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PHYSICAL CHEMISTRY
I. E. MIKHAILENKO and Academician Vikt. I. SPITSYN
NEW DATA ON THE EFFECT OF THE RADIOACTIVITY OF THE SOLID PHASE ON HETEROGENEOUS PROCESSES OF ISOTOPIC EXCHANGE
In a previous communication ($^{1}$) the authors showed that the rate of isotopic exchange of sulfur at a temperature of 840° in the system $K_2\overset{*}{S}O_4—SO_3$ depends substantially on the specific radioactivity of the preparation of $K_2\overset{*}{S}O_4$ used. In the investigated range of activities from 0.02–0.03 to 16.2 mCi/g, the maximum degree of exchange was observed at a specific radioactivity of potassium sulfate equal to 2–2.3 mCi/g.
At present the investigation has been extended to $K_2SO_4$ preparations of still higher specific activity (up to $\sim 130$ mCi/g). The new data, confirming the earlier results, make it possible to clarify somewhat the mechanism of the observed phenomenon. The apparatus and the experimental procedure were analogous to those described in ($^{1}$). Some of the samples were prepared by adding small amounts of $Na_2SO_4$ highly active in $S^{35}$ to a solution of chemically pure $K_2SO_4$. It had been established earlier that an impurity of $Na_2SO_4$ does not affect the rate of isotopic exchange of sulfur in the system $K_2\overset{*}{S}O_4—SO_3$. Samples of $K_2\overset{*}{S}O_4$ with the highest specific radioactivity were prepared by neutralizing labeled $H_2\overset{*}{S}O_4$ with chemically pure KOH. The results obtained are given in Table 1 and in Fig. 1.
Table 1
Isotopic exchange in the system $K_2SO_4—SO_3$ at 840°
| No. of $K_2SO_4$ preparation | Added $Na_2SO_4$ impurity in % | Observed specific activity, imp/min·g | Absolute activity, mCi/g | Number of experiments | Degree of exchange (average), % |
|---|---|---|---|---|---|
| 1 | 0.04 | $6.44 \cdot 10^5$ | $1.7 \cdot 10^{-2}$ | 5 | 11.7 |
| 2 | 0.1 | $9.37 \cdot 10^5$ | $2.6 \cdot 10^{-2}$ | 6 | 11.5 |
| 3 | — | $5.50 \cdot 10^6$ | $6.1 \cdot 10^{-2}$ | 5 | 14.2 |
| 4 | 0.1 | $12.1 \cdot 10^6$ | $3.4 \cdot 10^{-1}$ | 7 | 24.5 |
| 5 | 0.1 | $12.5 \cdot 10^6$ | $3.5 \cdot 10^{-1}$ | 4 | 26.7 |
| 6 | 0.4 | $72.6 \cdot 10^6$ | 2.0 | 5 | 65.5 |
| 7 | 0.4 | $80.4 \cdot 10^6$ | 2.3 | 5 | 66.9 |
| 8 | 0.5 | $13.5 \cdot 10^7$ | 3.0 | 4 | 60.9 |
| 9 | 2.6 | $28.2 \cdot 10^7$ | 7.8 | 5 | 33.3 |
| 10 | 3.0 | $58.5 \cdot 10^7$ | 16.2 | 4 | 36.6 |
| 11 | 2.0 | $96.4 \cdot 10^7$ | 27.1 | 4 | 31.4 |
| 12 | 1.8 | $12.3 \cdot 10^8$ | 34.6 | 7 | 25.2 |
| 13 | — | $55.1 \cdot 10^8$ | 61.1 | 4 | 31.5 |
| 14 | — | $74.7 \cdot 10^8$ | 74.9 | 5 | 43.2 |
| 15 | — | $17.6 \cdot 10^8$ | 98.8 | 4 | 52.8 |
| 16 | — | $21.2 \cdot 10^9$ | 131.3 | 8 | 85.5 |
The rate of isotopic exchange at a specific radioactivity of $K_2\overset{*}{S}O_4$ of the order of 0.02–0.03 mCi/g is practically constant. It begins to increase when the activity of the preparation exceeds the level of 0.05 mCi/g.
and reaches a maximum at a specific activity of \(\mathrm{K_2SO_4}\) on the order of 2–2.5 mCu/g (degree of exchange about 66% in 10 min). A further increase in the specific activity of potassium sulfate from 3 mCu/g to 35 mCu/g leads to a decrease in the degree of exchange to 25%. At a specific activity of \(\mathrm{K_2SO_4}\) equal to 61 mCu/g, the degree of exchange again begins to increase, and for a preparation with a specific activity of 131 mCu/g it amounts to 85% in 10 min.
