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Homogeneous isotope exchange reaction between hydrogen and deuterium
Volume
124, number
CHEMICAL PHYSICS LETTERS
1
7 February 1986
HOMOGENEOUS ISOTOPE EXCHANGE REACTION BETWEEN HYDROGEN AND DEUTERIUM Martin J. RABINOWITZ Department
of Chemistry,
and William C. GARDINER
Jr.
University of Texas, Austin, TX 78712, USA
Received 10 May 1985; in final form 18 November
1985
The isotope exchange reaction between hydrogen and deuterium was studied in incident and reflected shock waves over the temperature range 120%1800 K by vacuum ultraviolet absorption spectroscopy. The observed exchange reaction ensued after long induction periods at rates that proved to account for the amounts of exchange previously seen in single-pulse shock-tube and reflected-wave mass-spectrometric investigations. From the absence of detectable reaction during the induction period, lower bounds of 70 and 45 kcal were placed on the barriers to molecular exchange in four- and six-center transition structures, respectively.
1. introduction For a number of years there has been a controversy in the literature as to whether a four-center exchange reaction between molecular hydrogen and deuterium can occur at collision energies below that required for dissociation of a hydrogen molecule. Theoretical calculations of varying levels of sophistication gave no indication of such a low-barrier route, while singlepulse shock tube experiments suggested that it exists and could be rationalized as proceeding by a vibrational activation mechanism. (A review has been given by Bauer [ 1] .) An alternative molecular route could involve a six-center transition structure, but the quantum mechanical calculations again suggest that the barrier should be substantially higher than that suggested by the experiments [2]. In 1983 Lifshitz, Bidani and Carroll [3] examined the H-atom contamination levels during the shock-initiated exchange reaction under ultraclean conditions and concluded that the exchange reaction observed previously had been catalysed by unappreciated amounts of atoms introduced by impurities. A shortcoming of the experimental studies reported so far is that the only real time observations of reaction progress have been done using the reflected wave time of flight mass spectrometric method, which introduces the possibility of impurity contam0 009.2614/86/$03.50 0 Elsevier Science publishers B.V. (North-Holland Physics publishing Division)
ination at the sampling orifice [4,5] . We undertook to examine the rate of isotope exchange by optical spectroscopy in order to get real time product formation rates in the incident wave shocked gas flow far from the shock tube walls. Experiments were done in reflected shock waves also for comparison with the incident shock wave data and with earlier studies. It was indeed found that the observed exchange reaction had kinetic behavior suggestive of atom chain catalysis, namely long induction periods followed by rapid reaction at rates comparable to those of earlier studies. By examining the limits of undetected reaction during the induction period it was possible to set lower bounds for the barriers of the four- and six-center molecular exchange transition structures of 70 and 45 kcal, respectively.
2. Experimental Three optical spectroscopic techniques suggest themselves for kinetic spectroscopy differentiating between Hz, D, and HD - vacuum ultraviolet (VUV) absorption or conventional Raman or coherent Raman spectroscopy. Of these we elected vacuum ultraviolet absorption for its promise of greater sensitivity and time resolution. In principle the WV method should provide absolute discrimination between the isotopic 63
Volume124, number 1
CHEMICAL PHYSICSLETTERS
species, because the absorption lines are separated from one another by distances much greater than their linewidths and show only rare accidental overlaps [6]. In practice, however, it was found that in order to have sufficient intensity to provide the required time resolution, the source lamp had to be driven in an arc discharge that produced a high degree of line broadening and shifting, such that all three molecules absorbed the source light to different degrees. The combination of time resolution, sensitivity and discrimination eventually achieved permitted the exchange reaction to be observed over the temperature range 1250 to 1800 K at densities near 1 X 10m5 mol/cm3. The shock tube apparatus has been described in detail before [7]. Briefly, it