1164
M. BLANDER, W. R. GRIMES,N. V. SMITHAND G. M. WATSON
coal for nitrogen adsorption, in preference to argon adsorption, can be explained on this dimensional basis, although an electronic interpretation would be equally satisfactory. Further studies of these
Vol. 63
systems, with respect to the causes of this selectivity and to the nature and spacing of the supported modifying agent, should help to develop a better understanding of the actual forces involved.
SOLUBILITY OF NOBLE GASES IN MOLTEN FLUORIDES. 11. IN THE LiF-NaF-ICF EUTECTIC MIXTURE BY M. BLANDER, W. R. GRIMES,N. V. SMITHAND G. M. WATSON
.
Oak Ridge National Laboratory,' Reactor Chemistry Division, Oak Ridge, Tennessee Received December 19, 1868
Solubilities of He, Ne and A were measured a t pressures from 1 to 2 atmospheres in a mixture of LiF, NaF and K F (46.511.542.0 mole %) a t 600, 700 and 800'. The solubilities increase linearly with gas pressure, decrease with increasing atomic weight (radius) of the solute and increase with increasing temperature. Henry's law constants in moles of solute/ (cm.3 of solution)(atmosphere) at 600' are 11.3 =k 0.7 X 10-8, 4.36 f 0.20 x 10-8 and 0.90 =k 0.04 X 10-8 and the enthalpies of solution are 8.0, 8.9 and 12.4 kcal./mole for He, Ne and A, res ectively. A model which equates the free energy of solution of the gas to the free energy of formation of holes the size o r t h e gas molecules in a continuous fluid having the same surface tension as the solvent yields solubility values which are in good agreement with those observed.
Introduction Fused salts offer a radically different solvent medium for the study of gas solubilities. In this investigation the solubilities of helium, neon and argon were measured in the eutectic mixture LiFNaF-KF (46.5-11.542.0 mole %) at 600, 700 and 800". This eutectic mixture is convenient for study because of its relatively low melting point2 and because of the low partial pressures of its constituents over a wide range of temperatures. This enables one t o make measurements over a considerable range of temperatures and leads to a more accurate separation of the enthalpy and entropy of solution. A previous publicationa from this Laboratory described the measurements of the solubility of noble gases in molten fluoride mixtures. In that report, values were given for the solubility at 600 to 800" of He, Ne, A and Xe in a NaF-ZrR mixture containing 47 mole yo ZrF4 and a NaF-ZrF4-UF4 mixture containing 4 mole % UF4 and 46 mole ZrF4. This work is a continuation of the systematic study of gas solubilities in molten fluoride mixtures in progress at this Laboratory with the aim of elucidating the solvent properties which have an effect on gas solubilities. Experimental The rare gases used were obtained in cylinders from commercial sources. He was obtained from the Bureau of Mines at Amarillo, Texas; Ne and A were from Linde Air Products Company. All gases used were shown by masa spectrometric analysis to exceed 99.9% purity. The molten fluoride mixture was prepared from Reagent grade LiF, NaF and K F and purified in a closed system of nickel at 800' by alternate Aushing with anhydrous H F and Hz. Chemical analysis of such samples yielded these data
LiF-NaF-KF (46.5-11.5-42.0 Theor.
Na
K Li
F
a
Ni Fe Parts per million.
6.4 39.8 7.8 46.0 0 0
MOLE
% by wt-
%) Obsd.
7.5 40.1 7.1 45.3 30" 170"
The apparatus and procedure are identical to those described in & previous pub1ication.a
Results The solubilities and Henry's law constants for He, Ne and A in the molten LiF-NaF-KF eutectic at 600,700 and 800" are shown in Tables I, I1 and 111. Figure 1 is a plot of Henry's law constants as a function of temperature. The solubility values could be duplicated in separate experiments to about *5%. The solubility values are in moles of gas per cubic centimeter of solvent and may be converted to other units as desired by use of solvent densities calculated from the equation4 p
(g./cm.*) = 2.47
- 0.68 X lo-* t ("c.)
Discussion, Solutions of noble gases afford the simplest systems for the interpretation of gas solubilities. The solubilities of the gases studied, all of which obey Henry's law within the experimental precision of 570, increase with increasing temperature and with decreasing molecular weight (or atomic radius) of the gas. The enthalpies of solution of all the gases are positive and larger the larger the atomic weight (radius), It is important to calculate the thermodynamic properties of the solution in such a way that the entropy of solution of a gas is purely a function of solvent-gas interactions. To do this a standard
*
(1) Operated for the United States Atomic Energy Commission by the Union Carbide Corporation. (2) A. G. Bsrgman and E. P. Derguaov, Compt. rend. Acad. Sci. URSS, 81, 764 (1941). (3) W. R. Grimes, N. V. Smith and G. M. Wataon, THWJQVRNAL~ (4) 9. I. Cohen, W. D. Powers, N. D. Greene and H. F. Poppendiek, 62, 862 (1968). Oak Ridge Nationel Laboratory, personal oommunicationa.
