Energy Distribution Among Reaction Products Part 1 .-The Reaction Atomic Hydrogen plus Molecular Chlorine BY P. E. CHARTERS AND J. C. POLANYI Dept. of Chemistry, University of Toronto, Toronto Received 18th January, 1962 Infra-red chemiluminescence from the reaction Hf Cl2 +HClt+ Cl (HClt is vibrationally ex- cited HC1 in its ground electronic state) has been examined with improved resolution at roughly two orders of magnitude lower HCl pressure than heretofore. Under stationary state conditions the rotators in vibrational levels 1 to 4 appear to be in thermal equilibrium (135175°C) up to J = 7. There is, however, an excess of rotators in rotational levels J = 9, 10, 11, . . . of v = 2, 3 and 4 (v = 1 was not measured to J>9). This could be the residue of an even greater rotational excess present in the newly-formed HC1.The stationary state vibrational distribution is markedly non- Boltzmann, being characterized by " temperatures " ranging from 8000 to 2930°K. Relative rates of reaction, Rv, into the various vibrational levels of HClt, have been calculated from the observed stationary state distribution, in several ways. The rate of reaction is always found to be greater into lower vibrational levels, the rate into u = 3 being approximately 35 times that into u = 5. If the heat of a chemical reaction is sufficient to form products in various vibra- tionally and rotationally excited states, then there should exist a " fine-structure " to the reaction rate consisting in the specific rate constants for reaction into each vibrational and rotational level of the products.In the simplest exchange reaction the products have only three internal degrees of freedom, one vibrational and two rotational, all vested in the new molecule AB. There has existed for some time a substantial body of evidence indicating that in certain reactions of the type A+BC, almost the entire heat of reaction goes into vibrational energy of AB. The reactions in question are X+NaZ-,NaX+Na and Na + XM+NaX+ M, where X is C1, Br or I and M is Cd or Hg.13 2 Two avenues are at present being explored in the hope of extending this early data on energy distribution among the products of reactions A+ BC. A preliminary study has been made of the reaction K+BrH-+KBr+H in crossed Maxwellian molecular beams.3 It has been shown that it should be possible to calculate the recoil energy of the KBr product from its angular distribution.By subtracting the recoil energy from the total energy available (i.e., the heat of reaction plus the activation energy, Q+Ea) a value will be obtained for the total internal energy, rotation+vibration, of the KBr.4 As yet, no results are available for this system. A second approach depends upon the investigation of infra-red emission arising from the reactions H+Xz-+HXt+X(X = C1 or Br) in which the emitter HXt is a vibrationally excited molecule in its ground electronic state.5.6 In principle, it should be possible to obtain the " fine-structure " of the reaction rate, for a Max- wellian distribution of reagents, from measurements of the initial vibrational and rotational excitation of the product.The recoil energy could then be obtained by difference; this is the reverse of the procedure in molecular beam experiments. The two techniques should complement one another. The present paper presents some results obtained by the infra-red chemiluminescence technique. A+BC-,AB + C (1) 107108 ENERGY DISTRIBUTION AMONG PRODUCTS In the earlier work on both the systems H+X2, product HXt has been detected with vibrational energy up to and including the level having energy equal to the entire heat of reaction. For H+Cl2, an analysis has been made of the partially- resolved fundamental and first overtone en1issions.7~ * This analysis revealed that the stationary state distribution of HClf in the reaction vessel, at ca. 0.2 mm Hg pressure, deviated only slightly from a 2700°K Boltzmann distribution.From this stationary distribution a calculation was made of the rate of chemical reaction directly into each vibrational level of HClt, on the assumption that HClt had achieved the observed distribution through radiation and collision, but not by transferring vibra- tional energy among themselves. The rates of reaction derived in this way were found to be progressively larger into successively lower vibrational levels. This result ran counter to the general expectation that reaction A+BC would proceed most