was a Monel tube of 7.6 cm inner diameter having honed interior wails and piezoelectric transducers for shock velocity measurement. For the experiments reported here, flushmounted 1 mm thick LiF windows were used at the observation station. Aluminum diaphragms were pressure-burst by hydrogen or hydrogen-helium driver gas to initiate experiments. Incident and reflected shocked gas properties were computed by standard methods at the shock front and during subsequent reactions [8]. Starting pressures varied from 20 to 40 Torr to achieve shocked gas densities at the 1 X 10e5 mol/cm3 level as desired. Test gas mixtures were prepared manometricalIy from 99.99% Ar (Matheson), 99.995% H2 (Big Three) and 99.5% CP Grade D2 - the impurities being mainly H2 and HD - (Matheson) and allowed to mix for 48 h before use. The light source consisted of a discharge confined within a 5 mm inner diameter by 130 mm long quartz tube containing flowing D2 at 5 Torr pressure. Prior to experiments a 3 mA glow discharge was used to maintain conductance; upon arrival of the incident shock wave at a station 1.5 m upstream of the observation station, an arc was generated by lifting a 375 /JF capacitor charged to 1200 V to a potential high enough to discharge it at a power level of about 1 kW within the tube. The distance from the discharge to the fust LiF window was about 3 mm. On the opposite side of the shock tube, 15 cm from the second LiF window, the 2 mm entrance slit of an f/4.5,20 cm focal length vacuum spectrometer defined the end of the probe beam. Its 2 mm exit slit implied a triangular spectral bandpass of 8 nm full width at half maximum. (It was 64
7 February 1986
determined that using narrower slits only decreased the signal to noise ratio without improving the isotopic discrimination.) A salicylate-coated photomultiplier served as detector. Anode currents were amplified by a line driver and measured using an eight-bit transient recorder. The overall time resolution, governed by the flow speed of test gas across the beam, was about 3 ps. Full details of the apparatus, data acquisition and data reduction procedures are given elsewhere [9].
3. Results In preliminary experiments it was determined that the best combination of sensitivity and signal to noise ratio for hot test gas were obtained using the (0,2) band of the Werner transition near 110 nm. For discrimination between the isotopic species it was found that a D2 lamp was superior to an H2 lamp. Calibration of the molar absorption coefficients of H2 and D2 for the D2 lamp could then be carried out in a straightforward manner using 9% H2 or D2 mixtures in Ar. The results are shown in fig. la. It is seen that the temperature dependence is complex and only indirectly related to the Boltzmann population of absorber in the u = 2 state. For measuring the molar absorption coefficient of HD, the absorbance in a 6.7% H2, 3.3% D2 mixture was measured at times after shock passage long enough for isotopic scrambling to be complete. In one series of runs this completeness was ensured by adding 0.1% N20 to the mixture. Computer simulations using the H/N/O reactions rate coefficient set recommended by Hanson and Salimian [lo] confirmed that isotopic exchange equilibrium should be achieved on the time scale of the observations, about 500 ps, although qualitative differences between computed and observed profiles were found. The “final”, i.e. end of isotopic exchange, absorbances (fig. 1b) were decomposed to account for the absorbance due to H2 and D2 to obtain the molar absorption coefficient of HD. (fig. la) A representative profile showing the isotopic exchange reaction in real time is shown in fig. 2. All profiles had the same characteristic form: a decrease in transmission at the shock front, a long induction period during which no reaction was detected, and
Volume 124, number 1
CHEMICAL PHYSICS LETTERS
7 February 1986 I=0
r
Time
4
lntenslty
4
6
6
10
10 kK/T
10 kWI
Fig. 1. (a) Decadic molar absorption coefficients of Hz, D-J and HD for Da source lamp as a function of inverse temperature. The error bars indicate inferred ranges derived from peak-topeak noise levels on the profiles of the calibration experiments. See text for explanation of HD line. (b) Decadic molar absorption coefficients for isotopically scrambled Hz:Ds:HD:Ar = 4.44:1.12:4.44:90.00 mixture as a function of inverse temperature. o, NzO catalyzed mixture; A, thermally scrambled mixture. The line is a least-squares fit to all data points. Error bars as in (a).
