J. Phys. Chem. 1983, 87, 5422-5425
5422
Remarkable Isotope Effect on Production and Decay of D and H Atoms in y-Radiolysis of D2-H, Mixtures at 4 K. A Quantum-Mechanical Tunneling Effect Haruyukl Tsuruta, Tetsuo Miyaraki, Kenjl Fuekl, and Naoto Azuma Department of Synthetic Chemistry, Facult)’ (Received: January 18, 1983)
of Englneerlng, Nagoya Universl@, Chlkusa-ku, Nagoya 464, Japan
The radiolysis of solid D2-H2 mixtures has been studied at 4 K by ESR spectroscopy. The yields of trapped D atoms in the radiolysis of D2 decrease drastically upon addition of a small amount of H2and become zero above 25 mol % HF The yields of trapped H atoms, however, increase complementarily and only the trapped H atoms are observed above 25 mol % Hz. The remarkable isotope effect on the formation of the D and H atoms is explained in terms of a selective hydrogen atom reaction caused by a quantum-mechanical tunneling. The ratio of the rate constant for the D + H2reaction to that for the H + D2 reaction at 4 K exceeds 3 X lo4. The decay rates of the D atoms in the pure D2matrix and D2-H2 mixtures do not depend upon H2concentrations. H atoms do not decay in D2containinga small amount of H2,while they decay in the H2matrix and the D2-H2 (25 mol %) mixture. These results are explained in terms of tunneling migration of D or H atoms. The rate constant for the tunneling abstraction reaction is calculated by use of an unsymmetrical Eckart potential. The calculated rate constants are compared with the experimental results.
Introduction Basic to any theory of chemical kinetics of elementary reactions is an understanding of the simplest atom-diatomic molecule exchange reaction. A number of experimental and theoretical studies on the reaction of H (or D) with H2 (or D2) in the gas phase have been reported previous1y.l It is known that isotope effects on the reaction provide information on a quantum-mechanical tunneling effect. The ratio of the rate constant for the D + Hz HD H reaction to that for the H D2 HD + D reaction at 370 K is 6.3, suggesting a small contribution of the tunneling effect.2 In order to clarify the tunneling effect, it is desirable to study the isotope effect on the D (H) Hz (Dz)reaction at an ultralow temperature, such as 4 K. Previous studies on the hydrogen abstraction reaction by tunneling at low temperature have been limited to organic compound^.^ Trapped H atoms are produced by y-radiolysis of solid H2at 4 K.4 The maximum number of trapped hydrogen atoms that can be produced by exposing solid H2 or D2 to y-irradiation was investigated at 4 KS6 The effect of initial energy of H atoms, produced by the photolysis of hydrogen halides, on the reactions and trapping in solid D2 a t 4 K has been studied recently.6 Here we have studied the formation and the decay of D and H atoms in the radiolysis of D2-Hz mixtures at 4 K by ESR spectroscopy and have found a remarkable isotope effect.
+
+
- -
+
Experimental Section H2was more than 99.999 mol ?% pure. Dz was more than 99.5 mol 9% pure. A n aqueous solution of HI was vaporized and passed through Pz05to prepare hydrogen iodide. Then, the hydrogen iodide was subjected to trap-to-trap (1) Truhlar, D. G.; Wyatt, R. E. Annu. Rev. Phys. Chem. 1976,27,1. Related papers are cited therein. (2) Le Roy, D. J.; Ridley B. A,; Quickert K. A. Discuss. Faraday Soc. 1967, 44, 92. (3) (a) Le Roy, R. J.; Sprague, E. D.; Williams, F. J. Phys. Chem. 1972, 76, 546. (b) Iwasaki, M.; Toriyama, K.; Muto, H.; Nunome, K. Chem. Phys. Lett. 1978, 56, 464. (c) Adita, S.; Wilkey, D. D.; Wang, H. Y.; Willard, J. E. J.Phys. Chem. 1979, 83, 599. (4) (a) Jen, C. K.; Foner, S. N.; Cochran, E. L.; Bowers, V. A. Phys. Reu. 1958,112,1169. (b) Rexroad, H. N.; Gordy, W. Ibid. 1962,125,242. ( 5 ) Brown, D. W.; Florin, R. E.; Wall, L. A. J.Phys. Chem. 1962,66, 2602. (6)Miyazaki, T.; Tsuruta,H.; Fueki, K. J. Phys. Chem. 1983,87,1611.
