DECAY KINETICS OF
THE
PERHYDROXYL RADICAL
3209
The Acid Dissociation Constant and Decay Kinetics of the Perhydroxyl Radical1
by D. Behar, G. Czapski, J. Rabani, Department of Physical Chemistry, Hebrew University, Jerusalem, Israel
Leon M. Dorfman, Department of Chemistry, The Ohio State University, Columbus, Ohio
and Harold A. Schwarz Department of Chemistry, Brookhaven National Laboratory, Upton, New York 119'73
(Received March 86? 1970)
The acid dissociation constant of the perhydroxyl radical was found to be 4.88 It 0.10 in a pulse radiolysis study of oxygen-saturated aqueous solutions. The solutions were buffered with formic acid-sodium formate which also served to transform the hydroxyl radicals into perhydroxyl radicals by reaction with the formate and subsequent reaction with oxygen. This pK value is in agreement with one earlier value, but in disagreement with others. The discrepancy is shown to be most likely due to the absence of buffer in moat earlier work. The second-order kinetics of recombination of perhydroxyl radicals follow the equation, k = (0.76 X 106 + 8.5 X lO7X)/(l X ) 2 , where X is the ratio of the dissociation constant to the acid concentration, 0.76 X 106 M-1 sec-l is the rate constant for the reaction HOz HOz, and 8.5 X lo7 M-l sec-l is for the reaction 0 2 -is shown to be less than 100 M-l sec-I. The HOz 02-. The rate constant for the reaction 02results suggest that only two forms of the perhydroxyl radical, HOz and OZ-, exist in the pH region 0 to 13.
+
+ +
+
Introduction Until recently, there was a general consensus that the p K of the perhydroxyl radical
H++ 0 2 -
HOz
(1)
was 4.5 f 0.15.2-4 Rabani and Nielsen, in a pulse radiolysis study of the decay kinetics of H02,5challenged this value and concluded that the pK is really 4.8. Their work differed from the earlier studies in that acetate and phosphate buffers were used to establish the p H of the solutions. (Earlier work was performed in the absence of buffer.) It is not clear that any buffer can be considered a priori to be inert in an irradiated solution and it is possible that different peroxy radicals are produced in the presence of the buffers. Indeed, Behar and Czapski6found decay kinetics for HOz much different from those of Rabani and Sielsen (faster by several orders of magnitude in the p H range 6 to 9). We decided that further study of the perhydroxyl radical was needed to resolve some of the discrepancies. We chose to study the pulse radiolysis of oxygenated formate solutions because : (1) radiation chemical studies suggest that all radicals are converted to the perhydroxyl radical in this system and ( 2 ) the solutions e,,
H OH
+
+
0 2
0 2
+02-
+HOz
+ HCOO-
coz- +
0 2
+C02-
+0 2 -
+ coz
are self-buffering (pK(HC0OH) of the perhydroxyl radical.
=
3.75) near the pK
Experimental Section Reagent grade sodium formate was recrystallized from water. Triply distilled water was redistilled twice more just before preparing the solutions. The p H of the formate solutions was adjusted by adding either perchloric acid or sodium hydroxide. All solutions were saturated with oxygen. At p H 7 and above, oxygenation preceded the addition of sodium hydroxide, thereby removing the C 0 2from the system. The p H of the solutions was both measured and calculated from the known composition, the two values agreeing within 0.05 p H unit for all samples used. A linear accelerator operating a t 5 MeV and 200 mA was used as the radiation source. The pulse length was varied from 0.1 to 1.5 psec in order to change the dose per sample. The HO2 and 02- concentrations were followed spectrophotometrically. A deuterium light source was used to produce the analyzing light for the kinetic (1) This work performed under the auspices of the U. S. Atomic Energy Commission. (2) G. Czapski and €3. H. J. Bielski, J . Phys. Chem., 67,2180 (1963). (3) G. Caapski and L. M. Dorfman, ibid., 68, 1169 (1964). (4) J. Rabani, W. A. Mulac, and M. S. Matheson, ibid., 69, 53 (1965); K. Sehested, 0. L.Rasmussen, and H. Fricke, ibid., 72, 626 (1968). (5) J. Rabani and 9 . 0. Nielsen, ibid., 73, 3736 (1969). (6) D. Behar and G. Caapski, Israel J . Chem., in press.
