POLAROGRAPHIC CHARACTERISTICS OF ANODIC PEAKS OF ELEMENTS IN THE METHOD OF AMALGAM POLAROGRAPHY WITH ACCUMULATION

M. S. Zakharov, L. L. Kivritskaya, Kh. A. Lel’chuk

(Presented by the scientific seminar of the Faculty of Chemical Technology)

In works [1, 2, 3, 4] the great importance of applying various polarographic characteristics \((\gamma_{\mathrm{k}}, \gamma_{\mathrm{e}}, \gamma_{\mathrm{g}}, \gamma_{0}, \gamma_{\phi}, \gamma_{\mathrm{p}}, K''_{2}, K_{2})\) for evaluating the sensitivity of determining elements by the method of amalgam polarography with accumulation (APA), the degree of irreversibility of anodic processes, and so forth has been shown.

The indicated characteristics are represented by the following relations:

\[ \gamma_{\mathrm{p}}=\frac{I_{1}}{I_{3}}=\frac{K_{1}}{K_{3}}=\frac{q}{I_{3}\tau}, \tag{1} \]

\[ \gamma_{\mathrm{e}}=\frac{I_{2}}{I_{1}}=\frac{K_{2}}{K_{1}}\cdot\frac{c_{2}}{c_{1}}, \tag{2} \]

\[ \gamma_{\phi}=\frac{I_{2}}{I_{3}}=\frac{K_{2}}{K_{3}}\cdot\frac{c_{2}}{c_{1}}, \tag{3} \]

\[ \gamma_{\phi}=\frac{K_{2}}{K_{3}}, \tag{4} \]

\[ \gamma_{0}=\frac{K_{2}}{K_{1}}, \tag{5} \]

\[ \gamma_{\mathrm{k}}=\frac{c_{2}}{c_{1}}\frac{q}{zFvc_{1}}, \tag{6} \]

\[ K_{2}=\frac{I_{2}}{Sc_{2}}=\frac{I_{2}}{c_{1}}\frac{1}{12\pi K'_{1}r\tau}=\frac{I_{2}}{q}\frac{zFr}{3}, \tag{7} \]

\[ K''_{2}=\frac{K_{2}}{\sqrt{\omega}}, \tag{8} \]

\[ K_{1}=\frac{I_{1}}{Sc_{1}}, \tag{9} \]

where \(K_{2}\) and \(K''_{2}\) are constants of the anodic current;

$K_1$ — electrolysis constant, dependent on the regime of stirring the solution during electrolysis, $a,\ \mathrm{cm},\ \mathrm{mole}^{-1}$;

$\gamma_{\mathrm{e}}, \gamma_0, \gamma_{\mathrm{k}}, \gamma_4, \gamma_{\mathrm{p}}, \gamma_{\phi}$ — respectively, the coefficients of electrolysis, attenuation, concentration, sensitivity, stirring, and form;

$I_2$ — anodic current, a;

$S$ — electrode surface area, $\mathrm{cm}^2$;

$c_2$ — concentration of metal atoms in the amalgam, g-atom/$\mathrm{cm}^3$;

$I_1$ — electrolysis current, a;

$c_1$ — concentration of ions in solution, mole/$\mathrm{cm}^3$;

$I_3$ — cathodic current, a;

$K_3$ — cathodic-current constant;

$\tau$ — electrolysis time;

$q$ — area under the anodic peak, coulombs;

$v$ — volume of the mercury drop electrode, $\mathrm{cm}^3$;

$\omega$ — rate of change of potential, V/sec.

In [4] it was shown that, for comparison of the amalgam-polarographic behavior of elements by the indicated characteristics, the latter must be calculated under identical conditions chosen as standard. The following conditions are proposed as standard:

\[ K_1^{\ne} = 10^5 z D^{0.45}\ a\cdot \mathrm{cm}\cdot \mathrm{mole}^{-1};\quad \gamma_{\mathrm{k}}^{\ne}=100; \tag{10} \]

\[ \omega^{\ne}=10^{-2}\ \mathrm{V/sec};\quad t^{\ne}=25^\circ\mathrm{C}. \]

