STUDIES TO ELUCIDATE ADSORPTION, DESORPTION, AND HYDROLYSIS FROM \(10^{-8}\)—\(10^{-10}\) M SOLUTIONS IN THE APN METHOD BY THE VALUE OF THE ELECTROLYSIS CONSTANT

A. A. Kaplin, A. G. Stromberg, A. N. Pokrovskaya

(Presented by the scientific-methodological seminar of the Department of Analytical Chemistry)

The electrolysis constant \(\kappa_1\), used earlier in theoretical calculations on increasing the sensitivity of the method of amalgam polarography with accumulation (APN) [1–4], serves as a comparative characteristic of the intensity of delivery of a substance to the electrode when the solution is stirred by various methods [5] and is one of the basic quantities in computational APN [6]. Below, one more possible application of the electrolysis constant in the APN method is proposed.

The current of electroreduction of the ion being determined in solution \((i,\ a)\) is related to the concentration of ions in solution \((c_1\ \text{g-ion}/\text{cm}^3)\) by the relation

\[ i = \kappa_1 S c_1, \tag{1} \]

and the area under the anodic peak \((q,\ \text{coulomb})\)—in the absence of depletion of the solution—is related to the concentration of ions in solution by the relation:

\[ q = \kappa_1 S \tau c_1, \tag{2} \]

where \(S\) is the electrode surface, \(\text{cm}^2\); \(\tau\) is the electrolysis time, sec [1]; \(\kappa_1\) is the coefficient of proportionality between the concentration of ions in solution and the electrolysis current or the area under the anodic peak and does not depend on the concentration of ions in solution (with other conditions constant). Therefore, determined from the area under the anodic peak from the expression

\[ \kappa_1 = \frac{q}{S c_1 \tau} \tag{3} \]

the value \(\kappa_1\) should be constant at different concentrations of ions in solution. A change in the value of \(\kappa_1\) (at a constant stirring regime, temperature, and other conditions), calculated by formulas (1)—(3), in experiments with solutions of the ion under study of different concentrations indicates that the actual concentration of ions in solution does not correspond to the value that is substituted into formulas (1)—(3) in the calculations. This may occur if \(q\) increases, for example, due to desorption or leaching of the metal ion from the walls of the electrolyzer or the flasks for preparing standard solutions. A decrease in the area under the anodic peak at an unchanged initial concentration of ions may be associated with adsorption of ions or hydrolysis.

dilute solutions. It follows from this that the change in the value of \(\kappa_1\), determined from the area under the anodic tooth in a given solution, in comparison with a standard solution, can serve to estimate the error introduced into amalgam-polarographic measurements by adsorption, desorption, etc.

The standard electrolysis constant must be calculated under conditions where no change in the concentration in the solution is to be expected as a result of adsorption, desorption, or other causes.

The aim of the present work is to test the considerations set forth above concerning the possibility of using calculations of the electrolysis constant by formula (3) to establish the phenomena of adsorption and desorption of ions on the vessel walls, or hydrolysis, in very dilute solutions of the ions under investigation.

Let us consider variants for determining the standard electrolysis constant.

1. Use of a rotating disk electrode. According to Levich [7], the limiting electrolysis current at a rotating disk electrode is given by the expression

\[ i=\frac{z F D^{2/3}\omega^{1/2}}{1.61\cdot \nu^{1/6}}\,sC_1, \tag{4} \]

where \(\omega\) is the angular rotation rate, radian/sec; \(\nu\) is the kinematic viscosity; \(D\) is the ion diffusion coefficient, \(\mathrm{cm^2/sec}\). Comparing (4) and (1), we obtain for the electrolysis constant the expression

\[ \kappa_1=\frac{z F D^{2/3}}{1.61\cdot \nu^{1/6}}\,\omega^{1/2}. \tag{5} \]

Expressing the angular rate through the number of revolutions per second \((\omega=2\pi n)\), and the kinematic viscosity through the dynamic viscosity \((\eta)\) and the density of the solution \((d)\), we obtain

\[ \kappa_1=\frac{z F D^{2/3}(2\pi)^{1/2}d^{1/6}}{1.61\cdot \eta^{1/6}}\,n^{1/2} \tag{6} \]

or

\[ \kappa_1=\kappa^{1}\cdot n^{1/2}. \]

Thus, when using a rotating disk electrode satisfying the conditions of equal accessibility of the surface in the diffusion sense, the standard electrolysis constant in a given solution (characterized by the quantities \(d\) and \(\eta\)) and for a given ion (characterized by the quantities \(z\) and \(D\)) depends only on the number of revolutions.

