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Pulse Radiolysis of Supercritical Water. 2. Reaction of Nitrobenzene with Hydrated Electrons and Hydroxyl Radicals †

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Pulse Radiolysis of Supercritical Water. 2. Reaction of Nitrobenzene with Hydrated Electrons and Hydroxyl Radicals †
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  Pulse Radiolysis of Supercritical Water. 2. Reaction of Nitrobenzene with HydratedElectrons and Hydroxyl Radicals † Timothy W. Marin, Jason A. Cline, Kenji Takahashi, ‡ David M. Bartels,* andCharles D. Jonah Chemistry Di V  ision, Argonne National Laboratory, Argonne, Illinois 60439 Recei V  ed: August 21, 2002; In Final Form: October 1, 2002 The rate constants for the reactions of nitrobenzene with the hydroxyl radical (OH • ) and hydrated electron((e - ) aq ) in water have been measured from room temperature to 400  ° C using electron pulse radiolysis andtransient absorption spectroscopy. The diffusion-limited reaction of nitrobenzene with (e - ) aq  exhibitstemperature-insensitive activation energy up to 300  ° C, indicating that the activation energy for electrondiffusion remains high over this range. The (e - ) aq  reactivity is explained as a long-range electron transfer,and the results are interpreted in terms of extended Marcus theory and Smoluchowski relationships. At 380 ° C, the rate constant has a density dependence similar to that previously reported for other (e - ) aq  scavengingreactions. The reaction rate of nitrobenzene with OH • is very insensitive to temperature from room temperatureup to 300  ° C, in agreement with previous studies. Above 300  ° C, the rate constant increases as the criticaltemperature is approached and exceeded. Time-resolved electronic absorption spectra of the nitrobenzeneradiolysis transients reveal complex kinetics involving multiple absorbing species. I. Introduction Recent designs for more economic and thermally efficientwater-cooled nuclear reactors would operate the primary coolingloop at higher temperatures and pressures that exceed the criticalpoint of water (374  ° C, 221 bar). 1 - 3 The radiation-inducedchemistry of water remains largely unknown under theseconditions, and most of its reactions have been measured onlyup to 250  ° C (or less). 4 Water radiolysis has crucial implicationsfor the corrosion processes occurring in the primary coolingloop of the reactor. 3,5,6 This manuscript is the second in a seriesthat addresses the radiation-induced chemistry of water atsupercritical temperatures and pressures and provides represen-tative data for the reactivities of radiolytically produced species. 7 Hydrated electrons ((e - ) aq ) and hydroxyl radicals (OH • )represent two of the primary species formed in water radiolysis.It is therefore necessary to understand their individual reactivitiesand roles in water radiation chemistry. To date, few experimentshave been carried out to discern their reactivities in supercriticalwater. We perform pulse radiolysis followed by transientabsorption to follow the kinetics of (e - ) aq  and OH • scavengingby nitrobenzene. Nitrobenzene has been shown to be reactivetoward both species. 8 - 27 Experimentally monitoring the reactionsof (e - ) aq  and OH • with nitrobenzene is easy because bothreactions are characterized by strong visible absorption changes(discussed below). This makes nitrobenzene a convenientreference partner for competition kinetic studies of other OH • scavengers.The reaction of nitrobenzene with (e - ) aq  forms a nitrobenzeneradical anionThe process has been shown to be diffusion-controlled attemperatures up to 200  ° C. 25 A motivation for the current work was to determine whether reaction 1 exhibits diffusion-controlledbehavior up to supercritical conditions, which could give insightinto the electron diffusion coefficient over this temperaturerange. The present study extends previous measurements up to400  ° C and reports