Fig. 2. Representative experimental profde. Z = 0 and Zo represent the zero Intensity and pre-shock-arrival transmitted intensity of the signal. The fme line? through the signal were drawn by hand for each record. It is seen that the abrupt decrease in signal upon shock passage is followed first by a constant transmitted intensity and later by a gradual further decrease. The induction delay was found by locating the intersection of the best handdrawn straight lines through the late-time gradual decrease and the constant post-shock level. The slope of the late-time gradual decrease was used to determine the atom-catalyzed rate of isotope exchange, while the maximum slope that could be attributed to a straight line through the pre-induction-delay signal was used to determine the maximum molecular reaction rate (see text). Vibrational relaxation is too fast to be seen on thii time scale. The experiment shown is a 1465 K incident shock with shocked gas density 6.4 X 10” mol/cm3 in a H2:Dz:Ar = 6.7:3.3:90 test gas.
finally a steady decrease in transmission attributable to HD formation. For reflected shock wave experiments the induction delay was about 1300 ps at all temperatures, while for incident shock waves a strong temperature dependence was found (fig. 3). The postinduction transmission change was converted into an HD production rate using the temperature dependent molar absorption coefficients. It scaled directly with pressure. The first-order Arrhenius presentation is shown in fig. 3. These reaction rates can be compared with those inferred from previous studies. The Bauer and Ossa [ 1l] rate coefficient expression was used to compute the residence time required for (an arbitrary) 5% conversion, 1600 PS, at 1200 K and 1.2 X low5 mol/cm3 density. For this residence time, final HD concentrations were computed over their 1200 to 1450 K experimental temperature range. A time to 5% conversion at our post-induction period rate (fig. 3) at 1200 K was computed and added to the observed induction delay at that temperature to get an effective residence 65
CHEMICAL PHYSICS LETTERS
Volume 124, number 1
7 February 1986
4. Discussion 4
107 6
7
8
10kWT
Fig. 3.The ftied symbols are induction delay to onset of observable reaction as a function of inverse temperature (scale on left). l, experiments with shocked gas density 6 X lo6 mol/cm3; n, experiments with shocked gas density 1 X 10e5 mol/cm3. The line is a least-squares fit to the data given by 1.40 X lo3 exp(-692 K/Z’) + 0.292 exp(11480 K/T) in units of MSwith a standard deviation off 140 MS.The open symbols are the fnst-order growth constant after onset of observable reaction as a function of inverse temperature (scale on right). o, experiments with shocked gas density 6 X 10” mol/cm3; q, experiments with shocked gas density 1 X low5 mol/cm3; A, experiments in reflected waves with shocked gas density 1.2 X 10” mol/cm3. The line is a leastsquares tit to the data given by (3.26 f 0.96) X 1Or’ X exp[(-11632 f 435) K/q.
time of 5200 PS, about three times the Bauer and Ossa value - indicating that the level of contaminationcatalysed reaction is about three times smaller in our study than in theirs. Again assuming a constant residence time, but accounting for the temperaturedependent induction time, final HD concentrations were again computed. From these HD concentrations rate coefficients were computed, whose temperature dependence, as exp(-19500 K/7’), was close to the exp(-21270 K/7’) found by Bauer and Ossa. For comparison with the Kern and Nika [4] results, we computed the conversion rate coefficient from the 100 and 200 ps points on the 2525 K experiment shown in their fig. 1 to be 3.0 X log cm3 mol-l s-l. Our extrapolated rate coefficient for these conditions would be 3.3 X IO9 cm3 mol-l s-l. 66
The form and quantitative evaluation of the VUV absorption profiles reported here confirm the conclusion of Lifshitz, Bidani and Carroll [3] that the isotope exchange reaction observed in the single pulse and mass spectrometric experiments was due to atom chain catalysis introduced by impurities. In contrast to their conclusions about the source of these atoms, it appears from our results that the chain center sources are not present in the test gas, but enter the hot gas from the shock tube wall. Numerous computer simulations with a variety of assumptions about homogeneous chain center sources indicated that no plausible homogeneous chain initiation process would be able to account for the qualitative form of the exchange profiles observed. (Details are given by Rabinowitz [9] .) Instead, the induction delays are reasonably attributed to diffusive and convective transport of dissociable impurities - for incident shock waves at the transition from laminar to turbulent boundary layer flow - into the hot gas. The long induction period provides an opportunity to seek for slower reaction, in particular the possible. molecular exchange, before the atom chain appears. We considered first the maximum exchange rate that could be hidden beneath the noise level of the signal during the induction period, and converted this to a presumed bimolecular reaction rate coefficient between H2 and D,. As seen in fig. 4, this rate coefflcient is far below the expressions deduced from single pulse shock tube experiments [ 11,121. The upper limit rate coefficient can also be compared to the theoretical barrier height calculations for molecular exchange processes by attributing the difference between computed bimolecular or termolecular collision frequencies and the experimental upper limit value at the high temperature end of the experimental range to Boltzmann factors in the barrier heights. This was done using the IJ parameters of Hirschfelder et al. [ 131 and the termolecular collision frequency formulation of Smith [ 141. Assuming steric factors of one for formation of the transition structures implies barriers of 70 kcal for the bimolecular reaction and 45 kcal for the termolecular reaction. (Details are given by Rabinowitz [9] .) While these are still well below the theoretical values, they are also well above the barriers previously deduced from the cited experiments.
