J. CHEM. SOC. FARADAY TRANS., 1994, 90(6), 837-841 837

Temperature Dependence of the Rate Constant for the Reaction - + OH in Water up to 150'C =aq

A. John Elliot" and Denis C. OueHette System Chemistry & Corrosion Branch, Chalk River Laboratories, Chalk River, Ontario, Canada KOJ IJO

The temperature dependence of the rate constant for the reaction,

e, + OH +OH- (1)

has been measured in liquid water up to 150°C. The values of k , were derived from fitting the absorbance vs. time plots of the decay of the hydrated electron in pulsed-irradiated deoxygenated 1 x mot dm-3 sodium borate solutions using the computer programme FACSIMILE. The values for k , were (2.8 0.2) x 10,' (18"C), (5.0 f 0.4) x 10'' (75"C), (6.0 & 0.5) x 10" (100°C) and (7.2 & 0.3) x 10,' dm3 mol-' s-' (150°C). The tem- perature dependence of k , was found to be much less than for diffusion in water. The temperature dependence of E,,, for t h e hydrated electron has been determined up to 200 "C.

Over the last two decades, the temperature dependence of the rate constants for most of the important reactions involving the primary species formed in the radiolysis of light water have been measured.'-'4 In this paper we report on one of the remaining important reactions, the reaction of hydrated electrons with hydroxyl radicals to form hydroxide ions

e,; + OH --* OH- (1) In the course of this work we have evaluated the molar absorption coefficient of the hydrated electron as a function of temperature up to 200°C. This, in turn, allowed us to cal- culate the absolute bimolecular rate constant for dimer- ization of the hydrated electron [reaction (2), see later] from the data of Christensen and Sehested.'

Experimental The water was purified by passing once-distilled water through a Millipore Milli-Q system and then redistilling from alkaline permanganate. Solutions of 1 x lo-' mol dm-3 sodium tetraborate (Anachemia) were prepared and deoxy- genated by stripping with helium gas using the syringe- bubbler technique.

The high-temperature pulse radiolysis facility has been described in earlier An EG&G FNDl WQ photodiode was used for light detection for all experiments, except when a HTV R-166 photomultiplier was used to record the pulse shape by Cerenkov emission, The dosimeter was an oxygen-saturated KSCN solution (0.01 mol dm-3) where the G E ~ ~ ~ value of 2.39 x lo4 was ~ s e d . ' ' ~ ' ~ G is defined as the number of species formed per 100 eV and the molar absorption coefficient, E, is expressed in dm' mol-' cm-'. Thus, throughout the paper G E ~ , ~ has units: (number of species) (100 eV)-' dm3 mol-' cm-'. (In this paper we have used the term g for the yield of the primary species formed in the radiolysis of water at ca. s after ioniza- tion; G is used for the experimental value.)

Results The decay of the hydrated electron at its absorption maximum in a deoxygenated borate-buffered solution (pH 9.2 at room temperature) was used to monitor the rate of reac- tion (1) as shown in Fig. 1-4. The time profile of the absorp- tion trace was fitted using the parameter-fitting routines in the FACSIMILE' kinetic simulation programme; the reac- tion scheme used comprised reaction (1) and the following

0 . 1 2 , . . . , I . . . . , . . . . ,

time/l s

Fig. 1 Absorbance at 720 nm when deoxygenated loF3 mol dm-3 borate-buffered solutions are irradiated with a 22.54 Gy (upper), 11.00 Gy (middle) and 1.57 Gy (lower) pulse at 18°C. The dotted lines are the FACSIMILE fits to the experimental trace and the dash-dot lines are fits where k, is either 30% larger or smaller than the fitted value.

a 0.07

5 0.06 f! $, 0.05 n

0.04 0.03 0.02

0.01

2.0 4.0 6.0 0 . 0 O I ' " ' " " ' ' ' I . ' 0.0

time/l 0-6 s Fig. 2 Absorbance at 780 nm when deoxygenated mol dm-3 borate-buffered solutions are irradiated with a 23.46 Gy (upper), 11.06 Gy (middle) and 1.81 Gy (lower) pulse at 75°C. The dotted lines are the FACSIMILE fits to the experimental trace.

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838 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90

0.05

0.04 Q) 0

m + 0.03

n 0.02

s

0.01

time/l O-'j s 5.0 10.0

0 . 0 O I ' . ' . ' . . ' Fig. 4 Absorbance at 880 nm when deoxygenated mol dm-3 borate-buffered solutions are irradiated with an 11.00 Gy (upper) and 1.80 Gy (lower) pulse at 150°C. The dotted lines are the FAC- SIMILE fits to the experimental trace and the dash-dot lines are fits where k, is either 30% larger or smaller than the fitted value.

