Physical Chemistry

V. N. Shubin and P. I. Dolin

RADIATION TRANSFORMATIONS OF A MIXTURE OF Fe²⁺ AND Fe³⁺ IONS IN ACID SOLUTIONS SATURATED WITH HYDROGEN UNDER PRESSURE

(Presented by Academician A. N. Frumkin, July 19, 1960)

In previous works (¹–³), the oxidation of Fe²⁺ and the reduction of Fe³⁺ in solutions saturated with hydrogen under pressure were investigated, and certain kinetic characteristics of the oxidation and reduction processes were determined. Study of the radiolysis of solutions containing a mixture of Fe²⁺ and Fe³⁺ ions under H₂ pressure makes it possible, by varying the concentrations of the solution components, to obtain these data in several ways and, from their comparison, to draw more reliable conclusions about the mechanism of the process.

The system Fe²⁺ + Fe³⁺ has already been studied (⁴, ⁵). However, in works (⁴, ⁵) the determination was limited to some single dependence, and on the basis of the data obtained one cannot draw definite conclusions about the mechanism of radiolysis and, consequently, about the rate constants of the reactions taking place.

It is evident that, in the presence of molecular hydrogen in the solution, part of the OH radicals is transformed into H atoms by the reaction

\[ \mathrm{H_2 + OH \to H_2O + H}, \tag{I} \]

which competes with the reaction

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

As a result of reaction (I), instead of the oxidizing OH radicals, H atoms appear, which can participate in both oxidation and reduction reactions. This broadens the limits of variation of the transformation yield and makes it possible to obtain more accurate dependences.

In the present work, the yields of oxidation of Fe²⁺ under the action of Co⁶⁰ γ-rays were measured at various concentrations of Fe³⁺, H₂, and Fe²⁺ in 0.8 N H₂SO₄ solution.

Method

The glass cell and the procedure for saturating the solution with hydrogen were described in detail earlier (¹, ²). The solutions were prepared from chemically pure reagents in twice-distilled water. The dose rate was \(\sim 2 \cdot 10^{15}\) eV/cm³·sec. The concentration of Fe²⁺ ions was determined spectrophotometrically with o-phenanthroline.

Results and Discussion

The dependence of the oxidation yield on the Fe³⁺ concentration was determined for a \(\sim 10^{-3}\) M Fe²⁺ solution in 0.8 N H₂SO₄ saturated with H₂ at 100 atm. For each Fe³⁺ concentration, the initial portions of the oxidation curve were taken; the maximum change in the initial concentrations did not exceed 10%. The initial oxidation yields calculated from these data as a function of the Fe³⁺ concentration in the solution (\([\mathrm{Fe^{2+}}] = 1.05 \cdot 10^{-3}\) M; \(P_{\mathrm{H_2}} = 100\) atm.) are given in Table 1.

Table 1

* The minus sign indicates that reduction is taking place.

As is seen from the table, with an increase in \([\mathrm{Fe}^{3+}]\) the oxidation yield falls to zero, and with a further increase in \([\mathrm{Fe}^{3+}]\) its reduction begins. Such a form of the dependence can probably be explained by competition for H atoms in the following two reactions:

\[ \mathrm{H}+\mathrm{Fe}^{3+}\to \mathrm{H}^{+}+\mathrm{Fe}^{2+}; \tag{III} \]

\[ \mathrm{H}+\mathrm{H}^{+}\to \mathrm{H}_{2}^{+}. \tag{IV} \]

The \(\mathrm{H}_{2}^{+}\) ions formed are removed by the reaction

\[ \mathrm{Fe}^{2+}+\mathrm{H}_{2}^{+}\to \mathrm{Fe}^{3+}+\mathrm{H}_{2}. \tag{V} \]

Assuming that the initial yield is determined by the occurrence of reactions (I)—(V), and also

\[ \mathrm{Fe}^{2+}+\mathrm{H}_{2}\mathrm{O}_{2}\to \mathrm{Fe}^{3+}+\mathrm{OH}^{-}+\mathrm{OH}, \tag{VI} \]

we obtain the following expression for the oxidation yield:

\[ \begin{aligned} G(\mathrm{Fe}^{3+}) &=G_{\mathrm{H}}+G_{\mathrm{OH}}+2G_{\mathrm{H_2O_2}} -\left[ G_{\mathrm{H}}+ \frac{G_{\mathrm{OH}}+G_{\mathrm{H_2O_2}}} {1+\dfrac{k_{2}[\mathrm{Fe}^{2+}]}{k_{1}[\mathrm{H}_{2}]}} \right] \frac{2}{1+\dfrac{k_{4}[\mathrm{H}^{+}]}{k_{3}[\mathrm{Fe}^{3+}]}} \\ &\equiv A-\frac{2\alpha}{1+\dfrac{k_{4}[\mathrm{H}^{+}]}{k_{3}[\mathrm{Fe}^{3+}]}} . \end{aligned} \tag{1} \]