rapidly into the highest accessible vibrational states of AB.9-11 The most persuasive experimental evidence for the expectation of higher reaction rate into higher vibrationd levels in reactions A+ BC, came from the quantitative results on the systems X+ Na2-+NaX+ M, referred to above.The spectroscopic identification of highly vibrating AB among the products of several reactions A+BCD+AB+CD further strengthened this expectation.129 13 The presence of highly vibrating AB was fully established in this work but the precise extent to which this species was formed directly by chemical reaction remained in doubt. Quantitative evidence came from studies of infra-red emission arising from the reaction of H+03+ OH? + 0 2 , which yielded roughly comparable rates of reaction into all the 9 accessible vibrational levels of OHt,14 and H + NOCl-+HClt +NO, which gave progressively larger rates of reaction into successively lower vibrational states.15 Earlier work on H+C12 appeared to suffer from two major defects.In the first place, resolution, especially in the overtone region of the spectrum, was poor, and analysis had to be made from overlapping partially-resolved bands. Secondly (this criticism could apply also to the results cited above for H+O3 and H + NOCl), the observation of a Boltzmann, or nearly-Boltzmann, distribution of the excited product among vibrational states suggested that, in the interval between product formation and emission (- 10-2 sec), the vibrational energy might have been to some extent randomly redistributed among vibrational states as a consequence of collisions between product molecules, ABt and AB. In a general way it is clear that this randomization would tend to destroy the " memory " that thevibrationallyexcited species had of their original distribution.More precisely, the result would be to invalidate the argument by which stationary state distribution in the reaction vessel is translated into rates of chemical reaction into the various vibrational levels.8 These considerations point to the need for a fresh analysis of the infra-red emission arising from the reaction H+Cl2, at lower partial pressures of HClt (to reduce the likelihood of HClt + HCl exchange), and at the same time, with improved resolution. In order to achieve this, a system with greatly improved " light "-gathering power is required. An apparatus with 120 times the reaction volume of that used in our earlier work on H+Clz, and with internal mirrors to collect the radiation, has already been described in connection with an investigation of the system H + 02.16 A preliminary investigation of the reactions H + Cl2 and H + NOCl in this apparatus 17 showed that at - 10-2 mm Hg total pressure ( N 10-1 times the total pressure used in the earlier work) the stationary distribution of HClt in the reaction vessel was markedly non-Boltzmann. Emission previously observed from the highest vibrational levels was no longer observed at the low pressure.This emission may have been due to secondary processes occurring at higher pressures of HClf. The new observationP. E. CHARTERS AND J . C. POLANYI 109 had the effect of strengthening the conclusion regarding the relative rates of chemical reaction arrived at on the basis of the earlier work, namely, that the rate of reaction is greater into the lower vibrational levels in the system H + C b In the present work this result is supported by further, quantitative, evidence.The fact that the result is in contradiction to the information concerning the only other reactions A+ BC for which data are available (X+Na2 and Na+XM), need not, of course, be taken to mean that one or the other result is wrong, since the reactions are of quite different types. RESULTS The apparatus has been described previously.16 In the present work, in addition to coating the reaction vessel with phosphoric acid, a phosphoric-coated Pyrex lining was placed inside the vessel in the hope of decreasing the loss of H atoms at the wall. The four discharge tubes were drawn down to 3 mm at their tips.The reaction vessel was at room temperature. Internal mirrors were front-surface coated with gold. The spectrometer was a model 112G Perkin-Elmer double-pass grating instrument. FIG. 1.-Trace of the emission in the region of the HCI fundamental ; slit width 0.30 rrm. Fig. 1 shows an actual trace of the fundamental region of the HCl emission (approx. 