The Journal of Physical Chemistry, Vol. 83, No. 8, 1979
Reaction of H Atoms with Halogens
1007
(19) J. D. McDonald, P. R. LeBreton, Y. T. Lee, and D. R. Herschbach, J . Chem. Phys., 56, 769 (1972). (20) J. Grosser and H. Haberland, Chem. Phys., 2, 342 (1973). (21) R. A. Meinzer, United Technologies Research Center, prlvate communication. (22) J. P. Sung and D. W. Setser, J . Chem. Phys., 69, 3868 (1968). (23) R. N. Sileo and T. A. Cool, J. Chem. Phys., 65, 117 (1976). (24) J. M. Herbelin and G. Emanuel, J . Chem. Phys., 60, 689 (1974). (25) K. K. Cashion, J. Chem. Phys., 89, 1872 (1961); 41, 3988 (1964). (26) R. Herman, R. W. Rothery, and R. J. Rubin, J . Mol. Spectrosc., 2, 309 (1958); 9, 170 (1962). (27) D. Bogan and D. W. Setser, ACS Symp. Ser., No. 66 (1978).
Ber. Bunsenges. Phys. Chem., 80, 902 (1976). (14) R. G. Albright, P. F. Dodonov, G. K. Lavrovskaya, I. I. Mavosov, and V. L. Tal'roze, J. Chem. Phys., 50, 3632 (1969). (15) (a) J. C. Polanyi and K. B. Woodall, J. Chem. Phys., 57, 1573 (1972); (b) D.S.Perry and J. C. Polanyi, Chem. Phys., 12, 469 (1976); (c) M. J. Berry, J. Chem. Phys., 59, 6229 (1973). (16) D. E. Mann, B. A. Thrush, R. D. Lide, J. J. Ball, and N. Acquista, J . Chem. Phys:., 34, 429 (1966). (17) D.H. Rank, D. P. Eastman, B. S. Rao, and T. A. Wiggins, J . Opt. SOC.Am., !52, 1 (1962). (18) D. J. Bogan, J. P. Sung, and D. W. Setser, J. Phys. Chem., 60, 888 (1977).
Comparison of Rate Constants for Reactions of Hydrogen Atoms with Chlorine, Fluorine, Iodine Chloride, and Chlorine Fluoride J. P. Sung, R. J. Malins, and D. W. Setser" Chemistry Department, Kansas State University, Manhattan, Kansas 66506 (Received September 13, 1978) Publication costs assisted by the National Science Foundation
The infrared emission intensities from the HCl and HF products have been used to assign relative rate constants for the reaction of H atoms with Clz, Fz, ClF, and IC1. The experiments were done in a fast flow apparatus utilizing -1 torr of Ar carrier gas. The vibrational distributions obtained from analysis of the chemiluminescence recorded with a Fourier transform spectrometer at the first window of the flow reactor were very close to the initial distributions produced by the chemical reaction. Except for a small residue of population in the high J levels of HC1 from the H + IC1 reaction, the rotational populations had relaxed to a room temperature Boltzmann distribution. The relative rate constants for HC1 formation from the Fz, Clz, ClF, and IC1 series are 0.053:1.00:1.99:2.42. Since the absolute rate constant is well known for Clz, these data, plus the vibrational-rotational distributions of product states, give absolute rate constants for formation of individual product quantum states. Summation of the HC1 and HF relative intensities from H + C1F gave a macroscopic branching ratio of 5.2 favoring the HCl channel. For the H + IC1 reaction, the HI/HC1 ratio is [XX’]. For constant [HI the relative values of hPS are and delivered the majority of the Ar carrier gas. The equal to the relative values of hg. The earlier work3 should physical arrangement of the reaction vessel and inlet be consulted for justification of use of the differential rate plumbing is shown in Figure 1. A Roots-type blower plus law, rather than the integrated rate law for interpreting mechanical pump provided flow velocities of -90 m s-l. the emission intensity a t the first window for these exThe total flow of Ar is -7 mmol s-l. Fifteen percent of periments. Since the emission intensity is proportional the Ar flow was mixed with H 2 and passed through the to [HX], relative values for hPS were obtained by plotting discharge; the remainder was added via the bypass the total relative HX concentration (obtained from the mentioned above. Normal operating pressure was 0.7 torr. intensity) vs. the flow (or concentration) of the XX’ reagent The halogen reagents were diluted with argon and stored (see Figure 2). Since all of the experiments were run at pressures of -600 torr in 12-L storage reservoirs (typical pairwise against Clz without changing reaction conditions, Ar:halogen ratios were 1OO:l). The reservoirs were Pyrex the ratio of the slopes of these plots, Lyxx’, is the same as glass for IC1 and C12 and stainless steel for F2 and C1F. the ratio of the bimolecular rate constants. Stainless steel lead lines also were used for C1F and F2. aXX’/aC12 = kpsXxAt/hpsC’2At = Typical flows from the reagent reservoirs were 0.1-5.0 pmol s-l; which corresponds to 0.3-15 X 10l2 molecule ~ m - ~ . (hBXX’/kgC1z)(H] / [H])(At/At) = kgxx‘/hgC1z (2) Assuming 50% dissociation, the [HI was -2 X lo1* The linearity of the plot is a confirmation of the pseumolecule ~ m - All ~ , experiments were run pairwise with Clz, do-first-order conditions. As should be clear from this the reactor pressure, hydrogen flow, etc. remaining exactly discussion, the method