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Reaction of Hydrogen Atoms with Hydroxide Ions in High-Temperature and High-Pressure Water †

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Reaction of Hydrogen Atoms with Hydroxide Ions in High-Temperature and High-Pressure Water †
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  Reaction of Hydrogen Atoms with Hydroxide Ions in High-Temperature andHigh-Pressure Water † Timothy W. Marin ‡ and Charles D. Jonah Chemistry Di V  ision, Argonne National Laboratory, Argonne, Illinois 60439 David M. Bartels*  Notre Dame Radiation Laboratory, Notre Dame, Indiana 46556  Recei V  ed: July 22, 2004; In Final Form: December 9, 2004 The rate constant for the reaction of hydrogen atoms (H • ) with hydroxide ions (OH - ) in aqueous solution hasbeen measured from 100 to 300  ° C by direct measurement of the hydrated electron ((e - ) aq ) product growthrate. In combining these measurements with previous results, the reaction is observed to display Arrheniusbehavior in two separate temperature regions, 3 - 100 and 100 - 330  ° C, where the data above 100  ° C showan obvious decrease in activation energy from 38.2  (  0.6 to 25.4  (  0.8 kJ mol - 1 . The value of the rateconstant is smaller than that estimated previously in the 200 - 300  ° C range. The very unusual activationenergy behavior of the forward and backward reactions is discussed in the context of transition state theory. I. Introduction To make predictions of the radiation-induced chemistry inthe primary heat transport system of nuclear reactors, it isnecessary to understand the kinetics of many important reactionsover the range of reactor operating temperatures. In recent years,rate constants for several vital reactions have been determined. 1 - 6 In our continuing study of high-temperature and pressure waterradiation chemistry, we have reexamined the very unusualreaction of the hydrogen atom (H • ) with the hydroxide ion(OH - ) in the 100 - 300  ° C temperature range.The equilibrium processis of critical importance in both radiation chemistry and nuclearreactor engineering as it determines the lifetime and limitingconcentration of the hydrated electron ((e - ) aq ) in water. Sinceboth the H • and hydrated electron free radicals are highlyreactive, the equilibrium constant has been determined byseparate measurements of the forward 4,7 - 9 and reverse 10 - 13 reaction rates. Determination of their temperature dependencehas allowed the evaluation of the (e - ) aq  solvation thermodynam-ics. 9,11,14,15 The equilibrium constant for reaction 1,  K  1 , can be expressedaswhere  k  1  and  k  - 1  respectively represent the rate constants forthe forward and reverse reactions,  K  H  is the equilibrium constantfor H • atom ionization,and  K  w  corresponds to the ionic product for water dissociation K  w  and  K  H  have been measured from room temperature up to1000 16 and 250  ° C, 15 respectively. 17,18 A polynomial for p K  H has been reported as a function of temperature just above theliquid/vapor coexistence pressure, 19 and ref 16 gives an equationfor  K  w  that includes both its temperature and density depen-dence. With knowledge of   K  w  and  K  H , values for  K  1  can becalculated reliably up to 250  ° C. However, knowledge of   K  1  asa function of temperature merely defines the temperaturedependence of the ratio  k  1 / k  - 1 , and does not explicitly assignvalues to either  k  1  or  k  - 1 .Previous measurements in this laboratory examined  k  1  fromroom temperature to 98  ° C 8,9 and from 200 to 380  ° C, 4 demonstrating that the Arrhenius behavior observed below 100 ° C cannot be extrapolated to higher temperatures. In the currentpaper, we have measured  k  1  from 100 to 300  ° C, filling in thegap where data were missing between 100 and 200  ° C andreconfirming the overall non-Arrhenius behavior of the rateconstant. We find that the activation energy suddenly decreasesnear 100  ° C. Given prior knowledge of   K  1 , the rate constantfor the back reaction between (e - ) aq  and H 2 O can also becalculated. Transition state theory is used to explore thethermodynamics of the forward and backward reactions. II. Experimental Section Pulse radiolysis/transient absorption experiments were carriedout using 4-ns pulses from the Argonne Chemistry Division’s † This is document number NDRL-4565 from the Notre Dame RadiationLaboratory.