RECOILTRITIUM REACTIONS IN METHANE-HYDROGEN MIXTURES
45 1
Recoil Tritium Reactions in Methane-Hydrogen Mixtures. CD,-H,1 by John W. Root and F. S. Rowland Departments of Chemistry, University of California, Davis, California 96616 and University of California, Iruine, California 99664 (Received June 9 , 1969)
The variations in absolute yield of HT, DT, and CDsT have been studied over the entire range of mole fractions for CD*-Hz mixtures. The specific activity of CDsT/CD4increases at high CD4 mole fractions, while that of HT/H, is almost constant for all composition. These specific activity changes imply that an appreciable amount of HT-forming reaction occurs below the threshold for CDaTformation, No combination of reactivity integrals and a factors has been found which will simultaneously fit all binary mixtures involving CH4, CDI, H2, Hz, and Ar.
Introduction Energetic tritium atoms from nuclear recoil react with D2 to form DT and with CH4 to form predominantly H T and CH3T. While the total hot yield of D T in pure D2 is approximately 93% and that of the hot products from CH4 totals only 53%, the specific yield ratio (CH3T/CH4)/(DT/Dz) is remarkably constant over the entire range of mole fractions in CH4-D2 mixtures.2 This fortuitous circumstance permits relatively simple extensions of the model for such high energy reaction^,^,^ and the data can be quantitatively reproduced with reasonable values of the normal parameters of the kinetic theory of hot atom reaction^.^^*^-^ The success of this parametric treatment encourages additional tests of the theory with suitable systems. As more and more binary systems are satisfactorily fitted in this way, the freedom of choice of parametric values becomes more restricted, since the most important parameters for a particular molecule should remain constant in its binary mixtures with all other molecule^.^ I n light of the earlier CH4-D2 data,2 CD4-H2 mixtures should be especially useful for such tests of the invariance of kinetic theory parametric values from system to system, for this combination would then permit cross comparisons with the H2-D2 and CH4-CD4 The only hot processes occurring with appreciable yield for recoil tritium atoms in the CD4-H2 system are the abstraction of D to form DT, the substitution for D to form CDaT, and the reaction with HP to form HT, as indicated in eq 1-3. The use of isotopically different molecules permits direct measurements of the yields of the reaction products from these three reactions.
+ CD4 T * + CD4 T* +
T*
--t
+ *CD, CD3T + D HT + H
DT
----f
H2 --j
(1) (2)
(3)
Experimental Section The CD4-H2 experiments described here were carried
out with the same procedures used for the CH4-D2 mixtures, and the two sets of experiments can be directly compared.2bs8 The only additional information needed for the description of these experiments is that resulting from the isotopic differences in the molecules in the two systems, e.g., the recoil loss calculations are somewhat dependent on the stopping powers assumed for the individual molecules. We have assumed only slight variations between the stopping powers of isotopic molecules: range (in cm a t 1 cm pressure and 20”) for CD4, 16.9 (us. 16.7 for CH4); range for Hz, 55.0 (DS. 55.6 for Dz).8 The use of identical range values for isotopic molecules would result in trivial changes in the calculated values. An additional isotopic correction must be applied to the measured yields of HT, DT, and CD3T associated with the presence of CD3H as an isotopic impurity in the CD4. Measurement of the molecular hydrogen radioactivity from CD4 (containing about 1% CD3H) shows an (HT/DT) ratio of 0.0158 in systems scavenged with 1-3% 0 2 . 0 Correction for this reaction with CDaH is of importance only in the methane-rich samples of the CD4-H2 competitions, amounting to approximately 3% a t most (18.7 X 0.0158 = 0.30; H T from H2 = 11.4 - 0.30 = 11.1). The measured D T yield has been increased by the multiplicative factor 1.012, (1) This research has been supported by Atomic Energy Commission Contracts No. AT-(11-1)-407 and AT-(ll-1)-34, project agreement 126. (2) (a) J. W. Root and F. 8. Rowland, J . Chem. Phys., 38, 2030 (1963); (b) J. W. Root and F. S. Rowland, ibid., 46,4299 (1967). (3) P. Estrup and R. Wolfgang, J . Amer. Chem. Soc., 82, 2661, 2666 (1960). (4) R. Wolfgang, J . Chem. Phys., 39,2983 (i963). (6) R. Wolfgang, Progr. Reaction Kinetics, 3, 97 (1965). (6) D. Seewald and R. Wolfgang, J . Chem. Phys., 47, 143 (1967). (7) E. K. C. Lee, J. W. Root, and F. 9. Rowland, “Chemical Effects of Nuclear Transformations,” Vol. 1, International Atomic Energy Agency, Vienna, 1966, p 66. (8) J. W. Root, Ph.D. Thesis, University of Kansas, Lawrence, Kan., 1964. (9) The (HT/DT) ratio is substantially larger in Izscavenged systems, as shown in ref 8, because of the inability of IZ to suppress completely the thermal reactions of hydrogen atoms. Volume 74, Number 9 January 22, 1970
452
JOHN W. ROOTAND F. S. ROWLAND which allows for both the isotopic impurity and an H/D isotope effect in the abstraction reaction, to obtain the estimated yield for isotopically pure CD4 in the specific yield calculations.