the density dependence of the reaction rateat 380  ° C, just above the critical temperature.The addition of OH • to nitrobenzene forms the nitrohydroxy-cyclohexadienyl radicalA recent pulse radiolysis study examined this reaction up to390  ° C and showed that the rate constant is very insensitive totemperature up to 350  ° C. 12 Above the critical point, the rateconstant was shown to increase approximately two-fold. TheC 6 H 5 NO 2 (OH • ) product has a strong visible absorption in the400 nm region, making reaction 2 a useful reference to gaugeagainst OH • reactivity with other species. We have repeatedprevious measurements 11,12 to confirm reported rate constantsin preparation for a study of the OH • +  H 2  reaction. Time-resolved spectra of the nitrobenzene radiolysis transients revealcomplex kinetics involving multiple absorbing species. Mostnotably, it appears that H • atom addition to nitrobenzene stronglyinterferes with the measurement of OH • kinetics at temperaturesabove 300  ° C. II. Experimental Section Pulse radiolysis/transient absorption experiments were carriedout using 4 ns pulses from the Argonne Chemistry Division’s † Work performed under the auspices of the Office of Science, Divisionof Chemical Science, US-DOE under Contract No. W-31-109-ENG-38.Additional funding was provided under Nuclear Energy Research Initiativegrant No. M9SF99-0276 and the Ministry of Education in Japan.* To whom correspondence should be addressed. ‡ Present address: Division of Quantum Energy Engineering, HokkaidoUniversity, Sapporo 606-8628, Japan. C 6 H 5 NO 2  +  (e - ) aq f  C 6 H 5 NO 2 •- (1)C 6 H 5 NO 2  +  OH • f  C 6 H 5 NO 2 (OH • ) (2) 12270  J. Phys. Chem. A  2002,  106,  12270 - 1227910.1021/jp026812u CCC: $22.00 © 2002 American Chemical SocietyPublished on Web 12/03/2002  20 MeV electron linac accelerator. The sample cell and flowsystem were described in our previous publications. 7,28 AFaraday block on a shutter placed before the sample cell wasused to check the charge per pulse (dose) periodically to ensuresimilar pulse amplitudes over the course of a day. Typical dosefluctuations over a day were  ( 5% and shot-to-shot variationswere  ( 2%.Analyzing light was obtained from a 75 Watt xenon arc lamp,pulsed for ∼ 300  µ s. The lamp pulse was timed so that the linacpulse coincided with the most stable, flattest portion of the lampresponse. For (e - ) aq  scavenging experiments, the decay of the(e - ) aq  absorption spectrum was monitored. Because the (e - ) aq absorption spectrum is sensitive to both temperature and density,wavelengths for electron scavenging experiments were chosento coincide with the absorption maximum at each temperature.(The red shift and width of the (e - ) aq  spectrum at elevatedtemperatures will be the subject of a future publication. 29 )Wavelengths were selected using 10 nm bandwidth interferencefilters (Andover Corporation) and ranged from 750 to 1200 nm.A germanium photodiode (Germanium Power Devices GMP566)was used for detection. The small correction needed for its non-single-exponential response has been described in detail. 30 Thewavelength for OH • scavenging experiments was 400 nm andwas isolated using a 40 nm bandwidth interference filter. Time-resolved spectra of the nitrohydroxycyclohexadienyl radical wereacquired from 400 to 520 nm using 10 nm bandwidth interfer-ence filters and a silicon photodiode (EG&G FFD-100) and from320 to 390 nm using a monochromator (Photon TechnologiesSID-101) and photomultiplier (Hamamatsu R1913).The flow system and sample cell have been describedpreviously. 