistry Mulliken and Harkins, THISJOVRNAI,, 44,37 (1922'
1034
ROBERT S. MULLIKEN
method, as applied to the separation of isotopes, are rather fully discussed. Equations analogous to those for the other methods of separation are obtained, and used in a study of the applicability of the methods to various isotopic elements. Conclusions are reached as to the practical value of the two methods. Equations for Diffusion and Evaporation Processes ’The most important equations obtained in the previous paper will here be reviewed briefly, using the same equation numbers as there given. For a mixture of two isotopes, the equations for the residue in an evaporation or diffusion process are, or approximately, and
or approximately,
h z =
-k )
2(x1
+ kxzi xlxz
. 17% c
=
-4 ;,t
c
(6)
( M z - M d XlX2 , In AN1 = 2M A M = .4(M1-MI) In C = B In C (Mz-Mi) xixz AM* In C 2M
Similar relations hold for a mixture of any number of isotopes.
(6a) (7) (Ta) The x’s denote
mol-fractions, the M’s atomic or molecular weights; k = .\IMl/MS; and C, the “cut,” is the ratio of the initial to the final number of mols present in the r e ~ i d u e . ~The subscript 1 refers t o the lighter, 2, to the heavier isotope. M without subscript stands for the ordinary, average, atomic or molecular weight. B is called the sepzration coefficirnt. For the diffused or evaporated material, the equations are,
- AxZ=A 1% C/(C-1) - A M = B In C/(C-1)
and
(15)
(16)
The total dzference in atomic weight‘ between the two fractions is then
A A M= A M - ( - A M ) = [ B - (Mi- M1) 2x1x?
+ BI(C-l)]In
C = B CIn C/iC-l)
(19)
. - lit C, nearly i1Ya) 2M c- 1 For C = l , A A M = B ; for C=2, A A M = 2 B In 2=1.389 B; for C = 4 , A A M = ( 8 / 3 ) B In 2 = 1.848B; etc. The value for C = 2 is of the most interest, since it corresponds to a division of the material into two equal fractions. All the above equations hold for a mixture of more than two isotopes, except that the expressions for A and B arc more complex (see previous paper) Thermal Diffusion It has been shown theoretically5 and ~ x p e r i m e n t a l l ythat ~ ~ ~if a gaseous a I n the case of gaseous diffusion, the numerical factor in the denominator is probably always greater than 2. This factor is equal to the exponent c in the value of k : ci n general, k = d;M1/M2. This equation was not given in the previous paper. Enskog, Physik. Z., 12, 538 (1911); A m . Physik, 38, 750 (1912); and Chapman, Phil. Trans., 217A, 115 (1916); Ph,il. Mug., [6] 34,146 (1917). Chapman and Dootson, Phil. Mug., [SI 33,248 (1917). Ihbs, Proc. Roy. Sor., 99, 385 (1921).
SEPARATION OF ISOTOPES BY DIFFUSION
1035
mixture is present in a container, one portion of which is kept hot, and another cold, an equilibrium state is attained in which there is an increased concentration of the larger or heavier molecules a t the cold end, and vice versa. For a mixture of two is,otopes, Chapman deducess the relation (here altered to conform to the present notation),
for pnoleczdes which behave like elmtic spheres, Atxz standing for the difference between the values of x2 in the regions a t the two temperatures. Actually, in the case of a mixture of hydrogen and carbon dioxide, k, proves to be only about ' 1 2 or 1/3 as large because the molecules do not behave as assumed. Approximately, since A M =
(Ms-M , ) AX?,
AtM = K.
(M
MI)
22M2
~1x2
112
T', T = K R In T' T
(21)
The analogy to Equations 7A and 19 is obvious. Except for some variability in K for different types of molecules, the separation coefficient KB for thermal diffusion depends in nearly the same way on the molfractions and molecular weights of the isotopes as does the coefficient R for ordinary diffusion. Thermal diffusion is apparently however a much weaker agent than ordinary diffusion, under any practicable conditions, for if K = ' 1 4 , a reasona.ble estimate, then a temperature ratio of 15.5 (e. g., 80" absolute against 1240' absolute) will give AtM = (','4)BIn 15.5 = 0.693 B = 13 In 2 . Even if the mixture is divided almost wholly into two equal fractions a t the two extreme temperatures, the value of AtM is only half as great as the corresponding value (2B In 2) of A AM for a cut of 2 by one of the diffusion methods previously considered. This is in spite of the very large temperature ratio, corresponding to a range from liquid air temperature to 1000". Evidently the method of thermal diffusion cannot competeg with the other diffusion methods as a means of separating isotopes. Evaporative Thermal Diffusion.-Probably the most favorable way to apply thermal diffusion would be to use a method of procedure similar to that proposed in the case of centrif;gal separation, viiz., to have a supply of the liquid mixture in the cold bulb, and to draw off gas very slowly from the hot bulb. The rate of separation'O would be the same as for an ordinary diffusion or an irreversible evaporation having a separation coefficient equal t o AtM. ,4s a matter of theoretical interest i t is intended t o test this method of "evaporative thermal diffusion" experimentally with mercury. If the process of drawing off the gas took place through a
* Chapman, Phil. Mag.,
[6] 38, 182 (1919). The method of thermal diffusion can, it is true, be adapted to rapid continuoiis operation, but probably only at a large sacrifice of efficiency icf Thbs, Ref 7 ) . lo Compare discussion under centrifugal separation.
