A. K. PIKAEV, P. Ya. GLAZUNOV, Academician Vikt. I. SPITSYN

APPROXIMATE VALUES OF THE RATE CONSTANTS OF RADIATION REACTIONS INVOLVING THE HYDRATED ELECTRON

At the present time, questions connected with the participation in radiolytic transformations in aqueous solutions of two forms of reducing radicals formed during the radiolysis of water are being widely discussed in the literature. There is definite evidence that these forms are the hydrated electron \(e_{\mathrm{aq}}^{-}\) and the hydrogen atom H, the former being converted into the latter as a result of reaction with hydrogen ions. Clearly, investigation of the influence of pH on the yields of radiolytic transformations in aqueous solutions makes it possible in a number of cases to study the reactivity of these intermediate products of radiolysis toward dissolved substances.

Earlier \((^{1})\), by using two independent methods of kinetic treatment of experimental data obtained in a study of the radiolysis of solutions of ferrous sulfate in \(0.4\ M\ \mathrm{H_2SO_4}\), containing oxygen, under the action of pulsed electron radiation, we estimated the absolute values of the rate constants of the reactions \(\mathrm{H}+\mathrm{O_2}\), \(\mathrm{H}+\mathrm{OH}\), and \(\mathrm{Fe^{2+}}+\mathrm{OH}\). It therefore seemed possible, by studying radiolytic transformations in this system under conditions where reactions involving the hydrated electron proceed, i.e., at sufficiently high pH, to compare the reactivity of \(e_{\mathrm{aq}}^{-}\) and H.

Fig. 1. Dependence of \(G(\mathrm{Fe^{3+}})\) on dose rate for a \(3\cdot 10^{-3}\ M\) Mohr’s salt solution saturated with air:
1—\(0.4\ M\ \mathrm{H_2SO_4}\) \((^{1})\);
2—pH 3

Fig. 2. Dependence of \(G(\mathrm{Fe^{3+}})\) on \(\mathrm{H_2SO_4}\) concentration for a \(3\cdot 10^{-3}\ M\) Mohr’s salt solution saturated with air, at a dose rate of \((1.3—1.5)\cdot 10^{23}\ \mathrm{eV/ml\cdot sec}\)

As the source of ionizing radiation we used a directly accelerated electron tube \((^{2})\). High dose rates were produced by means of single electron pulses. Their duration was \(5\cdot 10^{-6}\) sec. The electron energy was \(1.0\) MeV. The methods of generation and measurement of the pulses, as well as the experimental procedure, have been described in our previous communications \((^{1,3})\). The absolute accuracy of the measurements was \(\pm 10\%\).

The reagents used were of sufficiently high purity. The solutions in all cases were sulfuric-acid solutions and were saturated with air. Trivalent iron was determined spectrophotometrically at a wavelength of \(304\ \mathrm{m}\mu\).

The molar extinction coefficient of \(\mathrm{Fe}^{3+}\) in \(0.4\,M\ \mathrm{H_2SO_4}\) at \(24^\circ\mathrm{C}\) was taken to be 2170 \((^4)\). In the calculations, allowance was made for its dependence on the acidity of the solution \((^{5,6})\), as well as for its variation with temperature (0.7% per degree). The pH value was measured on an LP-58 potentiometer.

Figure 1 shows the dependence of \(G(\mathrm{Fe}^{3+})\) for a \(3\cdot10^{-3}\,M\) solution of Mohr’s salt at pH 3 on the dose rate (curve 2). The same figure gives, for comparison, the analogous dependence for \(0.4\,M\ \mathrm{H_2SO_4}\) (curve 1), which we obtained earlier \((^1)\). Figure 2 illustrates the dependence of \(G(\mathrm{Fe}^{3+})\) on pH for a Mohr’s salt solution of the same concentration at a dose rate of \((1.3—1.5)\cdot10^{23}\ \mathrm{eV/ml\cdot sec}\). Finally, Fig. 3 gives the dependence of \(G(\mathrm{Fe}^{3+})\) on the solution concentration at a dose rate of \(3\cdot10^{22}\ \mathrm{eV/ml\cdot sec}\) and at different pH values*: curve 1—\(0.4\,M\ \mathrm{H_2SO_4}\), curve 2—pH 2, and curve 3—pH 3. As is evident from these figures, \(G(\mathrm{Fe}^{3+})\) at a constant concentration of \(\mathrm{Fe}^{2+}\) ions decreases with increasing pH. A similar course of the dependence of \(G(\mathrm{Fe}^{3+})\) was also observed in \((^8)\) for the case of low dose rates.

