J. Phys. Chem. 1994,98, 8946-8951
a946
Oxygen Atom Exchange in Aqueous Solution by 0H2O OH. A Study of Hydrogen Atom Transfer
+
+ H20
-
O H + OH and OH
+ H20
-
Ulrik K. Klining' Chemistry Department, Aarhus University, Langelandsgade 140, DK 8000 Aarhus C, Denmark
Elfinn Larsen and Knud Sehested Ris0 National Laboratory, DK 4000 Roskilde, Denmark Received: March 30, 1994; In Final Form: June 1I, 1994'
The title reactions were studied by measuring the oxygen isotope composition of H202 and 0 2 produced by electron pulse irradiation and y-irradiation of solutions of NzO and B r 0 4 in water enriched with H2'80. The fraction, 5, of the reaction 0- HzO O H OH that takes place by hydrogen atom transfer is found to be 0.22 f 0.02 at 22 O C and increases with temperature. The difference between the enthalpies of activation for hydrogen atom transfer and proton transfer is estimated to be 16 f 2 kJ mol-' and the corresponding entropy of activation at 22 O C to be 44 f 8 J K-l mol-'. A molecular model is sketched according to which 10-100 reversible proton transfers take place for each hydrogen atom transferred. Assuming no interference from impurities, the rate constant for the exchange reaction *OH HzO Hz*O OH is found to be 57 f 6 s-1 at 30 OC.
+
-
+
-
+
Introduction Hydrolysis of a base takes place by transfer of a proton from the solvent water to the base. However, in thecaseof the hydroxyl radical anion, 0-, the hydrolysis may conceivably also take place by transfer of hydrogen atom. The two processes, proton transfer
0-+ H 2 0
-
OH
+ OH-
k, = 1.5 X 10' s-', ref 1 (1)
and hydrogen atom transfer, differ only in the sense that by proton whereas by transfer the oxygen atom of OH is that of 0-, hydrogen atom transfer the oxygen atom of OH comes from the solvent water. Thus, hydrogen atom transfer is equivalent to an exchange of oxygen atom between O-/OH and H2O and may be detected by 1 8 0 labeling of 0 - o r H2O in the isotopic composition of OH. However, the interpretation of the measurements may be complicated by a subsequent oxygen isotope exchange between OH and H20: *OH
+H20
-
H2*0
+OH
(2)
So far, no observation of such an exchange has been reported. However, studies of the decomposition of isotopically labeled ozone in water,2 and of oxygen atom exchange between 0 2 and H20 induced by y-irradiation,3 suggest that oxygen exchange does take place between liquid water and O-/OH. An upper limit of 7 X lo6 M-I s-1 for the rate constant for this process has been estimated from measurements of the yields of C6H5180H and C6H5I60H formed by y-irradiation of benzene in aqueous solutions saturated with 180-enriched 0 2 . 4 In the present work we have determined the fraction, E, of reaction 1 that takes place by hydrogen atom transfer as the degree of oxygen isotope exchange that occurs by reaction 1:
*Abstract published in Advance ACS Absrracts, August 1, 1994.