.
TABLE I SOLUBILITY OF HELIUMIN LiF-NaF-KF
TEMPERATURE ( " C ) ,
(46.9-1 1.5-42.0
-7
700
800
600 I
Temp.
("C.)
600
650 700
800
Saturating pressure (atrn.)
Solubility x 108 (moles He)/ (cc. melt)
Kp = E / P x 108 (moles He)/ (cc. melt) (atrn.)
2.08 1.77 1.51 1.00 1.00
22.1 19.0 16.9 11.0 12.8
10.6 10.7 11.2 11.0 12.8
2.08 2.05 2.04 1.75 1.51 0.98 2.06 2.04 1.77 1.51 0.99
28.5 35.5 34.8 30.8 26.3 17.6 48.3 48.2 41.8 33.6 21.7
600
700
800
Saturating pressure (atrn.)
2.07 1.49 1.01 2.05 1.51 1.02 2.07 1.50 1.03
Solubility x 108 (moles Ne)/ (CC. melt)
9.57 6.42 4.20
1
I
I
Av. 1 1 . 3 f 13.7 17.3 17.1 17.6 17.4 17.9
-
Av. 17.5 1 23.5 23.6 23.6 22.3 21.9 Av. 23.0 1
TABLEI1 SOLUBILITY OF NEONIN LiF-NaF-KF (46.5-11.5-42.0 MOLE %) . _. Temp. ("C.)
1165
SOLUBILITY OF NOBLE GASESIN LiF-XaF-KF EUTECTIC M~XTURE
July, 1959
KP =
C/P
x
108
(moles Ne)/ (cc. melt) (atm.)
4.61 4.30 4 . IG
10.00
9.00
Fig. 1.-Temperature dependences of Henry's law constants for He, Ne and A in LiF-NaF-KF eutectic mixture. TABLEI11 SOLUBILITY OF ARGONIN LiF-NaF-KF MOLE
-
15.06 11.04 7.99
Av. 4.36 f 0 . 2 0 7.36 7.33 , 7.84
22.53 16.53 12.05
Av. 7 . 5 1 1 0 . 2 2 10.89 11.00 11.66
600
-
-
Av. 11.18 10.26
state is chosen in terms of a number of moles per unit volume in both the gas and the liquid and the standard entropy change for the dissolution of a gas is that for the process X ( & C d ) +X ( d , C d ) (A) where X represents one mole of gas. The subscripts g and d denote the gas and liquid phases and c d is the concentration of the gas dissolved in the liquid which is in equilibrium with the gas at concentration C,. I n the range of concentrations where the behavior of the gas phase is ideal and where the solubility follows Henry's law in solution, the entropy change for this process is independent of the value or units of c d . This choice of standard state, which is not the usual one,6 eliminates the trivial contribution
12 .oo
11.00 IO~/TPK),
700
2.02 1.50 1.01 2.04 1.50 1.00 2.03 1.51 1.00
(46.5-11.5-42.0
%)
1.93 1.38 0.83
0.96 0.92 0.83
-
3.81 2.71 1.74
Av. 0.90 10.04 1.87 1.80 1.74
6.84 5.16 3.41
Av. 1.80 f 0.04 3.37 3.42 3.40
-
Av. 3.40 f 0.03
to the standard entropy of solution which arises from the arbitrary choice of the concentration scale. The standard entropy change ASo is by this choice purely a function of the properties of the gas in the solvent studied since the only change of significance is the environment of the gas atoms. The total entropy of solution of the gas, which is the entropy change for the equilibrium process X(&Cd
X(d.Cd)
(B)
(5) H. 9. Frank and M. W. Evans, J . Chem. Phys., 13, 478 (1845).