1036
ROBERT S. MULLIKEK
porous wall, the effect of ordinary diffusion would be added to that of thermal diffusion, and the result would be the same as for an ordinary diffusion A t M ) , instead of B. This increase with a separation coefficient ( B would, however, hardly be worth the added difficulties.
+
Pressure Diffusion Development of Equations.--The problem of the separation of isotopes by “pressure diffusion,” that is, by virtue of variation of composition along a pressure gradient, due either to a gravitational field or to centrifugal force, has been discussed by Lindemann and Aston,” and by Chapman,8 who compares the method with that of thermal diffusion. Lindemann and Aston derive equations applicable to a gaseous mixture of tzeo isotopes. These, slightly modified, and transcribed, are as follows g
For gravitational separation, r separation r
=
e
D?(.\f>____ MI) 2RT
A h(.$f?--M:~
K7
= c
,
(22) and for centrifugal XL XI
( 3 3 ) . Here r stands’? for ____ , the sub(Xdu h i 0
script o referring to the point of reference, for example, the center of the centrifuge, or the level of the earth; v is the peripheral velocity. Chapman gives the equation (here transcribed), applicable to any type of pressure diffusion,
analogous to his equation for thermal diffusion. Equations can be derived for the case of pressure diffusion, analogous to those for other types of diffusion, which show clearly the factors on which the change of atomic weight depends. It will be best to go through with the derivation from the beginning, since the methods and notation are different from those of Lindemann and Aston, and of Chapman. For a gaseous misture of two isotopes a t total pressure p and density p , v 2 p 1 dr M1p1w2rdr subjected to centrifugal action, dpl = - = plw2rdr =
RI’
r
Here p1 and p l refer to the partid pressure and density of the lighter isotope, and v, w, and r , denote respectively linear velocity, angular yelocity, and radial distance An analogous equation holds for the heavier dP1 isotope. The above equation gives P1
=
d ln p,
=
M1W2
rdr. RT
Then
Lindemann and Aston, Phil. hfag.,[61 37, 523 (1918). The quantity r is analogous to the “enrichment ratio” of Rayleigh (see hlulliken arid Harkins, Ref 2), but differs in that i t corresponds to 2io-l1instead of t o A h 1 l1
1037
SFPARATION OF ISOTOPES BY DIFFUSION
If ro = 0, ua = 0. By combining Equation 25 with the corresponding expression in terms of p ~ and , putting vo = 0, Lindemann and Aston's relation (23) can be obtained. The following relation, which will be useful in another connection, can also be seen to hold approximately,
Chapman's relation (24) for Ap.r2 can be obtained by a derivation analogous to that used in the paper of IJIulliken and Harkins in arriving a t Equations 2, 5, and [j. Thus from the equations above given for dpI/p1 and dp2/pz, dp2/ps = ( l V ~ / M L ) . d p ~ / pThen ~. since p1 = pxl and
derivation is precisely analogous to that used in obtaining Equation 6 of the previous paper, everything being unchanged except that p everyc-
= C), and M2/M1 replaces d M l / M z where replaces N ( p a / preplaces = k . Thus we obtain the relation, formally analogous13to Equation 6, (1--IIiz:MI)XIKz . In po AQXZ = XI .t(hi2lnll)XP p Then
which is formally analogous13 to Equations 7 and 7A. Combining (26) and (27), there results the approximate relation14 for the difference in atomic weight a t points r and 70
For the general case of a mixture OF several (atomic, or molecular) isoZ ( M a 2 ~ a-) [ ~ ( M , X , ) ] ~ . topes, the corresponding relation': is A P Ji' = 2RT 13 AQXZand I g J I are really more nearly analogous to 11x2 and 1 A h 1 (compare Equation 19), in plzy~zcalmeaning, than to 1x2 axid A M . 14 Similarly, for g m z ~tciizonalseparation, which is of course not a pructicnl method, . I p M = ( M 2 - M i ) 2 ~ i ~g(h--ilo)/RT=2I' r I h (29). l5 This is obtained 3 s follows Ar~alognlisto Equation 6' of the previous paper, Zn ( S- k'
