SELECTION OF ELECTROLYSIS CONDITIONS AND ELECTRODE SHAPE IN THE APA METHOD TAKING INTO ACCOUNT THE SOLUBILITY OF THE METAL OR INTERMETALLIC COMPOUND IN MERCURY

A. G. Stromberg, N. K. Dzhabarova, A. A. Kaplin

In the process of preliminary electrolysis in the APA method, conditions may be created under which the solubility limit of the metal being determined is reached within the volume of the electrode. This substantially limits the analytical capabilities of the method not only in determining elements that are sparingly soluble in mercury, but also in determining elements that are fairly readily soluble when electrodes with a small volume of mercury are used (a mercury–graphite electrode, ultramicroelectrodes). Therefore, when selecting the electrolysis conditions and the shape of the electrodes, it is necessary to take into account the possibility that a solid phase may precipitate within the electrode volume when the solubility limit of the metal in mercury is reached. An analogous situation occurs when a precipitate of an intermetallic compound that is sparingly soluble in mercury separates within the electrode volume.

To take the solubility of the metal into account when selecting polarographic conditions, it is necessary to estimate the maximum concentration of ions of the electroactive metal in an aqueous (or nonaqueous) solution and the minimum volume of solution. This estimate will depend on the conditions of the preliminary electrolysis and on the shape of the electrode.

As the basis for the calculations we shall take the equations of the parametric theory of the APA method /1, 2/.

\[ C_a^* \, v = \gamma \, C_{u}^{\max} \, V_{\min}, \tag{1} \]

\[ \gamma = 1 - \exp[-B], \tag{2} \]

\[ B = \frac{K_e \tau_e}{zF}\cdot \frac{S}{V_{\min}}, \tag{3} \]

where \(C_a^*\) is the solubility of the metal in mercury, g-atom/l; \(C_u^{\max}\) is the maximum concentration of ions in the solution at which, after electrolysis under the specified conditions, a saturated amalgam is obtained in the electrode, g-ion/l; \(v\) is the volume of mercury in the electrode, ml; \(V_{\min}\) is the minimum volume of solution at which, after electrolysis, a saturated amalgam is obtained in the electrode, ml; \(\gamma\) is the degree of depletion; \(B\) is a dimensionless parameter characterizing the electrolysis conditions; \(K_e\) is the electrolysis coefficient, characterizing—

electrolysis conditions; \(K_e\) is the electrolysis coefficient characterizing the intensity of stirring of the solution at its boundary with the electrode, \(\mathrm{A}/\mathrm{cm}\cdot\mathrm{mol}^{-1}\); \(\tau_e\) is the duration of electrolysis, sec; \(S\) is the electrode surface area, \(\mathrm{cm}^2\); \(z\) is the number of electrons participating in the electrode reaction per metal atom.

We shall consider two types of stationary mercury electrodes: in the form of a drop and in the form of a film on a silver cylindrical support.

Let us introduce the notation:

\[ \mu=\frac{C_a^*}{C_u^{\max}}, \tag{4} \]

\[ \omega=\frac{V_{\min}}{v}, \tag{5} \]

\[ \chi=\frac{S}{v}, \tag{6} \]

\[ \mathcal{J}=\frac{K_e \tau_e}{zF}. \tag{7} \]

Using this notation, equations (1)–(3) take the following form:

\[ \mu=\gamma \omega \tag{8} \]

\[ B=\frac{\mathcal{J}\chi}{\omega} \tag{9} \]

Hence

\[ \omega=\mathcal{J}\chi\,\frac{1}{B} \tag{10} \]

and

\[ \mu=\mathcal{J}\chi\,\frac{\gamma}{B} \tag{11} \]

If all conditions except \(\gamma\) and \(\mathcal{J}\) are specified, then from (8) we find

\[ \gamma=\frac{\mu}{\omega}, \tag{12} \]

where \(\mu\) and \(\omega\) are determined from experimental data by equations (4) and (5).

Substituting (12) into (2), we obtain

\[ B=-2.3\,\lg(1-\mu/\omega) \tag{13} \]

and from (9)

\[ \mathcal{J}=-\frac{\omega}{\chi}\,2.3\,\lg(1-\mu/\omega). \tag{14} \]

From equation (7) we estimate the values of \(K_e\) and \(\tau_e\) required in order to obtain the prescribed value of \(C_u^{\max}\) according to equation (4).

If all conditions except \(C_u^{\max}\) and \(V_{\min}\) are specified, then, according to (4) and (5), these quantities are estimated from the relations

\[ C_u^{\max}=\frac{1}{\mu}C_a^* \tag{15} \]

\[ V_{\min}=\omega v \tag{16} \]

Knowing from experiment the values of $\chi$, $\vartheta$, $\gamma$, and $B$, it is necessary to determine $\mu$ and $\omega$.

