HYDROGEN-DEUTERIUM EXCHANGE REACTION
The Hydrogen-Deuterium Exchange Reaction. I.
45
63P, Mercury Photosensitized
by H. Niki,'. Yves Rousseau,lband Gilbert J. Mains Department of Chemistry, Carnegk Institute of Technology, Pittsburgh, Pennsylvania (Received April 19, 1064)
16215
The kinetics of the 3P1 Hg-photosensitized Hz-Dz exchange is described by the differential rate law, d(HD)/dt = A - k(HD). The photostationary constant, Qm = (HD)2/(H2). (D2),at 25' is a function of initial H2-D2 ratio, the total pressure in the range 0.2-30 cm., and surface-to-volume ratio, and is larger than the equilibrium constant, K . Initial rate studies of the forward reaction at 25' as a function of H2-Dz pressure indicate the exchange reaction to occur via both a heterogeneous and a homogeneous mechanism. Initial rate data for H D formation are shown to be consistent with a heterogeneous combination of atomic hydrogens in competition with a reversible homogeneous chain mechanism. At 25' and 1 cm. of Hz-Dz pressure, approximately 80% of the H D is formed on the walls; at 25' and 30 clli. of Hz-D2 pressure, the wall reaction accounts for no more than 15% of the HD. Qm is shown to approach K as both the temperature and pressure are raised. The mechanistic implications of these observations are discussed.
sensitized exchange of H2 and Dz has not been reported Introduction although the analogous ortho-para hydrogen conversion The exchange reaction between hydrogen and was studied to 20% conversion by this technique. deuterium, L e . , H2 Dz + 2HD, is one of the simplest kinds of chemical reactions and, therefore, is frequently (1) (a) Postdoctoral Fellow 1962-1963; (b) Postdoctoral Fellow chosen as a test of the theories of chemical kinetics.2 1963-1964. The homogeneous, thermally induced reaction occurs (2) I. Shavitt, J . Chem. Phys., 31, 1359 (1959). a t a measurable rate only at temperatures in excess of (3) A. Farkas and L. Farkas, Proc. Roy. SOC.(London), A152, 152 450°, and, in spite of the frequency and care of the in(1935). vestigati~ns,~-s is still subject to some (4) M.Van Meersche, Bull. SOC.Chim. Belge8, 60,99 (1951). (5) G.Boato, G. Careri, A. Cimino, E. Molinari, and G. G. Volpi, The heterogeneous, thermally induced reaction occurs J . Chem. Phys., 24, 783 (1956). at lower temperatures in the presence of various cata(6) A. Cimino, E.Molinari, and G. G. Volpi, ibid., 3 3 , 616 (1960). lysts (such as Xi, Cu, or Au) and these studies have been (7) P. G. Ashmore, "Catalysis and Inhibition of Chemical Reaccritically reviewed elsewhere.' The exchange reaction tions," Butterworth and Co., Ltd., London, 1963,p. 196. may also be induced by ionizing radiationg-16 which, (8) P.C. Capron, Ann. SOC.Sci. Bruzellea, 55, 222 (1935). (9) J. Hinchfelder, H.Eyring, and B. Topley, J . Chem. Phys., 4, 170 according to recent studies,14-16 initiates an ionic (1936). chain reaction of 700 to 1100 cycles. (10) W.Mund, T.DeHorne, and M.Van Meersche, Bull. SOC.Chim. Because of the fundamental import to the field of Belges, 56, 386 (1947). radiation chemistry of the ionic chain reactions postu(11) W.Mund and M. Van Meersche, ibid., 57, 88 (1948). lated by Schaeffer and Thompson,14-16 this laboratory (12) L. M. Dorfman and F. J. Shipko, J . Phys. Chem., 59, 1110 (1955). initiated a study of the H2-D2 exchange induced by (13) L. M.Dorfman and H. C. Mattraw, ibid., 57, 72 3 (1953). ionizing radiation which would extend to temperatures (14) S.0. Thompson and 0. A. Schaeffer, J . Chem. Phys., 2 3 , 759 as high as 250'. During the course of this investi(1955). gation17 it was found desirable to obtain data for com(15) S. 0. Thompson and 0. A. Schaeffer, J . A m . Chem. SOC.,80, 553 (1958). parable exchange studies which occurred ma an atomic mechanism, such as might be expected in the 3 P ~ (16) S. 0. Thompson and 0. A. Schaeffer, Radiation Res., 10, 671 (1959). mercury-photosensitized reaction. A careful search (17) H. Niki and G: J. Mains, part I1 of this study, to be pubof the literature revealed that the mercury-photolished.