0022-3654/83/2087-5422$01.50/0
sublimation on a vacuum line several times. y-Irradiation a t 4 K was performed by 6oCoy-rays to a total dose of 0.06 Mrd. UV illumination was performed with a low-pressure mercury lamp. The solid sample was made by rapid cooling of the hydrogen gas in a sample tube from room temperature to 4 K. The details of the cooling procedure were described in a previous papera6 In order to cool completely the sample to 4 K, we kept the sealed sample for 40 min before y (or UV) irradiation. The trapped hydrogen atoms in the irradiated samples were measured at 4 K with a JES-3BX ESR spectrometer whose microwave power was initially calibrated by a power meter. The relative yields of the H and D atoms were obtained by double integration of the ESR signals.
Results When pure D2, pure H2, and D2-H2 mixtures are y-irradiated at 4 K, trapped D and H atoms, denoted here as D, and H,, respectively, can be observed clearly by ESR spectroscopy at 4 K. Figure 1shows the microwave power saturation behavior of the trapped D and H atoms produced by the y-radiolysis of solid hydrogen at 4 K. Though neither H, nor D, atoms produced by the photolysis of HI in the D2 matrix a t 4 K saturate a t a microwave power of 40 pW,6 the hydrogen atoms produced by the y-radiolysis saturate already at a microwave power of 1pW. The power saturation behavior of the D, atoms is approximately the same as that of the H, atoms. Thus, the ESR signals were measured at a microwave power of 1 pW for the rough estimation of the relative yields of H, and D, atoms. Since the isotope effect on the H and D atom production is quite large, discussions in this paper are not influenced seriously by the errors involved in the rough estimation of the relative yields. Figure 2 shows a fraction of trapped D atom yield in the total trapped hydrogen atom yield against a fraction of D2 in the Dz-H2 mixtures in the radiolysis of D2-H2 mixtures at 4 K. In order to minimize the influence of the decays of the trapped D and H atoms, the relative yields of the atoms were measured immediately after y-irradiation for 15 min. Since the total yields of the trapped D and H atoms are approximately constant in the whole range of D2 fractions, the D, yields decrease sharply upon the addition of H2, while the H, yields increase complementarily. 0 1983 American Chemical Society
y-Radiolysis of D,-H,
The Journal of Physical Chemistry, Vol. 87, No. 26, 7983 5423
Mixtures at 4 K
B‘ 8.6‘
0
0
1
2
3
JPower
4
5
I p ~ ? ~
Figure 1. Microwave power saturation behavior of trapped hydrogen atoms produced by y-radiolysis at 4 K: (A) D atoms in pure D,; (0) H atoms in pure H,.
-
E
I
1.0 0 8 0.6 0:4 012 [D21 1(D21 + [H21)
8
Figure 2. Fractions of D atom yield in total hydrogen atom yield against mixtures at 4 K: (0)D atoms in the y-rafractions of D, in D,-H, diolysis of the D,-H, mixtures; (A) D atoms in the UV photolysis of a D,-H, (5 mol %)-HI (0.05 mol % ) mixture.
:41 O
i
0
100
3 C
4m IO-
0
0 -0
0-
0 0
$ 2
-602FIi 0
c
200
300
I 400
Time after I-lrradlatlon / mln
Figure 3. Decay of D atoms after y-radiolysis of D,-H, mixtures at 4 K: (0)pure D;, (0) D,-H, (0.5 mol YO)mixture; (A) D,-H, (1 mol % ) mlxture.
Figure 3 shows the decay of D atoms in the radiolysis of D2-H2 mixtures at 4 K. The initial yield of the D atoms is normalized to 10. It is seen that the decay rate of the D atoms does not depend upon the concentration of H2. Figure 4 shows the decay of H atoms in the radiolysis of D,-H, mixtures at 4 K. The initial yields of the H atoms are normalized to 10. Though the H atoms in the D,-H2 (0.5 and 1 mol % ) mixtures do not decay, they decay in the D2-Hz (25 mol % ) mixture and pure H2. Figure 5 shows the relative yields of the H and D atoms in the radiolysis of the D2-H2 (10 mol %) mixture against the time after y-irradiation. It should be noted that the yield of H atoms is much higher than that of D atoms. In this case the H atoms do not decay, while the D atoms decay at a similar rate to those in Figure 3.
Discussion Remarkable Isotope Effect on Ht and D,Formation at 4 K . It has been shown in Figure 2 that the yields of trapped D atoms in the radiolysis of solid D2 at 4 K decrease drastically upon the addition of a small m o u n t of
-A-A-
AA --
A-A
5424
The Journal of Physical Chemistty, Vol. 87, No. 26, 1983
Tsuruta et al.