0.0 time/l s

Fig. 3 Absorbance at 810 nm when deoxygenated mol dm-3 borate-buffered solutions are irradiated with a 9.86 Gy (upper) and 1.69 Gy (lower) pulse at 100°C. The dotted lines are the FAC- SIMILE fits to the experimental trace.

sequence : It was necessary to add reaction (12) (assumed to be a

pseudo-first-order reaction) to the reaction set to allow for the reaction of the hydrated electron with trace impurities. This reaction will be discussed later.

ea; + ea; -+ H, OH + OH -+ H,O,

(2)

(3)

(4)

(5 )

(6)

(7)

The following equilibria were also used: ea; + H,02 + OH + OH-

OH + H,O, -+ HO; + H,O OH + H, + H + H20

H,O H+ + OH- (13)

(14)

(15)

ea; + H + H, HO; + OH- * 0;- + H,O

B(OH), + OH- * B(OH)i

OH + 0;- + 0, + OH-

H + OH- + e; + H,O

(8)

H+H+H, (9)

(10)

(1 1)

(12)

H + OH -+ H,O ea; + impurity -+ products

The temperature dependence used for the rate constants of reactions (3),14 (4)," (6),3 (7),'v4 (8),13 (9),"714 (lo)', and (11)14 were taken directly from the literature. The tem- perature dependence for reaction (2)' was recalculated as described below. The temperature dependence for reaction (5) has not been reported; we used the value k , = 2.5 x 1O1O dm3 mol- s - at 23 "C 2o and gave it the same temperature dependence as diffusion in water. The values for the rate con- stants are given in Table 1.

The temperature dependence for K13 was taken from Sweeton et a1.,2' and the value of k-13 was extrapolated to higher temperatures from the data at 0-48°C of Natzle and Moore2, using the Smoluchowski equation assuming a diffusion-controlled reaction.' The temperature dependence of K14 was calculated from the data of Christensen and Sehested,6 Buxton et and Schwarz and B i e l ~ k i ~ ~ and from the data for K,,;,l k14 was taken to be 1.3 x 10" dm3 mol- s- at 25 "C, and the temperature dependence was cal- culated to be diffusion controlled." For K1,, the tem- perature dependence as reported by Mesmer et ~ 1 . ~ ~ was used; k,, was assumed to be 1 x 10" dm3 mol-' s - l at 25 "C with an activation energy of 14 kJ mol- '.

The borate buffer, which does not react with e,;, OH or H, was used to ensure that reaction (16) did not compete with the above reactions.

ea; + H+ + H (16)

Table 1 Rate constants for the reactions

k/dm3 mol-' s-'

reaction number 20 "C 75 "C 100 "C 150°C

1 2 3 4 5 6 7 8 9

10 I 1 12"

(2.8 f 0.2) x 10" 2k = 1.1 x 10" 2k = 8.6 x lo9

1.2 x 10" 2.3 x 10"

3.5 x 10'

2k = 9.0 x lo9

1.5 x 10"

2.7 x 107

9.0 x 109

1.9 x 107

(1.9 _+ 0.2) x 104

(5.0 f 0.4) x 10" 4.2 x 10" 1.6 x 10" 2.8 x 10" 7.2 x 10''

1.1 x 10' 2.1 x 10" 2.7 x lo1' 2.3 x 10' 2.7 x 10"

(3.1 _+ 0.4) x lo4

6.4 x 107

(6.0 f 0.5) x 10" 6.7 x 10'' 1.8 x 10" 3.6 x 10" 1.1 x 10" 8.6 x lo7 1.7 x 10' 2.7 x 10" 3.8 x 10" 5.6 x lo8 3.1 x 10"

(3.9 f 0.2) x 104

(7.2 f 0.3) x 10" 1.4 x 10" 2.4 x 10'' 5.7 x 1 O ' O 1.9 x 10'' 1.4 x lo8 3.4 x lo8 4.1 x 10" 6.6 x lo1' 2.4 x 10'' 4.0 x 10''

(8.4 f 0.4) x lo4

' Units, s - ' .

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J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 839

The g values for the primary species were taken from Elliot et Since the Cerenkov radiation did not contribute signifi-

cantly to the absorption profiles, the data were fitted through the pulse using the pulse shape determined from the Ceren- kov emission near 250 nm. The data were recorded at the absorption maximum for the hydrated electron at each tem- perature.'