+
Volume 69, Number 1 January 1966
4ci
The only other related study was by Melville and Robb,Ig who attempted to use the ortho-para conversion reaction as a measure of the hydrogen atom concentration in the mercury-photosensitized dissociation of hydrogen. Since neither of these studies dealt directly with the H2-Dz system and were too fragmentary for comparison with the radiolysis studies, l7 this laboratory also studied the 3P1Hg-photosensitized exchange reaction of Hz and Dz. The results of this investigation are reported here.
Experimental Materials. Matheson Co. hydrogen and Stuart Co. deuterium were purified by passing them separately through a palladium thimble a t about 500'. Mixtures of hydrogen and deuterium contained a small amount of H D as the only impurity detected by mass spectral analysis. HD, obtained from AIerck Ltd., Canada, was found by mass spectrometry to contain 0.43% Hz and 0.22% Dz and was used without further purification. Airco reagent grade xenon, helium, and argon were used without further purification. They were mass spectrometrically pure, except for traces of other inert gases. Bethlehem Apparatus Co., triply distilled, instrument grade mercury was used in the mercury-sensit ized experiments. International Stckel Co. nickel wool was used for the nickel-catalyzed exchange reaction of the mixture of hydrogen and deuterium. Apparatus and Procedure. The light source was a Hmovia SC-2537 low-pressure mercury lamp coiled in;o a helix form. Three types of reaction vessels were used. All irradiations performed inside the coil of the lamp were carried out in a 100-cc. Vycor tube fitted with a three-way stopcock. The lamp intensity in this reaction vessel a t 2337 A. was estimated to be 1.08 f 0.05 >( 1016 photons CC.-' min.-l by propane actinometry as described by Bywater and Steacie. 2o For high-temperature experiments, the cylindrical vessel was inserted in an oven which was coiistructed by wrapping heating coils between two pieces of Vycor tubing of 3.5- and 5.2-cm. diameter. Steady temperature was controlled to within *2' by a Variac and was monitored by an alumel-chrome1 thermocouple. An end-on-window type Vycor reacidionvessel was used in the initial rate studies and was 15 cm. long and 3.3 cni. in diameter. For the latter experiments, a reflector niirror was placed inside the coil of the lamp to obtain the parallel light beam, and the. reaction vessel was inserted into a black, paper cylinder to prevent scattered light from entering the system. A larger end-on-window type quartz reaction vessel (7 cm. in diameter and 12 cm. long) was used for The Journal of Physical Chemistry
H. NIKI, Y. ROUSSEAU, AND G. J. MAINS
comparing the rates a t which Hz, HD, and DI quench Hg 6(3P~)atoms. The vessel was positioned as described for the initial rate studies except for the insertion of a neutral density filter before the window to reduce the intensity. The light fiux, measured by butanenitrous oxide actinometry,21was 6.8 X 1014 photons cm.-2 min.-'. Twenty pliters of mercury was placed in the reaction vessels for the photosensitization. The reaction vessels were preconditioned by irradiating a H z - D ~mixture a t 30 cm. for about 2 hr. All analyses of the isotopic hydrogens were performed using a Consolidated Electrodynamics Corp. Model 21-103C mass spectrometer. Standard mass spectra were based on the data by Friedel and Sharkey.22 The validity of the mass spectral analyses in these experiments was confirmed by a determination of the equilibrium constant, 3.27 f 0.02, for the nickel-catalyzed exchange reaction a t 23'.
