Studies of the Operation of a Circulation Electrolyzer in the APN Method. Influence of Various Factors on the Electrolysis Constant

A. G. Stromberg, V. I. Kuleshov, A. V. Konkova

(Presented by the Scientific-Methodological Seminar of the KhTF)

In a number of works [1—6], one of us has shown theoretically that the sensitivity of the method of amalgam polarography with accumulation (APN) can be substantially increased by increasing the value of the electrolysis constant through more intensive stirring of the solution. A significant increase in the electrolysis constant was achieved by one of us with the aid of a circulation electrolyzer [7]. A distinctive feature of this electrolyzer is the presence of a capillary tube whose lower end is immersed in a vessel containing the solution under investigation. A mercury film electrode is placed inside the capillary; it consists of a silver wire (diameter 0.2 mm), at the end of which a (silver) ball is fused, which is then amalgamated. The second electrode is a saturated calomel electrode. During preliminary electrolysis the solution is set into reciprocating motion through the capillary tube by means of a pump driven by an electric motor. The circulation of the electrolyte is then stopped and the anodic polarogram is recorded. In this way it is possible to increase the sensitivity of the analysis by more than an order of magnitude and, with a short electrolysis time, to determine the content of an element in solution on the order of \(10^{-9}\) M and below. The aim of the present work is to study the influence on the electrolysis constant and on the volume of the circulating solution of the frequency and amplitude of the piston stroke, as well as of the diameter of the capillary tube and of the spherical electrode, in order to identify the optimum conditions for carrying out the preliminary electrolysis.

To determine the volume of the circulating solution, a graduated tube with divisions of 0.1 cm\(^3\) was soldered above the capillary.

Preliminary electrolysis was carried out under conditions of practically no depletion (less than 10%) of the solution in the lower vessel after electrolysis\(^1\). To calculate the effective electrolysis constant we used the formula [8]:

\[ K=\frac{\delta}{s c_1 t}\, I, \tag{1} \]

\(^1\) Only at the very largest values of the electrolysis constant did the degree of depletion become greater than 8%, as shown by the following approximate calculation. Taking \(K'_{1/2}=3\cdot10^3\) A·cm/equiv; \(s=2\cdot10^{-2}\) cm\(^2\); \(t=300\) sec; \(V=3\) ml, we obtain for the dimensionless parameter in [9]:

where \(l\) is the depth of the anodic tooth, \(a\); \(s\) is the electrode surface, \(\text{cm}^2\); \(c_1\) is the concentration of ions in solution, g-ion/\(\text{cm}^3\); \(t\) is the duration of electrolysis, sec; \(\delta'=\dfrac{q}{l}\) is the effective half-width of the tooth, sec; \(q\) is the area under the anodic tooth, coulomb. The quantities \(c_1\), \(t\), \(\delta'\) in all experiments in this work were constant and had the following numerical values: \(c_1=5\cdot10^{-8}\) g-ion/l Bi (3+) in \(0.25\,N\) HCl; \(t=300\) sec; \(\delta'=15\) sec.

The electrode surface was taken to be equal to the surface of the amalgamated silver bead (\(s=\pi d^2\), \(d\) being the bead diameter). A small part of the current during electrolysis also passes through the amalgamated silver wire, to the end of which the bead is fused. But when recording the anodic polarogram, the solution meniscus in the capillary is located only slightly above the amalgamated bead, and therefore only the metal deposited on the bead participates in the anodic process.

The electrolysis constant calculated by formula (1) is an effective one and differs from the true value, since in the solution flowing through (through the gap between the capillary wall and the electrode surface) the concentration of the solution may differ noticeably from the initial concentration because of depletion of the solution. However, for analytical purposes it is precisely the effective electrolysis constant, calculated by formula (1), that is significant.

The constant values of the experimental conditions (apart from the factor whose influence was being studied) were as follows: piston-stroke frequency \(f=40\) strokes/min; piston-stroke amplitude \(l=2\) cm; capillary diameter \(D=1\) mm; spherical electrode diameter \(d=0.50\), 0.87, and 0.95; solution volume 3 ml; electrolysis duration \(t=5\) min; electrolysis potential \(-2\) volts (vs. S.C.E.).

Four series of experiments were carried out on the influence of various factors on the electrolysis constant \(K\) and the volume of solution \(V\) flowing through the capillary (per one piston stroke).

1. Influence of the piston-stroke frequency in the range 10–140 strokes/min (Fig. 1).
2. Influence of the piston-stroke amplitude in the range 1–3 cm (Fig. 2).
3. Influence of the capillary diameter in the range 1–2 mm (Fig. 3).
4. Influence of the diameter of the spherical film electrode in the range 0.5–0.95 mm (Fig. 4).

As can be seen from Fig. 1, with increasing piston-stroke frequency the values of \(K\) at first increase rapidly, but at \(f=40\) strokes/min they reach a maximum value (\(K=35\cdot10^3\) A·cm/g-eq and do not increase).

