NOT‘ES
1016
concentrations, the solution was filtered just before measuring the absorbancy.
Results and Discussion Second-order plots, first order in each Tl(II1) and Fe(I1) yielded straight lines up to 60-65% of complete reaction; presumably the deviation a t higher reaction percentages is the result of prior equilibrium (1). The slope of the straight line portions of the second-order plots were compared with the results taken from the graph in the paper by Forchheimer and Epple.2 The results are presented in Figure 1. It is evident that a minimum in the rate of reaction occurs between chloride concentration of 0.1 and 0.2 M . Then the curve rises steeply and levels off between 1.5 and 2 M chloride. The conclusion drawn is that Tl(I1) must complex chloride for the following reasons:
0.2
C
-1
J
Vol. 60
T H E RELATIOX OF FORCE CONSTANT TO ELECTRONEGATIVITY &ID COVALENT RADIUS BY R. L. WrLLIAnm
.
Ministry of Supply, E . R . D . E., WaEtham Abbey, England Received December IS, 1955
Numerous attempts’ have been made to relate force constants with interatomic distance, of which perhaps the best known are Badger’s and Gordy’s rules. In the case of the latter, the force constant, AB, of the bond between the atoms A and B, is given by the equation AB = a N ( x A x B / d 2 ) 8 / 4 + b (1) where a and b are constants, N is the order of the bond between A and B, d, the internuclear distance, and XA, X B the electronegativities. This equation is of interest since it involves the electronegativities of atoms A and B. However, it is difficult to understand why the force between two atoms should be a function of the product of electronegativities, when most physical and chemical properties, e.g., dipole moment, have been shown to be related to their difference. If the logarithm of the electronegativity2v3of elements in Groups IV to VI1 is plotted against the logarithm of the corresponding covalent radius2m3 divided by the number of its valence electrons, a good straight line is obtained, Fig. 1, corresponding t o the equation XA
XA
I
Fig. 1.-Effect
l
l
I
I
I
of chloride on the second-order rate constant for the Fe(I1)-Tl(II1) reaction.
1. Fe(II1) does not associate with chloride sufficiently t o increase the equilibrium concentration of Tl(I1) in reaction (1) to the extent indicated by the data in Fig. 1. 2. Reaction (2) does not appear to be strongly catalyzed by free chloride ion, because the leveling off a t high chloride ion concentrations would not be expected from participation of chloride merely in the activated complex. 3. The only other alternative is to allow the formation of Tl(II)-Cl- complexes with a stability somewhat less than that of the Tl(II1)-Cl- complexes. This interpretation of the data serves to explain the C1- effect on the Tl(1)-TI(I1I) exchange.6 T1+ $ T1+2 Consider the reaction TlC1+2 +TlCl+. If the dissociation of TlCl+ is slow coinpared with the reverse of the indicated reaction, the equilibrium would be largely non-exchanging. When the [Cl-I reaches the point that the reaction is TIClz+ T1+ TlCl+ +,TlCl+, the exchange rate should increase, particularly if the slow reaction is GI- catalyzed.
+
+
= 0.761(Z~/TA)~”~
(2)
where ?A is the covalent radius and ZA the number of valence electrons. A similar equation, vix.
+
= 0 . 3 1 ( ~ ~ l)/fA
+ 0.50
(3)
has been derived by Gordy.8 However, if (2) is used to substitute for electronegativity in Gordy’s rule, (l),it is found that AB = A(zAzB)’J~~ X d-2.525 4-0.30 (4) where A = 1.058aN, provided that (TATB)0.625 =
(TA
+
TB)/2
= d/2
which is a very good approximation for the range of possible values of covalent radii. It can be seen that (4) is of the form of an equation put forward by Guggenheimer4 . AB = A’(zAzB)OJX d-2.46 Consequently, Gordy’s result that the force constant between two atoms depends on the product of electronegativities, is accidental. The main factors determining the force constant are the covalent radius and the number of valence electrons of each atom. Electronegativity enters the force constant equation only because it is a simple function of both these quantities. It may also be noted that (1) on substitution with Gordy’s second equation, (3), does not go over easily into Guggenheimer’s equation. (1) For a recent summary: H. 0. Pritohard and H. A. Skinner, Chem. R e m , 56,745 (1955). (2) L. Pauling, “The Nature of the Chemical Bond,” 2nd edn., Corne11 University Press. Ithaoa, N. Y..1948. (3) W. Gordy, P h w . Rev., 69, 604 (1946). (4) K. M. Guggenheimer, Proc. Phys. Soc., 58, 346 (1946).
1,
NOTES
July, 1956
0.8 r;
e 23 0.7 M
0
e
0.6
Si,Bi,
0.5
0
0.1
0.2
0.3 0.4 log 2. Fig. 1.