requires the full determination of the same for the reagent and for Clz, The C1F was taken the intensity plots of C12 for each XX’ reagent. from a tank purchased from Ozark Mahoning Co. The Because of the high resolution of the Fourier transform tests for purity were described in the previous paper. The technique and the Boltzmann rotational distribution, it Clz was used directly from a Matheson tank. The IC1 was was not necessary to sum the entire HX spectrum in order purchased from PCR, Inc. It was purified by multiple to obtain the total emission intensity. The relative vifreeze/thaw/pump cycles followed by 5 min of pumping bration populations were determined by first choosing a t 0 “ C ; the vapor was admitted to the reservoir after this several appropriate rotational lines (appropriate in the treatment while the temperature of the sample was still sense that they were not obscured by COz or H20 abbelow room temperature. The F2 was obtained from sorption) of each u level and measuring their height. The Matheson as a 10% mixture in Ar; the sample was metered heights were converted to total populations for that u level directly from the tank. by dividing by the product of the Einstein coefficient, the The infrared chemiluminescence was observed with a response function, and the Boltzmann fraction for that J Digilab FTS-20 Fourier transform spectrometer. The state. The rotational lines belonging to the same u level detection system and the method used to convert rotawere averaged to give the final result. The relative vitional line intensities to relative populations were as brational populations were then scaled to relative total HC1 described in the preceding paper. The individual rota-
The Journal of Physical Chemistry, Vol. 83, No. 8, 1979
Reaction of H Atoms with Halogens
fashion are listed in Table I. The rate constants divided by the mean thermal velocity also are listed in Table I; these values are roughly equivalent to the thermal reactive cross sections. The HC1 formation rate constant values for ClF and IC1 are based upon three and two experiments, respectively. The experiments agreed to f1070. The H + Fz rate constant is only based upon one experiment. Since the largest single source of error is the composition of the gas mixture and since we were using a commercially prepared mixture, further experiments were not considered very useful. The entry for IC1 is for HC1 formation only; our attempts to observe HI, which are described below, were unsuccessful. The steady-state vibrational distributions observed from the rate constant experiments are listed in Table 11, along with some arrested relaxation distributions reported in the literature. These reactions do not give any u = 0 and scaling of the rate constant data to account for HCl(u = 0) formation is not necessary. The macroscopic branching ratios of reactions 111, h H C l / k H F , and IV, ~ H I / ~ H C are I , of considerable interest. The ratio for reaction I11 is easily obtained from direct analysis of the intensities of HC1 and HF, which gives C,N,(HCl)/C,N,(HF). Based upon analysis of two spectra, this ratio was 5.2 f 0.5. Care was taken to include both the H35Cland H37Clemission in computation of this ratio. This result is higher than the ratio (4.8) measured in the arrested relaxation experiment^.^ The difference may be due partly to the secondary F t H2reaction (which is 1.4 times faster than H Clz) which contributes HF(u = 1-3). One experiment was conducted a t higher hydrogen flow and it gave a lower branching fraction (4.0) and slightly higher populations in u = 1-3. However, the total relative rate constant for H C1F was equal, within the experimental error, to that listed in Table I. The branching fraction found here probably is more reliable than from the cold wall experiment because the rotational distributions are less extended and because correction for the F + H2 reaction was unnecessary. For the H + IC1 reaction, we can only estimate a lower limit to the branching ratio because HI emission was not observed. The thermochemistry of reaction IVb and the typical energy disposal for H + X2type reactions indicates that u = 1 and u = 2 states of HI should be formed. A thorough search of both the overtone and fundamental spectral regions of HI showed no indication of HI emission, even when the entire system (interferometer, fore optics, and space between interferometer and flow tube) was purged with dry N2to eliminate C 0 2 and H 2 0 absorption. An upper limit to the branching ratio was estimated from
+
I
+ -2.0 1.6
24
p mol e si sec
Figure 2. Rate constant plots for H atom reactions. For convenience of presentation the CIF, ICI, and F2 results have been normalized to the same CI, experiment. Only one experiment each for CIF, F, and IC1 are presented. A flow of 1.0 p m l s-' corresponds to a concentration of 3.2 x 10'~ molecules ~ m - ~ .