0022-3654/94/2098-8946$04.50/0
+
By reaction la a hydrogen atom is transferred and by reaction l b a proton. The rate constant kl equals kl, + klb. For the reverse of reaction 1 we have k-1 = k-1, + k-lb = 1.8 X 1O1O M-l s-l,ref 1. [maybeexpressedbytt kla/(kl,+ k1b)orequivalently by [ = k-IJ(k-1, + k-lb). In order to determine 5 and the rate constant k2 of reaction 2, we prepared (by irradiation) 0-from N20 and Br04-containing oxygen isotopes in natural abundance dissolved in water enriched with 1 8 0 . The primary radiolytic process is
H20 w> e,;,
OH, H,O,, H, H,, H+
(3)
0-is produced by the reactions N20
-
+ e,,
k4 = 9.1 X and Br0,-
+ e,,
0-+ N,, ref 5
lo9 M-'
-
(4)
s-', ref 6
0-+ Br03-, ref 7
(5)
k, = 2.4 X 10" M-ls-', ref 8 Thus, OH arises from two sources: directly from the solvent water by process 3 and indirectly by reaction 1 subsequent to reactions 4 and 5, in the latter case with an isotopic composition between that of the water and that of N20 or Br04-, depending on the degree of exchange. Likewise, H202 is formed directly from the solvent water as well as indirectly from two OH radicals. 0-formed by reactions 4 and 5 is taken to have the same isotopic composition as the oxygen atoms in the parent compounds N20 and Br04-. This implies a negligible exchange of the oxygen atoms of BrO, and NzO with the oxygen atom of water and, moreover, the assumption that no exchange occurs in connection with reactions 4 and 5. In order to separate reaction 1 from reaction 2, we have measured the oxygen isotope exchange between O-/OH and H2O induced by high-intensity electron pulse irradiation, where the lifetime of OH is short owing to the reactions 0 1994 American Chemical Society
Oxygen Atom Exchange in Aqueous Solution
--
H + 160H H "OH
+
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 8947
H2160 k, = 1.5 X 10" M-'s-l, ref 10 H2"0
(7)
as well as by low-intensity y-irradiation where the lifetime of OH is long. It turned out that, under the conditions of the pulse irradiation, reaction 2 and all other reactions except reactions 6 and 7 are insignificant. Hence, 6 could be calculated from
5 = (P - d / ( 4 - 7)
(8)
where q is the relative yield of 18OH produced by process 3 (equal to themolefractionofH2I80in thesolvent water),qis the fraction of I8O in N 2 0 and Br0; (in all experiments taken equal to 0.0020), and p is the relative yield of 180Hformed from 0-by reaction 1 subsequent to reactions 4 and 5. p was calculated from the relative yield of Hl60180H (the fraction of H202 formed that is HI60l80H), as shown in the Appendix. The rate constant k2 for reaction 2 was determined from the pulse irradiation and the y-irradiation experiments jointly. We denote by A the degree of exchange between OH and H20 that takes place by reaction 1 and reaction 2 in the lifetime T of OH during the y-irradiation. A was calculated from
where r is the relative yield of 180Hformed by reactions 1 and 2. The stable product in the y-radiolysis is molecular oxygen. r was calculated from the relative yields n and m of 1 6 0 1 8 0 and l80l8O, respectively, as shown in the Appendix. The degree of exchange, (3, taking place by reaction 2 during the lifetime T of the OH radicals is b = (A - [)/( 1 - 5). The rate constant k2 is given by
k, = -7-l ln(1 - p ) = T - ~ln((1 -[)/(l - A ) )
(10)
T was calculated from the dose rate and the yield (the G-values) in process 3 (see the Appendix).
Experimental Section Materials. Natural water was triply distilled. Water with a specified content of l8Oand 170(I7Ocontent 1.4-2.6% of the I 8 0 content) and deuterium in natural abundance wereobtained from ICN Biomedicals Inc. The oxygen isotope composition of solutions enriched with l80was measured by mass spectrometric analysis of 02formed by y-irradiation of a sample saturated with N2O and made alkaline with solid NaOH to pH 12 to secure complete oxygen atom scrambling between OH/O- and H20. The isotopic composition of mixtures of natural water and water enriched with 1 8 0 and 170in a known ratio was determined by measuring the density (at 25 "C) relative to that of natural water using 10- or 20-mL pycnometers. The error limits in the determination of the mole fraction of H218O was f0.0005 by mass spectrometric analysis and fO.OO1 by density measurements. Perbromic acid in aqueous solution was obtained from Dr. Evan H. Appelman, Argonne National Laboratory. Nitrous oxide (N40) was ALPHA GAZ. Helium (N56), argon (N40), and nitrogen (N40) were Dansk Ilt og Brint. Other chemicals were Merck pea. or Suprapur. Measuring Equipment. Mass spectrometric gas analysis was performed on a magnetic MAT CH-4 instrument equipped with a thermostated gas-inlet system that gave a molecular flow into