7,28 Details pertaining to these experiments and slightmodifications to the flow system are given below. Two samplereservoirs were used simultaneously in (e - ) aq  scavengingexperiments, one containing deionized water (18.2 M Ω -cm,Barnstead Nanopure system) and the other a solution of nitrobenzene (Sigma-Aldrich, 99 + %) in water. The nitrobenzeneconcentration was verified via UV/Vis absorption (  268.5nm  ) 7800 M - 1 cm - 1 ). Both water reservoirs contained 10 - 5 M KOH(diluted from Sigma-Aldrich 0.991 N standard) to eliminate(e - ) aq  scavenging by protons and were continuously purged withambient pressures of Ar. For OH • scavenging reactions, KOHwas not added, and both reservoirs were initially saturated withN 2 O or O 2  for  ∼ 30 min and kept sealed with a slightlypressurized headspace over the course of experiments, givingN 2 O and O 2  concentrations of 0.024 and 0.0013 M, respectively.N 2 O and O 2  serve as electron and electron/H • atom scavengers,respectively. N 2 O was used for all measurements up to 275  ° C,and O 2  was used for all measurements at 300  ° C and above.Use of N 2 O in these experiments has the added advantage of rapidly generating additional OH • viaand thus is preferred for use below 300  ° C. As discussed below,the switch is made to O 2  at 300  ° C and above to aid inscavenging the greater yield of H • atoms in this temperaturerange. 7 In all experiments, the concentration of nitrobenzene wascontrolled by changing the scavenger solution flow rate relativeto the pure water flow rate using two independent HPLC pumps(Alltech 301). System pressure was maintained by restrictingthe system output flow with a length of stainless steel capillarytubing. The capillary tubing was immersed in a controllabletemperature bath. The bath temperature was adjusted to changethe water viscosity. With a fixed flow rate controlled by theHPLC pumps, this viscosity adjustment regulates the samplepressure. System pressure and temperature were continuouslymonitored during the experiments via a piezoelectric pressuretransducer (Omega PX02 series) and thermocouples. Normalsystem stabilities were ( 0.2  ° C and ( 0.1 bar. System flow rateswere generally 2.0 - 2.5 mL/min, adjusted as necessary to setthe proper pressure. Each time the nitrobenzene concentrationwas changed, the system was flushed for 3 - 4 min to ensureadequate time for sample renewal in the flow system and samplecell.Previous supercritical water oxidation experiments haveshown that nitrobenzene decomposed in supercritical water at440  ° C; 31,32 however, its stability was confirmed under thepresent concentration and temperature conditions. Spectra of nitrobenzene samples were taken after passing through thesample cell with both N 2 O and O 2  present at various temper-atures and were compared to spectra taken before heating. Nodegradation of the nitrobenzene was observed up to 400  ° C,even in the presence of O 2 . III. Results and DiscussionA. Hydrated Electron Scavenging.  In this section, we firstpresent the experimental kinetic results and data analysis of the(e - ) aq  reactivity with nitrobenzene. We then explain the (e - ) aq reactivity in terms of long-range electron transfer. The resultsare interpreted in terms of extended Marcus theory andSmoluchowski relationships. 1. Kinetics.  A survey of hydrated electron scavenging bynitrobenzene (reaction 1) was carried out as a function of temperature up to 400  ° C by monitoring the decay of the intensehydrated electron absorption in the near-infrared. All data werecollected at a pressure of 240 - 250 bar except at 400  ° C, wherethe pressure was 300 bar, and at 380  ° C, where data were takenat a series of pressures. In the limit of high nitrobenzeneconcentration, the production of nitrobenzene anion occurs viapseudo-first-order kinetics and the observed rate depends linearlyon the nitrobenzene concentration. The applied dose wasadjusted to give (e - ) aq  concentrations of  ∼ 5 × 10 - 7 M, and allnitrobenzene concentrations used were greater than 4  ×  10 - 6 M to ensure pseudo-first-order kinetics. Five nitrobenzeneconcentrations were run at each temperature/pressure state point,as well as a zero concentration. The fitted rates were plottedversus initial concentration (concentration at room temperaturebefore heating and pressurizing) and showed a linear concentra-tion