Solvated Electron Reactions in Water-Alcohol Solutions (14) R. J. Field and R. M. Noyes, J . Chem. Phys., 60, 1877 (1974). (15) R. J. Field and R. M. Noyes, A c c . Chem. Res., 10, 214 (1977). (16) (a) W. C. Bray and H. A. Liebhafsky, d. Am. Chem. Soc., 57, 51 (1935); (b) A. Skrabal and S. R. Weberitsch, Monatsh. Chem., 36, 211 (1915).
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978
1359
(17) (a) R. Aris, "Elementary Chemical Reactor Analysis", Prentice Hall, Englewood Cliffs, N.J., 1969, p 156. (b) K. G. Denbigh and J. C. R. Turner, "Chemical Reactor Theory", Cambridge University Press, London, 1971, p 60. (18) (a) Reference 17a, p 198; (b) ref 17b, p 197.
Solvated Electron Reactions in Water-Alcohol Solutions B. H. Milosavljevl6 and 0. I. MiCiC" Boris KidriE Institute of Nuclear Sciences, VinEa, P.O.Box 522, 11001 Beograd, Yugoslavia (Received October 20, 1977; Revised Manuscript Received April 5, 1978)
Rate constants for solvated electron reactions with oxygen, hydrogen peroxide, benzoquinone, nitrobenzene, and iodine in aqueous binary solutions of methanol and ethanol were determined by pulse radiolysis. The measured rate constants were used in conjunction with known diffusion coefficients to calculate reaction radii from the Debye-Smoluchowski equation. The calculated radii for the electron-oxygen reaction are found to be independent of the water-alcohol ratio for both solvent systems. The radii for the electron reaction with hydrogen peroxide show a similar behavior. For electron reactions with nitrobenzene, benzoquinone, iodine, and carbon tetrachloride the reaction radii increase with the increasing alcohol content in the solution, while the sums of diffusion coefficients of the reactants decrease. A correction for tunneling is suggested to explain the large reaction radii (6-15 A) for solvated electron reactions with several effective solutes.
Introduction Rate constants have been measured for reactions of solvated electrons, e;, with many solutes in aqueous solutions and also, but less extensively, in organic liquids. Since rate constants >1O1O M-l s-l are observed with many solutes, it is assumed that the reaction occurs a t every collision. The reaction radii in aqueous solutions, estimated from the Debye-Smoluchowski equation, are usually in agreement with the distances between the reactants a t contact as calculated from crystallographic data. However, it has been noticed that in aqueous solutions,l and also recently in alcoholic solutions,' strong oxidizing agents have reaction radii two or three times greater than radii estimated from crystallographic data. Relatively very little work has been done on solvated electron reaction rates in water-alcohol solution^.^ The addition of alcohol to water has a pronounced effect on the kinetics of slow electron transfer reaction^.^ For fast, diffusion-controlled reactions, such as reactions of the solvated electron with neutral solutes, the effect of similar changes in the composition of the solvent could be expected to depend solely on the values of the diffusion coefficients of the reactants. In our earlier paper5 the diffusion coefficients of the solvated electron in wateralcohol solutions were determined from direct conductance measurements. In this work a study of the solvated electron reactions with several different neutral solutes in water-ethanol and water-methanol solutions was undertaken to shed additional light on the mechanism of solvated electron reactions.
Experimental Section
cohols of analytical reagent grade were used without further purification. Air-free samples were prepared by bubbling with argon. Deaerated solutions of different solutes were prepared by injecting, after bubbling, appropriate concentrations of a solute into the solvent. Hydrogen peroxide concentration was determined by permanganate titration, and that of iodine by mixing pulse-irradiated solutions with 0.2 M KI and by measuring the optical density a t 350 nm. The extinction coefficient of the Is- was taken to be 2.5 x lo4 M-l cm-1.6 Different oxygen concentrations were obtained by mixing appropriate volumes of Ar- and O'-saturated solutions from two syringes. Oxygen concentrations for all samples were determined by gas chromatography using a Perkin-Elmer 154 DG apparatus and a molecular sieve column. A pulse radiolysis technique was used to measure the decay rates of solvated electrons at 600 nm in the presence of different solutes. This technique has been described previously7 and it suffices here to outline the method. Concentrations of several micromoles of e; were produced in the samples by irradiation with 20-ns pulses from a Febetron 707 (Field Emission Corp.) electron accelerator. The absorbed doses were in the range 0.5-1 krd/pulse. The variation of e; concentration with time was observed by fast spectrophotometric methodsa8 The rise time of the light measuring system is 10 ns. The measurements were taken a t 19 f 1 "C.