Results The Rate Law. The extent of mercury-photosensitized exchange of a 1: 1 mixture of Hz and Dz may be conveniently displayed graphically by plotting Q, defined as (HD)2/(Hz)(Dz), as a function of time. Typical curves (chosen from data for almost 100 experiments) are displayed in Figure 1. Sigmoidal curves of this type arise from a differential rate of the form d(HD)/dt = A - k(HD), where A and k are constants. The integrated form of this rate law, In [(HD), - (HD)]/(HD), = -kt, where (HD), is the final time-independent concentration of HD, i.e., A/k, has been shown to describe accurately the progress of the thermally-induced, homogeneous exchange, the thermally-induced, catalyzed exchange,' the radiation-induced exchange, 12,13,16 and the niercury-sensitized, radiation-induced exchange. l7 I t is not altogether surprising that the kinetics of the mercuryphotosensitized exchange reported here should also be accurately described by a rate law of identical form. The differential form of the rate law requires only a constant initial rate of H D formation, A, and a backreaction which is first order in (HD). These mechanistic requirements are easily fulfilled so long as the concentrations of the kinetic intermediates are independent of the extent of conversion, regardless of (18) L. Farkas and H. Sachsse, 2. physik. Chem., B27-28, 1 1 1 (19341935). (19) H. W. Melville and J. C. Robb, Proc. Roy. SOC.(London), A196, 445 (1949). (20) S. Bywater and E. W. R. Steacie, J . Chem. Phys., 19, 319 (1951). (21) Y. Rousseau and H. E. Gunning, Can. J . Chem.. 41, 465 (1963). (22) R. A. Friedel and A. G. Sharkey, Jr.. J . Chem. P h y s , 17, 584 ( 1949).
47
HYDROGEN-DEUTERIUM EXCHANGE REACTION
*
t
1
failure to alter the rate of the reaction is especially significant. Efect of Pressure. Reduction of the initial pressure of the 1 : l H r D 2 mixture from 30 to 15 cm. at 25' in the reaction vessel packed with quartz tubing (S/V = 4.7 CEL-~)resulted in a shift of the photo0.03. stationary state, Qm, from 5.40 f 0.05 to 6.10 The fornis of the Q vs. t curves for these experiments were similar to those given in Figure 1 and, therefore, are not of particular interest. However, the observation that the photostationary state, Qm, is pressure dependent as well as surface dependent was of considerable interest, and it was decided to investigate the effect of pressure and composition on Qm at 25'. The results of this study (S/V = 1.4 cm.-') are displayed in Figure 2. Each point on the curves represents a separate experiment. It should also be noted that each of the curves was extended into the lowpressure region, but, for clarity, these points are not included in Figure 2. The remarkable increase in Qm for the 1 : l mixture from 4.55 0.05 at 30 cm, to a maximum 6.75 f 0.05 at about 2 cin., followed by a sharp decrease at lower pressures, is especially noteworthy. For comparison, the equilibrium coniposition, K = 3.25, is also depicted in Figure 2, where it will be observed that Qm is greater than K for all the experiments below 30 cm. a t 25'. Effect of Temperatures. While extensive kinetic studies have not been carried out at elevated temperatures, a few experinients were performed to determine the effect of temperature on the photostationary state, Qm. The data, displayed in a graph of Q,/K us. T
*
I;
I
I
IO
20 30 T i m e (minute)
40
I
Figure 1. Effect of the surface-to-volume ratio on the isotopic quotient in the 3P1mercury-photosensitized reaction of an equimolar mixture of Hz and Dz a t 30 cm. and a t 25'.
whether these intermediates are hydrogen atonis, either in the gas phase or on a surface, or whether they are ionic. Under these circumstances the gross forin of the rate law is of little help in choosing a mechanism and a detailed study of the effects of many variables is necessary. Effect of Surface-Volume Ratio. The effect of varying the surface-to-volume ratio a t 25' is depicted in Figure 1 where it niay be observed that increasing the ratio froni 1.4 to 4.7 cm.-l by the addition of sections of quartz tubing to the reaction vessel resulted in a decrease in the initial rate of the reaction and an increase in the photostationary isotopic quotient, Qm, froni 4.55 f 0.05 to 5.40 f 0.05. Therefore, the exchange reaction must occur partially via a heterogeneous mechanism at 25' at a pressure of 30 cm. Efect of Added H e and Xe. Several experiments were conducted in order to ascertain whether the presence of an unreacting gas would alter either the rate of the reaction or the photostationary state, Q m , at 25'. In one experiment 13.0Oj, Xe was added to 30 cm. of a 1:l H2-D2 mixture. In another experiment, 36.2% He was added. The results of these experiments yielded data which fell precisely on the line drawn in Figure 1 for S / V = 1.4 cm.-l, indicating these gases had no observable effect. Schaeffer and also failed to find an inert gas effect in their experiments involving the mercury-photosensitized exchange. It is worthwhile mentioning that He would be expected to be an ideal inert gas to thermalize any translationally "hot" hydrogen atoms, and its
_______________------3
I
IO
20
Pressure
- - - -k I
30
(cmHg)
Figure 2. Effect of pressure on the photostat,ionary state constant Q.. in the 3P1 mercury-photosensitized exchange of Hz and Dz mixtures a t 25". (Hz)/(DZ)ratio values: 0, 1.0; @, 1.6; 0 , 6.9; 9 , 8.9. K is the thermodynamic equilibrium.
