ON THE EVALUATION OF THE ACCURACY OF A VISUAL-COLORIMETRIC METHOD FOR DETERMINING MICROCONCENTRATIONS OF OXYGEN IN NITROGEN

V. Ya. Dubrovinskii, R. P. Elikova

To determine small concentrations of oxygen in gases, various variants of the colorimetric method are most often used, based on the easy oxidizability of the cuprous ion in ammoniacal solutions. Although some of these methods have been adopted as certification methods [1], information on their accuracy is highly contradictory, which makes it necessary to treat the evaluation of the results obtained with caution.

Using our experimental data as an example, we wish to show some possible reasons for obtaining different estimates of the accuracy of measurements of oxygen microconcentrations by the visual-colorimetric method in Mugdana-type instruments [2].

Since, at microconcentrations of oxygen in nitrogen, the volume of oxygen is much smaller than the volume of nitrogen, calculation of the analysis result is carried out according to the formula:

\[ C = \frac{V_{\mathrm{O}_2}}{V_{\mathrm{N}_2}}\cdot 100\% \text{ by volume.} \tag{I} \]

Carrying out the analysis by the static method in Mugdana-type instruments amounts to comparing the color of the absorbing solution placed in the instrument with the colors of the standard scale solutions before and after absorption of oxygen from the analyzed volume of the gas mixture \((V_{\mathrm{N}_2}\), the volume of the instrument):

\[ V_{\mathrm{O}_2}=V_{\mathrm{p-pa}}\cdot t, \tag{II} \]

where \(V_{\mathrm{p-pa}}\) is the volume of absorbing solution in the instrument, ml;
\(t\) is the change in oxygen concentration in the absorbing solution, calculated from the results of colorimetry, ml \(O_2\)/ml of absorbing solution.

Taking (II) into account, formula (I) takes the form

\[ C=\frac{V_{\mathrm{p-pa}}\cdot t}{V_{\mathrm{N}_2}}\cdot 100\% \text{ by volume.} \tag{III} \]

The quantities \(t\) and \(V_{\mathrm{N}_2}\) are related to each other in such a way that an increase in \(V_{\mathrm{N}_2}\) leads to an increase in \(t\). Taking this into account, formula (III) should be given the form

\[ C=\varepsilon\cdot V_{\mathrm{p-pa}}\,100\% \text{ by volume,} \tag{IV} \]

where the quantity \(\varphi=\dfrac{t}{V_{\mathrm{N}_2}}\) has the meaning of the amount of oxygen that can be recorded during colorimetry, per unit volume of the gas being analyzed—a kind of “colorimetric output” of the instrument.

The total root-mean-square error in calculating the oxygen concentration by formula (IV), estimated in the usual way, is:

\[ \sigma^{2}=C^{2}\left[\left(\frac{\Delta\varphi}{\varphi}\right)^{2}+ \left(\frac{\Delta V_{\mathrm{r-ra}}}{V_{\mathrm{r-ra}}}\right)^{2}\right]. \tag{V} \]

According to this formula (V), the quantity \(\sigma\) is related to the value of the detected concentration \(C\), the relative error in measuring the volume of the absorbing solution, and also the relative error in calculating the “colorimetric output” of the instrument. The principal role in forming the error of the analysis result is played by the quantity \(\dfrac{\Delta\varphi}{\varphi}\), since the error introduced by measuring the volume of the absorbing solution can be neglected because of its smallness (0.3% relative for KLP II, class).

The error in calculating the quantity of the instrument’s “colorimetric output” depends, as is seen from the relations given above, on the volume of the instrument used and on the resolving power of the colorimetric scale; by the latter is meant the magnitude of the step of the standard scale and the convenience with which the eye can reliably notice changes in the color of the absorbing solution during colorimetry.

Table 1

*) The analysis was carried out at the sensitivity limit of the instrument.

Below (Table 1) are given experimental results on the effect of the capacity of the instrument and the magnitude of the detected concentration \(C\) on the limiting value of the root-mean-square error of the analysis result \(\sigma\) (for the transition from \(S_n=\sqrt{\dfrac{\sum \Delta^{2}}{n-1}}\) to the value \(\sigma\) by the formula \(\sigma \leq S_n(1+g)\), tabulated data [3] were used at \(\alpha=0.95\)). The colors of the absorbing solution were compared with a scale of standards prepared according to Table 2. The colors of the solution before absorption corresponded to standards 2–4.

The results presented show that the error in determining oxygen decreases as the volume of the instrument is increased. Increasing the detected oxygen concentration reduces the error of the analysis result, which would seem to contradict the cited

formula (V), but is easily explained if one takes into account that the values of the “colorimetric yield” do not remain constant in going from lower concentrations to higher ones, since the increase in oxygen concentration makes it necessary to carry out colorimetry in the region of higher color intensities of the absorbing solution, which leads to large errors in determining \(t\) and, correspondingly, \(\varphi\). The predominant change in the error of the analysis result in the noted direction indicates that the main component of the error of the colorimetric method consists of the causes that produce a change in the “colorimetric yield” of the instrument.

Table 2

SCALE OF STANDARD SOLUTIONS

The quantity of 0.05 N CuSO\(_4\) solution indicated in the table was introduced into a 3% NH\(_4\)OH solution

Our results show that describing the accuracy of colorimetric measurements necessarily requires information on the design features of the instrument, as well as the characteristics of the standard scale used; without this, comparison of results obtained by different laboratories is impossible.

REFERENCES

1. E. M. Malkova, T. L. Radovskaya. Methods for certification of calibration gas mixtures. Izmeritel’naya tekhnika, 5, 1963.
2. Mugdan M., Sixt J., Angew. Chemie 46, 5, 90, 1933.
3. L. Rumshiskii. Elements of Probability Theory. Moscow, 1965.