Results Solvated electrons react with solutes present in water-alcohol solutions according to eq 1 and also with es-
Solutions were prepared from analytic grade chemicals (BDH or Merck). The water was triply distilled and al-
+
S + product
alcohol according to eq 2.
0022-3654/78/2082-1359$01,00/00 1978 American Chemical Society
(1)
1360
B. H. MilosavljeviE and 0.I. Mi%
The Journal of Physical Chemistry, Vol. 82, No. 72, 1978
TABLE I: Diffusion Coefficients of the Solvated Electron in Alcohol-Water Mixtures at 21 C
sums of calculated values of diffusion coefficients of solutes and of solvated electrons, DT (Table I) are also given for each solute separately.
Mole Dielectric Viscosity,a Des- X l o s Cosolvent fraction constant,a E 17, CP cm2 s-' Methanol
0.00 0.10 0.20 0.30 0.40 0.50 0.70 0.80 1.00
80.4 71.4 63.9 59.4 53.5 48.3 40.3 36.5 32.5
1.01 1.59 1.85 1.82 1.71 1.32 1.17 1.01 0.62
4.9c 3.6 2.7 2.4 2.0 1.8 1.6 1.1 1.5d
Ethanol
0.10 0.20 0.50 0.70 0.80 1.00
69.2 57.1 36.7 28.8 27.5 24.3
2.25 2.84 2.20 1.76 1.55 1.21
3.3 2.6 1.7 1.2 1.0 0. 6gd
a From ref 9. ref 11.
e,-
+ ROH
-+
From ref 5.
From ref 10.
Discussion The solutes 02,H202,C6H5N02,C6H,02 (benzoquinone), and I2 were chosen for this study since they are commonly used electron scavengers in water and alcohol radiolysis. In water, their reaction rate constants are equal to or higher than those calculated for diffusion-controlled reactions. The hydrated electron reaction with oxygen in aqueous solutions is a diffusion-controlled process. Previous s t u d i e ~ ' ~have J ~ shown the solvated electron reaction with oxygen to have nearly the same kinetics in water and pure alcohol with the rate constants lying within the range of (1.5-2.0) 1O'O M-l s-l. In water-methanol and water-ethanol solutions (Tables I1 and 111) the rate constants for this reaction are not independent of the water-alcohol ratio and show minima between 0.2 and 0.5 mole fractions of alcohol, corresponding to the maxima in the viscosity of water-alcohol solutions. In this region the viscosity of the solution increases by more than 100% over that in pure water, whereas the corresponding rate constants decrease by only 35%. For other solutes (Tables I1 and 111) the minima are even less pronounced, and for H z 0 2 and C6H402the rate constants decrease with increasing mole fraction of alcohol. Such behavior arises, most likely, from a nonlinear correlation between diffusion coefficients of reactants and reciprocal values of matrix viscosity, since water-alcohol solutions are nonideal solvent systems. We attempted to correlate the rate constants with the sum of diffusion coefficients of reactants in the whole range of water-alcohol solutions according to the Debye-Smoluchowski equation
From
H t RO-
(2)
Both reactions are pseudo first order since the concentrations of solvents and solutes are much higher than that of e8-. The first-order decay rate in a given solvent was measured as a function of solute concentration in the to 5 X M. T h e value for h l was obregion 1 X tained from the slope of a plot of reactivity against solute concentration for at least three different concentrations. Table I presents diffusion coefficients of solvated electrons, De, , determined from direct conductance mea~urements,~J~*" and also the data used for the dielectric constants, e, and viscosities, 7.9 The diffusion coefficients of the solutes, D,, were calculated by the Himmelblau12 interpolation method. According to this method, diffusion coefficients in mixtures are given by