-
the ion source. Electron-impact ionization was done at 70 eV with a 40-pA trap current. A single Faraday collector was used as detector. Oxygen isotope abundances were determined by scanning the region from m / z 32 to 36 repeatedly. To minimize contamination by air, the various operations were made in a nitrogen atmosphere. The residual contamination by air was determined from the measured intensity at m / z 40 (Ar). 7-Irradiations. y-Radiolysis was carried out with a ~ C O y-source. Doses were measured with the Fricke dosimeter." The dose rate was 0.57 Gy s-1. The reaction vessel was a roundbottom Pyrex flask fitted with a stopcock. The total volume was 120 mL. Aliquots of 20-30 mL of Br0; solution saturated with Heor 20mLofwatersaturatedwithN20wereirradiatedwithout stirring. Deaerating was performed by repeating a freeze, pump, thaw, fill, and shake cycle with He (the Br04- solutions) or with N20. The vessel containing the irradiated solution was frozen in liquid N2 and evacuated. Upon heating the solution to room temperature, the gases evolving were fed into the gas-inlet system of the mass spectrometer through a liquid N2 trap. Contents of 02 ranging from 15 to 70% of the calculated yield (113-5-3 X 10-5 mol) were measured. Electron Pulse Irradiations. Electron pulse radiation was carried out with the Riser 10 MeV Linac accelerator. The radiation vessel was a 30-mL flat-bottom syringe with a side-on delivering tube at the bottom. Samples were deaerated by bubbling through with H e (Br04- solutions) or with N20. Aliquots of 10 mL of solution were irradiated through the flat bottom of the syringe with a single 2- or 4-ps pulse (rise time 0.1 ps) giving a dose of 260-730 Gy (measured by the concentration of H202 formed in a solution saturated with NzO at 1 atm). H202 formed by electron pulse irradiation of the 180-enriched solutions was oxidized to 02 with ceric sulfate. Separate experiments showed that the isotopic composition of hydrogen peroxide is identical to that of oxygen formed by oxidation of the hydrogen peroxide with ceric sulfate. A solution (0.1 mL) containing 0.1 M ceric sulfate and 2 M sulfuric acid was introduced through the side-on delivering tube of the syringe by means of a Hamilton syringe. The solution in the syringe containing the liberated oxygen was fed into an evacuated 200-mL round-bottom flaskattached to the mass spectrometer through a septum mounted on a flask. The valve between the flask and the mass spectrometer was opened and the evolved gas allowed to expand into the gasinlet system through a cold trap in liquid Nz. Calculations. Numerical integrations of rate equations were made by use of the Program Package SCAMP developed by H. M. Sauro and D. Fill.
Results Electron Pulse Irradiations. Table 1 shows the data obtained by electron pulse irradiation of N 2 0 and BrOL with natural isotopic composition dissolved in neutral water containing H2'80 and H2170in the mole fractions q and 6, respectively. The table shows from the left in the first seven columns the experimental parameters: temperature, concentration of BrOd-, concentration of NzO, dose of the electron pulse, duration of the pulse, mole fraction, q, of H2180 in solvent water, and mole fraction, 6, of H2170in the solvent water. The next two columns show the relative yields, s and t , of H160180Hand H180180H (fractions of H202 formed that are H160180H and H180180H),respectively. The last column shows 6 calculated from eq 8 in the main text and eqs B2 and B3 in the Appendix. The G-values (yields in molecules/lOO eV) used for the calculation of 6 are shown in Table 2. By the calculation of $. from eq 8 we have assumed that reactions -1 and 2 may be neglected in the pulse irradiation experiments and, furthermore, that no oxygen atom exchange takes place in
8948 The Journal of Physical Chemistry, Vol. 98, No. 36, 1994
Kllning et al.
