T H E
J O U R N A L OF
SICAL CHEMISTRY
Registered in U . 8. Patlent Ofice
@ Copyright, 207'2, by the American Chemical Society
VOLUME 75, NUMBER 2 JANUARY 21,1971
A Complemenitary Shock Tube Technique Study of the Exchange en Chloride and Deuterium1 by It. D. Kern, Jr.,* and G. G. Nika2 Department of Chemistry, Louisiana State Universitv in New Orleans, New Orleans, Louisiana (Rect!ived August 10, iQ70)
YO13.8
Publkatwn costs assisted bu the National Science Foundation
Kinetic data for the homogeneous exchange of equimolar mixtures of hydrogen chloride and deuterium in the presence of a n inert gas diluent were obtained by the analysis of infrared emission profiles of HC1 and DC1 and time-resolved mass spectra of m/e 36 and 37. The reaction was studied behind reflected shock waves over a temperature range of 1700-2800°K, a total density variation of 1.7-4.0 X 10-6 mol/cm3, and observation times of 500-750 Msec. Equilibrium amounts of HC1 and DC1 were observed in several of the experiments performed a t higher temperatures. Both argon and neon were used separately as diluents. The results from the infrared emission shock tube and the time-of-flight mass spectrometer shock tube were in agreement within one standard deviation of the Arrhenius plots. The rate of product formation was found to be nonlinear with respect to time. The formation of the mole fraction of DC1 ( ~ D C I = [DCl]t/[HCl]o) using both sources of data is represented by the equation (1 ~ D C I [ ~ ( ~ E C I / ~ D C I ) = ~ ~ ]exp(-k[M]t2), ) where k = 1016J2~o.80 exp(-34,340 i. 3130/RT), cms mol-l.sec-3. When the rate is expressed on a concentration basis, the combined order dependence of the reactants was shown to be consistent with a value of one. The difficulties in explaining the rate lam in terms of an atomic or molecular mechanism are discussed.
-
Introduction Isotopic exchange reactions have been examined by the shock tube technique forseveralyears, and the interpretation of the experimental rate laws has generated considerable theoretica1 interest. Bauer and his group a t Cornel1 IJniversity have studied many systems involving deuterium and other simple molecules with the single pulse ahock tube as have Burcat and LifHzS,30NH3, 3d,e shitz. The exchange of Dzwith H2,38,b and C H 4 3 f are charasterized by activation energies that are lower than predicted by an atomic or molecular mechanism. The rate of product formation was dependent upon the inert, gas concentration. These experimental results along with vibrational relaxation data of led to the postulation Kieffer and Lutz for HZ4*and D24b of a wibrational excitation mechanism for the exchange process.3a Other exchange reactions studied by the
+
+
+
single pulse technique include 3oN2 2sNz,3g 12C180 1 0 6 0 , 3 h 3202 3602,8i and CH4 CD4.3j
+
+
(1) Support of this work by the National Science Foundation under grant GP-23137 and also funds for equipment from NSF Departmental Science Development Program GU-2632 are gratefully acknowledged. Funds for the construction of the infrared emission shock tube from PRF Grant No. 1028-G2 were most appreciated. (2) NDEA Fellow. (3) (a) S. H. Bauer and E. Ossa, J. Chem. Phys., 45, 434 (1966); (b) A. Burcat and A. Lifshitz, ibid., 47, 3079 (1967); (c) A. Burcat, A. Lifshitz, D. Lewis, and S. H. Bauer, ibid., 49, 1449 (1968) ; (d) A. Lifshitz, C. Lifshitz, and S. H. Bauer, J. Amer. Chem. Soc., 87, 143 (1965); (e) A. Burcat and A. Lifshite, J. Chem. Phys., 52, 337 (1970); (f) W. Watt, P. Borrell, D. Lewis, and S. H. Bauer, ibid., 45, 444 (1966); (g) A. Bar-Nun and A. Lifshitz, ibid., 47, 2878 (1967); (h) A. Burcat and A, Lifshitz, ibid., 51, 1826 (1967); (i) H. F. Carroll and S. H. Bauer, J. Amer. Chem. Soc., 91, 7727 (1969); (j) A. Burcat and A. Lifshitz, J. Chem. Phys., 5 2 , 3613 (1970). (4) (a) J. H. Xiefer and R. W. Lutz, ibid., 44, 668 (1966); (b) J. H. Kiefer and R. W. Lutz, ibid., 44, 658 (1966).
