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BIBLER, Ned Eugene, 1937- THE TRITIUM BETA-RAY INDUCED REACTIONS IN DEUTERIUM OXIDE VAPOR AND HYDROGEN OR CARBON MONOXIDE AND THE EXCHANGE OF H-ATOMS WITH WATER MOLECULES.
The Ohio State University, Ph.D., 1965 Chemistry, physical
University Microfilms, Inc., Ann Arbor, Michigan THE TRITIUM 3ETA-RAY INDUCED REACTIONS IN DEUTERIUM
OXIDE VAPOR AND HYDROGEN OR CARBON MONOXIDE AND THE
EXCHANGE OF H-ATOMS WITH WATER MOLECULES
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
Ned Eugene B ib le r , B .S ., M.S
* * * * *
The Ohio S ta te U n iversity 1965
Approved by
Adviser Department of Chemistry ACKNOWLEDGMENTS
Several groups were influential in the completion of this work and the culmination of my graduate career at the Ohio State
University. I have singled out two who deserve special acknowledg ment.
I wish to express my appreciation to the members of my family for their understanding and sympathetic guidance during this demanding period. In particular, I thank my wife, Jane, who was a source of encouragement, for her devotion, scientific advice, and unswervingly honest criticism ; and my mother in law, Mrs.
Pauline Pycraft, who typed a major portion of the first draft of this thesis.
I am indebted to the stimulating research group headed by
Dr. R. F. Firestone for many fruitful discussions and altercations on an array of subjects, including the radiation chemistry of water vapor. Specifically, I thank Dr. Firestone for his keen interest and set of high scientific standards which, when applied to the course and completion of this study, made it a maturing and g r a tify in g experience. VITA
July 25, 1937 Born - Bucyrus, Ohio
1959 .... B.S., Denison University, Granville, Ohio
1959 - 1962 . Teaching Assistant, Department of Chemistry, The Ohio State University, Columbus, Ohio
1962 .... M. S., The Ohio State University, Columbus, Ohio
1962 - 1965 . Research Fellow, Department of Chemistry, The Ohio State University, Columbus, Ohio
i i i CONTENTS
Page
ACKNOWLEDGMENTS ...... i i
VITA...... i i i
TABLES ...... v
ILLUSTRATIONS ...... v i i
Chapter
I . INTRODUCTION...... 1
I I . HISTORICAL REVIEW ...... 4
I I I . EXPERIMENTAL APPARATUS AND PROCEDURES ...... 10
Reagents Apparatus Procedures
IV. EXPERIMENTAL RESULTS ...... 6 8
Hydrogen:water vapor systems Carbon monoxide:water vapor systems
V. DISCUSSION...... 85
VI. CONCLUSIONS...... 146
BIBLIOGRAPHY . . . . ; ...... 148 TABLES
T ab le Page
1. Amount of Impurities Present in the Carbon Monoxide . . . 11
2. Calibration of the Metering T ube...... 22
3. Determination of Vtotal/Vcal T°r ^1 ...... 33
4. Determination of Vtotal/^cal - Vunk for ...... 35
5. Determination of V3 ...... 37
6 . Calibration of the Gas Chromatograph Using Deuterium . . 41
7. Variation of the Ratio Time ...... 46
8 . Isotopic Ratios in the Calibration Standards ...... 49
9. Ratio of the Mass 3 Signal to the Mass 2 Signal in H2 . . 50
10. Observed Signal Ratios R^ 3 and R/j.^2 an a Mixture of 2.06% HD and 6 x 10"7% D 2 ...... 51
11. Pressure Dependence of R2 , 3 anc* ^ 3 , 2 ...... ^
12. Pressure Dependence of R§?2 a Mixture when the Ratio
nH c/nU2 is 0 , 0 2 ...... 53 13. Dependence of the Sensitivity Ratio H on the Sample Com position ...... ’ .2 ...... 54
14. Variation of R^L u w ith Sample Pressure in HD 9 2 Syn thetic M ixture No. 2 . (13% H D )...... 55
15. Determination of nHE/nH2 *n ExP®riment 49 when the values of R^^ are Pressure Dependent...... 56
16. Comparison of kD 2 pp as Determined by the Equilibrium and Synthetic Mixtures ...... 58
17. Assay of the Tritium-Water...... 62
v TABLES ( c o n td .)
T able Page
18. Results of the Mass Spectrometric Determination o f nHD/n H2, nD2/n HD, and 70
19. Values of G(HD), G(D2), G(T) and the Separation Factor Below 245°C 72
20. E ffect o f Temperature Above 266°C on G(HD), G(D2 ), G(T), and the Separation Factor at a Vapor Density of 0.595 m g/m l...... 75
21. E ffect o f Temperature Above 297°C on G(HD), G(D2 ), G(T) and the Separation Factor a t a Vapor D ensity o f 0.319 mg/ml...... 76
22. Effect of Changing the Mole Fraction of H2 a t 320°C and Vapor Densities of 0.590 m g/m l...... 78
23. Effect of Changing the Mole Fraction of H2 a t 319°C and Vapor Densities of 0.319 m g/m l...... 78
24. E ffect o f Changing the Vapor D ensity on G(HD), G(D2 ), G(T) and the Separation F a c t o r...... 80
25. The Results of an Experiment in which a Large Percentage of Hydrogen was Converted to Hydrogen Deuteride ...... 80
26. The Effect of Temperature and the Mole Fraction of CO on G(C02), G(D2), G(T), and the Separation Factor .... 82
27. Mass Spectrum of the Samples Collected at -78°C ...... 84
28. Values o f G(D)/G(HD) and iA h2 Taken from the Data of Baxendale and G ilbert...... 135
29. Comparison of the G Values for the Chain Mechanism at 278°C for the D2 0tH2 and the H20:D2 S y s t e m s...... 142
v i ILLUSTRATIONS
Figure Page
1. Sample Preparation Vacuum System...... 13
2. Collection Vacuum System ...... 14
3 . Io n iza tio n Chamber ...... 16
4 . Mass Spectrometer I n le t S y s t e m...... 18
5. Calibration of the Metering Tube ...... 23
6 . Samplers ...... 27
7. Determination of V totalA cal ...... 34
8 . Determination of VtotalAcal " ^unk...... ^
9. Chromatograph Calibration ...... 42
10. Effect of Time on the Ratio Rhd,H2 * ...... ^
11. Temperature Dependence of G(HD), Vapor D ensity of the Chain Region is 0.595 mg/ml ...... 94
12. Temperature Dependence of (G(HD)-G(HD)0 ) at Vapor D e n sitie s of 0.319 mg/ml and 0.595 mg/ml ......
13. Temperature Dependence of (G(T)-G(T)0) at Vapor D e n sitie s o f 0.319 mg/ml and 0.595 m g / m l...... H °
14. Temperature Dependence of G(D2) and G(C02) in the D2 0 sC0 S y s te m...... ^ 2
15. Temperature Dependence of (G(D2 ) - G(D2 )g ) a t a Vapor Density of 0.319 m g/m...... l *2 2
16. Variation of (G(HD) - G(HD)0) with Vapor Density at 319°C ...... 12 2
17. Yield of HD in the D2OSH2 System. Taken from Baxendale and Gilbert, Disc. Faraday Soc., 36, 295 (1963) ...... 1 3 4
v i i ILLUSTRATIONS (con td .)
Figure Page
18. Kinetic Analysis of the Data of Baxendale and Gilbert . . 134
19. Comparison of G(HD) for the Radiolysis of the D2 0 :H2 and H2 0 :D2 S y ste m s...... 138
20. The Separation Factor at Several Temperatures ...... 138
v i i i CHAPTER I
INTRODUCTION
The object of this research was an examination of the chemical reactions induced by ionizing radiation in mixtures of heavy water
(D2 O) and hydrogen or carbon monoxide.
It has been observed that exchange reactions occur in isotopic mixtures of water vapor and hydrogen which are exposed to high energy 1—3 ^ radiations. More specifically, R. F. Firestone has reported0 th at hydrogen deuteride is formed by the tritium beta ray radiolysis of normal water (HgO) in the presence of small amounts of deuterium (D2 ).
The rate of the exchange was essentially constant between 84°C and
150°C, but above this range it increased exponentially with the temper ature. It was decided to repeat Firestone’s experiments using the exact isotopic analog of the system which he studied; that is using heavy water and hydrogen. Since the ratio of the amounts of water vapor to hydrogen in the two systems was almost identical, the effect of isotopic substitution on the radiolysis and the subsequent reactions
(1) J. H. Baxendale and G. P. Gilbert, Disc. Faraday Soc.. 36, 295 (1963).
(2) J . Y. Yang and L. H. Gevantman, J . Phys. Chem. ,6 8. 3115 (1964).
(3) R. F. Firestone, J. Am. Chem. Soc., 79, 5593 (1957).
1 2
could be evaluated.
Mixtures of D20 , l c f 4 mole % TOD, and 0 .3 to 1 .0 mole % H2 were heated at temperatures ranging from 84°C to 381°C for varying lengths of time. The amount of sample used was always adjusted to insure that the pressure in the reaction vessel was less than the vapor pressure of water at the temperature of the experiments.
After the desired length of time, the hydrogen was collected from the mixtures and analyzed for hydrogen deuteride. In addition to studying the exchange of D atoms, the sensitive analytical procedure for the determination of tritium afforded the method for obtaining data for the exchange of T atoms between the tritiated water molecules and hydrogen.
The large rate of the exchange reaction above 150°C reported by Firestone indicates that a chain reaction sequence is occurring.
It was proposed in his paper that the exchange mechanism involved atoms and radicals produced by the radiolysis. There are then two possible reaction sequences which lead to the chain production of hydrogen deuteride. The first involves an exchange reaction (1) followed by H atom attack of deuterium (2), while the second is a series of two abstraction reactions, (3) and (4). The last sequence
D + HOH —* HOD + H (1 )
H + D2 — ? HD + D (2)
D + HOH —s- HD + OH (3)
OH + D2 — > HOD + D (4) 3 was said to be negligible in its contribution to the formation of
HD because of the endothermicity of reaction (3).
R. A. Back and A. Y.-M. Ung^ have shown that carbon monoxide
is oxidized to carbon dioxide by hydroxyl radicals produced by the
photolysis of water vapor. It was thus thought that a study of the
production of carbon dioxide in gaseous mixtures of D2 O, 10”^ mole %
TOD, and 1 to 7 mole % CO would elucidate which of the proposed
mechanisms is occurring in the H2OSD2 system above 150°C.
(4) R. A. Back and A. T.-M. Ung, Can. J. Chem., 24. 753 (1964). CHAPTER I I
HISTORICAL REVIEW
The subject of the radiation chemistry of water, or the chemical effects induced in water by ionizing radiation, has been thoroughly 1 9 reviewed in two books. ’ An excellent review has also been presented by Schwarz in which the modes of formation of the different reactive species, H, OH, and e~q^, and the rate constants for their dis appearance are discussed. Reading any of these references leads one to the conclusion that the effects on liquid water have been studied much more extensively than those in gaseous water. The excellent monograph by S. C. Lind^ discusses the radiation chemistry of water vapor and other gases and reviews the significant experiments performed before I960.
In 1913, Duane and Scheuer^ studied the formation of hydrogen resulting from the irradiation of water vapor by the alpha particles
(1) A. 0. Allen, "The Radiation Chemistry of Water and Aqueous Solutions," D. Van Nostrand Co., Inc., New York, 1961. (2) J. W. T. Spinks and R. J. Woods, "An Introduction to Radiation Chemistry," John Wiley and Sons, Inc., New York, 1964. (3) H. A. Schwarz in "Advances in Radiation Biology," Vol. 1, L. G. A ugenstein, R. Mason, and H. Q uastler, e d s ., Academic P ress, 1964. (4) The symbol e^q represents the solvated electron which has been shown to be one of the reducing sp ecies formed in the radiolysis of liquid water. (5) S. C. Lind, "Radiation Chemistry of Gases," Reinhold Publishing Corp., New York, 1961. (6 ) W. Duane and 0 . Scheuer, Le Radium. 10. 33 (1913).
4 5
from radon gas mixed with the water. The yield of hydrogen is reported as 0 . 0 2 molecules formed for every ion pair formed in the water by the radiolysis. This corresponds to an upper lim it of the
G value for hydrogen production of 0.06. 7 In a la te r work Gunther and Holzapfel® found that the G value for the production of hydrogen was greater than 3.0 when they irradiated xenon and water vapor with x-rays from an external source.
In 1957 Firestone^ studied the radiation chemistry of water vapor by using tritium as the source of the radiation. His results on the irradiation of pure water agreed with those of Duane and
Scheuer when the reaction vessels were thoroughly outgassed. Also he found that an isotopic exchange reaction between water vapor and deuterium occurs readily in the presence of ionizing radiation and has the stoichiometry corresponding to reaction (l). The G value for the exchange
H20 + D2 HD + HOD (1) was 11.6 and constant between 84°C and 150°C. Above 150°C it increased with .an apparent activation energy of 18 Kcal/mole. On the basis of the proposed mechanism, this G value also corresponds to the number of water molecules that undergo a chemical change
(7) G value - 3 x ion pair yield. See page 6 of Reference 3. The G value i s defin ed as the number of m olecules formed or decom posed per 1 0 0 electron volts of energy absorbed by the system. (8 ) P. Gunther and L. Holzapfel, Z. phsik. Chem., B42, 346 (1939). (9) R. F. Firestone, J. Am. Chem. Soc.. 79, 5593 (1957). 6
as the result of the absorption of 1 0 0 ev of energy.
Pure water vapor was again irra d ia ted in 1963 by Hoffman and h is co-workers.10 Exposure of the vapor to alpha particles emitted from a capsule of Po-210 in the vapor caused hydrogen to be formed at a rate corresponding to a G value of 5.9 in agreement with that obtained by Gunther and Holzapfel. The difference of these results from those of F ireston e and Duane and Scheuer was a ttrib u ted by them to the fa c t that the source of the radiation was distributed homogeneously through out the vapor in the experiments of the latter workers.
Baxendale and Gilbert^ irradiated water vapor in the presence of small amounts of methanol, cyclohexane, and ether at 116°C using
Co-60 gamma rays. The scavenger molecules presumably reacted with
H atoms formed by the radiolysis to produce hydrogen. The G value for its production, which was again, according to their proposed mechanism, equal to that for the decomposition of water, was 8 . 0 .
This value is lower than 11.7 reported previously.^ They also irradiated heavy water^ (D2 O) and reported that the G value for the isotopic exchange with hydrogen to produce hydrogen deuteride
(HD) was 10.5 while that for the production of hydrogen deuteride by the reaction of D atoms with methanol or propanol was 7.0.
(10) H. S. Hoffman, N. R ieh l, W. Rupp, and R. Sizmann, Radiochimica Acta. , 1, 203 (1963). (11) J. H. Eaxendale, and G. P. Gilbert, Disc. Faraday Soc., 36. 186 (1963) (12) Ibid., p. 516. 7
Deuterium (D2 ) was found in these mixtures after the irradiation, and the G value for its production was determined to be 0.5.
According to their reasoning deuterium cannot be formed from heavy water via a thermal atom mechanism. Recently these authors reported^ that the presence of trace amounts of nitrous oxide decreased the G value for hydrogen formation from 8.9 to 5.9 in the radiolysis of water vapor in the presence of methanol. They attributed this to the reaction of nitrous oxide with reactive intermediates, presumably free electrons.
Knight and Anderson^ found that pure water vapor decomposed very little in the presence of ionizing radiation, in agreement with
F ireston e, and Duane and Scheuer. They a lso added tra ces of ammonia and calculated from the G value for the production of hydrogen and nitrogen in a free-radical mechanism that the G value for the decomposition of the water was in the range of 6.4 to 7.2 as found by Baxendale and G ilb ert.
The G value for the yield of hydrogen in the radiolysis of light water was determined by Knight, Anderson, and Winter^.
In the presence of ammonia and oxygen or perdeuated benzene they found a G value of 0.47, in agreement with the value determined by
Baxendale and Gilbert for D2 production from heavy w ater.
(13) J. H. Baxendale and G. P. Gilbert, Science, 147, 1571 (1965). (14) A. R. Anderson and B. Knight, Disc. Faraday Soc., 36, 299 (1963). (15) A. R. Anderson, B. Knight, and J. Winter, Nature. 201, 3115 (1964). The exchange of tritiu m atoms from T2 for hydrogen atoms in
1 fit water vapor was recen tly studied by Yang and Gevantman. They observed a second order dependence of the rate of formation of tritiated water on the tritium concentration indicating, according to their mechanism, the formation of H atoms and OH radicals.
All of the results of these investigations can be rationalized by mechanisms which involve H atoms and OH radicals as the reactive intermediates which lead to thermodynamically stable products.
Data obtained with a mass spectrometer are helpful in explaining the process leading to these intermediates. The ion molecule 1V reaction (2) has been observed to occur very efficiently. Other
H2 0+ + H20 H3 0+ + OH (2) ionic species of the form H+(H2 0)n, where n may vary from 1 to8 , have been observed by Hogg and Kebarle1® using a specially designed high pressure mass spectrometer. Mixtures of 0.5 mm H2 O and 40 mm of He, Xe, or N2 were irradiated with alpha particles form Po-210.
The resulting ions then diffuse via a molecular leak into the magnetic field of the mass spectrometer and were analyzed. Unfor tunately, the low vapor pressures of water at reasonable temperatures have thus far limited the precision and sensitivity of their measure ments.
(16) J . Y. Yang and L. H. Gevantman, J . Phvs. Chem. . 6 8. 3115 (1964) (17) F. H. Field, J. L. Franklin, and F. V/. Lampe, J. Am. Chem. Soc. 79, 6132 (1957). (18) A. M. Hogg and P. Kebarle, J. Chem. Phvs., 42, 789 (1965). Reaction (2) is the source of the OH radicals, and the neu tralization of HgO+ by free electrons is presumed to be the source of the H atoms. Either one or two H atoms can be produced as the two following reactions illustrate. In either event, the overall result is the
H3 0+ + e~ — » H + H20 (3)
H3 0+ + e - --* 2H + OH (4) formation of H atoms and OH radicals in equal numbers.
Thus far no papers dealing with the radiolysis of mixture of water vapor and carbon monoxide have been published. CHAPTER I I I
EXPERIMENTAL APPARATUS AND PROCEDURES
Reagents
Deuterium oxide was donated by Dr. E. J. Hart of the Argonne
National Laboratory. This water had been purified at the Argonne
Laboratory by a method described in the literature-1- and was used with out further treatment. The deuterium content was estimated by Dr. Hart to be well over 9 9 percent.
Approximately twenty curies of carrier-free tritium were obtained from the Oak Ridge National Laboratory. This gas was diluted by a factor of sixty with deuterium and purified by passage through a palladium diffusion apparatus. When the gas was placed in a 2 1. flask, its pressure was approximately 0.5 atm at 25°C. These procedures were performed by a co-worker in this laboratory and thus w ill not be 2 described further. The details are available in another source.
This mixture was then used to prepare tritiated water.
Deuterium was obtained in a high pressure cylinder from the
Matheson Company who state its purity to be 98.5 atom percent deuterium.
This gas was also passed through the palladium diffusion apparatus and used without further purification.
(1) E. J . Hart, S. Gordon, and D. A. H utchison, J . Amer. Chem. Soc. , 75, 6165 (1953).
(2) R. H. Lawrence, Ph.D. dissertation, Ohio State University, Columbus (1965). 10 11
Deuterium hydride was obtained from Merck, Sharp and Dohme, Ltd, of Montreal, Canada in a one liter Pyrex flask closed with a break- seal. The purity of this material according to their specifications was 98 atom percent deuterium . I t was used without fu rth er p u r ific a tio n .
High purity protium (H2 ) was purchased from the Matheson Company in a one liter Pyrex flask which was closed with a break-seal. The lim its of the impurities according to their specifications were nitrogen,
0.03 mole percent; carbon dioxide, 0.005 mole percent; and water,
0.001 mole percent. This gas was used without further purification.
Carbon monoxide was obtained from the Matheson Company in a one liter flask closed with a break-seal. This reagent was analyzed mass spectrometrically by the Air Reduction Sales Company, Riverton, New
Jersey. The results of their analysis are given in Table 1. The gas was used without further purification.
TABLE 1
Amounts of Im purities Present in the Carbon Monoxide
Concentration Impurity ppm(v/v)
Iron Carbonyl 5 Hydrogen 190 Oxygen 4 Carbon Dioxide 1140 Argon 24 Methane and ethane were Phillips Petroleum Research Grade and used without further purification.
Apparatus
Two Pyrex high vacuum systems were used in this study. Figure
1 illustrates schematically the system used for the preparation of the tritium water and the reaction mixtures. Pressures on the order of lo r 6 mm were maintained by an oil diffusion pump which was obtained from D istillation Products, Inc. and filled with 55 cc of Octoil manufactured by Consolidated Vacuum Corporation. An ionization gauge, purchased from the National Research Corporation, Cambridge, Massa chusetts, was used to measure the pressure. The other system shown in Figure 2 was employed for the collection of gases after the reaction had occurred. A single stage mercury diffusion pump was used on this system and pressures, as measured by a McLeod gauge, of approximately lCT^ were maintained.
The controlling relay of the automatic Toepler pump was triggered by changes in capacitance of two copper coils caused by the rise and fall of the mercury instead of the conventional device allowing the mercury to make or break the circuit directly. This method of control avoided equilibration of isotopic mixtures of hydrogen which might have been induced by sparking between the mercury and the direct contacts of a conventional Toepler relay circuit. The forepumps of both systems were Duo-Seal vacuum pumps; catalog No. 1400 of the
W.M. Welch S c ie n tific Company, Chicago, I l l i n o i s . TD CO
Pumps
Ionization Gauge Nichrome Quartz Wire Furnace Combustion Tube Reservoir Metering Tube
Reaction VesseI Figure I. Sample preparation vacuum system. pumps
joint mm scale F=0
Cold ' ^ traps
Reaction vessel
Pump control j~ To pump
Toe pie r Gas McLeod pump buret gauge
Figure 2. Collection vacuum system. 15
Vacuum stopcocks, Pyrex No. 7544, were used in both systems and were lubricated with Apiezon N stopcock grease.
A sand bath, purchased from Techne (Princeton) Ltd., Princeton,
New Jersey, was used to obtain the temperatures desired in this
study. Sand which had been screened to approxim ately 80 mesh was
fluidized in an insulated stainless steel container by means of
compressed air flowing through a porous ceramic plate in the bottom
of the container. A heater, rated at 750 watts at 100/120 volts AC was just below this plate. The working volume in the bath was a
cylinder approximately 4.5 inches in diameter and 7 inches high.
Various temperatures could be maintained by adjusting the voltage to
the heater with a Variac and the maximum obtainable temperature was
390°C.
Temperature stability was maintained with the potentiometer
controlled switch manufactured by the Foxboro Company, Foxboro,
Mass., using an iron-constanan thermocouple inserted in the bath as a sensing device. 3 A Borkowski io n iza tio n chamber, shown in Figure 3, was used to measure the radioactivity of the tritium. This chamber could be
attached to the c o lle c tio n vacuum system by means o f the fle x ib le
connector also shown in Figure 3. The ion current produced in the
chamber was measured by using a Cary, Model 31, v ib ra tin g reed
(3) W. J. Price, "Nuclear Radiation Detection," McGraw-Hill Book Co., New York, 1958, p. 73. 16
30
30
To applied voltage
Tygon tubing Epoxy cement
Collector 30 " electrode
3 0 0 cc internal volume
Mounti ng A ssem bly
Figure 3. Ionization chamber. 17
electrometer. A multiple range Brown recorder, Model 39, automatically
recorded the voltage decrease caused by the ion current flowing through
a resistor of 1.078 X 10*® ohms.
Isotopic analyses were performed on a Consolidated Electrodynamics
Corporation Model 21-620 mass spectrom eter. This instrum ent had been modified with a DC amplifier and an isotope ratio accessory, which
facilitated the measurement of the ratio of the concentrations of two
different species in a gaseous sample. It permitted the response from
any two masses to be quickly and easily set up for comparison. The
sig n a l from the sp ecies presen t in th e la rg er amount was attenuated
by a series of resistors in the form of a stacked-dial, until it
equalled the signal produced by the species present in the lesser
amount. Then the signal ratio of the amounts of the two species could
be read directly from the stacked-dial.^ The inlet system of the
spectrometer was metal with a molecular leak of gold foil and is
shown in Figure 4 .
A model 609 temperature programmed chromatograph manufactured
by the F and M Scientific Corporation, Avondale, Pennsylvania, was used for the analysis of methane in the experiments with carbon monoxide and water vapor. This instrument employed a flame ionization
detector. The column used in this determination was eight feet long
and one fourth inch ou tsid e diam eter and f i l l e d w ith 80 to 1 0 0 mesh
silica gel.
(4) Procedures employed in calibrating the mass spectrometer are described later in the isotopic analyses section. Expansion bulb
Sample pressure gauge
diffusion and fore pump
To analyzer
Thermocouple gage
Figure 4, Mass spectrometer inlet system. 19
The quantitative analysis of deuterium in the presence of carbon monoxide was performed by using an Aerograph chromatograph Model A-350-
B equipped with a thermal conductivity detector, A six foot by one
fourth inch diameter column filled with 40 to 60 mesh silica gel was
sufficient to give a good separation.
The amount of water used in each experiment was determined by measuring the length of the column of water in a metering tube (2 mm
inside diameter) at 25°C with a cathetometer manufactured by the
Scientific Corporation, Chicago, Illinois. This tube had previously been calibrated with mercury so that the volume of the tube was known
as a function of the length of the column of liquid in the tube.
The reaction vessel was a 250 ml round bottom flask containing
a 2 mm inside diameter thermocouple well biaxially centered as shown
in Figures 1 and 2. The volume of the vessel was determined to be
270 ml within an uncertainity of 1%.
The temperature of each experiment was measured using an iron-
constantan thermocouple placed in the thermocouple well.
Procedures
Preparation of tritiated water and sample reservoir
The mixture of tritiu m and deuterium was placed on the vacuum
system as shown in Figure 1. A quartz tube (1 cm diameter and 18
cm long) with quartz to Pyrex graded seals on both ends was filled
with reagent grade wire form copper (II) oxide obtained from the
A llied Chemical Company. I t was attached to th e vacuum system and 20
wrapped with nichrome wire covered with asbestos paper. The reservoir was made from a p iece of 30 mm diam eter Pyrex tubing closed at one end. After being washed and dried, it was attached to the quartz tube by a 12/30 standard taper joint using a minimum amount of Apiezon L stopcock grease.
The system was then evacuated and flamed with an oxygen-gas torch.
The current through the nichrome wire was adjusted until the temper ature of the quartz tube was 500°C. The copper (II) oxide was degassed for sixteen hours and the pressure after this time in the system was
5 x 1 CT6 mm.
After lowering the temperature to 400°C., stopcock 2 was closed and stopcock 3 was opened allowing the tritium-deuterium gas mixture to come into contact with the copper oxide. Water droplets adhering to the walls just above and below the combustion tube were observed immediately. Gentle heating using an orange flame of the torch was necessary to cause the water to diffuse into the reservoir where it was frozen with liquid nitrogen. The reaction was allowed to proceed for nine hours. It was estimated by visual inspection that the volume of water collected was 0.3 ml.
After removing the reservoir from the vacuum, the tritium water was quickly diluted with 10 ml of D2 O. The D2O had been previously made 1 0 “^ N in ferrous ion by the addition of anhydrous FeS0 4 and acidic (pH 1 on pHydrion paper) by bubbling dry SO3 through it.
The reservoir was then sealed on the vacuum line in the position 21
shown in Figure 1 . The ferrous ion was added in order to minimize the steady state concentration of hydrogen peroxide formed by constant 5 radiolysis of the liquid.
The quartz furnace was then removed from the vacuum m anifold by pulling it off above stopcock S2 by using a gas-oxygen flame.
Calibration of the metering tube
The m etering tube which was used to determine the amount of water taken from the reservois for each experiment is shown in Figure 1,
It was made of a piece of 2 mm inside diameter tubing 11 cm long and closed at one end. On the closed end was scratched a mark, which shall be called the zero mark. Mercury was used to calibrate the volume of this tube as a function of the height of a column of liquid above the zero mark by the following procedure.
After a sample of mercury had been put into the tube, the posi tion on the cathetometer of the zero mark (L0), and the meniscus of the mercury (Lreacj) were noted. The length of the column of mercury could then be calculated by subtraction. The tube and its contents were then weighed on a Mettler single pan micro balance and, using the density of mercury at the temperature of the experiment, the volume of the column was calculated. This procedure was repeated for several different lengths of mercury. The data are presented in
Table 2 and the results are plotted in Figure 5. The intercept of the straight line is not zero because the zero mark did not coincide
(5) R. F. Firestone, J. Am. Chem. Soc., 79. 5593 (1957). 22
TABLE 2
Calibration of the Metering Tube
Weight of empty tube 9.8098 gm.
Specific volume of mercury at 26.5°C. 0.07391 ml/gm
Expt. L0 L Weight Hg Weight Hg Length of Volume of No. cm. read and tube gm. Column of Hg cm. gm. Hg cm. m l.
1 34.280 35.155 10.4518 0.642 0.875 0.0475 2 34.020 35.455 10.7019 0.829 1.425 0.0659 3 33.430 35.705 11.0710 1 .2 1 6 2.275 0.0392 4 34.850 38.100 11.5174 1.708 3.250 0 .1 2 6 2 5 33.815 38.860 12.3224 2.513 5.045 0.1857 6 30.730 38.285 13.4599 3.650 7.555 0.2698 7 35.690 44.575 14.0633 4.253 8.885 0.3143
a "Handbook o f Chemistry and P h ysics," 40th Ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1959, p. 2115. 23
0 .3 0 0
0.200
Volume ml.
0 . 1 0 0
0.000n i i i I i i i i i i 0.0 1.0 3.0 5.0 7.0 9.0 Length , cm, Figure 5. Calibration of metering tube. 24 with the bottom of the column of mercury. The tube was then placed on th e vacuum system as shown in Figure 1.
