July, 1956
NOTES
,
1015
And, in addition, the increased activation energy often compensates for even this increase. For example on the 1600°K. isotherm, in going from 10 to 100 mm. pressure the coverage increases from approxiqately 0.25 to 0.35. But the activation energy increases from 4.5 to 5.5 kcal. so that the relative ratio of the two velocities will be
saturation is to measure the activation energy as a function of pressure over as wide a pressure range as feasible. If it remains constant, or approaches a limiting value, the surface is very likely close to saturation. A third point is the importance of using initial rates rather than “half times” since the activation vlo0 X 108/1.99 X 1600 energy can change significantly as the pressure de- = I).&-6.5 0.36e-4.5 X 108/1.99 X 1600 = creases. This is very important for the model used vl0 Thus a tenfold pressure increase leads to only a 2% in the present paper in the 100-10,000 mm. region increase in velocity. Of course it is only by chance a t 900°K. However, most studies of the ammonia that the compensation is so complete. In the same decomposition fail to state what initial pressures pressure region on the 900°K. isotherm a tenfold were used; and at least one did not even report increase actually leads to an SO% decrease in ve- the temperature interval. Kunsman’ found 45.3 locity. This would still probably be considered as and 43.2 kcal. activation energies for the reaction an approximately zero-order reaction (though some by the use of “half” and “quarter times,”’ respecexplanation would very likely be proposed to ac- tively. Since the assumption of a surface having sites of count for the slight decrease in rate). uniform activity is probably a poor one, it would be From this discussion there are a number of points which should be emphasized. First, it is of interest to carry out similar calculations for a not true that zero-order kinetics necessarily imply a heterogeneous surface and see how this affects Fig. saturation of the catalytic surface with reactant. 2. At present this is being done for the simple ‘In fact, in the author’s opinion, there are probably case of a linear variation in activity of the surface very few cases of thermal decompositions in the sites. I n addition the relationship between this 900°K. range where the surface becomes even as work and that of Brunauer, Love and Keenang will much as nine-tenths saturated. And very likely it is be discussed in a future paper, The author would like to express his appreciation more often well under half covered because the heat of adsorption of ammonia at full coverage is as of financial support from the California Research great as the heat of adsorption of many gases a t Corporation and acknowledge many helpful discussions with Drs. Antonino Fava and Izumi Higuzero coverage. A second point to be emphasized is that the only chi. way in which one can be reasonably certain of (9) S. Brunauer, K. 8. Love and R. G. Keenan J . Am. Chem. Soe. being in a region where the surface is very close to 64, 751 (1942).
NOTES THE Fe(I1)-Tl(II1) REACTION AT HIGH CHLORIDE CONCENTRATION B Y FREDERICK R. DUKEAND
BERNARD BORNONG
Contribution N o . 402 from the Institute for Atomic Research and Department of Chemistry, Iowa Stale College, Ames, Iowa’ Received October l d , 1966
The reaction between Tl(II1) and Fe(II)2a has been shown to be retarded by chloride.2b This is readily explained in terms of the prior equilibrium* Tl(II1)
+ Fe(I1)
Fe(II1)
+ Tl(I1)
(1)
followed by the slow reaction
-
Tl(I1)
+ Fe(I1) +Fe(II1) + Tl(1)
(2)
in conjunction with the associated equilibria, Ti(II1) C1T1C1+2,TlClz+ and higher complexes.4
+
(1) Work was performed in the Ames Laboratory of the Atomic Energy Commission, Iowa State College, Ames, Iowa. (2) (a) C. E. Johnson. J . A m . Chem. SOC.,7 4 , 959 (1952); (b) 0. L. Forchheimer and R. P. Epple, ibid., 74, 5772 (1953). (3) K. G. Ashurst and W. C. E. Higgonson, J. Chem. Soc., 3044 (1953). (4) R. Benoit, Bull. S O C . chim. France, 6 , [6]518 (1949).
However, since chloride is usually a catalyst for such reactions in the absence of a prior equilibrium, it is of interest to determine the effect of high chloride on the rate, particularly in view of the work on the Tl(1)-Tl(II1) exchange where chloride has a retarding effect a t low concentration and then a catalytic effect a t higher concentrations.6 Experimental The Tl(II1) and Fe(I1) perchlorates were repared as described by Forchheimer and Epple.6 C.P. HE1 was used, as well as C.P. LiCl, for maintaining ionic stren th and acidity. LE104 was prepared by dissolving C.P. &OH in C.P. HC10,. The appropriate amounts of reagents were added to a volumetric Aask in a constant temperature bath (25’) to make the final concentration of Fe(I1) = 0.095 M , TI(II1) = 0.05 M , [Cl-] varying from 0.2 to 2.0 M , [H+] = 2.50 M , dnd p = 3.30. The method of analysis used was to measure the absorbancy at 430 mp, where the ferric chloride complex absorbs. The absorbancy index of the Fe(II1) for a particular solution was taken from the “infinite time” value of the absorbancy. Since TiCl precipitates at these (5) G. Harbottle and R. (1951).
W*.Dodson, J . A m . Chem. SOC.,7 3 , 2442
(6) 0. L. Forchheimer and R. P. Epple, Anal. Chem., 28, 1445 (1951).
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 electronegativity2v3 of 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,