Fig. 3. Dependence of \(G(\mathrm{Fe}^{3+})\) on the concentration of \(\mathrm{Fe}^{2+}\) ions in air-saturated solutions (dose rate \(3\cdot10^{22}\ \mathrm{eV/ml\cdot sec}\)): 1—\(0.4\,M\ \mathrm{H_2SO_4}\); 2—pH 2; 3—pH 3

Earlier \((^1)\) we showed that the decrease in \(G(\mathrm{Fe}^{3+})\) in \(0.4\,M\) sulfuric-acid solutions containing oxygen, in the case of high absorbed-dose rates, is satisfactorily explained by competition among reactions 3, 4, and 5:

\[ \mathrm{H_2O}\leadsto \mathrm{H},\ \mathrm{OH},\ e_{\mathrm{aq}}^{-};\ \mathrm{H_2},\ \mathrm{H_2O_2}, \tag{1} \]

\[ e_{\mathrm{aq}}^{-}+\mathrm{H_3O}^{+}\to \mathrm{H}+\mathrm{H_2O}, \tag{2} \]

\[ \mathrm{H}+\mathrm{O_2}\to \mathrm{HO_2}, \tag{3} \]

\[ \mathrm{H}+\mathrm{OH}\to \mathrm{H_2O}, \tag{4} \]

\[ \mathrm{Fe}^{2+}+\mathrm{OH}\to \mathrm{Fe}^{3+}+\mathrm{OH}^{-}, \tag{5} \]

\[ \mathrm{H}^{+}+\mathrm{Fe}^{2+}+\mathrm{HO_2}\to \mathrm{Fe}^{3+}+\mathrm{H_2O_2}, \tag{6} \]

\[ \mathrm{Fe}^{2+}+\mathrm{H_2O_2}\to \mathrm{Fe}^{3+}+\mathrm{OH}+\mathrm{OH}^{-}. \tag{7} \]

Obviously, in \(0.4\,M\ \mathrm{H_2SO_4}\) the hydrated electrons are completely converted into H atoms. At \(\mathrm{pH}\geq 2\), reactions (8) and (9) may apparently compete with reaction (2):

\[ e_{\mathrm{aq}}^{-}+\mathrm{O_2}\to \mathrm{O_2}^{-}, \tag{8} \]

\[ e_{\mathrm{aq}}^{-}+\mathrm{OH}\to \mathrm{OH}^{-}, \tag{9} \]

\[ \mathrm{O_2}^{-}+\mathrm{H}^{+}\rightleftarrows \mathrm{HO_2}. \tag{10} \]

If it is assumed that the mechanism of oxidation of \(\mathrm{Fe}^{2+}\) ions in the presence of oxygen at \(\mathrm{pH}\geq 2\) is expressed by reactions (1—9), and if it is further assumed that \(K_3=K_8\) and \(K_4=K_9\), then, using the steady-state method, the following equation can be obtained:

\[ \frac{\left[{}^{1}/_{2}\,G(\mathrm{Fe}^{3+})+G_{\mathrm{H_2}}-G_{\mathrm{H_2O_2}}\right]\left[G(\mathrm{Fe}^{3+})-2G_{\mathrm{H_2}}\right]} {3G_{\mathrm{red}}+G_{\mathrm{OH}}+2G_{\mathrm{H_2O_2}}-G(\mathrm{Fe}^{3+})} = \frac{K'K_5}{K''}\,(\mathrm{Fe}^{2+})(\mathrm{O_2})\left(\frac{100N}{I}\right), \tag{11} \]

