Isotope Effects in Gas-Phase Chemistry - American Chemical Society

Chapter 6

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on April 17, 2018 | https://pubs.acs.org Publication Date: September 8, 1992 | doi: 10.1021/bk-1992-0502.ch006

Isotope Effects at High Temperatures Studied by the Flash or Laser Photolysis—Shock Tube Technique J. V. Michael Chemistry Division, Argonne National Laboratory, Argonne, IL 60439

During the past five years, the flash or laser photolysis-shock tube (FP or LP-ST) technique has been used to measure absolute thermal bimolecular rate constants in a previously difficult temperature range, ~700-2500 K. The technique is described. Protonated and deuterated versions of six reactions have been studied to date. The reactions are C H(C D) + C H (C D ), Ο + C H (C D ), H(D) + O , H(D) + H O(D O), Ο + H (D ), and D(H) + H (D ). These results are reviewed. In many cases the high temperature results can be combined with lower temperature results, and the experimental isotope effects can then be determined over a very large range of temperature. For one of the cases to be discussed, namely the isotope effect between D + H and H + D , the range of temperature is from ~2002000 K . This large range then gives an unprecedented opportunity for experimental comparison to theoretical predictions of isotope effects since data now exist (a) at low temperatures where quantum mechanical tunneling predominates and (b) at high temperatures where tunneling is unimportant. 2

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The flash or laser photolysis-shock tube (FP or LP-ST) technique for studying thermal bimolecular reaction rates was originally envisioned by Burns and Hornig (7). Following this pioneering work, Zellner and coworkers (2,3) studied three OH-radical with molecule reactions. The use of atomic resonance absorption spectroscopy (ARAS) for atomic detection in such experiments is relatively recent and started about five years ago (4£). Subsequently, the technique has been used on about twenty reactions (6) many of which are isotopic variations of the same reaction. These cases will be reviewed in this article. Since the method is useful at high temperatures, it can and has been used, along with lower temperature data sets, to extend the temperature range of a specific reaction thereby giving an accurate understanding of the rate behavior over a very large temperature range. For reactions in which Η-atoms are abstracted and which have relatively high activation energies, the technique can be used in a temperature range where tunneling is relatively unimportant. Hence, the measured activation energy relates directly to the barrier height on the potential energy surface for the given reaction. This feature of the results has recently been discussed in detail (7).

0097-6156/92/0502-O080S06.00/0 © 1992 American Chemical Society

Kaye; Isotope Effects in Gas-Phase Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1992.


6. MICHAEL

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Isotope Effects at High Temperatures

When absolute determinations are used for individual isotopic modifications of the same reaction, the derived isotope effect is calculated from the ratio of the absolute rate constant values. With any gas phase chemical kinetics method, this procedure is never as accurate as classical relative methods that are based on product analysis in systems where both isotopic reactions are simultaneously occuring. With the FP or LP-ST technique, the absolute accuracy of the results is typically between ±15 to 25%. Taking the square root of the sum of variances, the ratio value will be accurate to ±21 to 35%. When isotope effects approach unity at high temperature, it will be difficult with this technique alone to assess whether an isotope effect significantly different from unity actually exists. This is the reason that combinations of data sets with lower temperature results are desirable because the continuous changes in the kinetic isotope effect can be documented from low to high temperature. Experimental The FP or LP-ST technique has been described previously (7-7), and therefore, only a brief description of the method will be given here. Figure 1 shows a schematic diagram of the apparatus. The shock tube is of general design (8) and consists of a driven section that is separated from a driver section by a thin A l diaphragm. He is used as the driver gas, and the driven or test gas is predominantly A r with small quantities of added source molecule and reactant molecule. The source molecule is chosen so that on photolysis it will photodissociate to give the transient species that will subsequently be spectroscopically measured as it reacts with the reactant molecule. In some cases the source molecule and the reactant molecule are the same; eg., H + N H 3 ( 9 ) or H + H 0 (10). However, in most cases, two different molecules are used, and accurate determinations of their compositions in premixtures in A r are necessary. This is accomplished with capacitance manometric measurement. Experiments are performed behind reflected shock waves where the hot gas is effectively stagnant and not flowing. Flash or laser photolysis occurs after the reflected shock wave has gone past the spectroscopic observation station, the A R A S photometer system. Transient species are observed radially across the shock tube. Reflected shock pressure and temperature are kept sufficiently low so that concurrent thermal decomposition is minimized. Therefore, the initial transient species concentration will be totally controlled by photolysis, and its subsequent decay will be totally controlled by bimolecular reaction. Diffusion out of the viewing zone is negligibly slow on the time scale of the experiment. This experiment is then an adaptation of the well known static kinetic spectroscopy experiment with the reflected shock serving as a source of high temperature and density; \ e., shock heating is equivalent to a pulsed furnace. Pressure transducers, mounted at equal intervals along the shock tube, are used to accurately measure the incident shock wave velocity. Temperature and density in the reflected shock wave regime are calculated from incident shock velocities through well known relations and correction procedures (5,8,11) that take boundary layer formation into account. Since the initial mole fractions of the source and reactant components are known, the absolute concentrations of both species can then be determined in the reflected shock wave regime. In the A R A S adaptation of the method, atomic species are spectroscopically monitored as a function of time. H - (6,7,9,10), D- (12,13), O- (74,75), and N-atom (16,17) reactions have been studied by the technique. Beer's law holds if absorbance, (ABS), is kept low. Then, (ABS) = -ln(I/I ) (where I and I are transmitted and incident intensities of the resonance light, respectively) is proportional to the atomic concentration; i . e., (ABS) = c[A] l. σ is the effective cross section for 2