We fabricated and tested a rotating disk electrode made of a fluoroplastic cylinder, into the end of which an amalgamated silver disk 5 mm in diameter was pressed. Using bismuth \((+3)\) in a hydrochloric acid supporting electrolyte \((0.25N)\) as an example, a comparison was made of the value of the constant \(\kappa_1\), found from the area under the anodic tooth at various rotation rates of the disk electrode, with that calculated from the Levich equation for the same values of \(n\). After substituting into formula (6) the values \(\eta=0.01\) poise, \(d=1.0\ \mathrm{g/cm^3}\), and \(D=6.6\cdot10^{-6}\ \mathrm{cm^2/sec}\) (found from the Ilković equation), the expression for the constant \(\kappa_1\) takes the following form:

\[ \kappa_1=228\cdot n^{1/2}. \tag{8} \]

From a comparison of curves 1 and 2 in Fig. 1 it follows that the experimental points on curve 2 fall on a straight line (as also follows from the theoretical con-

...expression (7), but the numerical value of the experimental angular coefficient is 1.7 times greater than the theoretical value calculated by formula (8) \((50.4 : 29.4 = 1.7)\). The overestimated experimental values of \(k_1\), apparently, are explained by the imperfection of the design of our electrode and by the vibrations of the electrode during rotation that arise because of this, which is not taken into account by the theoretical formula¹. For our purposes, such a discrepancy between theory and experiment is not of great significance. The advantage of a rotating disk electrode is the stability of the stirring regime and the reproducibility of the results obtained.

Fig. 1. Comparison of the electrolysis constant calculated theoretically from the Levich equation (curve 1) and determined experimentally (2). Experimental conditions: \(0.25N\mathrm{HCl}\); \(\mathrm{Bi}^{+3}\); \(V = 30\ \mathrm{ml}\); \(s = 8.7 \cdot 10^{-3}\ \mathrm{cm}^2\); \(n = 78\ \mathrm{rpm}\).

However, in subsequent work we abandoned its use, since for the study of dilute solutions we required higher values of the electrolysis constant, while in experiments with a rotating disk electrode at \(1000\ \mathrm{rpm}\) we could not obtain \(k_1\) greater than \(3 \cdot 10^3\ \mathrm{l \cdot cm/g\text{-}ion}\).

II. When using hanging mercury drop or film electrodes to determine the standard electrolysis constant, one may apply the methods proposed in [8]. Below, one more variant is proposed for determining \(k_1\) from curves of anodic current—time under conditions of complete depletion of the solution². The anodic current under partial depletion [1] of the solution is related to the limiting anodic current under complete depletion of the solution \((I)\) by the relation:

\[ I = I_{\infty}\left(1 - e^{-b}\right). \tag{9} \]

For \(b \leq 0.1\), with an accuracy of up to 5%:

\[ I = b I_{\infty} \tag{10} \]

and at \(b = 0.1\)

\[ I = 0.1 \cdot I_{\infty}. \]

On the curve \(I - \tau_{\mathrm{el}}\), we find the value \(I\) equal to \(0.1 I_{\infty}\), and the electrolysis time \(\tau\) corresponding to this value of \(I\). Then from the relation

\[ b = \frac{k_1}{zF}\, s\, \frac{\tau}{v} \tag{12} \]

we determine

\[ \kappa_1=\frac{0.1\cdot zF\cdot v}{s\tau} \tag{13} \]

for known values of \(v_p\), \(s\), \(z\), \(F\), and \(\tau\).

III. As the standard value \(\kappa_1\), one may take the value of the constant \(\kappa_1\) found from the area under the anodic peak, but under conditions excluding adsorption, desorption, etc., for example at comparatively high concentrations of the ion being determined in solution. The concentration interval studied in the APN method is \(10^{-6}—10^{-8}\) g-ion/l.