The Journal of Physical Chemistry, Vol. 74, No. 17,1970
D. BEHAR,G, CZAPSKI, J. RABANI, L. M. DORFMAN, AND H. A. SCHWARZ
3210
studies and for the measurement of initial optical densities in formate solutions. A xenon lamp was used for the measurement of initial optical densities in solutions not containing formate. The light made three passes through a 4-cm cell. A ‘Lsolar-blind’’ photomultiplier, R166, was used to measure light intensities a t wavelengths below 260 mp. Scattered light was less than 3% of the signal in all cases and was ignored. The radiation dose was measured with an NzOsaturated low3 M IGFe(CN)e solution7 containing about 2 X loF6M ferricyanide, the latter to react with the hydrogen atoms, and the ferricyanide yield was assumed to be 5.7 (calculated as G,,, GoH - GH). The extinction coefficient of Fe(CN)63- a t 400 mp is 980 M-l cm-1, It was determined that a t least 10 pulses of 2000 rads each could be given a single sample without observable effect on the initial absorption of HO2 or 0 2 - in formate solutions. Consequently we sometimes gave as many as six pulses per sample.
+
Results Preliminary experiments established that the absorbance per pulse a t 240 nm in formate solutions was M independent of formate concentration between and low2M, both a t pH 2 and a t p H 7. All subsequent work on formate solutions was performed with 5 X M formate. Absorption Spectra. Spectra of HO2 and 0 2 - were measured in oxygen-saturated formate solutions a t pH 2.0 and 7.2, respectively. First, spectra relative to a standard wavelength (240 nm for HOZand 260 nm for 02-) were obtained by splitting the light beam with a half-reflecting mirror and comparing the absorption at a
A , nrn
Figure 1. Absorption spectra of 0 2 - (upper curve) and KO2 (lower curve) obtained from the pulse radiolysis of oxygen-saturated 5 x 10-8 iM sodium formate solutions. The Journal of Physical Chemistry, Vol. 74, No. i7,1870
given wavelength, using one monochromator, with the absorption at the reference wavelength, using a second monochromator. Thus, there was an internal dosimeter for each pulse of radiation. Second, the ratio of absorption of Oz- to HOz at 240 nm was determined by relying on the reproducibility of consecutive pulses from the accelerator (a standard deviation of *4% per pulse). By alternating samples at the two pH’s, (EO~-/EHOJ 240 nm was found to be 1.78 0.03, assuming the radical yields independent of pH. Third, absolute values of eo2- were obtained by alternating samples at pH 7,2 with nitrous oxide-saturated ferrocyanide dosimeter. The resulting absorption spectra are given in Figure 1. Some of the points are averages of 2 or more determinations. The resolution of the monochromator was f3 nm for these experiments. Acid Dissociation Constant. The pK of HOz could be determined by comparing a curve of absorbance vs. pH at some wavelength with a computed curve which is based on the assumption that the shape of the curve is due only to the acid-base equilibrium.
*
A = e ~ o ~ ( H 0 2f) €oa-(02-)
where
and
(HOz), = (HOz)
+
(02-1
Instead of this procedure, we have chosen to determine the pK from the effect of pH on the ratio of the absorptions a t two wavelengths, obtained as described above for the absorption spectra. Ideally, the reference wavelength should be the isobestic point of the absorption spectra of H 0 2 and 0 2 - , Le., the wavelength a t which A , the absorbance, is independent of pH. Such a crossover is below 220 nm, as may be seen from Figure 1, and is inaccessible due to the absorption of formate and formic acid. From eq 2, the ratio of absorbance a t 260 nm to that a t 240 nm is
I n principle, the extinction coefficients could be taken from Figure 1,but this is not satisfactory in the present case as the band width of the monochromators were increased significantly (to 7 nm) for the pK measurement to increase the signal to noise ratio, and 260 nm is on the steeply changing portion of the spectra. The ~ /the E ratio ~ ~ ~~ ~o ~ O - ~ ~ found ~ / ~ H o ~ ~ ~ ratio E ~ ~ - ~ ~and with the increased band width, were 1.78 and 1.57, in (7) J. Rabani and M. S. Matheson, J. Phys. Chem., 70, 761 (1966).