Results The radioactivity data obtained from the series of CDd-Hz binary mixtures are summarized in Table I, together with the gas pressures of the various components of the mixtures. The number of counts actually observed from the counter for each sample has been corrected for the time of irradiation, the volume of tho sample bulb, the pressure of 3He, and the size of the gas aliquots used for assay. The data listed are thus comparative data for equivalent conditions for the production of total tritium and can be directly compared with the CH*--D2 data of ref 2b. After correction for recoil loss, the amounts of radioactivity have been compared with known standards, and the radioactive product yields are listed in Table I in units of per cent total tritium (stopped in the gas phase) for each of the three measured components. The data of Table I are plotted in Figure 1, together with curves which represent the comparable data for the CH4-D2 system.2b Our best estimate of the errors involved is that the total activity of our standard was known to * 5 % . While this represents reasonable accuracy, the hot yields in H2-rich samples approach the 90% level, and the estimate of thermalized tritium (100% minus the sum of hot yields) thus has the rather large error of 10 rf 5% attached to it. The relative accuracy of intersample comparisons is higher and is apparently f2% or less, as judged from the consistency of the observations. Comparisons with the CH4-Dz data should also be accurate to 2% or less. Estimates of the total hot yield from reactions with CD4 include an estimate of the yield of .CDzT radicals from the decomposition of excited CD3T. Evaluation of this number in a bromine-scavenged system shows a factor approaching 0.2 X (CD3T) for the yield of .CD2T, which is close to the value observed for CH4.6 However, we have used 0.1 X (CDZT) in our calculations for consistency with the published data for CH4Dz mixtures. The results are only slightly affected by this difference in assumptions, and any error would essentially be cancelled in the cross comparisons. The per bond specific yield ratio (HT/2Hz)/(CDgT/ 4CD4) varies from 5.5 to 7.5 as the mole fraction composition changes, in contrast to the nearly constant value of 4.3 observed for (DT/SD,)/(CHaT/4CH4). These observations indicate (a) isotope effects in recoil tritium reactions with methane and/or hydrogen, and (b) a difference in the average energy at reaction between CD4 and Hz. The specific yield of CD,T displays a steady increase with decreasing methane content in CD4-H2 mixtures, which is similar to the behavior observed for CH3T in CI&-D2 mixtures. The
*
The Journal of Physical Chemistry
RECOILTRITIUM REACTIONS IN METHANE-HYDROGEN MIXTURES
YIELD
- C H4- D2 (Rsf.2)
50%
Figure 1. Yields of CDaT and H T from recoil tritium reactionR with CDd-Hz mixtures: 0,H T ; 0, CDsT; -, corresponding yields of D T and CH3T from reactions with C H r D z mixtures.
specific yield of HT is approximately constant over the entire range of mole fractions in the CD4-HZ experiments, however. The sum of hot yields from reactions 1 t o 3 is almost identical over the entire range of CD4Hz mole fractions with the corresponding sum of yields from the CH4-D2 system.