* To whom correspondence should be addressed. E-mail:bartels@hertz.rad.nd.edu. Fax: (574) 631-8068. ‡ Current address: Chemistry Department, Benedictine University, Lisle,IL 60532. H • h  (e - ) aq + H + (3)H 2 O h  H + + OH - (4)H • + OH - h  (e - ) aq + H 2 O (1) K  1 ) k  1 k  - 1 ) K  H K  w (2) 1843  J. Phys. Chem. A  2005,  109,  1843 - 184810.1021/jp046737i CCC: $30.25 © 2005 American Chemical SocietyPublished on Web 02/12/2005  20-MeV electron linac. The high-temperature/pressure samplecell, flow system, and basic experimental setup and character-istics were described in previous publications. 4,20 Normaltemperature and pressure stabilities were  (  0.2  ° C and  (  0.1bar, respectively. Analyzing light from a pulsed 75-W xenonlamp (Photon Technology International) was selected using a40-nm bandwidth interference filter (Andover Corporation) witha center wavelength corresponding to the maximum absorptionof (e - ) aq . Because the (e - ) aq  absorption spectrum is sensitiveto both temperature and density, wavelengths were chosen tocoincide with the absorption maximum at each temperature. (Thered shift and width of the (e - ) aq  spectrum at elevated temper-atures will be the subject of a future publication. 21 ) A germaniumphotodiode (GMP566, Germanium Power Devices, Inc.) wasused for detection. The inherent biexponential transient responseof the photodiode 22 was accounted for in the data fitting as aconvolution with the (e - ) aq  absorption. Kinetics were measuredfrom 100 to 300  ° C in steps of 50  ° C. Unfortunately, data couldnot be acquired at temperatures higher than 300  ° C, assignificant corrosion began to occur in the sample cell underalkaline, hydrogenated water conditions, altering the (e - ) aq kinetics.Standardized 0.991 M potassium hydroxide (KOH) solutions(Aldrich, used as received) were diluted to the appropriateconcentration in deionized water (18.2 M Ω -cm, BarnsteadNanopure system). Alkaline water samples were kept undernitrogen or argon at all times to avoid contamination bycarbonate ions arising from possible carbon dioxide absorption,and were purged with Argon for at least 30 min prior tocollecting data. Pressurized hydrogenated water samples wereprepared in our laboratory-built gas - liquid saturator. Detailsof this device have been previously published. 2 Individual control over the hydrogenated water and KOHsolution flow rates was achieved with two separate HPLC pumps(Alltech 301). In all experiments, the hydrogen concentrationwas kept at a constant 0.024 mol kg - 1 (m) in the sample cell.Four different KOH solutions were used to give total OH - concentrations of 1.00 × 10 - 2 , 4.00 × 10 - 3 , 1.50 × 10 - 3 , and3.00  ×  10 - 4 m in the sample cell (solution concentrationsconsidered reliable within 2%). System total flow rates weregenerally  ∼ 1.8 mL/min, adjusted as necessary to achieve anexperimental pressure of 250 bar.The radiolysis of water by  γ  photons, high-energy electrons,neutrons, or recoil ions can be represented byWater radiolysis is kinetically complex, and entails some 50competing reactions involving the water decomposition speciesshown above. 19,23 Many of these are second-order recombinationreactions, which can be suppressed by carrying out pulsedexperiments using low radiation doses. Moreover, in hydroge-nated alkaline water, the transient absorption from (e - ) aq  canbe approximated by just three dominant reactions:The rate constant for reaction 1 is easily measured by monitoringthe growth of (e - ) aq , which has a strong absorption in the redand near-infrared spectral regions (  max ) 18 400 M - 1 cm - 1 atroom temperature 26 ). This growth is followed by a second-orderdecay arising from reaction 7. At low radiation doses, thesecond-order decay rate is suppressed, allowing the hydratedelectron to live for many tens of microseconds. In the limit of high hydrogen concentration ( > 0.010 M), reaction 6 becomesfast compared to reaction 1, and thus the growth of (e - ) aq  islimited by the rate of reaction 1. Nonetheless, knowledge of the reaction 6 rate constant ( k  6 ) is essential to properly ascertainthe reaction 1 rate constant ( k  1 ), especially in the limit of veryhigh OH - concentrations ( ∼ 0.01 M), where the reaction 1 rateapproaches that of reaction 6. Values of   k  6  were previouslydetermined in our laboratory up to 350  ° C. 2 Since k 1  .  