On the molecular hydrogen formation in the gamma radiolysis of water and aqueous solutions

Int. J. Radiat. Phys. Chem. 1973, Vol. 5, pp. 197-206. Pergamon Press. Printed in Great Britain

ON THE MOLECULAR H Y D R O G E N F O R M A T I O N IN THE G A M M A RADIOLYSIS OF WATER A N D A Q U E O U S SOLUTIONS M. FARAGGI Atomic Energy Commission, Nuclear Research Centre-Negev, P.O.B. 9001 Beer-Sheva 84190, Israel (Received 28 January 1972; in revised form 29 May 1972)

Abstract--The radiolytic hydrogen yield GH, from deaerated aqueous solutions of various di- and tri-positive metal ions was found to be in many cases independent of the solute concentration (up to 0"1 tool dm-8). However, in Cd a+, Cu ~+, Cr a+, Pb 2+ and acidic Hg a+ solutions, GH, decreased with increasing solute concentration. The efficiency of these ions in reducing the hydrogen yield is in the order: Hg a+ > Pb a+ > Cr 2+ ~ C u a+ > Cd 2+. The fact that all these metal ions are good scavengers for the reducing species produced in the radiolysis of water (eaq- and H atoms) leads to the conclusion that they are not the main precursors of Hz. Homogeneous kinetics was used to express the dependence of G ~ on solute concentration. The rate-determining step is considered to be the pseudo first-order disappearance of the H2 precursor. It could be either the hydride ion produced by the reaction of subexcitation electrons with water as proposed by Platzman, the dry electrons suggested by Hamill, or the HzO radicals of Sworski and Smaller. The chemical reactivity of the above ions toward the H2 precursor is shown to be parallel to the rate of ligand substitution in the aquated metal ions as measured by Eigen. It is also shown that part ( ~ 20 per cent) of the Ha may be produced by a radical-radical reaction mechanism.

INTRODUCTION

ONE OF the p r o b l e m s still u n s o l v e d in the r a d i a t i o n chemistry o f water is c o n c e r n e d with the d e t e r m i n a t i o n o f the n a t u r e o f the p r e c u r s o r o r precursors o f the m o l e c u l a r h y d r o g e n f o r m e d in the g a m m a radiolysis o f w a t e r a n d a q u e o u s solutions (1-9). A c c o r d i n g to the s p u r diffusion m o d e l {lb~ the r e c o m b i n a t i o n r e a c t i o n s o f e a q a n d H a t o m s are generally c o n s i d e r e d to c o n t r i b u t e p r e d o m i n a n t l y to Gas, the " m o l e c u l a r " h y d r o g e n yield in the radiolysis o f water. (1)

eaq-+eaq-

(2)

e~q- + H

(3)

H + H

(10)

> Hz+2OH-

k 1 = 4.5 x 10 ~ dmSmo1-18 -1

> H z+ OH-

k 2 = 2-5 x 101° d m ~ mo1-1 s -1 c10),

> H2

k a = 1-3 x 101° d m a mo1-1 s -1 (10)

M a h l m a n a n d Sworski (1) c o n c l u d e f r o m o b s e r v a t i o n s o f p H effect on the r e d u c t i o n o f Gn2 as a f u n c t i o n o f N O 3 - a n d N~O c o n c e n t r a t i o n , t h a t e a q - is n o t the p r e c u r s o r o f H~. T h e y suggest t h a t H 3 0 o r excited H~O m a y be the precursors. Schw~rz (3) a t t e m p t e d to a d a p t the s p u r diffusion m o d e l to several a q u e o u s systems which have been c l a i m e d to be a n o m a l o u s . This m o d e l explains the m a j o r p a r t o f the G~ta; however, one t h i r d o f Grr~ results f r o m processes different f r o m those described b y reactions (1) to (3). This same m o d e l assumes t h a t e a q - is on the average at 2 3 A f r o m the center o f the spur. H a m i l l (4,5), following o b s e r v a t i o n s at high solute concentrations, p r o p o s e s t h a t the d r y electrons ( e - ) are the p r e c u r s o r s o f H 2 a n d t h a t their scavenging involves c o m p e t i t i o n with p r o m p t r e c o m b i n a t i o n a n d with h y d r a t i o n . H e suggests t h a t c o n v e n t i o n a l kinetics is n o t a p p l i c a b l e a n d prefers to c o n s i d e r t h a t relative 197