TABLE 11: Calculated R a t e Constant ( k ) a n d Tunneling Correction
( r ) for Tunneling Abstraction Reactions at 4
reaction
-
D + H, + HD + H (4) H + H, H , + H (5) D t D, -+ D, + D ( 3 ) H + D,-HD+ D(6)
K
a = 0.5 A a
a = 0.6 A a
k , s-l
rb
k , s-'
6.9 x 104 1.1 x 104 8.4 x 10-3 5.1 x 10-51
4.9 x 1 0 3 1 8 7 . 8 x 10317
2.2 x l o 6 4.2 X 10' 3.6 5.3 x 1 0 - 4 9
1.4x
10410
8.2 x 10361
rb 1.6 x 3.0 x 5.8 X 8.5 x
10320 10319
lo4" 10363
a The value of a represents a width of a potential barrier. In the case of a symmetrical potential, 1 . 7 6 ~ is equal t o t h e Tunneling correction ( r )is a ratio of t h e rate constant that takes account of width of the potential curve at a half-height. tunneling to the rate constant that has been calculated without taking account of tunneling (see text).
produce trapped D atoms or lose their energies to become trapped H atoms, resulting in the [Dt]/([Dt] + [H,]) ratio of 0.13-0.27.6 In the photolysis of the D2-H2 (5 mol %)-HI (0.05 mol %) mixture, however, the ratio of [Dt]/([Dt] + [H,]) is only 0.06, which is similar to the value in the radiolysis of the D2-H2 (5 mol %) mixture. The hydrogen atoms, formed by the photolysis, produce preferentially H, atoms in the D2-H2 mixture. Thus, the preferential formation of H, atoms in the radiolysis of the D2-H2 mixtures may be due to the selective reaction of hydrogen atoms. I t was reported previously that the preferential formation of solute radicals in the radiolysis of neopentane-alkane (as a solute) mixtures at 77 K is due to the selective reaction of hydrogen atoms.g Hydrogen atom reactions in the radiolysis of the D2-H2 mixtures can be described as follows: D2 2D, (1) H2 2H, (2) Dt D2 D2 Dt (3) D, + H2 HD H, (4) Ht Hz H2 + Ht (5) H, D2 HD Dt (6) Trapped hydrogen atoms, produced by radiolysis of solid hydrogen, react with hydrogen molecules in the neighborhood of the atoms by reactions 3-6. Though these reactions have activation energies, the reactions may take place even at 4 K by a quantum-mechanical tunneling reaction which has been found in organic compounds at low temperature^.^ Since the yields given in Figure 2 represent the initial yields, the decay processes need not be considered here. If the rate constant for reaction 4 is much larger than for reaction 6, H, atoms are preferentially formed. The ratio of an apparent rate constant (kb+HJ for reaction 4 to that (kk+Dz) for reaction 6 is estimated by eq 7.1° The ratio of the rate constants is shown in ~ / D + H J ~ / H + D=~ [HtI [D21/([Dtl[H211 (7)
+
+ +
-----
+ +
+
Table I. The ratio decreases with decrease of H2 con(9) (a) Miyazaki, T.; Hirayama, T. J. Phya. Chem. 1975, 79,566. (b) Miyazaki, T.; Kasugai, J.; Wada, M.; Kinugawa, K. Bull. Chem. SOC. Jpn. 1978,51, 1676. (10) Though eq 7 is a kind of empirical expression, it can be derived by the following model. Trapped hydrogen atoms, produced by radiolysis of hydrogen, react with hydrogen molecules by reactions 3-6, which take place very fast as compared with the time (about 10 min) for ESR measurement. Since the amounts of H, and D, are observed to be kept constant for several tens of minutes, a steady-state condition for H, and Dt concentrations after formation of the trapped hydrogen atoms holds for this period. Since the amounts of Dt and Ht are unchanged by reactions 3 and 5, these reactions need not be considered in the kinetic treatment. Thus d[Dtl/dt e k'1i+~~[Ht][Dz1 - k'~+~~[Dtl[Hzl =0
k b+HZ/k'"+Dz = [Htl[Dzl/l[Dtl [Hzll This model may be applied at high concentrations of both Hz and Dz in which reactions 4 and 6 can take place successively in the limited region near the trapped hydrogen atoms.
