5 The Hydrated Electron in Radiation Chemistry MAX S. MATHESON
Downloaded by UNIV OF MICHIGAN ANN ARBOR on October 22, 2014 | http://pubs.acs.org Publication Date: January 1, 1965 | doi: 10.1021/ba-1965-0050.ch005
Chemistry Division, Argonne National Laboratory, Argonne, Ill.
The hydrated electron, e is the major reducing species in water. A number of its properties are important either in understanding or measuring its kinetic behavior in radiolysis. Such properties are the molar extinction coefficient, the charge, the equilibrium constant for interconversion with H atoms, the hydration energy, the redox potential, the reaction radius, and the diffusion constant.
Measured or esti-
mated values for these quantities can be found in the literature.
The rate constants for the re-
with other products of water action of e radiolysis are in many cases diffusion controlled.
These rate constants for reactions
between the transient
species
in
aqueous
radiolysis are essential for testing the "diffusion from spurs" model of aqueous radiation chemistry.
J h e faith of radiation chemists i n the existence of the hydrated electron, el , has varied through the years. In his book, published i n 1947, L e a (27) proposed that electrons i n irradiated water escaped the parent ion. Stein (40), i n 1952, proposed that methylene blue i n irradiated aqueous solutions might be reacting with e" , and Platzman (33), i n 1953, reported his calculations on the mechanism of formation and some of the properties of the hydrated electron, including its blue color and the hydration energy of ~ 2 e.v. However, contrary to the situation i n another discipline (32), i n radiation chemistry " f a i t h i s " not " t h e evidence of things not seen," and these prophets were largely without honor in any country for several years. Finally, beginning with work by H a y o n and Weiss (20), Baxendale and Hughes (3), and Barr and Allen (1) evidence rapidly accumulated (17, 30) supporting the existence of . T h e mounting tide of corroborating data culminated i n (a) the demonstration that the major reducing species i n irradiated neutral q
aq
a q
45
In Solvated Electron; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
46
SOLVATED ELECTRON
water has unit negative charge (5, 7), and (b) the observation of the tran sient hydrated electron absorption spectrum i n pulse radiolyzed aqueous solutions (4,18,24). It now seems reasonably definite that an entity such as the hydrated electron exists. Further, the rate constants of reaction of e~ with a large number of species have now been measured using the technique of pulse radiolysis. T h i s paper describes some of the properties of e~ and discusses the rate constants of reaction of e~ with the other species produced in the pulse radiolysis of water. These rate constants are significant for any diffusion theory model of the radiolysis of water. aq
aq
Downloaded by UNIV OF MICHIGAN ANN ARBOR on October 22, 2014 | http://pubs.acs.org Publication Date: January 1, 1965 | doi: 10.1021/ba-1965-0050.ch005
aq
Properties
of the Hydrated
Electron
A b s o r p t i o n S p e c t r u m o f e~ . T h e absorption spectrum of the hydrated electron is shown in Figure 1. T h e evidence that this spectrum is that of e is at least four-fold. First, the spectrum is suppressed by known electron scavengers, such as H 0 , 0 , N 0 (4, 18). Second, it resembles i n form the absorption bands of the solvated electron i n liquid ammonia and methylamine (4, 18). T h i r d , the rate constants calculated from the decay of this absorption in the presence of scavengers aq
aq
3
ι
ι
ι
3000
4000
5000
+
2
ι 6000
2
ι
ι
ι
7000
8000
9000
λ in Â
Figure
1.
The absorption spectrum of the hydrated electron. Data from Hart (17).
In Solvated Electron; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
5.
MATHESON
47
Radiation Chemistry
give rate constant ratios which agree with those obtained by competi tive studies with these scavengers in steady radiolysis (15). F o u r t h , the absorbing species responsible for the absorption has unit negative charge (11,15). T h e molar extinction coefficient of e~ at 5780 A . has been measured (36) as e = 10,600 ( ± 1 0 % ) M - c m . " T h i s was done by using Reac tion 1 aq
e
5780
1
e Downloaded by UNIV OF MICHIGAN ANN ARBOR on October 22, 2014 | http://pubs.acs.org Publication Date: January 1, 1965 | doi: 10.1021/ba-1965-0050.ch005
aq
+ C(N0 ) 2
4
1
-
C(N0 ) 2
8
+ N0
(1)
2
and measuring the molar extinction coefficient of C ( N 0 ) ~ at 3660 A . T h e n , with c being known ( N F ~ = C ( N 0 ) " ) , ee was calculated from pulse radiolysis experiments using the initial absorption at 5780 Α . , the final absorption at 3660 Α . , with corrections for the small fraction of e~ that reacted other than with C ( N 0 ) . C(N0 ) ~ does not absorb at 5780 A . F r o m € and the relative extinction coefficients (17, 24) as a function of wavelength e is detennined at any wavelength. € (max) = 15,800 ± Ι β Ο Ο Μ ^ α η . F r o m Figure 1, assuming e = 0 at 1820 and 13,300 A . the oscillator strength, / , was estimated to be 0.65, a value identical to that published for the solvated electron i n ammonia (9). 2
N F
3 e e 0
aq
β
2
8
2
4
8
5780
2
3
Π80
x
e
e
7200
1
x
e
O t h e r P r o p e r t i e s o f e~ . hydrated electron. aq
Table I.