TABLE I: Relative RaateConstants compd _
_
_
~
c1z
rate constanta I
_
cross sectionb
_
1.00 0.052 1.98 2.42
1.00 0.053 1.99 2.40
F2 CIFC ICld
1009
a The absolute value of the H t C1, rate constant at room temperature is 2.06 X lo-" cm3 molecule-'s-'; Defined as k/(v). This average value from ref 5 and 6. entry is for the sum of ~H,-J and k H F of reaction 111. The ratio of k & k H F observed in this work was 5.2. The entry is for the HC1 channel; attempts t o observe HI were unsuccessful (see text).
+
+
populations by the intensity ratios of the lines. For the IC1 reaction, which gives significant amount of HC1 rotational excitation, emission from the high J levels still was observed even a t 1 torr, and these intensities were individually converted to relative populations and added to the Boltzmann envelope to obtain the total vibrational population. This method directly involves the Einstein coefficient and no further corrections for radiative lifetimes are necessary. The plots of relative product concentration vs. reagent flow are shown in Figure 2. For convenience of presentation the ClF, IC1, and F2results have been normalized to the same C12 experiment. However, as we have emphasized above, all experiments were done pairwise. The relative values of the rate constants obtained in the above TABLE 11: Comparison of Vibrational Distributionsa this workb
__
other studies
U =
reaction
H t C1,
1
U =
2
3
4
5
6
7
0 , 1 2 0.38 0.40 0.10
H H
+
H
+ ICI(HC1)"
F,
+ ClF(HC1) [HF)
0.02 0.05 0.08 0.16 0.33 0.39 0.04 0.08 0.13 0.09 0.11 0.15
0.17 0.27 0.29 0.15 0.12 0.25 0.31 0.19 0.20 0.20 0.17 0.08
0 0.00 0.00 0.00 0.00 0.00 0.00
1
2
0.42 0.44 0.03 0.35 0.10 0.06 0.12 0.11 0.12 0.02 0.17 0.04
3
4
0.45 0.40 0.05 0.38 0.14 0.15
0.01 0.04
Ea
6
4
8
ref
1 11,12 0.10 0.20 0.31 0.16 0.13 1 3 0.10 1 0.19 0.28 0.22 0.03 1C 0.15 0.18 0.19 0.14 2
The entries in this table all are considered t o be inztzal distributions, Le., the entries a r r relative values of k , . The populations from this work and ref 1 were obtained using the same transition probabilities t o relate intensities to populations. Slightly different probabilities were used by ref 2, 13, and 11 and exact agreement would not be expected on this basis. For each reaction the contribution t o u = 0 is taken t o be zero. Thz distribution listed here is the one that has been corrected for seco: dary reaction, see Table I of ref 1. d This distrrbuticitJwas obfained a t the lowest flow which corresponds t o [IC11 = 9.3 X 10l1molecules cm At [ICl] of 1.5 x 10l2 and 2.1 X 10" molecules cm the distributions observed were 0.10/0.13/0.17/0.19/0.20/0.15/0.07 and O . l O / O . l ~ l O . 1 8 / 0 . l 9 / 01 4 0 6 , respectively. Extrapolation of the data t o zero pressure gives a distribution [ 0.9/0.10/0.14/O.19/0.21/0.3 SjO.09: i S T \ n experimental error of that entered above. a
a
1010
The Journal of Physical Chemistry, Vol. 83, No. 8, 1979
the signal-to-noise ratio a t the frequency of the adjacent, but not overlapping, HCl(u = 6)P5 and HI(u = l)R3 lines. The HCl(u = 6)P5 line was 30 times the noise level; this number was taken as an upper bound to the ratio of the HC1 and HI lines, If the ratio of Einstein coefficients of l~ the HCl(u = 6)P5/HI(w = l ) R a lines is a p p r o ~ i r n a t e das 130:1, the upper limit to the HCl(u = 6)P5and HI(u = l)Rs line intensity ratio gives relative vibrational populations of HCl(u = 6) and HI(u = 1)as 12. If HI(u = l):HI(u = 2) is 1.0:0.5, the limit for kHIis 50.5hHc~.The surprisingly high value for the limit arises