Volume 69,Number 1
January 1966
H. NIKI,Y. ROUSSEAU, AND G. J. MAINS
48
rately by the technique of initial rates. For these studies the end-on reaction vessels were used to ensure reproducibility of the lamp-reaction vessel geometry. The forward reaction was studied by filling the reaction vessel with the desired pressure of the 1 : I HZ-DZ mixture and exposing the system to the actinic radiation, for a sufficient time to achieve a maximum of 1% conversion to HD. The effect of initial H2-D, pressure on the rate of H D formation is depicted in Figure 4. The marked decrease in the initial rate of H D formation below 1 cm. is especially significant. The linear region of the curve, between 1 arid 5 cm. in Figure 4, has been experimentally confirmed to 30 cm., but the data above 5 cm. are not included in order to depict clearly the curve below 1cm. The effect of surface on the forward reaction was studied by inserting a quartz disk into one of the endon reaction vessels. This disk, which had twelve 0.16-em. diameter holes bored in it to permit free diffusion of gas, could be moved forward until it touched the window through which the actinic light entered the vessel (z = 0 em.) or back until it touched the rear window (5 = 9 em.) The disk was supported by quartz rods so that it remained approximately parallel to the front window at all locations. The effect of window location on the initial rate of H D formation is given in Figure 5 for initial Hz-D2 mixture pressures of 6 cm., 1cm., and 1 em. with 5 cm. of argon. It should be noted in the 6-cm. experiments that the disk location did not alter the initial rate until it was within 2 cm. of the front window where it decreased the rate considerably. At 1 cm. of H2-DZ pressure, the disk decreased
Temperature *C Figure 3. Effect of temperature on Q / K in the equimolar mixture of HI and D:! at 5 cm.
t ,'e 9'
/'e I'
I
I
I
I
I
2
3
4
(H,:D,)
5
cm H g
Figure 4. Effect of pressure on the rate of HD formation in the 3P1 mercury-photosensitized exchange of a n equimolar mixture of H2and DZat 25'.
in Figure 3, indicate that the photostationary state and the equilibrium state become virtually indistinguishahle at temperatures above 250'. It should be noted that the thermally-induced exchange is negligible at 2.50' and, therefore, is not responsible for the approach of Qm to K in this temperature region. Initial Rate Studies. In order of ascertain the pressure and surface dependence of the forward and backward reactions, it was necessary to study them sepaT h s Journal of Physical Chemistry
't I
I
1
I
L
I
l
I
l
u l
I
l
I
T
I
8
Distance (cm) Figure 5. Effect of the location of a diffusion-free quartz disk in the 3P, mercury-photosensitized exchange of a n equimolar mixture of Hzand Dz a t 2 5 " .