dependence. The slope divided by the density of water ateach temperature was taken as the reaction rate constant.Typical fitted kinetic data taken at 300  ° C are shown in Figure1, and the corresponding pseudo-first-order plot showing theconcentration dependence of the fitted rate is shown in the inset.The decays shown are the (e - ) aq  transient absorption at 900 nm.Nitrobenzene concentrations range from 4.4  ×  10 - 6 to 2.2  × 10 - 5 M, corresponding to the longest through shortest observeddecay rates (0 concentration trace not shown on plot). The curveswere fitted starting approximately 35 ns after the linac pulse toavoid minor distortions from linac noise and spur recombinationchemistry.An Arrhenius plot for reaction 1 is shown in Figure 2, andfitted rate constants are given in Table 1. Vertical error barsreflect statistical errors arising from the fits shown in Figure 1,and most are on the order of the data point size. We haveextrapolated an Arrhenius fit of data taken up to 100  ° C by N 2 O + (e - ) aq f  O •- + N 2  (3)O •- + H 2 O f  OH - + OH • (4) Pulse Radiolysis of Supercritical Water. 2.  J. Phys. Chem. A, Vol. 106, No. 51, 2002  12271  Freeman and co-workers 22 and superimposed it for comparison.Clearly, our measurements agree quite well with the previouslyreported activation energy up to ∼ 200  ° C. From 175  ° C up tothe critical region, the new data exceed the extrapolatedArrhenius values. Above the critical temperature, the rateconstants cross over and then undershoot the extrapolation.The density dependence of the rate constant at 380  ° C isillustrated in Figure 3. Fitted rate constants are reported in Table2. Data were obtained at nine different pressures ranging from190 to 325 bar, corresponding to a density range of 0.11 - 0.55g/cm 3 . Because this represents a region where water is highlycompressible, the density is very sensitive to minor pressureand temperature changes. Horizontal error bars are given toindicate possible density fluctuations. A sharp drop in the rateconstant is seen as we proceed from the highest density downto  ∼ 0.40 g/cm 3 . Continuing to yet lower densities, the rateconstant increases again. A very similar trend has been observedpreviously for reactions between (e - ) aq  and other hydrophobicspecies in supercritical water. The behavior was ascribed to thepotential of mean force separating the (e - ) aq  from the hydro-phobic species in a compressible fluid. 7 We do not ascribe thebehavior to (e - ) aq  diffusion because the reaction of H • atomswith OH - has the same density dependence well below thediffusion limit. 7 2. Electron-Transfer Model.  Previous reports have demon-strated that there are few reactions that are truly diffusioncontrolled in water over a wide temperature range. 4,25,33 Manyreactions that appear to be diffusion-limited near room-temper-ature become limited by some small activation barrier as thetemperature is increased. Reaction 1 was claimed to demonstrate“diffusion-limited” behavior up to 200  ° C, 25 but this claim wasmade without knowledge of the (e - ) aq  diffusion rate. Theactivation energy for (e - ) aq  diffusion in water measured up to100  ° C is 20.3 kJ/mol. 33 The same activation energy applies tothe diffusion-limited bimolecular recombination of two electronsup to 150  ° C. 34 Consequently, it can be assumed that thediffusion-limited activation energy for a reaction involving (e - ) aq Figure 1.  Sample fitted data for hydrated electron scavenging bynitrobenzene at 300  ° C and 250 bar. Nitrobenzene concentrations rangefrom 4.4 × 10 - 6 to 2.2 × 10 - 5 M, corresponding to the longest throughshortest observed decay rates (0 concentration trace not shown in rawdata). Inset: pseudo-first-order plot illustrating the concentrationdependence of the observed hydrated electron scavenging rate at 300 ° C. Figure 2.  