DECAY KINETICS OF I
THE
PERHYDROXYL RADICAL
I
I
I
3211
I
0' .I9O 1
0,5
2
1
I
3
4
1 5
I 6
I
-*
L
I
7
PH Figure 2. The effect of pH on the absorbance of the perhydroxyl radical a t 260 nm compared to 240 nm, obtained from oxygen-saturated 5 X 10-3 M sodium formate solutions a t 27.5". The total radical concentration was 2.1 p M . Curve is calculated for pK = 4.88.
pK, obtained by comparing the data of Figure 3 with agreement with Figure 1, but the ratio E H O ~ ~ ~ ~ was 0.39, 10% smaller than the corresponding ratio in Figure 1. This corresponds to a shift in effective wavelength of only 2 nm, however. The data are given in Figure 2. The curve is that calculated for a pK of 4.88. The standard deviation of the mean of the pK is only 0.02, but taking into consideration the uncertainties in relative values of E as well as possible errors in pH measurement we believe the pK is reliable to j=O.lO. This value of the pK is 0.4 higher than earlier estimatesz-4 and it was considered worthwhile to repeat the determination on one of the unbuffered systems studied previously: oxygen-saturated watera3 The OH radical contributes to the absorbance in this system8 so that the ratio of absorbances a t high and low pH are not the same as in Figure 1. The decay of the absorbance in the absence of formate is principally by the rapid reaction of OH with HOz and 02-. We extrapolated the absorptions measured between 5 and 15 psec after the pulse back to the end of the pulse (an extrapolation of 9% in the worst case). This time range certainly allows for equilibration at pH's below 5 and above 9. A somewhat shorter wavelength was used for the reference in these experiments, 230 nm being a compromise between p H independence and signal-to-noise ratio (which is smaller a t shorter wavelengths). The data are given in Figure 3. It is very difficult to know the pH of samples between 5 and 9 in the absence of any buffer, due both to the vagaries of micromolar quantities of hydrogen ion or hydroxide ion and to the contribution of the HOz itself to the pH. Consequently, the upper limit of the curve was measured above pH 9 and the points between p H 5 and pH 9, while displayed in the figure, were ignored in estimating the pK. The pH's used in Figure 3 are measured values, obtained before irradiation, and corrected for the estimated ionization of the HOz (which was about 2 p M ) . The best value of the
/ the ~ H equation O ~ ~ ~ ~
R
Azao
= -=
A230
+ +
0.550 1.131X 1 1.143X
(4)
is 4.80. It is less precise than the value obtained in Figure 2 because the pH's of the solutions are not as well characterized. Kinetics. One of the purposes of this work was to obtain additional evidence concerning the recombination rate of perhydroxyl radicals. The decay of the absorption spectrum should be second order. We studied the decay in oxygen-saturated 5 X lo-* M sodium formate solutions. The decay is strongly pH dependent above pH 3, and very low doses (producing 1-4 pM HOz) were used to minimize the effect of the dissociation of HOz on pH, since sodium formate has little buffer capacity in this region. The decay was not strictly second order but included a pseudo-first-order component, apparently due to reaction of HOz and 0 2 with impurities. The decay curves were fit to the mechanism (HOzTrepresents both forms of the radical) 2HOzT +HzOz
+ 02
HOzr +product
Icl
The integrated rate expression is e - klt 1 2kz 1 - e-k1t A - Ao l e kl
+-(
)
(5)
which is similar in form to the normal second-order equation, the term in parentheses approaching t for small values of ICl. Below pH 6, a t the lowest concentrations studied (1 p M ), the first-order component accounted for about half the initial rate of decay. At the highest concentrations (20 pM in very acid solutions) the first-order term represents less than 5% of (8) J. K. Thomas, J. Rabani, M. S. Matheson, E. J. Hart, and S. Gordon, J. Phys. Chem., 70, 2409 (1966).
The Journal of Physical Chemistry, Vol. 74, No. 17,1970
D. BEHAR,G. CZAPSKI, J. RABANI,L. M. DORFMAN, AND H. A. SCHWARZ
3212
the decay. Above pH 6, the first-order component was always quite appreciable (at least 20%). The observed values of k2 are given in Table I. At pH 4 and below, the reproducibility was 5%.
