5271
J . Phys. Chem. 1985, 89, 5271-5274 potential of 2-hydroxyethyl disulfide to 2-mercaptoethanol (Eo = -0.22 V) can be calculated from the half-wave potential reported by Stricks et al.I9 The thioureas, S202-, and I- appear to cluster as a distinct group exhibiting a slope of 1.0, while C1-, Br-, and SCN- cluster as another distinct group with a steeper slope of 8.5. However, 2-mercaptoethanol does not appear to correlate with either group of nucleophiles. A linear free energy relationship of the following form can be written:
where S is the slope, C is the intercept and K,,, (log KrmC= nFEm,,/2.3RT)is the equilibrium constant of the overall reaction. Equation 22 is similar in form to the Edwards equation20 log ( k l / k o )= a E ,
+ BH
(23)
where ko corresponds to the rate constant for water as a nucleophile, E, is a nucleophilic constant characteristic of the particular electron donor, H i s the relative basicity of the donor to protons which has been defined at H 3 pHa + 1.74, and a! and @ are the substrate constants. E,,, which depends on the polarizability,*' is calculated from the electrode potential of the nucleophile. Comparison of eq 22 to 23 suggests that E,,, should be comparable to E,, that S is equivalent to the substrate constant, and that C can be equated to (PH + log ko). The minimal contribution (Le., LYE">> B H ) of the basicity term to relative reactivity and the existence of two apparently inde(19) Stricks, W.; Frischmann, J. K.; Mueller, R.G. J. Electrochem. SOC. 1962, 109, 518.
(20) Edwards, J. 0. J . Am. Chem. SOC.1954, 76, 1540. (21) Edwards, J. 0. J . Am. Chem. SOC.1956, 78, 1819.
+
pendent linear free energy domains as shown in Figure 5 may be explained within the context of Pearson's HSAB theory.22 The observed order of nucleophilic reactivity should be similar to the order of softness of bases. The relative order of softness for various nucleophiles is thiourea > SO3*-> SCN- > I- > Br- > N O T > C1- > F which is similar to the observed order to nucleophilic reactivity. Since H202is soft center,23polarizability rather than basicity should be the more important factor. Thiosulfate and I- are considered as soft bases, whereas C1-, Br-, F, and Ne3are considered to be hard bases. As a consequence, the former group will have higher polarizabilities and hence greater nucleophilic reactivities than the latter group. The departure of 2-mercaptoethanol from this correlation implies that its rate of the oxidation also depends strongly on its basicity. The relative basicity of 2-mercaptoethanol ( H = 11.1) is significantly higher than all other nucleophiles listed in Table 111. This indicates that the addition of 2-mercaptoethanol to hydrogen peroxide is energetically more favorable than the other listed sulfur compounds.
Acknowledgment. Support for this research was provided by a grant from the U S . Environmental Protection Agency (R809198-01). We gratefully acknowledge the assistance of the Pollution Control Processes/Environmental Engineering Section (U.S. EPA) and Dr. Donald Carey. Registry No. HOC2H4SH,60-24-2; (HOC2H& 1892-29-1. (22) Pearson, R. G., Ed. "Hard and Soft Acids and Bases"; Dowden, Hutchinson & Ross: New York, 1973. (23) Pearson, R. G. Chem. Brit. 1967, 3, 103. (24) Abel, E. Monatsch. Chem. 1907, 28, 239. (25) Sandved, K.;Holte, J. B. Chem. Abstr. 1939, 33, 4856. (26) Ross, S. D. J . Am. Chem. SOC.1946,68, 1484. (27) (a) Schung, K.; Gilmore, M. D.; Olson, L. A. Inorg. Chem. 1967,6, 2180. (b) Schung, K.; Miniatas, B.; Sadowski, A. J.; Yano, T.; Vedo, K. Ibid. 1968, 7, 1669. (28) Caldwell, S.M.; Norris, A. R. Inorg. Chem. 1968, 7, 1667. (29) Edwards, J. 0.; Fortnum, D. H. J . Org.Chem. 1962, 27, 407.
Activation Energy for the Reactlon H OHeaq-. Kinetic Determlnation of the Enthalpy and Entropy of Solvation of the Hydrated Electron -+
B. Hickel* IRDI/DESICP/DPC-SCM, Unite Associee au CNRS UA 331, CEA - CEN/Saclay, 91 191 Gif sur Yvette Cgdex. France
and K. Sehested Accelerator Department, Riso National Laboratory, DK 4000 Roskilde, Denmark (Received: April 17, 198s)
-
The reaction between atomic hydrogen and hydroxide ion in aqueous solutions H + OH- eaq-+ H 2 0 has been studied by pulse radiolysis. The rate constant was measured at pH 11.7 and 12 by following the growth of the hydrated electron absorption at 600 nm. The activation energy of the reaction has been determined over the temperature range 15-60 "C as 6.3 f 0.6 kcal/mol(26.4 f 2.5 kJ/mol). From this value and the activation energy of the reverse reaction, the ea; enthalpy of formation AHf = -32.6 f 1.6 kcal/mol (-136.4 f 6.7 kJ/mol) and its standard entropy So = 16.7 f 5.4 cal/(mol deg) (69.8 f 22.5 J/(mol deg)) were calculated. The high entropy of solvation A& = 11.7 f 5.4 cal/(mol deg) (49 22.6 J/(mol deg)) when electrons are transferred from gas phase into aqueous solution indicates that the hydrated electron is a structure breaker.