S
I
HYDROGEN-DEUTERIUM EXCHAXGE REACTION
49
the initial rate over the entire range of locations. It is especially significant that the addition of 5 cni. of argon alters the shape of the low-pressure curve to approach that of the curve at 6 mi. These observations indicate that the exchange reaction is occurring in a reaction zone near the front window, the depth of which decreases as the total gas pressure in the system is increased. Furl hermore, these experiments confirm the observations (vide supra and Figure 1) made using the cylindrical vcssels located in the center of the lamp to the effect that an increase in surface to volume decreased the initial rate of HD formation. The initial rate of the mercury-photosensitized back Hz Dz, was also studied at reaction, i e . , 2HD 25' as a function of H D pressure. The results of this study are displayed in Figure 6. I t should be noted that the data in Figure 6 are reported in terms of the rate of D2 production because less uncertainty is attached to D2 analysis in excess H D than to Hz analysis. However, the rate of Hz production was found to equal the rate of D2 production within experimental error. A comparison of Figures 4 and 6 reveals that, while the initial rate of the forward reaction diminishes very rapidly below 1 cm. of H2-Dz mixture, the back reaction showed signs of becoming constant in this low-pressure region. A similar "leveling-off" trend is observed in a graph (not reproduced here) of the initial rate of Hz production as a function of H D pressure.
-
In any experiment involving mercury photosensitization it is necessary to consider first the primary photophysical act, vix.
The very large extinction coefficientz3of Hg vapor at 25', i.e., 6 cni.-', results in a very inhomogeneous distribution of Hg atoms which, in the absence of a large concentration of quenching molecules, is not given by an exponential decrease from the incident window but is coniplicated by radiation diffusion.2 4 I n the presence of a large concentration of quenching molecules, say H2, the competition between radiation and qn~nching,Liz.
Hg*
("1)
c
+
Discussion
Hg*-(3Pi)
c " ' " i
--
+ Hz
+ hv Hg + 2H
Hg ('So)
(2)
I
I
I
2
3
I
4
5
I
(HD) c m H g
Figure 6. Effect of pressure on the rate of DPformation in the 3P, mercury-photosensitized decomposition of HD at 25".
readily estimated to be about 0.8 cm. from the SternVolmer equation and the corrected radiative lifetiiiie?4 of the 3P1 state. Thus, at hydrogen pressures above 0.8 cm. the rate of reaction 3 is approximately equal to Ia, below this pressure the rate of reaction 3 will fall, and reaction 2 will become more important. Similarly, any reaction initiated by the hydrogen quenching reaction should also fall below 0.8 cni. It is interesting to note that a marked decrease in the initial rate of H D formation is observed below 1 cm. of H2-D2 pressure (see Figure 4). I n view of the uncertainties in the corrected radiative lifetime, the agreement between the predicted and experimental pressure for complete quenching is good. On the other hand, the initial rate of D2 formation from H D (Figure 6) does not fall off below 1 cm. Based upon the quenching cross respectively,2j sections for H? and D2, 6.0 and 8.4 .i.z3 the rate constants for Hz and Dz quenching are almost iderit ical. The quenching cross section of H D for Hg 6(T1) atonis has not been measured, and one may suppose that the difference observed betneen the H2-D2 system and the H D system at low pressure could possibly be ascribed to a difference in the quenchiilg rate constants
(3)
greatly favors the latter, reaction 3, and over 99% of the incident radiation is absorbed within 1 cm. of the incident Lvindow. The hydrogerl pressure at which 95% of the Hg* ('PI) a t o m are quenched niay be
(23) K. G. W. Korrish and A . B. Callear. Proc. R o y . S O C .(London), A266, 299 (1962). (24) T. Holstein, Phys. Rec., 72, 1212 (1947). ( 2 5 ) K, J , Laidler, ,,The Kinetics of Excited States,,, Oxford Vniversity Press, London, 1955, p. 107.
