NOTES
814
Thc sulfur was pre awd by melting flowers of sulfur, coolin and grinding t i e crystals in a mullite mortar. Both myfur and silver were sieved to give uniform sixes 2.1576 grams of silver powder was thorou hly mixed with 0.3206 of sulfur powder of the same size pkced in weighed sinteref glass-bottom crucibles at 25' for periods of time ranging from 1 to 50 days. At suitable time intervals a crucible was extracted five times with about 10 ml. of fresh carbon disulfide and the loss in weight gave the amount of sulfur still unreacted. Experiments were also carried out in which the powders were pressed into pellets under pressure of 3 tons per sq. inch, as in thc experiments of Fischbeck.6 There was no significant difference in reaction ratc between the pressed and iinl)resscd powders arid the act of compression gave no appreciable reaction. This lack of action on compression was unexpected because preliminary work on KBr and AgN03 indicated that compression under high pressures does bring about some reaction.
.
The data on the reaction between silver and sulfur a t 25" are given in Fig. 1. These data fit well the rate equation for solids, based on diffusion, as derived by Mason3 and checked by him on NaBr KC1 and CsCl KBr, and checked by Itiemen and Daniels4 on Rg2S04 CaO and SrO. The formula is
+
1
-x
= G / d
"
+
+
1
3 exp(--n21ct)
n=l
x is the fraction of the reaction a t time t, D is the diffusivity, a is the radius of particles, and IC is the rate constant = a2D/az; kt is evaluated from 1 z by I.B.M. calculations.' Figure 2 shows the Ict plot against time which permits a calculation of IC. For 55 p particles, IC is 0.039 day-', for 85 p , k is 0.019 day-' and for 285 p , IC is 0.002 day-'. Figure 3 shows that the rate constant k is inversely proportional to l / a 2 in agreement with the formula. The author is glad to acknowledge the help of Professor Farrington Daniels with whom this research was carried out and to acknowledge the support of the U. S. Atomic Energy Commission through Contract AT(l1-1)-178. DECOMPOSlTION OF HYDROCARBONS BY SILICA-ALUMINA CATALYSTS BY J. 1,. FRANKLIN A N D D. E. NICHOLSON Refining Technical and Research Divisions. Humble Oil and Refining Company, Baytown, Texas Received October I, 1066
The kinetics of the catalytic decomposition of eight low molecular woight hydrocarbons have been reported previously.' It was found that the eight hydrocarhons studied could be divided into two groups kinetically, tlepeilding on whether rates of disappearance of starting material obeyed a firstorder or a 1.5-order law. Some recent studies have shown that the activation energy for cracking of 2methylpropane remained constant, within experimental accuracy, as the specific surface of the catalyst was systematically varied from 303 to 81 sq. m. by heat and stleain sintering. These data are recorded in Table I.
Vol. GI TABLE I Catalyst ~ u r f a c earea, m.'/g.
Pore vol., 111I./g.
AB*, koal./mole
81 122 224 303
0.423 .477 ,507 515
30.7 31.5 29.8 30.0
I
The experimental procedure for making the rate measurements was described previously, On the basis of the data cited above, the average activation energy for the decomposition of 2-methylpropane on the different catalysts is 30.5 f 0.6 kcal./mole. An error was made it, the calculation of the activation energy for disappearance of 2-methylpropane as originally presented (AE* = 37.1 kcal./ mole) for the catalyst having specific surface of 81 sq. m. Thus the active centers on the silicaalumina catalysts of the investigation are shown to be quite similar in nature. It may be noted that, a linear relationship exists between the logarithm of the frequency factor (expressed per unit surface area) and the activation energy for decomposit,ion of all of the hydrocarbons obeying first-order kinetics. Such a relationship has been reported before in catalysis.2 (2) D. A . Dowdon, Rseearch, 1, 239 (194R).
NOTE ON T H E CALCULATION OF THE MOLECULAR WEIGHT DISTRIBUTION O F A LINEAR AMORPHOUS POLYMER FROM ITS RELAXATION DISTRIBUTION I N T H E RUBBERY REGION BY HIROSHI FUJITA A N D KAZUHIKO NINOMIYA Physical Chemiatry Laboratory, Department o j Fisherras, University a/ Kuoto, Mazauru, J a p a n Receiued October 6 , 1066
In a recent article' (hereafter referred to as Paper I) a method was presented by means of which the distribution of molecular weights in a linear amorphous polymer may be predicted from relaxation spectrum data obtained over the timescale of rubbery consistency. Stress-relaxation data on polyviiiyl acetate2 and on polystyrene' from this Laboratory were analyzed in terms of this method, with results in both cases which compared quite favorably with the observed data. No essential difficulty which would violate the basic assumptions of the theory was found in those applications, except for an apparent anomaly which appeared in the low molecular weight regions of the calculated molecular weight distributions. Since very extensive viscoelastic data recently have become available3 on a sample of high molecular weight polyisobutylene distributed by the National Bureau of Standards for an international cooperative program of dyriamic tests, it seemed of interest to use those data as a basis for the calculation of the molecular weight distribution, even though no experimental check of the results is possihle. It was found through this calculation that ( I ) 11. Piijita and K. Ninolniya, J . Poli/mer Bci., in press. (?) I
