J. Phys. Chem. 1982,
1588
86, 1588-1590
hartree than the energy of the 3A MC-SCF wave function calculated at the By, geometry and expressed over orbitals which were supposedly optimized for that geometry. Thus, multiconfiguration SCF calculations for openshell systems are susceptible to a form of the same type of electronic symmetry breaking as plagues open-shell single-configuration SCF calculations, and which has been described in detail in an earlier section of this paper. Explicit use of symmetry in optimizing the orbitals, or implicit use through use of symmetry orbitals as the initial guess, may lead to discontinuous potential surfaces. On the other hand, dropping all constraints may lead to wave functions of broken symmetry even when fairly elaborate MC-SCF functions are used.
geometry gave an energy of -259.2822 hartree, identical with that previously determined for the 12-configuration 3B3u wave function when symmetry orbitals were used as the initial guess. On the other hand, reducing the geometric symmetry to C2u by changing the z coordinate of only one nitrogen in such a way as to elongate the N-N axis by 0.01 bohr radius revealed serious difficulties. The 123A MC-SCF wave function (with new C1 MOs) retained its 3(mr*) character at this C2v geometry, but the total energy changed discontinuously by -0.00490 hartree to -249.297 09 hartree. (This may be compared to a “more reasonable” energy change of +0.00003 hartree resulting from a displacement of the same nitrogen atom by the same amount along its y coordinate.) The discontinuous electronic potential energy surface for the small MC-SCF wave function rendered impractical, for the time being, an unconstrained MC-SCF normal mode analysis for the 3(nir*) state. More fundamentally disturbing, however, were the results of the following experiment. Another 3A Cl wave function was calculated over the orthogonalized MC-SCF orbitals that had been optimized at the slightly distorted C2u geometry (having one N displaced along the z axis). This time, however, the nuclear geometry used was the By, optimal geometry. The energy of this second 3A wave function was -259.286 69 hartree. This is lower by 0.00450
Acknowledgment. We thank Drs. Michelle Dupuis and John Wendelloski of the National Resource for Computation in Chemistry for providing us with copies of their GAMESS program, which performs analytic gradient SCF and MC-SCF geometry optimizations, and for assisting us in its use. The assistance of Dr. Larry McMurchie with certain details of the computations is also gratefully acknowledged, as are valuable discussions with Professor Alvin Kwiram, and with Dr. Richard Martin of the Los Alamos National Laboratory. This research was sponsored by a grant from the National Institutes of Health.
Reactions of Hydroxyl Radicals with Hydrogen Peroxide at Ambient and Elevated Temperatures Hilbert Christensen,* Studsvlk Energiteknik AB, S-61182 Nykoping, Sweden
Knud Sehested, and Hanne Corfltzen Accelerator Department, Rise National Laboratory, DK 4000 Roskilde, Denmark (Received: September
10, 1981)
The reaction of hydroxyl radicals with hydrogen peroxide has been studied in the pH range 6.8-13.8. &oh+h2o2 was determined to be (2.7 ± 0.3) X 107 dm3 mol'1 s'1 and *o'+ho2" to be (4.0 ± 0.5) X 10s dm3 mol'1 s'1. The rate constants of the cross reactions OH + H02" and O' + H202 could not be determined separately. However, an upper limit of & '+ 2 2 = 5 X 108 dm3 mol'1 s'1 was measured. Consequently, by disregarding this reaction, &oh+ho2- was determined to (7.5 ± 1.0) x 109 dm3 mol"1 s'1. The reaction between OH and H202 was studied at pH 7.8 in the temperature range 14-160 °C, and an activation energy of 14 kJ mol"1 (3.4 kcal mol'1) was derived from the Arrhenius plot with a rate constant of (2.7 ± 0.3) X 107 dm3 mol'1 s'1 at 20 °C.