3.2-3-7 p). A further region (to 4.0 p) was traced at 0.50 mm and 2.00 mm slits. The majority of lines exhibit partial isotopic splitting. Fig. 2 shows a trace of the first overtone emission (approx. 1.7-2-0 p). The times required to trace these spectra were lt h for the fundamental and 1 h for the overtone. In order to check on the constancy of the emission a central portion of each spectrum was traced immediately prior to and subsequent to the recording of the spectrum itself.Flow rates of reagents were 60 p moles/sec of hydrogen through the discharge tubes, and 285 p moles/sec of chlorine into the reaction cell. Total pressure in the cell was 1.4 x 10-2 mm Hg. These spectra constitute the raw data of expt. 2. Expt. 1, an overtone trace made 5 months earlier, provided (along with similar data for H +Noel), the basis for our preliminary conirnunication.17 The results of the detailed analysis of expt. 1, as it related to H+C12, are presented here along with the results of expt. 2. The H+Cl:! first-overtone trace of expt. 1 is not reproduced. Reagent flows were the same as in expt. 2. Relative peak Resolution was similar to that in fig. 2.110 ENERGY DISTRIBUTION AMONG PRODUCTS heights differed from those of fig.2 since a different setting was used for the potassium bromide prism in the fore-prism monochromator ; this has a marked effect on the transmissivity against wavelength curve for the spectrometer. FIG. 2.-Trace of the emission in the region of the HCl first overtone ; slit width 0-25 mm. In both expt. 1 and 2 the areas under the peaks in the recorded spectra were corrected to uniform spectrometer transrnissivity by comparison with a trace, made over the same spectral region at the same slit width, using a black body emitter asP. E. CHARTERS AND J . C . POLANYI 111 source. This corrects at the same time for varying response of the PbS detector, with changing wavelength. The agreement between the overtone traces of expt.1 and 2 after correction for transmissivity (see table 2) attests to the validity of this method of correction, as also does the consistency between relative populations (table 2) taken from the fundamental and those derived from the overtone of expt. 2 ; transmissivity corrections within the fundamental differ considerably from those within the overtone. No correction has yet been made for any variation with wavelength of the reflectivity of the gold mirrors in the reaction cell. Somewhat different reflectivity is to be expected between the fundamental and the overtone regions. However, this would not affect our results since we have only made use of relative intensities within the fundamental, and within the overtone. The data obtained from these two sources, as already remarked, are consistent.This implies either that the re- flectivity of the gold is changing in an identical fashion over the spectral region covered by the fundamental as over the spectral region covered by the overtone or, more probably, that the reflectivity is not changing markedly in either region. i at\ J’(J’+ 1) FKG. 3.-Stationary-state distribution of HClt among rotational states of vibrational levels and 3, as calculated from the fundamental emission. 0 from v(1-0), 0 from v(2-1), A v(3-2). Filled-in points from P branch lines, the remainder from the R branch. 1, 2 from That the latter supposition is correct is suggested by the fact that the ratio of P line to R line intensity within a band does not show the anomaly (enhancement of P) which would be expected if the mirror reflectivity were changing markedly, nor do the Boltzmann plots of fig.3 and 4 show the expected downward curve of R line values. Variation in reflectivity during an experiment, due to chemical attack on the mirrors, cannot be important, since the observed emission intensity changed by no more than 10 %/h.112 ENERGY DISTRIBUTION AMONG PRODUCTS If there is a Boltzmann distribution among the rotational states of HClt present in the reaction vessel, then log (IJ/o.$SJFJ) plotted against J’(J’+ 1) should yield a straight line of slope -Bhc/kT. Here, rJ is the relative emission intensity of a rota- tional line within some vibrational band, COJ is the wave number frequency of that line, SJ = J’ (the upper state rotational quantum number) for an R branch line and SJ is equal to J’+ 1 for a P branch line.FJ, which varies by a factor of 3 in our range of J’, is defined as FJ = 1 -4yem, where y is the frequency ratio of rotational S(S+ 1) FIG. 4.