Volume 69, S u m b e r 1
January 1966
50
H. NIKI,Y. ROUSSEAU, AND G. J. MAINS
for Hz, HD, and Dz. A measurement of the relative quenching rates of Hz, HD, and D2 for Hg 6(3P1) atoms was then undertaken. CvetanoviEZ6has shown that when a hydrocarbon is subjected to mercury photosensitization in the presence of different relative concentrations of NzO, the following relationship is obeyed
- 1= I + 4%
k,(RH) kb(Xz0)
(4)
Where 4~~ is the quantum yield of nitrogen formation, (RH) and (KZO) are the concentrations of the hydrocarbon and nitrous oxide, respectively, k, is the rate constant for the reaction of R H with Hg 6(3P1)atoms, and k b represents the rate constant for the reaction of IYzO with Hg ("1) atoms. The mechanism of reaction of Hg 6(3P1)atoms with hydrogen is similar to that observed for hydrocarbons, and relation 4 should also be obeyed. Mixtures of Hz, HD, and Dz with NzO were irradiated in the presence of mercury, and the resulting grapk of 1/4x2 as a function of (Hz)/(NzO), (HD)/(SzO), and (Dz)/(NzO) is shown in Figure 7. Although there is some scattering in the experimental points, the graph clearly shows that the rate constants for the reaction of Hg 6(3P1)atoms with Hz, HD, and Dz are all approximately equal. Therefore, the source of the difference in the low-pressure behavior of the HZ-DZ mixture and H D is not readily ascribed to differences in quenching cross sections and will have to be investigated further. I n any case, it seenis reasonable to assume complete quenching of Hg* in all experiments at pressures greater than 1 cm., and the overall primary processes in HZ, H D , and Dz mixtures may be written as
+
-
Hg* ( 3 P ~ ) H Z Hg*
(T1)
Hg*
("1)
+ HD + DZ
+
+ Hg ('SO) + H + D Hg ('SO) + 2D Hg
+
('SO) 2H
(3) (5)
(7f and 7r)
(8f and 8r)
At the relatively low gas pressures used in these experiments, the removal of H and D atoms from the system by homogeneous three-body combination is negligible, a point somewhat substantiated by the failure of large amounts of Xe and He to influence the rate of the reaction. The ultimate fate of these atoms must be combination reactions a t the walls. Linnett2* has shown that hydrogen atoms rapidly adsorb on glass walls and saturate the available surface. Thus, the following equilibria may be assumed to be rapidly established (9)
H + W e H W
(10)
D+W&DW
where W denotes the wall. Subsequent collisions of H and D atoms with the wall may be e x p e ~ t e d ~ ! ~ ~ to result in combination reactions 11, 12, 13, and 14
+W D + HW HD + W H + DW HD + W D + DW + Dz + W H +HW+Hz
(11)
+P
(12)
+P
(13)
(14)
It is possible to rule out any large contribution to the exchange by heterogeneous reactions analogous to I
I
I
I
I
I
I
I
1
I
-I
%
3-
((3)
I t should be noted that while HgH has been spectroscopically observedz7 when mixtures of hydrogen antl mercury vapor are irradiated a t 2537 A,, this hydride is presumably formed by secondary reactions antl not in the quenching act.25$27Since the HgH concentration must be quite low, it is not considered in the exchange mechanism. The hydrogen and deuterium atoms produced by quenching reactions 3, 5 , and 6 undergo collisions with the Hz, HD, and Dz molecules present, some of which lead to chemical reactions. These honiogeneous prooesses may be described in terms of two reversibIe horuogeneous reactions, viz. The Journal of Physical Chemistry
+ DZe H D + D D + Hz HD + H H
Figure 7. Comparison of the Hg 6(SP1)quenching rate constants for HP, HD, and D2 relative to NPO.
(26) R. J. Cvetanovik, J . Chem. Phya., 23, 1208 (1955), (27) C. R. Masson and E. W. R. Steacie, ibid., 18, 210 (1950). (28) M. Green, K. R. Jennings, J. W. Linnett, and D. Schufield, Trans. Faraday SOC.,55, 2152 (1959). (29) P.Kebarle and M.Avrahami, Can. J . Chem., 40, 2409 (1962).