Arrhenius plot for the reaction of nitrobenzene with hydratedelectrons. An Arrhenius fit to previous data 22 taken up to 100  ° C isextrapolated to higher temperatures and superimposed for comparison. TABLE 1: Fitted Rate Constants for Hydrated ElectronScavenging by Nitrobenzene (Reaction 1) temp(C)rate constant(M - 1 s - 1 ) × 10 - 10 temp(C)rate constant(M - 1 s - 1 ) × 10 - 10 28 3.53 ( 0.04 250 83.4 ( 3.250 6.27 ( 0.19 300 109 ( 175 9.43 ( 0.28 325 118 ( 4100 14.0 ( 0.2 350 122 ( 3150 24.7 ( 0.7 380 113 ( 3175 33.0 ( 1.4 400 85.3 ( 3.2200 45.7 ( 1.0 Figure 3.  Effect of density on the rate constant for hydrated electronscavenging by nitrobenzene at 380  ° C, just above the critical temper-ature of 374  ° C. TABLE 2: Fitted Rate Constants for Density Dependence of Hydrated Electron Scavenging by Nitrobenzene at 380  ° C pressure (bar) density (g/cm 3 )rate constant(M - 1 s - 1 ) × 10 - 11 190 0.107 9.72 ( 0.02215 0.150 9.16 ( 0.04230 0.209 7.07 ( 0.04235 0.295 5.48 ( 0.07240 0.383 3.97 ( 0.02250 0.451 5.74 ( 0.12275 0.506 8.92 ( 0.33305 0.538 11.27 ( 0.40325 0.554 13.33 ( 0.43 12272  J. Phys. Chem. A, Vol. 106, No. 51, 2002  Marin et al.  should be 20.3 kJ/mol up to 150  ° C and also at highertemperatures if the (e - ) aq  diffusional activation energy remainsconstant. Analysis of the data points in Figure 2 from roomtemperature up to 100  ° C gives a value of 17.6  (  0.8 kJ/mol,similar to previous reports. 18 - 24,26,27 The slope remains nomi-nally the same within error limits up to 150  ° C. It was arguedby Schmidt et al. 33 that reaction 1 is a diffusion-limited, long-range electron transfer process, which accounts for its activationenergy slightly below 20.3 kJ/mol in the low-temperature region(see below). There is an apparent increase in the activationenergy of reaction 1 from 150  ° C up to where the rate beginsturning over near 300  ° C, and fitting the slope from 150 to 300 ° C gives a value of 20.8  (  1.1 kJ/mol. These values suggestessentially diffusion-limited behavior for reaction 1 from roomtemperature up to 300  ° C. Above 300  ° C, we have insufficientinformation to make this assertion.Assuming a diffusion-limited reaction, from the experimentaldata, we can calculate the average reaction distance  R  at eachtemperature using the Smoluchowski equation 35,36 where  k   is the diffusion-limited rate constant at each temperatureand  D )  D a +  D b  is the relative diffusion coefficient of reactantsa and b. Diffusion coefficients for (e - ) aq  are extrapolated fromdata below 100  ° C. 33 On the basis of previous measurements, 37 nitrobenzene diffusion coefficients are assumed to followStokes - Einstein behavior in water, scaling as  T   /  η ( T  ), where η ( T  ) is the temperature-dependent viscosity of water. Figure 4illustrates the calculated reaction distance for both the currentdata and data obtained by Freeman et al. 22 Note that the shortestreaction distance estimated is  ∼ 0.7 nm at 100  ° C. Thenitrobenzene radius may be estimated as a constant 3.6 Å fromthe van der Waals’ equation of state for benzene. 38 A temper-ature-dependent (e - ) aq  radius in the 2.4 - 4.0 Å range can beestimated from moment analysis modeling of the (e - ) aq  absorp-tion spectra, 29 where the radius becomes larger with increasingtemperature. The large average reaction distances stronglysuggest that reaction 1 occurs as a long-range reaction of asolvent-separated pair even up to 300  ° C rather than a traditionaldiffusion-limited reaction that occurs upon “contact” of thereactants.The long-range electron-transfer reaction of (e - ) aq  withnitrobenzene can be viewed in terms of the (e - ) aq  moving fromits solvent potential well into a potential well centered on thenitrobenzene. Such a process can be analyzed in terms of extended Marcus theory. The result of Marcus theory and itsextensions incorporating quantum vibrational degrees of freedomis an electron-transfer rate expression taking the form 39 - 43 where  λ  is the solvent reorganization energy,  H  ab  is the electroniccoupling matrix element for reactants a and