Sample preparation
In order to minimize the evolution of foreign gases during the experiment, the reaction vessels were treated as follows before the ad d ition o f the r ea cta n ts. Each v e ss e l was washed with d is t il le d water and baked in air for approximately 3 hours at 500°C before attachment to the vacuum system. After evacuation each vessel was pumped and baked at 500°C for at least 24 hours. The tritium water was outgassed six times by means of freezing-pumping-melting cycles.
Liquid nitrogen was used as the coolant to freeze the water. While the water was frozen, all the stopcocks except those leading to the gas storage vessels were opened to the pumps to insure that their bores had been thoroughly evacuated. When the pressure in the system had reached 5 x lCT^ mm or less, stopcocks S4 and S5 were closed.
A fter th e water had m elted, the d esired amount was d is t il le d in to the metering tube. At no time was the water allowed to freeze in the metering tube. While this distillation was being performed, the oven which had been surrounding the reaction vessel was removed, and the position on the cathetometer of the zero mark of the metering tube was noted. When the column of water had reached the necessary height, stopcock S5 was closed and the position on the cathetometer of the middle of the meniscus of the water was noted. At this time the temperature of the tube was also recorded. Stopcock S7 was then 25
closed, and stopcock S5 opened. The bottom half of the reaction vessel was placed in a Dewar f i l l e d w ith liq u id nitrogen and the water was transferred from the capillary to the vessel. In order to prevent the water from freezing in the capillary, heat was often applied to it by using a hot air blower. After the transfer was complete, the water was melted and refrozen, forming a disc approximately 2 cm in diameter on the bottom of the vessel. Stopcock S5 was then closed and Sy was opened to the pumps until the pressure again read 5 x 10“^ mm or less.
After stopcock Sy was closed, either carbon monoxide or hydrogen was introduced into the reaction vessel by allowing the gas to expand from the reservoir flask into the metering volume and from there into the reaction vessel. The volumes of the metering tubes were estimated by knowing the pressure of the gas in the reservoir flask and the amount desired in the reaction vessel. The vessel was then sealed off with a gas-oxygen flame at the constriction and immersed in the sand bath at the desired temperature.
Calibration of the thermocouple
The thermocouple was calibrated by using it to determine the melting point of lead. The thermocouple was placed in a Pyrex
glasS^test tube and was inserted into Baker Analyzed Reagent Grade
lead until the level of the lead was above the junction of the
thermocouple. The lead was melted and then allowed to cool slowly.
The cooling curve was automatically recorded using a 20 m illivolt
recorder whose scale was calibrated with a Rubicon Potentiometer. 26
The average of the voltages at which the plateau occurred in three different experiments was 17.67 mv. The voltage corresponding to
327°C which is the melting point of lead ^1 i s 17.84 mv. The referen ce junction of the thermocouple was at 0 °C. The accuracy of the thermocouple was then placed in the sand bath and it was determined that the relationship between the reading of the thermocouple and the temperature was linear throughout the range used in this study.
Collection of the gas for analysis after reaction
The procedures described first pertain to the experiments with hydrogen and water vapor.
Collection of the hydrogen after the desired length of reaction
time was carried out by attaching the reaction vessels via the break-
sea l tube to th e c o lle c tio n vacuum system shown in Figure 2 . A small piece of metal enclosed in glass to be used as a breaker had been placed on the break-seal. An hour was required to again evacuate the
system to 10"^ mm after attaching the reaction vessel. During this
time th e reaction v e ss e l was immersed in liq u id n itrogen , and a
storage vessel shown in Figure 6 was placed on the system via the
10/30 joint on the gas buret and evacuated. After closing stopcocks
S2 and S3 , a Dewar flask of liquid nitrogen was placed over the first
trap, and the break-seal was broken using a magnet to manipulate the
(6) "Handbook of Chemistry and Physics," 40th Ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1959, p. 2322. 27
Stor a g e sampler
VPC sampler
Self ^ se aling septum
20
30
Figure 6. Samplers. 28
breaker. Then stopcock S4 was turned to is o la t e the Toepler pump from
the reaction vessel and traps, a Dewar of liquid nitrogen placed over
the second trap, and stopcock S2 was opened. These procedures were performed to insure that the tritiated water was completely frozen
and would not be collected with the sample for analysis. After
closing stopcocks S5 and Sg, stopcock S4 was opened to the Toepler pump and the noncondensable gas transferred to the buret. The
Toepler pump was operated continuously by means of the automatic
c o n tr o l.
Aliquots of the gas were expanded into the buret, measured,
and pushed into the storage vessel.”^ When the readings of the buret
showed that no gas was expanding into it, stopcock S2 was closed,
the three Dewars removed, and the water transferred from the reaction
vessel to the first trap by placing the first trap in liquid nitrogen.
After the Dewar on the second trap had been replaced, stopcock S2
was opened to the Toepler pump and any gas th at was p resent was
transferred to the buret, measured, and stored. This procedure was
performed in order to measure how much gas had been trapped with
the frozen water. The sum of the volumes of all the aliquots
collected to this point in the procedure was recorded as the volume
of protium present during the experiment. Stopcock S2 was again
closed and the water was melted and frozen again using a Dry Ice-
(7) The procedures for calibrating and using the gas buret are given in the next section. 29
isopropanol slush. The second trap was also placed in a slush of this typ e. A fter is o la tin g th e reaction v e sse l and traps system from the
Toepler pump, stopcock S2 was opened. After several minutes stopcock
S4 was opened to the Toepler pump and any gas present was transferred to the buret and the amount was measured. This was done to determine the amount of impurities condensable at -196°C but volatile at -78°C which had evolved from the walls of the reaction vessel during the reaction. If enough was present it was stored in another storage v e s s e l.
Mercury was pushed into the storage vessels far enough to prevent the samples from coming into contact with the stopcock grease.
The tritium and deuterium would probably enter into exchange reactions with the hydrogen atoms of the stopcock grease in the presence of the r a d ia tio n .
Aliquots of the sample were removed from the storage vessels for the analyses. Any gas that remained after all the analyses were performed was stored in 5 mm outside diameter tubes fitted with 5/20 male ground joints at their open ends. These storage tubes fitted a
5/20 female joint, equipped with a small mercury cup at its upper end and mounted via the 10/30 joint on the stopcock of the gas buret.
After pressing the gas into a storage tube, the stopcock closed, and the tube lifted slightly from its seat in the female joint, allowing the gas within to adjust itself to atmospheric pressure by drawing mercury part of the way up the tube. Filled storage tubes were kept 30
open end down in small bottles of mercury.
In those experiments with carbon monoxide and water it was attempted to separate the carbon dioxide formed in the radiolysis from the carbon monoxide using liquid nitrogen. This procedure had been performed successfully by R. Steinmann.® The carbon monoxide was c o lle c te d and measured ex a ctly th e same as in the case of the hydrogen up to the point just after the traps were placed in the
Dry Ice-isopropanol slush. The gas remaining here was expanded into the gas buret, measured, and stored. An analysis of this gas using the mass spectrometer showed that it was predominantly carbon dioxide containing carbon monoxide. Thus, the final analysis for the amount o f carbon d ioxid e formed in the experiments was performed using the mass spectrometer and will be described later in the appropriate section. Samples of the two fractions were stored as described previously.
Calibration of the gas buret
The quantity of gas collected after each experiment was determined by compressing the gas into several known volumes in the gas buret and reading the pressures on an attached manometer.
The details of the design of the buret are shown in Figure 2.
Four marks were scratched on the 6 mm diameter tube at various p o s itio n s beneath stopcock Sg and the volumes defined by th ese marks
(8 ) R. Steinmann, Ph.D. dissertation, Stevens Institute of Technology, Hoboken, New Jersey, 1962. 31
and the stopcock designated as Vj, V2» Vg, and V4 . On the back of the measuring column which was always open to the pumps, was placed a scale graduated in millimeters. The purpose of the float valve on the opposite side of the buret from the measuring column was to prevent mercury from rising into the Toepler pump.
A procedure based on Boyle's law was used to calibrate the volumes of the buret using air as the noncondensable gas. The first step was to determine the volume of a vessel which was used to introduce the air into the buret via the 10/30 joint on the stopcock of the buret. The volume of the vessel, including the bore of the stopcock, was measured by weighing the amount of water needed to f i l l it completely. Its volume was 9.840 ml and is designated as Vca^.
When the mercury was allowed to rise in the buret by admitting air into the Erlenmeyer flask through stopcock, mercury also rose in th e measuring column. I f no gas was in the buret then each mark had its respective zero reading on the measuring column. The pressure of a gas confined in a certain volume of the buret could then be calculated by subtracting the zero reading from the reading with the gas present.
The following symbols will be used in the derivation of the equations used for the calibration*
.=the volume of the calibrated introduction vessel including the bore of the stopcock on the vessel. (S^q).
Vunk=^ e volume between the stopcock of the introduction vessel and the highest point of the uniform tube of the buret. This also includes the bore of the stopcock on the buret. 32
V.=the volume defined by the ith mark and the stopcock at the top of the b u ret. i = l ,2 ,3 , and 4 .
The following procedure was used to deteimine V^. Air was put into the introduction vessel which was placed on the stopcock of the buret. Then stopcock S^q was closed, Sg opened, and the air in pumped out. Mercury was allowed to rise to a position above the flo a t valve and the a ir was introduced in to the buret by turning S-^q.
Then the level of the mercury was adjusted to coincide with the scratch defining and the pressure of the air in V^otal was deter mined by subtracting the zero reading from the reading on the measuring column. According to Boyle's law then, pa-tmVcal = piVtotal* If the atmospheric pressure were known, V^ 0 ^.a 2 could be calculated. Stop cock S-^q was then closed and the air below it pumped out. The stop cock was opened again and the air allowed to expand into V-total* The
Boyle’s law equation can be generalized to
^n+l^total fn^cal (1 ) where n is the number of times that stopcock S^q has been manipulated.
Rearrangement of equation (1) gives
^n+1 (pn)(V Ca l A t o t a l ) (2 )
A plot of pn+^ against Pn should be linear with a slope equal to
^cal^total* c*ata and results 0;f °ne °f these determinations is given in Table 3 and Figure 7. 33
TABLE 3
Determination of vtotaA al for V1
n pn Pn+ 1 Pn Pn+1
1 404.2 2 2 1 .2 1.827 2 2 2 1 .2 121.3 1.824 3 121.3 67.1 1.818 4 67.1 36.2 1.85 5 36.2 19.7 1.84 6 19.7 1 0 .8 1.95
The slope of the line in Figure 7 is 1.824, therefore = 17.29 ml.
If stopcock Sg is manipulated instead of S^q, the fraction
Vcal+Vunjc can be determined. The data are given in Table 4 and
^ to ta l are plotted in Figure 8 . 34
400
300
(mm)
200
1 0 0
100 200 P n + , (mm)
Figure ■7 7. Determination n ♦ • of * V — to------^ ' V Cal 35
TABLE 4
Determination o f vto t a l for V^. ^cal+Vunk
n n P n Pn+1 pn mm mm Pn+1
1 40 6 .9 26 8 .4 1.516 2 26 8 .4 177.0 1.516 3 177.0 117.1 1.512 4 117.1 7 7 .8 1.51 5 7 7 .8 50 .8 1.53 6 50 .8 3 3.3 1.53 7 33.3 2 2 . 0 1.51
The slope of the straight line is 1.523.
Since Vto t a l = V1+Vcal+Vunk then
i l = 1 - Vunk+Vcal O ) ^total ^total
Enough information is now available to calculate V^.
V1 = (0.3434)(17.29 ml) = 5.937 ml
The volume defined by V2 was also determined in this manner.
To calibrate V3 and V^, a procedure based on knowing ^ and was u sed . Air was placed in and the pressure read. The mercury was then allowed to r is e to V3 and the pressure again read. The
volume Vg could then be calculated using equation (4) where 36
I 400
300
200
100
100 200 Pn+1 (mm)
Figure 8. Determination of — VCal Vunk 37
and Pg refer to the respective volumes.
Representative data and results are given in Table 5.
TABLE 5
Determination of Vg
Mark P ress. V c Pl* vn b P2 n pn Pn No. mm ml ml
1 171.0 2 233.1 0.7336 4.355 3 415.1 0.4119 2.445 0.5616 2.4 an = mark number Calculated using = 5.937 ml.
°Calculated using Vg = 2.340 ml.
Using this same method, the volume was found to be 0.382 ml.
The amount of gas c o lle c te d a fte r each experiment was calcu lated from readings obtained using the gas buret. The gas was compressed in to V^, Vg, V^, or V4 and its pressure determined. The temperature of the buret was a lso noted. The amount o f gas presen t was then calculated using the equation n = P.V-/RT where n is the number of moles of gas present in V. at pressure P-, R is the gas constant, and
T is the temperature of the buret. 38
Determination of the amount of methane formed in the experiments with added carbon monoxide
The amount of methane present in an a liq u o t of the gas collected while the traps were immersed in liquid nitrogen was determined by comparing the signal from a flame ionization detector caused by the methane to that caused by a known amount of ethane in the aliquot after they were separated using a F and M chromatograph.
The optimum operating con d ition s for the F and M chroma tograph were the followings detector temperature, 230°C, injector port temperature, 230°C, flow rates for H2 j N2 > and air, 40, 36, and 30 cc/min respectively, and a temperature program of 9°/m:Ln beginning at 60°C. Under these conditions the retention time for methane is 2 min and th at fo r ethane,
5 min.
An equimolar mixture of methane and ethane was prepared using the gas buret. Aliquots of this mixture were introduced into the chromatograph sampler shown in Figure 6, which were placed on the 10/30 joint of the gas buret using a 5/20 to
10/30 adaptor. Mercury was pushed to a position above the stopcock on the sampler and then stopcock Sg was closed. The sampler was then removed from i t s sea t in the mercury cup of the 39
adaptor allowing the atmosphere to push mercury into the 5/20 joint below the stopcock. After the end of the 5/20 male joint was immersed into a pool of mercury, the stopcock on the sampler was opened and the gas inside allowed to adjust itself to atmospheric pressure by drawing more mercury into the sampler. The sampler
remained in this position for the remainder of the analysis.
Aliquots of the sample were withdrawn using a Hamilton gas
tight syringe and then injected into the injection port of the
instrument. At this time the temperature program and the recorder were started.
The areas of peaks r e su ltin g from th e methane and ethane were
determined planimetrically and compared. It was found that the
ratio of the sensitivities of the detector for methane to ethane was 1.00-: 1.50.
The samples of the gas collected while the traps were in
liquid nitrogen in the experiments with carbon monoxide and water
vapor were then analyzed. A measured amount of ethane was placed
into a known amount of the sample. This mixture was then placed
in the sampler and analyzed on the chromatograph exactly as the
calibration mixture. The ratio of the amounts of methane and
ethane in th is sample was then determined and the amount o f
methane in the aliquot calculated. The total amount of methane
formed during an experiment was then calculated. 40
Determ ination o f the amount of deuterium formed in the experi ments with added carbon monoxide
Operating the Aerograph chromatograph with the detector, injection port, and column at room temperature was sufficient to give a good separation of deuterium and carbon monoxide. The current passing through the filament in the thermal conductivity detector was maintained at 150 ma and the flow rate of the nitrogen carrier gas was maintained at 50 ml/min. The retention time for deuterium was approximately 45 sec and that for carbon monoxide, 1 min 15 sec.
The instrument was calibrated in the following manner before each series of analyses. A sample of deuterium was measured using the gas buret and placed in the chromatograph sampler.
The gas in the sampler was allowed to adjust to atmospheric pressure as described previously. It was then diluted with
300 ul of air using the Hamilton gas tight syringe, and allowed to stand for one minute. The entire sample was then removed and injected into the chromatograph. This procedure was repeated for several samples. A measurement of the height of the peak caused by the deuterium was sufficient to allow a
good determ ination of th e amount of deuterium p resen t. The
results of a typical calibration are given in Table6 and plotted in Figure 9. 41
TABLE 6
Calibration of the Gas Chromatograph Using Deuterium
3 Sample Moles Amplitude Measured Calculated No. D2 Setting on D2 Peak Hgt. D2 Peak H gt. xlO^ the instrument cm cm
1 1 .1 9 x4 23.2 92.8 2 0 .8 6 0 x4 16.5 6 6 .0 3 0.542 x 2 2 2 .1 44.2 4 0.7 5 4 x4 15.1 60.4 5 0.2 0 9 x l 17.2 17.2
Measured D2 peak height x amplitude setting
The slope of the line shown in Figure 6 is 1.26+ 0.01 moles D2/ Cm.
A measured amount of the samples which were collected while
the traps were immersed in liquid nitrogen was placed in the
sam pler. The e n tir e amount o f th is a liq u o t was then in jec te d in to
the chromatograph. The height of the peak corresponding to the
retention time of 45 sec is proportional to the amount of all the
hydrogen present. This includes any 2 H which may have diffused
from the walls of the vessel during the experiment. Mass
spectrometric analyses for the isotopic forms of the hydrogen proved im possible due to th e large amount o f carbon monoxide
present in the mixture. An attempt to separate the hydrogen
species from the carbon monoxide using a palladium diffusion 42
100
Response (cm.)
5 0
0.25 0.50 0.75 1 . 0 0 1.25 Moles deuterium C106) Figure 9. Chromatograph calibration. 43
apparatus also proved fruitless. Further experiments to determine
the composition of the species forming the peak at a retention
time of 45 sec were not performed and it was assumed that this
peak was due to deuterium a lo n e. The amount in the a liq u o t was
then determined from the ca lib ra tio n curve and the to ta l amount
in the sample calculated. This was repeated several times
using different amounts of the sample and the results were
averaged. The amount in the to ta l sample was corrected fo r the
hydrogen present initially in the carbon monoxide as an impurity.
Analysis for hydrogen isotopes
Samples of the gases which were to be analyzed were put into
the sampler shown in Figure 6 and the sampler placed in the
Teflon ring seal J, of the inlet system of the mass spectrometer.
While valve 2 (see Figure 4) remained closed, the others along
with the stopcock to the expansion bulb were opened and the
system was evacuated. When the thermocouple gauge registered
zero, valves 3 and 5 were closed and the sample was allowed to
expand into the inlet system and the expansion bulb. In order to
prevent the possibility of isotopic fractionation this and all the
other expansions were allowed to take place for at least one
minute. Valves 1 and 4 were then closed and the sample confined
by the volume between valves 3 and 4 expanded further into the
system. If the sample pressure which was read from the thermo
couple was less than 200 microns, valve 2 was opened and the
I 44
sample was analyzed* After the analysis valve 1 was opened and the remaining portion of this aliquot was pumped away. When the thermocouple gauge again registered zero, valves 1 and 3 were closed and the expansion procedure was repeated in order to introduce another aliquot from the sample.
The mass selector of circuit 1 on the isotope ration accessory was set to maximize the peak height of the isotope present at the smaller concentration of the two being compared. The mass selector of circuit 2 , which contained the stacked dial attenuator, was set to maximize the peak height of the other isotope. A peak selector switch allowed the signal from either of these isotopes to be alternated instanteously with the signal from the o th er.
The sig n a l r a tio s which were read from the v o lta g e d iv id er are designated by Rjj where the signal for the ith isotope is given by c ir c u it 1 , and that for the jth isotope by circuit
2. It should be noticed here that the values for R.^ are always less than 1. The ratio of the concentrations of the isotopes i and j in the ionization chamber of the mass spectrome ter at any time, t, is then given by the equation n./n.= (k.•)(R. •). X J •** J X J The constant k^j is the ratio of the sensitivities of the instrument for the isotopes. 45
It was found that the signal ratios changed as a function of the time that the sample was in the ionization chamber due to a difference in the diffusion rates of the isotopes through the molecular leak in the inlet system. The following procedure was employed to enable the ratios from different samples to be meaningfully compared. After the sample was expanded through valve 4 and the peak selector switch set to circuit one, valve two was opened allowing the sample to diffuse into the analyzer tube. The recorder immediately sensed a signal and traced a vertical line of the chart paper and thus automatically recorded the time of introduction of the sample. This time was designated as tg. Ratios were selected using the voltage divider so that the decaying signals of the two isotopes intersected on the chart paper. The distance of each such intersection from the line defining t^ multiplied by the chart speed is equal to the time at which the signal ratio was equal to that particular value set on the voltage divider. Time versus log ratio plots were then made and extrapolated to tQ. In th is way the i n i t i a l signal ratios, Rij° were determined. See Table 7 and Figure
10 for an example of this procedure applied to determining o Rrd pj in the gas collected from experiment 47. It can be seen that the ratio increases with time as would be expected from the d iffu sio n rates of as compared to HD. The value o f R ^ H was 0.07170. 46
TABLE 7
3 Variation of the Ratio R^ ^ with Time
Aliquot 1 Aliquot 2 b RHD,H2 - L°gRHD,H2 Time(cm) rHD,H2 - l °9rHD,H2 Time(cm)
0.0740 1.1308 3.9 0.0750 1.1249 4.6 0.0760 1.1192 7.2 0.0770 1.1135 8 . 8 0.0790 1.1024 12.0 0.0800 1.0969 13.6 0.0820 1.0862 16.7 0.0830 1.0809 18.5
3 The sample pressure in these two determinations was 11 microns.
^This is the distance measured on the chart paper as described above. The duration of time that the sample has been in the analyzer tube is equal to this number divided by the chart speed which was .083 cm/sec.
In order to determine the sensitivity ratios, calibration
mixtures with known isotopic ratios were analyzed following the
same procedure as above. At tg the ratio of the concentrations
of the two isotopes is known, thus ~(n^/nj)known(R°^), where
R?. i s th e recip rocal of R ?.. j i iJ At the beginning of this study the calibration standard was
a mixture of H2 and D2 that had been allowed to equilibrate
over a glowing Nichrome wire. The initial concentrations of
H2 and D2 were equal thus at equilibrium, n^ / n^ 47
.1400
.1200
-Log
HD,H2
.1100
O Aliquot I
□ Aliquot 2
1.0800 20 Time (cm ) Fig u re lO.Eff ect of time on the ratio RHD 48
Thompson and Schaeffer^ have determined that the equilibrium constant defined by the relation % i s 3 .2 3 . Then at tg the isotopic ratios defined above are equal to 0.556. Using this mixture then k is given by Rj Later in the study measured amounts of HD, D2 » and H2 were mixed in those proportions approximating the composition of the mixtures
obtained from the experiments for the calibration standards.
The isotopic purity of the individual components and the sensi
tivity ratios of the calibration mixture were determined simul
taneously using a method of successive approximations. The
isotopic ratios for the calibration standards used in the latter part of this study are given in Table 8 .
The sensitivity ratios (k^j) are a function of the electronic
system of the instrument such as the repeller voltages and the
filament current, the pressure at which the sample is analyzed,
and the composition of the sample.
(9) S. 0 . Thompson and 0 . A. S ch aeffer, J . Chem. P h y s., 2 3 , 759 (1955). 49
TABLE 8
Isotopic Ratios in the Calibration Standards
Mixture No. nHD/nH2 nD2/ nHD
1 0.1373 0.00398 0.029 2 0.1302 0.00833 0.064
The electronic system of the instrument was left undisturbed as long as the instrument did not malfunction. It was found, though, that the sensitivity ratios varied slowly from day to day.
They were, therefore, determined immediately preceding each a n a ly s is . H" The ion s H3 and H2 D+ which 'are products of the ion molecule reactions cause the sensitivity ratios to be dependent on the pressure and composition of the sample. 10 In Table 9 are shown data for the ratio of the signal of mass 3 to that of mass 2 in a sample of technical grade protium (H2) obtained from the Liquid
Carbonic Co. The ratio of the signals is decreasing with pressure and also time as would be expected if the signal at mass 3 were due to Hj.
(10) I. Kirschenbaum, "Physical Properties and Analysis of Heavy Water," McGraw-Hill Book Co., Inc. New York, 1951, p. 69. 50
TABLE 9
Ratio o f the Mass 3 Signal to the Mass 2 Signal in H2
Sample 3 Pressure Ratio Time (cm.) (mu.)
350 0.0041 1 . 0 250 0.0039 3 .5 2 0 0 0.0036 6 .5 150 0.0034 1 0 . 1 0 0 0.0031 14. 80 0.0028 18. 50 0.0023 27. 25 0.0018 43. a See footnote b of Table 7.
Also a mixture of H2 and HD was prepared and analyzed fo r mass 4. The composition of the mixture was 2.06% HD. From the
D^ present in the HD the ratio nj^/n^=0.003 and n^/nj^pO.00006
The results are shown in Table 10. 51
TABLE 10
Observed Signal R atios R^.^ and R.4,2 a Mixture
of 2.06% HD, 6xl0“7% D2, and 98.0% H2
Sample Pressure R4,3 R4,2
300 a 0.00025 150 0.014 a 1 2 0 a 0.00025 a Not determined
As can be seen in the table the ratios are larger than expected even when corrected for the sensitivities of the instrument.
This correction is probably in error since at least part of the signal at mass 4 results from the species H2D+. The sig n a l ratio was not pressure dependent within the range 300 to 120 u., but the height of the peak one signal (mass 4) was only 2 to 5 divisions out of 100 on the chart paper so this would be very difficult to observe,
The D+ ion resulting from the fragmentation of either HD of D2 on electro n bombardment in te r fe r e s w ith the determ ination o f H2 . This interference is dependent on the sample composition and the energy of the bombarding electrons. 52
11 + Friedel and Sharkey determined the intensity of the D peak
in both D2 and HD to be approxim ately 1% of the intensity of
the parent peak (Dg or HD ). Their experiments were at electron
energies of 70 ev. The energy of the electrons in the instrument
used throughout the present study was approximately 70 volts.
For accurate results in the determination of the sensitivity
ratios, the calibration standard should have nearly the same
composition as the unknown samples, and the two mixtures should
be analyzed a t the same in l e t p ressu res.
The a n a ly sis fo r HD was performed d iffe r e n tly from th a t for
D2 due to the small concentration of D£ in the samples. The
analysis for HD will be duscussed first.
The results of a study of the pressure dependence of ^2 , 3
in the equilibrium mixture and Rg 2 ^-n ‘t'^e calibration standard
are presented in Table 11.
(11) R. A. Friedel and A. G. Sharkey, Jr., J. Chem. Phys., 17. 584 (1949). 53
TABLE 11
Pressure Dependence of ^2,3 anc* R3,2
Equilibrium a Calibration mixture mixture Sample Sample pressure (u) 3 pressure (u) R3 2
30 0.4031 5 0.2474 35 0.4016 50 0.2575 65 0.4090 70 0.2489 70 0.4183 2 0 0 0.2454 1 6 0 0.3999 ——
3 b 74% HD. 13% HD.
In Table 12 data are presented data for the pressure dependence o f 1* 3 ^ 2 in an aliquot of the gas collected from Experiment 39. The value of RHD/H2 calibration mixture 2, (13% HD), on the day of
the analysis of this aliquot was 0.157. Thus, it can be safely
assumed that the HD content of the calibration mixture was
TABLE 12
Pressure Dependence of ^ ^ 2 in a Mixture* When the Ratio of is 0.02
Ro Samp1 c pressure (u) 3 ,2
15 0.03592 2 0 0.02543 1 1 0 0.02655 2 0 0 0.02692 2 0 0 0.02692
*This mixture was an aliquet of the gas collected in Experiment 39. 54 approximately six (0 . 16/ 0 . 0 2 6) times greater than that of the experi mental sample. The contribution of the Hg4" ion to ^ 2 musb be small since R- ^ 2 increased only by a factor of 1.04 with a 20-fold pressure increase. These data show that there is no significant pressure dependence of the ratio R^^ below 2 0 0 microns in mixtures containing more than 2% HD.
To check the effect of composition, the sensitivity ratios were determined using the equilibrium mixture and synthetix mixture No. 1 and compared. The results of three separate experiments are shown in Table 13.
The average of the ratios in the last column is 1.032*0.014.
TABLE 13
Dependence pf the Sensitivity Ratio knD,H2 on SamPle Composition3
^HD,H2 ^HD,H2 ^Synthetic Experiment Equilibrium Synthetic (k^ ^ )Eauil. number mixture mixture 1 * ^
1 0.5286 0.5492 1.039 2 0.4412 0.4459 1.011 3 0.4354 0.4450 1.046
a Inlet pressures were in the range 10 u to 200 u.
From these data it is established that there is no significant dependence ( 4%) of the sensitivity ratio on pressure
(below 200 u) or composition (2% to 47% HD) of the sample. Thus,
the value of nj^j/n^ i-n bhe gases collected in the experiments was 55 calculated using the sensitivity ratio determined on the day of the analysis and the value of R^ ^ in the sample determined at any con venient pressure below 200 u. It should be stressed that this is only true so long as the electronic parameters of the instrument remain constant. Later in the study, the repeller voltage had to be changed to a new valu e and a s ig n ific a n t pressure dependence was ob served.
In Table 14 the variation of R® 2 with pressure i s shown fo r the synthetic mixture No. 2 at the new repeller setting.
The valu e of R392 in creasin g with pressure probably because of the increased formation of H3 +. It has been observed that the appearance of H3 + is dependent upon the repelling voltage in the
TABLE 14
Variation of R^q ^ w ith Sample Pressure in Synthetic Mixture No. 2 (13# HD)
Sample pressure (u) **3,2
13 0.07418 25 0.07926 35 0.09246
ionization chamber.-*^ Changing this voltage changes the residence time of the ions in the ionization chamber and, thus, the time during
(12) I. Kirschenbaum, "Physical Properties and Analysis of Heavy Water," McGraw-Hill Book Co., Inc., New York, N. Y., 1951, p. 114. 56 which ion molecule reactions may take place.
Under these conditions the samples were analyzed at the same pressures as the calibration standards. A specific example for the determination of n^p/n^ is given in Table 15
TABLE 15
Determination of in Experiment 49 when the o ^ Values of R^ 2 are Pressure Dependent
Sample v a R° pressure (u) kHD,H2 r 3 ,2 nHE/nH2
13 1.755 0.3491 0.06127 25 1.643 b b 35 1.409 0.4523 0.06042
a These were determined using calibration standard No. 2. The actual values for R^ H used to calcu late these are given in Table 14.* ^ Not determined.