0.5
0.6
1017
actinium samples could be determined by neutron counting techniques. Pure actinium 227 is only mildly alpha active since 99% of the material decays by ,&emission, but the intensity of a-emission grows considerably as the various radioactive daughters accumulate. Accordingly, the intensity of neutron emission from any light element impurity should grow as more and more of the active daughters are formed. The actinium alpha growth was computed from the available nuclear data.4 The neutron growth was then determined from this alpha growth and from the fluorine neutron yields a t the various a-particle energies in the actinium decay chain.s6 A correction for the limited volume of fluorine that is available for nuclear reztction was applied,’ and it was found that the theoretical neutron emission rate for 17.4 mg. of actinium fluoride (corresponding t o one curie of actinium 227) should grow from about 1,000 neutrons per second immediately after separation of the actinium from its daughters to a maximum of 1.07 X lo6 neutrons per second after 0.7 180 days.
The extension of this treatment to the remaining elements is made difficult by the problem of deciding what constitutes the “covalent” radius of these elements. Gordy used Pauling’s values2 of tetrahedral covalent radii to establish (3), but it is doubtful whether these radii are covalent radii in the same sense as those of the more electronegative elements, since the former have been derived from crystal lattice distances. I acknowledge with gratitude the award of a Senior Research Fellowship from the Ministry of Supply. Thanks are also due to Dr. L. J. Bellamy for several helpful discussions.
A sample of actinium fluoride, weighing 0.77 mg., was prepared by adding an aliquot of actinium chloride solution to 24% hydrofluoric acid in a special Teflon centrifuge tube. This tube was constructed in such a manner that a small molybdenum cup, pressure sealed to the Teflon, formed the bottom of the tube. The precipitate waa centrifuged into this container, and the container and its contents were removed from the centrifuge and dried. The container was then closed with a special lid, apd the assembly was sealed by an even coating of nickel which was deposited from the thermal decomposition of nickel carbonyl. The sealed assembly was then neutron counted periodically for approximately four months. During‘ this period the radioactivity content was determined by periodic calorimetric analysis.
The sample was found t o contain 0.044 curie of actinium, and it attained a maximum neutron count of 53,400 f 600 neutrons per second. Thus, the neutron emission rate from actinium fluoride was found to be 1.21 X 106 neutrons per second per curie of actinium in equilibrium with its daughter products. This compares favorably with the NEUTRON EMISSION FROM ACTINIUM theoretical value of 1.07 X 106 neutrons per second FLUORIDE per curie. Both these values are subject to errors which may BY K. W. FOSTER AND J. G. STITES, JR. be quite large. The theoretical value is based on Mound Laboratory, Monsanto Ch‘hamicalCompany, 1 Miamiaburg, Ohio some rather uncertain neutron yields in the higher Received January 18, 1968 a-energy range, and the relation that was used to One of the methods developed t o prepare the ele- correct for a finite fluorine volume is empirical and ment actinium is the reduction of actinium fluoride has never been determined accurately for fluorine with lithium.2 Since fluorine is an excellent neu- and actinium. The theoretical value may be tron producer when bombarded by a-particles,8 wrong by as much as a factor of 2. and since actinium 227 and many of its daughter The experimental value suffers from the fact products are a-emitters, it is to be expected that that the neutron emission rates were determined by actinium fluoride would be naturally neutron ac- comparing the sample with a radium-beryllium tive. Likewise, it is to be expected that any ap- standard neutron source. There is no assurance preciable fluorine traces in metallic actinium would that the actinium-fluorine neutron energy apeoresult in detectable neutron emission. Therefore, trum is sufficiently similar to the radium-beryla study of the neutron yield from actinium fluoride lium neutron energy spectrum to give the same was made, and from the data obtained in this study over-all detector efficiency. I n addition, the aba method was developed whereby the purity of (4) Circukr 499, Nstional Bureau of Standards, Septembor 1 , (1) Mound Laboratory is operated by Monsanto Chemical Company for the United States Atomic Energy Commission under Contract Number AT-33-1-GEN-53. ( 2 ) J. G. Stitea, M. L. Sslutaky and B. D. Stone, J. Am. Chem. SOC., 77, 237 (1955). (3) H. L. Anderson, “Neutrons from Alpha Emitters,” Preliminary Report No. 3, NP-851, December, 1948.
1950. (5)
a. T. Seaborg and I. Perlman, Ram. Mod. Phys., 20, 585 (1948). (6) E. Seere and C. Wiegand, “Thick-Target Excitation Functions for Alpha Particles,” MDDC-185, September 15, 1944. (7) 0. Sisman, “Development of a Process for Produotion of Radium-Beryllium Sources,” Final Report CNL-17. p. 4, January 28, 1948.
