DECOMPOSITION AND SYNTHESIS OF HYDROGEN IODIDE BY ALPHA PARTICLES' K E R E N GILMORE BRATTAINl
School of Chemistry, University of Minnesota, Minneapolis, Minnesota
Received August 1.4, 1997
The radiochemical decomposition and synthesis of hydrogen iodide have been studied by Vandamme (15) a t 20°C. and lOO"C., respectively. He used comparatively small amounts of radon. The author also studied these reactions under somewhat different conditions. The decomposition of hydrogen iodide by alpha particles was determined by two methods: (1) the rate of reaction was followed by pressure measurements, which were made a t 25OC.; ( 2 ) closed-system experiments were performed at 27", looo, and 2OO0C., and the amount of reaction determined by chemical analysis at the end of the experiment. Similar closed-system experiments on synthesis were made a t temperatures ranging from 25OC. to 200°C. EXPERIMENTAL PROCEDURE
In the first set of decomposition experiments the radon and hydrogen iodide were enclosed in a small bulb connected to a mercury manometer. The apparatus and procedure were the same as those employed by Lind and Bardwell (11). There was practically no contamination of the mercury until the experiment was well along. A phosphoric acid lubricant (13) was used on the stopcocks in all systems in which hydrogen iodide was present. The closed-system decomposition experiments were performed in reaction bulbs, with two capillary tubes connected along one diameter. These bulbs, which had an approximate volume of 60 cc., have been described by Truesdale and Lind (14). The experimental procedure was as follows: Small fragile glass ampoules filled with radon were sealed into the reaction bulb. The bulb was then connected to a highvacuum system and pumped for several hours. During this time it was washed with small volumes of hydrogen iodide. An approximate amount of hydrogen iodide was then frozen in the reaction bulb and the bulb was sealed off. Extreme care was taken to obtain a capillary tip that could be broken readily later. The ampoule containing the radon was broken, This article is based upon a thesis submitted by Keren Gilmore to the Graduate School of the University of Minnesota in partial fulfillment of the requirements for the degree of Doctor of Philosophy, August, 1932. * Present address: 270 West 11th Street, New York City. 617
618
KEREN GILMORE BRATTAIN
and the reaction bulb placed in a constant-temperature apparatus a t onre. A small electrically heated oven, constant to within &l"C., was used for all experiments with the exception of those run at 25OC and 27°C. I n these cases the bulbs TTere placed in a constant-temperature water bath. At the end of the experiment the bulbs were quickly cooled to room temperatllre, and one of the tips was broken off under a solution of potassium iodide A sufficient amount of the solution entered the bulb to dissolve the iodine. The second tip was broken, and the bulb rinsed with small amounts of potassium iodide. The resulting solution was used for the deteirnination of both the iodine and the remaining hydrogen iodide. Firat the amount of iodine present was determined by titration with sodiurn thiosulfate to a water-white solution. The acid was then titrated with sodium hydroxide, bromothymol blue being used as the indicator. A blavl; run wntaining no radon accompanied each experiment. From this the rmount of thermal reaction was obtained. 'Pie procedure used for the synthesis experiments was very similar to thn! cf the closed-system decomposition experiments described above. A fragdc glass ampoule containing iodine and one containing radon were introduced into the reaction bulb before it, was sealed onto the vacuum line. Thc~bulb was pumned and washed with hydrogen. A known volume of hydrogen was introduced in the reaction bulb from a Ramsay buret, and the bulb sealed off. The experiment was then performed in the manner given above. The following method was used for preparing the hydrogen iodide used in the decomposition experiments: First, a fuming solution of hydriodic arid was prepared, in an all-glass system, by dropping water on phosphorus and iodine. The resulting gas was passed through four traps cooled with an ice-salt mixture, and then into an absorption bulb containing distilled water. This bulb was also cooled by an ice-salt mixture. The solution thus prepared was stored in a refrigerator. The hydrogen iodide was prepared from the stock solution as it was needed by the following series of vacuum distillations. Twenty cubic centimeters of the hydriodic acid was placed in a distilling flask, and the flask was sealed onto a high-vacuum line The pumps were well protected with liquid air. The solution was frozen with carbon dioxide snow. The air was thoroughly pumped out of the system, and then the solution was allowed t o warm up slowly. The resulting gas was passed through a trap cooled with solid carbon tetrachloride, which removed most of the water vapor, then dried over phosphorus pentoxide. The hydrogen iodide was frozen down with liquid air and the system well pumped. The gas was then distilled through two traps cooled with carbon dioxide snow, and finally frozen in the reaction bulb with liquid air. For the decomposition experiments the hydrogen was prepared by the electrolytic decomposition of a potassium hydroxide solution. The gas from the generator was passed over palladinized asbes-
DECOMPOSITION
AND SYNTHESIS OF HYDROGEN IODIDE
619
tos, heated to 300°C., dried over phosphorus pentoxide, end stored in a 2-liter bulb. This bulb had been pumped and flushed with hydrogen several times previous to the storage. The iodine was purified by three consecutive sublimations (9) of chemically pure iodine obtained from the Mallinckrodt Company. The resublimed iodine was dried over calcium chloride in an ungreased desiccator and stored in a dark glass-stoppered bottle. For experimental use small quantities of the iodine were placed in fragile glass ampoules, pumped for an hour, and then sealed off. TABLE 1 Pressure decomvosition experiments
Expt. KO.I. Volume = 3.99 cm.3: T = 25°C.: R = 0.984 cm.; Eo = 125.9 mc. houra
0 1.o 2.0 3.0 4.0 8.0 12. 18. 24. 36.