198

M. FARAGGI

p r o b a b i l i t i e s o f scavenging a n d p s e u d o first-order r e m o v a l o f e - c o u l d be fitted by a l [ S ] / a 2 where [S] is the solute c o n c e n t r a t i o n a n d ~ are the cross-sections. A n b a r t2~ a n d F a r a g g i et al. ts,9~, following P l a t z m a n ' s p r o p o s a l ~,12~, suggested t h a t the m a i n p r e c u r s o r s o f the m o l e c u l a r h y d r o g e n are the h y d r i d e ions f o r m e d in the reaction o f subexcitation electrons (e~bex.-) with water. It has also been shown ts~ t h a t the scavenging efficiency o f C d 2+, C u z+, P b 2+ a n d H g z+ at low c o n c e n t r a t i o n s (10 - 3 - 10 -1 m o l d m -3) follow p s e u d o first-order kinetics, a n d t h a t the chemical efficiency o f the scavenger is related to its ligand exchange rate constant. In the present study further evidence is given to show t h a t the m a i n p a t h w a y for the f o r m a t i o n o f the " m o l e c u l a r " h y d r o g e n in the radiolysis o f water is n o t the one suggested b y the spur diffusion m o d e l [reactions (1)-(3)] b u t involves p s e u d o firsto r d e r kinetics a n d is related to its ligand exchange rate constant.

EXPERIMENTAL Material Water was triply distilled; inorganic chemicals were of analytical grade and were used without further purification. Lanthanide sulfates and perchlorates (from Alfa Inorganic Inc., New York) were of 99.9 per cent purity, other perchlorates were from G. F. Smith. Solutions of chromous perchlorate were prepared from the corresponding Cr(C104)z by electrolytic reduction, and its oxygen-free solutions were stored at 5°C in syringes{la~. All solutions studied were at neutral pH except that of Hg z+ which was at p H = l . Acidity was adjusted by H~SO4 for the sulfates and by HC104 for the perchlorates ; alkalinity was adjusted by NaOH. Samples of 10 dm 3 of argon saturated aqueous solution in the presence of 10-4 tool dm -3 KBr in syringes were irradiated with a 6°Co gamma ray source (Gamma Cell 200, Atomic Energy of Canada Ltd.) which provided a dose rate of about 3 × 1017 eV g-lmin-1, as determined by the Fricke dosimeter taking G(Fea+) = 15"5. For gas analysis gas chromatography cs~ was used. Part of the Ga, results obtained for deaerated aqueous solutions of Ni 2+, T1+, Co 2+, Zn z+, Cu ~+, Cd 2+, Hg 2+ and Pb 2+ as scavengers, already published, were performed at the C.E.N., Saclay, FrancetSk For these experiments the dose rate was of 4 × 10~8eV g-lmin -1. Each G value measured is the result of at least six irradiations carried out at different times to give a linear yield dose curve. The accuracy of the values is better than + 2 per cent.

RESULTS M o l e c u l a r h y d r o g e n yields (Gn2) m e a s u r e d in air-free a q u e o u s solutions o f different positive ions are given in T a b l e I a n d in Figs. 1 a n d 2. T a b l e I shows all the cations which d i d n o t decrease the m o l e c u l a r h y d r o g e n yield a l t h o u g h m o s t o f t h e m are k n o w n to react r a p i d l y with the h y d r a t e d electron. C o l u m n 5 gives the specific rate c o n s t a n t o f the positive ion with e~q- a n d c o l u m n 6 its ligand exchange rate constants. In other experiments where the a n i o n was c h a n g e d f r o m sulfate to p e r c h l o r a t e the s a m e h y d r o g e n yields were observed. The effect o f these c a t i o n s o n GH2 in the c o r r e s p o n d i n g nitrate solutions (10 -3 m o l d m - Z < [NO~] < 10 -2 m o l d m -3) was also investigated. T h e results were always similar to the h y d r o g e n yield in the nitrate solutions 114}, i.e. these cations d i d n o t affect the decrease o f Gri~ by N O 3 - . W i t h 5 × 10 -4 m o l d m -3 N O 3- a n d with 5 × 10 -5 m o l d m -3 M n O 4 - , which are k n o w n to react with the u n s t a b l e r e d u c e d scavenger (S'~-1), i.e. S ~ + e ~ q - ~ S '~-1 where n, the charge o f the cation, is equal to + 1 , + 2 or + 3 , the h y d r o g e n yield decreased to a value o f 0.38 +_0.02. Figures 1 a n d 2 show the cations which decrease the h y d r o g e n yield.