-
TABLE 1: Isotopic Composition of H202 Formed by Electron Pulse Irradiation of Aqueous Neutral Solutions of NzO and BrO; and the Degree of Exchange of Oxygen Atom, I, between O-/OH and Hz0 by the Reaction 0- + HzO OH O H T/OC
BrOr/ mol dm-3
22 22 22 22 22 22 22 22 22 22 22 22 22 22 6 46
NzO/ mol dm-3 dose/Gy pulselps 0 0 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 0.535 2.65 4.2 1.3
1 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0
430 430 470 470 430 430 430 430 430 260 560 290 440 730 730 730
q, mole fraction
of H2180
4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4
0.09656 0.18S6
0.09874b O.0912Ob 0.1055b 0.1O S 6 0.1055b 0.1055b 0.1055b 0.06106 0.21296 0.10606 0.1018b 0.1094c 0.1094c 0.1094c
6, mole fraction s, relative yield of H2170 X lo3 of H160180H 1.76 0.1226 2.96 0.2159 1.76 0.1270 1 .66 0.1160 l.Sb 0.1335 1.8b 0.1328 1A6 0.1344 1.it6 0.1343 1 0.1346 1 .86 0.0813 5.6b 0.2461 2.86 0.1321 1 .96 0.1321 1.86c 0.1365 1.86c 0.1322 1 .86c 0.1436
+
1, relative yield of H180180H
0.0050 0.0180 0.0049 0.0053 0.0051 0.0057 0.0059 0.0060 0.0024 0.0226 0.0063 0.0053 0.0060 0.0066 0.0070
P O.22ld 0.174d 0.246d 0.214d 0.227d 0.218d 0.239d 0.238d 0.242d 0.247d 0.237d 0.203d 0.236e 0.208d0.134* 0.147f0.072' 0.29310.238,
The G-values used for calculating 4 are shown in Table 2. Determined by density measurements. Determined by mass spectrometric analysis. Refer to G-values shown in Table 2.
a
d-J
TABLE 2: GValues Used for Calculation of 4 in Table 1' d
e f B h
i j
G, 3.18 2.85 3.12 3.18 2.65 2.60 2.72
GOH 2.86 2.70 2.74 3.00 2.75 2.64 2.91
GH,O~
0.74 0.70 0.78 0.7 1 0.70 0.73 0.67
GH 0.61 0.64 0.59 0.64 0.65 0.63 0.67
a The values shown in lines d-g are those listed in ref 15 corrected for spur reactions as prescribed in ref 17 and for the temperature difference ( t - 22) OC according to ref 16. The values in lines h-j are those listed in ref 15 corrected for the temperature difference ( t - 22) OC only.
conc/M
1.oX1o4C
I
electron adduct of NzO occurs prior to its dissociation,5 makes us believe that no oxygen atom exchange takes place in connection with reactions 4 and 5. The difference between the enthalpies of activation for hydrogen atom transfer (reaction l a ) and for proton transfer (reaction 1b), AH*',- m*Ibmay , be estimated from a plot of ln([/(l - F ) ) against PI. Using the values 0.147, 0.208, and 0.293 for f determined in identical solutions at 6,22, and 46 O C , respectively, we find AH*', - u * l b = 16 f 2 kJ mol-'. The corresponding difference between the entropies of activation at 22 OC is MIla - h S * l b = 44 f 8 J K-' mol-'. 7-Irradiations. Table 3 shows the isotopic composition of molecular oxygen formed a t 30 OC by y-irradiation a t a dose rate of 0.57 Gy s-l of N20 and B r 0 4 with natural isotopic composition dissolved in water enriched with l 8 0 . The first five columns from the left show the experimental parameters: concentration of Br04-, concentration of N20, pH, radiation dose, and mole fraction, q, of H2180. The next two columns show the relative yields, n and m, of l6OI8Oand 180180 (fractions of 0 2 formed that are 1 6 0 1 8 0 and 180'80), respectively. The last two columns are the degree of exchange A and kz, respectively. A is calculated from eq 9 in the main text and eqs B6-B11 and B16-Bl9 in the Appendix with the G-values listed in Table 4. kz is calculated from eq 10 with f = 0.24, a value estimated for 5 a t the