mm.
597 558 514 482 453 405 390 370 356 327
mm.
mm.
507 520 431 367 309 213 182 143 115 57
38 83 115 144 192 208 227 241 270
0.161 0.295 0.405 0.496 0.764 0.965 1.20 1.38 1.57
Expt. No. 11. Volume = 11.50 cm.3; T = 25°C. 0 1.o 5.3 9.0 18. 25. 45. 69.
676 657 587 540 467 425 370 359
676 638 498 403 258 174 64 42
19 89 136 209 251 306 317
0.228 1.03 1.69 2.54 2.94 3.41 3.64
0.000 0.000 0.003 0.007 0.030 0.052 0.088 0.123 0.208
1.00 2.16 3.00 3.74 4.99 5.39 5.90 6.27 7.02
6.21 7.32 7.42 7.54 6.54 5.58 4.90 4.54 4.47
6 = 1.40 cm.; Eo = 103.8 mc. 0.006 0.020 0.041 0.106 0.160 0.371 0.533
1.44 6.67 10.3 15.7 18.9 23.0 23.2
6.31 6.48 6.08 6.20 6.43 6.73 6.37
The sodium thiosulfate used in the titrations was resublimed, and the solution standardized against a weighed amount of resublimed iodine. A water-white solution was used as the end point. The normality of the solution was redetermined a t various intervals. The sodium hydroxide solution was standardized against Mallinckrodt’s reagent quality oxalic acid with phenolphthalein as the indicator. EXPERIMENTAL RESULTS
The experimental results are given in tables 1, 2, and 3. The last four columns in table 1 will be discussed later. I n tables 2 and 3 the pressure
620
KEREN GILMORE BRATTAIN
of hydrogen iodide was calculated from the chemical analysis. The pressure of hydrogen in table 2 was calculated from the iodine analysis, since equal amounts of hydrogen and iodine are formed by the decomposition of hydrogen iodide. 111table 3 the hydrogen pressure was calculated from the Ranisay buret measurements. The vapor pressure of solid iodine was computed by the method of Giauque (4), and that of liquid iodine was TABLE 2 Closed-system decomposition experiments EXPT. NO.
REACTION TEMPERATURE
TlMB
BULB VOLUME
INITIAL RADON
Pkl
FINAL
PI, FINAL
- _ _ _ I _ _
1. . , . . . . , . . 2. . . . , . , . . . 3, .. , . . . . . .
4. , . .. . . . . . 5 ,.., , . , . .
“C.
hours
cm.1
millicuviea
mm.
mm.
mm.
27.5 27.5 100. 203. 203.
53.0 53.2 88.9 63 .8 63.5
54.9 57.2 57.2 54.9 57.2
41.2 31.7 30.1 13.9 15.1
383. 806. 252. 215. 212.
49.7 87.8 28.4 12.5 11.2
0.3 0.3 28.4 12.5 11.2
-___
TABLE 3 Synthesis experiments E m . NO.
REACTION TEMPERATURE
_I_.
‘C.
1. . , , , . . , 2 , ..., . , . 3. , , . , . . . 4. .... . . . 5. . . . . . . . 6. .. . .. . . 7,,. . .. . . 8 .. .. . .. 9 ...,.. . 10 . . . , , . . 11... . . . . . 12 . . . . . . 13. . . . . . . , 14 , . . . . . . 15. . . . . . . .