Molecular hydrogen formation in gamma radiolysis of water and aqueous solutions

199

TABLE I. MOLECULAR HYDROGEN YIELDS FROM METALLIC ION AQUEOUS SOLUTIONS* k e ~ - +M

kligand

Solute

[MSO~]

pH

G(H~)i"

(dm z mo1-1 s -1)

(s -1)

La2(SO4) a Cez(SO4) a Prz(SO4)a Nd2(SO4)3 Sm2(SO4)a

10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-4-10 -1 10-¢-10 -1 10-4-10 -1 10-4-10 -1 10-&10 -1 10-4-10 -1

5"7 + 0"3 5'4 + 0"4 6.1 + 0"5 5"9 + 0'3 6-3 + 0-2 5'8 + 0'2 5'9 + 0"3 5"7 + 0"3 6"0 -4-0'3 5'8+0'2 5"9 + 0-3 6"0 _+0'3 5'5__.0"3 5"3 + 0'3 5"2 + 0"1 6 ' 2 - 5"4 5.3 - 4.8

0"43 + 0"03 0"45 + 0"02 0'42 + 0"03 0.44 + 0'03 0-43 + 0"03 0'45 + 0"02 0"44 + 0"03 0'43 -4-0"03 0"44 + 0'02 0"44+0'03 0'45 + 0"02 0"43 + 0-02 0"44___0'02 0"44 + 0'02 0'42 + 0"02 0'45 + 0"01 0-45 __+0'01

3"4 x 10 s < 109 2.9 x l0 s 5'9 x 108 2'5 x 101° 6'1 X 1010 5'5 x l0 s 3'7 x 10s 4'6 x 108 2 ' 4 x 109 7"0 x 107 3"0 x 109 4"3 x 10 TM 2"9 x 101° 3'0 x 10l° 1 "2 x 10l° 1.5 x 109

8"6 x 107 9'5 x 107 8'6 x 107 9'3 x 107 9'6 x 107 8"2 X 107 5"2 x 107 3"0 x 107 1"7 x 107 1.4x 107 1 "0 x 107 1 "1 x 107 1"1 x 107 1"1 x 104

EHz(SO4) a

Gde(SO4) a Tb2(SO4)a Dy2(SO4) a Ho2(SO4)z Er2(SO4) 3 Tme(SO4)3 Yb2(SO4) 3 NiSO4 TIzSO4 CoSO4 ZnSO 4

2"0 x 105 2'0 x 107

* Solutions in the presence of 10 -4 mol dm -a KBr to protect H2 from O H radical attack. t Experimental values. DISCUSSION F r o m t h e e x p e r i m e n t a l results it c a n be c o n c l u d e d t h a t , w h e r e a s t h e t r i p o s i t i v e l a n t h a n i d e ions, as well as T1 +, N i 2+, C o 2+ a n d Z n 2+, d o n o t d e c r e a s e t h e m o l e c u l a r h y d r o g e n yield in t h e c o n c e n t r a t i o n r a n g e o f 10 -4 t o 10 -1 m o l d m -a, o t h e r i o n s a r e effective s c a v e n g e r s f o r t h e p r e c u r s o r o f t h e m o l e c u l a r h y d r o g e n f o r m e d d u r i n g t h e r a d i o l y s i s o f w a t e r ; t h e o r d e r o f efficiency is H g ~+ > Pb~+ > Cu~+ g Cr2+ > C d 2+. Assuming a pseudo first-order for the formation of H 2 (4)

X + H20

) H2,

w h e r e X is the " m o l e c u l a r " h y d r o g e n p r e c u r s o r , s i m p l e c o m p e t i t i o n kinetics c a n be assumed when one introduces a scavenger S which captures X: (5)