temperature of the y-irradiations (30 "C), and 7 8 X s obtained from eq B22 (Appendix) with the dose rate of 0.57 Gy s-l and the G-values of Table 4. Impurities that react with OH radicals make the actual value of 7 smaller than the calculated value. However, the fairly high reproducibility of the determinations of k2 in different solutions of the same acidity suggests that the effect of impurities may be small. The observation that k~ is larger in neutral solution than in acid solution (Table 3) is ascribed toreaction-1. Consequently, we take k2 in the limit of no impurities present equal to 57 f 6 s-1, the mean of the three values for kz determined in acid solution. G-Values. Owing to reactions among radiolytic products located in spurs, the pertinent G-values (yields in molecules/ 100 eV) for calculating [ and A are not precisely known.12 Thus, owing to reactions 4 and 5 in the spurs, G H contains ~ ~ ~a contribution from H202formed in the spurs from OH and 0originating in N20 and BrO4.I3J4 The G-values used here (shown in Tables 2 and 4) are those listed by Schwarz,Is with temperature coefficients given by Elliot et a1.'6 Corrections for the reactions in spurs of NzO and Br04- with eaq-were made as prescribed by DraganiE and DraganiE17with published data for k418 and for the solubility of N20.19
-
Figure 1. Concentration of H202, OH, H2, and H' as a function of time after irradiation with a 4-ps electron pulse yielding 500 Gy. The concentrationswere computed by integration of rate equations listed in ref 7. Concentrations of erq-,OF, and 0 2 are at all times less than 1V M.
connection with reactions 4 and 5. Theseassumptionsare justified as follows: Calculations simulating an irradiation of N20 in water by a 4 - ~electron s pulse yielding 500 Gy are represented in Figure 1, which shows the concentration of OH and of H202 formed from OH by reaction 6 as a function of the time elapsed after 2 X 103 s-l, we the pulse. Since pH -7 and k-l[OH] estimate from Figure 1 that less than 1% of OH reacts with OH-. Hence, reaction -1 may be neglected. Moreover, the value of k2 derived below implies that reaction 2 is unimportant. Finally, Table 1 shows that 5 determined in Br04- solutions does not differ significantly from 5 determined in N20 solutions. This observation, together with the finding that no protonation of the
-
Oxygen Atom Exchange in Aqueous Solution
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 8949
TABLE 3 Isotopic Composition of Molecular Oxygen Formed by y-Irradiation of Aqueous Solutions of NzO and BCOi, the Degree of Exchange of Oxygen Atom, A, between HzO and 0-/OH, and the Rate Constant, kz, for the Reaction *OH H20 H2*0 OH (Dose Rate 0.57 CYs-l, Temperature 30 f 1 "C)
+
+
Broil mol dm-3
N20/ mol dm-3
0 0 0 0 0.0236 0.0200 0.113 0.0203
0.0265 0.0265 0.0265 0.0265 0 0 0 0
0
q!
PH a
a
a a 2.9 2.9 2.1 a
dose/Gy 4100 4100 4100 8200 7100 8200 5100 8200
mole fraction of H2'80 0.0506 0.0506 0.0506 0.1139 0.0944 0.1006 0.1204 0.1078
Neutral unbuffered. b Determined by mass spectrometric analysis.
GValues Used for Calculation of A and kz in
TABLE 4 Table 3' C
d
e f 8
G, 3.18 3.24 3.14 3.47 3.27
GOH 2.86 2.94 2.89 3.02 2.89
GHlOl
GH
GHl
0.74 0.75 0.75 0.805 0.75
0.61 0.75 0.79 0.75 0.60
0.31 0.33 0.34 0.27 0.34
The G-values shown are those listed in ref 15 corrected for spur reactions as prescribed in ref 17 and corrected for the reaction H+ + eH (see text).