1166
M. BLANDER, W. R. GRIMES,N. V. SMITHAND G. M. WATSON
Vol. 63
is given by A# = A H / T , where AH for this process in the LiF-NaF-KF solvent as calculated from Fig. 1 is 8000, 8900 and 12400 cal./mole for He, Ne and A, respectively. Cg is the concentration of gas in the gas phase in equilibrium with the liquid a t zt concentration c d . To calculate the standard entropy of solution from this one subtracts the entropy change for the isothermal expansion of the gas
Although a real liquid cannot be considered a continuous fluid it is interesting to speculate that it behaves as if it were one and that ymicis related to the macroscopic surface tension ymac. The area A is a t least as large as the surface area of the spherical gas molecules. Because of thermal motions one would expect the size of the hole to be larger than the gas atom. The radii of the rare gas atoms in the solids will be a lower limit of the radius XhCd XhCd) ( 0 of the hole and the solubility calculated on this from (B) to get basis would be high. In Table V are listed the values of c d / c g calculated for the rare gases assuming that ~~i~ = Tmac and using the radii of the rare Values of ASo for the noble gases are listed in Table gas atoms in the solid.g The numerical values for IV and prove to be small as had been observed pre- the surface tensions of the solvent and of the atomic viously3 in fused salt solutions. Recalculation of radii of the noble gases are given in Tables VI and data in the literature6 indicates that this is true in VII. A comparison in Table V of the calculated and measured values of for solutions of noble other solvents. gases in LiF-NaF-KF and NaF-ZrFd3 shows good TABLEIV agreement in view of the oversimplified nature of ENTHALPY AND ENTROPY CHANGES O N SOLUTION OF NOBLB the model. The magnitude and the variation of GASESIN MOLTENFLUORIDE MIXTURES AT 1000°K. the solubility with size of the gas molecule are corIdeal gas rectly predicted. This order of the solubility has AH, expansion not often been observed experimentally as most cal./ ASO. TAS Solvent Gas mole e.u. cal./mble other liquids have surface tensions so low that other NaF-KF-LiF He 8000 -0.3 8300 solution effects predominate. The difference be(11.542Ne 8900 -1.0 9900 tween the calculated and experimental values is in 46.5mole %) A 12400 -0.1 12500 the direction one would expect if the estimated size NaF-ZrF41 of the hole were too small except for argon in LiFHe 6200 -1.0 7200 NaF-KF). (5347 Ne 7800 -0.4 8200 mole
%I
A Xe
-1.5 -0.1
8200 11100
9700 11200
The interpretation of these gas solubilities can be made using a model similar to that of Uhlig.6 Although the model is naive it yields an interesting correlation with experiment. If a gas does not interact with a liquid in which it is dissolved, then the free energy change upon solution is related to the “surface” energy of the hole created by the gas. The solubility of such a gas in a continuous fluid medium can be estimated from the free energy changes in the following steps. 1. Expand the gas from the concentration C,
’
TABLEV COMPARIBON OF CALCULATED AND OBSERVED VALUESOF HENRY’S LAWCONSTANTS Gas
NaF-ZrFd
He
600 700 800
Ne
600
A
to c d .
AF1 = fRT1n-
cd
(2) G 2. Shrink the gas atoms to a point and pour in the liquid. The free energy change for this is AP2. 3. Expand the point particles’: The free energy change for this is AFa
kAymi.
- AFz
Xe NaF-KFLiF
CZ
= kAymio
(4)
(6) H. H.Uhlig, THISJOURNAL, 41, 1215 (1937). (7) Another path is to decrease the surface tension of the liquid, mix it with the atoms and then increase the surface tension to obtain this same result as suggested by Scatchard.* (8) G . Scatchard, private communioation.
He
Ne
(3)
where A is the area of the hole created by the particle, ymicis a microscopic “surface” tension and k is a constant necessary to obtain the correct units of energy. For spherical atoms A = 47rr2N and kA = 18.08r2where r is in A. The sum of the free energy changes of steps 1-3 is zero if the gas phase is at equilibrium with the gas in the liquid and -RT In c-d
Tern CoCT‘
Solvent
A
Xe
700 800 600 700 800 600 700 800 600 700 800 600 700 800 600 700 800 600 700 800
Koa
Exptl.
15.5 23.3 37.0 8.09 14.7 21.7 3.62 6.44 10.6 1.39 2.84 5.56 8.09 14.0 20.3 3.12 6.00 9.84 0.645 1.43 2.99
... . .. .. .
x
108 Calcd.
137 188 243 45.9 74.9 112 7.33 16.0 30.2 1.77 4.84 10.7 (28.3) (46.8) (70.7) (3.94) (8.63) (16.4) (0.146) (0.509) (1.41) (0.011) (0.057) (0.212)
KC exp. KO oalcd. 0.11 .12 .15 .18 .20 .20 .49
.40 .35 .79 .59 .52 ( .29) ( .30) ( .29) ( .79) ( .70) ( .60) (4.4) (2.8) (2.1)
Kc = Cd/Cg.
Thus far solvation effects have been neglected. Polarization of the rare gas atoms by the highly (9) V. M. Goldschmidt, “Geochemistry.” Oxford University Press, London, 1954.