*
Table I : Recombination Rate Constants of the Perhydroxyl Radical kobsd
PH
0 1.1 2.05 2.90 3.91 6.5 6.6 6.8 7.0 7.5 7.7
M-1
x
lo-’,
0ec-1
1.04 0.83 1.09 1.79 10.4 3.8 2.4 1.0 0.45 0.3 0.2
----Literature---
koslod
0.76 0.77 0.88 1.61 8.9 2.0
0.79. 0.68 0.89 1.7 9.3
1.6 0.93 0.64 0.23 0.12
Recalculated from ref 9 using E from this paper. lated from curve given by Rabani and Nielsen.6 a
b 0.81 10.5 1.5 1.2 0.72 0.47 0.15 0.10
The recombination rate constants we measured are in good agreement with those determined by Bielski and Schwarn9and those determined by Rabani and Nielsen6 (given in the Table I for comparison). Again, we find no evidence for the decrease in rate constant below pH 2 which was observed earlier and attributed to the formation of HzO2+.l0 Our results above pH 6 are subject to the same criticism expressed earlier, namely that the pH is poorly defined due to the low buffer capacity of formate in this region. The values of Rabani and Nielsen are probably more precise. Our results do disagree with those of Behar and Czapski6 who found the decrease in k in basic solutions to occur at pH values 2.5 units higher than ours (leading to discrepancies of several orders of magnitude in k ) . They relied on calculated pH values which, as we have found, can be high by several units in this region. Rabani and Nielsen interpreted their rates in terms of the mechanism (originally proposed by Baxendale”).
HOz
* Interpo-
H02
+ HOz
-
HzOz
+
0 2
+ 02-2 H20z+ O2 + OH-
hi k12
while the reaction
Discussion The analysis of this work has been based on the premise that the perhydroxyl radical is the only free radical present in significant quantities in oxygensaturated sodium formate solutions. It is barely conceivable that an HCO4 radical might exist (or GOe-, as it would have to be in the pH range considered, in view of the high oxygen content of the proposed radical). We rule the possibility out on several grounds. Firstly, the shapes of the absorption spectra (Figure 1) agree well with spectra obtained previously for the KOz and Oz- radicals. 3 , 6 , e , g Secondly, the relative extinction coefficients of the two radicals agree well with those obtained by Rabani and Nielsen5 and by Behar and Czapskia in systems not containing formate (though there is disagreement with others3jg). Thirdly, the absolute extinction coefficient of H 0 2 agrees with that obtained by several others. ,6r6 The pK of HO2 obtained in this work, 4.88 5 0.10, agrees well with the value obtained by Rabani and Nielsent5who also used buffers (acetate and phosphate) but is 0.4 unit higher than that obtained by other^.^-^ The discrepancy is most likely due t o the fact that buffers were not used in the earlier work. The pH was estimated by dilution of stock solutions. This procedure is widely recognized to lead to uncertainties in pH corresponding to several pM of H f or OH-. Our own experience in unbuffered solution indicated that near pH 5 the measured pH was always higher than the calculated pH, probably due to the influence of glass, while around pH 7 to 9 the measured pH was considerably lower than calculated pH. 9
The Journal of Physical Chemistry, Vol. 74?N o . 17, 1970
+ 02-2 HzOz + + 20H-
02-
0 2
~ Z Z
is too slow to contribute to the overall rate below pH 9. This mechanism leads to the rate equation
where X is defined earlier. Using our pK value, 4.88, and our data, the data of Bielski and Schwarz, and the data of Rabani and Nielsen below pH 5, we find kll = 0.76 X lo6and klz = 8.5 X 10’. Rate constants calculated from eq 6 are given in Table I. We conclude that there is only one equilibrium, reaction 1, operating from pH 0 to at least pH 9. We have attempted to extend this range and to measure kZ2in 0.2 M NaOH solution, without formate. The 0 2 - is very long-lived at this pH. Czapski and Dorfman3 noted this but attributed the long lifetime to another, unknown, species. We find that a M 02solution exhibits a first-order decay, probably reaction with a catalytic impurity, at high pH. The pseudo-first-order rate constant is much smaller at pH 13 than pH 9, possibly because the concentration of the impurity is limited by a pH-dependent solubility. In further work at pH 13, concentrations of 0 2 - as high as loh4 M were generated by giving several pulses of (9) B. H. J. Bielski and H. A. Schwars, J. Phys. Chem., 72, 3836 (1968) (10) B. H. J. Bielski and A. 0. Allen, Proc. Second Tihany Sump. Radiat. Chem., 81 (1967). (11) J. H. Baxendale, Radiat. Res,, 17, 312 (1962). I
KINETICS OF DEUTERIUM SESQUIOXIDE radiation to the sample. There was some evidence for a second-order component but results were not very reproducible. They serve only to place an upper limit of 100 M-' sec-l on kzz and to extend the range in which reaction 1 is sufficient to explain available data to pH 13.3.