Discussion Parameters of the Kinetic Theory of Hot Atom Reao tions. The kinetic theory of hot atom reactions describes the reaction probability for a given reaction between an energetic atom and a particular molecule in terms of two parameters, a and I , the average logarithmic energy loss and the reactivity integral, respecA )a particular reaction tively.2b-6 The ratio ( I A / ~ for can be directly estimated from the total hot yield observed in a system consisting of pure species A. The experimental approximation to this situation is obtained by ignoring the presence of small quantities of 3He and 02,required as hot tritium source and thermal tritium scavenger, respectively. Thus, in the present experiments only CD4 and H2 are considered as components. The hot yields for reactions 1 and 3 are then measured individually for pure CDI and Hz, or, as in the present case, they are determined by extrapolation to the pure system values from the measured yields in binary mixtures. The total yields for CD4 and for Hz are measured using the extrapolation technique as 50 and 92%, respectively. These yield values can be converted into estimates of (IA/CYA) ratios through the use of eq 4.3*4310 The ratios obtained from the present experiments are ( I c D ~ / = ~c 0.70 D~ and ) (IH*/cYHJ = 2.6. These values are quite similar to those found by extrapolation for the CH4-Dz system: (IcH,/~cH~) = 0.76 and ( I D J ~ D = J2.7. PA =
1 - eXp(-IA/aA)
(4) Adjustment of Parameters for the Kinetic Theory. One of the most basic assumptions implicit in any use of the formulation given above for a kinetic theory of recoil tritium reactions is the assumption that an energy
453
loss parameter exists which can accurately describe the fractional energy losses in collisions over a substantial range in kinetic energies of the hot atoms involved.11 If this is approximately true, then the absolute energy loss in a collision is not as significant as the fractional energy loss, and the appropriate energy scale is the logarithmic energy scale used in the definition of the reactivity integral.*r4 If,however, the value of a,the average logarithmic energy loss, does vary appreciably with energy, then the approach followed in the usual kinetic theory treatments has serious 1irnitations.l' Virtually no data exist which would permit calculations of a values at different energies, especially for the energy region pertinent for recoil tritium reactions, or roughly 1-20 eV. Accordingly, one can look upon the kinetic theory of hot reactions as a plausible framework within which to attempt a crude description of hot atom ehemical systems-a description utilizing two empirical parameters to summarize the data. One can attempt first to determine whether values exist for the empirical parameters, a and I, which will accurately reflect the experimental data. If such values exist, one can then search for additional tests of the plausibility and utility of these values. Computer simulation has shown that the parameters have validity for certain reasonable representations of the probable course of hot atom proOne of the most useful tests for such parameters is a determination of their utility for the description of energetic reactions in systems other than those in which the values were estimated. Application of the pure system values to binary mixtures furnishes one critical test; application of data from one binary system to another binary system furnishes another such test. Estimates of total hot yields in mixed systems require assumptions regarding the combination rules for I and a values in mixed systems. The usual assumption for a values is directly adapted from the theory of neutron moderation cy
=
c i
fiffi
(5)
in which the fi terms represent the respective fractions of energetic collisions occurring with the ith species in the mixture. The I t values are also assumed here to follow linear combination rule
I
=
c fJ( i
(6)
Total Hot Yields and specific Yield Ratios. The total hot yields of all products in CD,-H2 mixtures can readily be fitted over the whole mole fraction range by a simple linear combination of values for the pure cdmponents, (10) P. Coulter and F. 8.Rowlrtnd, Radiochim. Acta, 2 , 163 (1964). (11) P.J. Estrup, J . Chem. Phys., 41, 167 (1964). (12) R.M.Felder and M. D. Kostin,ibid., 43,3082 (1965). (13) R.M.Felder, ibid., 46,3185 (1967). Volume 7dVNumber 8 January 9.9,1070