-Stationary-state distribution of HClt among rotational states of vibrational levels 2, 3 and 4, as calculated from the overtone emission. 0 from o(2-0), A from 4 3 - l), V from 44-2). Filled-in points from P branch lines, the remainder from the R branch. to vibrational motion, 8 is close to unity for HCI, and m is an integer equal to +J’ for R branch lines and - (J’ + 1) for P lines.18 The constants in - Bhc/kT have their usual meanings; values used for B were taken from Rank, Eastman, Rao and Wiggins.19 Rotational Boltzmann plots for three fundamental bands of expt.2 are reproduced in fig. 3, and those for three overtone bands in fig. 4. Table 1 lists rotational temperatures taken from the slopes of the lines in fig. 3 and 4 in their linear regions. TABLE 1 .-STATIONARY-STATE ROTATIONAL TEMPERATURES fundamental overtone band temp. (OK) band temp. (OK) 1“ 507 2-1 470 2-0 379 3-2 450 3-1 358 4-2 439P. E. CHARTERS AND J . C. POLANYI 113 Relative stationary-state populations in the various vibrational levels can be calculated by two methods. One method involves summing the intensities of all the lines arising from the same vibrational upper state, I;; = CI;;”’, J’ whereupon N,. oc I~;/(courVAut,). Here coVfv can be taken as the band origin frequency ( u ) ~ ) ~ , ~ . A1)tV cc (oo)$, 1 R;’ 12, where Ri’ is the transition moment for the (forbidden) transition between the rota- tionless states v’, J’ = 0 and v, J = 0 (the values used for this constant were those of ref.(15)). Eqn. (2) implies that the total emission intensity for a particular band bears a fixed relation to the total number of molecules in the upper vibrational state for that transition, irrespective of the rotational distribution within that upper state. This result, which is due to an accidental cancellation of effects in the HCl molecule, is derived in ref. (18). In earlier work we have been obliged to calculate N,, from eqn. (2) since, in the overtone region of the spectrum from which we obtain most of the information concerning relative populations, individual rotational lines could not be resolved.As a consequence, only total emission intensity I:: could be obtained. In the present work, improved resolution permits us to test the ac- curacy of eqn. (2) by calculating our relative populations also from the general expression, which requires a knowledge of the individual rotational line intensities I:!’. Relative populations calculated from eqn. (3) agree with those taken from eqn. (2) to within experimental error. TABLE 2.-sTATIONARY-STATE VIBRATIONAL POPULATIONS N, EXPRESSED RELATIVE TO N4 ; TEMPERATURES Tv CALCULATED FROM NllN, o = l v = 2 v = 3 v=4 u = 5 expt. 1 Nu (overtone) - 13.7 5.4 1.0 ca. 0.2 expt. 2 Nu (overtone) - 13-0 5.9 1.0 ca. 0.12 - - N , (fundamental) 21.5 (1 3-0) 5.1 Tv (OK) - 8000 5450 * 3770 2930 6050 t * from the fundamental of expt.2. t from the overtone of expt. 2. I The values obtained for the stationary-state populations N,, expressed relative to N4 = 1, are listed in table 2 for expt. 1 and 2. Relative populations in the funda- mental of expt. 2 have been brought to the same scale as the overtone by equating N2 in each series. If the distribution of HClt among vibrational levels were Boltzmann, then where N is the total population of HCl in all levels (including v = 0), and Go(v) is the energy of level v relative to the zeroth level. If this expression holds, then a plot of log (N1/Nv) against Go(u) - Go( 1) (cm-1) will yield a straight lineof slope 0-625/T. Fig. 5 shows such a plot for the results of expt. 2. The distribution deviates markedly, and systematically, from Boltzmann, in the sense that the population falls off more and more rapidly (corresponding to lower and lower “ temperatures ”) towards higher vibrational levels.114 ENERGY DISTRIBUTION AMONG PRODUCTS DISCUSSION In previous studies of H+C12 chemiluminescence we have only been able to ob- serve the rotational distribution within the 1-0 band.In the present work, improved intensity and resolution have enabled us, despite roughly two orders of magnitude lower reagent pressure, to make similar measurements on the 2-1 and 3-2 bands of the fundamental and the 2-0, 3-1 and 4-2 bands of the first overtone. The form of the Boltzmann plots (fig. 2 and 3) suggest the following observations, (a) The rotators in any given vibrational level are in thermal equilibrium up to roughly J’ = 7.