The amount of D^ in the samples c o lle c te d from th e experiments
was so small that the extrapolation of the signal ratios Rp and
^ 2 ^ 2 t 0 was i mP0 SSibie* The trace formed by the signal in
c ir c u it 1 (D2 ) even at the maximum sensitivity of the instrument had
a slope of nearly zero on the chart paper. This was also true of the
trace formed by the attenuated signal from circuit 2. Thus it was
impossible to determine any points of intersection of the two traces
and consequently the time dependence of the ratios. The first ratio 57 that was read from the stacked dial after the introduction of the sample was used as the initial ratio. This reading was not difficult to determine and was constant for at least 15 seconds.
In the first part of the study, only the ratio Rd 2,HD was ^e_ termined in some of the analyses and the ratio /nH was then calcu- 2 lated from the relation, n^ /n^ = n^p/nH x n^/n^p. This was done 2 2 ^ because the ratio RnJJ 2»“2 u had to be read using the smallest divisions of the stacked dial. In later analyses the value of n^ /n ^ was determined and compared with th e ca lcu la ted v a lu e. The maximum error in the agreement was 15% and the minimum error 0%, among 19 sam ples.
The values of the sensitivity ratio as determined from equilibrium mixture and the synthetic mixtures are compared in
Table 16 for two separate experiments. The samples were analyzed at the same pressures. The value of R^jHD was lar9er with respect to the value of n^^/n^ an the synthetic mixture than the equilibrium mixture. This is probably due to the increased contribution of
H2 0 + in the small ratio nD2/nHD as comPared to 0.556) in the synthetic mixture. The significance of the results shown in
this table will be discussed in a later section. 58
TABLE 16
Comparison of kp ^ as Determined by the Equilibrium and Synthetic Mixtures
Synthetic kD2 ,HD (kD2 ,H o)syn. mixture used Eq. mixture Syn. mixture (kD2 ,HD^Eq.
1 1.1 5 1.00 0.87 2 1 .7 4 1.49 0 .8 6
The pressure dependence of the sensitivity ratios involving was not determined. In those analyses when the calibration standard was a synthetic mixture, the sample was analyzed at the same pressure as the calibration mixture. This was not done when the equilibrium mixture was used due to the large difference in the composition of
the two mixtures. The significance of the errors resulting from this will be duscussed later.
The mole fractions of HD and D2 were then calculated for each
sample using the following equations.
. _ nH D /" H2 HD ------7------— 7------'D' 1 + nffl/nH2 + n°2 H2
*d 2 = ------1— :— <6) 1 + nH2/ n D2 + nH D /nD2 59
Mass spectrometric analysis of carbon monoxide-carbon dioxide m ixtures
The ratio of the concentrations of carbon monoxide and carbon dioxide present in the samples collected from the experiments was determined by comparing the heights of the parent peaks in the mass spectrum of the sample. The height of the signal corresponding to mass 44 was compared to the h eig h t of th e sign al from 28 which had been corrected for the contribution from the carbon dioxide and the sensitivity of the instrument. Analysis of the breakdown pattern of carbon dioxide obtained from the vacuum distillation of Dry Ice, showed that the ratio of the height of the 28 peak to the parent peak was 0.104. This in an agreement with the value of 0.089 given in the operation manual for the instrument.
A calibration mixture (58.8% C02) was introduced into the mass
spectrometer as described in the previous section. The mass spectrum was then scanned from mass 12 to 50. A nalysis o f r e su ltin g chart data was performed by measuring the peak heights, correcting the peak at mass 28, and then calculating the ratio of the resulting heights. The sensitivity factor was then determined by comparing the peak ratio to the known ratio.
Assay of the tritium-water and dosimetry
The tritium-water was assayed for tritium content by conversion of an aliquot to hydrogen by passage over metallic zinc and measure- 60
ment of the radioactivity per mole of hydrogen produced. This procedure was adapted from that described by Graff and Rittenberg.13
The apparatus used for the reduction was a U-tube of 6 or
10 mm Pyrex tubing with a cold finger on either side of the U.
This apparatus was connected to the sample preparation vacuum system at that position where the reaction vessels were placed. The vacuum stopcock between the system and the U-tube was lubricated with a minimum amount of Dow Corning s ilic o n e grease.
In some of the experiments the glass which was to come in contact with the hydrogen was baked the same as the reaction vessels were, that is at least 3 hr in air at 500°C and at least
24 hr at 500°C at 10“^ mm on the sample preparation vacuum system.
In these experiments, the zinc was in a side arm which did not extend into the oven. In another experiment both the zinc and glass were baked at 250°C. After this point, the procedure was the same in all the experiments.
After the water in the reservoir had been degassed six times, and the oven removed from the U -tube, a small amount (le ss than
0 .0 1 ml) was distilled into the reduction apparatus where it was frozen with liquid nitrogen and pumped to a pressure of 6x 1 0 “^ mm or less. After closing the stopcock and cracking the apparatus just above the stopcock to remove it from the system, the apparatus
(13) J. Graff and D. Rittenberg, Anal. Chem.. 24, 878 (1952). 61 was tilted in those experiments when the zinc was not in the oven,
to cause the zinc to fall to the bottom of the U-tube. The side
aim was then carefully sealed off with a gas-oxygen torch.
This apparatus was then put on the collection vacuum system
in the same place as the Reaction vessels with the bottom of the
U-tube extending into an oven heated to 380°C. The water was
caused to pass over the zinc by placing one and then the other of
the cold fingers in liquid nitrogen. It was then frozen and the
hydrogen th a t had been formed removed by opening the stopcock and
allowing the gas to expand into both traps which were also immersed
in liquid nitrogen. After closing the stopcock, the water was
melted and passed again over the zinc. It was frozen again and
the hydrogen removed. This procedure was repeated until no further
gas was produced.
An aliquot of this gas was expanded into the gas buret, measured,
and pushed in to the io n iza tio n chamber by allow in g the mercury to
rise to just below the stopcock on the chamber. This stopcock was
closed and the io n iza tio n chamber placed on another vacuum system
where it was filled with nitrogen to atmospheric pressure.
The decrease in voltage as the ion current was passed through
the resistor of the vibrating reed electrometer was then determined.
The amount of radioactivity in the chamber was calculated using the
following equation:
Activity(microcuries) = x W (5) Eav x e x 3.7xl0 4 62
where, e = 1 .6 0 2 x 10~19 coulomb/ion-pair
I = saturation current in amperes = voltage decrease 1.078x10^ ohms
Eav = average energy of the tritium beta particles = 5.69x10^ ev-*-^
w = the average energy mecessary to produce an ion pair in
nitrogen = 34.9 ev/ion pair* 5
The results of the analysis of the tritium water are presented in Table 17. The average of the four determinations was 19.9*0.4 curies/mole.
The. dates of the experiments are included to show that there was no enrichment in the tritium content of the water in the r ese rv o ir .
TABLE 17
Assay of the Tritium Water
Expt. Date Moles of Microcuries Curies No. Performed Gas Produced o f Tritium mole d o 5 ) Produced
1 Apr. 14, 1965 0.5356 109.1 20.37 2 June 15, 1965 3.693 708.0 19.17 3 Aug. 5, 1965 3.958 784.9 19.83 4 Aug. 15, 1965 2.738 552.3 20.17
(14) W. L. Pillinger, J. J. Hentges, and J. A. Blair, Phys. Rev., 121, 232 (1961). (15) W. P. Jesse and J. Sadauskis, Phys. Rev.. 97. 1668 (1955). 63
The gas produced in the reduction of the water was also analyzed on the mass spectrometer for the protium content. The maximum isotopic impurity in the water was five percent H atom.
This figure is stated as a maximum because of the possibility of exchange of D atoms with H atoms in the glass of the apparatus. ^
At the vapor densities employed in the sample vessels used in this work, it is estimated that over 99% of the energy of the tritium beta particles is absorbed by the water vapor. This estim ate i s based on the data reported by L. M. Dorfman on the absorption of tritium beta particles in homogeneous mixtures of the tritium and oxygen, hydrogen, or helium in spherical vessels.
He found that the absorption could be described by an exponential expression, (A/A q^ ^ where A/A q is the fraction of the radiation which is not absorbed by the gas, P is the pressure of the gas, and k is a constant dependent upon the volume of the vessel, the temperature, and the nature of the absorbing gas.
From plots of the logarithm of the fraction of the radiation absorbed versus pressure, values of the half pressures (the pressure when A/A q = 0.5) were determined. Using the following
equation, half thicknesses for the gases were calculated.
di / 2 = Pl / 2 M (°»75r) (g) RT
(16) L. M. Dorfman, Phys. Rev., 95. 393 (1954). 64
Here Pjy2 *s half pressure, M the molecular weight of the gas,
R the gas constant, T the temperature, and r the radius of the vessel. The factor 0.75r is the average distance of any point 1 7 within a sphere to the wall.
The fact that the absorption process can be described by an exponential expression resembling that for the absorption of electromagnetic radiation, gives credence to the use of the 1 R additivity principle* to estimate the absorption coefficient for water vapor. Since the mass absorption coefficient is inversely proportional to the half thickness, the following equation applies.
1 - 4 + 16 ______(9) ( d i/ 2 )D2 ° (2)(20)(d 1/ 2 )H2 (2 )(2 0 )(d 1/ 2 )02
Using the data of Dorfman, the half thickness of D20 is calculated to be 0 . 1 2 mg/cm2 , independent of tem perature.
The half pressures can now be calculated for any temperature and spherical vessel using equation 8. The radius of the reaction vessels was 4.0 cm. An example of the calculation for the fraction of the energy absorbed w ill be given for an experiment in which the vapor density of the water was 0.318 mg/ml and the temperature was 350°C. The h a lf pressure was calcu lated to be 78 mm and th e
(17) S. C. Lind, "The Chemical Effects of Alpha Particles and Electrons,” The Chemical Catalogue Co., New York, 1928, p. 94. (18) J . W. T. Spinks and R. J . Woods, ”An Introduction to Radiation Chemistry,” John Wiley and Sons, Inc., New York, 1964, p. 57. 65 pressure in the vessel was 622 mm. The fraction of the energy
absorbed is then
1_A/aq = 1-e” 6 2 2 = 1- e - 5 ’ 5 = 0.996 (10)
It should be mentioned that for experiment 17 this calculation
gave a fraction of 0.983 at a vapor density of 0.239 mg/ml at 85°C.
Under these conditions the half pressure was 45 mm. This was the
only experiment in which this fraction was less than 0 . 9 9 6.
It is then true that the rate of energy output by the tritium
in the reaction vessel is equal to the rate of energy absorption
by the water vapor within *1% or less in all experiments.
The specific activity of the tritium water was converted to
the more convenient form of curies/ml using 1.108 as the specific 19 gravity of deuterium oxide and 0.9970 as the density of normal
water at 25°C.20 The dose received by the water was then calculated
using the following equation
Dose (electron volts) = 7.59x10^ v x s x t (11)
where v is the volume of water used (ml), si is the activity per
unit volume (curies/ml), and t is the reaction time (hours). The
fa c to r 7.59x10^9 has the units of ev/curie hr and contains 5 .6 9
kev as the average energy of the beta particle.
(19) I. Kirshenbaum, "Physical Properties and Analysis of Heavy Water," McGraw-Hill Book Co., Inc., New York, 1951, p. 11. (20) "Handbook of Chemistry and Physics," 14th ed., Chemical Publishing Co., Cleveland, Ohio, 1959, p. 2113. 66
Evaluation of G values
The results of this study are expressed in terms of the G value or the number of molecules of a product formed per 1 0 0 electron volts of energy absorbed by the contents of the sample vessel. The G values for HD and D2 were calculated from the following equation G(Y) = Xyx,, n n m N inn 100 ( 12) dose where Xy is the mole fraction of species y relative to all the isotopic forms of hydrogen as determined using the mass spectrometer, n i s the number of moles of hydrogen c o lle c te d , and N i s Avogadro's number.
In those experiments with carbon monoxide and water vapor, the G values were calculated using the number of moles of D2 , CH^, or
CC>2 formed which was determined as described under each specific s e c tio n .
Isotope effect calculations
The isotope effect calculated in the study is defined by the following separation factor.
Separation Factor = (nj/nyJgas/Cno/n^ater (13)
Where n^ and n^ are the number of the resp ectiv e atoms e ith e r in the gas that was collected after the reaction or in the water vapor before the reaction. The number of T atoms in the gas after the 67 reaction was determined by placing an aliquot of the gas in the ionization chamber, determining the total activity (curies) in the gas and multiplying it by the constant2.066x10*9 atoms/curie.
This was determined by using 12.26 years as the half life of
21 7 tritium and 3.156x10 as the conversion factor for years to seconds.
(21) G. Friedlander, J. Kennedy, and J. M iller, "Nuclear and Radiochemistry," John Wiley and Sons, Inc., New York, 1964, p. 535. CHAPTER IV
EXPERIMENTAL RESULTS
Hydrogen:water vapor systems
The exchange reactions occurring in the radiolysis of gaseous mixtures of heavy water and hydrogen were examined by varying the I experimental conditions of temperature, mole fraction of hydrogen, and vapor d e n sity .
In the calculations for the values of G(HD) and G(D2) the sources of error are in the determination of the amount of gas collected after the irradiations, the dose received by the vapor, and the mole fractions of HD and D2 in the gas.
The accuracy of the gas buret was determined by measuring a known amount of gas and found to be 1%.
The calculation of the dose depends upon the determination of the reaction time, the quantity, and the specific activity of the water.
The reaction times were usually 15 hours or more, thus, the uncer tainty here was negligible. The error introduced by the effect of temperature changes on the density of the water at the time that the samples were distilled from the reservoir was only 0.2%. This figure is based on the data presented by Kirschenbaum1 on the thermal ex pansion of heavy water. As seen in Table 17, the precision of the
(l) I. Kirschenbaum, "Physical Properties and Analysis of Heavy Water," McGraw-Hill Book Co., Inc., New York, N. Y., 1951, p. 38.
68 69
experiments determining the specific activity of the water was 2%.
The uncertainty in the accuracy of the specific activity is probably
no greater than the uncertainty of the W value for nitrogen which
Platzmann states to be in the range of one to two p e r c e n t .^
The results of the determinations of the isotopic ratios are
presented in Table 18. Separate determinations of nnc/nH2 usuaH y
agreed within 4% or less, and this figure is cited as the maximum
uncertainty in this ratio. Whenever possible the values of the ex
perim ental and ca lcu la ted r a tio s were compared. As shown in
the table this agreement was on the whole quite good even though
there were often large errors in the precision of the separate deter minations. This large error is in part due to the small size of the
ratios being measured, and w ill be discussed later in reference to
specific experiments.
The maximum uncertainty in the value of G(HD) and G(T) is thus
estimated to be 1%.
The results of the experiments in which the temperature dependence
of G(HD) was small are shown in Table 19. The vapor density varied
from 0.239 mg/ml to 1.07 mg/ml, the concentration of hydrogen from
0.3 5 mole % to 1.6 mole % and the temperature from 84° to 245°C. The
longest reaction time in this series of experiments was 22 1 hours
and the sh o r te st, 4 2 .8 hours. The separation fa cto r which was defined
e a r lie r was ca lcu la ted from equation ( l ) on page 73.
(2) R. L. Platzmann, In tern . J . App. Radn. and Iso to p es. 10, 116 ( 1 9 6 1). TABLE 18
Results of the Mass Spectrometric Determination of n^£/nH2 > nD2/ nHD» anc* nD2/ nH2
Calb. No. of % Error No. of % Error No. of % Error Exp. std. nHD/n^ analy- in pre- nD2/n HD analy in pre nD2 ^nH2 analy in pre nD2/ nH2 no. used ses c isio n ses c isio n ses c isio n C alc.
6 Eqn. 0.0462 1 m m a __ a MM _ _ 7 Eqn. 0.0285 2 1 .4 a ------— a ------: —
— 8 Eqn. 0.0548 1 0.073 1 — 0.0047 1 — 0.0040 9 Eqn. 0.0588 1 — 0.041 1 ~ 0.0026 1 — 0.0024
11 Eqn. 0.0203 2 1 .5 0.070 1 — a ------— 0.0014
1 2 Eqn. 0.0815 2 3 .2 0.056 1 _ _ a ____ 0.0047
14 Eqn. 0.0373 2 1 .3 0.095 1 — a ------— .0034 15 Eqn. 0.0834 2 2 . 8 0.047 1 — ■ a --— 0.0040 16 Eqn. 0.0445 2 1 . 2 0.087 1 , — a ------— 0.0040
17 Eqn. 0.0198 2 1 . 0 0 .0 6 8 1 — a ------— 0.0013
19 Eqn. 0.0313 2 0 .9 0 .0 6 0 1 _ ~ a ____ 0.0017 2 0 Eqn. 0.0374 1 — 0.065 1 — a --- — 0.0024 21 Eqn. 0 .0 6 9 6 1 — 0.056 1 — a ------— 0.0039 2 2 Eqn. 0.0643 1 — 0 .0 6 1 1 — a --- — 0.0039 25 Eqn. 0.0490 2 2 . 0 a — — 0.0016 1 — a
26 Eqn. 0.0348 2 0 .7 0.045 1 _ _ 0.0016 1 _ _ 0.0016 27 1 0.0477 2 3 .5 0.033 1 — 0 .0 0 1 6 1 — 0.0017 29 1 0.0895 1 — 0.050 1 — a --- — 0.0046 30 1 0.0572 2 6 .3 a —— 0.0015 1 — a 31 1 0.2900 2 1 .4 a -— 0.0246 2 1 . 6 a
-j o TABLE 18 (Cont'd.)
C alb. No. of % Error No. of % Error No. o f % Error Exp. std . nHD/nH2 analy in pre nD2 ^nHD analy in pre analy in pre "D2/ nH2 no. used se s c isio n ses c isio n ses c isio n C alc.
32 1 0.0401 2 2 .5 a — — 0 .0 0 1 0 2 5 .8 a 33 1 0.0180 2 3 .4 0.049 2 4 .1 0.0009 2 7 .5 0.0009 34 1 0.0363 2 1 . 2 0.024 2 9 .3 0.00091 2 6 . 6 0.00086 35 1 0.1363 1 — 0.042 1 — 0.0057 1 — 0.0057 36 1 0.0811 1 — 0 .0 2 1 1 — 0.00196 1 — 0.0017
38 2 0.0452 2 8 .9 0 .0 2 1 1 0.00086 1 — — 0.00093 39 2 0.0218 1 — 0.018 1 ----- 0.00038 1 ----- 0.00038 40 2 0.0599 3 4 .2 0.023 3 6 . 6 0.00014 3 11 .4 0.00014 41 2 0.0551 2 0 .1 0.023 2 4 .3 0.00105 2 5 .0 0.0013 42 2 0.0163 2 0 .7 0.026 2 5 .8 0.00042 2 4 .8 0.00042
43 2 0.0245 1 0.019 1 __ 0.00048 1 — 0.00046 44 2 0.0067 1 ----- 0.077 1 — 0.00050 1 — 0.00052 45 2 0 .1 1 9 2 1 ----- 0.036 1 — 0.0043 1 — 0.0043 47 2 0.0512 3 1 . 0 0.033 3 1 2 .1 0.0017 3 14.3 0.0017 49 2 0.0614 2 0 .9 0.034 2 8 . 8 0.00195 2 2 . 6 0.00209
51 2 0.0491 2 2 . 0 0.026 2 3 .8 0 .0 0 1 2 2 8 .3 0 .0 0 1 2 52 2 0.0573 1 — 0.030 1 — 0 .0 0 2 0 1 — 0.0017 54 2 0.0517 1 — 0.029 1 — 0 .0 0 1 2 1 — 0.0015 55 2 0.0633 1 — 0.029 1 — 0 .0 0 1 6 1 — 0.0018
a Not determined TABLE 19
Values of G(HD), G(D2 )» G(T) and the Separation Factor Below 245°C
Exp. Temp, Dosage Vapor Mole Composition3 no. °C ev x 1 0 " * 8 d en sity fra ctio n of the gas G(HD) G(D2 ) G(T) D2/HD Separation m g./m l. H2 x 103 XHD Xd 2 x 102 factor
14 84 10.3 0.308 12.1 0.0359 0.0033 10.8 0.99 0.305 0.092 1.43 17 85 5 .9 2 0.239 15.9 0.0194 0.0013 10.2 0.69 0.214 0.067 1.86 11 95 6.48 0.455 8.27 0.0199 0.0014 9.56 0.67 0.536 0.070 1.34 19 99 8 .0 4 0.544 6.84 0.0303 0.0017 11.7 0.65 0.245 0.057 1.82 7 105 7.94 0.632 5.85 0.0277 b 10.7 b b b b
12 110 18.9 0.649 5.7 3 0.0752 0.0045 12.2 0.7 0 0.345 0.057 1.35 6 114 10.3 0.717 5.21 0.0442 b 13.3 b b b b 8 125 11.9 0.617 6 .1 0 0.0517 0.0044 13.5 1 .2 0.323 0.084 1.66 5 126 1 8 .4 0.677 5.66 0.0768 0.0037 13.2 0 .6 4 b 0.048 b 9 134 13.2 1.07 3.50 0.0554 0.0024 13.0 0.56 0.317 0.043 1.53
20 137 8 .3 3 0.629 5.9 9 0.0360 0.0023 13.5 0.86 0.308 0.064 1.69 22 143 1 1 .4 0.582 6.4 0 0.0540 b 14.6 b 0.343 b 1.45 16 144 8 .4 3 0.580 6.61 0.0425 0.0038 16.0 1 .4 0.369 0.091 1.74 21 150 15.8 0.629 6.0 2 0.0649 0.0036 12 .9 0.71 b 0.056 b 25 168 9.56 0.709 5.35 0.0466 0.0015 15.1 0.48 0.359 0.032 1.53
27 184 9.09 0.379 9.78 0.0454 0.0015 15.4 0.50 0.342 0.032 1.63 35 184 2 8 .4 0.620 7.3 8 0.119 0.0050 15.1 0.63 0.372 0.041 1.50 29 224 8 .9 3 0.603 3.64 0.0818 0.0042 16.5 0.85 0.481 0.050 1.30 30 245 5.07 0.575 3.68 0.0540 0.0014 19.2 0 .5 0 0.466 0.026 1.44
3 ~ 1 “XHD“XD2 k Not determined 73
(np/nTiqa3 = GfHm + 2G(D2 ) . xT a (1) (nD/nT 'liq u id G(T) where X-j^ ag^ is the initial atom fraction of tritium in the tritiated water sample. The atom fra ctio n of D is 1 .0 0 . The value of G(T) was calculated by dividing n^ gas by the dose in1 0 0 ev u n its .
The equilibrium mixture was used to calibrate the mass spectrom
eter for the isotopic analyses in all of these experiments, except
27, 29, 30, and 35. For the latter analyses, synthetic mixture No. 1
was used. The experimental error (19%) in the precision of the "
values of G(D2 ) in these four experiments nullifies any justification
for the application of the correction factor shown in Table 16 for
the differences in the composition of the equilibrium and synthetic
mixtures. Also, there is no apparent systematic error in G(D2 ) in
the comparison of the two sets of data. The average of all the
values of G(D2 ) is 0.75*0.19 which is higher than 0.5 found by Knight n A and Anderson0 and by Baxendale and G ilb ert. Dropping the high
results of experiments 8 and 16 lowers the average to 0.67*0.11.
The values of G(T) and G(HD) e x h ib it a s lig h t but experim entally
insignificant dependence between 110° and 150°C. The average
value of G(HD) in this region is 13.5*0.4, and the average value of
G(T) is 0.327 x 10”^. The uncertainties are the average deviations
from th e mean.
(3) A. R. Anderson, B. Knight, and J. Winter, Nature, 201, 1026 (1964). (4) J. H. Baxendale and G. P. Gilbert, Disc. Faraday Soc., 36, 186 (1963). At 266'°C G(HD) increased to 31.5 (Exp. 33) indicating that a chain mechanism similar to that found by Firestone had begun. The
G values were then studied at constant vapor density (0.595 mg/ml) and mole percent of hydrogen (0.71%) while varying the temperature
from 266° to 320°C. The longest reaction time in this series of ex periments was 20.9 hours (Exp. 32) and the shortest was 4.0 hours
(Exp. 39). The results of these experiments are given in Table 20.
The values of G(HD) and G(T) show a s ig n ific a n t in crease with tem perature. Although G ^ ) values have increased from those obtained at the lower temperatures, the experimental variance was too large
to allow a reasonable determination of the activation energy.
The high value of 4.5 for G ^ ) in Experiment 36 where 8% of
the hydrogen had been converted to HD, indicated that G ^ ) may be dependent on the concentration of HD. Experiments were then performed
in which the reaction time was varied with the temperature so that
the mole fraction of HD in the gas that was collected was nearly con
stant. Table 21 shows the results of these experiments. The vapor d en sity was 0.319 mg/ml which i s lower than th a t of the e a r lie r
experim ents. The temperature was varied from 297° to 381°C and the
reaction times from 5.8 to 39.7 hours. Although the mole fraction
of HD formed varied by a factor of 1.2, the temperature dependence
o f G(D2 ) was clearly shown.
It is interesting to note here that comparison of the data
(5) R. F. Firestone, J. Am. Chem. Soc., 79. 5593 (1957). I
TABLE 20 E ffe c t o f Temperature Above 2660C on G(HD), G(D 2 ) , G(T), and the Separation Factor at a Vapor Density of 0.595 mg./ml.
Exp. Temp. Dosage Vapor Mole Composition3 no. °C ev x 1 0 “ 18 d en sity fra ctio n of the gas G(HD) g (d 2 ) G(T) d 2/ hd Separation m g./m l. H2 x 1 0 3 XHD xD2 x 102 fa cto r
33 266 2 . 0 2 0.593 7.36 0.0176 0.00090 31.6 1 . 6 0.792 0.050 1.50
32 281 2 .5 5 0.590 7.37 0.0385 0.00099 54.4 1 .4 1.16 0.025 1 .6 8
34 296 1.51 0.586 7.41 0.0350 0.00088 83.3 2 . 1 1.57 0.025 1.90
38 304 1 .2 4 0.600 7.0 9 0.0432 0.00083 123. 2.4 2.2 4 0.019 1.94
41 311 1.39 0.590 6.90 0.0523 0.00098 127. 2 .4 2 . 6 0 0.019 1.73
39 319 0.491 0.595 7 .0 0 0.0213 0.0037 150. 2 . 6 4.27 0.017 1.24
36 330 1.45 0.609 7 .1 0 0.0749 0.0018 185. 4 .5 4.0 8 0.024 1.63
3 ^ = 1 “
- j CJi TABLE 21 E ffe c t of Temperature Above 297°C on G(HD), G(D2 ) , G(T) and the Separation Factor at a Vapor Density of 0.319 mg./ml.
Exp. Temp. Dosage Vapor Mole Composition3 no. °C ev x 10-18 density fraction of the gas G(HD) G(D0) G(T) Do/HD Separation m g./m l. H2 x 10 XHD XD2 x 10 factor
49 297 2.61 0.318 6.37 0.0577 0.0018 37.2 1 . 2 0.874 0.031 1.54
47 319 1.30 0.320 6.3 0 0.0486 0.0016 63.1 2 . 1 1.39 0.033 1.65
51 360 0.051 0.318 6 .3 2 0.0468 0 .0 0 1 2 155. 3 .9 3.4 4 0.025 1.62
52 381 0.383 0.320 6 .3 2 0.0541 0.0019 237. 8 . 2 5.05 0.035 1.71
xh 2 ~ 1 " % t xd 2
-j ON 77 presented in Table 20 with that of Table 21 shows that G(HD) is dependent on the vapor density of the water. This effect was not observed in the low temperature region.
Firestone reported that the chain propagation step in HOH;D2 mixtures was probably an exchange reaction involving D atoms and water to produce hydrogen atoms and deuterated water. The other possibility for this step is an abstraction reaction involving the
same reactants but resulting in hydrogen deuteride and an hydroxyl
radical. It was thought that an examination of the effect of lowering
the mole fraction of hydrogen on the yields of HD and 2 D would aid
in establishing which is the predominant reaction. The results of
these experiments are shown in Table 22. The mole fraction of hydrogen was varied from 3 .50 x 10"^ to 10.5 x 10“^ a t a vapor d en sity of
0.590 mg/ml and a temperature of 319°C. The reaction tim es ranged
from 2 . 2 hours to 6 . 0 hours.
As can be seen G(HD) d ecreases from 166 to 103 and G(T) from 3.45
to 2.07 with a three-fold change in the mole fraction of hydrogen.
The amount of D2 formed in these experiments was quite small. Thus,
errors in the D2 analyses could be as large as 50%. Inlet pressures
on the order of 300 u were required in order to get a reliable signal
(5 divisions out of 100 on the chart paper) from mass 4. Reference
to Table 12 shows that at this pressure the contribution of H2D+
to the small ratio is significant. Further attempts to analyze these mixtures for Dg were not attempted because of the high pressures TABLE 22
Effect of Changing the Mole Fraction of H2 at 320°C. and Vapor Densities of 0.590 mg./ml.
Exp. Temp. Dosage Vapor Mole Composition3 no. °C ev x 10“ 1 8 d en sity fra ctio n of the gas G(HD) g (d 2 ) G(T) D2/HD Separation m g./m l. H2 x 10 3 XHD xD2 x 1 0 2 fa cto r
42 318 0.265 0.590 3.50 0.0160 0.00041 103 2 . 6 2.0 7 0.025 1.78 39 319 0.491 0.595 7 .0 0 0.0213 0.00037 150 2 . 6 b 0.017 b 43 322 0.733 0.590 10 .5 0.0239 0.00047 166 3 .3 3.4 5 0 .0 2 0 1.70
XH2 ~ 1 “ XHD_X£>2 k Not determined
TABLE 23
Effect of Changing the Mole Fraction of H2 at 319°C and Vapor Densities of 0.319 mg./ml.
Exp. Temp. Dosage Vapor Mole Composition3 no. °C ev x 10“^® d en sity fra ctio n o f the gas G(HD) G(Do) G(T) D0/HD Separation m g./m l. H2 x 10 3 XHD XD2 x iq2 2 fa cto r
53 319 1.09 0.319 5.0 3 b b b b 1 .3 4 b b 47 319 1.30 0.319 6.30 0.0486 0.0016 63.1 2 .1 1.39 0.033 1.65 48 319 2.85 0.319 18.9 0.0382 0.00096 67.3 1.7 1.48 0.025 1.65
XH2 - 1 “ XHD XD2 k Not determined 79
n ecessary.
