Effect of the Size of a Hanging Mercury Drop on Its Active Surface in Extraction Anodic Stripping Polarography
Abstract Generated abstract
This study examines how the size of a hanging mercury drop affects its active electrode surface in extraction anodic stripping polarography, with attention to possible shielding by the platinum contact and the influence of surface active complexing agents. Effective surface areas were determined from oscillographic current, time curves under conditions approximating linear diffusion, using copper in an oxine, chloroform, ammonium nitrate, methanol medium and lead and thallium in a dithizone based medium, then compared with geometrical surfaces calculated for spherical drops or spherical segments. The results indicate that, under the studied conditions, the active surface is about 85 to 87% of the calculated surface for copper and lead, while for thallium it is close to 100%, suggesting that the active fraction depends on the metal and its response to surface active substances.
Full Text
EFFECT OF THE SIZE OF A HANGING MERCURY DROP ON ITS ACTIVE SURFACE IN THE EXTRACTION APN METHOD
Yu. A. Karbainov, A. G. Stromberg
In connection with the development of the extraction APN method, comparison of the working surface (effective) and the calculated surface of a mercury drop is of great interest.
On the one hand, it may be assumed that part of the surface of a mercury drop suspended on a platinum contact of a certain diameter (sealed into a glass tube) will be shielded. On the other hand, in the extraction APN method, where the behavior of elements in nonaqueous media is studied in the presence of various complexing agents—particularly oxine, dithizone, sodium diethyldithiocarbamate, etc.—it is important to evaluate the role of the latter as surface-active substances.
Clarification of the indicated causes makes it possible to judge with what accuracy, in calculations, a mercury drop suspended on a platinum contact can be replaced by an ideal sphere.
The effect of the size of a mercury drop on its active surface was studied using copper as an example in a nonaqueous medium: 1% oxine in chloroform + 0.2 N NH₄NO₃ in methanol; thallium and lead—in a nonaqueous medium: 5·10⁻³% dithizone in chloroform + 0.2 N NH₄NO₃ in CH₃OH.
The effective surface was determined by recording an \(i \sim \tau\) curve on an oscillographic polarograph over such a time interval that the diffusion front moved only a small distance away from the surface of the mercury drop and diffusion could thus be considered linear. In this case, for calculating the effective surface, the equation [1] can be used:
\[ i = zF \cdot S \cdot D_i^{1/2} \cdot C \cdot \frac{1}{\sqrt{\pi \tau}}, \tag{1} \]
\(i\) — current in amperes, the value of which at the given moment of time is calculated from the \(\tau\) curve;
\(z\) — number of electrons participating in the electrode process;
\(F\) — Faraday number, 96500 coul.;
\(S\) — effective surface of the electrode;
\(D_i\) — diffusion coefficient, cm²/sec.;
\(C\) — concentration of metal ions in solution, mol/l;
\(\tau\) — time, sec.;
If a plot is constructed in the coordinates \(i \sim f(1/\tau^{1/2})\), then the angular coefficient of the straight line in these coordinates, proceeding from equation (1), will be equal to:
\[ \tan \nu=\frac{zF\cdot D_i^{1/2}\cdot C}{\pi^{1/2}}\cdot S. \]
From this expression, knowing \(D_i\) and determining the value of \(\tan \nu\) graphically, one can calculate the effective surface \(S\). The effective surface was determined using lead and thallium as examples for the cathodic process, and copper as an example for the cathodic and anodic processes. Accumulation during recording of a single anodic \(i \sim \tau\) curve was carried out with an OH-101 Hungarian polarograph. The concentration of metal atoms in mercury was calculated from the area under the anodic peak according to the formula
\[ C_2=\frac{q}{zF\cdot V_k}, \]
where \(q\) is the area under the anodic peak, coul;
\(V_k\) is the volume of the mercury drop, \(\mathrm{cm^3}\).
In studying cathodic currents, the values of the diffusion coefficients for \(\mathrm{Cu}^{2+}\) were taken as, respectively: \(3.02\cdot 10^{-6}\), \(2.4\cdot 10^{6}\), and \(5.45\cdot 10^{-6}\ \mathrm{cm^2/sec}\); in studying anodic currents, the value of the diffusion coefficient of copper in mercury was taken as \(0.93\cdot 10^{-5}\ \mathrm{cm^2/sec}\) [2].