454 and the fit obtained for CDI-H2 closely parallels the corresponding results found for CH4-DZ mixtures. I n the latter case the almost constant ratio of specific yields between CH4 products (HT and CH3T) and the Dz product (DT) permitted the simplifying assumption that the energy ranges of reaction were quite similar for all species, and a good fit was obtained for the individual product yields over the entire mole fraction range.2r4 Any suitable calculation of individual hot yields in the CD4-Hz system requires a satisfactory explanation for the observed variations in the ratios of the specific yields with mole fraction. Although variations in a can easi!y alter the average number of energetic collisions available a t each mole fraction, variation in the ratio of specific yields requires different energy dependences for the hot reaction cross sections for the two components. Study of simple models based upon smooth, continuous energy-dependent cross sections quickly demonstrates that the only choices that can account for the constant specific yield of HT, while also permitting a decrease in the (CD3T/CD4) ratio with increasing mole fraction of CD,, involve modeIs in which recoil tritium reactions with H2 proceed with reasonable probability down to energies substantially below the threshold energy for reactions with CD,. Applications to Other Binary Mixtures. Enough data are now avialable for recoil tritium systems involving binary mixtures of Ar with CHrCD,-H2-D2 that the relative magnitudes of the parameters of the kinetic theory of hot reactions have been fixed within fairly narrow limits for the pure compounds. Conibinations of these parameters can produce information that should be applicable to other binary mixtures.5 As an example, the formation of CHIT from CH4 is favored by a factor of 1.31 f 0.04 over the formation of CD3T from CD4 in direct competition experiments involving CHsCD4 mixtures.' Small differences in the energy ranges of hot reaction can be anticipated for CHI and CD,, based upon the observation that the specific yield ratio (CHgT/CH,)/(CD,T/CDJ rises to a value of about 7 when the tritium atoms are introduced into the system a t 2.8 eV through TBr photoly~is.'~ On the other hand, the total yields for substitution reactions are very small at 2.8 eV, and the contribution of these reactions to the total hot yield is presumably almost negligible. Unpublished experiments by Chou have shown that nuclear recoil tritium reacts in both neon- and argon-moderated CHrCD4 mixtures to give specific yield ratios in the range of 1.32 f 0.03. This agreement between moderated and unmoderated values for the nuclear recoil systems implies the absence of any appreciable difference in the average energy at reaction for the two isotopic methanes. Similar conclusions have been reached from comparisons of competitions with cyclobutane'6 and with helium16 for the isotopic pair CH3F-CD3F. Based on the specific yield ratio 1.31 f 0.04 8s 8 The Journal of Physical Chemistry
JOHN W. ROOTAND F. S. ROWLAND good approximation for the ( I C H J I C Dratio, ~ ) together C H ~(ICD~/CYCD,) ) ratios obwith values of the ( I C H ~ / C Yand tained from experiments with the pure molecules, the relative a values of the isotopic methanes can be estimated as
(0.70)(1.31 f 0.04) (0.76)
= 1.21 52 0.05 ( 7 )
This calculation shows that energetic tritium atoms lose more energy on the average in collisions with CH4than in collisions with CD4. Furthermore, the calculated (LYCHJLY'CD~) ratio is in good agreement with the earlier estimate of ( C Y C H ~ F / ~ C D ~ = F ) 1.23 f 0.O8.l6 I n both cases collisions with the protiated species remove more energy on the average than collisions with the deuterated species. This effect is qualitatively in the opposite sense from that anticipated for a quasi-elastic collision model. The latter model is based upon momentum conservation in atom-atom ~ollisions'~ and suggests larger energy transfer between the colliding atoms which are more nearly matching in mass.I8 The rather similar total absolute yields of hot products formed in pure CHI and pure CD, are thus not inconsistent with the rather large reactive isotope effect between these two molecules, because the greater reactivity in CH4 is essentially cancelled by the greater collisional energy loss in CH4, so that fewer collisions are available in the protiated medium. The I and a parameters have been measured for H2 and Dz and have been shown to be quite similar in magnitude-not only are the ( I / a ) ratios about equal (compare our values of 2.7 and 2.6), but the ( I H ~ / I D J ratio has been estimated as 1.15 f 0.04 in argonmoderated direct competition experiments. l9 These data can be combined to show that the average energy losses in Hz and D2must be rather similar, but not very accurately known: ( C X H J C X D J = 1.1 f 0.1. Such calculations with Hz and D2 are particularly subject to large errors because of the very high total hot yields, and the inherent inaccuracy in estimates based upon differences between hot yields of 100 and 90-95%. Despite the experimentally measured near-equality of IHZand ID,,the specific yield ratio (HT/Hz)/(DT/D2) (14) C. C. Chou, Ph.D. Thesis, University of California, Imine, Calif., 1968. (15) E. K.C. Lee and F. S. Rowland, J. Amer. Chem. SOC.,85, 2907 (1963). (16) E.K.C.Lee, G. Miller, and F. 8. Rowland, ibid., 87, 190 (1965). See also T. Smail and F. S. Rowland, J . Phys. Chem., 74,456 (1970). (17) H. Jurgeleit and R. Wolfgang, J. Amer. Chem. SOC.,85, 1057 (1963). (18) The maximum collisional energy transfer between an energetio recoil atom of mass 3 and a free atom of mass 2 is 96%; between the mass 3 species and a free atom of mass 1is 75%. (19) D. Seewald, M. Gersh, and R. Wolfgang, J. Cham. Phys., 45, 3870 (1966).