Volume 124, number 1
CHEMICALPHYSICS LETTERS
7 February 1986
to be attributable to atom chain reactions rather than molecular processes. Lower bounds on the bimolecular and termolecular energy barriers of 70 and 45 kcal, respectively, could be set by measuring the maximum unobservable exchange rates during the induction zone preceding onset of chain reaction.
Acknowledgement This research was supported by the National Science Foundation and the Robert A. Welch Foundation.
‘;;I 5
6
References
10 k&-f Fig. 4. Minimum detectable four-center exchange rate coefficient. BO, Bauer and Ossa [ 111; LF, LIfshitz and Frenklach
1121.
Setting still higher lower bounds for the barriers to the molecular exchange processes can realistically be done only by extending the temperature range a few hundred degrees beyond what we have found to be feasible using VW absorption spectroscopy. (The limit is given by the progressive loss of isotopic discrimination; see fig. la.) Raman spectroscopy is the only route open to achieve this, coupled perhaps with the use of somewhat higher densities. Whether such experiments can be done with sufficient signal to noise ratio can only be determined by trial.
5. Conclusions The isotope exchange reaction between H2 and D2 observed in single pulse and mass spectrometric studies of the reaction in shock waves is confirmed
[1] S.H. Bauer, Ann. Rev. Phys. Chem. 30 (1979) 271. [2] J. Wright, Chem. Phys. Letters 6 (1970) 476; D.A. Dixon, R.M. Stevens and D.R. Hershbach, Faraday Discussions Chem. Sot. 62 (1977) 110. [3] A. Lifshitz, M. Bidani and H.F. Carroll, J. Chem. Phys. 79 (1983) 2742. [4] R.D. Kernand G.G. Nika, J. Phys. Chem. 75 (1971) 1615. [5] R.D. Kern and G.G. Nika, J. Phys. Chem. 75 (1971) 2541. [6] P.G. Wilkinson, Can. J. Phys. 46 (1968) 1225. [7] J.E. Hardy, Dissertation, University of Texas, Austin (1976). [8] W.C. Gardiner Jr., B.F. Walker and C.B. Wakefield, in: Shock waves in chemistry, ed. A. Lifshitz (Dekker, New York, 1981) p. 319. [9] M.J. Rabinowitz, Dissertation, University of Texas, Austin (1985). [lo] R.K. Hanson and S. Salimian, in: Combustion chemistry, ed. W.C. Gardiner Jr. (Springer, Berlin, 1984) p. 361. [ 111 S.H. Bauer and E. Ossa, J. Chem. Phys. 45 (1966) 434. [ 121 A. Lifshitz and M. Frenklach, J. Chem. Phys. 67 (1977) 2803. [ 131 J.O. Hirschfelder, C.F. Curtiss and R.B. Bird, Molecular theory of gases and liquids (Wiley, New York, 1954) p. 110. [14] F.T. Smith, Discussions Faraday Sot. 33 (1962) 183.