Experiments of this type were repeated in order to obtain better data for the dependence of G ^ ) on the mole fraction of hydrogen.
The results are presented in Table 23. The vapor density of this series was 0.320 mg/ml and the temperature 310°C. In this case no significant decrease in G(HD) in a three-fold decrease of the mole fraction of hydrogen (1.6 mole % to 0.63 mole %) was observed.
The two values of GCDg) differ by 19% which is nearly the error in the precision of the analyses for in Experiment 47. Three separate determinations of and n^/n^ showed precisions of 12% and
14% respectively. Unfortunately the conditions of the mass spectrometer at the time of Experiment 53 did not allow the yield of HD and D2 to be determined. Again the effect of vapor density on the G values can be observed by comparing the results in' Table 23 with those in Table 22.
Since the effect of vapor density on G(HD) had been observed at only two different values, it was decided to do two further experiments varying this parameter. The results are shown in Table 24. Vapor d e n s itie s of 0.458 mg/ml and 0.699 mg/ml were used. The tempera ture reported is again the arithmetic mean of the high and low tempera tures read during the heating and cooling cycles of the sand bath.
The difference between these extremes was 6°C. A dependence on the vapor density is clearly shown. Unfortunately, the vapor density of the water could only be varied in the whole range by a factor of
2.2. The lower lim it was governed by the dosimetry requirement of TABLE 24
E ffect o f Changing the Vapor D ensity on G(HD), G(D2 ) , G(T) and the Separation fa cto r
Exp. Temp. Dosage Vapor Mole Composition3 no. °C ev x 10“18 density fraction of the gas G(HD) G(D2 ) G(T) D2/HD Separation m g./m l. H2 x 10 3 XHD ^ 2 x 10 2 fa cto r
54 321 1.35 0.458 7.11 . 0.0491 0 .0 0 1 2 98.1 2 .3 1.97 0.023 1.78
55 316 1.45 0.699 6 .93 0.0505 0.0015 164. 4 .1 3.3 0 0.025 1.78
3 >
TABLE 25 The Results of an Experiment in which a Large Percentage of Hydrogen was Converted to Hydrogen deuteride
Exp. Temp. Dosage Vapor Mole Composition3 no. °C ev x 1 0 “ 18 d en sity fra ctio n o f.th e gas G(HD) G(D2 ) G(T) d 2/ hd Separation m g./m l. H2 x 10 3 XHD XD2 x 1 0 2 fa c to r
31 295 9 . 1 2 0.661 6.55 0.221 0.0187 86.7 7 .4 1.91 0.085 1.81
a \ = 1 - *HD - % 2
03 O 81 complete absorption of the beta rays, and the upper by the size of the vessel. The pressure of the water in Experiment 55 was 1.7 atm.
Table 25 shows the results of an experiment in which the reaction time was such that a large fraction of the hydrogen (22%) was converted to HD. The value fo r G(D2 ) was higher than that obtained at a lower percent conversion (3%) at the same temperature. (See the results of Experiment 34 in Table 20). This difference in the G values cannot be attributed to errors in the analyses for D2 .
Carbon monoxidetwater vapor system
The reactions induced by tritium radiation in gaseous mixtures of carbon monoxide and heavy water were examined while varying the temperature and the mole fraction of carbon monoxide. The results of a brief but rewarding study are presented in Table 26.
The maximum uncertainty in the values of G(T), G(D2 ) , and
G(methane) is estimated to be 6% while that in GfQ^) is probably
10%. The higher estimated error in G(C02) is due to the uncer tainties in the mass spectrometer analyses.
Six of the experiments were performed at constant temperature
(215°C) while varying the concentration of CO from 1.5 mole % to
6.5 mole %. The other two had a constant mole fraction of CO of
1.6% and the temperature was varied from 278° to 318°C. The vapor density of all the experiments was 0.56 mg/ml. The G values
(calculated on the assumption that all the energy is absorbed by the water) show an increase with temperature indicating the presence TABLE 26 The E ffect o f Temperature and the Mole Fraction of CO on G(C02)» G(D2 )» G(T), and the Separation Factor
Exp. Temp. Dosage Vapor Mole no. °C ev x 10"*® d en sity fra ctio n G(C02) G ^ ) G(T) G(methane) Separation m g./m l. CO x 10^ x ic £ fa c to r
9 213 9.8 5 0.544 1.51 9 .0 b b b b
7 215 8.0 8 0.548 1.59 a 7 .2 0.31 b 1 .6
1 217 10.3 0.556 3 .4 2 a b 0 .3 0 b b
2 215 10.2 0.556 5 .0 3 7 .0 b 0.31 0 .6 0 b
3 212 13.5 0.564 6 .4 8 a b 0.2 8 b b
4 218 10.2 0.558 6.47 12. 9.7 0.32 0.64 2.1
6 278 5.1 6 0.563 1.61 31. 32. 1 .3 b 1.7
8 318 1.99 0.554 1.63 93. 95. 3 .9 b 1.7
a Not determined. In the majority of these cases, air has leaked into the small samples ( 20 ul at STP) and caused the mass spectrometric results to be unreliable.
k Indicates not determined. 83
of a chain mechanism.
The results of the mass spectrometric analyses of the fraction of the gaseous samples collected at -78°C are given in Table 27.
As can be seen, many species were present along with CO and CO2 . In this table the heights of the peak corresponding to the mass numbers are given relative to the height of the CO2 parent peak
(mass 44). Also, for ease in interpretation, the height of this peak is given in column three. All of the peaks have been corrected for the background in the instrument. Also, those peaks formed by the breakdown patterns of CO and CO2 have been disregarded since these were by far the largest components in the mixtures and made analyses for the small contribution from the other species impossible. TABLE 27 Mass Spectrum o f the Samples C ollected a t -78°C
Peak height x (10)2 relative to C02 peak height Exp. c o 2 no. T(°C) peak h g t. Mass numbers x 10t 2 52 51 50 49 48 47 43 42 41 40 39 38 36
9 213 30 0 .0 4 0.03 0.11 0.0 5 0.05 0.03 0.0 4 0.07 0.05 0.05 0.04 0.03 0.1 7 215 44 0.02 0.03 0.03 0.03 0.03 a a a a a a a 0.06 4 218 35 a a 0.06 0.06 0.07 0.06 0.06 0.06 0.09 0.09 0.04 a 0.11 6 278 66 a a a a a a a a a a a a 0.02 8 318 50 a a a a a a a 0.02 a a a a 0.04
C02 Exp. peak h g t. Mass numbers no. T(°C) x 1 0 - 2 35 34 33 32 31 30 27 26 20 19 18 15
9 213 30 0 .0 8 0.45 0.22 1 .7 0.47 1.1 a 0.17 0.32 0.08 1.1 0.07 7 215 44 0 .02 0.20 0.1 4 b a 0 .6 a 0.23 a a 0 .3 0.02 4 218 35 0 .06 0.28 0.20 1.8 0.40 0.54 0.11 0 .1 4 0.06 a 0 .3 0.04 6 278 66 a 0.02 a 0.03 0.03 0.14 0.06 0.06 0.03 0.02 0.15 0.02 8 318 50 0 .02 0.18 0.12 0.16 a 0.16 0.4 0.08 a a b 0.03
a This symbol indicates that peak was absent
k Undetermined
CO CHAPTER V
DISCUSSION
When beta particles pass through a medium, they lose energy by emmission of electromagnetic radiation (bremsstrahlung). by inelastic collisions, and by elastic collisions with the molecules of the medium. In the range of the energies of the beta particles emitted by tritium (0.018 mev to 0 mev), inelastic collisions form the dominant mode of energy transfer to the medium.^ The result of this process is the production of ions and excited molecules. 2 Bethe has derived an equation which demonstrates that the rate of energy loss from beta particles to the molecules of the medium is proportional to the number electrons in the molecules. Since water vapor is by far the largest mole percent (usually98%) in the mixtures irradiated in the experiments using hydrogen in this work, i t can be s a fe ly said th a t more than 99% of the energy is absorbed by the water molecules. Energy partition in the'exper- ments using carbon monoxide w ill be discussed later.
In order to discuss the mechanism involved in the exchange reactions, the nature of the reacting species must be ascertained.
All of the following remarks are taken from investigations of normal
(1 ) J . W. T. Spinks and R. J . Woods, "An Introduction to Radiation Chemistry," John Wiley and Sons, Inc., New York, 1964, p. 41. (2) H. A. Bethe and J. Askin in "Experimental Physics," E. Segre, ed., Vol. 1, John Wiley and Sons, Inc., New York, 1953, p. 166.
85 86 water vapor and are applicable in a general sense to gaseous heavy w ater.
In a convential mass spectrometer where the pressure of the water vapor is less than 10"^ mm, Mann jet al.^ found that the positive ions
HgO+ and 0H+ formed 91% of the total ion current while the negative ions H” and 0“ formed only0.11%, This has been further substan tiated by the mass spectrometer study by Cottin.^ At a sample pressure of 10"^ mm and electron energies of 50 ev, the intensity
of the negative ions relative to that for H2 0 + (intensity of =
100) were H~, 0.0044; 0", 0.9; and OH”, 0.03. Cottin further determined that the OH” ion resulted from an ion molecule reaction.
The formation of negative ions from water vapor in the presence of
oxygen was studied by Wobschall, Graham, and Malone^ using an ion
cyclotron resonance spectrometer. They observed that the ions H”
and 0” were formed at electron energies of 5.6 and 7 ev respectively.
The H20” ion was also observed at electron energies of 70 ev, but
in very small yields. Its mode of production was not established.
The principal ions formed in the primary event by electrons
passing through water vapor are, then, H20+, 0H+, H“, and 0“ .
(3) M. M. Mann, A. H u stru lid , and J . L. Tate, Phys. Rev. , 58 340 (1940). (4) M. C o ttin , J . Chim. Phys. , 5 6 , 1024 (1959). (5) D. Wobschall, J. R. Graham, Jr., and D. P. Malone, J. Chem. Phvs.. 43, 3855 (1965). 87
The 0H“ ion is absent from the primary mass spectrum of water because, according to L a id le r ^ , the states of H20 correlate with repulsive states of 0H“ leading to 0" or H”.
The electronic excitation spectrum of water vapor has been stud ied by the electron trapping technique7 and the electron impact
Q technique. Both methods showed absorption maxima at approximately
7.5 ev, 9.5 ev, and 12.5 ev. Energy absorption at 7.5 ev and 9.5 ev 0 results in the production of H atoms and OH radicals.7 The absorption at 12.5 ev corresponds to the first ionization potential of water.
Neutral species formed in the primary event by the irradiation of water vapor are then H atoms and OH r a d ic a ls.
The primary ionic species may react with water molecules as fo llo w s:
h2o+ + h2o ^ h3o+ + OH (1)
H" + H20 > 0H“ + H2 (2)
Reaction (l) has been observed in the high pressure mass spectrometer stu d ies of Lampe, F ie ld , and F r a n k lin .^ This s p e c ific reaction was postulated for the formation of H^O4" because the intensity of the
(6) K. J. Laidler, J. Chem. Phys.. 22, 1740 (1954). (7) G. J. Schultz, J. Chem. Phys.. 33, 1661 (I960). (8) E. N. Lassettre, Rad. Res. Supp. 1, 530 (1959). (9) M. Burton, J. S. Kirby-Smith, and J. L. Magee, "Comparative Effects of Radiation," John Wiley and Sons, Inc., New York, I960, p. 156. (10) F. W. Lampe, F. H. F ield , and H. L. Franklin, J . Am. Chem. Soc.« 72, 6132 (1957). 88 mass 19 peak depended on the square of the sample pressure, and its appearance potential was close in value to that of the ion.
When Muschlitz-'-^ studied the negative ion spectrum of water vapor, he observed that the intensity of the signal from the OH” ion was
small at low pressures but increased rapidly with the pressure. At
4 mm sample pressure, the OH” ion was the most abundant negative ion
in the spectrum. Muschlitz also found that the sum of the curves for
the ion currents from the OH” and H“ ions was always roughly p a r a lle l
to the 0“ curve as the pressure increased. On this basis, he postulated reaction (2). Further evidence for reaction (2) was
presented by Cottin.4 Also he observed that the 0H“ ion had the
same appearance potential as the 0“ ion. This along with the fact
that the intensity of the OH” ion depended on the square of the
sample pressure led him to postulate reaction (3).
QT + H20 ---- > OH" + OH (3)
Another interesting ion molecule has been proposed by Henglein
and Muccini-^ to account for the absence of any chemical evidence for
the existence of the 0H+ ion in the radiolysis of water. Using a
specially designed mass spectrometer they could focus the primary ions
of a species and cause them to collide with a beam of neutral molecules.
The primary ion spectrum of water vapor in their instrument showed the
(11) E. E. Muschlitz, Jr., J. Appl. Phys., 28, 1414 (1957). (12) A. Henglein and G. A. Muccini, Z. Naturforschung, 17-A, 452 (1962). 89
*+* same relative intensity for OH as in the spectrum obtained by Mann et al.^ Surprisingly though, the 0H+ ion was completely absent from the secondary ion spectrum. They attributed this to the charge transfer reaction (4).
OH+ •+ H20 ---- > OH ■+ H20+ (4)
As a result of these ion molecule reactions, the secondary species formed in water vapor are OH radicals, the H^O-*- ion, and small y ie ld s o f H2 and OH".
The fact that the negative ion current is only a fractional percent of the positive ion current in a mass spectrometer does not justify neglecting the interaction of water molecules with electrons.
The energies of the electrons in mass spectrometers are much larger than those of the secondary electrons formed in radiation chemistry
1 ^ experiments. This energy distribution has been calculated by Bethexo for the secondary electrons formed by 1 kev electrons passing through a medium. The surprising result is that about half of the secondary electrons have energies less than 5 ev. Thus, the interac tion of water molecules with low energy electrons has to be considered.
Electron capture is a resonance process. Only those electrons which have energies that can accomodate the various energy levels of the negative ion formed will be captured. This reaction is schematically illustrated by (5).
(13) H. A. Bethe, "Handbuch der Physik," Vol. 24, Pt. 1, Julius Springer, Berlin, 1933. 90
A -+ e" — > A" (5)
The possibility of dissociative capture (reaction 6 ( )) a lso e x is t s .
A -+ e~ — > B" C (6)
This type of capture will occur if the attachment of the electron to 14 A w ill liberate enough energy to break the bond. Magee and Burton, from a consideration of the negative states of H2 0 , state that isolated water molecules w ill not interact with thermal electrons.
Also, both of the following reactions are endothermic.'
H20 4 e - _ * H“ -r OH (7)
H20 -t- e“ — > H -+ OH" (8 )
The first reaction is endothermic by 100 kcal/mole*^ (117kcal-17kcal) and the second by 67 kcal/mole, (I17kcal-50kcal). In these calculations, the H-OH bond energy is 117 kcal/mole^ and 17 kcal and 50 kcal are the electron affinities of H and OH,^ respectively. 17 Platzmann has stated that a rough estimate of the endothermicity
of reaction (8 ) is 46 kcal/mole. The uncertainty in these
calculations arises from the values for the electron affinities of
H and OH.
The interaction of water vapor and low energy electrons has
(14) J. L. Magee and M. Burton, J. Am. Chem. Soc.. 73, 523 (1951). (15) S. C. Lind, ‘'Radiation Chemistry of Gases,” Reinhold Publishing Co., New York, 1961, p. 289. (16) H. 0. Pritchard, Chem. Revs., 52, 529 (1953). (17) R. L. Platzmann in “Basic Mechanisms in Radiobiology,” Nat. Res. Council Publication 305, Washington D.C., 1953, p. 30. 91
been investigated by the electron swarm technique’*-® and the electron beam technique.^ in both studies, no interaction was observed below electron energies of 5.5 ev confirming the prediction by
Magee and Burton.^ In a recent paper^ Wobschall and co-workers studied the interaction of oxygen and mixtures of oxygen and water vapor with low energy electrons using the technique of ion cyclotron resonance spectrometry. This procedure enabled them to determine the mass of the negative ion formed and thus unequivocally establish its identity. In pure oxygen the ions CT and 0^" were observed. When water vapor was added, the ions H” and 0H“ were observed but at electron energies higher than 5 ev. They attributed the source of the OH” as dissociative capture. The works of
Muschlitz-*--*- and Cottin^ have firmly established that 0H“ is not formed by dissociative capture of an electron. Since 0” was present in their experiments, a more likely source of OH” would be reaction (3) suggested by Cottin.^ It is interesting to note though that Wobschall _et _al.observed the H2 O” ion but only in small yields at electron energies of 10 ev. It was suggested that an impurity or fa u lty vacuum technique could account fo r i t s production.
In any case, if negative ions form from an impurity interacting with the thermal electrons or otherwise, they decrease the amount
(18) G. S. Hurst, L. B. O'Kelley, and J. A. Stockdale, 2nd Int. Congr Rad. Res.. (Harrogate, 1962, Abstr.) p. 128. (19) I. S. Buchelonikova, Soviet Phys., JETP, 35, 783 (1959). 92
of excitation energy that will be released upon neutralization of a positive ion. This is illustrated by the following examples. The neu
tralization reaction (9) is exothermic by 25 kcal/mole.
H30+ + e------> 2H + OH (9)
This is calculated using the following reactions*
H30+ ----- * H+ + H20 (10)
H20 -----> H + OH (11)
e- + H+ — * H (12)
It can be seen-that AHg = AH^q + AH^ + AH^* The proton affinity
of water i s 167 kcal to 171 kcal.^O The heat of rea ctio n (11) was
determined by using heats of formation data from a compilation by
Benson, and AH^ is the negative of the ionization potential for
hydrogen atoms also obtained from Benson. The result of these
calculations is that AHg = (167 to 171) + 119*1 - 313 = -25*3kcal/mole.
This result is in agreement with -22kcal calculated by Fiquet-
Fayard.22 if neutralization by 0H~ is now considered, it can be
seen that reaction (13) is endothermic by approximately 25kcal/mole.
0H“ + H30+ 2H + 20H (13)
This endothermicity is caused by the 50 kcal/mole electron affinity
of OH.^ Another possible mode of neutralization is reaction (14).
(20) F. W. Lampe and F. H. Field, Tetrahedron, 7^, 189 (1959). (21) S. W. Benson, J. Chem. Edu., 42, 502 (1965). (22) Mme. Florence Fiquet-Fayard, J. Chim. Phys., 57, 453 (I960). 93
OH” + H3 0+ -----* H20 + H + OH (14)
This reaction is exothermic by the large amount of energy, 94 kcal/ mole. Thus, the presence of negative ions may tend to decrease
the number of H atoms and OH radicals formed by the neutralization
o f H30 +, depending upon the efficiency of the neutralization process.
Neglecting for the moment the possible presence of impurity
anions, the predominant reactive species in the radiation chemistry
of water vapor are KgO*, e**, H, and OH. The results of this study
can be rationalized using these species.
Figure 11 shows the values of G(HD) in the form of an Arrhenius
plot. The mechanism of the exchange below 250°C w ill new be
d iscu ssed .
Since the source of the radiation is distributed homogeneously,
the distribution of the reactive species will be spatially uniform
throughout the relatively low density reaction system.
Reactions involving ions will be considered first. It is evident
that these reactions must compete effectively against any neutraliza
tion reactions. One ionic reaction which could account for the
exchange is
D20tfH 2 j. D20H+ + H (15)
This could then be followed by neutralization to give HD. Field
and FranklinlO have found evidence for reaction (15) and have deter
mined its rate constant to be 3.1 x 10“^ cc/molec-sec. in the absence
of repeller voltage. The rate constant for reaction (16) is given 94
2.0
□
I. 6 2.0 2.5 2.8 I / T ( ° K x I03 ) Figure II. Temperature dependence of G(HD) vapor density of chain region is 0. 595 mg./ml. 95 by Field and Franklin-^ to be 2.2x10“^ cc/molec sec.
D20+ + D2° > D30+ + 00 (16)
It is then established that at the mole fractions of hydrogen used in this study (4x 1 0 - 3 to l x l 0 “2 ), hydrogen cannot effectively compete for the D20 + io n .
Another ionic mechanism which could form HD is the proton transfer reaction (17) followed by neutralization.
D3 °+ + H2 ------5. D20 + H2 D+ (17)
The proton a f f in it y of H2 O has been estimated by Lampe and Field^O to be 7.3 to 8 . 6 ev/molecule and that for hydrogen to be only 2.7 to 3.5 ev/molecule. Thus, reaction (17) would be approximately 5 ev/molecule endothexmic and would not compete significantly with neutralization.
One additional ionic reaction which could account for the formation of HD is the following exchange steps
D30+ + h2 — > D2 0H+ + HD (18)
This could then be followed by the proton transfer reaction (19).
D2 0H+ + D20 DOH + D3 0+ (19)
Henglein and M u c c i n i ^ 3 have found evidence for charge transfer reactions between like species as in reaction (2 0 ).
(23) A. Henglein and G. A. Muccini, Z. Naturforschung, 18-A, 753 (1963). 96
H20+ + H2° > H2 ° + H2 0+ (20)
Although proton transfer reactions between like species have not been observed by using a mass spectrometer, there is no reason that they should not occur. Such reaction s have been p o s tu la te d ^ and shown^S to be occurring in CH4 , CD4 mixtures subjected to tritium beta radiation.
There is no direct precedent for reaction (18). Indirect chemical evidence has been furnished for reaction (21) by R. H.
L a w r e n c e ^ in his study of the formation of CH^D in mixtures of
98% TD/D2 ( l : 1 0 0 )s 2%CH4 as compared to those containing 3% NH3 .
It was demonstrated that the presence of ammonia inhibits proton transfer steps by scavenging protons in this system, thereby lowering the frequency of the exchange reaction (2 1 ).
CHj + D2 ------* CH4D+ + HD (21)
There seems to be little doubt that (21) competes effectively with n e u tra liza tio n in the absence o f ammonia. The p o ssib le occurrence of reactions (18) and (19) cannot be ruled out from the lack of direct precedent. The significance of the contribution of these reactions will be considered later.
A suitable free radical mechanism for the exchange process
(24) R. F. F iresto n e, ad. FJ. Lemr, and G. J . Trudel, J . Am. Chem. Soc.. 84, 2279 (1962). (25) R. H. Lawrence and R. F. Firestone, J. Am. Chem. Soc., 87. 2288 (1965). (26) R. H. Lawrence, Ph.D. dissertation, Ohio State University, Columbus, Ohio, 1965. 97 below 250°C is the following sequence involving D atoms and OD r a d ic a ls.
D + H2 > HD + H (22)
OD + H2 > HOD + H (23)
H + H*S ------> H2 + S (24)
H + H + M -> H2 + M (25)
Direct experimental evidence to support this mechanism has been reported by Firestone2 7 in his study of the analogous
— H2 0 :D2 system. His results showed that G(HD) was always equal to
G(-D2) within + 10%. (In the above sequence G(HD) would equal
G(-H2 ) ) . OQ The exchange reaction (22) has been studied thermally, catalytically,29 and photochemically. 2 2 Benson2-1- reports that it has an activation energy of 4.9-5.4 kcal/mole.
Evidence for reaction (23) has been presented by Gevantman and
Yang, 22 who studied the rate of HTO formation in mixtures of tritium and light water vapor in the presence of excess amounts of inert gases. They found that the rate of production of HTO was second order with respect to the tritium concentration and first order with
(27) R. F. Firestone, J. Am. Chem. Soc., 79, 5593 (1957). (28) G. Boato, G. Careri, A. Cimino, E. Molinari, and G. G. Volpi, J. Chem. Phys., 24, 783 (1956). (29) W. R. Schultz and D. J. LeRoy, Can. J. Chem., 42, 2480 (1964). (30) H. Niki, Y. Rousseau, and G. J. Mains, J. Phys. Chem., 69, 45 (1965). (31) S. W. Benson, "The Foundations of Chemical Kinetics, "McGraw- Hill Book Co., Inc., New York, I960. (32) J. Y. Yang and L. H. Gevantman, J. Phys. Chem.,6 8, 3115 (1964). 98
respect to the dose rate, which was in turn proportional to (T2 )•
This indicates that the rate determining reaction in their system was
OH + T2 ____ > TOH + H (26)
Further evidence for reaction (23) was presented by Chen and
Taylor^ in their study of the photolysis of water vapor in a flow system. When pure water vapor was photolyzed, H202 was formed on a cold finger at the end of the reaction tube. Introduction of H2 into the system caused the rate of production of H2 O2 to decrease.
The rate was then found to be inversely proportional to the square of th e H2 pressure. This can be shown to be evidence for the following reaction.
OH + H2 ------» H20 + H (27)
Reaction (24) represents the first order recombination of radicals at a surface, S, and reaction (25) the second order homo geneous 3-body recombination.
Reference to Figure 11 w ill show that there is no segment of the Arrhenius plot with a slope characteristic of the activation energy for reaction (22). In order for an activation energy to be observed, there has to be a competing reaction for the removal of the reactive species (in this case D atoms). The competing reaction
(33) M. C. Chen and H. A. Taylor, J. Chem. Phys.. 27. 857 (1957). 99
is recombination, either heterogeneously at a surface or homogeneously
in the gas phase. The corresponding reactions for H atoms are reactions (24) and (25). Of course, D atoms could also recombine with OD radicals. These recombination reactions are favored by low mole fractions of hydrogen, high dose rates, and large surface-to- volume ratios. In this study, the surface-to-volume ratio was
0.75 cm- -1-. Changing the mole fraction of hydrogen from 3.50 x 10-3
(Exp 9) to 9.7 x 10-3 (Exp 27) and the dose ra te3^ from 0.473 x 1 0 ^
ev/l-min (exp 27) to 1.07 x lO1^ ev/l-min (Exp 9) had no apparent
effect on G(HD) in the temperature region 110°C to 224°C. In the data published by Firestone27 0n th e H20sD2 system , the 100
ev/exchange yields were independent of these variables below 200°C.
The surface-to-volume ratio was varied from 0.7 to 1.1 cm"-1-, the
dose rate from 0.674 x lO1^ ev/l-min to 8.22 x 10^ ev/l-min,
and the mole fr a c tio n of deuterium from 4.91 x 10- 3 to 9.21 x 10“3 .
In the study reported by Baxendale3^ on the radiolysis of mixtures
o f D2 O and H2 using Co^O gamma rays, G(HD) was found to be independent
of the variation of the mole fraction of hydrogen from 0.1 x 10-3
to about 1.2 x 10-3. Although the experimental details were not
specifically stated with this report, it is assumed that they are
the same as those reported in their study on the radiolysis of
(34) The dose rate in each experiment can be obtained by multiplying the vapor density by 1.31 x 10^-^. (35) J . H. Baxendale and G. P. G ilb ert, D isc . Faraday S o c ., 36, 295 (1963). 100
H2 O. 36 The dose rate was 0.3 x 10^ ev/l-min, the temperature was
116°C, and the surface-to-volume ratio was 0.28cm“l . Thus, within these conditions i t can be said that hydrogen effectiv ely scavenges the atoms produced in the radiolysis of water, and, consequently, no activation energy for reaction 2 ( 2 ) is observed.
The decrease in G(HD) between 110°C and 84°C can be attributed to a decrease in the effectiveness of the scavenging reaction to that of a reaction removing the radicals. The work of Firestone^ showed that the most important reaction for the removal of the radicals was the first order loss at the wall. It is, of course, possible to maintain adequate vapor densities at temperatures below 84°C by employing larger reaction v essels, since the half- pressure for tritium beta rays varies directly with the radius of the spherical vessel. Employment of larger vessels, however, requires the use of larger bake-out ovens and increases thetotal wall surface area in proportion to the squareof the radius.
Since the wall has been shown to the most important source of impurities, 27 the use of vessels large enough to accomodate studies in the temperature region required for the evaluation of the activation energy for reaction 2 ( 2 ) seemed inadvisable at this time.
In the ionic sequence for the production of HD represented by reactions (18) and (19), each cycle produces one molecule of HD while one molecule of H2 has reacted. Consequently, the equality of G(HD)
(36) Ib id ., p. 186. 101
and G(-D2 ) found by Firestone in the analogous system is still valid
and cannot be used to evaluate the importance of the ionic sequence
as compared to the atomic sequence.
The rate equation for the production of HD using reactions (22),
(23), the first order wall reaction (24), and the ionic reaction (18)
is given by expression (A).
d(HD)/dt = k2 2 (D)(H2) + k1 8(D3 0+)(H2) (A)
The necessary neutralization reactions to produce radicals are
D3 0+ + e- —=> 2D + CD (28)
D2 OH+ + e- Neutralization products (29)
The steady state concentration of D3 0+ can be evaluated in terms of measurable quantities by using a steady state rate equation for
electrons in the system.
d(e-)/dt = 0 = I/W - k2 8(D3 0+)(e-) - k2 9(D2 OH+)(e-) (B)
In this equation, I is the dose rate in ev/cc-sec and W is the mean
energy (ev) necessary to form an ion pair.
(e-)ss = (D30+)ss + (D20H+) ss (C)
Lawrence and Firestone2^ have presented evidence that the proton
transfer reaction in the case of methane has no thermal activation
energy. It will be tentatively assumed that reaction (19) requires
no thermal activation energy, and the effects of th is assumption
w ill be explained later. 102
r \ r The exchange reaction (21) has been reported to require a small but observable thermal activation energy, and thus it is conceivable that reaction (18) has a small activation energy.
Since the concentration of water is much greater than that of hydrogen and reaction (18) is assumed to have an activation energy, whereas reaction (19) does not, it may be said that
(e -)ss = (D 3 ° + ) s s (D)
Substitution of this expression into equation (B) results in
(D3 0+)ss = (I/Wk28) i (E)
The rate equation for the production and disappearance of
D atoms is then given by (F).
d(D)/dt = 0 = kQI + nk2 8 (D3 0+)s g - k2 2 (D)s s (H2) (F)
Again, I is the absorbed dose rate, kQ is a constant related to the production of D atoms by excitation of water molecules (molecules/ ev), and n is the number of D atoms produced in the neutralization on reaction (28). The steady state concentration of D atoms is then
(D)ss = I(k0 + n/W)/k2 2 (H2) (G)
The rate of production of HD is given by (H) and the G value by (I).
d(HD)/dt = I(k 0 + n/W) + k1 8(H2 )(l/Wk28)£ (H)
G(HD) = (kQ + n/W + k1 8(H2 )(!Wk2 8) 4 ) l 0 2 (I)
It can be seen that the magnitude of the la st teim in
Equation (I) is d irectly proportional to the concentration of hydrogen 103
and inversely proportional to the square root of the dose rate.
