Physical Chemistry

V. N. Shubin and P. I. Dolin

RADIATION REDUCTION OF FERRIC IONS IN SOLUTIONS SATURATED WITH HYDROGEN UNDER PRESSURE

(Presented by Academician A. N. Frumkin, May 20, 1960)

In deaerated sulfuric-acid solutions, under the action of radiation, the ion (\mathrm{Fe}^{3+}) undergoes no transformations, since the sum of the oxidizing components (G_{\mathrm{OH}} + 2G_{\mathrm{H_2O_2}}) is greater than the amount of reducing components, (G_{\mathrm{H}}); the (\mathrm{H_2}) formed during radiolysis escapes into the gas phase and does not participate in reactions. Therefore the study of the kinetic characteristics of the (\mathrm{Fe}^{3+}) ion has been carried out in systems containing various additives ((^{1-4})). Kinetic treatment of data for such systems is difficult because of their complexity and the large number of competing reactions.

In studies carried out in sulfuric-acid solutions, it was found that the reduction yield depends on the acidity of the solution. The cause of this dependence was not unambiguously established. It is evident that, when molecular hydrogen is present in the solution, some of the OH radicals are transformed into H atoms by the reaction (\mathrm{H_2 + OH \to H_2O + H}), thereby increasing the amount of reducing components at the expense of oxidizing ones. In addition, a decrease in the concentration of OH radicals hinders the recombination of radicals with formation of water.

In the present work the yields of reduction of ferric iron in acid solution under the action of (\gamma)-radiation from (\mathrm{Co}^{60}) were measured at various concentrations of (\mathrm{H_2}), (\mathrm{Fe}^{3+}), and acid.

Method. The investigated (\mathrm{Fe}^{3+}) solution was saturated with hydrogen in a glass cell ((^5)) at atmospheric pressure, after which the cell was sealed and placed in a steel bomb, where the solution was saturated with (\mathrm{H_2}) at the specified pressure.

Chemically pure reagents were used. The initial solutions were prepared with twice-distilled water. The dose rate was (\sim 3 \cdot 10^{15}\ \mathrm{eV}/\mathrm{cm}^3 \cdot \mathrm{sec}). The concentration of the (\mathrm{Fe}^{2+}) ion was determined by the o-phenanthroline method. The extinction coefficient was (10700\ \mathrm{l}/\mathrm{mol}\cdot\mathrm{cm}).

Results and discussion. The dependence of the reduction yield on the pressure of (\mathrm{H_2}) above the solution was determined for a (2 \cdot 10^{-3}\ M) solution of (\mathrm{Fe}^{3+}) in (0.8\ N\ \mathrm{H_2SO_4}). For each (\mathrm{H_2}) concentration, the initial portions of the reduction curve were recorded. The initial reduction yields calculated from these data are plotted in Fig. 1 as a function of the hydrogen pressure above the solution. As is seen from Fig. 1, the reduction yield increases with increasing pressure. This form of the dependence is explained by competition for OH radicals in the following two reactions:

[
\mathrm{H_2 + OH \xrightarrow{k_1} H_2O + H;}
\tag{1}
]

[
\mathrm{H + OH \xrightarrow{k_2} H_2O.}
\tag{2}
]

Atomic hydrogen, formed during radiolysis and by reaction (1), participates in the reduction of Fe³⁺ according to the reaction:

[
\mathrm{Fe}^{3+}+\mathrm{H}\xrightarrow{k_3}\mathrm{Fe}^{2+}+\mathrm{H}^+ .
\tag{3}
]

Reaction (3) is competitive with respect to reaction (2). It is obvious that, with an increase in the Fe³⁺ concentration, the reduction yield should increase.

The dependence of the yield on the Fe³⁺ concentration was determined in a 0.8 N solution of H₂SO₄ saturated with H₂ at a pressure of 50 atm. The reduction yields, calculated from the initial portion of the reduction curves, are plotted in Fig. 2 as a function of (\lg[\mathrm{Fe}^{3+}]).