171
R. D. KERN,JR.,AND G. G. NIKA
172 Exchange reactions involving l8O2 and 1 6 0 2 , CO,6* SO2, and C026bhave been reported by Kistiakowsky and his coworkers. The Harvard group used a timeof-flight mass spectrometer (TOF) coupled to the shock tube and observed a nonlinear time dependence for product formation with and without added amounts of NzO. An important finding was that even though the experimental activation energies were low with respect to an atomic mechanism, there was other considerably persuasive evidence that the exchange was dominated by three-center reactions. For example, addition of 0 atoms to the " 0 2 CO exchange5"via NzO led to rate constants which were consistent with rate constants obtained in the absence of iY20,assuming an atomic mechanism. A quadratic time dependence for product formation was determined. The exchange reaction that has received the most attention from theoretical considerations is H2 Dz. Xn two recent papers,O the calculation of the potential energy barrier to a four-center transition complex has been accomplished for this exchange and in all of the geometric configurations that led to products, the potential energy barrier was higher than that demonstrated by the three-center transition complex mechanism. Hence, according t o these calculations, the energetics of a homogeneous atomic mechanism (110 kcal/mol) are more favorable than that of a molecular mechanism ( 2 14 8 kcal/mol) . When comparison is made with the experimental value of 42 kcaI/mol for the H2-D2 reaction,3athe need for proposing a mechanism other than atomic or molecular is apparent. The nature of the single pulse shock tube technique is such that the time dependence of product formation cannot be easily determined. It was assumed to be linear.a The purpose of this work is to study an exchange reaction similar in many respects to H2 D2. The bond energy of HCI (102.3 kcal/mol) is very close to that of Bz(103.1 kcal/mol) although shock tube work on the dissociation of these two molecules yields quite different values for the activation energy of the dissociation pro817ckcal/mol for HC1, and 97 kcal/mols for cess: '70,7*,b H2. The time dependence of DC1 formation is of particular interest. Two independent and dynamic techniques may be used to monitor the HC1-D2 system: infrared emission and time-of-flight mass spectrometry. The application of these techniques to the same reaction system in the past (e.g., pyrolysis and oxidation of ethylene) has supplied important corroborating kinetic data. The comparison of data obtained from infrared emission profiles and the time-resolved mass spectra is particularly useful as a prelude to an investigation of the HZ$- Dziexchange since the TOF-shock tube combination is the only praubing. Four thin film velocity gauges are spaced at 20-cm intervals. The distance from the gauge which is closest to the end wall to the reflecting surface is 17.3 cm. The signals from the velocity gauges are recorded on the raster scope previously described. The signal from the last gauge is also fed into the time delay circuitry of a Tektronix 535 A oscilloscope, delayed for a selected time, and then used to trigger a multiple scan system16 whose function is to space a given number of successive mass spectra on the screens of four Tektronix 531 A oscilloscopes equipped with Type G plug-in units. Photographs of the spectra are taken with Polaroid 10,000speed film. The mass spectrometer is a Bendix Model 14-107, modified to operate in the range 30-50 kHz, and operated with a 100-cm drift tube for shock tube experiments. The mass spectra signals are increased by a lleithley Xodel 109 pulse amplifier. Bendix analog units are used to analyze the test gas in its preshock state. The various peak heights are monitored by a Clevite Mark 220 dual channel recorder. The shocked gas is htroduced into the ion source of the TOF through a reentrant nozzle,” the shape of which was pressed into a thin copper disk. The diameter of the hole is 3.7 mils and was drilled with a jeweler’s bit and