200 200 174 225 120 150 200 121 100 174 100 81 . O
54.7 25.0 25.0
BULB VOLUME
INITIAL
hours
cm.’
millicuries
mn.
mm.
mm.
58.9 59.0 211. 213. 209. 186. 183. 196. 213. 165.
58.3 57.0 58.4 58.5 56.9 58.4 57.1 56.9 56.4 56.9 56.4 57 .O 57.0 58.5 58.1
64.4 60.3 118.9 103.3 31.6 112.0 126.1 93.9 103.5 108.6 94.2
323. 320. 368. 346. 506. 530. 581. 570. 397. 676. 543. 687. 537.
285. 287. 358. 317. 109. 294. 353. 115. 45.9 70.3 45.9
26.8 27.3 80.6 81.6 27.9 99.4 129. 74.0 51.5 63 .O 59.6 52.7 22.0 4.5 9.4
RADON
_ _ _ _ _ ____-
208.
208. 192. 216. 238.
100.0
100.2
‘E1
‘is
FINAL
15.9
3.0 0.3 0.3
obtained from the data of Ramsay and Young (12). In all the synthesis experiments performed at temperatures below 150°C. a sufficient amount of iodine was present to maintain a constant pressure. In the experiment performed at 15OoC. the pressure of iodine was constant only during the first part of the run. The vapor pressure of iodine at this temperature is 294 mm. The amount of iodine introduced was sufficient t o give a pres-
DECOMPOSITION AND SYNTHESIS OF HYDROGEN IODIDE
621
sure of 309 mm. The final pressure of iodine was 259 mm. The initial pressure of iodine for all the synthesis experiments above 150°C. was obtained by adding one-half the calculated pressure of hydrogen iodide to the final pressure of iodine obtained from analysis. The number of molecules of hydrogen iodide where given as yields has been corrected for thermal reaction. These corrections were small. CALCULATIONS AND RESULTS
In order t o analyze the data it is necessary to determine some measure of the excitation produced by the alpha particles in each of the gases present. The accepted method for doing this is to calculate the number of ion pairs formed. The total number of ion pairs formed in the gaseous mixture was obtained from the following equation. where N L = total number of ion pairs formed, N o = number of alpha particles per curie of radon (1.764 X (61,
E
= number of curies of radon decomposed (corrected for non-
equilibrium decomposition) (14), g = specific ionization in gaseous mixture (7), F’= efficiency factor (6), and k ( r ) f = number of ion pairs produced by an alpha particle in its range in air (N.T.P.) (1.55 X IO5) (6). A slight modification of this equation was used for the calculation of the pressure experiments. An average F’ was calculated for each interval. This value was then used in calculating the number of ion pairs formed during each interval. The total number of ion pairs a t any time was then obtained by addition. The number of ion pairs formed in each component of the system was calculated from the following equation,
where s = stopping power and p = partial pressure of the component. The summation is over all components present. In the closed-system experiments the arithmetical mean of the initial and final pressures was used in all calculations. The stopping power of iodine was taken as 3.70 (5) and that of hydrogen iodide as 1.97, computed as an additive property from values of stopping powers of hydrogen and iodine. The values 1.31 (8) and 1.29 (IO) were used for the specific ionization of iodine and hydrogen, respectively. The results of the calculations for the decomposition of hydrogen iodide
622
REREN GILMORE BRATTAIN
are given in tables 1 and 4. In figure 1 the number of molecules of hydrogen iodide decomposed is plotted against the number of hydrogen TABLE 4 Decomposition results E m . NO.
RADON DECOYPOBEI)
N E , X 10-19
N E 1 X 10-19
N,,
x
10-1s
ME, x
10-10
G I
____.
millicuries
1. . . . . . . . . . 2. . . . . . . . . . 3. . . . . . . . . . . 4. . . . . . . . . . 5 ......... l*. . . . . . . . . 2*, . . . . . . . . 3*. . . . . . . . . 1'. . . . . . . . . 2*. . . . . . . . . 3*. . . . . . . . . 4*. . . . . . . . .