Introduction With the objective being to study the radiation chemistry of water at elevated temperatures as experienced in
the various protolytic forms. Some of these reactions have been studied previously; see, e.g., ref 1-5. The values given for the rate constant of reaction 1 vary between 1.2 X 1073 and 6.5 X 107 dm3 mol'1 s'1.2 Values of the rate constant of reaction 4 vary between 3.9 X 1081 and 1 X 109 dm3 mol'1
we have started a program to determine rates and activation energies of reactions by pulse radiolysis at increased temperatures. In the present investigations we have studied the reactions of the oxidizing radical with hydrogen peroxide in aqueous solutions. Due to protolysis both hydroxyl radicals and hydrogen peroxide exist in two forms in neutral and alkaline solutions. An electron pulse initiates reactions 1-4 which occur between OH + H202 — H20 + 02' + H+ (1)
power reactors,
O' + H202 OH + H02"
—
-*·
O' + H02'
OH' + 02' + H+
(2)
OH" + 02' + H+
(3)
OH' + 02'
(4)
—
0022-3654/82/2086-1588Í01.25/0
s'1.4
The rates of the two other reactions, 2 and 3, are difficult to determine separately. Rabani5 gives the value of Aq'+ha + 1.42fe0H+H02- as 1.18 X 1010 dm3 mol'1 s'1, whereas Buxton2 has determined this sum to be 8 X 109 dm3 mol'1 s'1; from these results an upper limit for &oh+ho2- °f 8.3 J. Rabani, Adv. Chem. Ser., No. 81, 131-52 (1968). G. V. Buxton, Trans. Faraday Soc., 65, 2150—58 (1969). H. Fricke and J. K. Thomas, Radiat. Res., Suppl., 4, 35-53 (1964). W. D. Felix, B. I. Gall, and L. M. Dorfman, J. Phys. Chem., 7Í, 384-92 (1967). (5) J. Rabani and M. S. Matheson, J. Am. Chem. Soc., 86, 3175 (1964). (1) (2) (3) (4)
©
1982 American Chemical Society
Hydroxyl Radicals and Hydrogen
The Journal
of Physical Chemistry,
Vol. 86, No. 9, 1982
1589
TABLE I: Reactions of Hydroxyl Radicals with Hydrogen Peroxide 10 sXkc,
pH
6.8 7.4
gas
s"1
N20
4.5 4.1
4.2 3.9 3.3 4.8 9.4 8.4 6.2 4.9 3.9
8.1 8.3 9.0
10.0 10.5 11.2 11.7 11.9 12.1 12.5 12.8 13.0 13.3 9.0 11.9 13.8 8.0 8.5 9.0 9.5
10"3[H2O2 + H02"], mol dm"3
2.6
Ar
1.85 2.8 2.2 3.2 4.2 2.3
3.9 2.4 3.6 3.3 6.0 8.6 9.2
10.0 10.5 11.0
15.6 14.65 14.9 15.1 7.39 3.15 3.23 1.08 0.3 2 0.22 0.156 0.151 0.146 0.36 0.36 7.39 0.22 0.36 15.96 10.08 9.23 6.01 5.66 2.83 1.13
Wzk, dm3
mol"1 s" 2.9 2.8 2.8 2.6 4.5 15.4 29 78 193 225 250 171 127 78 60 6.3 191 64 2.4 2.4 3.9 5.4 10.6 30 81
X 109 10and 5.7 X 109 dm3 mol"1 s'1, respectively, can be calculated. Buxton’s rate constants were determined by competition kinetics with carbonate. Rabani measured the buildup kinetics of 02" at 260 nm. The pK of OH and H202 are very similar, 11.95,6 and 11.8,7 respectively. Due to the variation in the literature values an investigation of the rate constants at room temperature in the pH region 6.8-13.8 was initiated.
Experimental Section The experimental procedure has been described in detail previously.8 For the investigations at ambient temperature the ordinary setup was used.9 The experiments at elevated temperatures were performed in the high temperature-pressure cell.8 The HRC linear accelerator at Riso delivered 10-MeV electrons in a single pulse of maximum 1.1 A and a pulse length of 0.5-1 gs. The dose varied from 1-10 krd/pulse and was measured with the hexacyanoferrate(II) dosimeter with e420 = 1000 dm3 mol'1 cm"1 and G = 5.3. The optical system consists of a 150-W Varían high-pressure Xenon lamp, a Perkin-Elmer double quartz prism monochromator, a 1P28 photomultiplier, and a Nicolet Explorer III digital storage oscilloscope. The data were treated on an on-line PDP8 computer. The reaction rates were measured by the buildup kinetics of the peroxy radical at 250-270 nm. Hydrogen peroxide of Merck p.a. quality was used throughout the experiments. The hydrogen peroxide concentration was measured by acidifying the solution with perchloric acid and then oxidizing ferrous ions and measuring the absorption of the ferric ions at 240 nm with f24o
=
4200 dm3 mol"1 cm"1.10
(6) G. E. Adams, J. W. Boag, J. Currant, and B. D. Michael, “Pulse Radiolysis”, Academic Press, London, 1965, p 117-129. (7) G. Czapsld and B. H. J. Bielski, J. Phys. Chem., 67, 2180-84 (1963). (8) H. Christensen and K. Sehested, Radiat. Phys. Chem., 16,183-86
(1980). (9) K. Sehested, H. Corfitzen, H. C. Christensen, and E. J. Hart, J. Phys. Chem., 79, 310 (1975). (10) K. Sehested, E. Bjergbakke, O. Lang Rasmussen, and H. Fricke, J. Chem. Phys., 51, 3159-66 (1969).