press. Ballast volumes of approximately 5-1. capacity each are attached above and below the TOF ion source cross. A cold cathode gauge is mounted in the upper ballast volumne. The lower ballast volume is connected to a 3-in. i.d. stainless steel bellows which leads to a CVC modular pumping system Type PAS-41C backed by a Cenco mechanical pump Model Hyvac 14. The 4-in. oil diffusion pump is charged with Convalex-10 fluid which does not contribute an observable amount t o the background mass spectra. Typical ultimate vacuums are: 1 X Torr in the shock tube (NRC ionization gauge Type 563-SP, NRC control 7’201, 5 X 10-7 Torr in the ion source ballast volume (NRC cold cathode gauge 524-2, s k c control 8521, and 2 X Torr in the TOP liquid nitrogen trap chamber (Veeco ionization gauge RG 75K, Bendix TOF vacuum gauge control). Addition of 5 Torr of a typical gas mixture (neon diluent) to the shock Lube raises the latter two pressures t o 4 X and 1 X 10-6 Torr, respectively. Outgassing rates in the TOF shock tube are less than 0.01 p/min. The gas handling system is similar to the one deThe Journal of Phvsical Chemistrg, Vol. 7 6 , No. 9, 1971
R. D. KERN,JR.,AND G. G. “A scribed for the ir shock tube. An ionization gauge is used rather than a McLeod gauge and a Toepler pump has been added. Signal-Concentration Ratio. A series of nonreacting mixtures was prepared to test the linearity of signal (TOF and ir) vs. reactant concentration. Matheson hydrogen chloride (99.0%) was purified by two liquid nitrogen bulb-to-bulb distillations, the middle fraction was accepted a t each stage. Liquid Carbonic argon (99.998%) was used as received as the diluent in the infrared experiments and was present at a 1% level in the TOF runs. Matheson research grade neon (99.995%) without additional purification was the diluent for the latter experiments. Reacting mixtures were prepared by addition of appropriate amounts of Matheson CP deuterium (99.5%). Nass spectrometric analysis of each gas indicated an impurity level for oxygen and chlorine indistinguishable from background. Rlixtures were allowed to stand 29 hr prior to use. Mass analysis of each mixture was performed with particular attention to oxygen content. Reference mixtures of various 0 2 compositions were prepared to establish the impurity levels of the test mixtures. I n all mixtures, the 0 2 content Kas found to be less than 25 ppm. This level \vas attributed to the TOF-shock tube system. Individual experiments performed on the TOF facility were first analyzed for 02 content followed by analysis of the test gas. No experiment was performed at an O2 level greater than 25 ppm. An exception to this statement was a series of runs performed on a. reacting mixture that contained a small amount of oxygen. The runs on the infrared facility were accomplished under the condition of an outgassing rate 50.5 p/min. Diaphragm rupture was initiated in all experiments in a time interval of less than 1 min after introduction of the mixture into the test section. The selection of appropriate infrared interference filters to monitor the fundamental vibrational-rotational envelopes of HCl and DC1 mas facilitated by a computer calculation of the envelopes as a function of temperature. The anharmonic oscillator, nonrigid rotator approximation was used.l* The intensities of the rotational levels for the first five vibrational energy levels were calculated as a function of temperature. Two Infrared Industries interference filters were selected with the following center wavelengths: 3.25 p (HC1) and 5.05 p (DC1). Both filters exhibited a half-band width of 0.1 p. (16) D. McL. Moulton and J. V. Michael, Rev. Sci. Irkstrum., 36, 226 (1965). (17) G. P. Glass, G. B. Kistiakowsky, J. V. Michael, and H. Niki, Sump. (It.)Combust. loth, 513 (1965). (18) G. Herzberz. “Molecular Saectra and Molecular Structure. I. ’Spectra of Diatomic Molecul&” D. Van Nostrand, Princeton, N. J., 1965. (19) S. S. Penner, “Quantitative Molecular Spectroscopy and Gas Emissivities,” Addison-Wesley, Reading, Mass., 1959.