L
-
POLPMERIZATION HYDRIDE TRANSFER IX PROPYLENE
July, 1959
1167
and expansion of the liquid lead to the decrease of y TABLE VI SURFACE TENSIONS OF MOLTEN FLUORIDE MIXTURES, with temperature one might speculate that the DYNES/CM.
Temp. (“C.)
LiF-NaF-KF’
NaF-ZrFP
600 (230) 128 700 (220) 120 800 (210) 112 a Surface tension of mixtures estimated from extrapolated values of surface tension of pure components11assuming additive surface tension. Surface tension measurements of this mixture have not a8 yet been made. ’ TABLE VI1 ATOMICRADIIO F NOBLEGASESg
Radius(ft.)
He
Ne
A
Xe
1.22
1.52
1.92
2.18
ionic salt would lead to a smaller standard free energy of solution and greater solubility of the gases. As the polarizability of the rare gas atoms increases in the order He, Ne, A, Xe, an ion induced dipole interaction would cause an increasing trend in the ratio (Cd/Cg)expt/(Cd/Cg)calod in this same order. The last column in Table V illOstrates t,his trend which may be a consequence of the polarization of the rare gas atom. Although the values of the solubility may be estimated in this manner, relatively large errors in the temperature coefficients of solubility can enter from even small effects which have been neglected since the derivative of a small number may be large. In the relation dy/dT is always negative. I n Table IV the standard entropy of solution of the gases listed is small. Since thermal motions of the atoms of the liquid (10) F. W. Miles and G. M. Watson, Oak Ridge National Laboratory, unpublished work. (11) F. M. Jager, 2. anow. Chem., 101, 177, 180, 185 (1917).
“surface area” of the hole created by the gas atom increases with the liquid expansion so that the product rA is relatively constant in the solvents studied. Equation 5 leads to another interesting speculation. For a non-spherical molecule dissolved in a liquid, the increase of the “surface area” of the hole created with an increase of temperature will be due not only to thermal translatory motions but will also be increased by the rotation of the gas molecules. At higher temperatures the rotation of the gas molecules becomes more free and the hole becomes larger. This would lead to a more negative entropy of solution for non-spherical molecules than for the spherically symmetric rare gases. This conclusion is consistent with observation in organic solvents.6
Conclusions The model described, in which the free energy of solution of noble gases in molten salts is equated to the free energy of formation of holes the size of the noble gas atom in a continuous fluid which has the same surface tension as the solvent, yields solubility values for the noble gases which agree with the measured values within an order of magnitude. Measurements in other solvents presently in progress a t this Laboratory will be needed to test the usefulness of this correlation. Acknowledgments.-The authors are especially indebted to Dr. P. H. Emmett who first suggested to them the surface tension model used in the present correla,tion. Many interesting and valuable discussions with Drs. F. F. Blankenship and R. F. Newton are gratefully acknowledged. We are also grateful to Mr. W. D. Harman and associates who were responsible for mass-spectrometric analysis of the many samples submit,ted.
HYDRIDE TRANSFER AND THE MOLECULAR WEIGHT DISTRIBUTION OF POLYPROPYLENE BY C. M. FONTANA~ Contribution f r o m the Research Department of the Socony Mobil Oil Company, Inc., Paulsboro, New Jerseu Received December 19, I968
Evidence is presented for the occurrence of a hydride transfer reaction in the low temperature polymerization of propylene. The theoretical molecular weight distribution assuming equilibrium hydride transfer agrees closely with the observed distribution. The results are discussed with reference to the mechanism of Friedel-Crafts reactions and the form of alkyl halide-metal halide complexes.
I n previous work on the polymerization of 1- in a formed polymer cha.in. This reaction leads to olefins with promoted aluminum bromide cata- the formation of a tree-branched polymer of wide l y s t ~ ,it~was , ~ postulated that a hydride transfer re- molecular weight distribution. The purpose of this action occurs in which the growing carbonium ion paper is to present the evidence for hydride transfer abstracts a hydride ion from a tertiary carbon atom gathered from a careful study of the molecular weight distribution of a sample of polypropylene. (1) Celanese Corporation of America, Summit Research LaboraTheoretical treatments of the molecular weight tories, Summit, New Jersey. distributions to be expected with and without hy(2) C. M. Fontana, G. A. Kidder and R. J. Herold, Ind. Eng. dride transfer under various conditions of polyChem., 44, 1688 (1952). merization are also presented and compared to the (3) C. M. Fontana, R. J. Herold, E. J. Kinney and R. C. Miller, ibid., 44, 2955 (1952). observed distribution.