13.5 10.4 14.6 5.28 5.71 13.1 12.4 10.4 7.98 7.95 8.22 8.25
3.28 5.38 1.84 0.450 0.490 5.06 6.26 6.10 4.62 3.26 3.62 1.20
* Calculated from Vandamme's
0.02 0.03 0.01 0.001 0.001 0.02 0.03 0.03 0.01 0.01 0.01 0,004
0.005 0.004 0.22 0.027 0.026 0.009 0.008 0.006 0.004 0.005 0.005 0.004
17.7 32.5 8.37 2.52 2.32 36.9 46.0 59.1 30.8 26.6 20.9 10.8
5.38 6.04 4.55 5.60 4.74 7.28 7.33 9.69 6.67 8.16 5.78 9.03
data.
12
EXPERIMENT N O 1 3 9 9 C M ' EXPERIMENT N O I I I1 5CM'A o -CLOSED. SYSTEM EXPERIMENTS A -VANDAMMES RESULTS -PRESSURE
x -PRESSURE
H I
IO2 0
2
1018
"I
FIG.1. Decomposition of hydrogen iodide
iodide ion pairs. It is seen that on the whole the amount of decomposition is proportional t o the hydrogen iodide ion pairs, and that for each
DECOMPOSITION AND SYNTHESIS OF HYDROGEN IODIDE
623
ion pair 6+ molecules of hydrogen iodide are decomposed. The various points scatter to some extent, and Vandamme’s results are on the average a little higher than the author’s. This last fact could be caused by differences in radon standards. The simplest explanation of the reaction is that, on an average, for each hydrogen iodide ion pair produced by an alpha particle two activated hydrogen iodide molecules are also produced. TABLE 5 Synthesis results E X P T . NO.
1. . . . , . . , 2. . . , . , . . 3. , . . . . , . , 4. .. , . ... 5. . . . , . . . 6. ., .. . . , . 7. . . . . , . . 8,. .. . . . , , 9. , , . . .., , 10. . . . . . . , . 11... . . . . , , 12. , , , . . . . , 13 . . . . . . , , 14. , . . , . , , , 15. . . . . . , , , l*. . . , . , . , 21. . . . . . . . 3*. . . . . . , . I*., . . , . . , 2*. . . . , . . . 3*. . . . . . . .
YKZ
x
10-10
0.333 0.312 1.64 1.19 0.626 2.26 2.44 2.04 1.64 2.24 2.02 2.88 2.37 3.16 3.18 0.206 0.218 0.414 0.036 0.171 0.245
‘iHI
x
10-11
0.149 0.145 2.02 1.59 0.187 2.35 3.04 1.45 1.16 1.13 1.20 1.20 0.518 0,147 0.298 0.031. 0.029 ,.056 0.005 0.012 0.013
N ~ x,
10-19
5.92 5.64 32.4 22.0 2.78 25.3 28.8 8.60 3.98 3.72 3.54 1.38 0.266 0.038 0.036 1.29 1.18 1.24 0.614 0.625 0.556
MI*
x
10-11
33.2 32.7 42.7 33.6 15.4 37.5 37.8 16.1 6.75 6.74 6.75 2.49 0.503 0.059 0.059 20.8 20.6 19.0 23.4 20.1 18.4
ME,
x
lo-’’
2.71 2.69 10.1 8.11 3.79 12.9 13.9 10.3 6.95 7.80 8.32 8.23 3.71 0.83 0.89 1.88 1.94 3.27 0.787 1.51 1.64
* Calculated from Vandamme’s data.
0.082 0.083 0.235 0.241 0.246 0.343 0.367 0.640 1.03 1.16 1.23 3.30 7.39 14.1 15.0 0.090
0.094 0.172 0.034 0.075 0.089
0.094 0.090 0.261 0.217 0.260 0.322 0.298 0.597 1.03 1.61 1.35 5.65 25.9 32. 25. 0.074 0.078 0.145 0.017 0.060 0,090
-
Each of these three reacts with a neutral hydrogen iodide molecule, thus giving a net result of six molecules decomposed.
+ -+HI+ + + e + -+ HI’ + a ] HI+ + H I -+ Hz + I+ 2[HI’ + H I Hz + HI
CY
2[HI
CY
CY
--j
121
The reaction, of course, may be much more complicated, but this mechanism is sufficient to explain the facts. In these decomposition experiments the number of hydrogen ion pairs was always so small as to be negligible, except possibly in the last two or
624
KEREN GILMORH BRATTAIN
three points of the pressure runs. Consequently no conclusions can be drawn from these data as to the effect of the hydrogen ion pairs on the reaction. The highest pressure of iodine occurred in the closed-system experiment S o . 3. In this experiment the average iodine pressure was one-fifteenth that of the average hydrogen iodide pressure. An iodine pressure of this relative magnitude appears to have no effect on the yield, provided one considers only the ion pairs formed in hydrogen iodide. The calculated results for the synthesis of hydrogen iodide are given in table 5. These data are not so easy to analyze. The reasons for this are obvious. One has a complicated mixture of three components and the ion pairs due to each component. In a general way one can say that the amount of synthesis should be some function of the various types of ion pairs present.