175
EXCHANQE O F HYDROQEN CHLORIDE AND DEUTERIUM
[HCi]
x 10." lmolecules I m ' )
Figure 1. Calibration plot of ir detector signal (mV) of emission at 3.25 p vs. HCI concentration at a temperature of approximately 2400'K.
The results of calculations a t 250O0I< indicated a partial overlap between the P branch of HC1 and the R branch of DCI, particularly with the first two HC1 vibrational levels. A series of experiments in which mixtures of HC1 (l%, 2%) in Ar were shocked revealed the HC1 contribution to the 5.05-p signal. This contribution was recorded as a function of HCI concentration and temperature and was used to correct the emission profile observed a t 5.05p for reaction mixtures in a manner to be described in the data reduction section. Figure 1 displays the linearity of the emission signal at 3.25 p as a function of HCI concentration, Similar plots were constructed for the HCI contribution to the 5.05-p filter. The calibration runs established the risetime for the infrared detector-amplifier system to be 7.5 psec which is in agreement with the manufacturer's specifications. Similar calibration experiments were conducted with the TOF apparatus. A diluent of r\'e-l% Ar was employed along with an electron beam energy of 30 eV. A linear relationship was observed between the ratio of the peak heights of m/e 36:40 and the concentration of HCI. Temperature Determination. Shock velocities decelerated in both shock tubes. The time that it took the shock wave to pass each gauge showed an increase with increasing distance, a typical increase being on the order of 1 psec/20 cm. The increase !vas extrapolated from the last velocity gauge to the respective observation station; the center of the slits for their shock tube, the end wall for the TOF facility. The physical properties for the reflected zone using ideal shock approximations were calculated on a PD1'10 computer. Thermodynamic data were taken from the JAXAF Thermochemical Tables.l' Corrections for nonideal behavior due to the endo- or exothermicity of a reactionswere not necessary for this thermoneutral system. Hydrogen was used as the driver gas.
W
I c
MASS Figure 3. Tracing of TOF experimental record from first two of four carnews. Equimolar mixture in neon reacting at 2480'K. Mass spectra repeated at 20-wec intervals.
Runs at the higher temperatures achieved an cquilibrium condition within the available observation times. Calculation of the equilibrium constant for the HCI-D, exchange as a function of temperature \vas accomplished with statistical thermodynamic formulas, and theresults were used to compare the computed ratio of DCI:HCI at equilibrium to the observed ratio.
Results Experimental records from the infrared emission and TOF shock tubes arc displayed in 1;igures 2 and 3, respectively. A total of four picturcs was taken for each TOP run. Figure 3 is composed of the first two pictures only. (20) "JANAF Thermochemical Tahles." The Dow Chemical Company, Midland, Mieh.. 1965.