Table I lists various properties of the
Properties of the Hydrated Electron
λ^χ Molar extinction coefficient at 5780 A . at 7200 A . (max) / = oscillator strength Charge pK Hydration energy (calc.) E°(e^ + H 0 Vt H + H 0 ) r /i (pure water at p H 7.0) Limited mostly by -f H 0 Diffusion constant Mean radius of charged distribution (calc.) Ge~ (in neutral water) 3
+
a q
2
7200 A . (1.72 e.v.) 10,600 ( ± 1 0 % ) M " c m . 15, βΟΟΜ^αη. 0.65 —1 9.7 > 1.72 e.v. ^2.67 volts 1
1
1
2
l
8
+
230 /usee. 4.5 X 10" ( ± 1 5 % ) cm. /sec. 2.5-3.0 A . 2.6 (reference 36)
a q
6
2
T h e fact that the major reducing species i n irradiated neutral water has unit negative charge (5, 7) has already been referred to. T h e evidence for this was obtained using the equation (5) log \ = 1.02 Z Z ko ft
b
Λ
1 +
(2)
χ /
αμ / 1
2
which is derived from the Debye-Huckel theory and the Brônsted model of ionic reactions, k is the rate constant for reaction between a and b with respective unit electronic charges Z and Z ; k is the value of k at zero ionic strength; μ is the ionic strength, and α is a constant which depends upon the distance of closest approach of ions a and b. In this earlier work under conditions of steady radiolysis the rate constants for reaction of e~ with charged species were measured relative a
b
0
aq
A. C S. Editorial Lîbraor
In Solvated Electron; Hart, E.; Advances in Chemistry; American Chemical Society: Washington, DC, 1965.
SOLVATED ELECTRON
48
to the rate constant for reaction of e" with an uncharged species as a function of ionic strength. More recently, this same equation has been applied using pulse radiolysis results in which the absolute rate constant for the reaction aq
e
(l(i
+ Fe[CN] ~ -
* '
6
(3)
was measured over a range of ionic strengths (15). T h e radius of F e [CN] was determined from mobility as 2.77 A (14), and this was used as the radius of reaction for Fe [ C N ] ~ . Jortner (23) recently has used a dielectric continuum model and self-consistent field theory to estimate the electron-binding energy in water. H e finds that the cavity that con tains the electron in water is smaller than the cavity containing the elec tron in ammonia. Indeed, it is possible that there are no additional cavities needed in water to accommodate the electron. H e calculated the mean radius for charge distribution in the ground state as 2.5-3.0 Α., and noted that this radius could be used for the reaction radius in the Debye equation for diffusion-controlled reactions of charged species. T h e encounter distance then for Reaction 3 will be about 6 A . and for such an encounter distance a may be set equal to 2. Thus, in Figure 2 the log of k has been plotted against μ / ( 1 + V ) In Equation 3, F e [ C N ] ~ has three negative charges. However, Dainton and Watt (6, 8) measured the rate constant for Reaction 3 relative to the rate constant for the reaction of e with N 0 and plotted the logarithm of this ratio against μ / ( 1 + Μ )· They used a slope of +2, and they noted that in their solutions the F e [ C N ] ~ was largely combined in the form K F e [ C N ] ~ . Their work extended to much higher ionic strengths than the highest used to obtain the data in Figure 2. In reference (11) from the equilibrium constant of James and M o n k (22), it was estimated that for points at μ / ( 1 + 2 μ ) , less than 0.1 association of F e [ C N ] ~ was not important. In Figure 2 the ex perimental results are consistent with a slope of +3 at low ionic strength, with the slope falling off to a value of +2 in the region studied by Dainton and Watt (8). One can conclude from Figure 2 that the ionic strength effect is large and approximately that expected if the absorbing species has a charge of —1. T h e p K for the hydrated electron is estimated from the individual rate constants in Reaction 4 as 9.7. However, even though 6
- 3
6
Downloaded by UNIV OF MICHIGAN ANN ARBOR on October 22, 2014 | http://pubs.acs.org Publication Date: January 1, 1965 | doi: 10.1021/ba-1965-0050.ch005
Fe[CN]
3
6
3
1 / 2
G
/
2
3
aq
1 / 2
2
1/2
6
6
1 / 2
6
e
aq
3
2
1/2
3
+ H 0