k  - 1 ,  k  1  can be determined by merely examiningthe growth rate of (e - ) aq , which under conditions of hydroge-nated, alkaline water and low doses of radiation, could bedescribed as a first-order growth atop the prompt (e-) aq  generateddirectly by radiolysis (see Figure 1). However, a wide range of OH - concentrations was used in these studies to ensureconfident fits to the reaction 1 rate constant. Over this entirerange, the observed pseudo-first-order growth of (e - ) aq  is notpreserved, as contribution of the reaction 6 rate becomesincreasingly important. At the highest OH - concentrations, thereaction 6 and reaction 1 rates are not well-separated, andtherefore the (e - ) aq  rise time is no longer purely limited byreaction 1. Furthermore, the intrinsic secondary response of thephotodiode 22 used in the experiment coincides with the timescale of the acquired kinetic data, and must be included as aninstrument response convolution. H 2 O 9 8  radiation H • , OH • , (e - ) aq , (H + ) aq , H 2 O 2 , H 2 , HO 2 (5)H 2 + OH • f  H • + H 2 O (6)H • + OH - h  (e - ) aq + H 2 O (1)(e - ) aq + (e - ) aq h  2OH - + H 2  (7) Figure 1.  Formation of (e - ) aq  at 150  ° C and an OH - concentration of a) 3.00 × 10 - 4 m and (b) 1.50 × 10 - 3 m. The signal is acquired at thewavelength peak of the (e - ) aq  absorption spectrum. The three tracescorrespond to three applied radiation doses. Fits to the kinetics aresuperimposed as solid lines. 1844  J. Phys. Chem. A, Vol. 109, No. 9, 2005  Marin et al.  The data were fit using a differential equation model thatincorporates all of the known recombination reactions as wellas yields of water radiolysis species at high temperature, asassembled by Elliott. 19 High-temperature rate constants forreaction 6 were taken from ref 2. The model is coupled to afitting routine based on Gauss - Newton minimization, incor-porating modifications from the traditional Marquardt - Leven-berg approach. 24,25 The program is set up to specifically fit the(e - ) aq  kinetics by iterating the reaction rate constants of ourchoice, while keeping all other (known) parameters fixed.A sensitivity analysis for all the radiolysis rate constantsconfirmed that for the radiation doses and OH - concentrationsused in these studies, only  k  1 ,  k  6 , and  k  7  need be examined indetail, as individual changes to other rate constants in the modelnegligibly affect the fitted  k  1  value. Yet, use of the full modeland incorporating all the reactions modestly benefits the qualityof the fit as a whole, and gives us more confidence that themodel is indeed reproducing the experimental data. Rateconstants for the remaining reactions were left fixed to the valuesprovided by Elliot. 19 The value of   k  6  was also fixed based onits previous determination. 2 The reaction 7 rate constant isknown to decrease with increasing temperature over the tem-perature range considered here, but reliable values of the rateconstant are not yet available. (Reaction 7 will be examined ingreater detail in the future.) Consequently this parameter wasfitted along with  k  1 . Global fits to  k  1  and  k  7  were performedover all applied doses for a given temperature and OH - concentration. The reaction 1 rate exceeds that of reaction 7 bya factor of   ∼ 50 so that their rate coefficients are relativelyuncorrelated. The fitted values to  k  7  are not significant here asa proper determination of   k  7  requires data to be acquired on amuch longer time scale than used in these measurements.Nonetheless, fitted values at lower temperatures were within ∼ 35% of rate constant values previously reported. 