-
0
In acid solutions G, and GH were corrected for the fraction of
-
n, relative yield
m,relative yield of 1 * 0 ' 8 0 A 0.0865 0.00255 0.696' 0.0846 0.00230 0.639' 0.0882 0.002 25 0.752' 0.1819 0.00950 0.696' 0.1459 0.006 67 0.539d 0.1549 0.007 47 0.535' 0.1773 0.010 13 0.497f 0.1708 0.009 40 0.6288 Refer to G-values used by the calculation of A and kz (Table 4).
of '80'60
k2 11Oc 89' 135' lloe 61d 6oC 5of
86e
However, we may attempt to sketch reaction 1 at a molecular level as follows. We picture 0-in water as being hydrogen bonded to surrounding layers of water molecules through which a number of reversible proton transfers to 0-take place by a Grotthuss mechanism before the final separation of the products OH and O H occurs:
*O-H 2 0 H 2 0 ~i *OH OH- H 2 0 e *OH H 2 0 OH-
$
*O-H 2 0 H 2 0 (1 3)
In a few instances a hydrogen atom instead of a proton is transferred in the first step:
eaq- that reacts in reaction 11:
eaq-+ H+
-
*O-H 2 0 H 2 0 ~i *OH-OH H,O ~i H
k, = 2.3 X 10" M-' s-', ref 7
(1 1)
Moreover, reaction 12,
H+ + 0-- OH
k, = 6.1 X 10" M-ls-', ref 14 (12)
competes with reaction 1 in acid solution, but in neutral solution it is significant in the spurs only.14 However, as chemical equilibria among species containing oxygen depend only slightly on the isotopic mass of the oxygen atoms, the oxygen exchange taking place by reaction 12 should be nearly equal to the exchange taking place by reaction 1, and consequently no correction for reaction 12 is required. It seems that [ and A are rather insensitive to the choice of G-values. Thus, it proved impossible to find plausible sets of G-values that give the extreme values 0 or 1 for f and A. Calculation of [ using the G-values given by Elliot et a1.16 gave the same values within 2% as those calculated from the values listed by Schwarz.15 Estimated contributions to the G-values of HzOz and OH from reactions 4 and 5 in the spurs increase [ and A by less than 6% and 3%, respectively. Even in the extreme case of no corrections to the G-values for reactions in spurs, reasonable values for E are obtained (Table 1).
Discussion Reactions corresponding to reactions 1 and 2 have been studied in the gas phase. By collisions between 0-and H20 at a translational energy less than 0.2 eV, 0-and HzO are reformed via a collision complex with the oxygen atoms completely scrambled.20.21 This result is in accordance with the present finding that the oxygen isotope exchange increases with temperature, since, owing to a negative enthalpy of formation,22the collision complex is highly excited. In agreement with our finding that reaction 2 is slow, no exchange between OH and HzO was observed in the gas phase (rate constant < 6 X 105 M-1 s-1).22,23 The values observed for AH*1,- , b s I * l b = 16 kJ mol-' and AS*',- m*lb= 44 J K-I mol-' are not easily rationalized.
*OH- H 2 0OH
H2*0 H 2 0 0- (1 4)
Here the reforming of *O-from Hz*O may be neglected because Hz*O rapidly diffuses away from 0-.We assume further that the rate-determining step in reaction 14 is the transfer of a or equivalently that every hydrogen atom hydrogen atom to 0-, transfer results in an exchange of oxygen atoms between *O-and H20. This assumption is based on the findings that the reaction in the gas phase corresponding to the second step of reaction 14 is very fast (rate constant > 1010 M-1 s-I 24) and that the rate constant for displacing a water molecule from the hydration shell of a chloride ion is on the order of magnitude 1012 s-1.25 The parameters in the microscopic model outlined above may be estimated from the macroscopic quantity [ as follows: The fraction of the products of reaction 1, OH and OH-, that arise from proton transfers only, is 1 - [. Denoting the probability in the microscopic processes of a proton transfer to 0-by Pp and the number of reversible proton transfers to 0-that occur before OH finally escapes by v, Pp may be expressed in terms of [:
Pp' = (1 - 5 )
(15)
Moreover, the difference between the activation enthalpies for transfer of a hydrogen atom and of a proton AH*H- A H l p in the microscopic processes (as distinct from A I P I , - A H * l b for the macroscopic processes) may be expressed by A H * H - A H * p=-Raln(P,/P,)/d(l/T)
(16)
where PH = 1 - Pp is the probability for transfer of a hydrogen atom. For large Y the ratio PHIPPapproaches [/v and eq 16 may be approximated by
AH*^ - AH*^ = -R a In [/a(i/T)
(17)
From the values of [ measured at 6 , 22, and 46 OC we estimate AH*H- AH*p = 12 f 2 kJ mol-'. By integration we obtain from eq 17, assuming that the integration constant is 0,
8950 The Journal of Physical Chemistry, Vol. 98, No. 36, 1994
At room temperature we then find the ratio between the probabilities of hydrogen atom transfer and proton transfer, PHI Pp, to be in the range from 10-3 to 2 X 10-2 and the number of reversible proton transfers that take place for each hydrogen atom transferred to be in the range from 10 to 100.