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ISOTOPE EFFECTS IN GAS-PHASE CHEMISTRY

Ρ

Figure 1. Schematic diagram of the apparatus. Ρ - rotary pump. D - oil diffusion pump. CT - liquid nitrogen baffle. G V - gate valve. G - bourdon gauge. Β - breaker. DP - diaphragm. Τ - pressure transducers. M - microwave power supply. F - atomic filter. R L - resonance lamp. A - gas and crystal window filter. P M - photomultiplier. DS - digital oscilloscope. M P - master pulse generator. TR - trigger pulse. D F - differentiator. A D - delayed pulse generator. L T - laser trigger. X L - excimer laser.


6. MICHAEL

Isotope Effects at High Temperatures

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resonance absorption by atom, A, and 1 is the path length. If the temporal behavior of species A is controlled by a bimolecular reaction, A + R, where R is the stable reactant molecule, then the rate of depletion of [A] will be given by the product of the bimolecular rate constant (kbi ), [R], and [A]. If [ R ] » [ A ] then the decay of A atoms will follow pseudo-first-order kinetics with the decay constant being given as k i s t kbim[R]. Because (ABS) is proportional to [A] , observation of the temporal dependence of (ABS) is sufficient to determine k i . Since [R] is known from the mole fraction and the final thermodynamic conditions as determined from the initial pressure and temperature and the shock strength, a value for kbim can be deduced from each experiment. Figure 2 shows a typical example of raw data and the derived first-order plot. The negative slope of the first-order plot ( k i ) is obtained by linear least squares analysis, and the value of kbim is determined by dividing by [R]. The results from many experiments are then usually displayed as Arrhenius plots, and, if curvature is not apparent in the results, a simple linear least squares line is derived from the composite set in order to describe the rate behavior over the experimental temperature range. It is also possible to carry out experiments with varying total density thereby measuring the pressure dependence of kbim i f such pressure dependence exists. This allows termolecular reactions to be studied with the method. m

=

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s t

st

Results and Discussion The FP or LP-ST results for six reactions are presented in Table I as Arrhenius expressions. The one standard deviation accuracy of the results and the temperature range of applicability is also given. The ratio of the results on isotopic modifications of the same reaction gives the high temperature kinetic isotope effect. To date, data have been obtained on three addition-elimination reactions (18-20) and on three H atom abstraction reactions (10,12,13,1521,22). C 2 H + C2H2 — C4H2 + H and C2D + C2D2 —· C4D2 + D. Rate constants

for these reactions have been measured with the LP-ST technique over the temperature range, ~1230 to 1500 Κ (20). The results are shown in Table I, and the kinetic isotope effect, KIE, is given by the ratio of k\\ to ko- The temperature independent result is 1.39 ± 0.40 indicating that an isotope effect different from unity is indeterminate. The absolute rate constants in both cases are fast, being about one half of the collision rate. The products of the reaction would strongly indicate that the reaction is a simple addition-elimination reaction, and therefore, the isotope effect would be secondary. Undoubtedly the initially formed adduct is vibrationally excited well above the dissociation energy for the forward process to diacetylene and H atoms, and therefore a large isotope effect would not be expected. This conclusion is corroborated by the experimental result Ο + C2H2 Products and Ο + C2D2— Products. Absolute rate constants have been measured for these reactions between -850 and 1950 Κ (18). Even though there are a significant number of lower temperature results for the protonated case, thereby allowing for an evaluation over the extended temperature range, 200 to 2500 Κ (18,23), comparable data do not exist for the deuterated case. Therefore, the kinetic isotope effect can be evaluated from only the FP-ST data at high temperature. The Arrhenius expressions that describe the results are presented in Table I, and the K I E is, KIE = 1.03 exp(26K/T).

(1)

Equation (1) gives 1.06 for 8 5 0 ^ 1 9 5 0 Κ with an error of - ± 3 0 % , and this indicates that the isotope effect is unity within experimental error.


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ISOTOPE EFFECTS IN GAS-PHASE CHEMISTRY π

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Isotope Effects in Gas-Phase Chemistry - American Chemical Society

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