J. Phys. Chem. 1981, 85, 2833-2834
2833
Temperature Dependence of the Gas-Phase Self-Reaction of HOz in the Presence of H,O' Ruey-Rong LH,* Myran C. Sauer, Jr.,* and Sheffield Gordon Chemistry Division, Argonne National Laboratory. Argonne, Illinois 60439 (Received: March 19, 198 I; In Final Form: June 1. IS8 1)
-
The dependence of the rate constant for the overall reaction HOz + HOz products on temperature (298-373 K) and on the concentration of HzO is reported. Analysis of the results in terms of a mechanism used earlier, where NH3was used instead of H20,yields information on AHo= and AGOzss for the formation of the HO2-H20 complex, but the error indexes are considerably larger than in the case of the H02-NH3 complex.
Introduction Hamilton and Lii first reported the accelerating effect of H 2 0or NH3 on the H02self-rea~tion."~This effect has been confirmed in more recent ~ o r k . The ~ , ~only explanation advanced to explain this effect is that a hydrogen-bonded complex is formed between H 0 2 and HzO or NH3 and that the reaction of this complex with H 0 2 is more efficient compared with the reaction of two uncomplexed H 0 2 molecule^.^^ The stability of the complex is supported by theoretical calculation^.^ The effect of temperature on the recombination (selfreaction) of H 0 2 in the absence of H20 or NH3 has been investigated thoroughly,6" and recent work has reported the temperature effect in the presence of H206and NH3.5 The latter studies add support to the hypothesis of the complex and its greater reactivity. Our results5with added NH3 provide thermochemical information on the H02-NH3 complex, and Cox and Burrows6 have analyzed their results with added H 2 0 to obtain analogous information on the H02-Hz0 complex. However, the results presented here will be seen to indicate that limitations peculiar to the H20-H02 system seriously limit the accuracy of the determination of the thermochemical properties of the HO2-H20 complex. Experimental Section The pulse radiolysis apparatus and the techniques used were the same as described earlier in the case of the NH3 for minor changes in technique necessis ~ s t e mexcept ,~ tated by the limiting vapor pressure of water at room temperature. The desired amount of water was collected in a side arm and vaporized into the reaction cell containing 1.8 X 1017molecules cm-3 of oxygen at the desired temperature. Hydrogen was then added to bring the total concentration to 3.8 X 1019molecules ~ m - ~ . As has been discussed under the experimental conditions employed, the electron pulse produces hydrogen atoms on a submicrosecond time scale, and the hydrogen atoms form H02 (- 1.2 X 1015molecules ~ m - within ~ ) a few microseconds. The reaction of HOzproceeds considerably (1) Work performed under the auspices of the Office of Basic Energy Sciences of the U.S. Department of Energy. (2) Department of Chemistry, Malcom X College, Chicago, IL 60612. (3) Hamilton, E. J., Jr. J. Chem. Phys. 1975, 63, 3682. (4) H p i l t o n , E. J., Jr.; Lii, R. R. Int. J. Chem. Kinet. 1977,9, 875. (5) LII,R. R.; Gorse, R. A., Jr.; Sauer, M. C., Jr.; Gordon, S. J.Phys. Chem. 1980,84,813. (6) Cox, R. A.; Burrows, J. P. J. Phys. Chem. 1979,83, 2560. (7) H.eilton, E. J., Jr.; Naleway, C. A. J. Phys. Chem. 1976,80,2037. (8)LII,R. R.; Gorse, R. A,, Jr.; Sauer, M. C., Jr.; Gordon, S. J.Phys.
Chem. 1979,83,1803.
0022-3654/81/2085-2833$01.25/0
more slowly; i.e., the f i s t half-time for decay is in the range of 80-400 ms. Results and Discussion The values of the rate constants (k,bsd) were obtained from the observed decay of absorbance ( A = log [&,/Itr]) at 230 nm by using the known absorption cross section of cm2 molecule-l, base e)e and eq I HOz (u = 2.17 X
_1 - 1 A -
2kobsd +-allog t e
where 1 is the optical path length and t is time. Secondorder kinetics were followed over three to four half-lives. Figure 1 shows the experimental results. As we have discussed earlier in detail in the case of the NH3 system? analysis of the data in Figure 1is done on the basis that the complex formed in reaction 2 of ref 5 has the same absorption coefficient at 230 nm as HOP Briefly, support for this is based on the observations that the initial absorbance changes little with added H20 or NH3394and that the addition of H20 or NH3has little effect on the shape of the observed absorption spectrum in the 220-250-nm r e g i ~ n . ~ In the same manner as in the case of NH3, these results were analyzed in terms of the following reactions: H 0 2 + HO2 A H202 + 0 k
HOz + H 2 0 & H20.-.H02 k-7
HzO...HOp + H 0 2
-
k0
H20..-H02+ H20. .HOP
2
( K = k7/k-,)
products1' kv
(7) (8)
products'l
(9) The reaction numbers are the same as those used in ref 5 for the case of NH3 in order to facilitate comparisons; H20 has replaced NH3 where appropriate. Reaction 1is an "overall" reaction; the detailed mechanism is thought to involve an H2O4 intermediate.* No pressure effect is observed in the range of 25-1200 t ~ r rand , ~the ~ ~reaction is observed to become pressure dependent when the pressure is below -4 torr.1° We have showns that, under (9)Paukert, T. T.; Johnston, H. S. J. Chem. Phys. 1972, 56, 2824. (10) Thrush, B. A.; Wilkinson, J. P. T. Chem. Phys. Lett. 1979,66,441. (11) Reaction 1 proceeds through an HzO, intermediatee8 Cox and
Burrows6 have proposed that reactions 8 and 9 yield this complex also. Under these conditions an equation of the same form as eq I1 results, but k8 and k8 are multiplied by a factor (=0.05) representing the ratio of the dissociation of HzOz+ O2 relative to dissociation into 2H02. A troublesome aspect of this proposal of Cox and Burrows is the large value of ks needed; Le., it must correspond to the gas-kinetic collision frequency.