Let us transform it as follows:

\[ 1+\frac{k_{4}[\mathrm{H}^{+}]}{k_{3}[\mathrm{Fe}^{3+}]} = \frac{2\alpha}{A-G(\mathrm{Fe}^{3+})}. \tag{2} \]

Since only \([\mathrm{Fe}^{3+}]\) changes in the solution, the expression on the right-hand side is a linear function of the ratio \([\mathrm{H}^{+}]/[\mathrm{Fe}^{3+}]\). In Fig. 1 such a dependence is presented, constructed from the data of Table 1. According to equation (2), the tangent of the angle of inclination is \(k_{4}/k_{3}=9\cdot10^{-3}\), and the intercept \(b_{1}=1\). From Fig. 1 we find \(b_{1}=0.142\alpha=1\), whence

\[ \alpha= \left[ G_{\mathrm{H}}+ \frac{G_{\mathrm{OH}}+G_{\mathrm{H_2O_2}}} {1+\dfrac{k_{2}[\mathrm{Fe}^{2+}]}{k_{1}[\mathrm{H}_{2}]}} \right] = \]

\[ =7.05. \]

Hence, using the known values of the yields \(G_{\mathrm{H}}, G_{\mathrm{OH}}\) and \(G_{\mathrm{H_2O_2}}\) and the concentration ratio \([\mathrm{Fe}^{2+}]/[\mathrm{H}_{2}]=0.013\), we obtain \(k_{1}/k_{2}=0.125\pm0.3\). This value can also be determined from the dependence of the oxidation yield on the hydrogen pressure. For this purpose we rewrite equation (1) in the form

\[ \frac{k_{1}[\mathrm{H}_{2}]}{k_{2}[\mathrm{Fe}^{2+}]} = \left\{ \frac{G_{\mathrm{OH}}+G_{\mathrm{H_2O_2}}} {\tfrac{1}{2}[A-G(\mathrm{Fe}^{3+})]\left(1+\dfrac{k_{4}[\mathrm{H}^{+}]}{k_{3}[\mathrm{Fe}^{3+}]}\right)-G_{\mathrm{H}}} -1 \right\}^{-1} \equiv X . \tag{3} \]

Fig. 1. Graphical solution of equation (2) from the data of Table 1.

Fig. 2. Graphical solution of equation (3) from the data of Table 2.

Table 2

If only \(P_{\mathrm{H_2}}\) changes, then \(X\) is a linear function of the ratio \([\mathrm{H_2}]/[\mathrm{Fe}^{2+}]\). Figure 2 presents the dependence of \(X\), constructed from experimental data (Table 2), on \([\mathrm{H_2}]/[\mathrm{Fe}^{2+}]\) for a solution with \([\mathrm{Fe}^{2+}] = 1.05 \cdot 10^{-3}\,M\), \([\mathrm{Fe}^{3+}] = 8.6 \cdot 10^{-3}\,M\).

The tangent of the slope gives the value \(k_1/k_2 = 0.138\). Previously this same quantity was determined by us in the radiolysis of \(\mathrm{Fe}^{2+}\) solutions in \(0.8\,N\,\mathrm{H_2SO_4}\), saturated with \(\mathrm{H_2}\) and \(\mathrm{O_2}\), and was found to be 0.135. The values of \(k_1/k_2\) obtained from radiolysis data by three methods agree well with the value obtained for radicals arising by reaction (VI) without radiation exposure\(^{(6)}\). This confirms the identity of the radicals arising by reaction (VI) and during radiolysis.