67
124, number
CHEMICAL PHYSICS LETTERS
1
7 February 1986
HOMOGENEOUS ISOTOPE EXCHANGE REACTION BETWEEN HYDROGEN AND DEUTERIUM Martin J. RABINOWITZ Department
of Chemistry,
and William C. GARDINER
Jr.
University of Texas, Austin, TX 78712, USA
Received 10 May 1985; in final form 18 November
1985
The isotope exchange reaction between hydrogen and deuterium was studied in incident and reflected shock waves over the temperature range 120%1800 K by vacuum ultraviolet absorption spectroscopy. The observed exchange reaction ensued after long induction periods at rates that proved to account for the amounts of exchange previously seen in single-pulse shock-tube and reflected-wave mass-spectrometric investigations. From the absence of detectable reaction during the induction period, lower bounds of 70 and 45 kcal were placed on the barriers to molecular exchange in four- and six-center transition structures, respectively.
1. introduction For a number of years there has been a controversy in the literature as to whether a four-center exchange reaction between molecular hydrogen and deuterium can occur at collision energies below that required for dissociation of a hydrogen molecule. Theoretical calculations of varying levels of sophistication gave no indication of such a low-barrier route, while singlepulse shock tube experiments suggested that it exists and could be rationalized as proceeding by a vibrational activation mechanism. (A review has been given by Bauer [ 1] .) An alternative molecular route could involve a six-center transition structure, but the quantum mechanical calculations again suggest that the barrier should be substantially higher than that suggested by the experiments [2]. In 1983 Lifshitz, Bidani and Carroll [3] examined the H-atom contamination levels during the shock-initiated exchange reaction under ultraclean conditions and concluded that the exchange reaction observed previously had been catalysed by unappreciated amounts of atoms introduced by impurities. A shortcoming of the experimental studies reported so far is that the only real time observations of reaction progress have been done using the reflected wave time of flight mass spectrometric method, which introduces the possibility of impurity contam0 009.2614/86/$03.50 0 Elsevier Science publishers B.V. (North-Holland Physics publishing Division)
ination at the sampling orifice [4,5] . We undertook to examine the rate of isotope exchange by optical spectroscopy in order to get real time product formation rates in the incident wave shocked gas flow far from the shock tube walls. Experiments were done in reflected shock waves also for comparison with the incident shock wave data and with earlier studies. It was indeed found that the observed exchange reaction had kinetic behavior suggestive of atom chain catalysis, namely long induction periods followed by rapid reaction at rates comparable to those of earlier studies. By examining the limits of undetected reaction during the induction period it was possible to set lower bounds for the barriers of the four- and six-center molecular exchange transition structures of 70 and 45 kcal, respectively.
2. Experimental Three optical spectroscopic techniques suggest themselves for kinetic spectroscopy differentiating between Hz, D, and HD - vacuum ultraviolet (VUV) absorption or conventional Raman or coherent Raman spectroscopy. Of these we elected vacuum ultraviolet absorption for its promise of greater sensitivity and time resolution. In principle the WV method should provide absolute discrimination between the isotopic 63
Volume124, number 1
CHEMICAL PHYSICSLETTERS
species, because the absorption lines are separated from one another by distances much greater than their linewidths and show only rare accidental overlaps [6]. In practice, however, it was found that in order to have sufficient intensity to provide the required time resolution, the source lamp had to be driven in an arc discharge that produced a high degree of line broadening and shifting, such that all three molecules absorbed the source light to different degrees. The combination of time resolution, sensitivity and discrimination eventually achieved permitted the exchange reaction to be observed over the temperature range 1250 to 1800 K at densities near 1 X 10m5 mol/cm3. The shock tube apparatus has been described in detail before [7]. Briefly, it was a Monel tube of 7.6 cm inner diameter having honed interior