(b) The rotational “ temperatures ” which characterize the rota- tional distribution in this region of J’ = 0-ca. 7 are similar for all vibrational Go(u)- Go(l), cm-1 of vibrators at the temperatures indicated would give points lying along the solid lines. FIG. 5.-Stationary-state distribution of HClt among vibrational states. A Boltzmann distribution levels, = 1-4. The differences are not great enough to merit discussion at the present time. All are about 100°C above room temperature (falling in the range 135+75”C). It is possible that this is the temperature of the Pyrex sleeve within the reaction vessel, since the sleeve is in poor thermal contact with the metal walls. (c) The measured intensities are not seriously affected either by self-absorption or by change in mirror-reflectivity with wavelength, since either of these effects would cause the Boltzmann plot to curve, starting at J’ = 0.For self-absorption the curvature would be most marked in the fundamental bands (for which the extinction coefficient is greatest), for reflectivity change the curvature would be most marked in the overtone (since reflectivity alters more rapidly in the near infi-a-red). No systematic deviation of this sort is evident. (d) For J’ = 9, 10 . . . there is an excess of rotators in all vibrational levels for which data are available. This excess isP. E. CHARTERS AND J . C. POLANYI 115 real, and not a consequence of faulty analysis, since it is not observed in experiments at 1-2mm pressure employing the same spectrometer and method of analysis.20 Despite the fact that the average emitter has suffered -103 collisions with C12 (the major constituent) since its formation, this excess rotational population may be a residue of an even larger excess present when the HClt was originally formed.Sufficient energy is available for this excitation. For example, HClt in u = 4, J = 20 requires 31.2 + 11 -7 kcal/mole whereas energy liberated per mole of HClt formed is 47.5 kcal. In general, a few collisions suffice to bring about rotational transfer J'+ J' - 1.22 However, this need not necessarily apply to high rotational states for which the rotational jump, AJ = 1, approaches in magnitude that of a normal vibrational jump. Moreover, many transfers could be required to convert an unorthodox rotational distribution into a Boltzmann distribution showing no trace of the original anomaly.Relative rates of chemical reaction, R,, into each vibrational level u have been calculated from the observed relative stationary state populations Nv on the assump- tion that vibrational transfer among HCl's can be neglected owing to the low partial pressure of HC1 (estimated to be -10-4mm). Though the total pressure in the reaction vessel is only an order of magnitude less in the present work than in our earlier experiments,g the partial pressure of HCl is two orders of magnitude less since the partial pressure of H2 is -2 x 10-3 mm whereas previously it was N 1 x 10-1 mm. Furthermore, the percentage dissociation of H2 will be lower in the present case owing to the tube and nozzle separating the discharge from the reaction vessel, and the metal surfaces within the vessel.If, despite the low pressure of HCl, HCl+ HC1 vibrational exchange were still of importance in determining the stationary- state distribution, we should expect the observed distribution to vary from one experiment to the next owing to changed H-atom pressure and hence changed HC1 pressure. We have not observed any such effect. R, has been calculated from the relation Rv = ( C A V U + czpvu + zp:o + 7 - l > N V - ( C A W V N W + C Z P W V N W ) ( 5 ) (5') U U W W = ( A + B + C + D) - ( E + F ) , where u < v < w, 2 is the number of gas-collisions per second suffered by the average molecule ( N 105 at 0.01 mm pressure), z is the number of wall-collisions with metal surfaces (360 per sec in our vessel), A,, is the Einstein radiational transition prob- ability (&, of eqn.