On the Role of Reducing Species in the Mechanism of Dihalide Ion Formation during Radiolysis of Frozen Hydrohalic Acids

E. N. Borisova, G. V. Koval’s, L. T. Bugaenko

(Presented by the scientific seminar of the Department of Radiation Chemistry)

It is known that, when ionizing radiation acts on aqueous alkali solutions at low temperatures, both stabilized electrons in the form of various color centers and stabilized radicals are formed. The yield of stabilized species in the event that the efficiency of back recombination is low should amount to several units per 100 eV.

In pure alkali-halide crystals the yield of stabilized species (electrons and dihalide ions) is only 0.01–0.001 species per 100 eV, i.e., 3–4 orders of magnitude lower than the number of species formed in the primary act of the action of radiation. It is obvious that the main fraction of the species generated by the radiation recombines into the initial forms. The reason for this phenomenon may be both the low efficiency of electron traps and the high electron-accepting ability of halogen atoms or dihalide ions with respect to the electron.

In this work an attempt was made to obtain information on the reactivity of dichloride and dibromide ions stabilized at the temperature of liquid nitrogen. As matrices modeling alkali-halide crystals, concentrated aqueous solutions of hydrochloric and hydrobromic acids with concentrations of 6 M and 8.6 M, respectively, were chosen; molecular chlorine and bromine were taken as additional electron acceptors. Both matrices were glassy, which made it possible to conduct spectrophotometric observations directly at the temperature of liquid nitrogen. The glassiness of the matrices was demonstrated experimentally by X-ray structural analysis.

Experimental Method

Irradiation of the samples was carried out with X-rays with a maximum energy of 60 keV at 77°K. Hydrochloric and hydrobromic-

hydrochloric acid was purified by double distillation. Before freezing, oxygen was displaced from the solution with nitrogen. The irradiation and spectrophotometric analysis procedures are described in [1]. The molar extinction coefficient of $\mathrm{Cl_2^-}$, determined in 6 M HCl at 77°K at the absorption maximum at a wavelength of 335 nm, was $12500\ \mathrm{L\,mol^{-1}\,cm^{-1}}$. The dibromide ion was analyzed in the region of the second maximum, whose position in 8.6 M HBr was determined to be at a wavelength of 670 nm; $\varepsilon_{\mathrm{Br_2^-}} = 810\ \mathrm{L\,mol^{-1}\,cm^{-1}}$.

The calculation of the extinction coefficients was based on the assumption that, upon thawing, the only reaction occurring is

\[ 2X_2^- \longrightarrow X_2 + 2X^- , \tag{1} \]

i.e., that there are no reducing species stabilized in the matrix (electrons or H atoms) that could, upon thawing, reduce dihalide ions to halide ions. According to ESR data [2], the yield of stabilized H atoms in frozen hydrohalic acids does not exceed 0.1 atom per 100 eV, and stabilized electrons are practically absent. Therefore the contribution of the reaction

\[ X_2^- + H \longrightarrow 2X^- + H^+ , \tag{2} \]

even if it occurs, will be too small.

Radiolysis of 6 M HCl and 8.6 M HBr without acceptors

In pure matrices the accumulation of the dichloride ion at low doses, and of the dibromide ion even at higher doses, proceeds linearly. The yield of $\mathrm{Cl_2^-}$ in hydrochloric acid is 7.1 particles, and that of $\mathrm{Br_2^-}$ in hydrobromic acid is 5 particles per 100 eV.

The mechanism of the processes occurring during radiolysis may be written in the form of the following reactions:

\[ X^- \rightsquigarrow X + \bar e \qquad G_X',\ G_{\bar e}' \tag{3} \]

\[ H_2O \rightsquigarrow OH,\ \bar e \qquad G_{OH}',\ G_{\bar e}'' \tag{4} \]

\[ OH + X^- \longrightarrow X + OH^- \tag{5} \]

\[ X + X^- \longrightarrow X_2^- \tag{6} \]

\[ \bar e + \bar e \xrightarrow{H_2O,\ H_3O^+} H_2 \tag{7} \]

\[ X_2^- + \bar e \longrightarrow 2X^- \tag{8'} \]

Reaction (8′) plays the role of a recombination reaction in the initial pro-

XVII.

If this mechanism is adopted, the observed yield of dihalide ions can be written in the form of the following expression:

\[ G(X_2^-)=G_X-G_{e^-}, \tag{1} \]

where \(G_X=G'_X+G_{OH}\), i.e., the total initial yield of atomic halogen due to the action of radiation on the halide ion and on water, and \(G_{e^-}=G'_{e^-}+G''_{e^-}-2G_{H_2}\), i.e., the total yield of electrons due to the action of radiation on the halide ion and on water, less the yield of molecular hydrogen according to reaction /7/. We assume that this reaction proceeds in the pores and that the introduction of an \(e^-\) acceptor does not affect this process.

Radiolysis of hydrobromic acid in the presence of bromine

To verify the occurrence of reaction /8/, molecular halogens, which are effective electron acceptors, were used as competing acceptors.

Fig. 1. Accumulation curve of \(Br_2^-\) in \(8.6\,M\ HBr + 0.03\,M\ Br_2\), \(77^\circ K\).