In th is study the concentration of hydrogen was not changed in the temperature-independent region. The variation of the mole fraction of hydrogen reported in the several tabulations of experimental data reflect only the changes in the water vapor concentration. The work of Firestone^ 7 shows no e ffe ct on G(HD) of a 3-fold change in the ratio (H2 )/ri' (1.0 x 10 ^ ) . ^ 7 Calculations on the data of Baxendale and Gilbert^ give a result of 0.6 x 10^ for this ratio. The largest value of the ratio used in present investigations was 5.0 x 10^-. This ratio has the dimensions of raolec cc“fsec2" i ev“2".
In their investigation of the jadiolysis of heavy water,
Baxendale and Gilbert^ obtained a higher G value for the production of hydrogen deuteride when hydrogen was used as a scavenger as opposed to methanol (10.5 compared to 7 .0 ). They suggest that the reason for the increase is that hydrogen enters into some reaction with an intermediate that is not possible with organic additives.
Conceivably, one such reaction is the ionic exchange reaction (18).
This is certainly not the case, however, at the dose rate used in
Baxendale’s investigation, for the effect predicted by equation (I) was not observed over a 1 2 -fold change in the concentration of hydrogen.
(37) See the results of experiments 2-1, 4-1, and 5-1 in reference (27). It should be mentioned here that the factor given in footnote 6 of Table II in that reference should be lCr1^ instead of 10~17 . 104
An upper lim it can now be set on the ratio ^g/k^g^" by using Equation (I). The value of W is probably approximately
30 ev/ion pair.38 In this investigation G(HD) was found to be
13.5+0.4. The f ir s t two terms of Equation (I) are constants and can be equated to 13.5. Consequently, any variance observed in experiments with the hydrogen concentration or dose rate can be equated to the third term. Thus the third term has a maximum value of 0.4, and the ratio ^iq/^ -2 ^ ^as an uPPer limit of
4 x 1 0 “-*-^cc£r/molecfrsec2
The ratio of the rates of reactions (18) and (28) can now be
evaluated from the following expression.
V R28 = kI8
/k28ss After substitution for the steady state concentration of 0 3 0 "*",
equation (J) becomes
^ 13/^28 =: ^18 ^ )
The calculated upper limiting value of this ratio is, then, after
substitution of the upper limit for ^1 3 /^2 8^’ equal "to H» This
indicates that, by equating the third term of equation (I) to 0.4,
a ratio of rate constants is obtained such that the ionic exchange
(38) R. L. Platzman and E. J . Hart, "Mechanisms in Radiobiology," Vol. 1, Academic Press Inc., New York, 1961, p. 176. (39) The dose rate which was used to calculate this value was 5.2 x 10-*-0 ev/cc-sec, a representative value. 105
reaction may compete favorably with the neutralization reaction.
If the experimental error were larger, this ratio would be larger.
The rate constant IC23 has not been measured for ions and
electrons in water vapor. An estimate can be obtained and is probably of the order of 10“^cc/molec~sec.^® This gives a value
of 1 0 - -^cc/molec sec for k^g, which is two orders of magnitude higher than lO’^cc/m o lec -sec estimated by Pratt and Wolfgang4"*-
for reaction (30), which they postulated.
CH5+ + t 2 ------> CH4T+ + HT (30)
Using a value lower by two orders of magnitude in equation (K) w ill
show that the ionic exchange reaction would not compete with neutralization. The assumption that E^g is nearly zero is not
necessary since the concentration of water is so much larger than
that of hydrogen, allowing the concentration of D2 OH4" to be ignored.
As shown above, the results of this investigation are not
sufficiently conclusive for the exclusions of reactions (18) or
(19). Also, a mechanism involving the complete efficiency of
reaction (18) and inefficiency of (19) could explain the fact that
Baxendale^ observed no dependence of G(HD) on the increased
concentration of hydrogen.
Firestone4 2 has stated that the lower G values obtained by
(40) A. von Engel, "Ionized Gases," 2nd ed., Oxford Press, London, 1965, p. 163. (41) T. H. Pratt and R. Wolfgang, J. Am. Chem. Soc., 83. 10 (1961). (42) R. F. Firestone, Disc. Faraday Soc., 36, 294 (1963). 106 using organic scavengers can be explained by the interaction of these additives with protons thus altering the nature of the neutralization reaction (28). This would decrease the yield of radicals as explained ea rlier.
The source of the "molecular yield" of D2 will now be discussed.
The mean valve of G(D2 ) (0.67+0.11) obtained in this study is some what higher than that found by Baxendale and Gilbert^ (0.53+0.06) and that of Anderson43 and co-workers (0.47+0.01). Due to the large experimental error in the present work and the rather optimistic uncertainties assigned to the other values, these three results have to be considered in essential agreement.
There are two obvious reactions which could form D2 in th is system. The first is the result of D atom attack on HD (reaction
(31)) and the second is the ion molecule reaction (32) analogous to that observed by Muschlitz^ and Cottin^ in the case of normal water vapor.
D + HD D2 + H (31)
D" + D20 ------* D2 + OD- (32)
The lower limit of the reaction cross section for the isitopic analog of reaction (32) has been reported to be lO^^cm^/molec'*''1- which makes i t s rate comparable to those for positive ion molecule
(43) A. R. Anderson, B. Knight, and J. Winter, Nature, 201, 4923 (1964). 107
r e a c tio n s.^ R. L. Platzman^ 4 has calculated the G values for the production of H2 from reaction (2 ), the isotopic analog of
reaction (32), to be 0.2*0.1 for the case of liquid water, and
suggests that the process should be just as efficient in the vapor phase.
If the D2 resulted from reaction (31), the G value would
obviously be expected to be dependent on the amount of HD present,
that is, on the percent conversion of the hydrogen. No trend in
G(D2 ) is apparent from 1.9% conversion (Exp. 17) to 12% conversion
(Exp. 35) as shown in Table 19. This observation may not be
significant because of the very considerable uncertainties in
G(D2 ) at the lower conversions. No percent conversion data were 34 presented by Baxendalq,and Gilbert. When reaction (31) is
included in the mechanism, the reaction of OD radical attack on
HD cannot be neglected. Further, it can be seen that the steady
state concentration of D atoms would be dependent on the amount of
HD or D2 present (eventually almost a ll the hydrogen would be in
the form of HD or D2 ). Thus, one would have to include a reaction
allowing D atoms to reach the wall of the vessel. As a result of
these additional reactions, the kinetic expressions appear to be
too complex to evaluate G(D2 ) as a function of the percent conversion.
Figure 11 clearly shows that two or more mechanisms are
(44) R. L. Platzman, 2nd. International Cong. Rad. R es., (Harrogate, 1962, Abstr.) p. 128. 108 contributing to the formation of hydrogen deuteride. Above ap proximately 245°C a strongly temperature dependent process is predominant and the curvature at the high temperature end of the plateau (i.e., at 150°C) can be attributed to the onset of this process.
The plateau value of 13.1 for G(HD) has been subtracted from the G values at the high temperatures, and an Arrhenius plot of the results is presented in Figure 12. The valve of 13.1+0.3 is the average of the values for G(HD) of experiments 5, 6, 8 , 9,
12, 20, and 21. The same procedure has been applied to the G values obtained at a lower vapor density of 0.319 mg/ml and these results are also plotted in Figure 12. The slopes of the lines drawn through these sets of points were determined by the least
squares method. The last point in the results found at 0.595 mg/ml has been disregarded because of the large relative error in the difference between two numbers which are nearly equal.
Apparent Arrhenius energies of 19.2 kcal/mole and 19.5 kcal/mole have been calculated for the high and low vapor densities,
respectively.
The data for G(T) (cf. Tables 20 and 21) have been treated
in identical fashion, and the results are plotted in Figure 13.
In the low temperature region the constant value of G(T) is
0.327+0.11 x 10“2, which is the average of the results of
experiments 8 , 9, 12, 20, and 21. At a vapor density of 0.595 mg/ml the Arrhenius energy for TH formation is 21 kcal/mole, and o o>
[ g (HD)- G(HD)0 1 2.00 2.20 2.40 1.40 1.80 Figure 12. Temperature dependence of of dependence Temperature 12. Figure .60 0. mg./mI. 9 1 .3 -0 0 0.55 mg./ml. 595 . -0 □ (Do a vpr este of densities vapor at G(HD)o] .1 m.m. n 055 mg./ml. 0.595 and mg./ml. 0.319 1.60 / (K"‘ I3) I03 ‘ x " (°K l/T
.0 .01.90 1.801.70 [ g (HD)~ 109
110
-1.40
-1.60
-1.80
O'
- 2.00
0-0.319 mg./ml.
□-0.595 mg./ml. - 2.20
1.60 1.70 1.80 1.90 I/ T (° K"‘ x I0 3 ) Figure 13. T em p eratu re dependence of [G(T)- G(T)0] at vapor densities of 0.319 m g./m l. and 0.595 mg./ml. I l l
at 0.319 mg/ml it is 19 kcal/mole.
Before discussing the mechanism involved in the high temperature radiation-induced chain exchange of water vapor and hydrogen, it is advantageous to examine the results of the experiments with water vapor and carbon monoxide.
In experiments 3 and 4 (of Table 25), the CO was present at approximately 6 mole percent. Thus, i t can be said that CO absorbs some of the incident energy and forms predominantly C0+ and excited CO molecules. Comparison of the ionization potentials^! of CO and H2 O shows that the charge transfer reaction (33) is exoergic by about 1.4 ev/molecule and cannot be ignored.
C0+ + D20 ------> CO + D20+ (33)
Similar reasoning indicates that charge transfer from D2 0+ to CO would not occur appreciably. Thus, the formation of C0+ would probably lead to the formation of D2 0 + . Although excited CO molecules undoubtedly are present in this system, their abundance is probably relatively low because of the small percentage of CO molecules present.
The temperature dependence of G(D2) and G(C0 2 ) in D20/C0 mixtures is shown in the Arrhenius plot of Figure 14.
The slope of the best straight line drawn through the experi mental points corresponds to an Arrhenius energy of 11 kcal/mole.
If it is assumed that the yields at the lowest temperatures 112
O G(D~)
□ G(C02) .80 [> Corrected G values
G(product)
1.40
.00
1.70 1.90 2.10 I/ T (° K“* x I03 ) Figure 14. Temperature dependence of G(D2) and G(C02) in the D20 : CO system. 113 correspond to a constant non-chain region, as in the case with hydrogen, then the appropriate subtraction procedures can be applied giving the lower line in Figure 14. The Arrhenius activation energy calculated from the slope of this line is 22 kcal/mole.
It is apparent from the results in Table 26 that G(D2 ) =
G(C02). The agreement is quite good in the high temperature experiments (above 200°C), and within 10% for the experiments at
215°C. The values of G(CC>2 ) show no apparent trend with increasing mole fraction of CO, but such a trend may be present in the case of the two determinations of G(D2 ).
The following free radical mechanism is consistent with these results for non-chain production of CO2 or D^.
D20 — D + OD (35)
OD + CO - > C02 + D (36)
D + D + M - 2> D2 + M (37)
D + D*S ~~----- > D2 + S (38)
Reaction (35) is a shorthand expression for a ll of the radiation induced processes which produce D atoms and OD radicals.
Reactions (37) and (38) are simply radical recombination reactions, in the gas phase and at a surface, respectively.
Unequivocal evidence for reaction (36) has recently been 114 presented by Stief and co-workers.^ A mixture of 18 mm and 0.5 mm of CO was condensed on a surface at -196°C. It was stated that only about 0.25 mm of CO was entrapped in the solid, and that the remaining portion was pumped away. Excitation of the water with 1470 A0 and 1236 A0 light resulted in the formation of C016018.
The activation energy of reaction (36) has been estim ated^ ’ to be in the range 2-7 kcal/mole. Stief and co-workers suggest that, since the reaction occurs readily at -196°C, the lower value is probably correct. On the basis of these observations, it is difficult to assign the observed activation energy of 11 kcal/mole to this reaction. (The activation energies of reactions (37) or
(38) are also zero or very small).
On the other hand, i f there were two mechanisms taking place, as in the case of the hydrogen and water vapor systems, the increase in the G values above 215°C could be attributed to the occurrence of the chain propagating reaction (39). Calculations using heats
D + D20 ----- D2 + OD (39)
of formation data from B e n s o n ‘S show this reaction to be endothermic by 15 kcal/mole, and thus the enthalpy of activation would have to be at least this great.
(45) L. J. Stief, V. J. DeCarlo, and J. J. Hillman, J. Chem. Phys., 43, 2490 (1965). (46) A. Y. -M. Ung and R. A. Back, Can. J . Chem., 42, 753"(1964). (47) L. E. Avramenko and R. V. Kolesnikova, Advan. Photochem., 2, 25 (1964). 115
Fenimore and J o n e s ^ 8 have found the activation energy for the analogous reaction (40) to be 25.5 kcal/mole,
H + D20 ------> HD+ OD (40) in reasonable agreement with the value of 2 2 kcal/mole obtained by subtraction of the assumed constant G value. The activation energy for the reverse reaction (41) has been r e p o r t e d ^ , 47 to be 7-10 kcal/mole, but Del Greco and K a u fm a n ‘S have suggested that it should be closer to 7 kcal/mole. In any event, the difference between EA (22 kcal) and is probably 12 to 15 kcal/mole, which
OH + H2 — > H20+ H (41) is in agreement with the endothexmicity of reaction (42) or the analogous reaction (39).
H + H20 > H2 + OH (42)
Table 26 shows that methane was formed with a G value of
0.62*0.02. This is in agreement with the value of 0.5*0.2 found by T in g e y ^ O in the radiolysis of approximately equimolar mixtures ■ of CO and H20 using Co^O gamma rays. He showed that the G value was independent of temperature in the range 100 to 500°C. He also obtained evidence for the formation of methanol. D o u g l a s ^ l found
(48) C. P. Fenimore and G. W. Jones, J. Phys. Chem., 62, 693 (1958). (49) F. P. Del Greco and F. Kaufman, D isc. Faraday Soc., 33, 128 (1962 ). (50) G. L. Tingey, Battelle-Northwest, Richland, Washington, private communication. (51) D. L. Douglas, J. Chem. Phys., 23, 1558 (1955). 116
that mixtures of hydrogen, tritium , and carbon monoxide produced formaldehyde, acetaldehyde, and some glycols. As can be seen from
Table 27, the mass spectrum-of the samples collected through a cold trap at -78°C is quite complex. In the majority of cases, however, the signals were very small ( 0 . 1%) when compared to the signal from CC^. This could be indicative of a small yield of organic products or, simply, of the low vapor pressure of these species at -78°C.
The peaks at mass numbers 36 and 34 have relative in ten sities 59 corresponding to perdeutero methanol. Likewise, the peaks at mass numbers 35 and 33 have relative in ten sities corresponding to mono- protonated methanol. Presumably, the H atoms could come from the walls of the reaction vessel. The response at mass 30 can be attributed to the DC0+ fragment of formaldehyde, acetaldehyde, or formic acid. A response at mass number 26 is present in all the experiments and could be due to C^D4" from the breakdown pattern of perdeutero acetylene.
Since the D and 0 atoms are not in the ratio of 2:1 in the known organic products, the equality of G ^ ) and GfCC^) would no longer be true, if the reactions producing the organic products were appreciable. This has been found by Tingey^O to be the case
(52) "Index of Mass Spectral Data," American Society for Testing Materials, Philadelphia, Pa., (1963). 117 below 300°C. Above this temperature the two G values become equal.
It is difficult to establish with certainty the G values for the production of these organic products. If G(HD) 0 is taken as a true measure of the radical yield in the radiolysis of water vapor in the presence of H2, then methane and deuterium account for 84% of the total D atom yield, as shown by the following calculation.
G(D2 ) + 4 G(methane) _ n>Q ( 1Q2) = 84% (L) G(HD) 0 13.1
Thus, an upper limit for the G value for the production of organic molecules is 2.1, assuming a maximum average of 2 D atoms per organic molecule. The absence of the majority of the peaks resulting from the organic products in the mass spectra obtained from the two experiments at the higher temperatures supports Tingey*s observa tions and the hypothesis that these organic products are formed
in even lower yields at higher temperatures.
A mechanism for the production of methane, methanol, or the
other organic products is not proposed for lack of sufficient data.
The fact that evidence for these is present supports the hypothesis
that reaction (42) is occurring.
D + CO + M — > DCO + M (42)
In th is equation, M represents any third body. The activation 118
energy for reaction (42) has been calculated by Dorman and Buchanan*^ to be 3 kcal/mole. Calvert^ suggests that 15.3 kcal/mole is the best value for the activation energy of the reverse of reaction (42).
The organic products could then be formed by subsequent reactions
of the DCO radical.
In order to account for the increase of G(D2) and G(C0 2 ) with
temperature, a thermal reaction between some species and water has
to be proposed. One such possibility is represented by reaction
(39). If the COOD radical is sufficiently long lived, the following
reaction could also occur at the higher temperatures ( 215°C):
COOD + D20 C02 + D2 + OD (43)
The formation of this radical via reaction (44) probably
requires a stabilizing collision.
OD + CO + M ------> COOD + M (44)
By using heats of formation data from the tabulation byB e n s o n ^ l ,
it can be shown that reaction (43) is exothermic by 8 kcal/mole.
The low activation energy for reaction (36) and the good evidence
presented by Ung and Back^ for the production of C02 without the
production of hydrogen, even at temperatures above 200°C, supports
(53) F. H. Dorman and A. S. Buchanan, Australian J. Chem.. 9,, 34 (1956). (54) J. G. Calvert, J. Phvs. Chem.. 61, 1206 (1957). 119 the hypothesis that this sequence involving COOD radical is improbable. Likewise, no feasible mechanism can be proposed using the DCO intermediate.
Using reactions (35), (36), (38), and (39), the rate laws for the production of D2 and CO2 are:
d(D2 )/dt = k3 9 (D)(D2 0) + k3 8 (D) (M)
d(C02 )/d t = k3 6 (0D)(C0) (N)
The steady state concentrations of D and OD are given by equations
(0) and (P). "
^ s s “ 2 k35I//k38
_ k35I ~ k39^D2°^2k35I/ k38 ^OD) ss - k36(co )
Substituting this in (M) and (N) results in expressions.
d(D2 )/d t = 2k35I ( l - k3 9 (D2 0) ^ (p)
k38 •)
d(C02)/dt = 2k35I p . - k3 9 (D20)^ (R) ^ ~k^o38 /
Thus, G(C02 ) = G(D2) and E^ - EC0 = ea*
The mechanism for the exchange occurring via a chain process in the experiments with hydrogen w ill now be discussed. The high activation energy observed and the fact that an atomic mechanism explains the results found at lower temperatures forces one to 120 choose a free radical process. Two chain propagating sequences can be proposed. The f ir s t , (45) and (22), involves an exchange reaction with water.
H + DOD -----> HOD + D (45)
D + H2 ----- > HD + H (22)
The second is an abstraction mechanism.
H + DOD -----> HD + OD (46)
OD + H2 ------> HOD + H (23)
Both sequences give rise to the chain formation of HD. Chain termi nation is accomplished by the loss of H atoms to the walls of the reaction vessel. In reaction (24), H-S represents a hydrogen atom
H + H-S ------^ H2 + S (24) adsorbed on the surface of the v essel, and k2 4 is , thus, a pseudo first order rate constant. The second order three-body homogeneous recombination process is eliminated on the basis of Firestone's 27 results, which showed that all constant pressure and temperature,
G(HD) did not change with a five-fold change in the dose rate. If chain termination were second order with respect to (H), G(HD) would vary with the reciprocal of the square root of the dose rate.
Evidence for the exchange reaction (45) has been presented by Geib and S t e a r c i e ^ and Boehm and Bonhoeffer^ in their studies using
(56) K. H. Geib and E. W. R. Steacie, Z. Physik. Chem., B29, 215 (1935). (57) E. Boehm and K. F. Bonhoeffer, Z. Physik. Chem., 119, 389 (1926). 121
hydrogen atoms formed in a Wood's tube. Farkas and M elville5^ also found evidence for exchange when they exposed mixtures of deuterium, water vapor (H2 0 ), and mercury to lig h t with a wave length of
2537 A0.
Fenimore and Jones^ have found evidence for reaction (45) by measuring the formation of HD caused by the addition of D2 O to flames of pre-mixed H2 , O2 , and CO2 . Further, it can be stated that the results presented in this investigation of the radiolysis of
D2 0 :C0 mixtures support the existence of the similar abstraction reaction (46).
The temperature dependence of G ^ ) has been firmly established, as the results in Table 21 show. Two thermal non-ionic reactions can be presented for the formation of D2 .
D + D20 ------> D2 + OD (39)
D + HD D2 + H (31)
The data in Table 21 were obtained at a constant percent conversion of H2 (5% to 6%). A constant G value of 0.67 (the non-chain G value) was subtracted from these and the results are plotted in Figure 14.
The slope of the best straight line through the points gives an
Arrhenius activation energy of 21*3 kcal/mole. As evidenced in the
scatter of the points, the experimental uncertainty is large. This activation energy is nevertheless in essential agreement not only
(58) A. Farkas and H. W. M elville, Proc. Roy. Soc. (London), A157, 625 (1936). 122
^ 0.3
-0.3
1.50 1.60 1.70 1.80 I/ T (°K_I x I03 ) Figure 15. Temperature dependence of [G(D2 )“ G(D2)o] of a vapor density of 0.319 mg./ml.
2.2
2.0
1.8
a»
1.6
0.50 0.30 0.10 -Log Vapor Density Figure 16.Variation of [G( HD)-G(HD)o] with vapor density at 3I5°C. 123 with that obtained using G(HD) and G(T), but also with the value obtained in the D2 0:C0 system.
The contribution of reaction (39) can be estimated by calcu lating the ratio of the rate of reaction (39) to the competing reaction (2 2 ).
D + H2 ------> HD + H (22)
The following expression is obtained for the ratio of the rates.
R22/ R39 = k2 2(H2)/k39(D2°) (S)
A value of 3 x 10 3 is found at 320°C using activation energies of
2 2 kcal/mole and 5 kcal/mole for reactions (2 2 ) and (39), respective ly. The value of 22 kcal/mole was obtained from the results of the
D2 0 :CO system, and 5 kcal/mole from the values presented by Benson. 33
Also for this approximate calculation, it can be assumed that the pre-exponential factors are equal within an order of magnitude. The ratio (H2 )/(D2 0 ) equals 3 x 1CT3 . Thus, water cannot effectiv ely compete with hydrogen for D atoms at the temperatures and concen trations of hydrogen used in th is investigation.
It was thought that lowering the mole fraction of hydrogen, as was done in experiments 42, 39, and 43 (cf. Table 22), would favor reaction (39) and cause an increase in G(D2). As seen from the data, this was not the case. The value of G(D2 ) remained constant
(2 .6) when the hydrogen concentration was decreased by a factor or
1.6, but increased to 3.3 when the hydrogen concentration was 124
increased by this same factor. This increase can probably be attributed to experimental error. On the other hand, however,
G(HD) decreased 20% with the decrease in the hydrogen concentration.
It also increased by 1% in the latter experiment, but this is probably due to the higher temperature by 5°C of this experiment.
The values of G(T) indicated this same trend.
This suggests a very strong dependence of G(HD) and G(T) on the concentration of hydrogen in th is range ( 3 x 10“%) which can only be explained by D atoms disappearing by a mode other than reaction with H2 . At the lower vapor density (0.319 mg/ml) this effect was not observed (cf Table 22) in the same range of hydrogen concentrations. Also, the values of G(HD) and G(T) were much smaller
(63 as compared to 150 for G(HD)) due to the smaller concentration of water.
There are two conceivable reactions which could compete with hydrogen for D atoms. One is the reaction of D atoms with water to produce D2 , and the other is either recombination or loss of D atoms at the wall of the reaction vessel. The first possibility has already been eliminated by the results of the calculation of the ratio of the
rates given by (S). The second possibility is not probable for two
reasons. F irst, the same mole fraction of hydrogen as that in the
experiment showing the decrease in G(HD) was su fficien t to react with a ll the D atoms produced at a lower temperature (Exp 29 at 224°C,
cf Table 19), and it would be expected that an increase in temperature 125
would favor the reaction with hydrogen. Second, the effect was not observed in those experiments at a lower vapor density. Even though the concentration of D atoms is undoubtedly influenced by
the concentration of water at the high temperatures, no change in
the efficien cy of the competing reactions would be expected unless
they were of different order with respect to (D). Since i t has
been demonstrated by Firestone^ that the chain termination
reaction is not second order with respect to the radical concen
tration, the concentration of water would not effect the compe
tition for D atoms. As a consequence of these arguments, there is
no apparent explanation for the results of Exp 42.
After insertion of reaction (31) into the free radical
mechanism represented by reactions (22)-(24), (35), (45) and (46),
the following expressions are obtained for the steady state
concentrations of H and D atoms, where l^ I is the rate of
(T)
k35T + 2k35 Ik4 5 (D0D) (U) k24 (D)ss k2 2 (H2) + k31 (HD)
production of the radicals induced by the radiation. The G value
for the production of D2 is then given by equation (V). 126
k3 l (HD) / k35 + 2 ^ 4 5 (DOD) . n2
G(D2 ) = HHf______(V) k2 2 (H2) + (HD)k31
Statistically, k22 = 2k3^ and this expression simplifies (V) to give
(HD) (^k35 + 2k35 k4 5(D0D)N' 1q2 (w)
G(I>2) = (H2) + iHDl 2
If the term (HD)/2 is considered negligible compared to (H2)
(the reactions were not allowed to proceed to more than 5% conversion), this equation predicts that G(D2) should be a function of the ratio
(HD)/(H2), and exhibit an activation energy characteristic of that
(E4 5) for the exchange reaction since k35 and k24 are independent of temperature. Also, the percent conversion has to be identical in all the experiments which are used to determine the temperature co efficien t. In an experiment in which 22%. of the H2 had been converted to HD (cf Table 25), the value of G(D2) was equal to 7.4 at 295°C. In a similar experiment at the same temperature but only
3.5% conversion, (Exp 34, Table 20), G(D2) was equal to 2.1. The difference between these two G values is too large to be attributed to experimental error, thus, G(D2) is dependent on the percent conversion. From the slope of the line in Figure 15, the activation energy for the production of D2 was 21+3 kcal/mole which is in essential agreement with that obtained for the abstraction reaction
(39) in the CO system. Since this reaction is probably not occurring because of the reaction of D atoms with H2 » it is probable that the exchange reaction has an activation energy which is nearly equal to that for the abstraction reaction. It can be seen from an examination of the proposed mechanism that the steady state concentration of the D atoms is not affected by the abstraction reaction (46) at low conversions. Thus, it is difficult to explain the existence of a temperature coefficient for G(D^) at low percent conversions without the occurrence of the exchange reaction (45).
Since the abstraction reaction (39) is occurring in the CO system, one has no reason for eliminating the corresponding reaction
(46) from the mechanism. The G value for the production of HD at low conversions, that is ignoring (31), is given by (X).
G(HD) - k35 + 2 k35^D2 ° ^ k45 * k46) io 2 ^ k24
The term kg^lO2) is equal to the non-chain G value, G(HD)q, and, thus, the chain value, G(HD) - G(HD)o, should be first order with respect to the water concentration. In Figure 16, a plot of log (G(HD) - G(HD)q) versus log (vapor density) at 315°C is pre sented. In order to correct the chain G values obtained at 320°C in experiments 54 and 55 (cf Table 24) to 315°C, a value of 19.5 kcal/mole was used for the activation energy. The slope of the best straight line drawn through the points is 1.6*0.4. Unfortunately, 128 the uncertainty in this number is quite large. This is due to the large variation (8%) in G(HD) caused by the temperature variations in the sand bath during the heating and cooling cycles (^3°C).
Another d iffic u lty which was encountered in the determination of this number was the fact that the vapor density could be changed by a maximum factor of only 2 . 2 due to limitations in the size of the vessel.
A second order dependence of G(HD)-G(HD) 0 upon (D20) can be explained by a consideration of the rate constant k24. This rate constant will be of the foim if the rate of reaction
(24) is controlled by the diffusion of H atoms to the surface of the vessel. In this expression M is the total concentration of gas in the vessel and k° 4 is a constant depending on the size and material of the vessel. The equation presented by Benson^ can be evaluated to show the possibility that diffusion can be the rate controlling step in the loss of H atoms. It is stated that, i f P, the pressure in the v essel, is greater than the ratio
'©o/Srec, then the wall termination reaction will be diffusion controlled. In this ratio DQ is the diffusion coefficient per unit pressure, r is the radius of the spherical vessel, c is the mean resultant velocity of the H atoms, and e is the recombination
(59) S. W. Benson, "The Foundations of Chemical K inetics," McGraw- H ill Book Co., Inc., New York, I960, p. 327. (60) Indem., ibid., p. 447. 129 coefficient or the probability that one H atom will be lost per co llisio n with the w all. The order of magnitude of Dq/c is 10~^ at 1 atm, and r is 4 cm in th is investigation. Thus, i f e i s of the order of 1 0 “^ or larger, the reaction will be diffusion controlled at pressures near 1 atm.
Smith^l has measured the recombination coefficien t for H atoms on Pyrex in water vapor and has obtained a value on the order of lCT^. Representative values in hydrogen gas on Pyrex range from
Iq-4 62 .(-q io - 6 63^ therefore likely that reaction (24) is diffusion controlled and that, as a result, k2 4 = k^/^O). By substituting this expression into equation (W) it is evident that a second order dependency of the G value on the vapor density is predicted.
This same effect has been observed by Armstrong and Spinks^ in th eir study of the radiation-induced reaction between hydrogen bromide and ethylene. At total pressures on the order of 0.25 atm at 34°C with HBr in a 4- to 13-fold excess over C2 H4, they observed that G(CH3 CH2 Br) was independent of the dose rate. It did, though, exhibit a second order dependence on (HBr). These results were interpreted by invoking a diffusion controlled loss of Br atoms to the walls of the reaction vessel.