Before we can analyse the experimental data for reaction (I), the molar absorption coefficient of the hydrated electron as a function of temperature must be known. The tem- perature dependence of GE,,, for the hydrated electron has been reported by a number of laboratories but, because of a lack of data on G(eJ, the actual molar absorption Coefficient has not been reported. Likewise, E,,, is required to calculate the temperature dependence for reaction (2) from the 2k, values reported by Christensen and Sehested' where a con- stant was assumed.

Molar Absorption Coefficient of ePg as a Function of Temperature

The GE,,, for the hydrated electron at its absorption maximum was measured at the end of the 0.2 ps pulse (1.5- 2.0 Gy) in a deoxygenated borate-buffered solution over the temperature range 20-200°C. Corrections of 2 and 7% for decay of the signal in the pulse were applied at 150 and 200"C, respectively. To calculate crnax, G(e,;) was taken as g(e,;) below 150 "C, while at 200 "C, G(ea;) was taken as g(e,;) + g(H). FACSIMILE calculations indicate that, at 200 "C, all atomic hydrogen was converted to hydrated electrons during the pulse at prevailing hydroxide ion concentration (ca. 4.6 x lop3 mol dmP3 as a consequence of the borate buffer present at 200°C) by reaction (10). The data of 150°C could not be used, as the conversion of hydrogen atoms to hydrated electrons is only partially completed during the pulse. The values for E,,, as a function of temperature are shown in Fig. 5. We report a value of 20000 & 700 dm3 mol-' cm-' at 715-720 nm for the molar absorption coefii- cient at 20°C; it should be remembered that this is based on the thiocyanate dosimeter using a G E ~ , ~ value of 2.39 x lo4, which was calibrated against the Fricke dosimeter.' 7,18

1 22000 ' " ' ~ " ' ' ~ ' " ' " " ~ ' ' " ' " " 1 ' " "

21 000

20000 c I 5 19000 - I -

18000 m E % 17000

- ' e ;; \Z, 0 \ -i

t h -

l6Oo0 I \

15000 r ~ " " ' " " " ' ~ ~ ' ~ ' ~ " " ' ' " ' ' " " ' 0 50 100 150 200 250 300 350

temperature/"C Fig. 5 Molar absorption coefficient at i,,, as a function of tem- perature: this work (m); Jou and Freeman (A);26 Michael et al. (0);25 and Christensen and Sehested (0).5 The dotted line represents the data of Shirashi et ~ l . , ~ ' and the dashed line is from eqn. (I) in the text. All molar absorption coefficients are normalized at 20000 dm3 mol--' cm-' at 20-25°C.

The temperature dependence of GE,,, of the hydrated elec- tron has been reported by a number of laboratories. Our data agree with those of Michael et ~ l . , , ~ who published values for 3 x lo-' mol dm-3 sodium hydroxide in water over the tem- perature range -4 to 90°C and using the Fricke solution as the dosimeter. At 20°C, our value of GE,,, of 5.32 x lo4 is in good agreement with their value of 5.23 x lo4 at 25°C. Other laboratories have used different dosimeters and, as such, their absolute values of Gcrnax differ slightly from ours at room temperature. Jou and Freeman26 have published values for the temperature range 1-107"C, and Shiraishi et have published data at 20-250 "C, for water. Christensen and Sehested' have reported GE,,, data for solutions containing 1 x lo- ' mol dmP3 sodium hydroxide and 0.12-0.2 mol dmP3 hydrogen in which all the hydroxyl radicals were con- verted to hydrogen atoms [reaction (7)], and these, in turn, were converted to hydrated electrons [reaction (lo)].

To estimate the temperature dependence of E,,, from these studies, we calculated the value of cmax from the published GE,,, data and then normalized the values to 20000 dm3 mol-' cm-' at 20-25°C. For the Christensen and Sehested data,' GE,,, values uncorrected for spur scavenging were used; G(e,;) was taken to be equal to the sum g(e,;) + g(0H) + g(H) for neutral pH solutions, and it was assumed that the temperature dependence would be the same as in the basic solution. As shown in Fig. 5, there is agreement between the results from the different publications, except for the data from Shiraishi et al.27 We have no explanation as to why the data of Shiraishi et a!. differ from the others. For fitting our data we have used the relationship (I),

~ ( t r C ) = 20364 - 20.4t (1)

which is given by the dashed line in Fig. 5. With this molar absorption coefficient we can now calcu-

late the true temperature dependence of the rate constant for reaction (2) from the values given in Table I1 in the paper by Christensen and Sehested,s where a constant molar absorp- tion coefficient of 18400 dm3 mol-' cm-' was assumed. From our corrected data, at 25"C, a value of 2k, = 1.29 x 10" dm3 mol-' s- ' was calculated and the Arrhenius activation energy for k , was found to be 20.3 kJ mol-' for temperatures up to 150°C. The corrected values up to 200°C are shown in Fig. 6. Christensen and Sehested reported an activation energy of 23 kJ mol-'.'