0 1981 American Chemical Society
2834
Lll et al.
The Journal of phvsical Chem/stry, Vol. 85, No. 19, 1981
TABLE I : Information Derived from the Fitting Procedure conditions of calcn
k , / k , (at 6 3 "Cy
E,=E,=O
24
E , = E , = -2.1 kcal mol-'
f
200
-0
6.8 f 100
1Oi9K298, cms molecule-'
k , / k , (at 63 "C)" f
300
1.3 i 0.9 4 . 1 i 27
6.1 * 30
AG0298,b
kcal mol-' -0.J'O.'
-0.3
-1.4:!.6
a The error limits on k , / k , , k , / k , , and K,,, are calculated from the standard deviations of A ' - A s and a table of matrix elements (provided by the computer program) which allows correlation between the different A values to be taken into account. The error limits on AG",,, are estimated from the spread in K,,,. 8
I
I
0
1
second, the vapor pressure of water limits the fraction of H 0 2 which can be complexed at a given temperature. Thus, it is not possible to complex a fraction of the H 0 2 sufficiently large to allow an accurate determination of Al, Az, AB,and Ab Values of the parameters (and their standard deviations as determined by the program) obtained by letting E8 = Eg= 0 are Al = (0.52 f 4.1) X cm3molecule-' s-', A2 = (0.12 f 7600) X cm3 molecule-' s-', As = (0.125 f 0.73) X lo-% cm3molecule-l, A4 = 8.2 f 2.0 kcal mol-', and A5 = (0.93 f 0.02) X cm3molecule-' s-'. The curves in Figure 1 are obtained from eq I1 using these values. The values of E8and Egare not known; therefore, the fitting procedure was also done with E8 = E9 = -2100 cal mol-', Le., the same value as for reaction 1. The values of the parameters obtained are Al = (0.63 f 9.2) X cms cm3molecule-' s-l, molecule-' s-', Az = (0.47 f 2.7) X As = (0.23 4.3) X cm3 molecule-', A4 = 5.8 f 0.3 cm3molecule-' kcal mol-', and A6 = (0.92 f 0.02) X s-'. The curves calculated by using these parameters are virtually identical with those shown in Figure 1. Table I shows the values of k8/kl, k9/k1,Km, and AGOzss for reaction 7, which are obtained from the parameters A1-A5. It is clear from the very large standard deviation of A2 that reaction 9 is unimportant under the present conditions, i.e., low conversion of H 0 2 to complex. The rate constant for reaction 8 and the value of K have large uncertainties, which means that the observed experimental effects can be explained nearly as well by lower values of k8 and higher values of K or by higher values of k8 and lower values of K. The values of A4 obtained, in view of the limited precision, cannot be considered to be in disagreement with = 7.4 kcal mol-l. Cox and the theoretical value' of Mom Burrowss have derived a value of 9.0 kcal mol-' (ref 12) from their data. The latter authors also obtained KzS8 = 1.9 X cm3 molecule-'; the values of &98 in Table I are consistent with this. It should be noted that the results of Cox and Burrows cover a smaller range of temperature and concentration of water than do the present results and are not of greater precision. The mechanism which they use to derive the thermochemical values can be shown to be essentially the same as that used here (see ref 11); therefore, their derived values should suffer from similar imprecision.
1
OO
I
2
[H~o]x 10-18 (malec cm-31 Figure 1. Rate constant for HOPdisappearance as a function of H20 ConcentratIciI at fou temperatwes. The uwves are calculated by using eq I1 (see text).
the assumption of equilibrium 7 being rapid in comparison with radical disappearance reactions, the observed rate constant, kom,is given by
kobsd =
kl + k&[HzOI + ~ 9 m H 2 0 I 2 (1 + K[HZOI)~
(11)
The data in Figure 1 were fitted to this expression by using a nonlinear least-squares technique with five variable parameters A'-A5, defined by the following: k8 = A1 exp(-E8/RT)
k9 = A2 exp(-E9/RT) K = AS exp(A4/RT)
kl = A5 exp(2100/RT) Although this method of analysis was satisfactory in the case of NH3 and allowed values to be obtained for the parameters with reasonably small error indexes, the analysis proves to be less precise in the case of H20. Essentially, the results of our fitting efforts show that the values of A', A2, and A3 have very large standard deviations. This is due to the fact that, if one parameter is made smaller, making another larger can bring the calculated results back into fair agreement with experiment. Qualitatively, the reason that this occurs in the H 2 0 system but not in the NH3 system is due to a combination of two factors. First, the equilibrium constant K is such that reaction 7 is more to the left in the case of H 2 0 and,
*
(12) We are not sure whether it is fortuitous, but, if we carry out our fitting procedure with A, fixed at 9 kcal mol-', the standard deviations of the results become considerably lower, i.e., k s / k l = 6 k 1, ko/kl = 8 f 2, and Kase= (8 4) X cm3molecule-'. If A, is fixed at 7.4 kcal mol-', the standard deviations are comparable to those in Table I.
*