X + S I

) H2

and (I) w h e r e k x + s is t h e s e c o n d - o r d e r r a t e c o n s t a n t o f r e a c t i o n (5) a n d k x + n ~ o t h e p s e u d o f i r s t - o r d e r r a t e c o n s t a n t o f r e a c t i o n (4). F i g u r e s 1 a n d 2 s h o w t h a t t h e i o n s w h i c h d e c r e a s e G r q f o l l o w t h e k i n e t i c b e h a v i o u r e x p r e s s e d b y e q u a t i o n (I). D e v i a t i o n s f r o m t h e s i m p l e e q u a t i o n (I) o c c u r at l o w solute c o n c e n t r a t i o n s ([S ] < 5 x 10 -3 m o l d m - 3 ) , so t h a t GH, ° = 0-38 o b t a i n e d by e x t r a p o l a t i o n is s m a l l e r t h a n t h e o b s e r v e d G~q ° = 0.45. T h i s difference o f 0.07, w h i c h is a b o u t 15 p e r c e n t o f t h e t o t a l m o l e c u l a r yield, is a p p r o x i m a t e l y t h e s a m e as w h e n a l o w c o n c e n t r a t i o n s c a v e n g e r ( N O B - ) f o r t h e u n s t a b l e r e d u c e d S n-1 is i n t r o d u c e d i n t o t h e s o l u t i o n , a n d this difference is s u g g e s t e d t o be d u e to t h e s a m e effect.

200

M. FARAGGI

0 m

0

I

I

I

I

I

2

3

4

[ M 2.]

(10 -2 mol

d m -3)

FIG. 1. Effect of Cr2+(Q), CdZ+(O) and Cu2+(D) on the molecular hydrogen yield.

7.5 15.0

.0~5.0

I0"0

2.5

5"0 ~mf

T 2

I 4

f 6 [ Mz+.I (10 -z m o l

f 8

I I0

d m -3)

FIG. 2. Effect of Pb2+(O) and Hg~+ (11) on the molecular hydrogen yield. F r o m these results it seems safe to assume that the contribution to the molecular hydrogen formation via the reactions predicted by the diffusion spur model [reactions (1)-(3)] is rather small. A p a r t from the ions which react rapidly with the hydrated electrons and have no scavenging effect on GH~, the order of reactivity of the ions which do have this scavenging effect toward eaq- is : Cd z+ > Cr z+ > Pb 2+ > Cu 2+. This order of reactivity is not the one observed for the scavenging reactivity of these ions toward the precursor of the molecular hydrogen. A rather peculiar finding is that Hg 2+ is the best scavenger for the precursor of H2. According to the diffusion spur model, this ion should be the least active because of its relatively small rate constant with H atoms (2 x 109 dmamo1-1 s-l), which has to compete only with reaction (3) having a rate constant of 1-3 × 101° dm 3 mo1-1 s -1. However, some one could still raise arguments which might show that even these results do not contradict the diffusion spur model. These are: a. Ionic strength effect. Czapski e t a / . t6,7), arguing in favour of the spur model, pointed out that when the positively charged scavenger concentration [S ] is raised, the ionic strength of the solution increases. Thus, according to the Debye theory, the

Molecular hydrogen formation in gamma radiolysis of water and aqueous solutions

201

rate c o n s t a n t o f e a q - (the m a i n p r e c u r s o r o f H 2 a c c o r d i n g to the spur m o d e l ) with [S ] should decrease (Table II) a n d th e r e f o r e the efficiency o f the scavenger to p r e v e n t the m o l e c u l a r h y d r o g e n f o r m a t i o n should decrease. A c c o r d i n g to these a u t h o r s te,7~, this effect c o u l d be the r e a s o n f o r the inefficiency o f some o f the m et al ions. This a r g u m e n t is n o t s u p p o r t e d by o u r results, which s h o w that, whereas C d ~+ an d C u ~+

TABLE I I .

Cation type TI(I)

Co(II)

Eu(III)

IONIC STRENGTH EFFECT ON THE REACTION OF HYDRATED ELECTRONS WITH METALLIC CATIONS

Concentration

/z

10 -4 10 -3 10 -2 10 -1 10 -4 10 -3 10 -8 10 -1 10 -4

2.0 x 10 -~ 1-1 x 10 -3 1-0 x 10 -2 1.0 x 10 -1 4-0 x 10 -4 3.1 x 10 -a 3.0 x 10 -2 3.0 × 10 -1 7-0 × 10 -4

10 -3

6.1 x 1 0 - 3

10 -8 10 -1

6.0 x 10 -2 6"0 × 10 -1

ko (dm 3 mo1-1 s -1)

kl* (dm 3 mol-ls-1)

k2t (dm 3 mol-ls-1)