(2)), Puu is the analogous gas-phase collisional transition prob- ability, PJo is the collisional transition probability for " quenching " (1130) at a metal surface, and z is the residence time in the reaction vessel (2-22 x 10-2 sec). Table 3 lists the values calculated for each term in eqn. (5). The first four terms in the equation give the total rate of transfer of HClt out of level u ; the remaining two terms give the rate of transfer into v, with the exception of direct chemical forma- tion. The difference is the rate of chemical formation R,. The first term A in eqn. (5') gives the total rate of radiational transfer out of level u.The secondand sixth terms, Band F, give the total rates of collisionaltransfer out of and into t). In table 3, R,' and R1:' assume B = 0, F = 0. RL1 and Riv assume B = maxi- mum, F = maximum. Comparison of R,' with R!, and R1;I with RLv, shows that col- lisional deactivation in the gas is not important at our pressures. We have been able to place an upper limit on B and I; from the observation that the system H + Cl2 at 1 mm pressure gives rise to HClt in a distribution which approaches a 3500°K Boltzmann distribution.20 The total vibrational energy per mole at this temperature is equiv- alent to about 10 % of the energy made available by the reaction forming HCl.I16 ENERGY DISTRIBUTION AMONG PRODUCTS It follows that even if the entire heat of reaction goes into vibration, collisional deactivation at 1 mm pressure (107 collisions per second per HClt) cannot remove more than 90 % of the energy.Writing Pvu = cA,, (according to the Landau- Teller theory 22) and solving the 6 stationary-state equations when only R6 is sig- nificant, one obtains a set of Nu in terms of an undetermined c. These Nu substituted in eqn. (6), c EUNU >Oslo, (6) ~ = 1 - 6 (Q+EJ c N , u=O-6 yield a value of ~ ~ 3 . 3 x 10-6. It follows that Ploy for example, is > 1.1 x 10-4, i.e., on the average >9.1 x 103 collisions are required to transfer HCl from u = 1-+0. This is a reasonable lower limit.21 TABLE 3 . D ” L A T N E RATES OF REACTION, &, INTO SPECIFIC VIBRATIONAL LEVELS OF HCl R: = (A+ D) - E R’,’= (A+ B + D) - (E+ F) RIL1= (A + C + D) - E Riv=(A+ B I- C + D) - (E + F) v Nu A B 5 0.12 16.7 < 5.4 <#*4 5.6 0 0 0.15 0.16 0.13 0.13 4 1.00 115 <37-2 <358 45-2 14.2 < 4.6 1.00 1-00 1-00 1-00 3 5.50 501 <163 <I970 249 104 <33*9 4.43 4.34 5.19 5.11 2 13-04 835 <271 <4670 589 476 <155 6.51 5.97 11.15 10.69 1 21.5 729 <237 97700 972 841 <273 5.91 4.62 17.0 15.9 The third term gives the total rate of “ quenching ” by collision with metal sur- faces.There is experimental evidence that a metal surface is very efficient in re- moving vibrational energy.23 (Pyrex has a low collision efficiency, - 5 x 10-4.23) In calculating R;I and RIV we have made the crude assumption that HClt is trans- ferred to v = 0 at every collision with metal surfaces, i.e., P,fo = 1.In calculating R: and we have gone to the opposite limit and assumed no quenching; P& = 0. More refined assumptions, for example, P;4 - 1 combined with P;uccAuu (this re- quires the introduction of a term, -czP$,N,,,, on the right-hand side of (5)) lead to series of R, somewhat similar to those obtained on the assumption that P$o = 0 . Thus, for P;4 = 1, PZu~Avu, we obtain R5 = 0.16, R4 = 1.00, R3 = 4.10, Rz, = 4.50, R1 = 1.10. Examination of table 3 shows that, under our experimental conditions, the de- cisive term in the calculation of relative rates of chemical reaction into levels 21 = 5, 4 and 3, is the rate of radiational decay. In order to reverse the trend in R, it would be necessary for the radiational transition probabilities to be altered to values well outside the estimated limits of error in theoretical and experimental determina- tions of these quantities.24 The feature that is common to all four series of R,, calculated under various limiting assumptions, is a rise in rate of reaction into successively lower vibrational states u = 5, ZI = 4, u = 3, 21 = 2. In passing from ZI = 5 to v = 3 the increase in rate amounts to a factor of roughly 35. WP. E . CHARTERS AND J . C. POLANYI 117 If (contrary to our expectation) HCl+HCl vibrational transfer is occurring to a significant extent in our system, this would have the effect of increasing the relative population in high vibrational levels under our stationary conditions. We would then have underestimated the increase of reaction rate into successively lower vibra- tional levels.The authors wish to express their thanks to Dr. B. N. mare for assistance with these experiments. They are grateful to the National Research Council of Canada, the University of Toronto Advisory Committee on Scientific Research and the Imperial Oil Company of Canada, for financial assistance. One of them (J. C. P.) thanks the Alfred P. Sloan Foundation for the award of a Fellowship. 1 Polanyi, Atomic Reactions (Williams and Norgate, London, 1932). 2 Evans and Polanyi, Trans. 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