where MHI is the yield. In analyzing these data the author found it a distinct advantage to consider ratios instead of absolute magnitudes. The particular ratios that were found useful were the various magnitudes divided by the average number of molecules of iodine present (M12). The synthesis results consist of the measurements of the yield a t the end of a long run. Since the number of ion pairs of the components varies throughout the run, and since back reaction is always possible, the yield is probbably given accurately only in terms of a complicated integral. However, an attempt was made to analyze the data using average values. From the results of this analysis the author has come to the conclusion that this procedure is justified where these data are concerned. As a first trial the author made the assumption that only the hydrogen ion pairs were effective in the synthesis of hydrogen iodide, and that the ion pairs of iodine and hydrogen iodide could be neglected. Figure 2 is a plot of MHI/M12versus NH,/M12. The data of Vandamme and of the author give results which follow a straight line. This relationship can be approximately represented by the following equation.
where k is a constant. Since the yield is not proportional to the hydrogen ion pairs, it would appear that there were other factors involved in the reaction. Therefore the assumptions were too simple. The relationship does indicate, however, that there is no large discrepancy between the results of Vandamme and those of the author. An attempt was made to see if a reasonable amount of back reaction would account for the fact that, the yield is not proportional to the hydrogen ion pairs. Farkas and Bonhoeffer (3) report that in equal mixtures of hydrogen iodide and iodine a
DECOMPOSITION AND SYNTHESIS OF HYDROGEN IODIDE
625
hydrogen atom combines one hundred times more readily with an iodine molecule than with a hydrogen iodide molecule. It was found that a back reaction based on the probability of a hydrogen atom reacting fifty to one hundred times more readily with iodine than with hydrogen iodide would affect only the last few points for large values of M H I / M ~ ~ These . points are seen to deviate from the straight line anyway, and in a direction which could be accounted for by a back reaction. No assumed value of the relative probability of these two reactions would make the yield proportional to the hydrogen ion pairs over any appreciable range. The next logical assumption which might be made is that the hydrogen iodide ion pairs as well as those of the hydrogen affect the yield. An examination of the possible reactions of an excited hydrogen iodide mole-
X-VANOAMMES
-3
10-2
RESULTS
IO
IO
o2
I
FIQ.2. Synthesis pf hydrogen iodide. MHIIMI, plotted against NHJMI,
cule indicates that the products of ionization or activation of hydrogen iodide could at most react with hydrogen or iodine in such a way that the net hydrogen iodide formed or decomposed is zero. Therefore the only effect of the hydrogen iodide ion pairs would be the decomposition of neutral molecules of hydrogen iodide. The simplest way of considering the effect of both the hydrogen and hydrogen iodide ion pairs is to assume that it is proportional to the number of ion pairs of each gas present.
where a and b are constants. The values of the constants which gave the best correlation were a = 10 and b = -4. However, the correlation a t
626
KEREN GILMORE BRATTAIN
best was very poor. Work by Eyring, Hirschfelder, and Taylor (1, 2) would indicate that six molecules of hydrogen iodide should be formed per hydrogen ion pair instead of ten. An examination of the data on the basis of the above correlation made it appear that the reaction was also dependent upon the number of ion pairs formed in iodine. An assumption was then made that each of the different ion pairs present affected the synthesis according to the following relationship.