RECOILTRITIUM REACTIONS IN METHANE-HYDROGEN MIXTURES has a value of about 1.5 in unmoderated mixtures of H2 and D2.10-21The reduced value of this ratio in moderated systems implies, by application of the kinetic theory of hot atom reactions, that the reaction with DZ must occur at a lower average energy than the reaction with Hz. This implication is consistent both with the results of trajectory calculations for the T H2 and T D2 systems22 and with the specific yield ratios (about 1.0) found for photochemically produced 2.8-eV tritium atom reactions in H2-Dz mixtures.23 A qualitative inconsistency can now be seen in the respective requirements that (a) the energy ranges of hot reactions for CHI and CD4 are approximately the same; (b) the ranges for CHI and D2 are about the same; (c) H2 reacts extensively a t energies below the CDq threshold; and (d) D2 reacts a t a lower average energy than H2. We have attempted a variety of simple model calculations for possible choices of reaction energy ranges, with the result that this qualitative inconsistency has been found to persist quite strongly. We have not been able to obtain even an approximately satisfactory set of reactivity integrals capable of reproducing the qualitative features of the experimental observations for all of the various binary pairs. While we do not wish to rule out entirely the possibility that a satisfactory fit might be based on the kinetic theory of hot atom reactions as applied to binary mixtures, we do feel that no fit will be possible involving rather broad, structureless reactivity integrals. The use of detailed hypothetical “fine structure” models seems inappropriate in connection with a theory which has been intended to provide only broad average outlines of reaction excitation functions. The present failure to obtain a mutually consistent set of reactivity integrals for this group of four molecules does not necesP:,rily eliminate the usefulness of this
+
+
455
kind of model for the description of other binary systems. The very high total reactivities, low masses, etc., of the molecular hydrogen species make them rather atypical molecules, so that deviations from simple kinetic theory behavior are perhaps more to be expected in their mixtures with alkanes than, for example, in mixtures of different alkanes with one another. It seems quite plausible to us that the assumption of an energy-independent a for each of the molecules in a closed cycle of binary systems js a t best only a rough approximation. Other similarities between the species to be compared may be required in order for the hot atom kinetic theory to be useful for simple descriptions of such binary systems. Such similarities could occur, for example, in the reaction energy ranges, such as might be expected for C-H bonds in species A vs. C-H bonds in species B, or in the nature of the energy loss processes involved, as may be true for CHI and CDI despite the 20% greater average energy loss in CH4. The present comparison involving CD4 and H2probably fails to mesh with earlier data simply because the nature of both reactive and nonreactive collisions with CD4 and H2 are too unlike to permit satisfactory averaging of the kind required. The failure in the CD4-H2 system furthermore makes us quite skeptical of the excellent fit found in our CHd-D2 mixtures2-the near constant ratio of specific yields may well involve some fortuitous “cancellations” of effects involving quite different energy ranges for reaction for CH4 and
D2. (20) J. K. Lee, B. Musgrave, and F. S. Rowland, J . Chem. Phys., 32, 1266 (1960). (21) J. W.Root and F. 8.Rowland, unpublished data. (22) M. Karplus, R. Porter, and R. Sharma, J. Chem. Phys., 45,3871 (1966). (23) C. C. Chou and F.5.Rowland, Jbt‘d., 46,812 (1967).
Volume 74, Number 2 January 22,1070