The quantity $\chi$ in expression (6) characterizes the ratio of the surface area of the mercury electrode to its volume and depends on the shape and size of the electrode. For a spherical electrode (drop) (index 1),

\[ \chi_1=\frac{S}{v}=\frac{3}{r}, \tag{17} \]

where $r$ is the radius of the sphere. For a film electrode (index 2),

\[ \chi_2=\frac{S}{v}=\frac{1}{h}, \tag{18} \]

where $h$ is the thickness of the mercury film.

The quantities $\vartheta$, $B$, and $\gamma$ characterize the electrolysis conditions. Let us consider, depending on the degree of depletion of the solution, two limiting cases. With practically no depletion of the solution (with an error of less than 5%) we have:

\[ B<0.05;\qquad \gamma=B,\qquad \frac{\gamma}{B}=1 \tag{19} \]

With practically complete depletion of the solution (with an error of less than 5%) we obtain

\[ B'>3,\quad \text{and}\quad \gamma \doteq 1. \tag{20} \]

Let us make numerical estimates of the quantities $\mu$ and $\omega$ for specified values of $\vartheta$, $\chi$, and $B$ for two types of electrodes and two limiting cases of solution depletion.

For the calculation of $\vartheta$ from equation (7) we take $k_2=5\cdot10^2$ A/cm·mol$^{-1}$; $\tau_p=4\cdot10^2$ sec; $z=2$; $F\simeq10^5$ A·sec/g-equiv$^{-1}$. In this case

\[ \vartheta \simeq 1. \tag{21} \]

For the calculation of $\chi$ we consider a drop of radius $r=0.04$ cm and a film of thickness $h=10^{-3}$ cm with the same surface area as that of the drop,

\[ S_1=S_2 \ \text{cm}^2. \tag{22} \]

Then, according to (14) and (15),

\[ \chi_1=75;\qquad \chi_2=10^3. \tag{23} \]

In this case

\[ v_1=\frac{4}{3}\pi r^3=2.5\cdot10^{-4}\ \text{ml} \tag{24} \]

and from condition (22) we obtain

\[ \frac{v_2}{v_1}=\frac{3h}{r}=\frac{1}{13},\qquad v_2=2\cdot10^{-5}\ \text{ml}. \tag{25} \]

Let us consider preliminary electrolysis without depletion and take $B=0.01$. Then, from relations (11), (10), and (16), taking into account the numerical estimates made above (21)—(25), we find

\[ \mu=\chi_1=75;\qquad \omega_1=\frac{\chi_1}{B}=7.5\cdot10^3. \tag{26} \]

\[ \mu_2 = x_2 = 10^3, \qquad \omega_2 = \frac{k_2}{B} = 10^5 . \tag{27} \]

In this case

\[ \frac{\mu_2}{\mu_1} = \frac{\omega_2}{\omega_1} = \frac{x_2}{x_1} = 13 . \tag{28} \]

From relations (26)–(28) and (12), (13) it follows that the maximum concentration of ions in the solution when electrolysis is carried out without depletion on a mercury drop, under the specified conditions \((k_2, \tau_2, r, B)\), must be 75 times less than the solubility of the metal in mercury, and on a mercury film—1000 times less. The corresponding minimum volumes of solution must be \(7.5 \cdot 10^3\) times greater than the volume of the drop and \(10^5\) times greater than the volume of the film.

If preliminary electrolysis is carried out with complete depletion, then, taking \(B = 3\), we obtain from relations (11), (10), and (20), taking into account the numerical estimates made,

\[ \mu'_1 = \frac{x_1}{B'} = 25, \qquad \omega'_1 = 25 \tag{29} \]

\[ \mu'_2 = \frac{x_2}{B'} = 330, \qquad \omega'_2 = 330 . \tag{30} \]

In this case condition (28) is satisfied.

Moreover, by comparing expressions (26) and (29), or (27) and (30), we obtain

\[ \frac{\mu_1}{\mu'_1} = \frac{\mu_2}{\mu'_2} = B' = 3, \tag{31} \]

\[ \frac{\omega_1}{\omega'_1} = \frac{\omega_2}{\omega'_2} = \frac{B'}{B} = 300 . \tag{32} \]

The corresponding solution volumes must be 25 and 330 times greater than the volume of mercury in the electrode, i.e., according to (32), 300 times less than under conditions in which there is no depletion of the solution.