Estimation of k, from Kinetic Traces

At 18 and 75"C, data were recorded at three different doses (and pulse lengths): 1.8 Gy (0.2 ps), 11 Gy (0.5 ps) and 22 Gy (0.8 ps). At 100, 150 and 200 "C, only the 1.8 and 11 Gy doses were studied. As noted earlier, it was necessary to incorporate reaction (12) to account for the reaction of the electron with trace impurities. The procedure to fit the data was to assume initially that k , , was zero, and then fit the highest dose traces for k , with FACSIMILE; this value of k , was then held fixed and k , , was varied to fit the low dose traces. The values of k , , were then fixed for the higher dose data and k , fitted again. This process was repeated until consistent values of k , and k , , were found. If intermediate dose data were available, these were then fitted with the fixed value of k 1 2 . This pro- cedure worked up to and including 150 "C, and examples of the fits are shown in Fig. 1-4. The fitted values of k , and k , , are given in Table 1 ; the values of k , are also displayed as an Arrhenius plot in Fig. 6 with an apparent activation energy of 7.9 kJ mol-'. The values of k , , are consistent with the pseudo-first-order rate constants expected from (1-2) x mol dm-3 trace impurities, such as oxygen, which react with the hydrated electron at near-diffusion-controlled rates. The

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F

V

vA

m .. 1

0.0020 0.0025 0.0030 0.0035 KIT

Fig. 6 Rate constants for reaction (1) from this work (+); reaction (3) from ref. 14 (m); and reaction (2) from ref. 5 after correction for the temperature dependence of the molar absorption coeficient at pH 10.9 (V), pH 12 (0) and pH 13 (A). The dash-dot line is an Arrhenius fit for reaction (1).

value of k , at 18 "C of (2.8 & 0.2) x lo1' dm3 mol-' s-' is in good agreement with the value of (3.0 & 0.7) x 10'' dm3 mol-' s C 1 estimated by Matheson and Rabani at 23 "C20

The error bars in Table 1 are one standard deviation based on three to six determinations of the rate constant in ques- tion. In Fig. 1 and 4, the dash-dot lines represent a +30% variation in the rate constant k, for 10 Gy traces. At 18"C, this is clearly an excessive error estimate but, at 150"C, the dashed lines are only just outside the noise envelope. Material transport calculations indicate that reaction (1) accounts for 50% of the hydrated electron loss at 18 "C, while reaction (2) accounts for only 15%. At 150"C, reaction (1) accounts for only 38%, whereas reaction (2) accounts for 50%. These calculations were based on a 10 Gy pulse and after 70% of the hydrated electron had decayed. Reaction (12) accounted for 16% of the hydrated electron loss at both tem- peratures.

Data were also collected at 200°C and the traces appeared to decay by first-order kinetics at that temperature. However, the observed first-order rate constant was dose dependent; it was 5.6 x lo5 s - l at 1.8 Gy and 9.0 x lo5 s - l at 9.5 Gy. Based on the values at lower temperatures, an estimate for the value of k , , of 1-2 x lo5 s-l at 200°C can be made. A number of ways of treating the kinetic data at 200°C were tried; for example, attempts were made to fit the kinetic traces using values for k , based on a continued Arrhenius dependence up to 200 "C, and on the much lower value calcu- lated from Table I1 in the paper by Christensen and Sehested' (see Fig. 6). Fits could be found, but our confidence in the results was low, owing to the relatively large contribu- tion of k 1 2 , the small contribution of reaction (1) to the overall kinetics in the case of the Arrhenius dependence for k , , and the relatively large value for k , found assuming the lower reported value for k , .'