where \(K'=K_3=K_8\), \(K''=K_4=K_9\), and \(K_5\) are the rate constants of the corresponding reactions; \(G_{\mathrm{red}}\), \(G_{\mathrm{OH}}\), \(G_{\mathrm{H_2}}\), and \(G_{\mathrm{H_2O_2}}\) are the initial yields, respectively, of reducing radicals, OH, \(\mathrm{H_2}\), and \(\mathrm{H_2O_2}\); \((\mathrm{Fe}^{2+})\) and \((\mathrm{O_2})\) are the molar concentrations of \(\mathrm{Fe}^{2+}\) and \(\mathrm{O_2}\); \(I\) is the dose rate (in \(\mathrm{eV/l\cdot sec}\)) and \(N\) is Avogadro’s number. We obtained the same equation for \(0.4\,M\ \mathrm{H_2SO_4}\) \((^1)\), except that in it, instead of the constants \(K'\) and \(K''\), the constants \(K_3\) and \(K_4\) appeared. Obviously, our assumption that the constants are equal will be correct only if the relative constant \(K'K_5/K''\) proves equal to the ratio \(K_3K_5/K_4\).

\[ \rule{4em}{0.4pt} \]

* In all cases, the ferrous sulfate solutions used did not contain NaCl. In the presence of chloride ions, \(G(\mathrm{Fe}^{3+})\) decreases \((^{7,1})\).

The value of the constant \(K'K_5/K''\), calculated from equation (11) using the experimental data shown in Figs. 1–3, proved to be equal to \((3.8 \pm 1.5)\cdot 10^7\) liters/mole·sec* . In the case of \(0.4\,M\) \(H_2SO_4\), \(K_3K_5/K_4=(3.2\pm1.2)\cdot 10^7\) liters/mole·sec \((^1)\). Thus, it may be assumed that \(K_3 \approx K_8\) and \(K_4 \approx K_9\).

In our preceding communication \((^1)\) it was shown that \(K_3=5.3\times10^9\) liters/mole·sec and \(K_4=4.5\cdot10^{10}\) liters/mole·sec. Then, evidently, \(K_8\approx5\times10^9\) liters/mole·sec** and \(K_9\approx4\cdot10^{10}\) liters/mole·sec. There are many data in the literature on the relative rate constants of reactions involving the hydrated electron. Therefore it is possible, starting from \(K_8=5\cdot10^9\) liters/mole·sec, to estimate approximately the absolute values of the rate constants of some of these reactions. Table 1 gives the values of the constants obtained in this way.

Table 1.

Approximate values of the rate constants of reactions of \(e^-_{aq}\) with certain dissolved substances

It should be noted that the mechanism of radiolytic oxidation of \(Fe^{2+}\), expressed by reactions (1–9), is apparently valid only at sufficiently high concentrations of \(Fe^{2+}\) ions. For example, for \(0.4\,M\) \(H_2SO_4\) the constant \(K_3K_5/K_4\) increases to \(6\cdot10^7\) liters/mole·sec already in the case of a \(10^{-3}\,M\) solution of \(Fe^{2+}\) ions. However, as the acidity is lowered, the value of this constant is independent of \((Fe^{2+})\) over a wider range of \(Fe^{2+}\) concentrations. Thus, at pH 3, even for a \(10^{-4}\) solution of ferrous sulfate, \(K'K_5/K''\) practically does not differ from the values in the case of higher concentrations \((4.9\cdot10^7\) liters/mole·sec). It is still difficult to give any definite explanation of this phenomenon. Perhaps it is associated with the fact that at low \(Fe^{2+}\) concentrations the \(OH\) radicals interact mainly with sulfuric acid. Clearly, further investigations are necessary for the final resolution of this question.

Institute of Physical Chemistry
Academy of Sciences of the USSR

Received
14 V 1963

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* In the calculations, the dependence of \(G_{\mathrm{rest}}\), \(G_{OH}\), and \(G_{H_2O_2}\) on pH \((^9)\) was taken into account, and the mean values of \(G(Fe^{3+})\) in each series of experiments were used.

** An estimate of this constant was also made in work \((^{10})\). According to the data of that work, it is equal to \(1.5\cdot10^{10}\) liters/mole·sec.