Fig. 1. Dependence of the Fe³⁺ reduction yield on the hydrogen pressure above the solution

Fig. 2. Dependence of the reduction yield on the Fe³⁺ concentration

Assuming that the initial yield is determined by the course of the three reactions indicated above, the following expression for the ratio of constants can be derived from the kinetic equations:

[
\frac{k_2}{k_1\cdot k_3}
=
\frac{[G_{\mathrm H}+G_{\mathrm{OH}}-G(\mathrm{Fe}^{2+})][\mathrm H_2][\mathrm{Fe}^{3+}]}
{[G(\mathrm{Fe}^{2+})+G_{\mathrm{OH}}-G_{\mathrm H}]\,G(\mathrm{Fe}^{2+})\cdot M}.
\tag{1}
]

In deriving the formula, on the basis of the data of Dale and Sutton (⁶), it was assumed that the H₂O₂ formed during radiolysis does not have time during irradiation to react to any appreciable extent with the Fe²⁺ ions produced during reduction. But even if all the peroxide reacted during irradiation, equation (1) would change only slightly—instead of the term in the denominator in square brackets, the term ([G(\mathrm{Fe}^{2+})+G_{\mathrm{OH}}-G_{\mathrm H}+2G_{\mathrm{H_2O_2}}]) would appear. However, the Fe²⁺ concentration after irradiation was several units multiplied by (10^{-5}\,M). At such a concentration, during the irradiation time (3–9 min.) only an insignificant fraction of the peroxide could react.

The irradiated solution was kept for 1 hour after irradiation under pressure. In this process, by the reaction (\mathrm{Fe}^{2+}+\mathrm{H_2O_2}\to\mathrm{Fe}^{3+}+\mathrm{OH}^-+\mathrm{OH}), a certain amount of the Fe²⁺ formed disappears, but the OH radicals produced are transformed by reaction (1) into H atoms, which reduce an equivalent amount of Fe³⁺ ions. Thus, the reduction yield remains unchanged.

From the radiolysis scheme proposed above it follows that the reduction yield should not depend on the acid concentration in the solution. Experimentally, such a dependence was observed in sulfuric-acid solutions. It is known, however, that in sulfuric-acid solutions trivalent iron forms complex ions. It is obvious that the rate constant for the interaction of such an ion with an H atom differs from the rate constant for the free ion. With a change in the H₂SO₄ concentration, the ratio between—

by the amount of free ion $\mathrm{Fe}^{3+}$ and complexed ion, which in turn will affect the yield. On the other hand, it is known that in $\mathrm{HClO}_4$ solutions the $\mathrm{Fe}^{3+}$ ion exists as a free ion. This makes it possible to compare the behavior of the free and the complex ion.

The dependences of the reduction yield on the concentration of $\mathrm{H}_2\mathrm{SO}_4$ and $\mathrm{HClO}_4$ are shown in Fig. 3. As is seen from Fig. 3, in sulfuric acid solution the yield increases as the concentration of $\mathrm{H}_2\mathrm{SO}_4$ decreases, whereas in $\mathrm{HClO}_4$ the yield does not change over the entire acid-concentration range studied. The results obtained in $\mathrm{HClO}_4$ solutions thus confirm the correctness of the above-proposed radiolysis scheme and of equation (I) derived on its basis.

To establish which of the anions is the complex-forming ion, experiments were carried out with additions of $\mathrm{Na}_2\mathrm{SO}_4$ and $\mathrm{NaHSO}_4$ to hydrochloric acid solutions. The experiments with added $\mathrm{Na}_2\mathrm{SO}_4$ were carried out at high pH so that only a small part of $\mathrm{SO}_4$ was converted into $\mathrm{HSO}_4^-$. In this case only a slight decrease in the reduction yield was observed (Fig. 3), even at concentrations of $\mathrm{SO}_4^{2-}\sim 1\,M$. By contrast, the presence of $\mathrm{HSO}_4^-$ in an amount of $0.3\,M$* sharply decreases the yield (see Fig. 3). The experiments were carried out in $0.2\,M\,\mathrm{HClO}_4$, where the dissociation of $\mathrm{HSO}_4^-$ was suppressed. These results make it possible to assert that the complex-forming ion is $\mathrm{HSO}_4^-$. Then, from the data on the dependence of the yield on the concentration of $\mathrm{H}_2\mathrm{SO}_4$, one can calculate the equilibrium constant of the reaction:

$$
\mathrm{Fe}^{3+}+\mathrm{HSO}_4^- \overset{K_a}{\rightleftarrows} \mathrm{FeHSO}_4^{2+}.
$$