Fig. 2. Dependence of the yield of dihalide ions on the concentration of molecular halogens at \(77^\circ K\):

I — \(Cl_2^-\) in \(6\,M\ HCl + Cl_2\)
II — \(Br_2^-\) in \(8.6\,M\ HBr + Br_2\)
III — \(Br_2^-\) in \(6\,M\ HCl + Br_2\)

It was found that in the presence of molecular bromine the yield of dibromide-ion formation increases. The accumulation curve of di-

bromide ions, as can be seen from Fig. 1, has an initial linear segment at low doses; at high doses the yield begins to decrease.

Figure 2 shows the dependence of the initial yield of formation of \(\mathrm{Br}_2^-\) on the concentration of molecular bromine, which was varied from \(10^{-4}\) to \(1\) M. With increasing bromine concentration, the yield of \(\mathrm{Br}_2^-\) increases and tends toward a certain limiting value equal to 15 particles per 100 eV. The curve has an S-shaped character, which can be explained by the presence of competing reactions:

\[ \mathrm{Br}_2^- + \bar e \longrightarrow 2\mathrm{Br}^- \qquad /8/ \]

\[ \mathrm{Br}_3^- + \bar e \longrightarrow \mathrm{Br}_2^- + \mathrm{Br}^- \qquad /9/ \]

In equation /9/ we write \(\mathrm{Br}_3^-\), since the equilibrium constant

\[ \mathrm{Br}_2 + \mathrm{Br}^- \rightleftharpoons \mathrm{Br}_3^- \qquad /10/ \]

at room temperature is \(17.8\,\mathrm{M}^{-1}\) [3], and calculation shows that in this system the predominant part of the dissolved \(\mathrm{Br}_2\) exists in the form of tribromide ions; moreover, since reaction /10/ is exothermic, when the temperature is lowered the equilibrium should shift still further toward the tribromide ion.

With complete suppression of reaction /8/, i.e., when all Br atoms and all electrons that have escaped recombination into molecular hydrogen take part in the formation of dibromide ions, the yield of the latter becomes equal to

\[ G(X_2^-)=G_X+G_{\bar e^-}. \qquad (\mathrm{II}) \]

Combining equations I and II, we obtain for the hydrobromic-acid matrix the value of the yield of halide atoms \(G_{\mathrm{Br}}=9.6\) and of free electrons \(G_{\bar e^-}=4.6\) particles per 100 eV.

The dependence of the \(\mathrm{Br}_2^-\) yield on the bromine concentration makes it possible to calculate the ratio of the constants of reactions /8/ and /9/ of the electron with \(\mathrm{Br}_2^-\) and \(\mathrm{Br}_3^-\). Treatment of the scheme by the method of stationary concentrations gives the following expression:

\[ \frac{d[\mathrm{Br}_2^-]}{dt} = G(\mathrm{Br}_2^-) = G_{\mathrm{Br}} + G_{\bar e^-} - \frac{2G_{\bar e^-}}{1+k_9[\mathrm{Br}_3^-]/k_8[\mathrm{Br}_2^-]} \qquad (\mathrm{III}) \]

Calculation of the exact value of the ratio of the constants is somewhat difficult, since the accumulation curves of the dibromide ions have a rather extended linear segment; therefore, in the calculation according to equation III it is necessary to use not the true concentration of \(\mathrm{Br}_2^-\), but

medium. Taking this into account, \(k_9/k_8 = 0.33 \pm 0.010\), i.e., the dibromide ion is a more effective electron acceptor by two orders of magnitude than \(\mathrm{Br_3^-}\). The curve calculated on the basis of the obtained ratio of constants and the values of the yields \(\mathrm{Br_2^-}\) and \(\bar e\) satisfactorily describes the experimental dependence.

The ratio of the constants \(k_9/k_8\) for the hydrobromic-acid matrix can also be found from the complete curve for dibromide-ion accumulation shown in Fig. 1. Integrating differential equation III, we obtain for the accumulation curve the logarithmic equation:

\[ \frac{[\mathrm{Br_2^-}]N}{(G_{\mathrm{Br_2^-}}-G_{e^-})} - \frac{2G_{e^-}\cdot k_9[\mathrm{Br_3^-}]N}{(G_{\mathrm{Br_2^-}}-G_{e^-})^2 k_8} \ln\left\{ 1+ \frac{(G_{\mathrm{Br_2^-}}-G_{e^-})}{(G_{\mathrm{Br_2^-}}+G_{e^-})} \cdot \frac{k_8[\mathrm{Br_2^-}]}{k_9[\mathrm{Br_3^-}]} \right\} =\eta \cdot D, \tag{IV} \]

where \(N\) is Avogadro’s number, \(D\) is the dose. Equation IV satisfactorily describes the accumulation curve of \(\mathrm{Br_2^-}\) at a value of the constant ratio \(k_9/k_8 = 0.032 \pm 0.010\). This value coincides with that calculated from equation III. The agreement of the quantities shows that inclusion in the calculation of the mean concentration of the intermediate particle does not introduce a noticeable error into the determination of the ratio of constants.