The Jottmol o f P h y s i m l Chcmislrv, Vol. 76. No. 8, 1971
R. D.KERN, JR.,AND G. G. “A
176
Data Reduction. The data from both sources were reduced according to the equation
{ 1 - fDCl[l
+ (fHCl/fDCl)eql] exp[-k’(t -
tind)’]
(1)
where fDCl is the mole fraction of DCl ([DCl]/ [HClIo), is the induction time for product formation, and x is the power dependence of the reaction time. There is no evidence for an induction period over the temperature range of the experiments, 1700-2800°K. Support for this statement is given after the treatment of the emission profiles is described. Nonreacting mixtures of HC1 (1%) 2%) in Ar were shocked in conjunction with reaction experiments. The emission signals from the 3.25-and 5.05-11. filters were plotted as a function of temperature. From these plots the average signal from HC1 at each filter was obtained at the temperature of a reaction experiment. Presence of the HC1 contribution at 5.05 p prompted calculation of the DC1 mole fraction on three bases. The “HC1 basis” and “DC1 basis” correspond t o individual treatments of the 3.25-and 5.05-p signals respectively, while the third basis is a point by point average of the first two. Each experiment was accompanied by a calibration run at approximately the same temperature. The signal heights were measured relative to a baseline generated by the quiescent detectors. The measurements were made at 9-psec intervals with the aid of a Stereozoom microscope and a graduated reticle. The precision of the readings was f0.05 mV. A computer program was written to manipulate the 360 points generated from each experiment and to adjust the points for the effect of parallax. The points for the DC1 basis had to be corrected for the HCl contribution at 5.05 1.1. The points at early times for the HC1 basis were extrapolated to a time zero condition with the help of the calibration plots. At the higher temperature runs, an equilibrium condition was observed and by using the calculated ratio of (DCl/HCl),,, a value of HC1 a t time zero was derived. Calibration runs with DC1 wcre not performed and hence [HCllo on a DCl basis could only be calculated. Early times of the reaction (0-100 psec) were observed by recording the vertical signal out from the first oscilloscope on a second oscilloscope set a faster sweep speed, 10 or 20 psec/cm. Treatment of the signal from the 5.05-p filter on the DC1 basis described above revealed the absence of a measurable induction period. Points up to 100 psec were analyzed with an expanded form of eq 1
kind
A preliminary value of z was obtained by plotting log fDCl us. log t and determining the slope. An initial The Journal of Physical Chemistry, Vol. 76, No. R, 1971
TIME (usec) Figure 4. Infrared profiles calculated using different time dependencies for a. run a t 2535°K: X, experimental points; - (uppermost), t 2 plot; - -, t 1 . 5 ; - (lower), t l .
-
+
guess for kobsd ( = k’/[l (fKCl/fDCl)eq])was obtained and by plotting fDC1 vs. t raised to various powers: 1, 2. Reproduction of an emission profile is depicted in Figure 4 for selected powers of x. Finally, a value for x was derived from plots of the log of the left-hand side of eq 1 us. log t. The best fit value of z from these sources was about 1.7. The profiles mere reproduced satisfactorily with ai1 exponent of 2. A quadratic time dependence can be related to an atomic mechanism as will be shown in the Discussion section. A nonintegral time dependence does not have a direct relationship t o any simple mechanism. A series of calculated profiles was constructed for various values of k’ and matched with experimental profiles to derive an initial guess for IC’. The computer then searched for the value of IC’ that reproduced the profile with the lowest standard deviation. Rate constants were calculated for each of the three bases. The differences were not significant, and rate constants are reported here using the average basis. Doubling the total initial reactant concentration did not affect k‘; doubling the total density doubled the value of the rate constant. Hence, le’ equals Ic[;\lI] where [MI is the total concentration of the shocked gas in mol cm-3. The total order of the reaction is two; the individual orders are first order with respect to the total density and a combined order dependence of one for the reactants €IC1 and D, when the rate is expressed on a concentration rather than mole fraction basis. An Arrhenius plot of the 2% HC1--2% Dz mixture in argon is presented in Figure 5 . The TOF data were reduced by measuring the peak heights of m/e 36, 37, and 40 at 20-psec reaction time intervals. The sum (E)of the ratios of 36:40was fit to the equation C=mt+b
(3)
where tis the reaction time in microseconds. The slope
EXCHANGE OF HYDROGEN CHLORIDE AND DEUTERIUM
lo4/ T
177
Figure 7 . Arrhenius plot of 2% EIC1-27, Dt mixture in neon, PI = 5 Torr, T O P experiments: log A = 16.03 d= 0.42; E* = 33.95 It 4.40 kcal mol+.
(OK)
Figure 5. Arrhenius plot of 2% HC1-2% Dg mixture in argon; P1 = 5 Torr; infrared emission experiments: log A = 16.45 =k 0.47; E* = 36.31 =k 4.90 kcal mol-'.