centration. At low concentrations of H2, reaction 4 may have a character of diffusion-controlled reactions and k b + ~k "+Dz ~ / shows relatively low values. Thus, the ratio at high H2 concentrations approaches a true value for the reaction steps. The extremely high value (> 3 X lo4) of k ' D + H z / k ; I + D 2 at 25 mol 5% H2 can be explained qualitatively from the viewpoint of energetics. Reaction 4 is exothermic and takes place at 4 K by a quantum-mechanicaltunneling. Reaction 6, however, is slightly endothermic and cannot occur at 4
K. Decay of Trapped D and H Atoms. Tunneling Migration. The decays of hydrogen atoms in Figures 3 and 4 have the following characteristics. First, the decay rates of the D, atoms in the D2 matrix do not depend upon the H2 concentration. Second, the H, atoms do not decay in the D2matrix, while they decay in the H2 matrix and the D2-H2 (25 mol % ) mixture. The motion of hydrogen atoms contributing to the decay process may be explained in terms of three models: thermal diffusion, thermal diffusion involving a tunneling abstraction reaction, and tunneling migration. Some experimental results, however, cannot be explained by the first and second models. Since the atomic diameters of H and D atoms are the same, it is expected from the thermal diffusion model that the decay rate of the H, atoms should be similar to that of the D, atoms in the same matrix. Actually, however, though D, atoms decay in the D2matrix (cf. Figure 3), H, atoms do not decay in the D2 matrix (cf. Figure 4). Thus, it is difficult to explain the decay of D, atoms by simple thermal diffusion. According to a model of thermal diffusion involving a tunneling abstraction reaction, the constant yield of the H, atoms in storage at 4 K in the D2 matrix containing a small amount of H2may be explained as follows. Though the H, atoms can also decay in the D2-H2 (0.5 or 1.0 mol %) mixture, the reaction of Dt atoms with H2 (reaction 4) produces H, atoms. Thus, the apparent yield of the H, atoms is kept constant in storage. Figure 5 shows that H, atoms do not decay in the D2-H2 (10 mol % ) mixture, while D, atoms decay. Since the yield of the D, atoms is much smaller than that of the Ht atoms, the constant yield of the H, atoms in storage cannot be ascribed to the occurrence of reaction 4. Therefore, the thermal diffusion model involving a tunneling abstraction reaction may not be responsible for the decay of D, and H, atoms. The results given in Figures 3-5 can be explained easily in terms of a tunneling migration model in which D, and H, atoms repeat tunneling abstraction reactions such as reaction 3-5 and migrate through solid hydrogen to recombine with each other. Since H, atoms cannot react with D2 because of its endothermic reaction, the H, atoms in the D2 matrix cannot migrate by successive tunneling abstraction reactions. Calculated Rate Constant for Tunneling Abstraction Reactions at 4 K. Extensive work on the theoretical
J. Phys. Chem. 1983, 87, 5425-5429
calculation of kinetic isotope effects on H (D) + HZ (Dz) reactions has been reported previously.'~2J1 These calculations, however, deal with the reactions in the gas phase above room temperature. In order to obtain qualitative information on the hydrogen atom reactions in the solid state at 4 K, the rate constants for reactions 3-6 are calculated here by a simple method such as that used in a recent paper.12 The rate constant ( k ) for the tunneling abstraction is given by
k = ( A / R T ) l m G ( W )exp(-W/RT) dW 0
(8)
where G ( W ) is the permeability of the particle with the kinetic energy of W 3and can be obtained exactly for the unsymmetrical Eckart p0tentia1.l~ A is the frequency factor. Since concentrations of H2 and D2 are practically constant during the proceeding of reactions in solid hydrogen, the reactions can be assumed to be pseudo-firstorder reactions. A is taken here as 1014s-', which is roughly equal to a vibrational frequency of a hydrogen molecule. In order to calculate the permeability (G(W))by use of the unsymmetrical Eckart potential, a barrier height and a thickness of potential energy curve for reactions 3-6 must be assumed. The barrier heights for reactions 3-6 are taken here as 7.8,6.0,6.0, and 7.8 kcal/mol, respective1y.l' The barrier heights for the reverse reactions of reactions 4 and 6 are taken as 6.8 kcal/mol.llc Since reaction 6 is endothermic by 1 kcal/mol, the integration in eq 8 was (11) (a) Karplus, M.; Porter, R. N. Discuss. Faraday SOC. 1967,44,164. (b) Weston, R. E. Science 1967,158,332. (c) Suplinskas, R. J. J. Chern. Phys. 1968,49,5046. (d) Quickert, K. A.; Le ROY,D. J. Zbid. 1970,53,