wails and piezoelectric transducers for shock velocity measurement. For the experiments reported here, flushmounted 1 mm thick LiF windows were used at the observation station. Aluminum diaphragms were pressure-burst by hydrogen or hydrogen-helium driver gas to initiate experiments. Incident and reflected shocked gas properties were computed by standard methods at the shock front and during subsequent reactions [8]. Starting pressures varied from 20 to 40 Torr to achieve shocked gas densities at the 1 X 10e5 mol/cm3 level as desired. Test gas mixtures were prepared manometricalIy from 99.99% Ar (Matheson), 99.995% H2 (Big Three) and 99.5% CP Grade D2 - the impurities being mainly H2 and HD - (Matheson) and allowed to mix for 48 h before use. The light source consisted of a discharge confined within a 5 mm inner diameter by 130 mm long quartz tube containing flowing D2 at 5 Torr pressure. Prior to experiments a 3 mA glow discharge was used to maintain conductance; upon arrival of the incident shock wave at a station 1.5 m upstream of the observation station, an arc was generated by lifting a 375 /JF capacitor charged to 1200 V to a potential high enough to discharge it at a power level of about 1 kW within the tube. The distance from the discharge to the fust LiF window was about 3 mm. On the opposite side of the shock tube, 15 cm from the second LiF window, the 2 mm entrance slit of an f/4.5,20 cm focal length vacuum spectrometer defined the end of the probe beam. Its 2 mm exit slit implied a triangular spectral bandpass of 8 nm full width at half maximum. (It was 64
7 February 1986
determined that using narrower slits only decreased the signal to noise ratio without improving the isotopic discrimination.) A salicylate-coated photomultiplier served as detector. Anode currents were amplified by a line driver and measured using an eight-bit transient recorder. The overall time resolution, governed by the flow speed of test gas across the beam, was about 3 ps. Full details of the apparatus, data acquisition and data reduction procedures are given elsewhere [9].
3. Results In preliminary experiments it was determined that the best combination of sensitivity and signal to noise ratio for hot test gas were obtained using the (0,2) band of the Werner transition near 110 nm. For discrimination between the isotopic species it was found that a D2 lamp was superior to an H2 lamp. Calibration of the molar absorption coefficients of H2 and D2 for the D2 lamp could then be carried out in a straightforward manner using 9% H2 or D2 mixtures in Ar. The results are shown in fig. la. It is seen that the temperature dependence is complex and only indirectly related to the Boltzmann population of absorber in the u = 2 state. For measuring the molar absorption coefficient of HD, the absorbance in a 6.7% H2, 3.3% D2 mixture was measured at times after shock passage long enough for isotopic scrambling to be complete. In one series of runs this completeness was ensured by adding 0.1% N20 to the mixture. Computer simulations using the H/N/O reactions rate coefficient set recommended by Hanson and Salimian [lo] confirmed that isotopic exchange equilibrium should be achieved on the time scale of the observations, about 500 ps, although qualitative differences between computed and observed profiles were found. The “final”, i.e. end of isotopic exchange, absorbances (fig. 1b) were decomposed to account for the absorbance due to H2 and D2 to obtain the molar absorption coefficient of HD. (fig. la) A representative profile showing the isotopic exchange reaction in real time is shown in fig. 2. All profiles had the same characteristic form: a decrease in transmission at the shock front, a long induction period during which no reaction was detected, and
Volume 124, number 1
CHEMICAL PHYSICS LETTERS
7 February 1986 I=0
r
Time
4
lntenslty
4
6
6
10
10 kK/T
10 kWI
Fig. 1. (a) Decadic molar absorption coefficients of Hz, D-J and HD for Da source lamp as a function of inverse temperature. The error bars indicate inferred ranges derived from peak-topeak noise levels on the profiles of the calibration experiments. See text for explanation of HD line. (b) Decadic molar absorption coefficients for isotopically scrambled Hz:Ds:HD:Ar = 4.44:1.12:4.44:90.00 mixture as a function of inverse temperature. o, NzO catalyzed mixture; A, thermally scrambled mixture. The line is a least-squares fit to all data points. Error bars as in (a).