I
0
Nozzles with slightly smaller holes are being constructed to overcome this trouble. The points were fit with a quadratic time dependence profile. A first-order dependence on [MI was assumed, and an Arrhenius plot of a 2% HCl-27, Dz mixture in Ne-l% Ar diluent is depicted in Figure 7 . Runs performed in the region 2480--2715°K indicated that the reaction had reached an equilibrium state. The ratio of m/e 37 :36 achieved a constant value of 2.2 which is greater than the square root of the calculated equilibrium constant ( K = 1.86). The observed ratio is understandable when account is taken of the selfexchange of HD
D~ 0
100
200
300
400
+HC~
.I/ '/d&+ '/zDz
500
TIME ( p s e c ) Figure 6. Fit of quadratic time dependence profile to TOF data taken a t 2525'8: 0 , experimental points; -, calculated.
m had a negligiblo value, and the intercept b was equal essentially to [36;4010,thus providing important checks on the apparatus and experimental technique. The mole fraction of DC1 was determined at each point by dividing 37:40 by the sum. Calculation of IC' was similar to the method described previously, and a fit of the experimental points to the profile is shown in Figure 6. Initial reactant concentrations were varied twofold with no apparent change in k'. The total density was not varied since o!peratioraal difficulties were experienced when an initial pressure of 10 Torr was shocked.
+
D C ~ HD
Writing the equilibrium expression for the D2-HC1 system jn the form =
(E)eps)eq
and using the calculated value of K , the ratio (HD/D!& has a value of 0.85. By employing the equilibrium constant for the self-exchange reaction, K = 4, the ratio of (HD/H2)eqis calculated to be 4.71. Agreement with the observed ratio was obtained by writing gram atom balance equations for equimolar amounts of Dz and HC1, making use of equilibrium constants, and solving for (DCl/HCl),,. Further support was gathered by the simultaneous recording of The Journal of Physical Chemistry, Vol. 76, No. 2, 1971
R. D. KERN,JR.,AND G. G. "A
178
104/T ( " K I
1 0 ~( O K1) ~
Figure 8. Comparison of dissociation rate constant data from T O F ((3) to extrapolated Arrhenius line from ref 7a.
m/e 2, 3, 4, 36, 37, and 40. The growth of m/e 2 was observed during the reaction process. A van% Hoff plot of (DCl/HCl),, was constructed over the temperature range covered by these experiments. Approprit,& values were substituted into eq 1 for all of the TOF and ir emission runs. A series of experiments with nonreacting mixtures of HC1 and Ne-1% Ar revealed a small decrease in the ratio 36:40 which may be attributed to the dissociation process, For a given run, values of the ratio R were fit to the equation fi = Ro
+ mt
(4)
by the method of least squares. The slopes in all but two runs21 had small negative slopes. These slopes can be related to the dissociation process by expanding the rate law
HCl/'HClo
=
= 1
- rlcl[n/l]t
(5)
and identifying m with -HCl&[M]. The results of several runs are plotted in Figure 8 and may be compared with an extrapolated Arrhenius plot.'" The scatter of the points is too great for them to be considered as kinetic data, but the experiments demonstrate results that we not inconsistent with previous work. A series of experiments were performed with the TOF on a 2(& HC1-2% Dz mixture into which had leaked a small quantity of oxygen. Mass analysis placed the level of iinpurity at approximately 150 ppm. Several observationn were at variance with eq 1. The higher temperature runs yielded values for the ratio (DCl/HCl),, 2 3. The mixture was diluted twofold, and the order with respect to reactant concentration The Journal of Physical Chemistry, Vol. 76,No. 8, 1971
Figure 9. Arrhenius plot of data in Table I: Al B; V, C; X, D; 0, E.
al mixture A;
was found to be zero. An activation energy of 18 kea1 mol-' was calculated. The results of the exchange experiments ([O,] < 25 ppm) are listed in Table I. An Arrhenius plot of the rate constants in the table is shown in Figure 9. Leastsquares treatment of the data yielded values of log A = 16.12 f 0.30 and E* = 34,340 f 3130 cal mol-l.
