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J . Phys. Chem. 1990, 94, 2465-2471
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Rate Constants for the Reaction D 4- D20 D, OD by the Flash Photolysis-Shock Tube Technique over the Temperature Range 1285-2261 K: Results for the Back-Reaction and a Comparison to the Protonated Case J. R. Fisher and J. V. Michael* Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received: July 13, 1989; I n Final Form: September 19, 1989)
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The absolute rate constant for the reaction of D atoms with deuterium oxide, D + D 2 0 D2 + OD, has been measured by using the flash photolysisshock tube (FP-ST) technique. D atoms are monitored by atomic resonance absorption spectroscopy (ARAS) using a LyaDlamp. The results, obtained over the temperature range 1285-2261 K, can be represented by the exp(-10815 f 356 K/T)cm3 molecule-' s-l. The experimental results have Arrhenius expression k = (2.90 i 0.73) X been compared with results from the analogous protonated case, and an isotope.effect of unity is indicated within experimental error. The rate constant for the back-reaction, OD D,, calculated through the equilibrium constant, is k = (6.6 f 1.7) X lo-" exp(-3320 i 356 K/T) cm3molecule-' 8,over the same temperature range, 1285-2261 K. Theoretical rate constants, based on a new potential energy surface by Kraka and Dunning, are calculated with conventional transition-state theory for both D D 2 0 and H + H20. Similar calculations for both back-reactions are presented, and the theoretical calculations are compared to the experimental results.
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Introduction The rate behavior for the reaction between D atoms and D 2 0 D + D 2 0 D2 OD (1) has never been studied by any absolute technique in any temperature range. However, the protonated reaction H + HzO H2 OH (2) has recently been studied by two techniques,',2 the first being a flash photolysis-resonance fluorescence (FP-RF) experiment,' in which OH radicals are detected in the approach to steady state, and the second being with the flash photolysisshock tube (Fl-ST) method.2 In the latter study, estimates of the rate constants for the back-reaction, O H + H2, were made from the measured rate constants combined with equilibrium constants as given in the J A N A F tables3 These derived values were then compared to directly measured values, and the comparisons were quite satisfactory and showed that the system obeyed microscopic reversibility. A three-parameter expression was evaluated for k-2 that is valid over the temperature range 250-2581 K. Hence, it can be concluded that the rate behavior for the protonated forward and reverse reactions is well-understood. A comparison of the experimental results for the protonated case2 with recent theoretical calculations4 was moderately successful; however, theoretical success was clouded by the fact that the parametrized fitSto the ab initio potential energy surface6 was not adequate in certain regions of potential energy space. Since the publication of these studies, a new and more accurate ab initio calculation has been carried out.' This calculation obviously has implications regarding the dynamics of reaction 2, and a new theoretical estimate of the thermal rate behavior is therefore required. Since the potential energy surface is invariant with regard to isotopic substitution, studies of the title reaction, reaction 1, would also be helpful in assessing the accuracy of the theoretical predictions. This has supplied a motivation for the present study. Rate constants for reaction (l), k , , are presented between 1285 and 2261 K. These are compared to the protonated case, k2, and the isotope effect is found to be unity within experimental error. Then k , and k2 are theoretically estimated by conventional
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( 1 ) Madronich, S.; Felder, W. J . Phys. Chem. 1984,88, 1857. (2) Michael, J. V.; Sutherland, J. W. J . Phys. Chem. 1988, 92, 3853. (3) Chase, M. W., Jr.; Curnutt, J. L.; Downey, J. R., Jr.; McDonald, R. A,; Syverud, A. N.; Valenzuela, E. A. J . Phys. Chem. ReJ Data 1982, 1 1 ,
695. (4) Issacson, A. D.; Truhlar, D. G. J . Chem. Phys. 1982, 76, 1380. (5) Schatz, G. C.; Elgersma, H. Chem. Phys. Letf. 1980, 73, 21. (6) Walch, S. P.; Dunning, T. H., Jr. J . Chem. Phys. 1980, 72, 1303. (7) Kraka, E.;Dunning, T. H., Jr., Private communication.