3-7 x 10TM

3"6 x 101° 3"3 x 10TM 2.9 x 101° 2.1 x 101° 1-1 x 10l° 9"5 x 10a 6-5 x 109 3.3 × 109 5-1 x 101° 3"8 × 101° 1"9 x 10TM 9"6 x 109

3"6 x 101° 3"3 x 101° 2.9 x 101° 2.0 x 101° 1.1 x 101° 9"4 x 109 6-2 x 108 3"0 x 109 5"1 x 101° 3"7 x 101° 1-6 × 10TM 6"6 × 10~

1"2 x 101°

6-1 x 101°

* Log kl = log ko-I'02ZM/z~/(1 + a/zt) where kl and ko are the rate constants at a given and at zero ionic strength, respectively. a = (rM+re -)/3, rMtI) = rMtIIl = 3"0 X 1 0 - a c m , r M ( i i i i = 5"0 X 1 0 - s c m

and

re~a- = 2"5 × 1 0 - a c m .

t Log k2 = log k0-1 '02ZM{[/Zt/(1 +/~t)]-0.2 /z}, where k2 is the rate constant at a given ionic strength.

are g o o d scavengers f o r the H e precursor, N i 2+ an d C o s+ have no effect o n GH2. A c c o r d i n g to Refs. (6) a n d (7) these f o u r divalent ions with identical charge and, f o r high dilution, similar rate constants, should have similar rate constants at the different ionic strength values (Table II). M o r e o v e r , the r e a c t i o n rate c o n s t a n t o f e a q - with T1 + should be less affected by the v a r i a t i o n o f the ionic strength (Table II). Thus, c o m p a r e d to the divalent ions, this i o n should have, a c c o r d i n g to Refs. (6) an d (7), a great effect on GH,. This c o n c l u s i o n is once again n o t s u p p o r t e d by o u r results, as T1 + has no effect on G H . F u r t h e r m o r e , a c c o r d i n g to T a b l e II, the lowest value o f the rate c o n s t a n t with e a q - in o u r solutions was o f the o r d e r o f 3 × 109. T h e same rate c o n s t a n t was o b t a i n e d for H g 2+, yet it was the best scavenger f o u n d in all the cations studied. W e have to conclude that the e a q - + S rate c o n s t a n t is n o t the criterion for the efficiency o f scavengers. 14

202

M. FARAGGI

b. Stability o f the reduced metal ion. It is assumed that when the original scavenger is reduced to form a stable species it would lead to a decrease in Gas, whereas an unstable ion would react with another e~q- or with another unstable ion to produce hydrogen (radical-radical reaction). This is not in agreement with our findings. According to this argument, Eu z+ should be a good scavenger as it reacts rapidly with eaq-, and the Eu 2+ formed is a stable species ~aS). On the other hand, Cd + formed from Cd 2+, or Cr + from Cr 2+, are unstable species but they reduce G n . Moreover, by introducing reagents which are known to react rapidly with the reduced metal ion, i.e. M n O 4- and NOz-, the decrease of Gn, is only of the order of - 1 5 per cent, which means that only this amount is due to the radical-radical reactions. c. The efficiency is related to metal ions with a high atomic number. This argument is based on the assumption that the best scavenger ions, i.e. Hg z+ and Pb z+, are of high Z value, 80 and 82, respectively, thus having higher cross-sections for their reaction with the H 2 precursor. This is not supported by our findings for T1+ (z = 81) which does not decrease G~, at all. Three proposed mechanisms seem to agree with the experimental findings and also explain the nature of the molecular hydrogen major precursor. Hamill proposed ~4,s) the dry electron to be the precursor of H 2, and its scavenging involves competition with p r o m p t recombination and hydration, which are assumed to be pseudo first order. This could be illustrated by the following reactions: (6)

e- + H20

> H 2+ O - ,

(7)

e-+H20

:, eaq-

(8)

e-+S

K

) H2.