Many authors believe that reaction (IV) and the following reaction (V) should be replaced by reaction \(^{(7)}\)

\[ \mathrm{Fe}^{2+}(\mathrm{H_2O})_n + \mathrm{H} \to \mathrm{FeOH}^{2+}(\mathrm{H_2O})_{n-1} + \mathrm{H_2} \tag{IVa} \]

or \(^{(8)}\)

![Figure 3 graph]

Fig. 3. Graphical solution of equation (2) as a function of \([\mathrm{Fe}^{2+}]/[\mathrm{Fe}^{3+}]\) according to the data of Table 1 (dashed line) and Table 3 (solid line)

\[ \mathrm{Fe}^{2+} + \mathrm{H} \to \mathrm{FeH}^{2+} \xrightarrow{+\mathrm{H}^+} \mathrm{Fe}^{3+} + \mathrm{H_2}. \tag{IVb} \]

In this case, evidently, in equations (1) and (2), \([\mathrm{Fe}^{2+}]\) will appear instead of the concentration of \(\mathrm{H}^+\). The dependence of the oxidation yield on \([\mathrm{Fe}^{2+}]\) was determined

Table 3

in a \(\sim 10^{-2}\,M\) \(\mathrm{Fe}^{3+}\) solution at a constant ratio \([\mathrm{Fe}^{2+}]/[\mathrm{H_2}]\). The results are given in Table 3 \(\left([\mathrm{Fe}^{3+}] = 8.6 \cdot 10^{-3}\,M;\ [\mathrm{Fe}^{2+}]/[\mathrm{H_2}] = \mathrm{const}\right)\).

Since only \([\mathrm{Fe}^{2+}]/[\mathrm{Fe}^{3+}]\) changes, the right-hand side of equation (2) must be a linear function of this ratio. The desired dependence, constructed from the data of Table 1 (dashed line) and Table 3 (solid line), is presented in Fig. 3. The slopes of the curves and the ratios of constants calculated from them do not coincide, as would be expected in the case of reactions (IVa) and (IVb). Thus, the experimental results do not confirm the occurrence of reactions (IVa) and (IVb).

![Figure 4 graph]

Fig. 4. Graphical solution of equation (4) according to the data of Table 3

The experimentally observed dependence of the yield on \([\mathrm{Fe}^{2+}]\) (see Table 3) is probably explained by the fact that, at low concentrations of \(\mathrm{Fe}^{2+}\), not all \(\mathrm{H_2^+}\) formed by reaction (IV) react with \(\mathrm{Fe}^{2+}\); some of them disappear by the reaction

\[ \mathrm{H_2^+} \to \mathrm{H}^+ + \mathrm{H}. \tag{VII} \]

In this case, as is easily verified, in equations (1) and (2) the quantity \(k_4/k_3\) must be replaced by

\[ \frac{k_4}{k_3} \Big/ \left(1 + \frac{k_7}{k_5[\mathrm{Fe}^{2+}]}\right). \]

For determining \(k_7/k_5\)

and \(k_4/k_3\), we rewrite equation (2) as follows:

\[ 1+\frac{k_7}{k_5[\mathrm{Fe}^{2+}]} = -\frac{\dfrac{k_4[\mathrm{H}^{+}]/k_3[\mathrm{Fe}^{3+}]}{2\alpha}} {\dfrac{A-G(\mathrm{Fe}^{3+})}{\,}-1} \equiv \frac{\beta}{\dfrac{2\alpha}{A-G(\mathrm{Fe}^{3+})}-1}. \tag{4} \]

The expression on the right-hand side is a linear function of the quantity \(\dfrac{1}{[\mathrm{Fe}^{2+}]}\). The desired dependence, constructed from the data of Table 3, is given in Fig. 4. The tangent of the angle of inclination is \(k_7/k_5 = 1.5\cdot 10^{-4}\) mole/l. The intercept is \(b_2=1\), whence \(k_4/k_3 = 1.03\cdot 10^{-2}\).

In conclusion it should be noted that in sulfuric-acid solutions the effective concentration of \(\mathrm{Fe}^{3+}\), as was shown earlier \((^3)\), may be considerably lower than the total concentration because of complex formation; this must be taken into account when determining the absolute value of the ratio \(k_4/k_3\).

Institute of Electrochemistry
Academy of Sciences of the USSR

Received
19 VII 1960

CITED LITERATURE

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4. W. G. Rothschild, A. O. Allen, Rad. Res., 8, No. 2, 101 (1958).
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7. T. W. Davis, S. Gordon, E. J. Hart, J. Am. Chem. Soc., 80, 4487 (1958).
8. J. Halpern, G. Czapski et al., Nature, 186, 629 (1960).