HYDROGEN-DEUTERIUM EXCHANGE REACTION
reactions 7f, 7r, 8f, and 8r involving H-W and D-W, even though these types of reactions are postulated in the presence of catalysts where H atoms are chemisorbed. It is difficult to reconcile the observed decrease in the initial rate of H D production (Figure 5 ) when fresh surface is brought into the reaction zone with a mechanism which includes significant contributions from heterogeneous analogs of reactions 7f, 7r, 8f, and 8r. If equilibria 9 and 10 are assumed rapid and the hydrogen pressure assumed to be over 1 cm., it is possible to deduce an explicit equation for the sum of the photostationary state concentrations of H and D atoms. On this basis, one would expect the sum of these atomic concentrations to be directly proportional to the incident intensity, inversely proportional to the surfaceto-volume ratio. I t can also be shown that the concentration ratio, (H)/(D), depends primarily on the initial ratio of hydrogen and deuterium in the system and shifts only slightly during the course of the exchange reaction. I t would uselessly lengthen this paper to write such equations explicitly, and, in view of the complications introduced by including diffusion considerations,3 0 t 3 1 their inclusion would serve no purpose. I t is sufficient to conclude that the concentrations of H and D are constant and inversely dependent on the surface to volume ratio in order to understand Figures 4 and 5. We may write the following differential equation for the ivztial rate of H D production in the experiments involving Hz-D2 mixtures
+
k n ( H )(Dz) ksr(D) (Hz) (15) The linear region of Figure 4 may be attributed to the last two terms in eq. 15; the intercept of the extrapolationof thelinear region to zero pressure may be attributed to the first two terms in ey. 15. If these assumptions are correct, it is possible to estimate the magnitudes of the initial rate of the heterogeneous reaction and the initial rate of the homogeneous reaction by comparing the extrapolated intercept of Figure 4, i.e., 0.59 pmole min.-', with the difference between the total observed rate and the extrapolated intercept. Thus, a t 1 cm. of Hz-D2 pressure the ratio of the heterogeneous reaction to the homogeneous reaction is 4.8, indicating that about 80% of the reaction occurs on the walls; a t 30 cm. of Hz-D2pressure, the ratio is 0.16, indicating that about 15% of the reaction occurs on the walls. The ratio of the rates of the heterogeneous reactions to the homogeneous reactions may be written explicitly from eq. 1.5 as
51
R(homo)
+
h ( H ) (Dz) kst(D)(Hz)
If we assume as a first approximation that (H) = (D), eq. 16 may be reduced to eq. 17.
(%)
()!
R(hetero) + k13 R(homo) k,t(Dz) -t h ( H d
(17)
Since the relative ratio of heterogeneous to homogeneous reaction may be estimated from Figure 4, it is possible to estimate k l z ( S / V ) kl3(S/V) if k7f and k8f are known. Using the calculated data of Shavitt2 for ksf and k7f a t 300"K., we estimate k l z ( S / V ) k l a ( S / V ) to be 865 set.-'. Since the surface-tovolume ratio varies with the depth of the reaction zone from about 3.7 cm.-' a t low pressures to perhaps as high as 6 or 7 cm.-' a t high pressures, considerable uncertainty must be attached to any calculation based upon it. Nonetheless, assuming ( # / I T=) 3.7, we obtain a value of 234 cm. set.-' for klz k13, a value consistent with the value reported by Kebarle29 for k11, ie., 98 cm. set.-', when the nature of the assumptions is borne in mind. The effect on the initial rate of H D formation of bringing fresh surface into the reaction zone (vide Figure 5) is also readily accounted for in terms of eq. 15. When the quartz disk is moved sufficiently forward to enter the reaction zone, it adds surface for reactions 11 to 14 and thereby reduces the H and D atom concentrations. The net effect is to increase the rate of the heterogeneous reaction and to decrease the rate of the homogeneous reaction. At an Hz-D? pressure of 1 cm. the reaction occurs mainly on the walls, and the effect of additional surface is small; a t an HTDz pressure of 6 cm., the wall reaction accounts for about half of the reaction, and the effect of fresh surface is more pronounced. The shapes of the curves in Figure 5 probably reflect the variation of the H and D atom concentration as a function of distance from the window. This interpretation is substantiated by the effect of 5 cm. of argon on the shape of the curve for an H2-D2 pressure of 1 cm. as argon would be expected to hinder the rate of diffusion of the H and D atoms from their zone of formation near the window. The effect of H D pressure on the initial rate of the reverse reaction, shown in Figure 6, should be given by an equation analogous to eq. 15, viz.
+
+
+
(30) H . Wise and C. M .Ablow, J . Chem. P h y s . , 29, 634 (1958). (31) W. It. Schulta and D. J. LeRoy, Can. J . Chem., 40, 2413 (1962).