Fig. 2. Representative experimental profde. Z = 0 and Zo represent the zero Intensity and pre-shock-arrival transmitted intensity of the signal. The fme line? through the signal were drawn by hand for each record. It is seen that the abrupt decrease in signal upon shock passage is followed first by a constant transmitted intensity and later by a gradual further decrease. The induction delay was found by locating the intersection of the best handdrawn straight lines through the late-time gradual decrease and the constant post-shock level. The slope of the late-time gradual decrease was used to determine the atom-catalyzed rate of isotope exchange, while the maximum slope that could be attributed to a straight line through the pre-induction-delay signal was used to determine the maximum molecular reaction rate (see text). Vibrational relaxation is too fast to be seen on thii time scale. The experiment shown is a 1465 K incident shock with shocked gas density 6.4 X 10” mol/cm3 in a H2:Dz:Ar = 6.7:3.3:90 test gas.
finally a steady decrease in transmission attributable to HD formation. For reflected shock wave experiments the induction delay was about 1300 ps at all temperatures, while for incident shock waves a strong temperature dependence was found (fig. 3). The postinduction transmission change was converted into an HD production rate using the temperature dependent molar absorption coefficients. It scaled directly with pressure. The first-order Arrhenius presentation is shown in fig. 3. These reaction rates can be compared with those inferred from previous studies. The Bauer and Ossa [ 1l] rate coefficient expression was used to compute the residence time required for (an arbitrary) 5% conversion, 1600 PS, at 1200 K and 1.2 X low5 mol/cm3 density. For this residence time, final HD concentrations were computed over their 1200 to 1450 K experimental temperature range. A time to 5% conversion at our post-induction period rate (fig. 3) at 1200 K was computed and added to the observed induction delay at that temperature to get an effective residence 65
CHEMICAL PHYSICS LETTERS
Volume 124, number 1
7 February 1986
4. Discussion 4
107 6
7
8
10kWT
Fig. 3.The ftied symbols are induction delay to onset of observable reaction as a function of inverse temperature (scale on left). l, experiments with shocked gas density 6 X lo6 mol/cm3; n, experiments with shocked gas density 1 X 10e5 mol/cm3. The line is a least-squares fit to the data given by 1.40 X lo3 exp(-692 K/Z’) + 0.292 exp(11480 K/T) in units of MSwith a standard deviation off 140 MS.The open symbols are the fnst-order growth constant after onset of observable reaction as a function of inverse temperature (scale on right). o, experiments with shocked gas density 6 X 10” mol/cm3; q, experiments with shocked gas density 1 X low5 mol/cm3; A, experiments in reflected waves with shocked gas density 1.2 X 10” mol/cm3. The line is a leastsquares tit to the data given by (3.26 f 0.96) X 1Or’ X exp[(-11632 f 435) K/q.
time of 5200 PS, about three times the Bauer and Ossa value - indicating that the level of contaminationcatalysed reaction is about three times smaller in our study than in theirs. Again assuming a constant residence time, but accounting for the temperaturedependent induction time, final HD concentrations were again computed. From these HD concentrations rate coefficients were computed, whose temperature dependence, as exp(-19500 K/7’), was close to the exp(-21270 K/7’) found by Bauer and Ossa. For comparison with the Kern and Nika [4] results, we computed the conversion rate coefficient from the 100 and 200 ps points on the 2525 K experiment shown in their fig. 1 to be 3.0 X log cm3 mol-l s-l. Our extrapolated rate coefficient for these conditions would be 3.3 X IO9 cm3 mol-l s-l. 66
The form and quantitative evaluation of the VUV absorption profiles reported here confirm the conclusion of Lifshitz, Bidani and Carroll [3] that the isotope exchange reaction observed in the single pulse and mass spectrometric experiments was due to atom chain catalysis introduced by impurities. In contrast to their conclusions about the source of these atoms, it appears from our results that the chain center sources are not present in the test gas, but enter the hot gas from the shock tube wall. Numerous computer simulations with a variety of assumptions about homogeneous chain center sources indicated that no plausible homogeneous chain initiation process would be able to account for the qualitative form of the exchange profiles observed. (Details are given by Rabinowitz [9] .) Instead, the induction delays are reasonably attributed to diffusive and convective transport of dissociable impurities - for incident shock waves at the transition from laminar to turbulent boundary layer flow - into the hot gas. The long induction period provides an opportunity to seek for slower reaction, in particular the possible. molecular exchange, before the atom chain appears. We considered first the maximum exchange rate that could be hidden beneath the noise level of the signal during the induction period, and converted this to a presumed bimolecular reaction rate coefficient between H2 and D,. As seen in fig. 4, this rate coefflcient is far below the expressions deduced from single pulse shock tube experiments [ 11,121. The upper limit rate coefficient can also be compared to the theoretical barrier height calculations for molecular exchange processes by attributing the difference between computed bimolecular or termolecular collision frequencies and the experimental upper limit value at the high temperature end of the experimental range to Boltzmann factors in the barrier heights. This was done using the IJ parameters of Hirschfelder et al. [ 131 and the termolecular collision frequency formulation of Smith [ 141. Assuming steric factors of one for formation of the transition structures implies barriers of 70 kcal for the bimolecular reaction and 45 kcal for the termolecular reaction. (Details are given by Rabinowitz [9] .) While these are still well below the theoretical values, they are also well above the barriers previously deduced from the cited experiments.