b, and  ∆ G  is thefree energy of the electron-transfer reaction. The weighted sumis termed an effective Franck - Condon density of states for theacceptor ground state with the vibrationally excited state of theproduct and is taken over quantized vibrational states of theproduct with energies  n f  h ν . The  S   terms are Huang - Rhyselectron-vibration coupling constants for each vibrational modewhere  S  ) ∆ 2  /2 h  and ∆ is the dimensionless mode displacement. W  (  R ,  T  ) is dependent on the reaction distance  R  through thecoupling matrix element, which behaves exponentially asHere,  R   is the coupling matrix element for a donor - acceptorpair at van der Waals separation  R 0  and    is a constant scalingthe distance dependence. The distance dependence of the rateis also manifested through the reorganization energy. Assumingspherical initial (i) and final (f) states, the solvent reorganizationenergy can be expressed as 44 where   opt  and   s  are the optical and static dielectric constantsof the solvent, respectively.The basics of Marcus theory demonstrate that an electron-transfer rate will be maximized when the barrier for the processis minimized. The rate maximizes when  ∆ G  +  λ  +  n f  h ν  )  0and, under this condition, is governed solely by the Franck - Condon factors and coupling matrix element (at a distance  R ).For most systems displaying large changes in free energy, acombination of multiple internal vibrational modes and solventmodes can almost always provide the required energy matchingand maximize the rate.The reaction free energy of nitrobenzene with (e - ) aq  at roomtemperature is known to be  ∆ G  ) - 2.38 eV. 33,45 Calculatedvalues of  ∆ G f   are available for (e - ) aq  from 0 to 250  ° C. 46 If weassume that ∆ G f   for nitrobenzene is constant up to 300  ° C, wecan estimate the change in free energy for reaction 1 withtemperature. The temperature-dependent ∆ G  is shown in Figure5. Also illustrated in Figure 5 is the temperature dependence of   λ  (eq 8) at infinite  R , taking into account changes in dielectricconstant and (e - ) aq  radius with temperature. If we assume thatthe electron-transfer rate for reaction 1 is maximized and, hence, - ∆ G =  λ , then we can solve for values of   R  that give  λ - ∆ G ) 0 at each temperature. The result is shown in Figure 6. Thisplot illustrates that allowing  - ∆ G  =  λ  at all temperaturesrequires unphysically large values for  R . To obtain sensible  R values, the solvent reorganization energy must be lower,dictating that reaction 1 must occur in the Marcus invertedregion (  λ  <  ∆ G ) at all temperatures. Figure 4.  Temperature dependence of the average reaction distancefor hydrated electron scavenging by nitrobenzene, calculated using theSmoluchowski equation with measured reaction rates. Data by Freemanet al. 22 below 100  ° C (squares) and the current data (triangles) up to300  ° C are shown, along with fits obtained with eq 9. The solid curveis the fit to data obtained by Freeman and the dashed line is the bestfit to both data sets, assuming temperature independence of   R   and   . k  ) 4 π   RD  (5) W  (  R , T  ) )  H  ab2 p  (  π  λ k  B T  ) 1/2 ∑ n f  e - S  S  n f  n f  ! exp [ - ( ∆ G +  λ + n f  h ν ) 2 4  λ k  B T   ] (6)  H  ab2 )R  exp( -   [  R -  R 0 ]) (7)  λ ) (  1  opt -  1  s )(  12 r  i +  12 r  f  - 1  R )  (8) Pulse Radiolysis of Supercritical Water. 2.  J. Phys. Chem. A, Vol. 106, No. 51, 2002  12273  By convention, to say that a reaction is diffusion-limitedimplies that it occurs with unit probability upon contact of thereactants. For a long-range electron-transfer reaction, contactneed not occur. Nonetheless, diffusion still takes a role indetermining the rate. The combined diffusion and distance-dependent reaction can be solved in the framework of theSmoluchowski equation by invoking the radiation boundarycondition. 