(61) W. V. Smith, J. Chem. Phvs.. 11, 111 (1943). (62) B. J. Wood and H. Wise, J . Phvs. Chem.. 6 6, 1049 (1962). (63) W. Steiner, Trans. Faraday Soc., 31. 962 (1935). (64) D. A. Armstrong and J. W. T. Spinks, Can. J. Chem., 37. 1210 (1959). 130
The observed^ activation energy for the production of HD is given by equation (Y), since k3 5 is independent of temperature.
_ k45E45 + k46E46 (Y) obs k , k 24 45 46
This equation was derived in the following manner. The expression describing the temperature dependence of the chain G value involves the product of a temperature independent term and the exponential, exp (-E 0 ks/RT). By differentiating with respect to T-"1, the equation for the logarithm of the chain G value, the following expression is obtained.
dln(G(HD)-G(HD)0 )/d(T"1) = -Eobs/R (Z)
After rearranging equation (X), and differentiating the logarithm of it with respect to T^, one obtains equation (AA).
din (G(HD)-G(HD)o )/d(T_ 1 j=dln (k4 5+k46)/d (T~X )-dlnk24/d (T 1) (AA)
Since for any function, f(x), dlnf(x) = df(x)/f(x), equation (AA) becomes
din (G(HD)-G(HD)0 )/d(T~1) = f^5_+_dk46 ------dln^ d(rl) (BB) dCT" 1 )(k 45+k46)
Also, for any rate constant k^, it can be seen from the Arrhenius expression that dk^/d(T"*1) = (^ (-E ./R ). By using this in equation
(BB) one gets equation (CC). 131
^45^45 + ^46^46 (CC) din (G(HD)-G(HD) )/d (T ) - — -----— ------E2 4 45 46
It can then be seen that equation (AA) is equal to equation (CC) and thus, equation (Y) results.
Again E2 4 can be considered to be zero. Thus, the observed activation energy is a weighted sum of 4 E 5 and E4 5 . The activation 56 5R energy for the exchange reaction has been estimated ’ to be at least 12 kcal/mole, while the experimental Arrhenius energy for the abstraction has been determined to be 25 kcal/m ole.^ 8 An intermediate value of 19.5+1 kcal/mole has been determined in the present investigation.
The curvature beginning at 150°C in the Arrhenius plot shown
in Figure 11 cannot be attributed to the initiation of a reaction with an activation energy of 12 kcal/mole. This was shown to be
the case by drawing, from the point where the curvature began, a
line which had a slope corresponding to an Arrhenius energy of
12 kcal/mole. This line was well outside of the region described
by the experimental points at reciprocal temperatures of 2 . 3 x l 0"3,
2.4x10-3, and 1.9xl0“3 °K"1. Thus, the lower limit of the
activation energy for the exchange reaction must be larger than 12
kcal/mole. The lack of substantial curvature in the Arrhenius
plots for the chain G values of both HD and HT (cf Figs 12 and 13
respectively) over a 1 0 0 degree temperature range indicates that
E4 5 and E4 6 are approximately equal, or that only one reaction is 132
contributing to the chain.
From the discussion concerning the temperature coefficient of
G(D2), and the results obtained from the D2 0 :CO system, it is
evident that both reactions are occurring above 250°C. Thus, their
activation energies are nearly equal, probably within 5 or6 kcal
or less. This figure was estimated by considering the curvature which could possibly be observed in Figs 12 and 13. Until the
absolute values of k^ and k^ are known, the contribution of each
reaction cannot be determined.
Baxendale and Gilbert^ have studied the radiolysis of water vapor at low concentrations of hydrogen, where the scavenging
reaction was not 100% efficient. It was thought that an analysis
of these data would be informative as to the mode of removal of
H atoms in the experiments at low temperatures. The alternatives
are a second order homogeneous three-body recombination or a first
order removal at the wall of the vessel or with an impurity. The
same mechanism as that proposed in the present study will be
considered.
D20 ----> D + OD (35)
D + H2 - ----^ HD + H (2 2 )
OD + H2 -----^ HOD + H (23)
H + H-S ------> h2 + S (24)
D + D-S ---- > d2 + s (25) 133
Reaction (47) represents first order removal of D atoms at the surface by some means, perhaps via reaction with an adsorbed atom,
D-S.
The steady state concentration of D atoms is
k35I (D) cc. = — ------(EE) k2 2 (H2) + k47 where I is the absorbed dose rate. The rate equation for the production of HD is then
krjrjkoc I d (H D )/d t = - 2 2 - 2 1 ------(FF) ki 2 (H2) + k4 7
Similarly, the rate of the wall reaction is
k47k35I (GG) d(W)/dt k22(e2) + k47
By dividing equation (GG) into equation (FF), one obtains an
expression for the ratio of the G values.
(G(HD)/G(W)) = k2 2 (H2 )/k4 7 (HH)
The maximum values of G(HD), as seen from Fig. 17, obtained in
Baxendale's experiments was 10.5. Thus, G(D) = G(HD) + G(W) = 10.5,
By substituting G(D) - G(HD) into equation (HH) and inverting and
rearranging, one obtains equation (II).
G(D)/G(HD) = k4 7/k 2 2 (H2) + 1 (II) 134
10.0
6.0
G(HD)
2.0
001 Mole % H2 0.10 Figure 17. Yield of HD in the D20:N2 system. Token from Boxendale and Gilbert, Disc. Faraday Soc., 36,296 (1963).
1.8
G(Total) G(HD) 1.4
1.0
0 1 .0 2.0 3.0 4.0 I/ Mole % Ho x 10
Figure 18. Kinetic analysis of the data of Baxendale and Gilbert. 135
From th is i t can be seen that a plot of G(D)/G(HD) versus
(t^)"* should be linear.
The following data in Table 28 were taken from the published
graph of Baxendale (see Fig 17) using a Vernier caliper precise to-
* 0 .1 mm.
TABLE 28
Values of G(D)/G(HD) and l/Xj^^a taken from the data of Baxendale and Gilbert
G (HD) G(D)/G(HD) Xh2 x io 5 i A H2 x 1 0 - 4
9.0 1 . 2 7.03 1.42 8 . 0 1.3 4.82 2.07 7.0 1.5 3.18 3.18 6 . 0 1 . 8 2.34 4.32 5.3 2 . 0 2 . 0 2 4.95
aXj_i^= (H2 )/(D2 0 ) The concentration of D2 O was approximately
2 x 1 0 " 2 m oles/l.
kj. H. Baxendale and G, P. Gilbert, Disc. Faraday Soc., 36, 295 (1963).
Figure 18 shows the results of plotting G(D)/G(HD) against the
'■reciprocal of the mole fraction of hydrogen. The fact that a straight
line is obtained shows that the data adhere to the general form of
the proposed mechanism. Failure to obtain an intercept of 1 is
probably a result of errors introduced in recovering the untabulated
data from the curve in Baxendale’ s published a r tic le . A smoothing 136
of the data after imposing an intercept of 1 is not justified because of the inherent errors in obtaining the data.
The slope in Figure 18 is equal to l^Y/k^O^O). From the
text of Baxendale*s paper it is determined that the concentration
of water is roughly 0.02 M, which gives a value of 4 x 10- 7 m oles/l
for l<4Y/k2 2 * The value of IC2 2 at 116°C is estimated to be 3 x 10 7
l/mole-sec from the values reported by Geib and Harteck^ or
Farkas and Farkas^ for the activation energy and the pre-exponen
tial factor for reaction (22). Thus, the first order rate constant,
k47, has a value of 1 x lO"*- sec“^ in the five liter, spherical
glass vessel used by Baxendale.
It is possible to estimate this rate constant for the reaction vessels in the present investigation if the reaction is diffusion
controlled. From a consideration of the arguments presented earlier
concerning the recombination coefficient for hydrogen on glass sur
faces, it is quite likely that the wall process, indeed, is diffusion
controlled in both works. Thus, the rate constant has the form
^4 7/ (D2 0 )r2 .
In the present investigation the radius of the reaction vessel
is 4 cm and the concentration of water is roughly 3 x 10“2M. The
resulting value for k4 7 in this study is, then, 50 sec-'*'.
The fraction of hydrogen atoms lo s t to the walls under the
(65) K. H. Geib and P. Harteck, Z. Physik. Chem.. Bodenstein Festband, 849 (1931). (6 6) A. Farkas and L. Farkas, Proc. Roy. Soc., A152, 124 (1935). 137
conditions of the low temperature (T<250°C) non-chain experiments can now be estimated. This fraction should be le ss than the relative experimental error in the measurement of G(HD), which was approximately 1%. The ratio k4 7/(k 4 7fk 2 2 (H2 )) is clearly this fraction, and it has a value of 0 .0 1 when the concentration of hydrogen was 1.7 x 10“^ M, the smallest used in th is investigation.
Thus, i t is apparent that hydrogen is an e ffic ie n t scavenger for
D atoms under the conditions of the present experiments. This
supports the conclusion that the absence of an appreciable tempera
ture coefficient below 250°C indicates that there is no competition
for the reaction of D atoms with hydrogen. Also, since Firestone
found that G(HD) = G(-D2 ) in the 1^ 0 : 0 2 system under sim ilar
conditions, i t may be assumed that hydrogen is effectiv ely
scavenging OD radicals.
The effect of isotopic substitution on the radiation chemistry
of water vapor can be evaluated by comparing the results of the
present investigation with those obtained by Firestone^ for the
H2 OSD2 system. The values of G(HD) below 160°C for the two systems
are shown as a function of temperature in Figure 19. In order to
fa c ilita te the comparison the ordinate of this figure is greatly
expanded. Both sets of data show a decrease in G(HD) below 110°C,
a portion of approximately zero slope between 110°C and 150°C, and
a region of positive slope above 150°C. Although the results of 138
O-DgO : Hg system 16.0 □ -HoO ; 09 system
14.0
G(HD)
12.0
10.0
80 100 120 140 f60 Temperature °C. Figure 19. Comparison of G(HD) for the radi- olysis of the D20 : H2 and H20: D2 systems.
2.00 OO o o 1 o rO o ° ° c C C C
------O’...... C Separation o o o O O
0 O Factor j o o O 1.00
— 1 1 ____1____ 1... 1 , 1 ____I 8 0 140 2 0 0 2 6 0 3 2 0 3 8 0 Temperature °C. Figure 20. The separation factor at several temperatures. 139
the study of the D2 O system appear consistently higher by
approximately 8%, it is felt that the data are not sufficiently precise to attribute this to an isotope effect. The average of
all the G values enclosed in the dashed line is 12.6-0.6 molec/ev where the uncertainty is the average deviation from the mean. This
result is higher than the original estimate reported by Firestone,on '
which was the average of a ll the results that were obtained below
150°C.
The apparent absence of an overall isotope effect in this
temperature region is not surprising on the basis of the proposed
mechanism. Since the radical scavenging reactions are essen tia lly
99% efficient, any observed effect would have to be on the reactions
producing the radicals. It has been estimated6*7 that isotopic
substitution has only a 5% effect or less on the molecule-ion
sensitivities or the total ionization of a molecule. Similarly,
the effect on electronic excitation has been stated to be small. 0
An interesting isotope effect has been observed by Jesse^ in his
studies of the ionization efficiencies of polyatomic molecules.
The results of his work correlate with the theory of super
excited states advanced by Platzmann.70 Super excited molecules
are molecules which have been excited to states which are higher
(67) F. H. Field and J. L. Franklin, "Electron Impact Phenomena," Academic Press, Inc., New York, 1957, p. 214. (6 8) J. G. Burr in "Tritium in the Physical and Biological Sciences," Vol. 1, International Atomic Energy Agency, Vienna, 1962, p. 137. (69) W. P. Jesse, J. Chem. Phys., 41, 2060 (1964). (70) R. L. Platzmann, The Vortex, 23, 372 (1962).
I 140
than the ionization potential of the molecule. As a result of having a lower zero point vibrational energy, the heavier molecule will have a larger probability of ionizing rather than dissociating than the lighter molecule. In the case of water vapor, Jesse found that the ionization efficiency of D2O was 3% larger than that for H2O. If 2 D atoms and two OD radicals are produced as a result of the ion molecule reaction (1 6) and the neutralization reaction (28) for every ionization while only one of each for
every neutral dissociation, it would be theoretically possible to observe an isotope effect. Only those molecules which are super 71 excited estimated by Platzmann to be 18%, though would exhibit
this effect, thus, the resulting difference in the G values would
be very small. Any experiments which could measure th is effect would require a high degree of accuracy and precision.
In the chain mechanism above 200°C, a kinetic isotope e ffe ct
can be observed by comparing the results of the two systems. This
effect can be attributed to the effect of isotopic substitution on 27 the rate of a thermal chemical reaction. Firestone reported an
observed Arrhenius energy of 18+ 1 kcal/mole while the Arrhenius
energy found in this study was 19*1 kcal/mole. Since the latter
value was determined four times from two different series of
experiments, it is probable that the difference between the two
(71) R. L. Platzmann, private communication. 141
activation energies is real and not a result of an experimental error. From a consideration of the transition state theory of reaction rates at low temperatures, the difference in the acti vation energies for two isotopic reactions is related to the
79 difference in the zero point energies of the isotopic species. ^ 73 Darling and Dennison have calculated that the zero point energy of D2 O is 3.6 kcal/mole lower than that for 1^0, thus, one would expect a higher activation energy in reactions involving D2 O.
In order to compare the rates of the chain propagating reactions, the G values for the production of HD by the chains, (G(HD)-G(HD)0) , have to be evaluated at identical temperatures and concentrations of water. Since Firestone^ has shown that the value of G(HD) was independent of the dose rate, this factor does not have to be considered. At 278°C and a vapor density of 0.774 mg/ml Firestone obtained a value for G(HD)-G(HD) 0 of 117. At the same temperature, but a lower vapor density of 0.590 mg/ml, a value of 41 was obtained from the results of this investigation. This value was read directly from Figure 12. The ratio of the concentrations,
(H2 0 )/(D 2 0 ), represented by these vapor densities is 1.46. In order to correct for this difference, an order for the mechanism has to be assumed. Values of 1, 1.6, and 2 were used, and the results of the calculations for the ratio of rates are shown in Table 29.
(72) L. Melander, "Isotope Effects on Reaction Rates," The Ronald Press Co., New York, I960, p. 44. (73) B. T. Darling and D. M. Dennison, Phvs. Rev., 57. 282 (1940). 142
TABLE 29
Order of Correction3 (g(hd )- g(hd )o)d 2o (g(hd)-g(hd)0 )h2o the Mechanism Factor (g(hd)-g(hd)0 )d2o
1.0 1.46 60. 1.9 1 .6 1.83 75. 1 .6 2.0 1.94 8 8. 1.3
Correction factor - (H2 0)/(D 2 0) n, where n is the order of the mechanism.
Roginsky,"7^ from an analysis of the data of Geib and Steacie, ^ 1
states that the difference in the activation energy for the exchange
reactions is 0.75 kcal/mole and the ratio of the rates of the
reactions at 183°C is approximately 1.7. This value was corrected
to 278°C by using the difference in the activation energies which he
cites. The result is that kHkp is equal to 1.1 at 278°C. The
reasonable agreement with the results in Table 29 is probably
fortuitous since the mechanisms in the two systems are somewhat
different. Geib and Steacie did not find evidence for the abstraction
reaction (46). The values in column 4 of Table 30, and the differ
ence in the activation energies, are of the same size as those
presented by Roginsky”7^ for other gaseous reactions involving H or
D atoms. Due to the fact that two different reactions involving
(74) S. Z. Roginsky, "Theoretical Principles of Isotope Methods for Investigating Chemical Reactions," tran sl. by Consultants Bureau, Inc., Technical Information Service Extension, Oak Ridge, Tenn., 1956, p. 280. 143 two different transition states are contributing to the formation of HD in the chain mechanism, and the relative contribution of each is not known, theoretical calculations concerning the isotope effect are not justified.
The third and, perhaps, most interesting isotope effect observed in this study was an intramolecular effect exhibited by the values of the separation factor. An average temperature indepen dent value of 1.6 was obtained for this factor as shown in Figure
20. Of course, a value of unity would indicate an absence of any influence of isotopic substitution.
Since the scavenging reactions for D or T atoms are essentially
1 0 0 % efficient, the cause of the isotope effect has to be assigned to one or more of the reactions which form these species. In the
H2 scavenged system, any process which favors the formation of a D atom from TOD rather than a T atom, will cause the separation factor to be greater than unity. This is a consequence of the fact that
T atoms in the form of OT will result in TOH and, thus, not con tribute to the value of nT for that specific experiment. Two conceivable processes which could account for this influence of isotopic substitution are the dissociation of electronically excited molecules or ions, and the proposed ion molecule reactions leading to the formation of D2 OT4'. Neutralization processes can be considered to be in the class of dissociation of excited neutral species. 144
The only direct experimental data for hydrogen isotopes effects on the dissociation of electronically energized molecules are for the dissociation of molecule-ions in a mass spectrometer. Although the isotope effect on this process in water vapor has not been measured, other molecules have been studied. Loss of an H atom from
®2^2+ approximately twice as probable as loss of a D atom.7^’7^
Similarly, loss of an H atom from C^H^D^ i s ^ » 7 times more probable than the loss of a D atom. 7 7 If this isotopic influence exists in the molecule TOD, this could explain the results found in the H2 scavenged system.
Isotope effects on proton transfer reactions have been observed in mass spectrometers. A pulsed ion source was used by Shannon and co-workers7® to study reactions of the type illustrated by (48) and
(49).
CH2dJ + ch2d2 CHD2 + CH3 DJ (48)
CH^J + CH2D2 CH-jD + CH2Dj (49)
They found an average value of -k^g/k^g of 1.3 for all the isotopic methanes. On the basis of this study, it would be expected that these effects would favor the formation of OT and DgO+ from the
(75) V. H. Dibeler and F. L. Mohler, J. Res. Natl. Bur. S td ., 45. 441 (1950). (76) D. 0. Schissler, S. 0. Thompson, and J. Turkevich, Disc. Faraday Soc., 10, 46 (1951). (77) J. G. Burr, J. M. Scarborough, and R. H. Shudde, J. Phys. Chem., 64, 1359 (1960). (78) T. W. Shannon, F. Meyer, and A. G. Harrison, Can. J. Chem., 43, 159 (1965). 145 reaction of DOT+ and D2 0.
Although evidence has been obtained for resonant charge transfer reactions,consideration of the small, if any, effect of isotopic Aft substitution on the ionization potential of a molecule ° allows one to ignore reaction (52) as the source of the influence.
DOT4- + D O D > DOD+ + DOT (52)
One further sequence can be proposed to account for this isotope effect. This is represented by reactions (53) and (54).
D2 OT+ + D20 ------D3 0+ + DOT (53)
D2 0T+ + D20 ------> D^T* + DOD (54)
No evidence has been reported for these reactions in water vapor.
In the CO scavenged system, the separation factor has a value of 1.7 in agreement with that found in the H2 scavenged system.
According to the proposed mechanism for carbon monoxide scavenging, both the T and D atoms on the affected water molecules appear as free hydrogen. Thus, isotope effects of the dissociation processes or the proton or triton transfer from DOT+ would not affect the value of the separation factor. Even an isotopic influence on the chain propagating reaction (39) would not change this value. On the contrary, though, any effect of isotopic substitution on the deuteron or triton transfer from D2 OT+or any other species lik ely to be neutralized to D20 would change the separation factor from a value of unity. This gives strong support to the possible existence of
such reactions as (54) and (53). CHAPTER VI
CONCLUSIONS
_From the foregoing discussion it is concluded that the exchange mechanism for the D20 /T0 D:H2 system can be written as follows:
From 84 to 150°C.
D + H2 -*■ HD + H (1)
OD + H2 ------> HOD + H (2)
H +H* S * H 2 + S (3)
From 150 to 380°C two additional reactions occur.
H + DOD ------> HD + OD (4)
H +DOD * HOD + D (5)
The rate of production of HD above 150°C is second order with respect to the concentration of water, and the rate of the termi nation reaction (3) is controlled by the diffusion of H atoms to the walls of the reaction vessel. The yield of D2 in this temperature
range can be attributed to reaction (6 ).
D + HD ?> D2 + H (6 )
The Arrhenius activation energy of the chain mechanism is
19.5*1 kcal/mole and can be assigned to the weighted sum of the
146 147
Arrhenius energies for reaction (4) and (5). These are equal to each other within 5 or 6 kcal/mole and the lower limit of the activation energy for the exchange reaction is probably 16 kcal/mole.
The mechanism in the D2 0 /TQD:C0 system at 215°C may be written as follows*
OD + CO ------> C02 + D (7)
D + D*S ------> D2 + S (8 )
From 278 to 312°C one additional reaction is occurring.
D + D O D ------> D2 + OD (9)
The Arrhenius energy for th is reaction has been determined to be
21+3 kcal/mole.
It is further concluded that below 150°C the results of the two analogous systems D^/TODsH^ and H2 0 /T0 HsD2 are identical and, thus, there is no overall isotope effect on the apparent yield of radicals in the radiation chemistry of water vapor. Above 150°C a kinetic isotope effect of 1.3 is obtained and 1 kcal/mole is found as the difference in Arrhenius energies of the two sets of chain propagating reactions.
An intramolecular isotope effect has been observed to be identi cal in both the H2 and CO systems with the result that it is due to one or both of the processes of dissociation of electronically excited molecules or proton transfer reactions. BIBLIOGRAPHY
Allen, A. 0., The Radiation Chemistry of Water and Aqueous Solutions, New York* D. Van Nostrand Co., In c., 1961.
Anderson, A. R., and Knight, B ., D isc. Faraday Soc.. 36. 299 (1964).
Anderson, A. R., Knight, B., and Winter, J ., Nature. 201. 1026 (1964).
Armstrong, D. A., and Spinks, J. W. T., Can. J. Chem.. 37. 1210 (1959).
Avramenko, L. E., and Kolesnikova, R. V., Advan. Photochem.. 2 , 25, (1964).
Baxendale, J. H., and Gilbert, G. P., Science. 147. 1571 (1965).
Baxendale, J. H., and Gilbert, G. P., J. Am. Chem. Soc., 86, 516 (1964).
Baxendale, J. H.,,and Gilbert, G. P., Disc. Faraday Soc., 36, 186 (1963).
Baxendale, J. H.^ and Gilbert, G. P., Disc. Faraday Soc., 36, 295 (1963).
Benson, S. W., The Foundations of Chemical K inetics, New Yorks McGraw-Hill Book Co., In c., I960.
Benson, S. W., J. Chem. Edu., 42, 502 (1965).
Bethe, H. A., Handbuch der Physik. Vol. 24, Berlins Julius Springer, 1935.
Bethe, H. A., and Askin, J., Experimental Physics, E. Segre, ed., Vol. 1, New Yorks John Wiley and Sons, Inc., 1953, p. 166.
Boato, G., Careri, G., Gimino, A., Molinari, E., and Volpi, G., J. Chem. Phys. , 24, 783 (1956).
Boehm, E., and Bonhoeffer, K. F., Z. Physik. Chem., 119, 389 (1926).
Buchelnikova, I. S., Soviet Phys., JETP. 35. 783 (1959).
Burr, J. G., Tritium in the Physical and Biological Sciences, Vol. 1, Viennas International Atomic Energy Agency, 1962, p. 137. 149
Burr, J. G., Scarborough, J. M., and Shudde, R. H., J. Phys. Chem., 64, 1359 (I960).
Calvert, J. G., J. Phys. Chem., 61, 1206 (1957).
Chen, M. C., and Taylor, H. A., J. Chem. Phys., 27,857 (1957).
Cottin, M., J. Chim. Phys., 56, 1024 (1959).
Darling, B. T., and Dennison, D. M., Phys. Rev., 57, 282 (1940).
Del Greco, F. P ., and Kaufman, F., D isc. Faraday Soc., 33, 128 (1962).
Dibeler, V. H., and Mohler, F. L., J. Res. Natl. Bur. Std., 45, 441 (1950).
Dorfman, L. M., Phys. Rev., 95, 393 (1954).
Dorman, F. H., and Buchanan, A. S ., Australian J. Chem., ,9, 34 (1956).
Douglas, D. L., J. Chem. Phys., 23, 1558 (1955).
Duane, W., and Scheuer, 0 ., Le Radium, 10, 33 (1913).
Farkas, A., and Farkas, L., Proc. Roy. Soc. (London), A-152, 124 (1935).
Farkas, A., and M elville, H. W., Proc. Roy. Soc. (London), A-157, 625 (1936),
Fenmore, C. P ., and Jones, G. W., J. Phys. Chem., 62, 693 (1958).
Field, F. H., and Franklin, J. L., Electron Impact Phenomena, New Yorks Academic Press, Inc., 1957.
Fiquet-Fayard, Mme. Florence, J. Chim. Phys., 57, 453 (i960).
Firestone, R. F., J. Am. Chem. Soc., 79, 5593 (1957).
Firestone, R. F., Disc. Faraday Soc., 36, 294 (1963).
Firestone, R. F., Lemr, F., and Trudel, 0. J., J. Am. Chem. Soc., 84, 2279 (1962).
Friedlander, G., Kennedy, J ., and M iller, J ., Nuclear and Radiochem- is t r y , 2nd ed., New Yorks John Wiley and Sons, In c., 1964. 150
Geib, K. H., and Steasie, E. W. R., Z. Physik. Chem.. B29, 215 (1935).
Geib, K. H., and Harteck, P., Z. Physik. Chem., Bodenstain Festband, 849 (1931).
Gunther, P ., and Holzapfel, L., Z. Physik. Chem., B42, 346 (1939).
Hart, E. J ., Gordon, S., and Hutchison, D. A., J. Am. Chem. Soc., 75, 6163 (1953).
Henglein, A., Lacmann, L., and Knoll, B., J. Chem. Phys., 43. 1048 (1965).
Henglein, A., and Muccini, G. A., Z. Naturforschung, 18A, 753 (1963).
Henglein, A., and Muccini, G. A. Z. Naturforschung, 17A, 452 (1962).
Hofmann, H. S ., Riehl, N., Rupp, W., and Sizmann, R., Radiochimica A cta., 1, 203 (1963).
Hogg, A. M., and Kebarle, P., J. Chem. Phys., 42, 789 (1965).
Hurst, G. S ., O'Kelley, L. B., Stockdale, J. A., 2nd Int. Congr. Rad. Res., (Harrogate, 1962, Abstr.) p. 128.
Jesse, W. P ., J. Chem. Phys., 41, 2060 (1964).
Jesse, W. P., and Saudauskis, J., Phys. Rev., 97, 1668 (1955).
Kirschenbaum, I ., Physical Properties and Analysis of Heavy Water, New Yorks McGraw-Hill Book C o.,In c., 1951.
Laidler, K. J., J. Chem. Phys., 22, 1740 (1954).
Lampe, F. W., and Field, F. H., Tetrahedron, 1_, 189 (1959).
Lampe, F. W., Field, F. H., and Franklin, J. L ., J. .Am. Chem. Soc., 79, 6132 (1957).
Lassetre, E. N., Rad. Res., Supp. 1, 530 (1959).
Lawrence, R. H., Ph.D. dissertation, Ohio State University, Columbus, (1965).
Lawrence, R. H., and Firestone, R. F., J. Am. Chem. Soc., 87, 2288 (1965). 151
Lind, S. C., Radiation Chemistry of Gases, New Yorks Reinhold Publishing Co., 1961.
Lind, S. C., The Chemical Effects of Alpha Particles and Electrons, TJew Yorks The Chemical Catalogue Co., 1928, p. 94.
Magee, J. L., Burton, M., and Kirby-Smith, J. S., Comparitive Effects of Radiation. New Yorks John Wiley and Sons, Inc., I960.
Magee, J. L., and Burton, M., J. Am. Chem. Soc., 73, 523 (1951).
Mann, M. M., Hustrulid, A., and Tate, J. L., Phys. Rev., 58, 340 (1940).
Melander, L., Isotope Effects on Reaction Rates, New Yorks The Ronald Press Co., I960.
Moran, T. F ., and Friedman, L., J. Chem. Phys., 42, 2391, (1965).
Muschlitz, E. E., J r ., J. Appl. Phys.. 28, 1414 (1957).
Niki, H., Rousseau, Y., and Mains, G. J., J. Phys. Chem., 69. 45 (1965).
Platzmann, R. L., The Vortex, 23, 372 (1962).
Platzmann, R. L., J . Appl. Radn. and Isotopes. 10, 116 (1961).
Platzmann, R. L., 2nd International Congr. Rad. R es., (Harrogate, 1962, Abstr.) p. 128.
Platzmann, R. L., in Basic Mechanisms in Radiobiology. Washington, D, C.s Natl. Res. Council Publication 305, 1953, p. 30.
Platzmann, R. L., and Hart, E. J ., Mechanisms in Radiobiology, Vol. 1, New Yorks Academic Press, Inc., 1961, p. 176.
Pratt, T. H., and Wolfgang, R., J. Am. Chem. Soc., 83, 10 (1961).
Price, W. J ., Nuclear Radiation Detection, New Yorks McGraw-Hill Book Co., 1958.
Pritchard, H. 0 ., Chem. Revs., 52, 529 (1953).
Pillinger, W. L., Huntges, J. J., and Blair, J. A., Phys. Rev., 121, 232 (1961) 152
Schissler, D. 0 ., Thompson, S. 0 ., and Tukevich, J ., D isc. Faraday Soc.. 10, 46 (1951).
Schultz, ( J., J. Chem. Phvs. . 33, 1661 (1961).
Schultz, V f. R ., and LeRoy, D. J ., Can. J. Chem.. 42. 2480 (1964).
Schwarz, }I. A., in Advances in Radiation Biology. Vol. 1, L. G. Augenstein, R. Mason, and H. Quastler, ed s., New York: Academic Press, Inc., 1964.
Shannon, ''. W., Meyer, F ., and Harrison, A. G., Can. J. Chem.. 43. 159 (1965).
Smith, W. V., J. Chem. Phvs.. 11, 111 (1943).
Spinks, J, W. T., and Woods, R. J., An Introduction to Radiation Chemistry, New Yorks John Wiley and Sons, In c., 1964.