Volume 124, number 1
CHEMICALPHYSICS LETTERS
7 February 1986
to be attributable to atom chain reactions rather than molecular processes. Lower bounds on the bimolecular and termolecular energy barriers of 70 and 45 kcal, respectively, could be set by measuring the maximum unobservable exchange rates during the induction zone preceding onset of chain reaction.
Acknowledgement This research was supported by the National Science Foundation and the Robert A. Welch Foundation.
‘;;I 5
6
References
10 k&-f Fig. 4. Minimum detectable four-center exchange rate coefficient. BO, Bauer and Ossa [ 111; LF, LIfshitz and Frenklach
1121.
Setting still higher lower bounds for the barriers to the molecular exchange processes can realistically be done only by extending the temperature range a few hundred degrees beyond what we have found to be feasible using VW absorption spectroscopy. (The limit is given by the progressive loss of isotopic discrimination; see fig. la.) Raman spectroscopy is the only route open to achieve this, coupled perhaps with the use of somewhat higher densities. Whether such experiments can be done with sufficient signal to noise ratio can only be determined by trial.
5. Conclusions The isotope exchange reaction between H2 and D2 observed in single pulse and mass spectrometric studies of the reaction in shock waves is confirmed
[1] S.H. Bauer, Ann. Rev. Phys. Chem. 30 (1979) 271. [2] J. Wright, Chem. Phys. Letters 6 (1970) 476; D.A. Dixon, R.M. Stevens and D.R. Hershbach, Faraday Discussions Chem. Sot. 62 (1977) 110. [3] A. Lifshitz, M. Bidani and H.F. Carroll, J. Chem. Phys. 79 (1983) 2742. [4] R.D. Kernand G.G. Nika, J. Phys. Chem. 75 (1971) 1615. [5] R.D. Kern and G.G. Nika, J. Phys. Chem. 75 (1971) 2541. [6] P.G. Wilkinson, Can. J. Phys. 46 (1968) 1225. [7] J.E. Hardy, Dissertation, University of Texas, Austin (1976). [8] W.C. Gardiner Jr., B.F. Walker and C.B. Wakefield, in: Shock waves in chemistry, ed. A. Lifshitz (Dekker, New York, 1981) p. 319. [9] M.J. Rabinowitz, Dissertation, University of Texas, Austin (1985). [lo] R.K. Hanson and S. Salimian, in: Combustion chemistry, ed. W.C. Gardiner Jr. (Springer, Berlin, 1984) p. 361. [ 111 S.H. Bauer and E. Ossa, J. Chem. Phys. 45 (1966) 434. [ 121 A. Lifshitz and M. Frenklach, J. Chem. Phys. 67 (1977) 2803. [ 131 J.O. Hirschfelder, C.F. Curtiss and R.B. Bird, Molecular theory of gases and liquids (Wiley, New York, 1954) p. 110. [14] F.T. Smith, Discussions Faraday Sot. 33 (1962) 183.
67