Figure 1. Rate constant of the reaction between hydroxyl radicals and hydrogen peroxide, komcn+H^Hon· as a function of pH. Each point is the average of six separate determinations: (+) N20 saturated; (O) Ar saturated. The solid line is the computed curve based on reactions
1-8.
Results and Discussion Reactions at Ambient Temperature. The apparent rate constants at various pHs in the region 6.8-13.8 are shown in Figure 1. The points on the curve represent the mean of six determinations carried out at 250, 260, and 270 nm, with a new solution for each determination. The dose was 17 Gy (1700 rd), and the solutions were either N20 or Ar saturated. Details of the experiments are given in Table I. The apparent rate constant is mixed and may be expressed as &oh(o-)+h2o,(ho2-)· The hydrogen peroxide concentration was varied between 15 and 0.15 mM, mainly to keep the reaction rates within certain limits. The [H202] in alkaline solution was measured both before and after the experiment, but no destruction of hydrogen peroxide was found during the experiments. From Figure 1 the following rate constants can be derived: reaction 1, & + 2 2 = (2.7 ± 0.3) X 107 dm3 mol"1 s"1; reactions 2 + 3, *£(0-+h2o2),(oh+ho2-) = (7.5 ± 1.0) X 109 dm3 mol"1 s"1; reaction 4, Aq-+ho2- = (4.0 ± 0.5) X 108 dm3 mol"1 s"1. k2 and k3 cannot be separated in these experiments.1,2 However, an attempt to determine k2 separately was done by the following experiments. An aqueous solution of hydrogen peroxide either 25 X 10"3 or 70 X 10"3 mol dm"3, pH 8.9, saturated with 4 or 0.1 MPa of N20 was irradiated with a single pulse of 50 or 25 Gy (5 or 2.5 krd). The optical densities at the end of the pulse, ODinitial, and at the maximum, ODmax, were measured. The reactions involved together with the appropriate rate constants and concentrations are given in Table II. The idea was to produce O" from the hydrated electron with 4 MPa of N20 and then let water and hydrogen peroxide compete for the O". If & -+ 2 2 5 x 108 dm3 mol"1 s'1, the yield from this reaction is 20% of the electron —
The Journal
1590
of Physical Chemistry, Vol. 86, No.
Christensen et al.
9, 1982
TABLE III:
Rate Constants for the Reaction of H202 at Various Temperatures (Dose, 20 or 40 Gy [H202] 1.59 x 10"2 mol dm"3;pH 7.8)
TABLE II: Reactions in N20-Saturated Aqueous Solutions of H202; Determination of the Upper Limit for fc0" + H202
OH
=
concn,
P(N20), MPa
reaction +
eaq '
eaq
+
-*
N20
O
mol dm"3
0.8 6 X 109 0.02 6 X 109 0.07 1.3 X 1010 0.07 02" 0" + H2G -> OH OH + H20, -> O,"
55
0.07
2 X 106
2.7
X
107
temp, °C rate constant,
kc, s'1
4.8 1.2
+
14 20 40 50 60 80 110 2.1 2.7 4.2 4.6 5.7 7.4 9.8
140 160 13 15
107 dm3
109 X 10s 9 X 10s 3.5 X 107 1.1 X 10s 1.9 X 106 X
mol"1 s'1
yield or 10% of the total OH yield. As the reaction with the assumed rate constant is 20 times faster than reaction I, the ODjnitiai should be increased. This was, however, not the case, and from that we conclude that & -+ 2 2 < 5 X 108 dm3 mol-1 s'1.
As pointed out by Rabani,1 reaction 3 should be expected to be much faster than reaction 2 as the former involves an electron transfer, whereas the latter requires a hydrogen atom transfer. With the assumption that k2 is comparable to kx Rabani found a rate constant k2 m 5 X 107 dm3 mol'1 s'1.