From Figs. 3 and 4 it is evident that, as the gap between the electrode and the capillary wall increases due to an increase in the capillary diameter, the electrolysis constant \(K\) decreases, although the volume of solution \(V\) increases; while when the gap between the electrode and the capillary increases due to a decrease in the diameter of the spherical electrode, \(K\) increases simultaneously with \(V\). Thus, with a change in \(D\) or \(d\) there is no

\[ b=\frac{K}{zF}\,s\,\frac{t}{V}=0.24 \]

and for the degree of depletion

\[ \gamma=1-e^{-b}=0.2. \]

The value of the electrolysis constant taking depletion into account is then [8]:

\[ K_{1/z}=K'_{1/z}\,\frac{2.3}{\gamma}\lg\frac{1}{1-\gamma^3} =32\cdot10^3\ \text{A·cm/g-eq}, \]

i.e., the error is small (8%).

Fig. 1. Dependence of the electrolysis constant (curves 1, 2) and of the volume of solution passed in one cycle (curves 3, 4) on the piston-stroke frequency. Curves 1 and 3—electrode diameter \(d=0.4\) mm; curves 2 and 4—\(d=0.87\) mm. Experimental conditions: capillary diameter \(D=1\) mm; piston-stroke amplitude \(l=2\) cm. Other experimental conditions are indicated in the text.

Fig. 2. Dependence of the electrolysis constant (curve 1) on the amplitude of the piston stroke. Experimental conditions: piston-stroke frequency \(f=40\) strokes/min; \(D=1\) mm; \(d=0.87\) mm.

Fig. 3. Dependence of the electrolysis constant on the capillary diameter. Experimental conditions: \(f=40\) strokes/min; \(d=0.87\) mm; \(l=2\) cm.

Fig. 4. Dependence of the electrolysis constant (curve 1) and of the volume of solution passed in one cycle (curve 2) on the electrode diameter. Experimental conditions: \(f=40\) strokes/min; \(D=1\) mm; \(l=2\) cm.

Fig. 5. Dependence of the electrolysis constant on the linear rate of flow of the solution through the capillary. Curve 1—\(d=0.0\) mm; 2—0.87 mm (open circles); 3—0.9 mm (solid circles). Experimental conditions: \(l=2\) cm; \(D=1\) mm. The volume of solution passed was varied by changing the piston-stroke frequency.

an unambiguous dependence of \(K\) and \(\dot V\) on the gap width \(\frac{1}{2}(D-d)\), and the absolute magnitude of \(D\) and \(d\) is also of importance.

From the experiments carried out it follows that the maximum value of the electrolysis constant in the investigated range of variation of \(f, l, D, d\) is equal to \(35 \cdot 10^3\ \mathrm{a \cdot cm/g\text{-}eqv}\), the optimum conditions being: \(f = 40\) strokes/min; \(l = 2\ \mathrm{cm}\); \(D = 1\ \mathrm{mm}\); \(d = 0.5\ \mathrm{mm}\). In this case \(\dot V = 1.5\ \mathrm{ml/stroke}\).

At these optimum values of \(f, l, D, d\), experiments were carried out to determine the minimum determinable concentration of \(\mathrm{Bi}(3+)\) against a background of \(0.25\,N\ \mathrm{HCl}\).

With an electrolysis duration \(t = 10\ \mathrm{min}\) and practically half-depletion of the solution, an anodic bismuth peak was obtained in a solution with a concentration of \(5 \cdot 10^{-10}\ \mathrm{g\text{-}ion/l}\ \mathrm{Bi}(3+)\), 32 mm deep at the maximum sensitivity of the polarograph, \(1 \cdot 10^{-9}\ \mathrm{a/mm}\).

Conclusions

1. Using as an example a solution of \(5 \cdot 10^{-8}\ \mathrm{g\text{-}ion/l}\ \mathrm{Bi}(3+)\) in \(0.25\,N\ \mathrm{HCl}\), the influence of the frequency and amplitude of the piston stroke, and of the diameter of the capillary and the spherical mercury film electrode, on the effective electrolysis constant in circulation electrolysis was studied.

2. It was shown that, under the conditions studied, the maximum value of the electrolysis constant obtained is about \(35 \cdot 10^3\ \mathrm{a \cdot cm/g\text{-}eqv}\), which is almost an order of magnitude greater than the value of the electrolysis constant obtained with ordinary mechanical stirring of the solution.

3. It was shown that the minimum determinable concentration of \(\mathrm{Bi}(3+)\) under the selected optimum conditions, using circulation electrolysis, is about \(5 \cdot 10^{-10}\ \mathrm{g\text{-}ion/l}\) with an electrolysis duration of 10 min and a polarograph sensitivity of \(10^{-9}\ \mathrm{a/mm}\).

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