because of the large difference in the Einstein coefficients. Since approach to the I end of the molecules should be favored, even this limit implies that a large fraction of the H-I-Cl encounters must migrate to C1 rather than give H I product. This is consistent with the microscopic branching ratio2 for reaction IVa since the high J component is fourfold larger than the low J component. Our limit also is consistent with the most recent molecular beam studylj which concluded that h H ~ l >hHI for reaction IV. Haberland and Grosser15did observe H I so reaction IVb may make a significant contribution to the total rate constant. An earlier beam study16 a t higher collision energies observed only HI product. In addition to the usual experimental difficulties, the microscopic branching ratio of reaction IV is energy dependent with migration being less important at higher energy,17and this may explain why McDonald et al. did not observe HC1. We, as well as Polanyi and Skrlac, explicitly searched for I(2P,jz-2P3jz) emission and none was observed. We can say with confidence that that formation of I(2Plp)has no importance for reaction IVa. B. Vibrational Distributions. The vibrational distributions listed in Table I1 for the H Clz, H Fz,and H + C1F reactions appear to be as good as the literature values from cold-wall arrested relaxation studies. Therefore, the relative distributions are the relative rate constants, h, (C,k, = hB), for product formation. For these three reactions the distributions did not vary more than -5% for the flow rates of Cl,, Fz, or C1F used to obtain the rate constant data. The distribution in the low u levels from H C1F actually appears better than the distribution from arrested relaxation,l because the populations of Table I1 decline smoothly with declining u. The HC1 distribution from H Cl, has been determined many times because it is the reference for comparison with other H atom reactions. The HC1 distribution from H + C12is always very reproducible and independent o f H2 and Clz flow, providing that the experiments are done in the low concen~ . H F distributions from tration regime, 5 3 x 10l2~ m - The H Fz and H C1F extend to high L' levels which have more rapid relaxation rates. However, even these levels show little, if any, relaxation. The arrested r e l a ~ a t i o n ' ~ and fast flow distributions from H + Fz agree well, except for u = 8. The fast flow distribution, which was invariant over the eightfold concentration range shown in Figure 1, has only a trace population in u = 8. Actually the signal-to-noise ratio in the fully resolved H F overtone spectra was very good and the intensity from u = 7 was an order of magnitude stronger than from u = 8. Since a specific relaxation mechanism for just HF(u = 8) is not expected and since the u = 1-7 levels showed no relaxation, we favor the results of the fast flow experiment. For these three reactions, molecular hydrogen appears to be the most serious source of relaxation and particular attention must be given to reducing [H2] as much as is feasible. Even in arrested relaxation studies,2 vibrational relaxation of HC1 by IC1 was a problem. We also found that
+
+
+
+
+
+
J. P. Sung, R. J. Malins, and D. W. Setser I
I
I
I
31'00
I I
a
I
I
1
I
30m
'
I
2900
I
I
i1
I
Flgure 3. A portion of a typical HCI emission spectrum from the reaction H 4- IC1 showing the presence of high J ( J > 20) emission. Note that the very high J lines (e.g., J > 27 for v = 1) lie at lower frequency than the "turning point" line ( J = 27 for v = 1).