Discussion The temperature dependence of reaction (1) is similar to that of the bimolecular reaction of the hydroxyl radical [reaction (3)], rather than that of the bimolecular reaction of the

hydrated electron [reaction (2)], as shown in the Arrhenius plot in Fig. 6. In fact, almost all near-diffusion-controlled reactions involving the hydroxyl radica12,'0*28 have a tem- perature dependence lower than that for self-diffusion in water (for the temperature range 20-200"C, Ediff is ca. 17 kJ mol- ').lo Interestingly, the activation energy of reaction (2) up to 150°C of 20.3 kJ mol-' is essentially the same as that measured by Schmidt et aL2' (19.8 kJ mol-') for diffusion in water of the hydrated electron over the temperature range 15-90°C. If reaction (2) is assumed to be a truly diffusion- controlled reaction up to 150"C, then using the Smolu- chowski equation, a reaction radius of nearly 0.5 nm can be calculated (assuming a spin statistical factor of 0.25). However, it is interesting that the rate constants measured by Christensen and Sehested' show no strong dependence on ionic strength (see Fig. 6).

Reaction (1) is an important reaction in the spur, as it is the major pathway for reforming water. In a recent pub- lication, Laverne and Pimblott3' used diffusion-kinetic mod- elling to simulate reactions in the spur as a function of temperature. In the absence of any other evidence, they assumed that reaction (1) had the temperature dependence of self-diffusion in water, although some calculations were made with an activation energy of 12.6 kJ mol-'. The present results, although not linear in the Arrhenius plot (Fig. 6), have an apparent activation energy of 7.9 kJ mol-l. The yields calculated by Laverne and Pimblott are obviously strongly influenced by the catastrophic drop in the rate con- stant k , between 150 and 200°C (Fig. 6). It is at this point that the calculated yields suddenly deviate sharply to lower values than the experimental yields for molecular hydrogen. It is becoming apparent that the temperature dependence of k , up to at least 200°C must be confirmed, perhaps at lower ionic strengths than the original work.' At present we are modifying our high-temperature apparatus to be able to satu- rate solutions under high pressures of hydrogen to reinvesti- gate reaction (2).

This work was funded by the CANDU Owners Group under working party 15. The authors thank Dr. G. V. Buxton (University of Leeds, UK) for discussions during the course of this work.

References 1 2

3

4 5 6 7

8

9 10

11

12 13

14

15

16

K. H. Schmidt, J. Phys. Chem., 1977,81,1257. H. Christensen and K. Sehested, Radiat. Phys. Chem., 1981, 18, 723. H. Christensen, K. Sehested and H. Corfitzen, J . Phys. Chem., 1982,86,1588. H. Christensen and K. Sehested, J. Phys. Chem., 1983,87,118. H. Christensen and K. Sehested, J. Phys. Chem., 1986,90, 186. H. Christensen and K. Sehested, J. Phys. Chem., 1988,92,3007. G. V. Buxton, N. D. Wood and S. Dyster, J. Chem. SOC., Faraday Trans. 1, 1988,84, 11 13. A. J. Elliot and D. R. McCracken, Radiat. Phys. Chem., 1989,33, 69. A. J. Elliot, Radiat. Phys. Chem., 1989,34,753. A. J. Elliot, D. R. McCracken, G. V. Buxton and N. D. Wood, J. Chem. SOC., Faraday Trans., 1990,86, 1539. K. Sehested and H. Christensen, Radiat. Phys. Chem., 1990, 36, 499. P. Han and D. M. Bartels, J. Phys. Chem., 1992, %, 4899. A. J. Elliot and G. V. Buxton, J. Chem. Soc., Faraday Trans., 1992,88,2465. G. V. Buxton and A. J. Elliot, J . Chem. SOC., Faraday Trans., 1993,89,485. A. J. Elliot, D. C. Ouellette and D. R. McCracken, AECL report,

A. J. Elliot, M. P. Chenier and D. C. Ouellette, J. Chem. SOC., Faraday Trans., 1993,89, 1193.

AECL-10667,1992.

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18 19

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22 23

24

E. M. Fielden, in The Study of Fast Processes and Transient Processes by Electron Pulse Radiolysis, ed. J. H. Baxendale and F. Bussi, Reidel, Dordrecht, 1982, p. 49. G. V. Buxton and C. R. Stuart, personal communication. A. R. Curtis and W. P. Sweetenham, FACSIMILE/ CHECKMAT, Harwell Laboratory, AERE R 12805, 1988. M. S. Matheson and J. Rabani, J. Phys. Chem., 1965,69,1324. F. W. Sweeton, R. E. Mesmer and C. F. Baes, J. Solution Chem., 1974, 3, 191. W. C. Natzle and C. B. Moore, J. Phys. Chem., 1985,89,2605. H. A. Schwarz and B. H. J. Bielski, J . Phys. Chem., 1986, 90, 1445. R. E. Mesmer, C. F. Baes and F. H. Sweeton, Znorg. Chem., 1972, 11, 537.

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Paper 3/06266J ; Received 20th October, 1993

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