(4) where N is Avogadro's number and R the reaction radius. T h e value of R also deDends on interactions between reactants, the effect beiAg most pronounced when both reactants are charged. For an uncharged reactant S, as in the case of our study, R is equal to the distance between the reactants at contact. The reaction radii for all the reactions studied in the whole range of water-alcohol ratios are calculated according to eq 4 using the data for h l and D,- + Ds given in Tables 11 and 111. These results are presented in Figure 1. For comparison we have also included the data for nitrobenzene in water-ethanol solutions3 and for carbon tetrachloride in water-methanol and water-ethanol solution^.^ The sums of the diffusion coefficients of es-and nitrobenzene or carbon tetrachloride
(3; where the subscripts m, 1, and 2 refer to mixture, water, and alcohol, respectively, while the values of X1 and X, correspond to mole fractions of water and alcohol, respectively. T h e diffusion coefficients in water, D1s, and in alcohol, D2s, are not available for all the solutes used. They were therefore calculated according to the Othmer and Thanker semiempirical correlation for aqueous solutions, and Scheibel's correlation for alcoholic solutions.13 T h e calculated values are accurate to within 10%. Mean values of the rate constants of solvated electron reactions with different solutes in water-methanol and water-ethanol are presented in Tables I1 and 111. The
TABLE 11: Solvated Electron Rate Constants in Methanol-Water Mixtures s = 0, S = H,O, S = C,H,NO, Mole fraction
10-lokl M-1 s - l
1 0 5 ~ ~ 10-lOk,
0.0 0.1 0.2 0.3 0.4 0.5 0.7 0.8 1.0
1.9P 1.58 1.30 1.25
cm' s-l 6. gb 4.9 4.5 4.3
1.33
4.1
0.572 0.498 0.506
1.71 2.108
4.7 6.6
0.438
M-I
s-l
1.25c 0.808 0.630
iOSDT cm' s-' 5.9d 4.4 3.4
10-lOkl M-I s - l
10SDT cm2 s'
3. 50e 2.50 2.22 1.96
5.6 4.2 3.1 3.0
2.7 2.4 2.3
1.78
2.6
2.3h
1.84 2.35'
2.2 2.7
S = C,H,O,
10-lOkl M" s-'
1 0 5 0 ~
cm' s-
2.30f 1.70 1.45
5.7 4.3 3.4
1.40 1.30 1.40 1.30 1.55
2.8 2.7 2.7 2.3 2.8
Published value 1.2 cm2 s" taken from ref 12a. DO = 2.00 x Published value 1.9 x lo1"M-I s- ' from ref 14. cm' szl taken from ref 15. e Published value 3 X 10" M-' s-l from ref D H o = 0.99 x 10'" M-' s-' from ref 14. DH,o, = 7.9 X 14. f Published value 2.7 X l 0 l o , I k 1s-I from ref 14. g Published value 2.0 X 10" M-' s-l from ref 16. lo-' cm' s-' taken from ref 15. I Published value 2.30 X lo'" M-l s- ' from ref 16.
X
The Journal of Physical Chemistry, Vol. 82, No. 12, 1978 1361
Solvated Electron Reactions in Water-Alcohol Solutions
TABLE 111:
I
S o l v a t e d E l e c t r o n R a t e C o n s t a n t s in Ethanol-Water Mixtures
s = 0,
1.92 1.40 1.23 1.36
6.9 4.8 4.1 3.7
1.63 1.80
4.1 4.5c
I
4
s = I,
S = H,O,
Mole 10-''kl l o 5 & 10-'"kl 105DTa10-"k1 1 0 S D ~ fraction M-' s" cm2 s-l M-' s-' cm2 s-l M-1 s-lc m Z s - l 0.00 0.10 0.20 0.50 0.70 0.80 1.00
I
WTER-METHANOL
1.25 0.700 0.525 0.389 0.375
5.9 3.8 3.0 2.1 1.6
0.280
1.0
5.15b 2.58 1.86 1.72
6.2 4.3 3.3 2.6
2.1 2.3d
2.1 2.0e
lot
Published DH,o, extrapolated values from ref 15. D O , = 3.9 X lo-' value 5 X lo'" M-l s-' from ref 14. Published value 2 X 10" cm2 s-' taken from ref 17. l\,I-I s - I from ref 2. e D12 = 1 . 3 X 10" cm' s" taken from ref 18.
were calculated from values of Des in Table I and from those reported for DC6HBNOP and Dccb. The data in Figure 1 show a complex dependence of the calculated reaction radii on the nature of solvent. They are constant only for reactions of O2 and H 2 0 2with e;. For C6H,5N02,C6H402, CCI,, and 12, the reaction radii increase with increasing alcohol content in the solvent. The radius for the reaction with oxygen is approximately constant a t 4.3 f 0.5 8, (Figure 1). This is in good agreement with the sum of the individual re, and rOpvalues obtained from other works. Hart and Anbar' report an res-value of 2.6 f 0.5 A for pure water and pure alcohol. Since the optical spectra of the solvated electron in alcohol-waterz0I2lare very similar to the spectra in the pure components, it is likely that this re value is applicable to these systems. The standard handbook value of f o pis 1.6
A.