The experimental procedure was as follows. One of the above-mentioned background solutions is prepared. On an oscillographic polarograph, an \(i \sim \tau\) background curve is recorded at a definite potential value (in our case, in the study of \(\mathrm{Cu}(2+)\), \(\varphi_{\mathrm{br}}=-0.7\); \(\mathrm{Pb}(2+)\) and \(\mathrm{Tl}(+)\), \(\varphi_{\mathrm{br}}=-0.8\) V relative to mercury at the bottom). An addition of a standard solution of one of the elements under study, of precisely known concentration, is introduced into the background solution, and an \(i \sim \tau\) curve is recorded. The curves are photographed on film (we used film with a sensitivity of 90 units according to GOST). Measurements on the negative film were made with an MIR-2 microscope. When recording the anodic \(i \sim \tau\) curve, the cell was switched to the recording polarograph; accumulation was carried out for a definite interval of time at a potential of \(-1.0\) V (relative to mercury at the bottom). Then it was again switched to the oscillographic polarograph and the anodic \(i \sim \tau\) curve was recorded at a potential of \(-0.1\) V. After this the accumulation of metal was repeated: the anodic peak was recorded on the recording polarograph, and the area under the peak was calculated, from which the concentration of the metal in the drop was determined. The concentrations of copper, lead, and cadmium in the solution were, respectively, \(2\cdot 10^{-3}\), \(2\cdot 10^{-3}\), and \(1.66\cdot 10^{-3}\ \mathrm{mol/l}\). To eliminate the influence of the platinum wire (in our case the contact diameter was \(0.15\ \mathrm{mm}\)) on the diffusion conditions inside the drop, the contact was polished “flush.” The geometrical surface of the mercury drop was calculated by two methods. In the first method, the surface of a sphere of known volume was taken as the geometrical surface of the mercury drop, on the basis of the formulas:
\[ V=\frac{m}{d}, \]
\[ S=4\pi\cdot r^2, \tag{5} \]
\(m\) is the weight of the mercury droplet in grams;
\(d\) is the density of mercury in \(\mathrm{g/cm^3}\).
In the second method, the surface was calculated by the formula for a spherical segment:
\[ S=\pi/4\,(c^2+4h^2), \tag{6} \]
where \(c\) is the base of the drop (contact diameter);
\(h\) is the height of the segment.
The height was found as follows [3]: by the formula
\[ V=\frac{q}{13,6}, \tag{7} \]
where \(q\) is the amount of mercury in grams deposited on the contact during the time \(\tau\); the volume of the drop in \(\mathrm{cm}^3\) is calculated. Here the quantity \(q\) is determined from the formula
\[ q=a \cdot I \cdot \tau, \]
where \(I\) is the electrolysis current, amperes; \(\tau\) is the electrolysis time, sec; \(a\) is the electrochemical equivalent (for \(\mathrm{Hg}_2^{2+}\), \(a=2,079\ \mathrm{mg}/\mathrm{A\text{-}sec}\) (4). After this, having determined the volume of the drop and knowing the base of the segment \(c\), by the formula
\[ V=\pi h\left(\frac{c^2}{8}+\frac{h^2}{6}\right) \tag{9} \]
Table 1
| Element | \(V\cdot 10^{1)}\), \(\mathrm{cm}^3\) | \(S\cdot 10^{2)}\), \(\mathrm{cm}^2\) | \(S\cdot 10^{3)}\), \(\mathrm{cm}^2\) | \(S_{\mathrm{k}}\cdot 10^{4)}\), \(\mathrm{cm}^2\) | \(S_{\mathrm{a}}\cdot 10^{5)}\), \(\mathrm{cm}^2\) | \(S_{\mathrm{k}}/S\) |
|---|---|---|---|---|---|---|
| Cu (2+) | 0,180 | 0,294 | 0,360 | 0,288 | 0,284 | 0,80 |
| Cu (2+) | 0,710 | 0,730 | 0,770 | 0,640 | 0,640 | 0,83 |
| Cu (2+) | 1,380 | 1,140 | 1,230 | 0,935 | 0,936 | 0,76 |
| Cu (2+) | 2,160 | 1,530 | 1,620 | 1,470 | 1,457 | 0,91 |