Steinman, R., Ph.D. dissertation, Stevens In stitu te, Hoboken, N. J ., 1962.
Steiner, \ Trans. Faraday Soc., 31, 962 (1935).
S tief, L. J., DeCarlo, V. J., and Hillman, J. J., J. Chem. Phys., 43, 2490 (1965).
Roginsky, S. Z., Theoretical Principles of Isotope Methods for Investigating Chemical Reactions, trah sl. by Consultants Bureau, Inc., Technical Information Service Extension, Oak Ridge, Tenn., 1956.
Thompson, S. 0., and Schaeffer, 0. A., J. Chem. Phvs., 23, 759 (1955).
Ung, A. Y . -M., and Back, R. A., Can. J. Chem., 42, 753 (1964).
Von Engel , A., Ionized Gases, 2nd ed., Londons Oxford Press, 1965, p. 163.
Wobschall , D ., Graham, J. R., and Malone, D. P., J . Chem. Phys., 43, 3855 (1965).
Wood, B. * J., and Wise, H., J. Phvs. Chem., 66, 1049 (1962).
Yang, J. Y., ’ and Gevantman, L. H., J . Phys. Chem., 68, 3115 (1964).
After substitution for the steady state concentration of 0 3 0 "*",
equation (J) becomes
^ 13/^28 =: ^18 ^ )
The calculated upper limiting value of this ratio is, then, after
substitution of the upper limit for ^1 3 /^2 8^’ equal "to H» This
indicates that, by equating the third term of equation (I) to 0.4,
a ratio of rate constants is obtained such that the ionic exchange
(38) R. L. Platzman and E. J . Hart, "Mechanisms in Radiobiology," Vol. 1, Academic Press Inc., New York, 1961, p. 176. (39) The dose rate which was used to calculate this value was 5.2 x 10-*-0 ev/cc-sec, a representative value. 105
reaction may compete favorably with the neutralization reaction.
If the experimental error were larger, this ratio would be larger.
The rate constant IC23 has not been measured for ions and
electrons in water vapor. An estimate can be obtained and is probably of the order of 10“^cc/molec~sec.^® This gives a value
of 1 0 - -^cc/molec sec for k^g, which is two orders of magnitude higher than lO’^cc/m o lec -sec estimated by Pratt and Wolfgang4"*-
for reaction (30), which they postulated.
CH5+ + t 2 ------> CH4T+ + HT (30)
Using a value lower by two orders of magnitude in equation (K) w ill
show that the ionic exchange reaction would not compete with neutralization. The assumption that E^g is nearly zero is not
necessary since the concentration of water is so much larger than
that of hydrogen, allowing the concentration of D2 OH4" to be ignored.
As shown above, the results of this investigation are not
sufficiently conclusive for the exclusions of reactions (18) or
(19). Also, a mechanism involving the complete efficiency of
reaction (18) and inefficiency of (19) could explain the fact that
Baxendale^ observed no dependence of G(HD) on the increased
concentration of hydrogen.
Firestone4 2 has stated that the lower G values obtained by
(40) A. von Engel, "Ionized Gases," 2nd ed., Oxford Press, London, 1965, p. 163. (41) T. H. Pratt and R. Wolfgang, J. Am. Chem. Soc., 83. 10 (1961). (42) R. F. Firestone, Disc. Faraday Soc., 36, 294 (1963). 106 using organic scavengers can be explained by the interaction of these additives with protons thus altering the nature of the neutralization reaction (28). This would decrease the yield of radicals as explained ea rlier.
The source of the "molecular yield" of D2 will now be discussed.
The mean valve of G(D2 ) (0.67+0.11) obtained in this study is some what higher than that found by Baxendale and Gilbert^ (0.53+0.06) and that of Anderson43 and co-workers (0.47+0.01). Due to the large experimental error in the present work and the rather optimistic uncertainties assigned to the other values, these three results have to be considered in essential agreement.
There are two obvious reactions which could form D2 in th is system. The first is the result of D atom attack on HD (reaction
(31)) and the second is the ion molecule reaction (32) analogous to that observed by Muschlitz^ and Cottin^ in the case of normal water vapor.
D + HD D2 + H (31)
D" + D20 ------* D2 + OD- (32)
The lower limit of the reaction cross section for the isitopic analog of reaction (32) has been reported to be lO^^cm^/molec'*''1- which makes i t s rate comparable to those for positive ion molecule
(43) A. R. Anderson, B. Knight, and J. Winter, Nature, 201, 4923 (1964). 107
r e a c tio n s.^ R. L. Platzman^ 4 has calculated the G values for the production of H2 from reaction (2 ), the isotopic analog of
reaction (32), to be 0.2*0.1 for the case of liquid water, and
suggests that the process should be just as efficient in the vapor phase.
If the D2 resulted from reaction (31), the G value would
obviously be expected to be dependent on the amount of HD present,
that is, on the percent conversion of the hydrogen. No trend in
G(D2 ) is apparent from 1.9% conversion (Exp. 17) to 12% conversion
(Exp. 35) as shown in Table 19. This observation may not be
significant because of the very considerable uncertainties in
G(D2 ) at the lower conversions. No percent conversion data were 34 presented by Baxendalq,and Gilbert. When reaction (31) is
included in the mechanism, the reaction of OD radical attack on
HD cannot be neglected. Further, it can be seen that the steady
state concentration of D atoms would be dependent on the amount of
HD or D2 present (eventually almost a ll the hydrogen would be in
the form of HD or D2 ). Thus, one would have to include a reaction
allowing D atoms to reach the wall of the vessel. As a result of
these additional reactions, the kinetic expressions appear to be
too complex to evaluate G(D2 ) as a function of the percent conversion.
Figure 11 clearly shows that two or more mechanisms are
(44) R. L. Platzman, 2nd. International Cong. Rad. R es., (Harrogate, 1962, Abstr.) p. 128. 108 contributing to the formation of hydrogen deuteride. Above ap proximately 245°C a strongly temperature dependent process is predominant and the curvature at the high temperature end of the plateau (i.e., at 150°C) can be attributed to the onset of this process.
The plateau value of 13.1 for G(HD) has been subtracted from the G values at the high temperatures, and an Arrhenius plot of the results is presented in Figure 12. The valve of 13.1+0.3 is the average of the values for G(HD) of experiments 5, 6, 8 , 9,
12, 20, and 21. The same procedure has been applied to the G values obtained at a lower vapor density of 0.319 mg/ml and these results are also plotted in Figure 12. The slopes of the lines drawn through these sets of points were determined by the least
squares method. The last point in the results found at 0.595 mg/ml has been disregarded because of the large relative error in the difference between two numbers which are nearly equal.
Apparent Arrhenius energies of 19.2 kcal/mole and 19.5 kcal/mole have been calculated for the high and low vapor densities,
respectively.
The data for G(T) (cf. Tables 20 and 21) have been treated
in identical fashion, and the results are plotted in Figure 13.
In the low temperature region the constant value of G(T) is
0.327+0.11 x 10“2, which is the average of the results of
experiments 8 , 9, 12, 20, and 21. At a vapor density of 0.595 mg/ml the Arrhenius energy for TH formation is 21 kcal/mole, and o o>
[ g (HD)- G(HD)0 1 2.00 2.20 2.40 1.40 1.80 Figure 12. Temperature dependence of of dependence Temperature 12. Figure .60 0. mg./mI. 9 1 .3 -0 0 0.55 mg./ml. 595 . -0 □ (Do a vpr este of densities vapor at G(HD)o] .1 m.m. n 055 mg./ml. 0.595 and mg./ml. 0.319 1.60 / (K"‘ I3) I03 ‘ x " (°K l/T
.0 .01.90 1.801.70 [ g (HD)~ 109
110
-1.40
-1.60
-1.80
O'
- 2.00
0-0.319 mg./ml.
□-0.595 mg./ml. - 2.20
1.60 1.70 1.80 1.90 I/ T (° K"‘ x I0 3 ) Figure 13. T em p eratu re dependence of [G(T)- G(T)0] at vapor densities of 0.319 m g./m l. and 0.595 mg./ml. I l l
at 0.319 mg/ml it is 19 kcal/mole.
Before discussing the mechanism involved in the high temperature radiation-induced chain exchange of water vapor and hydrogen, it is advantageous to examine the results of the experiments with water vapor and carbon monoxide.
In experiments 3 and 4 (of Table 25), the CO was present at approximately 6 mole percent. Thus, i t can be said that CO absorbs some of the incident energy and forms predominantly C0+ and excited CO molecules. Comparison of the ionization potentials^! of CO and H2 O shows that the charge transfer reaction (33) is exoergic by about 1.4 ev/molecule and cannot be ignored.
C0+ + D20 ------> CO + D20+ (33)
Similar reasoning indicates that charge transfer from D2 0+ to CO would not occur appreciably. Thus, the formation of C0+ would probably lead to the formation of D2 0 + . Although excited CO molecules undoubtedly are present in this system, their abundance is probably relatively low because of the small percentage of CO molecules present.
The temperature dependence of G(D2) and G(C0 2 ) in D20/C0 mixtures is shown in the Arrhenius plot of Figure 14.
The slope of the best straight line drawn through the experi mental points corresponds to an Arrhenius energy of 11 kcal/mole.
If it is assumed that the yields at the lowest temperatures 112
O G(D~)
□ G(C02) .80 [> Corrected G values
G(product)
1.40
.00
1.70 1.90 2.10 I/ T (° K“* x I03 ) Figure 14. Temperature dependence of G(D2) and G(C02) in the D20 : CO system. 113 correspond to a constant non-chain region, as in the case with hydrogen, then the appropriate subtraction procedures can be applied giving the lower line in Figure 14. The Arrhenius activation energy calculated from the slope of this line is 22 kcal/mole.
It is apparent from the results in Table 26 that G(D2 ) =
G(C02). The agreement is quite good in the high temperature experiments (above 200°C), and within 10% for the experiments at
215°C. The values of G(CC>2 ) show no apparent trend with increasing mole fraction of CO, but such a trend may be present in the case of the two determinations of G(D2 ).
The following free radical mechanism is consistent with these results for non-chain production of CO2 or D^.
D20 — D + OD (35)
OD + CO - > C02 + D (36)
D + D + M - 2> D2 + M (37)
D + D*S ~~----- > D2 + S (38)
Reaction (35) is a shorthand expression for a ll of the radiation induced processes which produce D atoms and OD radicals.
Reactions (37) and (38) are simply radical recombination reactions, in the gas phase and at a surface, respectively.
Unequivocal evidence for reaction (36) has recently been 114 presented by Stief and co-workers.^ A mixture of 18 mm and 0.5 mm of CO was condensed on a surface at -196°C. It was stated that only about 0.25 mm of CO was entrapped in the solid, and that the remaining portion was pumped away. Excitation of the water with 1470 A0 and 1236 A0 light resulted in the formation of C016018.
The activation energy of reaction (36) has been estim ated^ ’ to be in the range 2-7 kcal/mole. Stief and co-workers suggest that, since the reaction occurs readily at -196°C, the lower value is probably correct. On the basis of these observations, it is difficult to assign the observed activation energy of 11 kcal/mole to this reaction. (The activation energies of reactions (37) or
(38) are also zero or very small).
On the other hand, i f there were two mechanisms taking place, as in the case of the hydrogen and water vapor systems, the increase in the G values above 215°C could be attributed to the occurrence of the chain propagating reaction (39). Calculations using heats
D + D20 ----- D2 + OD (39)
of formation data from B e n s o n ‘S show this reaction to be endothermic by 15 kcal/mole, and thus the enthalpy of activation would have to be at least this great.
(45) L. J. Stief, V. J. DeCarlo, and J. J. Hillman, J. Chem. Phys., 43, 2490 (1965). (46) A. Y. -M. Ung and R. A. Back, Can. J . Chem., 42, 753"(1964). (47) L. E. Avramenko and R. V. Kolesnikova, Advan. Photochem., 2, 25 (1964). 115
Fenimore and J o n e s ^ 8 have found the activation energy for the analogous reaction (40) to be 25.5 kcal/mole,
H + D20 ------> HD+ OD (40) in reasonable agreement with the value of 2 2 kcal/mole obtained by subtraction of the assumed constant G value. The activation energy for the reverse reaction (41) has been r e p o r t e d ^ , 47 to be 7-10 kcal/mole, but Del Greco and K a u fm a n ‘S have suggested that it should be closer to 7 kcal/mole. In any event, the difference between EA (22 kcal) and is probably 12 to 15 kcal/mole, which
OH + H2 — > H20+ H (41) is in agreement with the endothexmicity of reaction (42) or the analogous reaction (39).
H + H20 > H2 + OH (42)
Table 26 shows that methane was formed with a G value of
0.62*0.02. This is in agreement with the value of 0.5*0.2 found by T in g e y ^ O in the radiolysis of approximately equimolar mixtures ■ of CO and H20 using Co^O gamma rays. He showed that the G value was independent of temperature in the range 100 to 500°C. He also obtained evidence for the formation of methanol. D o u g l a s ^ l found
(48) C. P. Fenimore and G. W. Jones, J. Phys. Chem., 62, 693 (1958). (49) F. P. Del Greco and F. Kaufman, D isc. Faraday Soc., 33, 128 (1962 ). (50) G. L. Tingey, Battelle-Northwest, Richland, Washington, private communication. (51) D. L. Douglas, J. Chem. Phys., 23, 1558 (1955). 116
that mixtures of hydrogen, tritium , and carbon monoxide produced formaldehyde, acetaldehyde, and some glycols. As can be seen from
Table 27, the mass spectrum-of the samples collected through a cold trap at -78°C is quite complex. In the majority of cases, however, the signals were very small ( 0 . 1%) when compared to the signal from CC^. This could be indicative of a small yield of organic products or, simply, of the low vapor pressure of these species at -78°C.
The peaks at mass numbers 36 and 34 have relative in ten sities 59 corresponding to perdeutero methanol. Likewise, the peaks at mass numbers 35 and 33 have relative in ten sities corresponding to mono- protonated methanol. Presumably, the H atoms could come from the walls of the reaction vessel. The response at mass 30 can be attributed to the DC0+ fragment of formaldehyde, acetaldehyde, or formic acid. A response at mass number 26 is present in all the experiments and could be due to C^D4" from the breakdown pattern of perdeutero acetylene.
Since the D and 0 atoms are not in the ratio of 2:1 in the known organic products, the equality of G ^ ) and GfCC^) would no longer be true, if the reactions producing the organic products were appreciable. This has been found by Tingey^O to be the case
(52) "Index of Mass Spectral Data," American Society for Testing Materials, Philadelphia, Pa., (1963). 117 below 300°C. Above this temperature the two G values become equal.
It is difficult to establish with certainty the G values for the production of these organic products. If G(HD) 0 is taken as a true measure of the radical yield in the radiolysis of water vapor in the presence of H2, then methane and deuterium account for 84% of the total D atom yield, as shown by the following calculation.
G(D2 ) + 4 G(methane) _ n>Q ( 1Q2) = 84% (L) G(HD) 0 13.1
Thus, an upper limit for the G value for the production of organic molecules is 2.1, assuming a maximum average of 2 D atoms per organic molecule. The absence of the majority of the peaks resulting from the organic products in the mass spectra obtained from the two experiments at the higher temperatures supports Tingey*s observa tions and the hypothesis that these organic products are formed
in even lower yields at higher temperatures.
A mechanism for the production of methane, methanol, or the
other organic products is not proposed for lack of sufficient data.
The fact that evidence for these is present supports the hypothesis
that reaction (42) is occurring.
D + CO + M — > DCO + M (42)
In th is equation, M represents any third body. The activation 118
energy for reaction (42) has been calculated by Dorman and Buchanan*^ to be 3 kcal/mole. Calvert^ suggests that 15.3 kcal/mole is the best value for the activation energy of the reverse of reaction (42).
The organic products could then be formed by subsequent reactions
of the DCO radical.
In order to account for the increase of G(D2) and G(C0 2 ) with
temperature, a thermal reaction between some species and water has
to be proposed. One such possibility is represented by reaction
(39). If the COOD radical is sufficiently long lived, the following
reaction could also occur at the higher temperatures ( 215°C):
COOD + D20 C02 + D2 + OD (43)
The formation of this radical via reaction (44) probably
requires a stabilizing collision.
OD + CO + M ------> COOD + M (44)
By using heats of formation data from the tabulation byB e n s o n ^ l ,
it can be shown that reaction (43) is exothermic by 8 kcal/mole.
The low activation energy for reaction (36) and the good evidence
presented by Ung and Back^ for the production of C02 without the
production of hydrogen, even at temperatures above 200°C, supports
(53) F. H. Dorman and A. S. Buchanan, Australian J. Chem.. 9,, 34 (1956). (54) J. G. Calvert, J. Phvs. Chem.. 61, 1206 (1957). 119 the hypothesis that this sequence involving COOD radical is improbable. Likewise, no feasible mechanism can be proposed using the DCO intermediate.
Using reactions (35), (36), (38), and (39), the rate laws for the production of D2 and CO2 are:
d(D2 )/dt = k3 9 (D)(D2 0) + k3 8 (D) (M)
d(C02 )/d t = k3 6 (0D)(C0) (N)
The steady state concentrations of D and OD are given by equations
(0) and (P). "
^ s s “ 2 k35I//k38
_ k35I ~ k39^D2°^2k35I/ k38 ^OD) ss - k36(co )
Substituting this in (M) and (N) results in expressions.
d(D2 )/d t = 2k35I ( l - k3 9 (D2 0) ^ (p)
k38 •)
d(C02)/dt = 2k35I p . - k3 9 (D20)^ (R) ^ ~k^o38 /
Thus, G(C02 ) = G(D2) and E^ - EC0 = ea*
The mechanism for the exchange occurring via a chain process in the experiments with hydrogen w ill now be discussed. The high activation energy observed and the fact that an atomic mechanism explains the results found at lower temperatures forces one to 120 choose a free radical process. Two chain propagating sequences can be proposed. The f ir s t , (45) and (22), involves an exchange reaction with water.
H + DOD -----> HOD + D (45)
D + H2 ----- > HD + H (22)
The second is an abstraction mechanism.
H + DOD -----> HD + OD (46)
OD + H2 ------> HOD + H (23)
Both sequences give rise to the chain formation of HD. Chain termi nation is accomplished by the loss of H atoms to the walls of the reaction vessel. In reaction (24), H-S represents a hydrogen atom
H + H-S ------^ H2 + S (24) adsorbed on the surface of the v essel, and k2 4 is , thus, a pseudo first order rate constant. The second order three-body homogeneous recombination process is eliminated on the basis of Firestone's 27 results, which showed that all constant pressure and temperature,
G(HD) did not change with a five-fold change in the dose rate. If chain termination were second order with respect to (H), G(HD) would vary with the reciprocal of the square root of the dose rate.
Evidence for the exchange reaction (45) has been presented by Geib and S t e a r c i e ^ and Boehm and Bonhoeffer^ in their studies using
(56) K. H. Geib and E. W. R. Steacie, Z. Physik. Chem., B29, 215 (1935). (57) E. Boehm and K. F. Bonhoeffer, Z. Physik. Chem., 119, 389 (1926). 121
hydrogen atoms formed in a Wood's tube. Farkas and M elville5^ also found evidence for exchange when they exposed mixtures of deuterium, water vapor (H2 0 ), and mercury to lig h t with a wave length of
2537 A0.
Fenimore and Jones^ have found evidence for reaction (45) by measuring the formation of HD caused by the addition of D2 O to flames of pre-mixed H2 , O2 , and CO2 . Further, it can be stated that the results presented in this investigation of the radiolysis of
D2 0 :C0 mixtures support the existence of the similar abstraction reaction (46).
The temperature dependence of G ^ ) has been firmly established, as the results in Table 21 show. Two thermal non-ionic reactions can be presented for the formation of D2 .
D + D20 ------> D2 + OD (39)
D + HD D2 + H (31)
The data in Table 21 were obtained at a constant percent conversion of H2 (5% to 6%). A constant G value of 0.67 (the non-chain G value) was subtracted from these and the results are plotted in Figure 14.
The slope of the best straight line through the points gives an
Arrhenius activation energy of 21*3 kcal/mole. As evidenced in the
scatter of the points, the experimental uncertainty is large. This activation energy is nevertheless in essential agreement not only
(58) A. Farkas and H. W. M elville, Proc. Roy. Soc. (London), A157, 625 (1936). 122
^ 0.3
-0.3
1.50 1.60 1.70 1.80 I/ T (°K_I x I03 ) Figure 15. Temperature dependence of [G(D2 )“ G(D2)o] of a vapor density of 0.319 mg./ml.
2.2
2.0
1.8
a»
1.6
0.50 0.30 0.10 -Log Vapor Density Figure 16.Variation of [G( HD)-G(HD)o] with vapor density at 3I5°C. 123 with that obtained using G(HD) and G(T), but also with the value obtained in the D2 0:C0 system.
The contribution of reaction (39) can be estimated by calcu lating the ratio of the rate of reaction (39) to the competing reaction (2 2 ).
D + H2 ------> HD + H (22)
The following expression is obtained for the ratio of the rates.
R22/ R39 = k2 2(H2)/k39(D2°) (S)
A value of 3 x 10 3 is found at 320°C using activation energies of
2 2 kcal/mole and 5 kcal/mole for reactions (2 2 ) and (39), respective ly. The value of 22 kcal/mole was obtained from the results of the
D2 0 :CO system, and 5 kcal/mole from the values presented by Benson. 33
Also for this approximate calculation, it can be assumed that the pre-exponential factors are equal within an order of magnitude. The ratio (H2 )/(D2 0 ) equals 3 x 1CT3 . Thus, water cannot effectiv ely compete with hydrogen for D atoms at the temperatures and concen trations of hydrogen used in th is investigation.
It was thought that lowering the mole fraction of hydrogen, as was done in experiments 42, 39, and 43 (cf. Table 22), would favor reaction (39) and cause an increase in G(D2). As seen from the data, this was not the case. The value of G(D2 ) remained constant
(2 .6) when the hydrogen concentration was decreased by a factor or
1.6, but increased to 3.3 when the hydrogen concentration was 124
increased by this same factor. This increase can probably be attributed to experimental error. On the other hand, however,
G(HD) decreased 20% with the decrease in the hydrogen concentration.
It also increased by 1% in the latter experiment, but this is probably due to the higher temperature by 5°C of this experiment.
The values of G(T) indicated this same trend.
This suggests a very strong dependence of G(HD) and G(T) on the concentration of hydrogen in th is range ( 3 x 10“%) which can only be explained by D atoms disappearing by a mode other than reaction with H2 . At the lower vapor density (0.319 mg/ml) this effect was not observed (cf Table 22) in the same range of hydrogen concentrations. Also, the values of G(HD) and G(T) were much smaller
(63 as compared to 150 for G(HD)) due to the smaller concentration of water.
There are two conceivable reactions which could compete with hydrogen for D atoms. One is the reaction of D atoms with water to produce D2 , and the other is either recombination or loss of D atoms at the wall of the reaction vessel. The first possibility has already been eliminated by the results of the calculation of the ratio of the
rates given by (S). The second possibility is not probable for two
reasons. F irst, the same mole fraction of hydrogen as that in the
experiment showing the decrease in G(HD) was su fficien t to react with a ll the D atoms produced at a lower temperature (Exp 29 at 224°C,
cf Table 19), and it would be expected that an increase in temperature 125
would favor the reaction with hydrogen. Second, the effect was not observed in those experiments at a lower vapor density. Even though the concentration of D atoms is undoubtedly influenced by
the concentration of water at the high temperatures, no change in
the efficien cy of the competing reactions would be expected unless
they were of different order with respect to (D). Since i t has
been demonstrated by Firestone^ that the chain termination
reaction is not second order with respect to the radical concen
tration, the concentration of water would not effect the compe
tition for D atoms. As a consequence of these arguments, there is
no apparent explanation for the results of Exp 42.
After insertion of reaction (31) into the free radical
mechanism represented by reactions (22)-(24), (35), (45) and (46),
the following expressions are obtained for the steady state
concentrations of H and D atoms, where l^ I is the rate of
(T)
k35T + 2k35 Ik4 5 (D0D) (U) k24 (D)ss k2 2 (H2) + k31 (HD)
production of the radicals induced by the radiation. The G value
for the production of D2 is then given by equation (V). 126
k3 l (HD) / k35 + 2 ^ 4 5 (DOD) . n2
G(D2 ) = HHf______(V) k2 2 (H2) + (HD)k31
Statistically, k22 = 2k3^ and this expression simplifies (V) to give
(HD) (^k35 + 2k35 k4 5(D0D)N' 1q2 (w)
G(I>2) = (H2) + iHDl 2
If the term (HD)/2 is considered negligible compared to (H2)
(the reactions were not allowed to proceed to more than 5% conversion), this equation predicts that G(D2) should be a function of the ratio
(HD)/(H2), and exhibit an activation energy characteristic of that
(E4 5) for the exchange reaction since k35 and k24 are independent of temperature. Also, the percent conversion has to be identical in all the experiments which are used to determine the temperature co efficien t. In an experiment in which 22%. of the H2 had been converted to HD (cf Table 25), the value of G(D2) was equal to 7.4 at 295°C. In a similar experiment at the same temperature but only
3.5% conversion, (Exp 34, Table 20), G(D2) was equal to 2.1. The difference between these two G values is too large to be attributed to experimental error, thus, G(D2) is dependent on the percent conversion. From the slope of the line in Figure 15, the activation energy for the production of D2 was 21+3 kcal/mole which is in essential agreement with that obtained for the abstraction reaction
(39) in the CO system. Since this reaction is probably not occurring because of the reaction of D atoms with H2 » it is probable that the exchange reaction has an activation energy which is nearly equal to that for the abstraction reaction. It can be seen from an examination of the proposed mechanism that the steady state concentration of the D atoms is not affected by the abstraction reaction (46) at low conversions. Thus, it is difficult to explain the existence of a temperature coefficient for G(D^) at low percent conversions without the occurrence of the exchange reaction (45).
Since the abstraction reaction (39) is occurring in the CO system, one has no reason for eliminating the corresponding reaction
(46) from the mechanism. The G value for the production of HD at low conversions, that is ignoring (31), is given by (X).
G(HD) - k35 + 2 k35^D2 ° ^ k45 * k46) io 2 ^ k24
The term kg^lO2) is equal to the non-chain G value, G(HD)q, and, thus, the chain value, G(HD) - G(HD)o, should be first order with respect to the water concentration. In Figure 16, a plot of log (G(HD) - G(HD)q) versus log (vapor density) at 315°C is pre sented. In order to correct the chain G values obtained at 320°C in experiments 54 and 55 (cf Table 24) to 315°C, a value of 19.5 kcal/mole was used for the activation energy. The slope of the best straight line drawn through the points is 1.6*0.4. Unfortunately, 128 the uncertainty in this number is quite large. This is due to the large variation (8%) in G(HD) caused by the temperature variations in the sand bath during the heating and cooling cycles (^3°C).
Another d iffic u lty which was encountered in the determination of this number was the fact that the vapor density could be changed by a maximum factor of only 2 . 2 due to limitations in the size of the vessel.
A second order dependence of G(HD)-G(HD) 0 upon (D20) can be explained by a consideration of the rate constant k24. This rate constant will be of the foim if the rate of reaction
(24) is controlled by the diffusion of H atoms to the surface of the vessel. In this expression M is the total concentration of gas in the vessel and k° 4 is a constant depending on the size and material of the vessel. The equation presented by Benson^ can be evaluated to show the possibility that diffusion can be the rate controlling step in the loss of H atoms. It is stated that, i f P, the pressure in the v essel, is greater than the ratio
'©o/Srec, then the wall termination reaction will be diffusion controlled. In this ratio DQ is the diffusion coefficient per unit pressure, r is the radius of the spherical vessel, c is the mean resultant velocity of the H atoms, and e is the recombination
(59) S. W. Benson, "The Foundations of Chemical K inetics," McGraw- H ill Book Co., Inc., New York, I960, p. 327. (60) Indem., ibid., p. 447. 129 coefficient or the probability that one H atom will be lost per co llisio n with the w all. The order of magnitude of Dq/c is 10~^ at 1 atm, and r is 4 cm in th is investigation. Thus, i f e i s of the order of 1 0 “^ or larger, the reaction will be diffusion controlled at pressures near 1 atm.
Smith^l has measured the recombination coefficien t for H atoms on Pyrex in water vapor and has obtained a value on the order of lCT^. Representative values in hydrogen gas on Pyrex range from
Iq-4 62 .(-q io - 6 63^ therefore likely that reaction (24) is diffusion controlled and that, as a result, k2 4 = k^/^O). By substituting this expression into equation (W) it is evident that a second order dependency of the G value on the vapor density is predicted.
This same effect has been observed by Armstrong and Spinks^ in th eir study of the radiation-induced reaction between hydrogen bromide and ethylene. At total pressures on the order of 0.25 atm at 34°C with HBr in a 4- to 13-fold excess over C2 H4, they observed that G(CH3 CH2 Br) was independent of the dose rate. It did, though, exhibit a second order dependence on (HBr). These results were interpreted by invoking a diffusion controlled loss of Br atoms to the walls of the reaction vessel.
(61) W. V. Smith, J. Chem. Phvs.. 11, 111 (1943). (62) B. J. Wood and H. Wise, J . Phvs. Chem.. 6 6, 1049 (1962). (63) W. Steiner, Trans. Faraday Soc., 31. 962 (1935). (64) D. A. Armstrong and J. W. T. Spinks, Can. J. Chem., 37. 1210 (1959). 130
The observed^ activation energy for the production of HD is given by equation (Y), since k3 5 is independent of temperature.