0022-3654/90/2094-2465$02.50/0
transition-state theory. The basis of these theoretical estimates in the new ab initio potential energy surface by Kraka and Dunning.' Lastly, the experimental and theoretical results for forward and reverse rate constants are compared for both protonated and deuterated reactions.
Experimental Section The present experiments were performed with the flash photolysis-shock tube technique2**in a recently constructed appar a t ~ s . ~ The ~ ' ~ method utilizes atomic resonance absorption spectroscopy (ARAS), and therefore, atom-molecule reactions can be monitored by observing the time dependence of atomic concentration. Since the techniques and apparatus have been discussed previously, only a brief description of the system, along with those features unique to the current experimental procedures, will be presented here. Apparatus. The apparatus consists of a 7-m (4-in. 0.d.) 304 stainless steel tube separated from the He driver chamber by a 4-mil unscored 1100-H18 aluminum diaphragm. The flanges throughout are "Conflat", and the system is always pumped to lo-* Torr between each experiment with an Edwards Vacuum Products Model CRlOOP packaged pumping system. The velocity of the shock wave is measured with eight equally spaced pressure transducers (PCB Piezotronics, Inc., Model 1 13A2) mounted along the end portion of the shock tube. The transducer signal is differentiated and recorded on a 4094C Nicolet digital oscilloscope. The pulse from the first transducer also initiates a master pulse which controls the triggering of the oscilloscope and the N2 flash lamp. The flash lamp is mounted axially on the end plate, and its output passes through a Suprasil filter and a 2411. MgF2 planoconvex lens into the photolysis region. The photometer system is radially located 6 cm from the end plate. All optics are MgF2. The resonance lamp beam transverses the tube, being detected by an EMR G14 solar blind photomultiplier tube. For spectral isolation of Ly,D, a continuous flow of dry air passes between the exit lens and the photomultiplier. In order to monitor D atom depletion due to reaction 1, a deuterium resonance lamp was constructed. Ly,D was produced by a 2450-MHz microwave discharge operating at 40 W in a 2-Torr flow of 5-10 ppm D2 in He. The lamp was cooled by a constant air flow giving a Doppler temperature of -450 K. These
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(8) (a) Michael, J. V.; Sutherland, J. W.; Klemm, R. B. I n r . J . Chem. Kinet. 1985, 17, 315. (b) Michael, J. V.;Sutherland, J. W. Ibid 1986, 18, 409. (c) Pirraglia, A. N.; Michael, J. V.; Sutherland, J. W.; Klemm, R. B. J . Phys. Chem. 1989, 93, 282, and references cited therein. (9) Michael, J. V. J . Chem. Phys. 1989, 90, 189. (IO) Michael, J. V.; Wagner, A. F. J . Phys. Chem., in press. - 1990 American Chemical Society 0
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The Journal of Physical Chemistry, Vol. 94, No. 6, I990
Fisher and Michael
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Figure 1. Plot of transmittance versus time in the photolysis of acetylene and acetylene-d,. The initial fast decrease is the flash lamp tail. The acetylene concentration is (1 .OO f 0.03) X loi5 and T, = 900 f 10 K. The flash lamp is unfiltered and operates at 98 J. (a) Ly,D lamp attempting to detect H atoms from C2H2;(b) LY,Dlamp with C2D2;(c) Ly,, with C2H2;(d) Ly,H with C2D2.
t/ms Figure 2. Absorbance versus reaction time for two consecutive H + D, experiments at 970 f 10 K. D atoms are detected with the Ly,D lamp, and H atoms (inset) are monitored by using the Ly,H lamp. [H20]= (1.10 f 0.02) X loi5 cm-) and [Dz] = (4.96& 0.05) X 1015 The solid line is determined from a chemical simulation, as discussed in the
conditions are quite similar to those in the Ly,H lamp used previously,2," and thus, a near-Doppler shape is expected for the D atom lamp. In this case Beer's law rigorously hold even to low transmittances ( T z 0.1). Since the transmittance values were never