From Figure 1 the reaction radius for H z 0 2is constant a t 2.7 f 0.3 A, and smaller than the distance between the centers of es- and H202a t contact, 4.3 8, (rH2OZ = 1.7 A22). Although the Debye-Smoluchowski reaction radius is lower by about 35%, it is hardly possible that the activation process has any influence on this reaction, since an excellent linear relationship between the rate constants and the sums of Des + DHpOzhas been found over the whole range of both mixtures. For diffusion controlled reactions, only the interaction between reactants contributes t o the value of R. In t h e reaction of a solvated electron with a neutral polar solute, the change of the dielectric properties from water to alcohol may affect the value of R; even then the magnitude of the effect is not higher than 2090 The radii obtained here for the solvated electron reactions with CGH5NO2, C6H402,CCI,, and I2 increase with increasing mole fraction of alcohol. This has also been observed earlier for the reaction of e; with CCl," as shown in Figure 1. In our previous paper we tried to explain the increase of R by the influence of dielectric properties on the interaction between the solvated electron and solvent. However, the examples given in Figure 1 show the different behavior of the solvated electron in reactions with different neutral solutes which could not be ascribed to the influence of dielectric properties of the matrix. Some solutes show an increase of R with increasing mole fraction of alcohol while, with others, R is constant over the whole range of solvent composition. I t seems hardly possible that the error in the determination of the diffusion coefficients of e,- and S could cause the observed discrepancy. Our results for C6H5No2, CCl,, C6H402,and Iz imply a regular increase of the reaction radius. This increase from water t o methanol is
.,
I
1
1
I
.2
.L
.6
I
I
.a
1.0 x2
Figure 1. Reaction radii of solvated electron reactions as a function of the alcohol mole fraction in water-methanol (a) and water-ethanol H202; (0) e; 0 2 ; ( 0 )es- + C6H402; (m)eSsystems (b): ( 0 ) e; I,; (v)e; CCI,, from ref 5.; (0)e; C6H5N02,for water-ethanol solutions from ref 3.
+
+
+
+
+
about 40% for C6H5N02 and CeH402and even much higher for I,, CCI4, and C6HSNO2in water-ethanol solutions. The large radii are consistent with a tunneling mechanism. Based on the analogy with the reactions of trapped electrons in rigid glassy matrixes, the tunneling has been proposed recently t o explain some reactions in l i q ~ i d s . ~Analysis ~ , ~ , of the results in Figure 1 shows that only some of the solutes seem t o react with the solvated electron by tunneling although all the reactions studied are very fast. This effect is not determined by a low value of the sums De- + Ds, since there is no common regularity between the value of R and Des-+ D s for all the solutes in the observed water-alcohol solutions. For example, H 2 0 2has values of D s similar to CsH5N02and CsH402, while O2 has values similar to Iz (Tables I1 and 111). Besides, the reaction radii for I2 and C6H5N02in waterethanol solvents show minima between 0.2 and 0.4 mole fractions of alcohol. T h e Smoluchowski theory can be modified by a tunneling correction which allows reactions to take place a t a distance, R,ff,which can be derived after inclusion in the theory of a reaction probability varying exponentially with the distance between the reactants. Schwarz and Gill2 have proposed a simple approximate expression
Reff= R
+ (2/b)(ln Z o + 0.577)
(5)
where Zo = 2u'J2/b(De-+ DS)'J2;the values of u and b are respectively. I t does not fit the cm l0l5 s-' and data presented in this work. For IzrC6H5NO2,CCI,, and C6H402,the reaction radii generally increase with decreasing values De, Ds, but not in the simple logarithmic manner expressed in eq 5. Since these systems show behavior which is complex and specific for each solute, 1,2323
+
1362
The Journal of Physical Chemistry, Vol. 82,No. 72, 1978
more solvated electron rate constants in media with low diffusion coefficient values are required to find a more approrpriate correlation between Reff and Des-+ Ds.
References and Notes (1) E. J. Hart and M. Anbar, "The Hydrated Electron", Wiley-Interscience, New York, N.Y., 1970, p 187. (2) H. A. Schwarz and P. S. Gill, J . Phys. Chem., 81, 22 (1977). (3) F. Barat, L. Gilles, B. Hickel, and B. Lesigne, J . Phys. Chem., 77, 1711 (1973). (4) 0. I. MiEiC and B. Cercek, J . Phys. Chem., 78, 285 (1974). (5) 0. I.Miti6 and B. Cercek, J . Phys. Chem., 81, 883 (1977). (6) A. 0. Allen, C. J. Hochanadel, J. A. Ghorrnley, and J. W. Davis, J . Phys. Chem., 56, 575 (1952). (7) V. MarkoviE, D. NikoliE, and 0. I.MiEiE, Int. J. Radiat. Chem. Phys., 6, 224 (1974). (8) 0. I.MiEiE and M. T. NenadoviE, J . Phys. Chem., 80, 940 (1976). (9) J. Timmermans, "Physico-Chemical Constants of Binary Systems", Vol. 4, Interscience, New York, N.Y., 1960.