26 Because the   2 surface for this system of equations is notquadratic, the least-squares standard deviation does not providea meaningful error estimate. 24,25 The   2 surface of the systemwas mapped out by changing and fixing the value of eachparameter near its optimum value, then reoptimizing all otherparameters. The change needed to double   2 is a reasonableestimate of the error in the fitted parameter, so long as twoparameters do not have very large covariance. In all cases thiserror is well below 10% and no large covariance is observed.We take 10% as a conservative estimate of the rate constantuncertainties, rather than reporting the entire analysis. III. Results and Discussion Typical data taken at 150  ° C and OH - concentrations of 3.0 × 10 - 4 m and 1.5 × 10 - 3 m are shown in Figure 1, with fittedcurves superimposed. The data reflect the growth of (e - ) aq  at900 nm, and the three different traces acquired at eachconcentration correspond to three applied doses. The subsequentdecay of (e - ) aq  due to reaction 7 occurs on a time scale of tensof microseconds in all cases, and was not examined in theseexperiments. Applied doses generated (e - ) aq  concentrations of  ∼ (20 - 130)  ×  10 - 9 m. As expected from pseudo-first-orderbehavior, an increase in OH - concentration gives an increasein the growth rate of (e - ) aq . Fitted values of   k  1  as a function of temperature are given in Table 1.An Arrhenius plot of   k  1  is shown in Figure 2 (squares)alongside data previously reported. Triangles indicate low-temperature data acquired from pulse radiolysis/EPR and opticalspectroscopy 8,9 and circles indicate high-temperature dataacquired from pulse radiolysis/optical spectroscopy. 4 The newdata slightly undershoot previous results over the 200 - 300  ° Ctemperature range. (Below 300  ° C, H • atoms account for lessthan 20% of the total radiolysis yield, giving weak experimentalsignals in the previous study. Above 300  ° C, the H • atom yieldrapidly increased, allowing reliable measurements in this range.The quality of the current data is not so dependent on the initialH • atom yield.) On the basis of our fitting sensitivity analysis,we can confidently report that errors in the fitted  k  1  values are < 10% at every temperature, whereas previous errors were upto ∼ 50% at 200  ° C. Note that at 300  ° C and above, where theH • atom yield becomes sizable, the data agree within 20%. Thesolid lines in Figure 2 represent Arrhenius fits in the 3 - 98  ° Cand 100 - 330  ° C temperature ranges, where the latter incorpo-rates two previously obtained data points at 328 and 330  ° C.Data at still higher temperatures and lower density do not showthe same Arrhenius behavior 4 and consequently are not includedin the Arrhenius fits. Compared to the low-temperature data,current results exhibit a smaller activation energy. An Arrheniusfit to data from 100 to 330  ° C gives an activation energy of 25.4  (  0.8 kJ mol - 1 and a prefactor of 1.76  (  0.36  ×  10 12 M - 1 s - 1 , where previous low-temperature results gave values TABLE 1: Values of the Reaction 1 Rate Constant as aFunction of Temperature, Acquired from Global Fits to the(e - ) aq  Kinetics at Each Temperature and OH - Concentration a temperature ( ° C) rate constant  k  1  (M - 1 s - 1 )100 5.01 × 10 8 150 1.34 × 10 9 200 2.79 × 10 9 250 4.76 × 10 9 300 8.59 × 10 9 a Uncertainties are  ( 10%. Figure 2.  