Hamill assumes that these reactions will lead to an expression similar to that given by (I), except that the rate constants would be replaced by cross-sections. This model fits our experimental results. Moreover, if reaction (6) (known to occur in the gaseous phase at any energy (in)) is the pathway for H~ formation, a decrease in the O H (O-) radical yield should be observed. This is in agreement with our previous results in the radiolysis of NO3 -(17), where we observed a material balance deficiency (G~,q- + Grt > GoE) which increased as the nitrate ion concentration increased and was shown to be related to the decrease in G E . The interpretation of these results by Hamill's model depends principally on the assumption of competition with rapid processes, such as prompt recombination and hydration. The question is whether metal ions in the range of the concentrations studied (10 -2 to 10 -1 mol dm -3) can compete with these processes. This is not known and as pointed out by Hamitl must be established by experience. The hydride ion mechanism t7, 8) would seem at first sight to be also in agreement with our results. However, this mechanism encounters a serious obstacle: the fact that there is no H + concentration effect seems to rule out this proposal because of the very fast reaction (9)

HaO++H -

> H2 + 2 O H - .

In particular, it would seem strange that this rate constant could be lower by four orders of magnitude than the reaction of the hydrated electron with H80 +

(10)

eaq- + HaO+

• H + H20.

Molecular hydrogen formation in gamma radiolysis of water and aqueous solutions

203

This could be explained by considering reaction (9) as a simultaneous transfer o f two electrons, while the h y d r o g e n a t o m formation in reaction (10) is a single electron transfer. However, the situation in the liquid state is complicated, and n o t even an approximate q u a n t u m mechanical calculation can be made. F r o m the qualitative point o f view it seems reasonable to rely on the fact that in the gaseous phase the probability o f the one-electron transfer is higher c o m p a r e d to the simultaneous transfer o f two-electrons tls,19). Recent E.S.R.-pulse radiolysis studies on H a t o m production in neutral and acid radiolysed water led Smaller t2°~ to conclude that part o f these atoms are in the f o r m o f HaO. According to Smaller, acid solutions c o m p a r e d to neutral solutions gave an increase in the yield o f 40 per cent at most. This is contrary to the accepted Grr values in neutral and acid solutions (0.55 and 3-65, respectively). The mechanism suggested is (11)

H~O-,,

(12)

H z O + + H~O

(13)

HaO++e -

> H20++e -

> H20*

> H+OH,

> HsO++OH, > HaO.

As pointed out earlier, HaO was suggested by Sworski tl) as a molecular h y d r o g e n precursor produced via a first-order mechanism which could be

(14)

HsO

> H~+OH.

This mechanism also indicates that there is a relation between the molecular h y d r o g e n H~ and the hydroxyl radical formation which resembles Hamill's mechanism. The order o f reactivity o f the metal ions toward the Hz precursor is in agreement with the order o f the specific rate constants for ligand substitution in the co-ordination sphere for these metal ions, as measured by Eigen ~1) (Table III). According to

TABLE III.

RELATIVE RATE CONSTANTS OF

Cd ~+, Cu z+, Cr z+, Pb z+

AND

Hg ~÷

WITH THE HYDRATED

ELECTRON, THE MOLECULAR HYDROGEN PRECURSORS AND THE LIGAND EXCHANGE

Solute ke,q- +s type (dma mol -is -1) Cd 2+ Cu 2+ Cr 2+ Pb 2+ Hg ~+

5-2 × 101°* 3'0 × 101°* 4.2 x 10l°* 3.9 x 10l°* 1.3 x 10"t

ke-+s/k,-+~s+ kx+s/kx+H~okx+s/Kx+cd~ 1"0 0"58 0"80 0.75 0'025

6'5 9"6 9'6 22 55

1-0 1"5 1"5 3-4 8-5

kL+s

2 x 10s:l: 3 x 10s:~ 3 x 10s:~ 1.5 x 109§ 2 x 109:~

kL+a/kL+cd~+ 1"0 1"5 1"5 7"5 10.0

* Ref. (10). t Specific rate constant of Hg2++ H, Ref. (8). Refs. (21) and (22). § This specific rate constant is unknown, but according to Ref. (21) it is comparable to that of Ba2+ which is 1.5 × 109.