Let us determine how the numerical estimates (21)–(32) and the values \(C^{\max}\) and \(V_{\min}\) change when the electrode dimensions or the experimental conditions are changed. If the film electrode has a volume identical to that of the drop at the same film thickness, then, according to (25), its volume and surface area will be 13 times larger. In this case the numerical estimates (21)–(32) do not change, but the minimum volume of solution for the film electrode increases 13-fold, i.e., it will be equal to 26 ml (without depletion of the solution) and 78 mm\(^3\) (with complete depletion of the solution).

If the electrolysis constant is 10 times greater \((K_e = 5 \cdot 10^3\ \mathrm{g}/\mathrm{cm}\cdot\mathrm{mol}^{-1})\), with the same values of \(\tau_e\) and \(Z\), then \(\nu = 10\) and, correspondingly, in expressions (26), (27) and (29), (30) the values of \(\mu\) and \(\omega\) are 10 times greater. In this case \(C^{\max}\) is 10 times smaller, and \(V_{\min}\) is 10 times greater than those calculated earlier.

It should be noted that in equation (12) the concentrations \(C^{\max}\) and \(C_a^*\) may be expressed in any units, but necessarily in identical units. If the concentrations of metals in the amalgam and in the solution are expressed in different units, then the numerical value of the proportionality coefficient will change. For example, if the solubility of a metal in mercury is expressed in weight percent \((\rho^*)\), and the concentration of metal ions in solution in \(\mathrm{g}/\mathrm{ml}\) \((m)\), then instead of relation (12) we obtain

\[ m = \frac{C \cdot 13.5}{\mu}\,\rho^* . \tag{33} \]

Let us consider the case in which, during preliminary electrolysis, two metals are simultaneously deposited, forming with each other an intermetallic compound (i.m.c.) in the amalgam. In this case their concentration in the amalgam must not exceed the value determined by the condition

\[ C_{a,1}^* = \frac{L}{\left(C_{a,2}^*\right)^n}, \tag{34} \]

where \(L\) is the solubility product of the i.m.c. in mercury; \(C_{a,1}^*\) is the concentration of the metal being determined \(M\); \(C_{a,2}^*\) is the concentration of the interfering metal \(N\); \(n\) is the composition of the i.m.c., \(MN_n\).

According to equation (4),

\[ C_{a,2} = \mu_2 \cdot C_{u,2}. \tag{35} \]

From (34) and (35) we find

\[ C_{a,1}^* = \frac{L}{\left(\mu_2 C_{u,2}\right)^n}. \tag{36} \]

Substituting (36) into (12), we obtain the desired expression

\[ C_{u,1}^{\max} = \frac{1}{\mu_1}\cdot \frac{L}{\left(\mu_2 C_{u,2}\right)^n}. \tag{37} \]

From equation (8) it follows that

\[ \mu_2 = \frac{j_2}{j_1}\,\mu_1 . \tag{38} \]

The degrees of depletion \(j_2\) and \(j_1\) for the two metals may differ because of their charges \((z_1\) and \(z_2)\), diffusion coefficients

ions in solution and other parameters entering into the electrolysis coefficient \(K_{e,1}\) and \(K_{e,2}\).

If \(z_1 = z_2\), then, taking approximately \(K_{e,1} \simeq K_{e,2}\), instead of (37) we obtain a simpler relation:

\[ C_u^{\max}=\frac{\mathcal{L}}{J^{n+1}\cdot C_{u,2}^{\,n}} . \tag{39} \]

The equations obtained make it possible to estimate the conditions under which the formation of a solid phase of the metal or intermetallic compound in mercury may disturb the linearity of the calibration graph and cause errors in analysis using the APA method.

Literature

1. A. G. Stromberg. Izv. SO AN SSSR, 5, 76 (1962).
2. A. G. Stromberg, A. A. Kaplin. ZhAKh, 20, 1045 (1965).

PURIFICATION OF REAGENT-GRADE CARBAZOLE

V. P. Lopatinskii, E. E. Sirotkina, V. D. Shirotov

The reagent-grade carbazole of the “pure” grade supplied in our country by the Kharkov Coke-Chemical Plant (VTU No. RU-463-51 and MRTU 6-09-3815-67) is a product of the isolation of carbazole from the anthracene fraction of coal-tar pitch. The methods for isolating carbazole at the Kharkov Coke-Chemical Plant are not constant, as a result of which the purity of the reagent-grade carbazole produced changes substantially. This carbazole contains (5–8)% impurities, mainly carbazole companions—anthracene and phenanthrene. A comparative assessment of the content of the principal components in reagent-grade carbazole of various series and dates of manufacture is given in Table I.

Table I.

Results of analyses of reagent-grade carbazole of various series