Discussion The results for the D2-HCl system are compatible with previous work on exchange reactions in which "low" activation energies have been determined3s6and also with the reporting of quadratic time dependence for product formation when the experiments were conducted with a dynamic sampling techniquea6e22 An atomic mechanism provides an explanation for the quadratic time dependence but requires an activation energy on the order of 77-110 kcal mol-'.
+ il1 "dt. 2D + &/I H C l f M -% H + C1 i- M H + Dz HD + D D2
(a) (b)
kexi
(e>
k0X-l
k W
D
+ HC1 _r DC1+
H
kex-2
Neglecting the back reactions
(21) These runs had small positive slopes. (22) 1. D. Gay, G. B. Kistiakowsky, J. V. Miohael, and H. Niki, J. Chem. Phys., 43, 1720 (1965).
EXCHANGE OF HYDROGEN CHLORIDE AND DEUTERIUM
179 CD I t = 2 b 1 ID2 Io [M It
Table I k
T6, Mixture
OK
P6
x
108,
mol cm - 8
x
10-11,
cma 11101-1 Bec - 2
Infrared 1849 2099 2157
1.76 1.86
1.88
13.7 37.4 62.8
2251 2277 2312 2436 2535 2806
1.91 1.92 1.93 1.97 2.00 2.07
181 57.3 94.7 184 218 355
B. 1% HCl-l% %)z PI= 5 Torr
1932 2014 2322 2437 2485 1994 2099 2149
1.76 1.79 1.89 1.93 1.94 3.64 3.72 3.76
36.0 33.5 49.1 57 1 247 25.0 48.1 97.2
c.
2149 2181 2230 2260 2290 2298
3.76 3.78 3.81 3.83 3.85 3.86
35.4 43.7 50.4 44.9 120 78.6
2384 1714 2066 2082 2098 2141 2159
3.91 1.70 1.92 1.93 1.93
144
2273 2273 2294 2369 2388 2481 2516 2523 2670 2780 1797 1831
1.99 1.96 1.93 1.91 1.96 2.07 2.00 1.92 2.08 2.07 1.70 1.71
36.5 92.4 41.2 164 77.1 176 125 88.2 115 353 13.7 37.4
2028 2073 2121 2208 2291 2548 2713
1.79 1.85 1.90 1.89
62.8 181 57.3 94.7 184 218 355
Argon diluent
A. 2% HCl-2% PI = 5 Torr
p32
2% 13C1-2% Dz PI = 10 Torr
1.88 1.92
1.88 1.96 2.08
(9)
The first-order dependence on [MI appears as does the quadratic time dependence. The activation energy is the sum of the activation energies for reactions a and d which is on the order of 100 kcal mol-'. If the atoms are generated via (b) and (e), the predicted activation energy would be 77 kea1 mol-'. This prediction uses the experimental value of 70 kea1 mol-' attributed to the dissociation of HCl.' A chain reaction involving vibrational energy transfer (the superscript v denotes one or more quanta of energy) may involve the following steps
HC1
+M
-
HClV
k0Xl
+ HC1= HDV+ D2
D2v
TOF Ne-l% Ar diluent
(8) Using published values of kd1,* it can be shown that the time required to attain an equilibrium amount of deuterium atoms via reaction a is much longer than the observed time for the exchange reaction to reach equilibrium. Substituting for [D]in eq 6 with eq 8 and integrating
7.08 21.2 12.5 44.6 46.6 34.2
Approximating [Dal1 'v [Dzlo, and substituting into the following equation and integrating
(7)
+ 31
+ HDV H D + DZv
DC1
(f)
(g)
(h) Other combinations are possible and the partitioning of the vibrational energy may be varied. A quadratic time dependence may be derived if the following approximations are valid
Reaction e may be taken to be a sequence of reactions in which the quanta are exchanged in a ladder climbing process. The vibrational relaxation times for reactions e4 and f Z ahave been measured for the transition 0 -+ 1 and are very much shorter than the observation times here. Hence, the assumption involved in the integration of eq 11 and its subsequent substitution to yield an equation with a quadratic time dependence is not valid. The absence of an induction period may also be explained by the short relaxation times. A direct four-center molecular exchange complex mechanism is rejected because of the requirements of zero-order dependence on [MI, an activation energy in (23) (a) W. D. Breshears and P. F. Bird, J. Chem. Phvs., 50, 333 (1969); (b) C. T. Bowman and D. J. Seery, ibid., 50, 1904 (1969); (c) P. Borrell and R. Gutteridge, ibid., 50,2273 (1969).