| Cu (2+) | 3,00 | 1,910 | 1,970 | 1,690 | 1,680 | 0,86 |
| Cu (2+) | 3,580 | 2,140 | 2,230 | 1,830 | 1,830 | 0,82 |
| Cu (2+) | 4,530 | 2,520 | 2,600 | 2,280 | 2,280 | 0,88 |
| Cu (2+) | 6,160 | 3,080 | 3,100 | 2,800 | 2,795 | 0,90 |
| Pb (2+) | 0,180 | 0,294 | 0,360 | 0,314 | — | 0,87 |
| Pb (2+) | 0,710 | 0,730 | 0,770 | 0,700 | — | 0,91 |
| Pb (2+) | 1,380 | 1,140 | 1,230 | 0,985 | — | 0,80 |
| Pb (2+) | 2,160 | 1,530 | 1,620 | 1,360 | — | 0,84 |
| Pb (2+) | 3,00 | 1,910 | 1,970 | 1,620 | — | 0,82 |
| Pb (2+) | 3,580 | 2,140 | 2,230 | 2,010 | — | 0,90 |
| Pb (2+) | 4,530 | 2,520 | 2,600 | 2,210 | — | 0,85 |
| Pb (2+) | 6,160 | 3,080 | 3,100 | 2,580 | — | 0,83 |
| Tl (+) | 0,180 | 0,294 | 0,360 | 0,431 | — | 1,2 |
| Tl (+) | 0,710 | 0,730 | 0,770 | 0,785 | — | 1,02 |
| Tl (+) | 1,380 | 1,140 | 1,230 | 1,226 | — | 0,998 |
| Tl (+) | 2,160 | 1,530 | 1,620 | 1,770 | — | 1,10 |
| Tl (+) | 3,00 | 1,910 | 1,970 | 1,905 | — | 0,97 |
| Tl (+) | 3,580 | 2,140 | 2,230 | 2,200 | — | 0,99 |
| Tl (+) | 4,530 | 2,520 | 2,600 | 2,840 | — | 1,08 |
| Tl (+) | 6,160 | 3,080 | 3,100 | 3,100 | — | 1,00 |
1) volume of the mercury drop; 2) surface according to formula (5); 3) surface according to formula (9); 4) cathodic active surface \(S_{\mathrm{k}}\); 5) anodic active surface, \(S_{\mathrm{a}}\).
By selection, the value of $h$ is found and the surface area of the mercury drop is calculated from formula (6). The data from the study of the effective surface area of a mercury drop as a function of different values of its radii for copper, lead, and thallium on various backgrounds are summarized in Table 1.
Each value given in this table is the average of two or three measurements.
It is evident from the table that the ratio of the active surface area of the mercury drop to the actual surface area in the case of thallium is close to unity, whereas in the case of copper and lead this ratio averages 0.85–0.87. The difference in the ratios of the active surface area calculated from the time dependence of the anodic current and of the cathodic current in the case of copper, and of the cathodic current in the case of thallium and lead, to the spherical surface area of the mercury drop obtained in our experiments (0.85–0.87 and 1.00) can apparently be explained by the fact that, other conditions being constant, the fraction of the active surface area of the mercury drop depends on the nature of the metal and its resistance to the action of surface-active substances.
Conclusions
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The effect of the size of a hanging mercury drop on its active surface area in the extraction APN method was studied using Cu(2+) as an example in the system 1% oxine in $\mathrm{CHCl_3} + 0.2N\ \mathrm{NH_4NO_3}$ in $\mathrm{CH_3OH}$ (1 : 1), and using Pb(2+) and Tl(+) as examples in the system $5 \cdot 10^{-3}\%$ dithizone in $\mathrm{CHCl_3} + 0.2N\ \mathrm{NH_4NO_3}$ in $\mathrm{CH_3OH}$ (1 : 1).
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It was shown that the fraction of the active surface area of a hanging mercury drop under the conditions studied is 85–87% in the case of Cu(2+) and Pb(2+), and 100% in the case of Tl(1+), and depends on the nature of the metal and its resistance to the action of surface-active substances.
References
- P. Delahay. New Instruments and Methods in Electrochemistry, IL, Moscow, 1957.
- E. A. Zakharova. Candidate’s dissertation, Tomsk, 1965.
- A. G. Stromberg, V. Z. Bashkatov. Proceedings of the Tomsk Polytechnic Institute (in press).
- Concise Handbook of the Chemist, Academy of Sciences of the USSR, 1962.