Arrhenius plot for the reaction 1 rate constant  k  1 . Threesets of data are presented: current data (squares), previous low-temperature data acquired from pulse radiolysis/EPR and opticalspectroscopy (triangles) and high-temperature data acquired from pulseradiolysis/optical spectroscopy (circles). Error bars for the current dataare on the order of the point size. Arrhenius fits (solid lines) to regionsabove and below 100  ° C are shown by solid lines. Reaction of Hydrogen Atoms with Hydroxide Ions  J. Phys. Chem. A, Vol. 109, No. 9, 2005  1845  of 38.2  (  0.6 kJ mol - 1 and 1.27  (  0.27  ×  10 14 M - 1 s - 1 ,respectively.Figure 3 shows (a)  K  w ,  K  H , and (b)  K  1  as a function of temperature, given the pressures specifically used in ourexperiments. It was noted by Shiraishi et al. 15 that  K  H  closelyparallels the temperature dependence of   K  w  because bothequilibria involve a neutral molecule dissociating into ions. InFigure 3,  K  w  and  K  H  suddenly increase by 30% at 100  ° Cbecause the data below this temperature were obtained at 1 barpressure, whereas those above 100  ° C were acquired at 250bar. Available data from the water ionic product dictates thisincrease for higher densities. Although pressure-dependent dataare not available for  K  H , the same trend as for  K  w  is assumed.The available  K  H  data 15 were acquired near the water gas/liquidcoexistence pressure (  p coex ). Since our data were collected at apressure of 250 bar, we multiply the molal  K  H  values by theratio  K  w (250 bar)/ K  w (  p coex ) to add a small  K  H  density correction.Values of   K  H  at  p coex  above 250  ° C are extrapolated usingShiraishi’s equation. 15 The plot shows that  K  1  is relativelyinsensitive to temperature, and at the lowest OH - concentrationused in these experiments (3.00  ×  10 - 4 m), the equilibriumratio of the concentrations of (e - ) aq  to H • should be in the rangeof 450 - 1200, allowing direct determination of   k  1 .On the basis of the  K  1  values, the rate constant for the reverseof reaction 1 ( k  - 1 ) can be obtained via eq 2. Again, Arrheniusfits can be performed on two regions of data above and below100  ° C with different activation energies, though in this casethe cause of the change at 100  ° C is merely the implicitdependence of   k  - 1  on  k  1  as we have calculated it here. A fit tothe data from 100 to 330  ° C gives an activation energy of 22.1 ( 1.3 kJ mol - 1 and a prefactor of 2.61 ( 0.83 × 10 5 s - 1 , wherebelow 100  ° C these parameters are 33.1  (  0.6 kJ mol - 1 and5.84  (  1.41  ×  10 8 s - 1 , respectively.Following the standard methods of transition state theory, 27 a measured rate constant can be represented bywhere  k  B  is Boltzmann’s constant,  h  is Planck’s constant,  R  isthe gas constant,  T   is temperature in K,  c o  ( ) 1 M) is the ratioof standard state concentrations for the transition state/reactantequilibrium, 28 and ∆ G † is the difference in free energy betweenthe transition state and reactants. We follow the usual assump-tion that all species reaching the transition state irreversibly formproduct and therefore set the transmission coefficient  κ  to unity.The free energy of activation breaks down into the entropy ( S  )and enthalpy (  H  ) of activation via  ∆ G † ) ∆  H  † - T  ∆ S  † . Thus,with rate constants in hand,  ∆ G † can be obtained for both theforward and reverse of reaction 1, and ∆  H  † and ∆ S  † can also beobtained.Figure 4 shows the temperature dependence of   ∆ G † for theforward and reverse reactions, respectively. Note that  ∆ G † forthe forward reaction ( ∆ G † (1)) is fairly temperature-insensitive,changing by only ∼ 6 kJ mol - 1 over the entire temperature range,whereas  ∆ G † for the backward reaction ( ∆ G † ( - 1)) changessignificantly, increasing by ∼ 48 kJ mol - 1 . The forward reactionis dominated by enthalpy, while the back reaction has a largeentropy component. The most curious aspect of the activationthermodynamics is the sudden change in the slope of   ∆ G † (1)at about 100  ° C. Nominally the activation entropy of reaction1 changes sign from positive to negative at this point. At 25 Figure 3.  Temperature dependence of equilibrium constants: (a)  K  H (dashed line) and  K  w  (solid line), (b)  K  1 . The ∼ 30% increase observedat 100  ° C for  K  H  and  K  w  is due to data acquisition at two differentpressures. Note that the  y -axis for panel a is a log scale and that forpanel b is a linear scale. Figure 4.  Temperature dependence of the Gibbs free energy of activation as acquired via transition state theory for (a) reaction 1 and(b) reaction  - 1. k  ) κ k  B T c o h  exp ( - ∆ G †  RT   )  (8) 1846  J. Phys. Chem. A, Vol. 109, No. 9, 2005  Marin et al.  ° C,  ∆  H  † and  ∆ S  † have values of 35.7 kJ mol - 1 and  + 16.8 Jmol - 1 K - 1 respectively, whereas at 100  ° C these values are 22.3kJ mol - 1 and  - 20.6 J mol - 1 K - 1 . It is straightforward to addadditional temperature dependence to the thermodynamics byfitting  ∆ G † (1) with a  ∆ C  p  term, as was done by Shiraishi etal. 15 for the equilibrium. However, since the temperaturedependence of  ∆ G † (1) is not quadratic (see Figure 4), this yieldsunphysically large values for  ∆ C   p  and still does not givereasonable fits, given the very sudden change in slope of   ∆ G † for reaction 1.It is unclear why there should be two separate Arrheniusregions for reaction 1. The properties of water and the solventstructure are not dramatically changing in this temperature range.The experimental pressure change between 98 and 100  ° Cshould not have greatly affected the thermodynamics. This leadsus to examine in more detail the assumptions we have made inapplying transition state theory to the problem.A first basic assumption is that we are dealing with a singleelementary reaction with a transition state bottleneck, and notwith a short-lived intermediate and a back reaction. In the lattercase, reaction 1 would actually be a consecutive process withtwo rate constants determining the overall reaction rate such asAssuming different Arrhenius parameters for each step of thereaction, it is possible that the rate-determining step of thereaction is dependent on the temperature and  k  b  could becomeless than  k  a  at 100  ° C. One might imagine that the excesselectron becomes localized on an intermediate of the form H 2 O - ,which then splits to give the H • and OH - products. However,this possibility was considered in a previous publication anddismissed for the temperature range below 100  ° C because of the equivalence of EPR and optical reaction rates. 9 An inter-mediate allowing the exchange of protons would be detectedas an additional spin relaxation rate in the EPR experiment.Perhaps this EPR experiment should be repeated for highertemperatures, but the existence of a short-lived intermediateseems very unlikely.A second assumption is in setting the transmission coefficient, κ , equal to unity, independent of temperature. This factoraccounts for both the possibilities of quantum mechanicaltunneling and for the contributions of solvent friction. At lowertemperatures, tunneling can be essentially ruled out experimen-tally. Previous experiments showed absolutely no kinetic isotopeeffect when H • in reaction 1 was replaced by deuterium 9 inmeasurements up to 100  ° C, and at most a ∼ 30% isotope effectexists between H • atom and the unstable light isotope muonium,where muonium shows a higher rate constant above 100  ° C, 29,30 but lower below 100  ° C. 31 The reaction enthalpy is overallpositive, so in general there is no place at lower energy on thebarrier for the H • atom to tunnel toward. The small apparentmuonium isotope effect then could be assigned to energydifferences of the reactants, i.e., zero point 32 and solvationenergies. 33 Another scenario to give  κ  a value less than unity isthe contribution of temperature or pressure-dependent Kramers 34 or Grote - Hynes 35 type solvent friction. This could conceivablyvary over the temperature range studied due to physicalrearrangements in the water solvent and changes in its properties.One would have to postulate a greater friction at highertemperature. However, this behavior should tend to cause theheavier isotope to have the larger rate constant.Finally, we have also made the assumption that semiclassicaltransition state theory applies to the reaction. If the reactionactually involves nonadiabatic transitions between coupledproton and electron states, the simple  κ k  B T  / c o h  prefactor willno longer apply. In this case a quantum treatment might beapplied to the proton transfer, 36,37 or a Marcus-type theory witha Fermi golden rule rate expression could be more appropri-ate. 38,39 As we are unable to qualitatively explain the rateconstant result via (adiabatic) transition state theory, we leantoward this (nonadiabatic) explanation, and invite others to takeup the challenge of elucidating the reaction mechanism. Acknowledgment.  