47,48 An exponential distance dependence is assumedfor the electron-transfer probability,  p ( r  )  ) R   exp( -   r  ) (i.e.,the behavior of   H  ab2 ), and  R  is replaced bywithHere  a  is the diffusional “distance of closest approach”, and  I  0,1  and  K  0,1  are modified Bessel functions of the first and secondkind, respectively. This equation had been previously appliedto rate constant data obtained below 100  ° C, 33 where theparameters  R   and    were iterated to give the best overall fit tothe reaction distance. Typical values for long-range electron-transfer reactions were obtained with  R )  2.5  ×  10 13 s - 1 and    )  0.75 Å - 1 . The raw data and fitted curve corresponding tothese values are shown in Figure 4, indicated by the squaresand solid line, respectively. The triangles correspond to the newdata taken up to 300  ° C, and the dashed line illustrates the bestpossible fit to both data sets, given by the values  R )  1.6  × 10 13 s - 1 and    )  0.90 Å - 1 . A more reasonable fit could beobtained by introducing a temperature-dependent    that de-creases with increasing temperature. The (e - ) aq  diffusion coef-ficient values are unknown above 150  ° C, and our extrapolationto higher temperatures is also a possible source of error. Thedata require either a decrease in    or an increase of the alreadyvery high (e - ) aq  diffusional activation energy between 150 °  and300  ° C. B. Hydroxyl Radical Scavenging.  In this section, we firstgive an overview of the experimental kinetic and transientspectral results of OH • radical reactivity with nitrobenzene. Akinetic model is then presented and used to assign the observedspectral features and fit the kinetics. We then compare theseresults to those of ref 12, pointing out both similarities anddiscrepancies. 1. O V  er  V  iew of Data.  Directly monitoring changes in OH • concentration as it reacts with nitrobenzene (reaction 2) isdifficult because of its deep ultraviolet absorption and lowextinction coefficient (  225 nm  )  500 M - 1 cm - 1 ). 10 The nitro-hydroxycyclohexadienyl radical has an absorption maximum at400 nm and a moderate extinction coefficient of 5660 M - 1 cm - 1 . 13 Therefore, we monitored the concentration increase of the reaction product rather than the concentration decrease of the OH • radical. The OH • radical can add to nitrobenzene inthree different positions to form three isomers. Data showingthe differences in absorption spectra for these isomers areunavailable to our knowledge and their spectra are assumed tocoincide. The reaction follows pseudo-first-order kinetics in thepresence of excess nitrobenzene. Nitrobenzene concentrationsused ranged from 2  ×  10 - 4 to 6  ×  10 - 3 M, and initial OH • concentrations upon radiolysis were  ∼ 5  ×  10 - 6 M, givingconditions well within the pseudo-first-order limit.A study of hydroxyl radical scavenging by nitrobenzene(reaction 2) was carried out as a function of temperature up to400  ° C. All data were collected at a pressure of 250 bar exceptat 380 and 400  ° C, where the pressure was 300 bar. Samplefitted kinetic data taken at 225  ° C are shown in Figure 7. Thegrowth in the data represents the formation of the nitrohydroxy- Figure 5.  Temperature dependence of the free energy change (dashedline) and solvent reorganization energy at infinite reaction distance (solidline) for reaction 1. Figure 6.  Optimum reaction distance for reaction 1 calculated via eqs8 and 9, based on setting  - ∆ G  )  λ  to achieve a barrierless electrontransfer.  R * )  2   [ 0.577 + ln [ 1   ( R   D ) 1/2 ] + K  0 (  x ) -  yK  1 (  x )  I  0 (  x ) -  yI  1 (  x )  ]  (9)  x )  2   ( R   D ) 1/2 exp ( - a   2  )  and  y ) ax   2 Figure 7.  Sample fitted data for OH • radical scavenging by nitroben-zene at 225  ° C and 250 bar. Nitrobenzene concentrations range from5.73  ×  10 - 4 to 2.82  ×  10 - 3 M, corresponding to the longest throughshortest observed rise rates. 12274  J. Phys. Chem. A, Vol. 106, No. 51, 2002  Marin et al.
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