3213 Acknowledgment. We are indebted to Mr. Jechiel Ogdan for the operation of the linear accelerator. L. M. D. and H. A. S. wish to thank the Department of Physical Chemistry of the Hebrew University for the kind hospitality and financial support extended during our stays.
Kinetics of Deuterium Sesquioxide in Heavy Water
by Benon H. J. Bielski Chemistry Department, Brookhaven National Laboratory, Upton, New York 1107.9 (Received March 18,lQ70)
The kinetic properties of deuterium sesquioxide have been studied in heavy water as a function of acidity and temperature. D208 decomposes to D20 and 02 by first-order kinetics with an activation energy of 17.5 kcal/ mol in 0.01 M DC104. The species has a maximum half-life of 139 sec at 0 "in 0.027 M DC104. The isotope effect on the rate of decay kEIOa/kD208 is 6. Long pulse experiments have been carried out in which the concentration of sesquioxide was increased to 0.5 mM.
Introduction The formation of hydrogen sesquioxide was originally deduced by Czapski and Bielski' from experimental results obtained when an acidified air-saturated aqueous solution was irradiated with an intense electron beam in a flow apparatus. Later Bielski and Schwarzz upon discovering the absorption spectrum of H203 rechecked the kinetic properties of this species under pulse radiolytic conditions, obtaining good agreement with the earlier results. The purpose of the present investigation is to determine the kinetic properties of Dz03 and to study experimental conditions which might eventually lead to the isolation of this species. As will become apparent from the results, there are advantages in studying the deuterium analog as its half-life is considerably longer than that of HzOa.
Experimental Section A pulsed 1.95-MeV Van de Graaff generator served as an electron source. The pulse length was kept constant a t 0.1 sec throughout this study. All jrradiations were carried out in a Supersil quartz cell (2 X 2 X 0.8 cm) with one 2 X 2-cm window thinned to 0.4 mm to allow penetration of the electrons. Yields were determined by ferrous sulfate dosimetry. Analyzing light from a deuterium lamp passed through the cell three times with a total optical path length of 6.1 cm. The emerging light passed through two in tandem coupled Bausch and Lomb f/3.5 monochromators to a 7200 RCA photomultiplier. The
signal generated by the photomultiplier was subsequently fed into an oscilloscope where it was recorded photographically as a function of time. The scattered light a t 200 nm was less than 0.3% of the total light signa1 measured. Since relatively slow scanning rates were used, interference from Cerenkov radiation or from luminescence could be neglected. A flow apparatus described in detail by Czapski and Bielski' was used for scavenging experiments. An airsaturated 0.01 N DC104 solution passed through a continuous beam of 1.95-MeV electrons and was mixed with the scavenging solution of ferrous sulfate (1.6 N in DzSOJ after any desired time interval above 5 msec. The iron(II1) formed was subsequently assayed spectrophotometrically at 305 nm. An experimentally determined molar extinction coefficient of 2186 was used at 24". The DzO was purified by preirradiation with 'Wo y rays and subsequent distillation from chromic acid and alkaline permanganate. The acidity of the solutions studied was adjusted by the addition of either DC10, or D2S04.
Results and Discussion In view of the similarity of the radiolytic yields in heavy3-7 and light water, it is safe to assume that the (1) G. Czapski and B. H. J. Bielski, J . Phys. Chem., 67,2180 (1963). (2) B.H.J. Bielski and H. A. Schwarz, ibad., 72, 3836 (1968). (3) d. Jortner and G. Stein, I n t . J. AppZ. Radiat. Isotopes, 7, 198 (1960).
The Journal of Physical Chemistry, Vol. 74, No. 17, 1970