We carried out experiments comparing the magnitude of the electrolysis constant using bismuth \((+3)\) as an example, on a hydrochloric acid background, over a wide concentration interval \((5\cdot10^{-7}—5\cdot10^{-10}\) g-ion/l). The studies were carried out in an electrolyzer of our design (Fig. 2), consisting of a quartz beaker of 20–30 ml volume with a fluoroplastic lid. As the electrode we used a rotating electrode with a spherical end directed perpendicular to the liquid flow. The electrode consists of a fluoroplastic cylinder, inside which a silver wire 1 mm in diameter is inserted, bent at a right angle in the vertical plane and in the form of a hook in the horizontal plane. The wire, except for the end, is coated with a rapidly hardening resin—styracryl. The end is a silver bead amalgamated by electrolysis from a saturated nitric-acid solution of mercury. The upper part of the wire entering the fluoroplastic cylinder makes contact through mercury with the voltage source. The electrode is set in rotation by an electric motor, the number of revolutions of which is regulated by a transformer and measured with an ORION 2371/V stroboscope. When working with concentrations of Bi \((+3)\) ions in solution \(c=5\cdot10^{-7}—5\cdot10^{-10}\) g-ion/l, the accumulation time was varied (from 3 to 30 min) and the sensitivity of the polarograph (from \(6\cdot10^{-7}\) to \(1\cdot10^{-9}\) A/mm). The true surface of the electrode was determined from electrolysis-current versus time curves using an oscillographic polarograph [10]. To clean the walls of the electrolyzer from contaminants, intensive stirring of the solution by rotation of a fluoroplastic rod at high angular velocity was used [9].

Fig. 2. Design of an electrolyzer with a rotating end electrode:
1 — quartz beaker; 2 — fluoroplastic lid; 3 — fluoroplastic electrode body; 4 — silver wire; 5 — resin coating; 6 — amalgamated silver bead; 7 — ball bearing; 8 — electric motor; 9 — tube for passing nitrogen; 10 — agar-agar bridge.

\[ k_1=\frac{zFv}{s\tau}\cdot 2.3\cdot \lg \frac{1}{1-I/I_\infty}, \tag{14} \]

which is obtained as a consequence of formulas (9) and (11).

In calculating the value of $\kappa_1$ from the area under the anodic teeth, a method was used in which the weight of the area (tracing paper) under the anodic tooth was compared with the standard area on the same tracing paper, using the expression:

\[ \kappa_1=\frac{Ai_*t}{sc_1}, \tag{15} \]

where $A$ is the area under the anodic tooth, $\text{cm}^2$; $i_*$ is the sensitivity of the polarograph, $\text{a}/\text{cm}$; $t$ is the time required for $1\ \text{cm}$ of the scale to pass through the recording device, $\text{sec}/\text{cm}$. Use of expression (15) is possible only in the absence of depletion of the solution $(b \leq 0.1)$. In our experiments, in a solution volume $v=30\ \text{ml}$, even at the maximum accumulation time $\tau=30\ \text{min}$, according to (12),

\[ b=\frac{6200\cdot 8.7\cdot 10^{-3}\cdot 1800}{3\cdot 10^5\cdot 30}\simeq 0.01, \]

i.e., depletion of the solution is practically absent. For each investigated concentration of ions in solution, 16 anodic teeth were recorded successively. The results of determining the electrolysis constant for concentrations $5\cdot 10^{-7}$–$5\cdot 10^{-10}\ \text{g-ion}/\text{l}$ are given in Table 1.

Table 1

Experimental conditions: $0.25\ N\ \mathrm{HCl}$; $\mathrm{Bi}^{+3}$; $v=30\ \text{ml}$; $s=8.7\cdot 10^{-3}\ \text{cm}^2$;
$n=78\ \text{rev}/\text{min}$

Experiments were carried out on the effect of the storage time of the standard solution on the possibility of adsorption, desorption, and hydrolysis. The value of $\kappa_1$ was determined immediately after preparation, in $0.25\ N\ \mathrm{HCl}$, of a bismuth solution at a concentration of $5\cdot 10^{-10}\ \text{g-ion}/\text{l}$ (Table 2-I), and after four-hour storage of this solution (Table 2-II). The influ-

effect of the method of preparing the standard bismuth solution on the value of \(k_1\). Unlike the preceding experiments, in which the standard solutions were prepared in flasks that had previously been used many times, flasks not previously used for preparing bismuth solutions were taken. In this case, both when \(k_1\) was determined immediately after preparation (Table 2-III) and after 4-hour standing of the standard solution in the flask (Table 2-IV), the value of \(k_1\) remained practically constant.