Introduction In water the hydrated electron is not stable; nevertheless, some of its thermodynamic properties have been derived from the equilibrium constant of the
eaq- + H 2 0
ki
H
+ OH-
(1) Baxendale, J. H. Radiat. Res. Suppl. 1964, 4, 139., (2) Marcus, R. A. J. Chem. Phys. 1965, 43, 3477.
(1)
At room temperature k, = 890 s-I4 and k2 = 1.8 X lo7 M-l From this the equilibrium constant
S-1.5
K = [HI [OH-] / [ea;] can be found by assuming K = k l / k 2 . The standard free energy of reaction 1 is AG," = 5.9 kcal/mol if the standard state of water (3) Jortner, J.; Noyes, R. M. J . Phys. Chem. 1966, 70, 770. (4) Hart, E. J.; Gordon, S.;Fielden, E. M. J. Phys. Chem. 1966, 70, 150. (5) Matheson, M. S.; Rabani, J. J . Phys. Chem. 1965, 69, 1324.
0022-3654/85/2089-5271~01.50/0 0 1985 American Chemical Society
5272
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985
is pure liquid and the standard states of the other species are ideal 1 m solution^.^ Then the free energy of hydration and the standard potential of the hydrated electron were derived from a thermodynamic The effect of temperature on the equilibrium constant K is not known but Fielden and Hart have measured the activation energy of reaction 1: E, = 6.7 f 0.7 kcal/moL6 This value was later revised to 4.5 f 1 kcal/mol to take into consideration the ionic dissociation of water.' If the activation energy of the reverse reaction can be measured, then with the same assumption as before the standard enthalpy AHo I and entropy ASo,of reaction 1 are easily derived. From this, the enthalpy and entropy of solvation of the hydrated electron can be calculated and compared with the predicted va1ues.j In the present paper we report the determination by pulse radiolysis of the activation energy for the reaction
H
+ OH-
-
eaq- + H 2 0
(2)
and the calculation of the enthalpy of formation and the standard entropy of the hydrated electron.
Experimental Section Pulse Radiolysis. The irradiations were performed on the HRC linac at Riso which delivers a single pulse of 10-MeV electrons with a maximum intensity of 1.1 A and a pulse length of 0.1-1 p s . The irradiations were done in a high-temperature cell which can stand a pressure of 150 atm and a temperature up to 300 OC.* The inner part of the cell is made of Suprasil and the light path is 2.5 cm. The optical detection system has been described previously? The data were recorded on a Nicolet Explorer I11 digital oscilloscope and stored on disks. Solutions. The solutions were prepared from triply distilled water and deaerated by bubbling argon before the addition of sodium hydroxide to minimize the formation of carbonate. The solution were then transferred into the irradiation cell and saturated with hydrogen under a pressure of 90-100 atm ((H2) = 7-8 X IOy2 M). The solutions were preirradiated in the cell by repetitive pulsing until the lifetime of the hydrated electron remained constant. Dosimetry. The dosimetry was performed directly on the absorption of the hydrated electron by taking geac= 2.7 and t = 11 500 M-I cm-I at 600 nm. For most of the experiments the dose was about 200 rad and the duration of the pulse between 0.1 and 0.2 p s . Results The rate constant k2 for a given temperature can be measured by following the growth of the hydrated electron absorption at 600 nm
H20
--
eaq-, H , OH, H2, H 2 0 2 ,H 2 0 f
-
After the electron pulse, the following reactions take place:
+ OHOH + OHOH + H2 0- + H2 H
OH-
10
In alkaline solution saturated with hydrogen under a pressure of 100 atm, OH and 0- are converted quickly into H atom by s) and then H reacts with OH- to reactions 4 and 5 (tl/2 < give eaq-. The hydrated electron is formed in two stages (Figure 1): (1) a fast formation during the pulse with a yield equal to geq-;(2) a slow formation from H atoms (reaction 2) with a yield goH. equal to g, When k,[H2] and k5[H2]>> k2[OH-] the rate of reaction 2 becomes the rate-determining step irrespective of the origin of H atoms and e,, formation depends on k2 but not on k, and k5. The hydrated electron decays on a longer time scale only by reaction 8 in absence of impurity. It was previously found that after preirradiation of the solution by repetitive pulsing, the lifetime of ea< increases and its decay follows second-order kinetics.]l The role of preirradiation is to destroy some impurities and to lower in particular, is the residual concentration of ~ x y g e n .HzO2, ~ destroyed by a chain reaction which leads to the hydrated electron (reaction 7 followed by reactions 3 and 2).12 However, in some experiments, after preirradiation of the solution the decay of e; remains faster than expected. This is due probably to residual traces of oxygen coming from the gas phase above the solution. The kinetics of hydrated electron formation and decay after the pulse is given by
+
d[e;]/dt = k2[HI[OH-I - 2ks[ea