TABLE 111: High" HC1 Rotational Energy Component from H t IC1 V
this work
ref 2
1 2
0.04 0.03 0.03 0.01
0.03 0.08 0.09 0.10
3 4
a High is defined here t o be J > 20. The numbers given are I;J > 2,J / I; ?I: Jp,J.
relaxation was observed for higher flows of 1C1. The entry in Table I1 is for the lowest IC1 concentration; the distributions for higher IC1 concentrations are given in footnotes. We conclude that the fast flow reactor can provide initial HC1 and H F vibrational distribution but that caution always must be exercised because vibrational relaxation may be exceptionally fast for some reagents. The H F and HCl rotational distributions observed in the flow reactor for F2 and C12 reactions were 300 K Boltzmann even a t the lowest pressure and lowest reagent flows. The initial distributions for both reactionsl~l1~l2 occupy rather low rotational levels ( J = 1-10), Since the relaxation of low J levels is fast a t 1 torr of Ar, these distributions relax to a Boltzmann distribution prior to our observation (-0.2 ms). The H F rotational distribution from H C1F was nearly Boltzmann; however, there were trace amounts ( 20) of the HC1 distribution from IC1 was clearly evident for the lower vibrational levels. These very high levels are present even though the intermediate energy rotational levels are absent. A sample spectrum from H + IC1 is plotted in Figure 3 to illustrate this effect. The presence of high J levels, even though the intermediate J levels are absent, can be explained by the dependence of the exponential gap rotational transition probabilities4 upon energy, The larger energy spacing between the high J states causes slower relaxation than for the intermediate J levels. The fraction of the high J component present
+
Reaction of H Atoms with Halogens
The Journal of Physical Chemistry, VoI 83, IVQ 8, I379
TABLE IV: Summary of H t XX’ Rate Constants and Branching Ratios
X’/X F C1
F 0.053 5.2
c1
Br
1.99 1.00
I 2.40b
Br
-2.ijC
-1.0d
I
Cl, > Fz. One might have expected the rate constant for reaction IV to be even larger. studies15 have shown that the cross sections increase by a factor -2 from el2to Iz and that the preferred scattering angle has been interpreted as an increase in the range of acceptable attack angles defined with respect to the molecular axis.15316r’21These data, as well as the branching ratios for C1F and BrC1, indicate that the preferred approach of the H atom to interhalogen molecules is to the end of the molecule with the heavier halogen atom. If the migratory channel is assumed to be enhanced by the difference in size of the two atoms, the extreme change in the branching ratios as one halogen becomes heavier can be explained. For the interhalogen molecules, the hydrogen atom initially reacts with the end of lower electron density, but larger size and greater polarizability, This differs from the electrophillic nature usually attributed to H atoms. An indication of the degree of charge separation in C1F is provided by the dipole moment, which is 0.85 The C1F and IC1 reactions give double maxima in the rotational distributions of the more exoergic channels with a significant peak in the population at high J values. T i i s high rotational energy disposal is generally interpreted as migration of the €1 atom from the atom initially attacked to the more electronegative halogen with the more exoergic energy release. The angular momentum of this “swing around” process is deposited as rotation of the hydrogen halide product. From an intuitive point of view, one expects these migratory collisions to correlate with h g e impact parameter collisions. The cross sections for reactions I11 and IV are larger than for W + C1, and provide mild support for this line of reasoning. The large impacr, parameter collisions presumably also correlate with loss of the collinear reaction pathway in the approach to the less electronegative, heavier halogen atoms. According to the model just discussed, the relative energy barriers determine which end of the interhalogern molecule the H atom initialljj attacks. This plus the degree of migration fixes the macroscopic branching ratio. This general view is strongly supported by molecular beam studies’l which show that the ratio of direct to migratory contributions to reaction IVa increases with increasing collision energy. This approach can be compared to the information theory prediction^^^-^^ based upon evaluation of entropy deficiencies of the reaction channels. Polanyi and Skrlac have applied some special case information theory equations to reaction V and discussed the branching H + BrCl HBr + C1 AHoo= -29.2 kea1 (Val HC1 Br AHoo = -50.7 kcal mol (Vbi ratio. We wish to discuss the branching ratio of reaction I11 in terms of the information theory approach. The information theory approach to the branching ratio begins by partitioning the entropy equation into “single channel” entropies and a “mixing” entropy. In eq 3, P,