204

M . FARAGGI

equation (1), the ratios of slope to intercept of each straight line in Figs. 1 and 2 yield the relative efficiency of the metal ion toward the molecular hydrogen precursor X (as+x/ax+n2 o according to HamiU, or k s + x / k x + E 2 o if the reactions are of conventional kinetic type). As the values of ax+rqo (or kx+n~o) are not known, it is impossible to evaluate the cross-section nor the specific rate constant of reaction (5). However, it is possible to calculate the relative reactivities ks+x/kcd~+ +x of the metal ions towards the precursor X, and to compare it with the ratio of substitution rate constants k c found by Eigen et al. (zl) Table III shows the good agreement between these values and the relative substitution rate constants. The fact that some metal ions did not reduce Ga~ is in agreement with their low ligand exchange rate constant ( < 10s). These findings are in accord with Wilkin's and Eigen's t~2) suggestion that substitution may be rate-determining in some redox processes. F r o m this correlation between the diminution of the molecular hydrogen and the ligand substitution rate, it is possible, following Eigen's idea t2a), to suggest that the scavenging reaction (5) may be broken down into several steps: M(H20)m'~++X .

k~

k~

~

M(H~O)m n+, X

kc

kD

" M(H20)m_IXn++H20.

The chemical reaction scavenging process occurs when the outer-sphere complex [M(H20),~n+,X] is converted into an inner-sphere complex [M(HeO)m_IX'~+]. The formation of an outer sphere complex, which corresponds to the aquated ions coming together to form an ion pair, is diffusion controlled and at this stage the molecular hydrogen may still be formed.

CONCLUSION At this point of the investigation of the precursors of "molecular" hydrogen, it seems that there is qualitative agreement on the fact that H 2 is produced by at least two different processes: a pseudo first-order reaction (precursor + water) and a secondorder reaction (radical-radical recombination). However, there is some quantitative disagreement. Schwarz ta), using the diffusion spur model, concludes that the contribution of the second-order processes to the molecular hydrogen is about 70 per cent and that only 30 per cent come from first-order processes. The present paper tries to show that about 80 per cent are first-order contributions. Whatever the precursor of H 2 may be, it seems that the efficiency of the metallic cations as molecular hydrogen scavengers is governed by the ligand exchange rate.

Acknowledgements--The author would like to thank Miss A. Amozig and J. D6salos for their

technical assistance.

REFERENCES la. H. A. MAHLMANand T. J. SWORSKI,in The Chemistry of Ionization and Excitation, edited by G. R. A. JOHNSONand G. SCrtOLES, Taylor & Francis, London, 1967, p. 253. lb. T. J. SWORSKI,5th Informal Conference on Radiation Chemistry of Water, Notre-Dame, Indiana, October 1966, CO0 38-519, 1967.

Molecular hydrogen formation in gamma radiolysis of water and aqueous solutions

205

2. M. ANBAR,in Fundamental Processes in Radiation Chemistry, edited by P. AUSLOOS,Wiley, New York, 1968, Chap. 10. 3. H. A. SCHWARZ, J. phys. Chem. 1969, 73, 1928. 4. W. H. HAMmL, J. phys. Chem. 1969, 73, 1341. 5. T. SAWAXand W. H. HAMILL, J. phys. Chem. 1970, 74, 3915. 6. E. PEL~D and G. CZAPSKI, J. phys. Chem. 1970, 74, 2903. 7. E. PELED, U. MIRSKI and G. CZAI'SKI, J. phys. Chem. 1971, 75, 31. 8. M. FARAGOI and J. DLSALOS, Int. J. Radiat. Phys. Chem. 1969, 1, 335. 9. M. FARAGGI, D. ZEnAVI and M. ANBAR, Trans. Faraday Soc. 1971, 67, 701. 10. M. AN~AR and P. NETA, Int. J. appl. Radiat. Isotopes 1967, 18, 493. 11. R. L. PLATZMAN, in Physical and Chemical Aspects of Basic Mechanism in Radiobiology, Natl. Acad. Sci.-Natl. Res. Council, 1953, 305, 22. 12. R . L . PLArZMAN, 2ndInt. Congr. Radiat. Res., Harrogate, 1962, N o r t h Holland, 1962, p. 22. 13. M. ANBAR a n d E. J. HART,J. phys. Chem. 1965, 69, 973. 14. H. A. MAnLMAN, J. chem. Phys. 1961, 35, 936. 15. M. FARAGGI and Y. TENDLER, J. chem. Phys. 1972, 56, 3287. 16. R. S. DXXON, Radiat. Res. Rev. 1970, 2, 237, 17. M. FARAGGI, D. ZEI~AVXand M. ANBAR,Trans. Faraday Soc. 1971, 67, 2057. 18. C. ZENER, Phys. Rev. 1951, 82, 403. 19. E. F. GURNEY and T. L. MAGEE, J. chem. Phys. 1957, 26, 1237. 20. B. SMALLER, private communication, 1971. 21. M. EIGEN, Pure appL Chem. 1963, 6, 97. 22. R. G. WmKINS and M. EIGEN, Adv. Chem. Ser. 1965, 49, 55. 23. F. BASOLO and R. G. PEARSON,in Mechanism oflnorganic Reactions, Wiley, New York, 1967, p. 154.