Fig. 1. Dependence of the degree of isotopic exchange on the specific activity of \(\mathrm{K_2SO_4}\)
It may be assumed that the increase in the degree of isotopic exchange for preparations with specific activity from hundredths of a unit to 2–3 mCu/g is associated with the appearance of positive charges on the surface of the solid phase due to the continuous emission of \(\beta\)-particles. Apparently, the isotopic exchange of sulfur proceeds through the interaction of \(\mathrm{SO_3}\) with \(\mathrm{SO_4^{2-}}\) ions on the surface of potassium sulfate and the formation, as an intermediate compound, of \(\mathrm{S_2O_7^{2-}}\) ions. Conditions for their formation will be more favorable in the presence of an increased number of positively charged active centers. The decrease in the degree of isotopic exchange for preparations with specific activity from 3 to 35 mCu/g may depend on partial neutralization of the positive charges of the active centers by the abundantly emitted electrons. In any case, measurement of the activation energy (see below) confirms the assumption of different mechanisms of the isotopic-exchange reaction depending on the specific activity of \(\mathrm{K_2SO_4}\) preparations.
The sharp increase in the degree of exchange when the specific activity of \(\mathrm{K_2SO_4}\) is increased above 35 mCu/g probably has a mechanism already different from that of the first branch of the curve in Fig. 1. Here, one must assume, purely radiation phenomena begin to play the decisive role, consisting in enhanced activation of \(\mathrm{SO_4^{2-}}\) ions and individual atoms of the crystal lattice, as well as \(\mathrm{SO_3}\) molecules, under the energetic action of the emitted \(\beta\)-particles. In the following communication \((^2)\), where the effect of external electron irradiation on isotopic exchange in the \(\mathrm{K_2SO_4}\)—\(\mathrm{SO_3}\) system is described, it will be shown that precisely in this region, at a dose of \(3 \cdot 10^{16}\) eV, which corresponds to radioactiv—
Table 2
Rate constants of the isotopic-exchange reaction between \(\mathrm{Na_2SO_4}\) of different specific activity and gaseous \(\mathrm{SO_3}\)
| No. of NaSO₄ preparation | Abs. activity, mCu/g | Temp., °C | Degree of exchange, % | Rate constant, \(k \cdot 10^2\) | \(\frac{1}{T}\cdot 10^4\) | \(\ln(k \cdot 10^2)\) | \(E=A \cdot R\), kcal/mol |
|---|---|---|---|---|---|---|---|
| 1 | \(1.7 \cdot 10^{-2}\) | 700 | 14.7 | 1.590 | 10.27 | 0.4637 | \(24 \pm 2\) |
| 1 | \(1.7 \cdot 10^{-2}\) | 750 | 24.9 | 2.864 | 9.77 | 1.051 | \(24 \pm 2\) |
| 1 | \(1.7 \cdot 10^{-2}\) | 800 | 38.1 | 4.894 | 9.32 | 1.587 | \(24 \pm 2\) |
| 1 | \(1.7 \cdot 10^{-2}\) | 840 | 49.2 | 6.772 | 8.98 | 1.914 | \(24 \pm 2\) |
| 2 | 1.02 | 700 | 25.8 | 2.984 | 10.27 | 1.0824 | \(23 \pm 2\) |
| 2 | 1.02 | 750 | 46.8 | 6.212 | 9.77 | 1.8251 | \(23 \pm 2\) |
| 2 | 1.02 | 800 | 64.7 | 10.41 | 9.32 | 2.3421 | \(23 \pm 2\) |
| 2 | 1.02 | 840 | 73.1 | 13.13 | 8.98 | 2.5754 | \(23 \pm 2\) |
| 3 | 10.7 | 700 | 24.3 | 2.784 | 10.27 | 1.0300 | \(19 \pm 2\) |
| 3 | 10.7 | 740 | 36.0 | 4.464 | 9.90 | 1.4960 | \(19 \pm 2\) |
| 3 | 10.7 | 800 | 56.0 | 8.210 | 9.32 | 2.1050 | \(19 \pm 2\) |
| 3 | 10.7 | 840 | 69.3 | 11.810 | 8.98 | 2.4469 | \(19 \pm 2\) |
| 4 | 24.5 | 700 | 20.4 | 2.282 | 10.27 | 0.8252 | \(18 \pm 1\) |
| 4 | 24.5 | 740 | 26.9 | 3.134 | 9.90 | 1.1400 | \(18 \pm 1\) |
| 4 | 24.5 | 790 | 34.7 | 4.263 | 9.41 | 1.451 | \(18 \pm 1\) |
| 4 | 24.5 | 830 | 56.9 | 8.418 | 9.07 | 2.125 | \(18 \pm 1\) |
potassium sulfate with a specific activity of 32 mCu/g, the action of accelerated electrons on the process under study begins to be observed.
Some factors affecting the rate of isotopic exchange in the \(\mathrm{K_2SO_4—SO_3}\) system were subjected to more detailed study. It might have been supposed that the presence in the \(\mathrm{K_2SO_4}\) preparation of chlorine ions, appearing in the process of decay of \(\mathrm{S^{35}}\), accelerates the exchange process in the \(\mathrm{K_2S^{*}O_4—SO_3}\) system. For
Fig. 2. Dependence of the rate constant of the isotopic-exchange reaction in the \(\mathrm{Na_2S^{*}O_4—SO_3}\) system on reciprocal temperature
Fig. 3. Dependence of \(\ln \dfrac{100}{100-W}\) on time in the isotopic-exchange reaction between \(\mathrm{Na_2S^{*}O_4}\) and \(\mathrm{SO_3}\)
checking this assumption, experiments were carried out with a potassium sulfate preparation whose specific activity was approximately 0.06 mCu/g and whose KCl content was 0.12%. The degree of isotopic exchange was 11.6% and thus proved to be practically the same as for a preparation without additives.
In studying the process of isotopic exchange in the \(\mathrm{K_2S^{*}O_4—SO_3}\) system we were interested in whether the value of the activation energy of the exchange reaction changes with an increase in the content of the radioactive isotope in the sulfate being studied. The use of \(\mathrm{K_2SO_4}\) in this case had to be abandoned, since the temperature at which the kinetics of the process could be studied exceeded \(1000^\circ\), which could lead to thermal dissociation of the salt. The necessary measurements of the kinetics of isotopic exchange were made for the \(\mathrm{Na_2S^{*}O_4—SO_3}\) system with sodium sulfate preparations of different radioactivity. The results of the measurements are presented in Table 2 and in Fig. 2.
Fig. 4. Change in the rate of isotopic exchange in the \(\mathrm{Na_2S^{*}O_4—SO_3}\) system
The activation energy was determined from the Arrhenius formula \(K = K_0 e^{-E/RT}\). The rate constant of the reaction was calculated from the formula \(\ln \dfrac{100}{100-W} = kt\), where \(W\) is the degree of exchange, \(t\) is the duration of the experiments, 10 min. The possibility of applying this equation is determined by the linear dependence of the left-hand side of the equality on time (Fig. 3). From the data presented it is seen that the mechanism of the isotopic-exchange reaction between \(\mathrm{Na_2S^{*}O_4}\) and \(\mathrm{SO_3}\) changes on going from preparations with specific activity of 0.02 and 1 mCu/g to 11 and 25 mCu/g.
The dependence of the rate of isotopic exchange in the \(\mathrm{Na_2S^{*}O_4—SO_3}\) system on the specific activity of \(\mathrm{Na_2SO_4}\) has the same character as in the \(\mathrm{K_2S^{*}O_4—SO_3}\) system. Sodium and potassium sulfates are similar in their nature. All this makes it possible to draw analogous conclusions for the mechanism of exchange in the \(\mathrm{K_2S^{*}O_4—SO_3}\) system.
The process of isotopic exchange of sulfur in the system we studied is clearly divided into two phases: during a short interval of time, on the order of 5 min.,
the exchange rate is very considerable—the exchange reaches 40%—and rapidly decreases. Here, evidently, exchange occurs in a thin surface layer of K₂SO₄. Then the exchange rate for each subsequent 5 min remains at an almost constant value of 10%, smaller than for the first 5 min (Fig. 4). In this case the rate of the process is evidently limited by diffusion of SO₄²⁻ ions in the solid phase.
Isotopic exchange between radioactive sulfur anhydride and stable potassium sulfate was also studied (Table 3). It was found that after 5 min of passage of sulfur anhydride, a constant value of the radioactivity of potassium sulfate is reached. The appearance of a relatively high concentration of S³⁵ atoms on the surface of the solid salt is undoubtedly the reason for the decrease in the exchange rate. Evidently, diffusion into the solid salt proceeds considerably more slowly than is observed for the escape of S³⁵ atoms from the solid phase into the gaseous phase during exchange of labeled K₂SO₄ with inactive SO₃.
Table 3
Isotopic exchange in the system K₂SO₄—\(\overset{*}{S}\)O₃ at 840°.
Charge of K₂SO₄ ≈ 0.28 g; initial activity of SO₃ 6.2 mCi/g
| Time of passage of \(\overset{*}{S}\)O₃, min | Amount of \(\overset{*}{S}\)O₃, g | Specific activity of K₂SO₄ after the experiment, mCi/g (average of 4 experiments) |
|---|---|---|
| 5 | 0.2881 | 0.28 |
| 10 | 0.5762 | 0.20 |
| 15 | 0.8643 | 0.28 |
| 20 | 1.1524 | 0.27 |
As is known, SO₃ at temperatures above 400° begins to dissociate with formation of SO₂. Therefore, isotopic exchange was studied in the system K₂\(\overset{*}{S}\)O₄—SO₂ with a specific activity of K₂SO₄ equal to \(5.9 \cdot 10^{-2}\) mCi/g, at different temperatures. Sulfurous gas, dried over CaCl₂ and conc. H₂SO₄, entered the reaction quartz tube at a rate of 13 l/hr and passed over a boat with labeled potassium sulfate. Then the remaining activity of K₂\(\overset{*}{S}\)O₄ was measured and the degree of isotopic exchange was calculated.
Table 4
Study of isotopic exchange of sulfur in the system K₂\(\overset{*}{S}\)O₄—SO₂ at different temperatures. Amount of SO₂ 0.6 g
| Temp., °C | Charge of K₂SO₄, g | Change in K₂SO₄ weight after experiment, % | Initial activity, imp/min | Activity of K₂SO₄ after experiment, imp/min | Activity of K₂SO₄ after experiment, % of initial | Degree of exchange, % |
|---|---|---|---|---|---|---|
| 600 | 0.3732 | −0.1 | \(1784 \cdot 10^3\) | \(1805 \cdot 10^3\) | 100.9 | |
| 600 | 0.3374 | +0.1 | \(1614 \cdot 10^3\) | \(1665 \cdot 10^3\) | 103.0 | |
| 600 | 0.3479 | −0.2 | \(1663 \cdot 10^3\) | \(1640 \cdot 10^3\) | 101.0 | |
| 600 | 0.3477 | −0.1 | \(1663 \cdot 10^3\) | \(1648 \cdot 10^3\) | 99.1 | |
| 700 | 0.3295 | −0.1 | \(1577 \cdot 10^3\) | \(1483 \cdot 10^3\) | 94.0 | 6.2 |
| 700 | 0.2900 | −0.2 | \(1388 \cdot 10^3\) | \(1307 \cdot 10^3\) | 94.2 | 6.9 |
| 700 | 0.3074 | −0.1 | \(1471 \cdot 10^3\) | \(1422 \cdot 10^3\) | 93.3 | 6.8 |
| 700 | 0.2732 | −0.1 | \(1308 \cdot 10^3\) | \(1237 \cdot 10^3\) | 94.6 | 7.5 |
| 840 | 0.3147 | — | \(1582 \cdot 10^3\) | \(1393 \cdot 10^3\) | 88.0 | 14.4 |
| 840 | 0.3373 | −0.1 | \(1696 \cdot 10^3\) | \(1527 \cdot 10^3\) | 90.0 | 13.1 |
| 840 | 0.3532 | −0.1 | \(1776 \cdot 10^3\) | \(1570 \cdot 10^3\) | 88.4 | 14.2 |
It has been established that sulfur exchange occurs at 700° and above. The rates of isotopic exchange at 840° in the systems K₂SO₄—SO₃ and K₂\(\overset{*}{S}\)O₄—SO₂ practically do not differ from one another.
Institute of Physical Chemistry
Academy of Sciences of the USSR
Received
10 XII 1959
CITED LITERATURE
- Vikt. I. Spitsyn, I. E. Mikhailenko, DAN, 121, 319 (1958).
- Vikt. I. Spitsyn, I. E. Mikhailenko et al., DAN, 131, No. 2 (1960).