_ k45E45 + k46E46 (Y) obs k , k 24 45 46
This equation was derived in the following manner. The expression describing the temperature dependence of the chain G value involves the product of a temperature independent term and the exponential, exp (-E 0 ks/RT). By differentiating with respect to T-"1, the equation for the logarithm of the chain G value, the following expression is obtained.
dln(G(HD)-G(HD)0 )/d(T"1) = -Eobs/R (Z)
After rearranging equation (X), and differentiating the logarithm of it with respect to T^, one obtains equation (AA).
din (G(HD)-G(HD)o )/d(T_ 1 j=dln (k4 5+k46)/d (T~X )-dlnk24/d (T 1) (AA)
Since for any function, f(x), dlnf(x) = df(x)/f(x), equation (AA) becomes
din (G(HD)-G(HD)0 )/d(T~1) = f^5_+_dk46 ------dln^ d(rl) (BB) dCT" 1 )(k 45+k46)
Also, for any rate constant k^, it can be seen from the Arrhenius expression that dk^/d(T"*1) = (^ (-E ./R ). By using this in equation
(BB) one gets equation (CC). 131
^45^45 + ^46^46 (CC) din (G(HD)-G(HD) )/d (T ) - — -----— ------E2 4 45 46
It can then be seen that equation (AA) is equal to equation (CC) and thus, equation (Y) results.
Again E2 4 can be considered to be zero. Thus, the observed activation energy is a weighted sum of 4 E 5 and E4 5 . The activation 56 5R energy for the exchange reaction has been estimated ’ to be at least 12 kcal/mole, while the experimental Arrhenius energy for the abstraction has been determined to be 25 kcal/m ole.^ 8 An intermediate value of 19.5+1 kcal/mole has been determined in the present investigation.
The curvature beginning at 150°C in the Arrhenius plot shown
in Figure 11 cannot be attributed to the initiation of a reaction with an activation energy of 12 kcal/mole. This was shown to be
the case by drawing, from the point where the curvature began, a
line which had a slope corresponding to an Arrhenius energy of
12 kcal/mole. This line was well outside of the region described
by the experimental points at reciprocal temperatures of 2 . 3 x l 0"3,
2.4x10-3, and 1.9xl0“3 °K"1. Thus, the lower limit of the
activation energy for the exchange reaction must be larger than 12
kcal/mole. The lack of substantial curvature in the Arrhenius
plots for the chain G values of both HD and HT (cf Figs 12 and 13
respectively) over a 1 0 0 degree temperature range indicates that
E4 5 and E4 6 are approximately equal, or that only one reaction is 132
contributing to the chain.
From the discussion concerning the temperature coefficient of
G(D2), and the results obtained from the D2 0 :CO system, it is
evident that both reactions are occurring above 250°C. Thus, their
activation energies are nearly equal, probably within 5 or6 kcal
or less. This figure was estimated by considering the curvature which could possibly be observed in Figs 12 and 13. Until the
absolute values of k^ and k^ are known, the contribution of each
reaction cannot be determined.
Baxendale and Gilbert^ have studied the radiolysis of water vapor at low concentrations of hydrogen, where the scavenging
reaction was not 100% efficient. It was thought that an analysis
of these data would be informative as to the mode of removal of
H atoms in the experiments at low temperatures. The alternatives
are a second order homogeneous three-body recombination or a first
order removal at the wall of the vessel or with an impurity. The
same mechanism as that proposed in the present study will be
considered.
D20 ----> D + OD (35)
D + H2 - ----^ HD + H (2 2 )
OD + H2 -----^ HOD + H (23)
H + H-S ------> h2 + S (24)
D + D-S ---- > d2 + s (25) 133
Reaction (47) represents first order removal of D atoms at the surface by some means, perhaps via reaction with an adsorbed atom,
D-S.
The steady state concentration of D atoms is
k35I (D) cc. = — ------(EE) k2 2 (H2) + k47 where I is the absorbed dose rate. The rate equation for the production of HD is then
krjrjkoc I d (H D )/d t = - 2 2 - 2 1 ------(FF) ki 2 (H2) + k4 7
Similarly, the rate of the wall reaction is
k47k35I (GG) d(W)/dt k22(e2) + k47
By dividing equation (GG) into equation (FF), one obtains an
expression for the ratio of the G values.
(G(HD)/G(W)) = k2 2 (H2 )/k4 7 (HH)
The maximum values of G(HD), as seen from Fig. 17, obtained in
Baxendale's experiments was 10.5. Thus, G(D) = G(HD) + G(W) = 10.5,
By substituting G(D) - G(HD) into equation (HH) and inverting and
rearranging, one obtains equation (II).
G(D)/G(HD) = k4 7/k 2 2 (H2) + 1 (II) 134
10.0
6.0
G(HD)
2.0
001 Mole % H2 0.10 Figure 17. Yield of HD in the D20:N2 system. Token from Boxendale and Gilbert, Disc. Faraday Soc., 36,296 (1963).
1.8
G(Total) G(HD) 1.4
1.0
0 1 .0 2.0 3.0 4.0 I/ Mole % Ho x 10
Figure 18. Kinetic analysis of the data of Baxendale and Gilbert. 135
From th is i t can be seen that a plot of G(D)/G(HD) versus
(t^)"* should be linear.
The following data in Table 28 were taken from the published
graph of Baxendale (see Fig 17) using a Vernier caliper precise to-
* 0 .1 mm.
TABLE 28
Values of G(D)/G(HD) and l/Xj^^a taken from the data of Baxendale and Gilbert
G (HD) G(D)/G(HD) Xh2 x io 5 i A H2 x 1 0 - 4
9.0 1 . 2 7.03 1.42 8 . 0 1.3 4.82 2.07 7.0 1.5 3.18 3.18 6 . 0 1 . 8 2.34 4.32 5.3 2 . 0 2 . 0 2 4.95
aXj_i^= (H2 )/(D2 0 ) The concentration of D2 O was approximately
2 x 1 0 " 2 m oles/l.
kj. H. Baxendale and G, P. Gilbert, Disc. Faraday Soc., 36, 295 (1963).
Figure 18 shows the results of plotting G(D)/G(HD) against the
'■reciprocal of the mole fraction of hydrogen. The fact that a straight
line is obtained shows that the data adhere to the general form of
the proposed mechanism. Failure to obtain an intercept of 1 is
probably a result of errors introduced in recovering the untabulated
data from the curve in Baxendale’ s published a r tic le . A smoothing 136
of the data after imposing an intercept of 1 is not justified because of the inherent errors in obtaining the data.
The slope in Figure 18 is equal to l^Y/k^O^O). From the
text of Baxendale*s paper it is determined that the concentration
of water is roughly 0.02 M, which gives a value of 4 x 10- 7 m oles/l
for l<4Y/k2 2 * The value of IC2 2 at 116°C is estimated to be 3 x 10 7
l/mole-sec from the values reported by Geib and Harteck^ or
Farkas and Farkas^ for the activation energy and the pre-exponen
tial factor for reaction (22). Thus, the first order rate constant,
k47, has a value of 1 x lO"*- sec“^ in the five liter, spherical
glass vessel used by Baxendale.
It is possible to estimate this rate constant for the reaction vessels in the present investigation if the reaction is diffusion
controlled. From a consideration of the arguments presented earlier
concerning the recombination coefficient for hydrogen on glass sur
faces, it is quite likely that the wall process, indeed, is diffusion
controlled in both works. Thus, the rate constant has the form
^4 7/ (D2 0 )r2 .
In the present investigation the radius of the reaction vessel
is 4 cm and the concentration of water is roughly 3 x 10“2M. The
resulting value for k4 7 in this study is, then, 50 sec-'*'.
The fraction of hydrogen atoms lo s t to the walls under the
(65) K. H. Geib and P. Harteck, Z. Physik. Chem.. Bodenstein Festband, 849 (1931). (6 6) A. Farkas and L. Farkas, Proc. Roy. Soc., A152, 124 (1935). 137
conditions of the low temperature (T<250°C) non-chain experiments can now be estimated. This fraction should be le ss than the relative experimental error in the measurement of G(HD), which was approximately 1%. The ratio k4 7/(k 4 7fk 2 2 (H2 )) is clearly this fraction, and it has a value of 0 .0 1 when the concentration of hydrogen was 1.7 x 10“^ M, the smallest used in th is investigation.
Thus, i t is apparent that hydrogen is an e ffic ie n t scavenger for
D atoms under the conditions of the present experiments. This
supports the conclusion that the absence of an appreciable tempera
ture coefficient below 250°C indicates that there is no competition
for the reaction of D atoms with hydrogen. Also, since Firestone
found that G(HD) = G(-D2 ) in the 1^ 0 : 0 2 system under sim ilar
conditions, i t may be assumed that hydrogen is effectiv ely
scavenging OD radicals.
The effect of isotopic substitution on the radiation chemistry
of water vapor can be evaluated by comparing the results of the
present investigation with those obtained by Firestone^ for the
H2 OSD2 system. The values of G(HD) below 160°C for the two systems
are shown as a function of temperature in Figure 19. In order to
fa c ilita te the comparison the ordinate of this figure is greatly
expanded. Both sets of data show a decrease in G(HD) below 110°C,
a portion of approximately zero slope between 110°C and 150°C, and
a region of positive slope above 150°C. Although the results of 138
O-DgO : Hg system 16.0 □ -HoO ; 09 system
14.0
G(HD)
12.0
10.0
80 100 120 140 f60 Temperature °C. Figure 19. Comparison of G(HD) for the radi- olysis of the D20 : H2 and H20: D2 systems.
2.00 OO o o 1 o rO o ° ° c C C C
------O’...... C Separation o o o O O
0 O Factor j o o O 1.00
— 1 1 ____1____ 1... 1 , 1 ____I 8 0 140 2 0 0 2 6 0 3 2 0 3 8 0 Temperature °C. Figure 20. The separation factor at several temperatures. 139
the study of the D2 O system appear consistently higher by
approximately 8%, it is felt that the data are not sufficiently precise to attribute this to an isotope effect. The average of
all the G values enclosed in the dashed line is 12.6-0.6 molec/ev where the uncertainty is the average deviation from the mean. This
result is higher than the original estimate reported by Firestone,on '
which was the average of a ll the results that were obtained below
150°C.
The apparent absence of an overall isotope effect in this
temperature region is not surprising on the basis of the proposed
mechanism. Since the radical scavenging reactions are essen tia lly
99% efficient, any observed effect would have to be on the reactions
producing the radicals. It has been estimated6*7 that isotopic
substitution has only a 5% effect or less on the molecule-ion
sensitivities or the total ionization of a molecule. Similarly,
the effect on electronic excitation has been stated to be small. 0
An interesting isotope effect has been observed by Jesse^ in his
studies of the ionization efficiencies of polyatomic molecules.
The results of his work correlate with the theory of super
excited states advanced by Platzmann.70 Super excited molecules
are molecules which have been excited to states which are higher
(67) F. H. Field and J. L. Franklin, "Electron Impact Phenomena," Academic Press, Inc., New York, 1957, p. 214. (6 8) J. G. Burr in "Tritium in the Physical and Biological Sciences," Vol. 1, International Atomic Energy Agency, Vienna, 1962, p. 137. (69) W. P. Jesse, J. Chem. Phys., 41, 2060 (1964). (70) R. L. Platzmann, The Vortex, 23, 372 (1962).
I 140
than the ionization potential of the molecule. As a result of having a lower zero point vibrational energy, the heavier molecule will have a larger probability of ionizing rather than dissociating than the lighter molecule. In the case of water vapor, Jesse found that the ionization efficiency of D2O was 3% larger than that for H2O. If 2 D atoms and two OD radicals are produced as a result of the ion molecule reaction (1 6) and the neutralization reaction (28) for every ionization while only one of each for
every neutral dissociation, it would be theoretically possible to observe an isotope effect. Only those molecules which are super 71 excited estimated by Platzmann to be 18%, though would exhibit
this effect, thus, the resulting difference in the G values would
be very small. Any experiments which could measure th is effect would require a high degree of accuracy and precision.
In the chain mechanism above 200°C, a kinetic isotope e ffe ct
can be observed by comparing the results of the two systems. This
effect can be attributed to the effect of isotopic substitution on 27 the rate of a thermal chemical reaction. Firestone reported an
observed Arrhenius energy of 18+ 1 kcal/mole while the Arrhenius
energy found in this study was 19*1 kcal/mole. Since the latter
value was determined four times from two different series of
experiments, it is probable that the difference between the two
(71) R. L. Platzmann, private communication. 141
activation energies is real and not a result of an experimental error. From a consideration of the transition state theory of reaction rates at low temperatures, the difference in the acti vation energies for two isotopic reactions is related to the
79 difference in the zero point energies of the isotopic species. ^ 73 Darling and Dennison have calculated that the zero point energy of D2 O is 3.6 kcal/mole lower than that for 1^0, thus, one would expect a higher activation energy in reactions involving D2 O.
In order to compare the rates of the chain propagating reactions, the G values for the production of HD by the chains, (G(HD)-G(HD)0) , have to be evaluated at identical temperatures and concentrations of water. Since Firestone^ has shown that the value of G(HD) was independent of the dose rate, this factor does not have to be considered. At 278°C and a vapor density of 0.774 mg/ml Firestone obtained a value for G(HD)-G(HD) 0 of 117. At the same temperature, but a lower vapor density of 0.590 mg/ml, a value of 41 was obtained from the results of this investigation. This value was read directly from Figure 12. The ratio of the concentrations,
(H2 0 )/(D 2 0 ), represented by these vapor densities is 1.46. In order to correct for this difference, an order for the mechanism has to be assumed. Values of 1, 1.6, and 2 were used, and the results of the calculations for the ratio of rates are shown in Table 29.
(72) L. Melander, "Isotope Effects on Reaction Rates," The Ronald Press Co., New York, I960, p. 44. (73) B. T. Darling and D. M. Dennison, Phvs. Rev., 57. 282 (1940). 142
TABLE 29
Order of Correction3 (g(hd )- g(hd )o)d 2o (g(hd)-g(hd)0 )h2o the Mechanism Factor (g(hd)-g(hd)0 )d2o
1.0 1.46 60. 1.9 1 .6 1.83 75. 1 .6 2.0 1.94 8 8. 1.3
Correction factor - (H2 0)/(D 2 0) n, where n is the order of the mechanism.
Roginsky,"7^ from an analysis of the data of Geib and Steacie, ^ 1
states that the difference in the activation energy for the exchange
reactions is 0.75 kcal/mole and the ratio of the rates of the
reactions at 183°C is approximately 1.7. This value was corrected
to 278°C by using the difference in the activation energies which he
cites. The result is that kHkp is equal to 1.1 at 278°C. The
reasonable agreement with the results in Table 29 is probably
fortuitous since the mechanisms in the two systems are somewhat
different. Geib and Steacie did not find evidence for the abstraction
reaction (46). The values in column 4 of Table 30, and the differ
ence in the activation energies, are of the same size as those
presented by Roginsky”7^ for other gaseous reactions involving H or
D atoms. Due to the fact that two different reactions involving
(74) S. Z. Roginsky, "Theoretical Principles of Isotope Methods for Investigating Chemical Reactions," tran sl. by Consultants Bureau, Inc., Technical Information Service Extension, Oak Ridge, Tenn., 1956, p. 280. 143 two different transition states are contributing to the formation of HD in the chain mechanism, and the relative contribution of each is not known, theoretical calculations concerning the isotope effect are not justified.
The third and, perhaps, most interesting isotope effect observed in this study was an intramolecular effect exhibited by the values of the separation factor. An average temperature indepen dent value of 1.6 was obtained for this factor as shown in Figure
20. Of course, a value of unity would indicate an absence of any influence of isotopic substitution.
Since the scavenging reactions for D or T atoms are essentially
1 0 0 % efficient, the cause of the isotope effect has to be assigned to one or more of the reactions which form these species. In the
H2 scavenged system, any process which favors the formation of a D atom from TOD rather than a T atom, will cause the separation factor to be greater than unity. This is a consequence of the fact that
T atoms in the form of OT will result in TOH and, thus, not con tribute to the value of nT for that specific experiment. Two conceivable processes which could account for this influence of isotopic substitution are the dissociation of electronically excited molecules or ions, and the proposed ion molecule reactions leading to the formation of D2 OT4'. Neutralization processes can be considered to be in the class of dissociation of excited neutral species. 144
The only direct experimental data for hydrogen isotopes effects on the dissociation of electronically energized molecules are for the dissociation of molecule-ions in a mass spectrometer. Although the isotope effect on this process in water vapor has not been measured, other molecules have been studied. Loss of an H atom from
®2^2+ approximately twice as probable as loss of a D atom.7^’7^
Similarly, loss of an H atom from C^H^D^ i s ^ » 7 times more probable than the loss of a D atom. 7 7 If this isotopic influence exists in the molecule TOD, this could explain the results found in the H2 scavenged system.
Isotope effects on proton transfer reactions have been observed in mass spectrometers. A pulsed ion source was used by Shannon and co-workers7® to study reactions of the type illustrated by (48) and
(49).
CH2dJ + ch2d2 CHD2 + CH3 DJ (48)
CH^J + CH2D2 CH-jD + CH2Dj (49)
They found an average value of -k^g/k^g of 1.3 for all the isotopic methanes. On the basis of this study, it would be expected that these effects would favor the formation of OT and DgO+ from the
(75) V. H. Dibeler and F. L. Mohler, J. Res. Natl. Bur. S td ., 45. 441 (1950). (76) D. 0. Schissler, S. 0. Thompson, and J. Turkevich, Disc. Faraday Soc., 10, 46 (1951). (77) J. G. Burr, J. M. Scarborough, and R. H. Shudde, J. Phys. Chem., 64, 1359 (1960). (78) T. W. Shannon, F. Meyer, and A. G. Harrison, Can. J. Chem., 43, 159 (1965). 145 reaction of DOT+ and D2 0.
Although evidence has been obtained for resonant charge transfer reactions,consideration of the small, if any, effect of isotopic Aft substitution on the ionization potential of a molecule ° allows one to ignore reaction (52) as the source of the influence.
DOT4- + D O D > DOD+ + DOT (52)
One further sequence can be proposed to account for this isotope effect. This is represented by reactions (53) and (54).
D2 OT+ + D20 ------D3 0+ + DOT (53)
D2 0T+ + D20 ------> D^T* + DOD (54)
No evidence has been reported for these reactions in water vapor.
In the CO scavenged system, the separation factor has a value of 1.7 in agreement with that found in the H2 scavenged system.
According to the proposed mechanism for carbon monoxide scavenging, both the T and D atoms on the affected water molecules appear as free hydrogen. Thus, isotope effects of the dissociation processes or the proton or triton transfer from DOT+ would not affect the value of the separation factor. Even an isotopic influence on the chain propagating reaction (39) would not change this value. On the contrary, though, any effect of isotopic substitution on the deuteron or triton transfer from D2 OT+or any other species lik ely to be neutralized to D20 would change the separation factor from a value of unity. This gives strong support to the possible existence of
such reactions as (54) and (53). CHAPTER VI
CONCLUSIONS
_From the foregoing discussion it is concluded that the exchange mechanism for the D20 /T0 D:H2 system can be written as follows:
From 84 to 150°C.
D + H2 -*■ HD + H (1)
OD + H2 ------> HOD + H (2)
H +H* S * H 2 + S (3)
From 150 to 380°C two additional reactions occur.
H + DOD ------> HD + OD (4)
H +DOD * HOD + D (5)
The rate of production of HD above 150°C is second order with respect to the concentration of water, and the rate of the termi nation reaction (3) is controlled by the diffusion of H atoms to the walls of the reaction vessel. The yield of D2 in this temperature
range can be attributed to reaction (6 ).
D + HD ?> D2 + H (6 )
The Arrhenius activation energy of the chain mechanism is
19.5*1 kcal/mole and can be assigned to the weighted sum of the
146 147
Arrhenius energies for reaction (4) and (5). These are equal to each other within 5 or 6 kcal/mole and the lower limit of the activation energy for the exchange reaction is probably 16 kcal/mole.
The mechanism in the D2 0 /TQD:C0 system at 215°C may be written as follows*
OD + CO ------> C02 + D (7)
D + D*S ------> D2 + S (8 )
From 278 to 312°C one additional reaction is occurring.
D + D O D ------> D2 + OD (9)
The Arrhenius energy for th is reaction has been determined to be
21+3 kcal/mole.
It is further concluded that below 150°C the results of the two analogous systems D^/TODsH^ and H2 0 /T0 HsD2 are identical and, thus, there is no overall isotope effect on the apparent yield of radicals in the radiation chemistry of water vapor. Above 150°C a kinetic isotope effect of 1.3 is obtained and 1 kcal/mole is found as the difference in Arrhenius energies of the two sets of chain propagating reactions.
An intramolecular isotope effect has been observed to be identi cal in both the H2 and CO systems with the result that it is due to one or both of the processes of dissociation of electronically excited molecules or proton transfer reactions. BIBLIOGRAPHY
Allen, A. 0., The Radiation Chemistry of Water and Aqueous Solutions, New York* D. Van Nostrand Co., In c., 1961.
Anderson, A. R., and Knight, B ., D isc. Faraday Soc.. 36. 299 (1964).
Anderson, A. R., Knight, B., and Winter, J ., Nature. 201. 1026 (1964).
Armstrong, D. A., and Spinks, J. W. T., Can. J. Chem.. 37. 1210 (1959).
Avramenko, L. E., and Kolesnikova, R. V., Advan. Photochem.. 2 , 25, (1964).
Baxendale, J. H., and Gilbert, G. P., Science. 147. 1571 (1965).
Baxendale, J. H., and Gilbert, G. P., J. Am. Chem. Soc., 86, 516 (1964).
Baxendale, J. H.,,and Gilbert, G. P., Disc. Faraday Soc., 36, 186 (1963).
Baxendale, J. H.^ and Gilbert, G. P., Disc. Faraday Soc., 36, 295 (1963).
Benson, S. W., The Foundations of Chemical K inetics, New Yorks McGraw-Hill Book Co., In c., I960.
Benson, S. W., J. Chem. Edu., 42, 502 (1965).
Bethe, H. A., Handbuch der Physik. Vol. 24, Berlins Julius Springer, 1935.
Bethe, H. A., and Askin, J., Experimental Physics, E. Segre, ed., Vol. 1, New Yorks John Wiley and Sons, Inc., 1953, p. 166.
Boato, G., Careri, G., Gimino, A., Molinari, E., and Volpi, G., J. Chem. Phys. , 24, 783 (1956).
Boehm, E., and Bonhoeffer, K. F., Z. Physik. Chem., 119, 389 (1926).
Buchelnikova, I. S., Soviet Phys., JETP. 35. 783 (1959).
Burr, J. G., Tritium in the Physical and Biological Sciences, Vol. 1, Viennas International Atomic Energy Agency, 1962, p. 137. 149
Burr, J. G., Scarborough, J. M., and Shudde, R. H., J. Phys. Chem., 64, 1359 (I960).
Calvert, J. G., J. Phys. Chem., 61, 1206 (1957).
Chen, M. C., and Taylor, H. A., J. Chem. Phys., 27,857 (1957).
Cottin, M., J. Chim. Phys., 56, 1024 (1959).
Darling, B. T., and Dennison, D. M., Phys. Rev., 57, 282 (1940).
Del Greco, F. P ., and Kaufman, F., D isc. Faraday Soc., 33, 128 (1962).
Dibeler, V. H., and Mohler, F. L., J. Res. Natl. Bur. Std., 45, 441 (1950).
Dorfman, L. M., Phys. Rev., 95, 393 (1954).
Dorman, F. H., and Buchanan, A. S ., Australian J. Chem., ,9, 34 (1956).
Douglas, D. L., J. Chem. Phys., 23, 1558 (1955).
Duane, W., and Scheuer, 0 ., Le Radium, 10, 33 (1913).
Farkas, A., and Farkas, L., Proc. Roy. Soc. (London), A-152, 124 (1935).
Farkas, A., and M elville, H. W., Proc. Roy. Soc. (London), A-157, 625 (1936),
Fenmore, C. P ., and Jones, G. W., J. Phys. Chem., 62, 693 (1958).
Field, F. H., and Franklin, J. L., Electron Impact Phenomena, New Yorks Academic Press, Inc., 1957.
Fiquet-Fayard, Mme. Florence, J. Chim. Phys., 57, 453 (i960).
Firestone, R. F., J. Am. Chem. Soc., 79, 5593 (1957).
Firestone, R. F., Disc. Faraday Soc., 36, 294 (1963).
Firestone, R. F., Lemr, F., and Trudel, 0. J., J. Am. Chem. Soc., 84, 2279 (1962).
Friedlander, G., Kennedy, J ., and M iller, J ., Nuclear and Radiochem- is t r y , 2nd ed., New Yorks John Wiley and Sons, In c., 1964. 150
Geib, K. H., and Steasie, E. W. R., Z. Physik. Chem.. B29, 215 (1935).
Geib, K. H., and Harteck, P., Z. Physik. Chem., Bodenstain Festband, 849 (1931).
Gunther, P ., and Holzapfel, L., Z. Physik. Chem., B42, 346 (1939).
Hart, E. J ., Gordon, S., and Hutchison, D. A., J. Am. Chem. Soc., 75, 6163 (1953).
Henglein, A., Lacmann, L., and Knoll, B., J. Chem. Phys., 43. 1048 (1965).
Henglein, A., and Muccini, G. A., Z. Naturforschung, 18A, 753 (1963).
Henglein, A., and Muccini, G. A. Z. Naturforschung, 17A, 452 (1962).
Hofmann, H. S ., Riehl, N., Rupp, W., and Sizmann, R., Radiochimica A cta., 1, 203 (1963).
Hogg, A. M., and Kebarle, P., J. Chem. Phys., 42, 789 (1965).
Hurst, G. S ., O'Kelley, L. B., Stockdale, J. A., 2nd Int. Congr. Rad. Res., (Harrogate, 1962, Abstr.) p. 128.
Jesse, W. P ., J. Chem. Phys., 41, 2060 (1964).
Jesse, W. P., and Saudauskis, J., Phys. Rev., 97, 1668 (1955).
Kirschenbaum, I ., Physical Properties and Analysis of Heavy Water, New Yorks McGraw-Hill Book C o.,In c., 1951.
Laidler, K. J., J. Chem. Phys., 22, 1740 (1954).
Lampe, F. W., and Field, F. H., Tetrahedron, 1_, 189 (1959).
Lampe, F. W., Field, F. H., and Franklin, J. L ., J. .Am. Chem. Soc., 79, 6132 (1957).
Lassetre, E. N., Rad. Res., Supp. 1, 530 (1959).
Lawrence, R. H., Ph.D. dissertation, Ohio State University, Columbus, (1965).
Lawrence, R. H., and Firestone, R. F., J. Am. Chem. Soc., 87, 2288 (1965). 151
Lind, S. C., Radiation Chemistry of Gases, New Yorks Reinhold Publishing Co., 1961.
Lind, S. C., The Chemical Effects of Alpha Particles and Electrons, TJew Yorks The Chemical Catalogue Co., 1928, p. 94.
Magee, J. L., Burton, M., and Kirby-Smith, J. S., Comparitive Effects of Radiation. New Yorks John Wiley and Sons, Inc., I960.
Magee, J. L., and Burton, M., J. Am. Chem. Soc., 73, 523 (1951).
Mann, M. M., Hustrulid, A., and Tate, J. L., Phys. Rev., 58, 340 (1940).
Melander, L., Isotope Effects on Reaction Rates, New Yorks The Ronald Press Co., I960.
Moran, T. F ., and Friedman, L., J. Chem. Phys., 42, 2391, (1965).
Muschlitz, E. E., J r ., J. Appl. Phys.. 28, 1414 (1957).
Niki, H., Rousseau, Y., and Mains, G. J., J. Phys. Chem., 69. 45 (1965).
Platzmann, R. L., The Vortex, 23, 372 (1962).
Platzmann, R. L., J . Appl. Radn. and Isotopes. 10, 116 (1961).
Platzmann, R. L., 2nd International Congr. Rad. R es., (Harrogate, 1962, Abstr.) p. 128.
Platzmann, R. L., in Basic Mechanisms in Radiobiology. Washington, D, C.s Natl. Res. Council Publication 305, 1953, p. 30.
Platzmann, R. L., and Hart, E. J ., Mechanisms in Radiobiology, Vol. 1, New Yorks Academic Press, Inc., 1961, p. 176.
Pratt, T. H., and Wolfgang, R., J. Am. Chem. Soc., 83, 10 (1961).
Price, W. J ., Nuclear Radiation Detection, New Yorks McGraw-Hill Book Co., 1958.
Pritchard, H. 0 ., Chem. Revs., 52, 529 (1953).
Pillinger, W. L., Huntges, J. J., and Blair, J. A., Phys. Rev., 121, 232 (1961) 152
Schissler, D. 0 ., Thompson, S. 0 ., and Tukevich, J ., D isc. Faraday Soc.. 10, 46 (1951).
Schultz, ( J., J. Chem. Phvs. . 33, 1661 (1961).
Schultz, V f. R ., and LeRoy, D. J ., Can. J. Chem.. 42. 2480 (1964).
Schwarz, }I. A., in Advances in Radiation Biology. Vol. 1, L. G. Augenstein, R. Mason, and H. Quastler, ed s., New York: Academic Press, Inc., 1964.
Shannon, ''. W., Meyer, F ., and Harrison, A. G., Can. J. Chem.. 43. 159 (1965).
Smith, W. V., J. Chem. Phvs.. 11, 111 (1943).
Spinks, J, W. T., and Woods, R. J., An Introduction to Radiation Chemistry, New Yorks John Wiley and Sons, In c., 1964.
Steinman, R., Ph.D. dissertation, Stevens In stitu te, Hoboken, N. J ., 1962.
Steiner, \ Trans. Faraday Soc., 31, 962 (1935).
S tief, L. J., DeCarlo, V. J., and Hillman, J. J., J. Chem. Phys., 43, 2490 (1965).
Roginsky, S. Z., Theoretical Principles of Isotope Methods for Investigating Chemical Reactions, trah sl. by Consultants Bureau, Inc., Technical Information Service Extension, Oak Ridge, Tenn., 1956.
Thompson, S. 0., and Schaeffer, 0. A., J. Chem. Phvs., 23, 759 (1955).
Ung, A. Y . -M., and Back, R. A., Can. J. Chem., 42, 753 (1964).
Von Engel , A., Ionized Gases, 2nd ed., Londons Oxford Press, 1965, p. 163.
Wobschall , D ., Graham, J. R., and Malone, D. P., J . Chem. Phys., 43, 3855 (1965).
Wood, B. * J., and Wise, H., J. Phvs. Chem., 66, 1049 (1962).
Yang, J. Y., ’ and Gevantman, L. H., J . Phys. Chem., 68, 3115 (1964).