The values of the APN coefficients under standard conditions are calculated from the following equations [4]:

\[ \gamma_{\phi}^{\ne}=\frac{K_2^{\ne}}{K_3^{\ne}};\quad \gamma_{\phi}=\frac{K_2}{K_3}, \tag{11} \]

\[ \gamma_{\mathrm{p}}^{\ne}=\frac{500z}{K_3^{\ne}}, \tag{12} \]

\[ K_3^{\ne}=K_3\frac{0.1}{\sqrt{\omega}}, \tag{13} \]

\[ \gamma_0^{\ne}=\frac{\gamma_{\phi}^{\ne}}{\gamma_{\mathrm{p}}^{\ne}}, \tag{14} \]

\[ \gamma_{\mathrm{e}}^{\ne}=100\gamma_0^{\ne}, \tag{15} \]

\[ \gamma_4^{\ne}=100\gamma_{\phi}^{\ne}. \tag{16} \]

(The index $\ne$ denotes the APN coefficients under standard conditions.)

In the present work we present the results of determining the amalgam-polarographic characteristics of several elements in different electrolytes under standard conditions.

Experimental Part

To determine the polarographic characteristics of the elements, experiments were carried out to obtain the cathodic and anodic peaks of elements currently determined by amalgam polarography with accumulation (Cu, Pb, Sb, Cd, Zn, Tl, Bi, In, Ga, Ge, Sn), in the following electrolytes: 0.1 N NaCl; 0.1 N CH$_3$COOH + 0.1 N CH$_3$COONa; 0.1 N NaF; 0.1 N CH$_3$COONa; 0.25 N HCl; 0.1 N NH$_4$Cl + 0.1 N NH$_4$OH; and 0.1 M Na$_2$C$_2$O$_4$. For each element the anodic and cathodic peaks were obtained three times, and for calculating

polarographic characteristics, the mean values of the experimental data were taken. The investigations were carried out on PA-1 and LP-55 polarographs. The design of the electrolyzer used is described in [5].

Table 1

Standard values of polarographic characteristics

From the experimental data obtained for elements giving stable cathodic and anodic peaks, the values of the polarographic characteristics under standard conditions were calculated. The latter are given in Table 1.

Discussion of the Results

The data obtained show that the anodic-peak constants of an element in different supporting electrolytes are approximately inversely proportional to the half-peak width (Table 3). As is known [1], the ratio of the half-peak widths of the same element in different supporting electrolytes characterizes the degree of irreversibility of the process of anodic oxidation of the element in different supporting electrolytes. This fact indicates that the magnitude of the anodic-current constant of an element depends on the degree of irreversibility of the anodic process; moreover, the more irreversible the process, the smaller the value of the anodic-current constant.

According to theoretical considerations [6],

\[ \frac{K_2 \delta}{z}=\frac{F}{3}\frac{r\omega}{\nu}, \tag{17} \]

\[ \nu=\frac{\delta_{\mathrm{eff}}}{\delta}, \tag{18} \]

\(\delta_{\mathrm{eff}}\) is the effective width of the anodic half-peak, sec;

\[ \delta_{\mathrm{eff}}=\frac{q}{I_2}. \tag{19} \]

It follows from expression (17) that, for identical \(r\) and \(\omega\), the quantity

\[ \frac{K_2\delta}{z} \]

must be the same for all elements in all electrolytes, if \(\nu\) is the same. Hence, for one element in different electrolytes there should be

\[ \frac{K'_2}{K''_2}=\frac{\delta''}{\delta'}=\mathrm{const}. \]

In our studies (with the exception of studies with the supporting electrolyte \(0.1\,M\,\mathrm{Na}_2\mathrm{C}_2\mathrm{O}_4\)), \(r\) and \(\omega\) were constant; however, the values of \(\frac{K'_2}{K''_2}\) and \(\frac{\delta''}{\delta'}\) for the same element in different supporting electrolytes are different. Consequently, the difference between the ratios \(\frac{K'_2}{K''_2}\) and \(\frac{\delta''}{\delta'}\) can be explained only by the fact that, in different supporting electrolytes, the quantity \(\nu\) has different values. Indeed, the values of \(\nu\) calculated from the experimental data proved, in most cases, to be different in different supporting electrolytes even for one element (Table 2).