Acknowledgment. The authors’ thanks are due to Dr. Harold A. Schwarz, Brookhaven National Laboratory, for outlining the method for calculation of the oxygen atom exchange by y-irradiation, to Dr. Evan H. Appelman, Argonne National Laboratory, for a gift of perbromic acid, and to Dr. Igor W. Plesner, Aarhus University, for computing the concentrations shown in Figure 1. Dr. Jargen R. Byberg, Aarhus University, is thanked for carefully reading and commenting on the manuscript. Appendix Below we derive the formulas we have used to calculate 5, A, and kz. (a) Calculation of & I was calculated from eq 8 in the main text:
5 = (P-dl(4-a) whereqdenotes the relative yield of 180H,which is formed directly by process 3 (equal to the mole fraction of H2I80 in the solvent water), q is the fraction I8O in 0-formed by reactions 4 and 5 (in the present experiments taken equal to 0.0020), and p is the relative yield of I80H that is formed by reaction 1 subsequent to reactions 4 and 5 . p was calculated from the relative yield of HI6O180H (Table 1) as shown below. By integration of the rate equations for the reactions among 02, the transient and permanent species (eaq-,OH, HzOz, H, 02-, N20, and Br04-) listed in ref 6 and the rate equation for the reaction Br04- H Br03- O H ( k A l = 1 X 107 M-1 s-1, ref 26), we find that reactions other than
+
-
+
and
may be neglected (Figure 1). Consequently, the yield of H202 (in molecules/lOO eV) formed from OH radicals is 1 / 2 ( G o ~+ G, - GH), and the total yield of H202 is GH,O~ + 1 / 2 ( G o ~+ G, - GH),where GH,o*denotes the yield of HzO2 formed directly by process 3.
The relative yield, s, of HI60180H may be expressed by
Klaning et al. of I7OH that is formed by reaction 1 subsequently to reactions 4 and 5 . Since a = S/q in the present measurements is a small quantity, eq B1 may be approximated by
2 4 1 - (1
+ a ) v ) ~ G ’ / ~ (B3) G
p was calculated from eqs B2 and B3. (b) Calculationof A. A was calculated from eq 9 in the main text:
A = (r - 0 ) / ( 4 - 7) where q and q have been defined above; r is the relative yield of I80H, which is formed by reactions 1 and 2 subsequent to reactions 4 and 5. r was calculated from q and the relative yields n and m of I 6 0 1 8 0 and 1 8 0 l 8 0 , respectively (Table 3). It is assumed that in addition to reactions 1, 2, 3, 4, or 5 and A1 the reactions shown below take place by low-intensity y-irradiation of aqueous N20 and Br04- solutions. The reaction schemes shown consist of sets of reactions among isotopic isomers except those containing I7O, Also shown are the relative yields of products of all isotopic isomers that are produced by the individual reactions in the set (water as a product is not shown; the I6O isotope is denoted by 0). The relative yields of I80H, HOI8OH, and H180180H are denoted by z , x, and y, respectively. The (equal) relative yields of HO1*Oand H I 8 0 0 are denoted by x’/2 and the relative yield of HI80180 by y’. reaction