5425
done over a range from 1 kcal/mol to m. The barrier thickness parameter ( a ) is taken as either 0.6 or 0.5 A, where 1 . 7 6 ~is equal to a width of a potential curve at a half-height when the potential function is symmetric. The barrier thickness in the present calculation is the same as that for the H + H2potential curve16 in the gas phase. The calculated rate constants for reactions 3-6 are summarized in Table 11. Tunneling corrections (F), defined by eq 9, are also shown in Table 11. k is the rate r = k/kclassicd k / ( A exp(-V/RT)l (9) constant that takes account of tunneling and is given by eq 8. kchid is the rate constant that is calculated without taking account of tunneling. V is the height of the potential barrier. The large value of the calculated kDtH,/ kH+D ratio is consistent with the experimental ratio (> 3 X loa) in Table I. The large value of the ratio is due to the tunneling plus the fact that reaction 6 is endothermic and reaction 4 is exothermic. Extremely large values of F indicate that the tunneling effect plays an important role in the reactions at 4 K. Since the rate constants for reactions 3-5 are relatively large, it may be possible for these reactions to take place before ESR measurements. Therefore, the tunneling migration may be probable in solid hydrogen at 4 K. The rate constant for the H + Dzreaction, however, is very small and thus Ht atoms in the D2 matrix cannot migrate by a successive tunneling abstraction. It is highly desirable to calculate the rate constants more precisely by use of an exact potential energy surface in solid hydrogen.
Acknowledgment. This work was supported in part by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science, and Culture. Registry No. Dz, 7782-39-0; H2, 1333-74-0; D, 16873-17-9; H,
1325. (e) K ~ p p lG. , W.Zbid. 1973,59,3425. (0M a w , H. R.Zbid. 1980, 7.? .-, -917. - .. (12) Aratono, Y.;Tachikawa, E.; Miyazaki, T.; Nagaya, S.;Fujitani, Y.; Fueki, K. J. Phys. Chem. 1983,87, 1201. (13) For a review, see: Caldin, E. F. Chern. Reo. 1969, 69, 135. (14) (a) Eckart, C. Phys. Reo. 1930,35,1303. (b) Johnston, H. S. J. Phys. Chern. 1962, 62,532.
12385-13-6. (15) Truhlar, D.G.;Horowitz, C. J. J. Chem. Phys., 1978, 68,2466.
Kinetics and Mechanism of the Oxidation of Aquated Sulfur Dioxide by Hydrogen Peroxide at Low pH James V. McArdiet and Michael R. Hoffmann' W. M. Keck Laboratories, Environmental Engineering Science, California Institute of Technology, Pasadena, California 9 I 125 (Recelved: January 21, 1983)
A stopped-flow kinetic study of the oxidation of sulfur dioxide by hydrogen peroxide was performed over the pH range 0.0-4.5. A rate expression of the following form was verified experimentally: d[S(VI)]/dt = klK,1[H2021[S(IV)](k2[H+] + k3[HAl)/((k-l+ k2[H+]+ k3[HA1)(Ka1+ [H+])J.The following kinetic parameters at 15 O C were determined: kl = (2.6 f 0.5) X lo6 M-' s-', k2/k-l = 16 f 4 M-',k z / k 3 = (5 f 1) X lo2 (HA = acetic acid), AH*'= 37 f 2 kJ mol-', and ASI1 = 4 f 4 J K-' mol-'. The reaction proceeds via a nucleophilic displacement of HSOf by Hz02to form a peroxymonosulfurousacid intermediate which undergoes acid-catalyzed rearrangement to form product: S02.Hz0 HS03- + H+ (Kal),H2Oz + HSO, HOOSO; (kl, k-J, HOOSO; H+ H+ + HSO, (k2),HOOS02- + HA HA + HS04- ( k 3 ) . Application of the above rate expression to reactions occurring in hydrometeors is discussed.
+
-
-
The oxidation of sulfur dioxide by oxygen, ozone, nitrogen dioxide, or hydrogen peroxide in aqueous microdroplets or hydrometeors has been suggested as a non-
--
'Current address: Smithkline Beckman Corp., Philadelphia, P A 19101. 0022-3654/83/2087-5425$0 1.50/0
photolytic pathway for the production of sulfuric acid in humid Oxidation by H202may be the (1) Hoffmann, M.R.;Boyce, s. D. "Advances in Environmental Science and Technology"; SChwdz, S. E., Ed.; Wiley: New York, 1983;v01. 12, pp 147-89.
0 1983 American Chemical Society