R6sum6---Le rendement radiolytique en hydrog6ne Grq dans les solutions d6sa6r6es de quelques cations m6talliques di- et trivalents est souvent trouv6 ind6pendant de la concentration du solut6 (jusqu'h 0,1 tool dm-e). Au contraire, dans les solutions de Cd e+, Cu 2+, Cr e+, Pb 2+ et les solutions acides de Hg e+, Ga, diminue a v e c l a concentration du solut6. L'effet de ces ions sur la diminution du rendement en hydrog~ne se range dans l'ordre: Hg e+ > Pb e+ > Cr e+ ~ Cu e+ > Cd e+. Le fait que tous ces ions m6talliques sont de bons intercepteurs des esp/~ces r6ductrices produites au cours de la radiolyse de l'eau (eaq- et atomes H) conduit ~t la conclusion que ceux-ci ne sont pas les pr6curseurs principaux de He. La d6pendance de Grq ~t l'6gard de la concentration du solut6 est repr6sent6e par une cingtique homog~ne. On consid6re la disparition du pr6curseur de He (qui est du pseudo-premier ordre) comme 6tape d6terminant la vitesse. II pourrait s'agir ou bien de l'anion hydrure produit par la r6action des 61ectrons de sousexcitation avec l'eau selon la proposition de Platzman, ou bien des 61ectrons "secs" sugg6r6s par Hamill, ou bien des radicaux HaO de Sworski et Smaller. On montre que la r6activit6 chimique des ions cit6s envers le pr6curseur de He varie parall61ement aux vitesses de substitution des groupes coordonn6s dans l'ion m6tallique hydrat6 telles qu'elles out 6t6 mesur6es par Eigen. On montre aussi qu'une part ( ~ 20 pour cent) de He peut 6tre produite par une r6action entre radicaux.

Zusammenfassung--Die radiolytische Ausbeute an Wasserstoff Grq aus entliifteten w~issrigen LOsungen yon zwei- und dreiwertiger Metallkationen wurde in vielen F~illen v o n d e r Solutkonzentration (bis zu 0,1 tool d m -3) unabh/ingig gefunden. I m Gegenteil n i m m t G~, in L6sungen yon Cd e+, Cu e+, Cr 2+, Pb a+ u n d in saueren L6sungen von Hg e+ mit zunehmender Solutkonzentration ab. Die Wirkungsf/ihigkeit dieser I o n e n zur Verminderung der Wasserstoffausbeute hat die Reihenfolge: Hg e+ > Pb e+ > Cr e+ ~ Cu e+ > Cd e+. Die Tatsache, dass alle diese Metallkationen gute F~inger fiir die reduzierende Spezies sind, welche bei der Radiolyse von Wasser entstehen (eaq- und H-Atome), fiihrt zur Schlussfolgerung, dass diese letzteren nicht die HauptvorRiufer von He sind. Die Abh/ingigkeit von Grq yon der Solutkonzentration wird durch homogene Kinetik ausgedriJckt. Als geschwindigkeitsbestimmender Schritt wird das in pseudo-erster Ordnung 6rfolgende Abklingen des He-Vorl~iufers gehalten. Es k6nnte sich entweder u m die yon Platzman vorgeschlagene Reaktion der Subexzitations-Elektronen mit Wasser handeln, oder u m die yon Hamill vorgeschlagenen "trockenen" Elektronen, oder u m die yon Sworski und Smaller vorgeschlagenen HaO Radikale. Es wird gezeigt, dass die relativen Reaktivit~tswerte zu der von Eigen gemessenen Geschwindigkeit der Ligand-Substitution in den hydratisierten Metallionen parallel verlaufen. Es wird auch gezeigt, dass ein Teil von H e ( ~ 20 Prozent) durch einen Radikal-RadikalMechanismus entstehen kiSnnte.

206

M. FARAGG!

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