It was found that the data of Vandamme and of the author could be well represented by equation 6, when the constants a, b, and c have the values
X-VANDAMME3 R E S U L T S .-AUTHOR'S RESULTS
6 4 NH - 4
0 NHrt O . 2 7 N
12
MI2
FIG.3. Synthesis of hydrogen iodide
6.4, - 4.0, and 0.27, respectively (table 5, column 8). A plot of this relationship using these constants is given in figure 3. The relationship indicates that 6.4 molecules of hydrogen iodide are formed per hydrogen ion pair. The value of the constant b is surprisingly high. However, it is possible that for every hydrogen iodide ion pair an average of two ionized or activated hydrogen iodide molecules will react with neutral hydrogen iodide molecules, thus causing a counter reaction. If the assumptions underlying equation 6 are correct, the data indicate that a small fraction of the iodine ion pairs react with hydrogen to form hydrogen iodide. There are two possible reactions which might explain this effect. First, a neutral hydrogen molecule may cluster with an :1 ion. The reaction of an electron with this cluster could give two molecules of hydrogen
DECOMPOSITION AND SYNTHESIS OF HYDROGEN IODIDE
627
iodide and excess energy. Second, it is also possible for an excited iodine molecule to react with a hydrogen molecule to form hydrogen iodide and excess energy. The explanation of the data by equation 6 requires only that one excited or ionized iodine molecule react for every seven ion pairs formed in iodine. We see in figure 3 that the last few points, for large values of M H I / M I ~ , still deviate from the straight line. This is probably the effect of the back reaction, which has been discussed in the first attempt to analyze these data. The deviation of these points could also be caused by the fact that in these experiments the pressure of the iodine is so low that a large portion of the excited hydrogen may become deactivated without coming in contact with iodine molecules. The number of the points and the accuracy of the data in this region are probably not sufficient to decide definitely between these two possibilities. The data, however, are not inconsistent with the probability that the activated hydrogen reacts one hundred times more readily with iodine than with hydrogen iodide. The author has also attempted to analyze these data on assumptions similar to those used by Eyring, Hirschfelder, and Taylor (2) to explain both the radiochemical synthesis and back reaction of hydrogen bromide, but arrived at the conclusion that these results can not be explained on this basis. The constants used for the stopping power of iodine and hydrogen iodide and for the specific ionization of iodine are more or less assumed values, because they have never been experimentally determined. Some experimentation with changes in these values indicated that the results were of the same general character, regardless of the exact values assumed for these constants. From such results it does not appear probable that the explanation of the synthesis reaction could be simplified by assuming different values for the specific ionization of iodine and the stopping power of iodine and hydrogen iodide. SUMMARY
It has been found that the work of Vandamme and of the author, on the decomposition of hydrogen iodide by alpha particles, can be explained on the basis that 6s molecules of hydrogen iodide decompose per hydrogen iodide ion pair. The experiments of Vandamme and of the author on the synthesis of hydrogen iodide give data for this reaction over a range of iodine pressure from 0.3 to 350 mm. All the data can be explained on the following basis: ( I ) for every hydrogen ion pair 6+ molecules of hydrogen iodide are formed; ( 2 ) for every seven iodine ion pairs 1 molecule of hydrogen iodide is formed; (3) for every hydrogen iodide ion pair 4 molecules of hydrogen iodide decompose. There is a further indication, from a few of the
628
KEREN GILMORE BRATTAIN
author’s runs at very low iodine pressure, that either an appreciable back reaction takes place, or not all the hydrogen ion pairs are used up in syntheses. The author wishes to express her thanks and appreciation to Professor
S. C. Lind under whose direction this research was done, and to Professors R. S. Livingston and George Glockler for their aid and criticism in the calculation of the experimental results. REFERENCES
(1) EYBING,HIRSCHFELDER, AND TAYLOR: J. Chem. Phys. 4, 479 (1936). AND TAYLOR: J. Chem. Phys. 4, 570 (1936). (2) EYRING,HIRSCEFELDER, AND BONHOEFFER: 2. physik. Chem. 132, 235 (1928). (3) FARKAS (4) GUUQUE: J. Am. Chem. SOC.63, 507 (1931). (5) GLASSON:Phil. Mag. [6]43, 477 (1922). AND HEISIG: J. Phys. Chem. 36, 769 (1932). (6) GLOCKLER AND LIVINGSTON: J. Phys. Chem. 38, 655 (1934). (7) GL~CKLER (8) KLEEMAN:Proc. Roy. SOC.(London) A79, 220 (1907). (9) KOLTEOFFAND FURMAN: Volumetric Analysis, Vol. 11, Practical Principles, p. 357. John Wiley and Sons, New York (1929). (10) LIND: The Chemical Effects of Alpha Particles and Electrons, revised edition. The Chemical Catalog Go., Inc., New York (1927). (11) LINDAND BARDWELL:J. Am. Chem. SOC.47, 2679 (1925). (12) RAMSAY AND YOUNG:J. Chem. SOC.49,453 (Im6). (13) STEPHENS,H. N.:J . Am. Chem. SOC.63, 625 (1930). AND LIND: J. Am. Chem. SOC. 64, 516 (1932). (14) TRUESDALE Bull. soc. chim. Belg. 41, 597 (1932). (15) VANDAMME: