THE SOLUBILITY COEFFICIENT OF RADON IN FISH OIL AND IN SOME VEGETABLE OILS

A. D. Shchelokov

1. Introduction

According to the literature, the solubility of radon is known for only 35–40 liquids and was investigated mainly in 1900–1910, over a temperature range of approximately from \(-20^\circ\text{C}\) to \(+60\)–\(80^\circ\text{C}\); moreover, for liquids—oils and fats—the solubility coefficient of radon has been studied for only 5–6 names, among which there are no liquids investigated in the present work.

In this work the solubility coefficient of radon in fish oil and in some vegetable oils was determined at room temperature and normal atmospheric pressure. The question is of interest for physical chemistry in the study of the solubility of small quantities of gas in liquids, and also for practical purposes in medicine.

2. Measurement Method

As the coefficient of solubility of radon in a liquid, the Ostwald absorption coefficient \(\lambda\) was adopted in this work, i.e., the ratio of the concentration of radon in the liquid \(c_{\text{ж}}\) to the concentration of radon in the air \(c_{\text{в}}\) above the liquid in the case of dynamic equilibrium, i.e.,

\[ \lambda=\frac{c_{\text{ж}}}{c_{\text{в}}} \quad \text{or} \quad \lambda=\frac{q_{\text{ж}} v_{\text{в}}}{q_{\text{в}} v_{\text{ж}}}, \tag{1} \]

where \(q_{\text{ж}}\) and \(q_{\text{в}}\) are the amounts of radon in the liquid and in the air;
\(v_{\text{ж}}\) and \(v_{\text{в}}\) are the volumes of the liquid and gaseous phases.

Determination of the value \(\lambda\) was reduced to determining the concentration of radon in the air above the liquid in a closed vessel after a certain time had elapsed from the moment when a known quantity \(Q\) of radon, taken from a standard, was introduced into this vessel. For this purpose, the vacuum method proposed by E. S. Shchepot’eva [1] was used mainly.

The amount of radon in the volume of air taken for determining \(c_{\text{в}}\) was determined with the universal GK instrument. The instrument had previously been calibrated against the RIAN standard, which gave an instrument constant equal to

\[ a = 1.13 \cdot 10^{-10}\ \frac{\text{curie}}{\text{div}/\text{min}} . \]

Determination of \(\lambda\) for the liquid under investigation was carried out by the following procedures.

I method. Taking radon from the standard

The liquid under investigation was placed in the Drechsel bottle \(B\) (see Fig. 1). Bottle \(A\) remained empty (air). A standard \(E\), with an amount of radon known by the time of the experiment and equal to \(Q\), was connected to them. The air from bottles \(A\) and \(B\) was pumped out to a pressure of \(1\)—\(1.5\) mm Hg with the stopcocks \(K_1\) and \(K_2\) closed. In this process the air previously dissolved in the liquid was also removed (degassing of the liquid). Then stopcock \(K_1\) was closed, stopcock \(K_2\)

Fig. 1

was opened, and stopcock \(K_1\) was opened slightly enough that atmospheric air passed through the standard solution in not very frequent bubbles. When the pressure in vessels \(A\) and \(B\) became equal to atmospheric pressure, stopcock \(K_2\) was closed and the standard \(E\) was disconnected from the bottles. In this operation practically all the radon was transferred from the standard into bottles \(A\) and \(B\).

II method. Circulation and dissolution of radon in the liquid

Bottles \(A\) and \(B\) were connected by rubber tubes with two one-way valves \(K_{\ell 1}\) and \(K_{\ell 2}\) and a rubber bulb into a closed circuit (Fig. 2). With the aid of bulb \(G\) and the valves, with stopcocks \(K_2\), \(K_3\), and \(K_4\) open, circulation of air with radon was produced in the vessels through the liquid under investigation.

Fig. 2

In this process the radon was absorbed by the liquid and its amount in the air decreased. After the time necessary for the establishment of dynamic equilibrium between \(c_l\) and \(c_v\), circulation was stopped,

the cocks \(K_2\) and \(K_3\) were closed, and flask \(A\) was disconnected from the apparatus. It is obvious that after this the radon concentration in the air volumes of flasks \(A\) and \(B\) will be the same.

III. Determination of the radon concentration in the air

Vessel \(A\), containing a certain amount of radon, was connected through the dryer \(O\) to the ionization chamber \(K\) of the universal GK instrument (Fig. 3). With cocks \(K_2\) and \(K_3\) closed and cocks \(K_5\) and \(K_6\) open, the chamber with the dryer was evacuated to a pressure of 1–1.5 mm Hg through cock \(K_6\), after which cock \(K_6\) was closed. Then cocks \(K_3\) and \(K_2\) were opened, and the air

Fig. 3

with radon from vessel \(A\) passed into chamber \(K\) and was supplemented to atmospheric pressure (in the chamber) by a considerably larger amount of atmospheric air, which “washed out” the remaining radon from the dryer and vessel \(A\). Cock \(K_5\) was then closed. Next, from the rate of fall of the electrometer leaf, the amount of radon in vessel \(A\), i.e. \(q_A\), was determined, and, consequently, the concentration of radon in the air \(c_v\), which is obviously equal to

\[ c_v=\frac{q_A}{V_A}=\frac{a\alpha'_{\max}}{V_A}, \tag{2} \]

where \(a\) is the instrument constant in \(\dfrac{\text{curies}}{\text{div}/\text{min}}\);

\(V_A\) is the volume of vessel \(A\), in liters,

\(\alpha'_{\max}\) is the maximum (i.e., 3 hours after the introduction of radon into the chamber) rate of fall of the electrometer leaf, in \(\text{div}/\text{min}\), caused by the radon in the chamber.

Knowing \(c_v\), it is easy to calculate also \(c_{\text{liq}}\):

\[ c_{\text{liq}}=\frac{q_{\text{liq}}}{V_{\text{liq}}} =\frac{Q_{\text{cr}}}{V_{\text{liq}}} -\frac{a\alpha'_{\max}}{V_{\text{liq}}V_A} \left(V_A+V_B+v-V_{\text{liq}}\right), \tag{3} \]

where \(V_{\text{liq}}\) is the volume of liquid, in liters,
\(V_B\) is the volume of vessel \(B\), in liters,
\(v\) is the volume of the bulb, valves, and connecting tubes, in liters.

Substituting the values \(C_{\mathrm{в}}\) and \(C_{\mathrm{ж}}\) from (2) and (3) into (1), we obtain the final value of the coefficient \(\lambda\) of the solubility of radon in the liquid under investigation at the temperature of the experiment:

\[ \lambda=\frac{Q k_p V_A}{a\alpha'_{\max} V_{\mathrm{ж}}}-\frac{V_A+V_{\mathrm{в}}+v}{V_{\mathrm{ж}}}+1 . \tag{4} \]

Here \(k_p\) is a coefficient that takes into account the decay of radon over the interval of time between the moment when the radon is taken from the standard and the moment when the radon is introduced into the ionization chamber, i.e., over the time of dissolution of radon in the liquid. \(k_p\) is taken from tables of radon decay.

The maximum deflection \(\alpha'_{\max}\) of the instrument, corresponding to the ionization current 3 hours after the introduction of radon into the chamber, was usually determined not after 3 hours, but from several values of the deflection \(\alpha'_i\), corresponding to different time intervals (within one hour), counted from the moment of introduction of radon into the chamber, using the Duane–Nörenberg tables. And from the several obtained values \(\alpha'_{\max,i}\) the mean value \(\alpha'_{\max}\) was found.

The amount of radon \(Q\) was determined from the time of its accumulation in the standard, according to the corresponding tables.

3. Results of measurements

The coefficient of solubility of radon was determined for fish oil, cottonseed, soybean, and fir oils. Before dissolving radon, the liquids were preliminarily degassed under vacuum at \(1\)—\(1.5\) mm Hg for 10—30 min. The duration of dissolution was taken to be different—from tens of minutes to a day, and in some cases even longer, in order

Fig. 4

to determine the time required for the establishment of dynamic equilibrium in the distribution of radon between the two phases, which proved to be of the order of one hour. The temperature of the experiments was room temperature, i.e. \(12\)—\(20^\circ\mathrm{C}\), and the pressure was atmospheric.

The results of measurements of \(\lambda\) are given in Tables 1, 2, 3, 4 and are presented graphically in Fig. 4, as an approximate dependence of \(\lambda\) on temperature (the problem of investigating the dependence of \(\lambda\) on temperature was not yet posed, but is planned for the future).

Table 1

Fish oil

Table 2

Cottonseed oil

Table 3

Soybean oil

Table 4

Fir oil

Table 5

Mean values of the radon solubility coefficients

The experiments showed the following:

1) The coefficient of radon solubility in fish oil, soybean, cottonseed, and fir oils is 2–3 times lower than in strong radon solvents—olive oils [3]—and 40–50 times higher than in water. These liquids may be assigned to the group of intermediate radon solvents, such as vaseline, turpentine, etc.

2) The solubility coefficient of these liquids, as of all other liquids [2], decreases with increasing temperature.

3) The rate of dissolution of radon in them is different: of the order of 2–3 hours for fish oil and not more than 1 hour for all the others, i.e., with increasing viscosity the dissolution time increases.

The large scatter of points on the graph for fish oil (Fig. 4) can be explained by the following probable causes:

a) different dissolution times of radon in different experiments;

b) different grades of fish oil;

c) somewhat different experimental conditions.

The points lying closer to the dashed line “ab” were obtained with dissolution times of more than one hour. They may be considered to satisfy the condition of dynamic equilibrium in the distribution of radon between the two phases. The points lying closer to the dashed line “vg,” however, were obtained with dissolution times of 16–30 min, and they gave values of \(\lambda\) smaller than the former ones (if one takes into account, on the basis of other graphs, the increase of \(\lambda\) with decreasing temperature). Apparently, they do not satisfy the equilibrium condition.

From the arrangement of the points for fish oil, among other things, a tendency is noticeable for radon dissolution to accelerate as the temperature is raised (obviously owing to the decrease in viscosity).

It should be pointed out that the mean values of \(\lambda\) obtained should be regarded as approximate for room temperature, since even in such a small temperature interval, 12–20°C, \(\lambda\) depends to a considerable extent on temperature.

It should also be noted that in the present work the solubility coefficient (more precisely, Ostwald’s absorption coefficient) was determined not under conditions of saturation of the solvent with radon, but under conditions of negligibly small amounts of radon, namely, of the order of \(10^{-17}\)—\(10^{-18}\) gram-moles of radon per 100–150 ml of solvent.

REFERENCES

1. Shchepot’eva E. S. Vacuum method for measuring the radon content in waters and gases, Reports of the Academy of Sciences of the USSR, vol. XII, No. 4, pp. 178–180, 1943.
2. Eremina B. G. Solubility of Monatomic Gases and Nitrogen, Leningrad, p. 27, 1950.
3. Technical Encyclopedia, reference book, vol. V, pp. 421–422, 429, 1930.