The Journal of Physical Chemistry, V'ol. 76, N o . 8, 1972
R. D. KERN,JR.,AND G. G. NIKA
180 the range of 6024kcal mol-l or perhaps higher16and a linear time dependence, all at variance with the results. Other mechanisms which invoke steady-state approximations are not acceptable because of the observed nonlinear time dependence. The appearance of H2 in the TOF experiments supporta either :tn atomic or molecular mechanism. Hydrogen may hc formed via atom-exchange reactions or the self-exchange of HD. The latter has been studied by the single pulse shock tube technique,26and the activation energy was determined to be 35.9 f 2 kcal mol-l. It is noted that tht: activation energies associated with all of the exchange reactions in the HCl-Dt system are similar. The order for thie HCl-Dt exchange is the least accurately determined quantity in this study. The data are clonsistent with the whole numbers reported here. A combined order of two for the reactant gases was tried and produced lesser agreement between the mixtures having B twofold difference in reactant concentrations than a combined order of one. The inert gas dependence was determined only with the ir emission technique because of previously mentioned difficulties with the TOF a t etading pressures of 10 Torr. No attempt was made to establish individual orders for HC1 and Dz. The overall order is taken to be two, a value consistent with previouij work on other exchange systems. Thc agreement of the kinetic results derived from both techniques is within one standard deviation. The values for log A arid E" are 15.83 f 0.31 and 16.56 f 0.47 and 32.58 A 3.21 and 37.50 f 4.78 kcal mol-' for
The .Journal
of
Physical Chemistry, Vol. 76,No. 2 , 1971
the TOF and ir, respectively. The experiments with Ne indicate a lower rate than those with Ar diluent, although this difference is not definitely established because of the magnitudes of the standard deviations. The sampling process is quite different, however, and the agreement attained is encouraging. T t may be argued that both the TOF and ir techniques are analyzing gas that is too closely associated with the end wall. Other workers have successfully employed vacuumultraviolet light absorption to measure rates of dissociation at a distance 3.0 mm from the end which is comparable to the distance used herein. An atomic mechanism can be written to accommodate a nonlinear time dependence for product formation, but the activation energy is much too low. The energetics involved with the dissociation reactions,s particularly the hydrogen halide^,^!^^ and the exchange reactions are indeed puzzling.
Acknowledgments. The assistance of Mr. Darryl Olivier and N!r. Joseph McPherson in the construction of the apparatus is greatly appreciated. The authors wish to thank the L.S.U.N.O. Computer Research Center (NSF Grant No. GP-2964 and GJ-131) for financial assistance. (24) S. W. Benson and G. R. Haugen, J . Amer. Chem. Soc., 87, 4036 (1965). (25) D. Lewis and S. H. Bauer, ibid., PO, 5390 (1968). (26) (a) J. P. Appleton, M. Steinberg, and D. J. Liquornik, J . Chem. Phys., 48, 599 (1968); (b) ibid., 52, 2205 (1970). (27) R. R. Giedt, N. Cohen, and T. A. Jacobs, ibid., SO, 5374 (1968).