If we, therefore, assume k2 to be negligible in comparison with k3, the latter can be calculated from the results in
Table I. The solid line shown in Figure 1 was calculated by computer simulation using a radiation chemical program The chemical equations developed by Rasmussen.11 consist of reactions 1-4 and 5-8. The best fit was obtained H202 + OH'
-
5 X 10® dm3
H02' + H20
->
H02' + H20
(o)
mol'1 s'1
HA
+ OH-
io)
5.7 X 104 dm3 mol'1 s'1
OH + OH'
O'
4-
H20
—
—
O' + H20 OH + OH"
4 X 1010 dm3 mol'1 s'1
(7)
mol'1 s'1
(8)
2 X 10® dm3
(7.5 X 1.0) X 109 dm3 mol'1 s'1 and (4.0 ± 0.5) X 10® dm3 mol'1 s'1. Rabani1 gives the values k3 = 8.3 X 109 and k4 = 2.74 X 10® dm3 mol'1 s'1. Apparently there is an increase in the overall k value shown in Figure 1 above pH 13.5. If real, this may be caused either by the appearance of a second dissociation
by using k3
=
=
of hydrogen peroxide, equation 9, or by the effect of the (9) HOf + OH" 022' H20 -*
increasing ionic strength with increasing hydroxide concentration. Our data may indicate that the calculated curve should be shifted about one-tenth of a pH unit higher. This cannot be accounted for by changing the rate constants, but the calculated line would give a better fit if the pK of hydrogen peroxide was changed from 11.8 to II. 9. Reactions at High Temperature. The rate constant of reaction 1 was measured at various temperatures in the region 14-160 °C at pH 7.8. The concentration of hydrogen peroxide was 15.9 X 10'3 mol dm3, and the solutions were saturated with N20 at a pressure of 1 MPa, allowing 15 min of stirring. The cell was then pressurized to 5 MPa with Ar. The dose was 20 or 40 Gy. Hydrogen peroxide was measured before and after the experiment after cooling to ambient temperature. On the basis of these analyses, the heating and cooling time, and the time the solution was (11) O. Lang Rasmussen, private communication.
Figure 2. Rate constant of the reaction between OH and H202 as a function of the reciprocal Kelvin temperature (pH 7.8). Temperaturepressure cell: (+) 2 krd, (O) 4 krd. Normal thermostated cell: ( ) 2 krd.
kept at the elevated temperature, the actual concentration at the time of the experiment was estimated. Below 100 °C there was only a few-percent correction, but at a temperature of 140 °C the hydrogen peroxide decreased about 30-35% during the heating and cooling cycle. The rate constant was determined from the buildup of absorption of 02" at 250-270 nm. A list of rate constants at the various temperatures is given in Table III, and an Arrhenius plot is shown in Figure 2. From the figure an activation energy of reaction 1 of (14.0 ± 1.4) kJ mol'1 ((3.4 ± 0.03) kcal mol'1) can be calculated. This value is close to the activation energy for diffusion in water, 13 kJ mol"1 (3 kcal mol'1), but lower than the value 4.5 kcal mol'1 given by Jenks12 in his list of assumed activation energies. The Arrhenius expression for the rate constant in the gas phase has recently been given as k = (2.51 ± 0.6) X 10'12 exp(-126 ± 76)/T cm3 molecule'1 s'113 and k = (2.96 ± 0.50) X 10~12 exp(-164 ± 52)/T cm3 molecule'1 s'1,14 corresponding to activation energies of 1.4 and 1.0 kJ mol"1, respectively. This indicates that the activation energy in aqueous solutions is caused mainly by the diffusion resistance in water. If we calculate the rate constant at 286 °C—the operation temperature of a BWR (boiling water reactor)—using our activation energy, k = 4.3 X 10® dm3 mol'1 s'1 is obtained in comparison with k = 1.1 X 10® dm3 mol'1 s'1 from Jenk’s activation energy. This significant difference, a factor of 2.5, demonstrates the importance of an improved knowledge of rate constants at elevated temperatures. Calculations of the radiation chemistry at high temperatures based on the existing data are necessarily of poor
reliability. Acknowledgment. We thank Erling Bjergbakke for his assistance in the computer calculations. H.C. gratefully acknowledges a grant from the Swedish Board of Technical
Development (STU). (12) G. H. Jenks, Oak Ridge Nat. Lab., [fiep.] ORNL-4173,10 (1967). (13) L. F. Keyser, J. Phys. Chern., 84, 1659-63 (1980). (14) U. C. Sridharan, B. Reinman, and F. Kaufman, J. Chem. Phys., 73, 1286-92 (1980).