-
-
AStot =
+
CP, In (P,/P,O) + CP,AS, Y
(31
Y
is the total probability of forming chemical species y in any state of that species; the first summation is the mixing entropy. The term AS., is the entropy of the y species molecules arising from the specific distribution among the states of y molecules, irrespective of any other species, Thus, if P, is the probability of any product state being formed, the usual entropy formulaz3 A S = C P , In (P,/P,O) (4) I
1012
J. P. Sung, R. J. Malins, and D. W. Setser
The Journal of Physical Chemistry, Vol. 83, No. 8, 1979
TABLE V: Entropy Deficiencies and Branching Ratio'
terbranch constraints. An interbranch constraint is an observable which depends upon a knowledge of all product species distributions (or conversely on the reactant distribution). The presence of such a constraint implies that the various reaction channels do not have access to equal volumes of reactant phase space. The simplest example of such a constraint is two exit channels with different barrier heights, i.e., different activation energies. Following the approach of Levine and Kosloff, we will identify an intrabranch constraint ( G ) defined by
I "
HF channel
HCl channel
1.32
0.39 1.44 1.05
AS,, eu ASuJ, eu A ~ ( J / U )eu ,~ nSHCl
-
2.17 0.85 -0.73 0.57'
ASHF
HCliHF r t HCliHF heory b r'o
0.83" 4.8' 0.17
E&/H F rtheory/rexpt
and Tg+Cl are 0.50, b This 0.31, 2.5, respectively, for H t BrCl; see ref value calculated with eq 8 b ; see text for results for eq l o b . The rotational contribution to the entropy deficiency is a The ratios
rYHBy,HC1,
.
A S ( J / U ) = A S u j - AS,.
( G ) = CPiGi = CPy(,Cpi'Gi) = CP,(G), I
P, = CPi i=l,
i = l,, 1,
P,Y = P,/P,
+ 1, ..., p,
AS, = CP,, In (P,'/P,O,)
(5b) (5c)
1
With this notation the branching ratio between chemical species y = a and y = b is rabas defined in eq 6. The rab
=
(6)
pa/pb
values of Paand P b to be used in eq 6 are those obtained by maximizing eq 3 with respect to the P, under whatever constraints are appropriate. The usual technique for evaluating the P, from eq 3 is to assume that there are no "interbranch" constraints and only intrabranch constraints. That is to say, the only observables which form constraints are those which belong independently to the individual sets of P,Y. For example, the average vibrational energy of the y species molecules is an intrabranch constraint because it is evaluated through knowledge of the P,' alone and does not require knowledge of the distributions in the other exit channels. Such intrabranch constraints are absorbed in the term AS,. The only constraint applied to eq 3 through the P,'s is that of normalization, eq 7. If eq 3 is maximized under the sole 1=
CP,
(7)
Y
constraint of eq 7, one obtains eq 8a and 8b for P, and r a b .
P, = PO , exp(-l rab
- Xo -
AS,/&)
= (p2/pbo)exp(-(AS, - A s b ) / R )
(84 (8b)
An important point is that the lack of interbranch constraints implies that any molecule which can react to form species a also has a nonzero probability of forming species b. Polanyi and Skrlac have compared their experimental measurements with the branching fraction for reaction V predicted by eq 8b. They found a large disagreement between the measurements and the information theory predictions. We also evaluated eq 8b using our H + C1F data and found large disparity between the calculated and experimental branching ratio (see Table V). The failure of eq 8b to match experimental data prompted us to reconsider eq 3 in light of possible in-
1=L
Y
(9)
and substitute this definition into eq 3 as a constraint; we obtain eq 10a and lob. Equation 10b is merely eq 8b
P, = PO , exp[-1 can be converted to eq 3 by including the definitions shown in eq 5 where states i = l,, 1, + 1, ...>p, belong to species Ye
7
- Xo -
(AS,/&) - h,(G),] (loa)
=
(P2/Pbo)exP(-[ASa
-