Volume 69,.Vumber 1
January 1966
H. NIKI, Y. ROUSSEAU, AND G. J. MAINS
52
d(D,) dt
=
kid
(F)
(D)
+ [k,,(D) + ks,(H)](HD)
(18)
and, while a linear regidn apparently exists above 2 cm. of HD pressure, the low-pressure region does not fa11 off as expected. Furthermore, the extrapolation of the linear region to zero H D pressure passes through the origin, implying the heterogeneous production of D:! (and Hz) is negligible. This conclusion, while in accord with the large photostationary yields of HD obtained a t low pressures (Figure 2), can scarcely be correct in view of the experimental magnitude of k11.29 In view of this apparent inconsistency, it seems prudent to await the results of further study rather than speculate about the low-pressure behavior depicted in Figure 6. The results reported here would indicate that the heterogeneous reactions 11 to 14 favor HD production. The reason for this effect is not clear and shall be investigated further. In view of the previously discussed effects of surfaceto-volume and hydrogen pressure on the initial rates of the forward and reverse reactions, the observed effect of these variables on the photostationary composition, i.e., Qm is readily understood. Addition of surface or the reduction in pressure results in a shift in the mechanism of the reaction in favor of the heterogeneous contribution. Since the heterogeneous reaction favors HD formation, Qm increases. [t should be observed that the homogeneous reactions, 7f, 7r, Bf, and Br, constitute a potential chain mechanism which would be expected to become more important a t high pressures and/or high temperatures. Under these high-temperature-high-pressure conditions the rate of HD consumption and formation occurs pr~dominantlyvza these homogeneous processes, and, a t the photostationary state, these reactions must occur at essentially equal rates in the forward and reverse directions. This equality of the rates of reaction of (7f) and (7r) and (8f) and (8r) requires6 that Qm equals k7rk8rIklrkSr. Furthermore, if each react ion involves species in thermal equilibrium, the principle of microscopic r e ~ e r s i b i l i t yrequires ~~ that the ratio of rate constants, k7rksrlk7,ksr,equals the equilibrium constant, K . It is significant that Qm does indeed approach K as the temperature is increased (Figure 3) and also appears to approach K as the pressure is increased (Figure 2). These observations are especially significant and rule out the participation of “hot” hydrogen atoms in the H2-D2 mercuryphotosensitized exchange reaction a t high temperature or high pressure, an observation also suggested
The Journal of Physical Chemistry
by the failure of added helium to affect the kinetics of the exchange at 30 cm. and 25”. It should be emphasized that the equality of Qm and K under high-temperature-high-pressure conditions is a consequence of the predominance of a reversible chain mechanism under these conditions and is not to be expected generally for photochemical reactions. Also, it should be noted that the temperature-pressure conditions a t which the reversible, homogeneous chain reactions predominate will be dependent upon experimental variables, such as incident intensity and surface-to-volume ratio. Nonetheless, these observations support the proposed mechanism and indicate the feasibility of a photochemical study of reactions 7f, 7r, 8f, and 8r under conditions where heterogeneous contributions to product formation are negligible. Such a study, planned in this laboratory in the near future, might hopefully result in reliable experimental rate constants for reactions 7f, 717, Bf, and 8r which, contrary to popular belief, are not readily available.2 Finally, it is necessary to mention the possible significance of these observations with respect to other studies. If, as the data reported here suggest, H D formation is favored in atomic combination processes a t the walls, considerable care should be exercised in estimating the extent of molecular detachment processes based upon the Hz, HD, and D, product distribution from the photolysis or radiolysis of a mixture of deuterated and undeuterated compounds. Such calculations, based on deviations of Q from K , should actually be based upon the deviation of Q from Q m and will, in general, underestimate the extent of molecular detachment. Furthermore, this research suggests that hydrogen formation in the mercury-photosensitized decomposition of hydrocarbons may occur partially on the walls, and mechanistic interpretations based upon exclusively homogeneous reactions should be reviewed.
Acknowledgments. This research was supported by Contract No. AT(30-1)-2007 from the U. S. Atomic Energy Commission and grateful acknowledgment ia made thereto. We also wish to express our gratitude to Ah-. Wrbican for careful determination of the mass spectra of the product gases. Special thanks are due Dr. Leon Dorfman, Argonne National Laboratory, and Dr. A. 0. Allen, Brookhaven Yational Laboratory, for helpful and stimulating discussions of the results of this study. 132) N. Davidson, “Statistical Mechanics,!: McGraw-Hill Book Co., Inc., New York, N. Y., pp. 230-235.