T. E. Boothe and H. J. Ache (10) K. H. Schmidt and W. L. Buck, Science, 151, 70 (1967). (11) P. Fowles, Trans. Faraday Soc., 67, 428 (1971). (12) (a) D. M. Hirnrnelblau, Chem. Rev., 64, 527 (1964); (b)Y. P. Tang and D.M. Himrnelblau, AIChE J . , 11, 54 (1965). (13) R. C. Reid and T. K. Sherwood, "The hoperties of Gases and Liquids", McGraw-Hill, New York, N.Y., 1966, p 548. (14) M. Anbar, M. Barnbenek, and A. B. Ross, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No 43 (1973). (15) K. G. Stern, Berichte, 66, 547 (1933). (16) G. L. Bokon and G. L. Freeman, J . Am. Chern. Soc., 98,6825 (1976). (17) W. R. Ware, J . Phys. Chern., 66, 455 (1962). 118) P. Chana and C. R. Wilke. J . Phvs. Chem.. 59. 592 11955). i19j I.A. Taib, D. A. Harter, M:C. Saier. and L. M. Dorfrnan, J . Chern. Phys., 41, 979 (1964). (20) S. Arai and M. C. Sauer, J . Chem. Phvs., 44, 2297 (1966). (21j L. Kevan, J . Phys. Chem., 79, 2846 (i975). (22) W. C. Schumb, C. N. Satterfield, and R. L. Wentworth, "Hydrogen Peroxide", Reinhold, Baltimore, Md., 1955, p 314. (23) J. R. Miller, J . Phys. Chem., 79, 1070 (1975). (24) M. J. Pilling and S.A. Rice, J . Chem. SOC.,Faraday Trans. 2 , 71, 1563 (1975).
Reaction of Recoil Tritium with Graphite. A Simulation of First Wall Controlled Thermonuclear Reactor Conditions' Thomas E. Boothe and Hans J. Ache* Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 2406 1 (Received August 26, 7977; Revised Manuscript Received February 6, 1978)
In order to simulate some of the conditions present at the first wall of a controlled thermonuclear reactor (CTR), recoil tritium from the 3He(n,p)Treaction has been allowed to react with nuclear and nonnuclear grades of graphite. Graphite has been proposed as a protective curtain for the first wall to prevent contamination of the plasma by sputtered materials. The results show that the energetic tritium species become strongly bound to graphite and are not released even at 1000 "C, if the graphite has been thoroughly degassed and annealed prior to tritium bombardment. Subsequent treatment of these samples with H2, H20, or NH, at elevated temperature leads to the release of up to about 47% of the tritium in form of HT and CH3T, with minor amounts of tritiated higher hydrocarbons present. The ratio of HT to CH3T depends on the temperature. At higher temperatures (- 1000 "C) the ratio is shifted largely in favor of HT. In relation to the first wall of the CTR, the results of this work would imply that the continuous buildup of the tritium in the graphite could, over an extended period of time, lead to a serious problem with regard to the tritium inventory of the CTR. The contamination of the plasma resulting from the reactions of the energetic tritium species with the graphite presents a lesser problem, especially if the curtain temperature is kept at 1000 OC, where even in the presence of a hydrogen source tritium is mainly released in the form of HT.
Introduction One of'the problems involved in the operation of controlled thermonuclear reactors (CTR) is the erosion of metallic vacuum walls (first wall) by charged particles leaking from tokamak plasmas and the effect of impurities resulting from these interactions on plasma operation.* Since it was found that high-Z impurities have the most significant effect on plasma performance it has been suggested to protect the first wall in the CTR by using a graphite curtain between the plasma and the metallic vacuum all.^!^ Several investigation^^.^ were carried out t o study the gas content and hydrogen sticking probabilities for atomic and molecular hydrogen at thermal energies from which 0022-3654/78/2082-1362$01 .OO/O
it was concluded that the vacuum properties of graphite would be compatable with the operating conditions prevalent in a CTR. However, while the reactions of' low energetic hydrogen species, which result in mostly surface reaction^^-'^ and ~ p u t t e r i n g , ' ~have ^ ' ~ been widely studied, very little information is available about the fate of the higher energetic hydrogen, deuterium, or tritium species which leave the plasma and become incorporated into graphite, their subsequent interactions, and their potential effect on plasma contamination.8 The flux of D+ and T+ which reach the first wall has been estimated to vary from 1OI3 to 10l6particles cm-2 s-' depending on the type of reactor with kinetic energies from
0 1978 American Chemical Society