Fig. 3. Reduction of $\mathrm{Fe}^{3+}$ in solutions with different concentrations of $\mathrm{H}_2\mathrm{SO}_4$, $\mathrm{HClO}_4$, and in solutions containing additions of $\mathrm{Na}_2\mathrm{SO}_4$ and $\mathrm{NaHSO}_4$.
1 — $\mathrm{H}_2\mathrm{SO}_4$ solution; 2 — $\mathrm{HClO}_4$ solution; 3 — $\mathrm{HClO}_4+0.1\,M\,\mathrm{Na}_2\mathrm{SO}_4$ solution; 4 — $\mathrm{HClO}_4+1\,M\,\mathrm{Na}_2\mathrm{SO}_4$ solution; 5 — $\mathrm{HClO}_4+0.3\,M\,\mathrm{NaHSO}_4$ solution.

From equation (I) the values

$$
\frac{k_2}{k_1\cdot k_3}\cdot \alpha,\quad \text{where}\quad
\alpha=\frac{[\mathrm{Fe}^{3+}]{\mathrm{total}}}{[\mathrm{Fe}^{3+}].}}
$$

were calculated. Then, if the quantities $\alpha$ for sulfuric acid solutions with pH 0.4, 0.8, and 1.4 are denoted by $\alpha_1$, $\alpha_2$, and $\alpha_3$, respectively, the ratio $\alpha_1:\alpha_2:\alpha_3$ can be determined.

To determine the amounts of trivalent iron existing as free and complex ions, the equation may be written:

$$
\mathrm{Fe}^{3+}{\mathrm{free}}+
K_a
\frac{f4^-}\cdot f}^{3+}}}{f_{\mathrm{FeHSO4^{2+}}}
[\mathrm{HSO}_4^-][\mathrm{Fe}^{3+}]}
=
[\mathrm{Fe}^{3+}]_{\mathrm{total}}.
\tag{II}
$$

Using this equation and the ratio $\alpha_1:\alpha_2:\alpha_3$, we calculated the value $K_a=91$ l/mole.

From the experimental data on the dependence of the reduction yield on the concentration of $\mathrm{H}_2$, $\mathrm{Fe}^{3+}$, and $\mathrm{H}_2\mathrm{SO}_4$, using equation (I) one can determine the value of the ratio of constants

$$
\frac{k_2}{k_1\cdot k_3}=71\pm 5.
$$

The concentration of free $\mathrm{Fe}^{3+}$ ions for substitution into (I) was calculated from equation (II).

To determine the absolute value of $k_3$, the following estimate of the absolute values of the constants $k_1$ and $k_2$ was made.

Reaction (2) proceeds without activation energy. The steric factor is 0.5. In this case the reaction rate constant, equal to the number

* In $0.8\,N$ $\mathrm{H}_2\mathrm{SO}_4$ solutions the concentration of the $\mathrm{HSO}_4^-$ ion is $\sim 0.3\,M$.

collisions, multiplied by the steric factor, is

[
k_2 = 2.8 \cdot 10^{11} \cdot 0.5 = 1.4 \cdot 10^{11}\ \text{L}/\text{mol}\cdot\text{s}.
]

Assuming that the value of (k_1) does not change substantially in going from the gas phase to the aqueous phase, we took it from the work of Avraamenko and Lorenzo ((^{7})): (k_1 = 2.5 \cdot 10^3\ \text{L}/\text{mol}\cdot\text{s}).

The value calculated on the basis of these data is (k_3 = (8 \pm 0.56) \times 10^5\ \text{L}/\text{mol}\cdot\text{s}).

Institute of Electrochemistry
Academy of Sciences of the USSR

Received
20 V 1960

References Cited

(^{1}) T. Rigg, G. Stein, J. Weisse, Proc. Roy. Soc., 211, 375 (1952).
(^{2}) E. J. Hart, J. Am. Chem. Soc., 77, 5786 (1955).
(^{3}) D. M. Donaldson, N. Miller, Radiation Res., 9, 487 (1958).
(^{4}) J. Bednář, Collect. Czechoslovak. Chem. communication, 25, 1104 (1960).
(^{5}) V. N. Shubin, P. I. Dolin, DAN, 125, 1298 (1959).
(^{6}) F. Dainton, H. Sutton, Trans. Farad. Soc., 49, 1011 (1953).
(^{7}) L. I. Avraamenko, R. V. Lorenzo, ZhFKh, 24, 207 (1950).