Table 2

Experimental conditions: \(0.25\,N\ \mathrm{HCl};\ 5\cdot10^{-10}\) g-ion/l \(\mathrm{Bi}^{+3};\ v = 30\) ml;
\(s = 8.7\cdot10^3\ \mathrm{cm}^{-2};\ i = 1\cdot10^{-9}\ \mathrm{A/mm}\)

It follows from Table 1 that, in the concentration interval studied, the value of the electrolysis constant remains practically constant. This indicates that, for bismuth solutions in a hydrochloric acid medium, over a fairly wide concentration interval there is no adsorption, desorption, hydrolysis, or alkalization either in the quartz electrolyzer or in the glass flasks. Increasing the storage time of the standard bismuth solution to 4 hours (Table 2) likewise does not lead to a change in the value of \(k_1\). It also follows from the data of Table 2 (III and IV) that, for bismuth in hydrochloric acid solution, there is no adsorption of it on the glass of a flask, even one used for the first time for preparing a standard solution. Thus, when determining bismuth by the APN method in a hydrochloric acid medium down to concentrations of \(5\cdot10^{-10}\) g-ion/l, no complications associated with adsorption on various materials, desorption of ions, hydrolysis, etc., are observed.

Let us also note that in practical work, instead of calculating the electrolysis constant \(k_1\) by formula (3) or (15), in the absence of depletion of the solution and with other conditions constant (\(s\), \(\tau\), etc.), one may calculate the ratio of the depth of the anodic notch \(l\) to the concentration of ions in the solution (\(c_1\)):

\[ l/c_1 = k'_1, \tag{16} \]

since it is obvious that the value \(k'_1\) is proportional to the electrolysis constant \(k_1\).

When depletion of the solution occurs during electrolysis, one of the methods for calculating the electrolysis constant considered in [8] may be used to estimate the value of the electrolysis constant.

In conclusion, let us dwell on the reproducibility of the results. From Tables 1 and 2 it follows that the reproducibility of the results on the rotating end electrode exceeds the reproducibility of the results obtained on a stationary mercury electrode with stirring—

stirring the solution with a magnetic stirrer or with a stream of gaseous nitrogen. The maximum error of determination for one concentration does not exceed \(\pm 3\%\). In most experiments the error of determination (out of 16 experiments) does not exceed \(1\%\).

Conclusions

1. A method is proposed for the combined evaluation of adsorption, desorption, and hydrolysis of ions in very dilute solutions by comparing the experimentally found value of the electrolysis constant with the standard value.

2. The possibility has been demonstrated of using a rotating silver amalgamated disk electrode for determining the electrolysis constant and for use in the APN method.

3. A design has been developed for electrolysis with a rotating silver amalgamated end electrode, making it possible to obtain large (about \(2 \cdot 10^3\ \mathrm{A \cdot cm/g\text{-}eq}\)) electrolysis constants and good reproducibility (about \(2 \cdot 10\ \mathrm{A \cdot cm/g\text{-}ion}\)) of the results.

4. Using bismuth in a hydrochloric acid solution as an example, a practically constant value of \(k_1\) has been shown in the concentration range \(5 \cdot 10^{-6}\)—\(5 \cdot 10^{-10}\ \mathrm{g\text{-}ion/l}\), indicating the absence of adsorption, desorption, and hydrolysis of bismuth under the conditions studied.

References

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2. A. G. Stromberg. Zavod. labor., XXXI, 10, 1175, 1965.
3. A. G. Stromberg. Izv. TPI, vol. 128, 1964.
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5. A. G. Stromberg, A. A. Kaplin, V. I. Kuleshov, E. K. Spirin, B. F. Nazarov, Yu. A. Karbainov. Proceedings of the Conference on Polymer Analysis. Kharkov, 1966.
6. M. S. Zakharov, A. G. Stromberg, ZhFKh, 38, 130 (1964).
7. V. G. Levich. Physicochemical Hydrodynamics. Fizmatgiz, Moscow, 1961.
8. A. G. Stromberg. Present collection, p. 128.
9. A. A. Kaplin. Dissertation, TPI, Tomsk, 1966.
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12. E. A. Zakharova. Dissertation. Tomsk State University, Tomsk, 1965.
13. L. N. Nekrasov. Dissertation. Moscow State University, Moscow, 1962.

1. Another reason for the increase in the experimental value of the angular coefficient may be connected with the fact that the Levich equation is valid only for an infinitely large electrode; on a disk of small radius the current increases in comparison with that theoretically calculated. ↩

2. If the value of the ratio \(I : I_{\infty} > 0.1\), then according to [8], to calculate the electrolysis constant \(k_1\) one should use the expression: ↩