OH + H2 H ”OH + H2 H OH + HOOH HOO 180H+ HOOH HOO OH + H0180H H0I80 OH + H0180H HI800 I80H + HOI8OH HOI8O I8OH + H0I80H H1800 OH + H180180H H180180 I80H + Hl80’80H HI80180 OH + HOO 00 OH + H0I80 OI8O OH + HIBOO 00 OH + HI800 0 x 8 0 OH + HI80180 1 8 0 l 8 0 OH + HI80180 0 1 8 0 I80H + HOO 00 I80H + HOO 0’80 ‘80H + HI800 0 1 8 0 I80H + H0I80 OI8O I8OH + H0180 1 8 0 1 8 0 l80H + Hl80l80 1 8 0 1 8 0 00 + H HOO
------ -----+ + +
-+
OL80 H
HOI80
l80O H
HI800
180180
+ H + HI80180
We note that the sum of the relative yields of l 8 0 0 H and 0’80H in reactions A6b and A6c equals n, the relative yield of 0 1 8 0 ,
n = (3/4)x’+ (1/2)y’+ (1/2)z- (1/2)zx’-zy’
where U = (qGOH
+pG,)/(Go,
+ G.J
(B2)
is the relative yield of 180H. CG and CG’denote ~GH,o,+ GOH GH, respectively. 6 denotes the relative yield of I7OH that is formed directly by process 3 (equal to the mole fraction of H Q 7 0in the solvent water); e is the relative yield
+ Ge- GHand GOH+ G,-
(B4)
and that the relative yields of 180180H in reaction A6d equals M , the relative yield of 1 8 0 1 8 0 ,
m = (1/2)zy’+ (1/4)zx’+ (1/2)y’
(B5)
In the following we denote the rate of a reaction by R followed by a number and a letter that refer to the particular reaction,
Oxygen Atom Exchange in Aqueous Solution
The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 8951
while the sum of the rates of the individual reactions is labeled by the number alone. The steady-state conditions for the various species may be expressed as
may be obtained from measurements of m and n using eqs B6B11 and eqs B16-B19. (c) Calculations of 4.The rate constant kz for reaction 2 was calculated from eq 10 in the main text: k,=T-’ln((l-t)/(l-A))
H,:
T, the lifetime of OH radicals during the y-irradiation, may be calculated from the steady-state concentration of OH, [OH], and the dose rate, DR. The steady-state condition for OH may be expressed as
OH: H,O,:
(GoH
+ G,)1.036 X 10-7DR = k,,[H,][OH] +
k4A[H2021 [OH]
HO,:
+ 2k1A[oH12 + k.5A[Ho,l
[OH] (B20)
Introducing G-values from eqs B6-Bll, we get [OH] = [(( /2)Ge H:
+ ( /2)G,,
- GH,O, - GH,
-
(1/2)G~)1.036X 10-7DR/2klA]1’Z (B21) The mean lifetime is then
0,:
7
The steady-state condition for H 0 I 8 0 + H 1 8 0 0 is 2R6b
+ 2R4c + 2R4e = 3R5b + 3R5i + R4g + R4h = 2R5f + R51
(B13)
Introducing n, m, x, y, x’, and y’in eqs B12 and B13, we get nR6
+ xR4 = x’R5
(B 14)
and mR6
+ yR4 = y’R5
(B15)
Eliminating x’and y’from eq B4 by means of eqs B14 and B15, we get
n = (3/4)nR6/R5
+
+
+
(3/4)xR4/R5 (1/2)mR6/R5 (1/2)yR4/R5 ( 1 1 2 ) ~ -(1/2)nzR6/R5 (1/2)zxR4/R5 - mzR6/R5 -zyR4/R5 (B16)
+
The relative yield z of 180H is given by
= (qGOH + rGe)/(GOH +
0317)
With HOI80H and HIgOIBOH in steady-state concentrations, x and y are given by x = 2q(l
- q)(R4 - R l ) / R 4
+ 2 4 1 -z)Rl/R4
y = q2(R4 - R l ) / R 4
+ z2R1/R4
+ GoH)1.036 X 10-7DR)
(B22)
References and Notes (B12)
and for H180180 R6d
= [OH]/((G,
(B18) (B19)
with z given by eq B17. Thus, r, the fraction of 180Horiginating in reaction 4 or 5 and contained in the expression for z (eq B17),
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