Radiolysis of hydrochloric acid in the presence of chlorine.

It is known that molecular chlorine dissolved in hydrochloric acid is in equilibrium

\[ \mathrm{Cl_2 + Cl^- \rightleftharpoons Cl_3^-} \]

whose constant at room temperature is \(0.17\text{–}0.19\ \mathrm{M^{-1}}\) [4,5]. An approximate calculation shows that somewhat more than half of the dissolved chlorine is present in the form of \(\mathrm{Cl_3^-}\), and the rest in the form of molecular chlorine. There are no data in the literature on the thermal effect of this reaction, and it is therefore impossible to draw a conclusion about the shift of the equilibrium when the temperature is lowered. If it is assumed that at \(77^\circ\mathrm{K}\) there exist two particles reacting with the electron, \(\mathrm{Cl_2}\) and \(\mathrm{Cl_3^-}\), then, when the scheme is treated by the method of stationary concentrations, a constant coefficient appears in the equation before the ratio of the constants of the competing reactions, and the value of the ratio of constants must be corrected with allowance for this coefficient.

The dependence of the initial yields of dichloride ions on the chlorine concentration is shown in Fig. 2. It is seen that here, as in the case of the \(\mathrm{HBr}+\mathrm{Br_2}\) system, the yield of dihalide ions increases; however, in this matrix, because of analytical difficulties, it was not possible to carry out experiments with high chlorine concentrations, and therefore it was not po-

the experimentally determined limiting value of the yield of dichloride ions has been obtained. However, from these data one can also calculate the yields of chlorine atoms and free electrons and the ratio of the rate constants of the competing reactions:

\[ \begin{array}{rcl} \mathrm{Cl}_3^- + \bar e &\longrightarrow& \mathrm{Cl}_2 + \mathrm{Cl}^- \qquad /10/\\ \mathrm{Cl}_2 + \bar e &\longrightarrow& 2\mathrm{Cl}^- \qquad /11/\\ \mathrm{Cl}_2 + \bar e &\longrightarrow& \mathrm{Cl}_2^- \qquad /12/ \end{array} \]

Treatment by the steady-state concentration method leads to the equation:

\[ G(\mathrm{Cl}_2^-)=\left(G_{\mathrm{Cl}}-G_{e^-}\right)+2G_{e^-} -\frac{2G_{e^-}}{1+\dfrac{K_{10}[\mathrm{Cl}_3^-]}{K_{11}[\mathrm{Cl}_2]}\cdot \alpha}, \qquad (V) \]

where

\[ \alpha=\left(1+\frac{K_{12}[\mathrm{Cl}_2]}{K_{10}[\mathrm{Cl}_3^-]}\right), \]

the solution of which gives the value \(G_{e^-}=8\pm1.5\) electrons per 100 eV. Hence the yield of chlorine atoms is \(15\pm3\) atoms per 100 eV and \(\alpha\cdot(K_{10}/K_{11})=0.0070\pm0.0011\), i.e., the dichloride ion is more than two orders of magnitude more effective with respect to the electron than \(\mathrm{Cl}_2\) (or \(\mathrm{Cl}_3^-\)). The calculated curve, computed on the basis of the obtained values, as is evident from Fig. 2, satisfactorily describes the experimental results.

Radiolysis of hydrochloric acid in the presence of bromine. In this system the yield only of dibromide ions was determined from the absorption maximum at 670 nm. As shown in Fig. 2, the yield of \(\mathrm{Br}_2^-\) increases with increasing logarithm of the bromine concentration along an S-shaped curve. The limiting value \(G(\mathrm{Br}_2)=10\pm2\) in this system is equal to the limiting value of the yield of free electrons, \(G_{e^-}\), and is in good agreement with the value \(G_{e^-}=8\pm1.5\) in the hydrochloric-acid matrix containing chlorine. Calculation of the ratio of the constants of the competing reactions in this matrix is difficult because of the complexity of the matrix composition.

\[ * \qquad * \qquad * \]

Thus, in both matrices a significant fraction of the dihalide ions formed upon irradiation is reduced during irradiation by free electrons to halide ions. These same concepts may also be extended to alkali-halide crystals. Of course, the relative reactivity of dihalide ions with respect to the electron in alkali-halide crystals—

... in our experiments is not established. It is impossible to transfer to crystals the values of the ratios of constants determined in other, though compositionally similar, matrices. But, generally speaking, the yield of electrons and hence the yield of all primary particles formed in alkali-halide crystals during radiolysis can be determined directly if crystals doped with a molecular halide, for example, molecular iodine, are obtained.

Moscow State University
Faculty of Chemistry

References

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2. V. N. Belovskii, L. T. Bugaenko, Dokl. Akad. Nauk SSSR, 39, 2589 (1965)

3. R. D. Griffith, A. McKeown, A. J. Winn, Trans. Faraday Soc., 28, no. 129, 101 (1932)

4. M. S. Sherill, F. Izard, J. Am. Chem. Soc., 53, 1667 (1931)

5. G. Zimmerman, F. G. Strong, J. Am. Chem. Soc., 79, 2063 (1957)