Asbl/R) exp(-XJ(G), - (G)bl) (lob)
multiplied by the additional constraint. If one uses the average energy of reacting molecules in each channel for (G), and (G)b, the additional constraint introduces the difference in the average energy of the reacting molecules in the two channels, which is the same as the difference in Tolman activation energies. Unfortunately, the difference in activation energies is not known. However, we can estimate the effect in eq 10b by letting E,(HF) E,(HCl) = 1.0 kcal mol-l and assuming XI to be nearly unity. Using these values and those in Table V for the other terms, we obtain r H C 1 HF = 4.7 as compared to our experimental value of 5.2. (Using the same correction to Polany's data for H + BrCl gives rH&/HC1 = 1.7 from eq lob; the experimental value was 2.5.) Clearly, this last estimation using eq 10b does not prove its applicability. It does however indicate the source of the failure of eq 8b and directs attention to the importance of interbranch constraints. As noted by Levine, any effect which limits the volume of reactant phase space which can access each product channel will easily outweigh the effect of the entropy deficiencies of the individual product channels. An important practical point to note for branching ratios is that the simple result, eq 8b, is only applicable if the barrier heights of the competing channels are equal. This is rarely ever true. Summary The rate constants for H atom reactions with the interhalogens C1F and IC1 are larger than for reaction with Clz by factors of 2.0 and 2.4. In both cases the HC1 channel is favored but for different reasons. With C1F the HC1 channel is favored because the activation barrier is lower than for the H F channel; the difference seems to be similar to the activation energy difference for H + C1, and F2. With IC1 the HC1 channel is favored because of the microscopic branching from collisions for which H initially approached the I end of the molecule but later migrated to C1 with ultimate formation of HC1. Although the reaction cross section for IC1 and C1F are somewhat larger than for C12 and much larger than for F2,the greater range of impact parameters is only partly responsible for the larger (fR(HCl))cwand (fR(HC1))Icl relative to the Clz and F2 reactions, Certainly for the latter, the migratory mechanism is the much more important aspect of the dynamics. It seems more likely that it is the reduction in importance of collinear geometry for increasingly heavy
Intermolecular Energy Transfer following Chemical Activation
halogens that is resplonsible for the enhancement of the migratory microscopic branching and rotational energy disposal. In general the H 1- X2 class of reactions do not have linear vibrational surprisal plots;29this implies that dynamical (in this case Linear momentum) constraints limit the vibrational energ:y disposal. An interesting aspect of the HF channel from C1F is that the vibrational surprisal is much more nearly linear than for Clz or F,. This is a consequence of fortuituous combination of the two microscopic distributions. This contrasts t o other example^^*^^^ for which two linear segments of a surprisal plot were used to identify two mechanisms giving the same product.
Acknowledgment. This work was supported by the National Science Foundation Grant 77-21380. We thank Dr. K. Tamagake for discussion and for permission to use the H F and HC1 transition probabilities given in the preceding paper. References and Notes (1) K. Tamagake and D. W. Setser, J. fhys. Chem., preceding paper in this issue.
(2) (a) J. C. Poianyi and W. J. Skrlac, Chem. fhys., 23, 167 (1977); (b) M. A. Nazar, J. C. Polanyi, and W. J. Skrlac, Chem. fhys. Lett.,
29, 473 (1974). (3) D. J. Smith, D. W. Seber, K. C. Kim, and D. ,I. Bogan, J. Phys. Chem., 81, 898 (1977). (4) J. P. Sung and D. W. Setser, J . Chem. fhys., 69, 3868 (1978). (5) P. P. Bemand and M. A. A. Clyne, J . Chem. Soc., Faraday Trans. 2. 73. 394 (19771. (6) H.'G. Wagne;., U. Welzbacher, and R. Zellner, Ber. Bunsengers. Phys. Chem., 80, 902 (1976). (7) P. F. Ambridge, J. N. Bradley, and D. A. Whytock, J . Chem. SOC.,
The Journal of Physical Chemistry, Vol. 83, No. 8, 1979