We thank Dr. Sergey Chemerisov formaintaining and operating the linac accelerator used in this work.We are grateful to Dr. Khashayar Ghandi, Prof. Paul W.Percival, and Prof. Sharon Hammes-Schiffer for helpful dis-cussions. Work at Argonne National Laboratory and at NotreDame Radiation Laboratory was performed under US-DOENuclear Energy Research Initiative Grant M2SF02-0060. References and Notes (1) Takahashi, K. J.; Ohgami, S.; Koyama, Y.; Sawamura, S.; Marin,T. W.; Bartels, D. M.; Jonah, C. D.  Chem. Phys. Lett.  2004 ,  383 , 445 - 450.(2) Marin, T. W.; Bartels, D. M.; Jonah, C. D.  Chem. Phys. Lett.  2002 , 371 , 144 - 149.(3) Marin, T. W.; Cline, J. A.; Bartels, D. M.; Jonah, C. D.; Takahashi,K.  J. Phys. Chem. A  2002 ,  51 , 12270 - 12279.(4) Cline, J. A.; Takahashi, K.; Marin, T. W.; Jonah, C. D.; Bartels,D. M.  J. Phys. Chem. A  2002 ,  106  , 12260 - 12269.(5) Lundstrom, T.; Christensen, H.; Sehested, K.  Radiat. Phys. Chem. 2004 ,  69 , 211 - 216.(6) Lundstrom, T.; Christensen, H.; Sehested, K.  Radiat. Phys. Chem. 2002 ,  64 , 29 - 33.(7) Matheson, M. S.; Rabani, J.  J. Phys. Chem.  1965 ,  69 , 1324 - 1335.(8) Han, P.; Bartels, D. M.  J. Phys. Chem.  1990 ,  94 , 7294 - 7299.(9) Han, P.; Bartels, D. M.  J. Phys. Chem.  1992 ,  96  , 4899 - 4906.(10) Fielden, E. M.; Hart, E. J.  Trans. Faraday Soc.  1967 ,  63 , 2975 - 2982.(11) Schwarz, H. A.  J. Phys. Chem.  1992 ,  96  , 8937 - 8941.(12) Swallow, A. J.  Photochem. Photobiol.  1968 ,  7  , 683 - 694.(13) Hart, E. J.; Gordon, S.; Fielden, E. M.  J. Phys. Chem.  1966 ,  70 ,150 - 156.(14) Jortner, J.; Noyes, R. M.  J. Phys. Chem.  1966 ,  70 , 770 - 774.(15) Shiraishi, H.; Sunaryo, G. R.; Ishigure, K.  J. Phys. Chem.  1994 , 98 , 5164 - 5173.(16) Marshall, W. L.; Franck, E. U.  J. Phys. Chem. Ref. Data  1981 ,  10 ,295 - 304.(17) The water solvent is taken to have unit activity at all temperaturesand pressures. The density of water changes as a function of temperature,decreasing approximately 25% over the range 100 - 300  ° C. Thus, the  K  H molal equilibrium constant is multiplied by the water density (in kg L - 1 )and the  K  w  molal ionic product is multiplied by the water density squaredto convert to molar units. This ensures consistency of units between ourreported equilibrium constants and rate constants. Corrections for changesin the water concentration as a function of temperature are obtained fromthe water equation of state, given in ref 18.(18) Wagner, W.; Kruse, A.  Properties of Water and Steam ; Springer-Verlag: Berlin, 1998.(19) Elliot, A. J. Rate Constants and G-Values for the Simulation of the Radiolysis of Light Water over the Range 0 - 300  ° C. AECL, 1994.(20) Takahashi, K.; Cline, J. A.; Bartels, D. M.; Jonah, C. D.  Re V  . Sci. Instrum.  2000 ,  71 , 3345 - 3350.(21) Bartels, D. M.; Takahashi, K.; Cline, J. A.; Marin, T. W.; Jonah,C. D.  J. Phys. Chem. A. , in press.(22) Cline, J. A.; Jonah, C. D.; Bartels, D. M.  Re V  . Sci. Instrum.  2002 , 73 , 3908 - 3915.(23) Draganic, I. G.; Draganic, Z. D.  The Radiation Chemistry of Water ;Academic Press: New York, 1971.(24) Levenberg, K.  Q. Appl. Math.  1944 ,  2 , 164 - 168.(25) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T.  Numerical Recipes , 2nd ed.; Cambridge University Press: Cambridge,England, and New York, 1992.(26) Christensen, H.; Sehested, K.  J. Phys. Chem.  1986 ,  90 , 186.(27) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L.  Chemical Kineticsand Dynamics ; Prentice Hall: Englewood Cliffs, NJ, 1989.(28) Robinsion, P. J.  J. Chem. Educ.  1978 ,  55 , 509 - 510.(29) Ghandi, K.; Addison-Jones, B.; Brodovitch, J. C.; Kecman, S.;McKenzie, I.; Percival, P. W.  Physica B  2003 ,  326  , 55 - 60. H • +  OH - y \ z  k  a intermediate  y \ z  k  b (e - ) aq  +  H 2 O (9) Reaction of Hydrogen Atoms with Hydroxide Ions  J. Phys. Chem. A, Vol. 109, No. 9, 2005  1847
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