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Faraday Trans. I , 72, 1157 (1976). R. G. AIBright, A. F. Dodonov, G. K. Lavrovskaya, I.I. Morosov, and V. L. Talroz, J . Chem. Phys., 50, 3632 (1969). J. B. Levy and B. S. W. Copeland, J . fhys. Chem., 72, 3168 (1968). K. H. Homann, H. Schweinfurt, and J. Warnatz, Ber. Bunsenges. Phys. Chem., 81, 724 (1977). K. G. Anlauf, D. S. Horne, R. G. MacDonald, J. C. Polanyi, and C. B. Woodhall, J . Chem. fhys., 57, 1561 (1972). A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi, and J. L. Schreiber, Faraday Discuss., Chem. SOC.,55, 252 (1975). (a) J. C. Polanyi and J. J. Sloan, J . Chem. fhys., 57, 4988 (1972). (b) See also J. C. Polanyi, J. J. Sloan, and J. Wanner, Chem. Phys., 13, 1 (1976). Absorption measurements in our laboratory gave absorption cross sections for the lP, lines of HCI and HI of 1.6 X lo-'' and 6.3 X lo-'' cm'/molecule, respectively. This yields a ratio of Einstein emission coefficients for these HCI:HI lines of 43:l. Since the Einstein coefficients of HCI for v = 6 are about twice that of v = 1 and since the rovibratlonal interaction term (P5:R3)gives an additlonal factor of 1.5, we have approximated the ratio of Einsteins coefficients for the lines noted in the text to be 13O:l. J. Grosser and H. Haverland, Chem. fhys., 2, 352 (1973). J. D. McDonald, P. R. LeBreton, Y. T. Lee, and D. R. Herschbach, J . Chem. Phys., 56, 789 (1972). J. W. Htidgens and J. D. McDonaki, J. Chem. Phys., 67,3401 (1977). B. A. Thrush, Prog. React. Kinet., 3, 88 (1965). R. A. Fass, J. fhys. Chem., 74, 84 (1970). R. J. Maiins and D. W. Setser, J . Chem. fhys., to be submitted. R. N. Porter, D. C. Thompson, L. M. Raff, and J. M. White, J . Chem. Phys., 62, 2429 (1975). B. Fabricant and J. S. Muenter, J. Chem. fhys., 66, 5274 (1977). R. B. Bernstein and R. D. Levine, Adv. At. Mol. Phys., 11 (1975). R. D. Levine and R. B. Bernstein, Chem. Phys. Lett., 29, 1 (1974). R. D. Levine and R. Kosloff, Chem. fhys. Lett., 28, 300 (1974). A. Ben Shaul, R. D. Levine, and R. B. Bernstein, J . Chem. fhys.,
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Application of Multistep Deactivation Processes in the Interpretation of Intermolecular Energy Transfer following Chemical Activation by Kinetic Techniques M. B. Callahan and Leonard D. Spicer" Depattrnent of Chemistry, University of Utah, Salt Lake City, Utah 84 112 (Received June 29, 1978) Publication costs assisted by the United States Depafiment of Energy
Interpretation of vibrational energy transfer following kinetically controlled chemical activation is refined by incorporatingmultistep deactivation processes into the RRKM treatment of the excited molecule. The functional form of the initial primary product energy distribution used is based on that suggested by Bunker. This model is applied in interpreting collisional energy transfer from cyclobutane-t, chemically activated by nuclew recoil reaction. New low pressure experimental data are used to estimate the average energy of the nascent cyclobutane-t and the average step sizes for energy transfer to He, Nz, COZ, and parent on collision based on a stepladder deactivation model. Step sizes found for cyclobutane, He, NS, and CO, are 10.0,0.5,2.0, and 5.0 kcal, respectively.
Introduction The kinetic technique of chemical activation by nuclear recoil stimulated chemical reaction has been shown earlier in this laboratory to yield data on intermolecular, vibrational energy transfer.1,2 Relative efficiencies for collisional transfer of vibrational energy from highly excited polyatomics to a variety of bath gases have been obtained from a combination of composition and pressure dependent data using a phenomenological appr0ach.l Detailed consideration of the competitive unimolecular behavior in recoil hot reaction systems based on RiceRamsperger-Kassel-Marcus (RRKM) t h e ~ r has y ~ yielded ~~ 0022-3654/79/2083-1013$01 .OO/O
a more complete description of the chemical activation process used in these energy transfer studies. The features explored to date using this approach are consistent with the phenomonological model and, in addition the detailed analysis, provides a formalism for extracting absolute energy transfer efficiencies from kinetic chemical activation data. The central feature in the refined treatment of systems chemically activated by kinetic techniques is an estimation of the functional form for the internal energy distribution of the nascent product molecule^.^^^ This distribution and those formed by collisional relaxation of internal energy 0 1979 American
Chemical Society