From expression (17), for identical \(r\) and \(\omega\) it follows that:

\[ \frac{K'_2\delta' z''}{K''_2\delta'' z'}=\frac{\nu''}{\nu'}. \tag{20} \]

The values calculated by us from the experimental data,

\[ \frac{K'_2\delta' z''}{K''_2\delta'' z'} \]

and \(\frac{\nu''}{\nu'}\), agree satisfactorily with one another (Table 3).

If the investigations are carried out under constant conditions, then, knowing the value of \(K_2''\), one can determine the concentration of the element in solution by a calculation method. Obviously, if during polarography

Table 2

Values of \(\gamma\) for elements in various electrolytes

all conditions are maintained constant, then from expression (7) one can write:

\[ K' = 12\pi K_2'' K_1 r\tau \sqrt{\frac{\omega}{zF}} . \tag{21} \]

From expressions (7) and (8), taking (21) into account, one obtains

\[ c_1=\frac{I_2}{K}. \tag{22} \]

Table 3

Values of \(\dfrac{K_2'\delta' z''}{K_2''\delta'' z'}\) and \(\dfrac{\gamma''}{\gamma'}\) for elements in different electrolytes

Thus, having determined the value of \(K\) under the given conditions and for the given electrolyte, and obtaining the anodic peaks of the element in this electrolyte, one can calculate by computation the concentration of the element in solution \((c_1)\).

For a number of the elements studied by us in some electrolytes, the element concentrations were calculated from expression (22). The deviations of the calculated concentrations from the true ones did not exceed the experimental errors. Some data from these studies are presented in Table 4.

Table 4

Results of studies on determining element concentrations in solution by the calculation method

It is of interest to compare the sensitivity of determining elements by the AAP method in different electrolytes. The characteristic of sensitivity is \(\gamma_4^{\ddagger}\). Attention is drawn to the somewhat larger values of \(\gamma_4^{\ddagger}\) for elements on an acidic background \((0.25\,N\ \mathrm{HCl})\). Apparently, with the same \(\gamma_k^{\ddagger}\) in all experiments, this fact can be explained by the circumstance that in acidic electrolytes the rate of the anodic process, and consequently also the sensitivity of determination \((\gamma_4^{\ddagger})\), is less affected by the stages following the electrochemical dissolution. In the other electrolytes, at the same concentration coefficient \((\gamma_k^{\ddagger}=100)\), the sensitivity coefficients of the elements studied are equal to 200–300.

From expression (3)

\[ \gamma_4=\frac{K_2}{K_3}\cdot\gamma_k . \]

From [1]

\[ K_2=KzD_2^{m}f(\delta), \tag{24} \]

where \(K\) is a constant;
\(\delta\) is the width of the anodic half-peak, depending on the degree of reversibility of the anodic process;
\(D_2\) is the diffusion coefficient of metal atoms in mercury.

It follows from expression (24) that \(\gamma_4\) for one element in different electrolytes, at the same \(\gamma_k\) \((\gamma_k=\gamma_k^{\ddagger})\), should depend on the degree of reversibility of the electrode processes. It is evident from Table 1 that, for one and the same element in different electrolytes, \(\gamma_k^{\ddagger}\) do indeed have different values. For different elements, the value of \(\gamma_4^{\ddagger}\), in addition to the degree of reversibility, is also affected by differences in the diffusion coefficients of the atoms of the elements in mercury.

From expression (2), under the standard conditions selected by us,

\[ \gamma_{\mathrm{e}}^{\ne}=f(K_{2}^{\ne}), \tag{25} \]

and

\[ K_{2}^{\ne}=f(\delta D_{2}^{m}). \tag{26} \]

Consequently,

\[ \gamma_{\mathrm{e}}^{\ne}=f(D_{2}^{m}, \delta). \tag{27} \]

Thus, \(\gamma_{\mathrm{e}}^{\ne}\) for a single element should depend on the reversibility of the anodic process. From Table 1 it is evident that, indeed, the values of \(\gamma_{\mathrm{e}}^{\ne}\) for one and the same element are different in different electrolytes. For different elements, the magnitude of \(\gamma_{\mathrm{e}}^{\ne}\), in addition to the degree of reversibility of the electrode process, is also affected by the diffusion coefficient of the metal atoms in mercury. The experimental data show, as follows from theoretical considerations, that the smaller \(\gamma_{\mathrm{e}}^{\ne}\), the more irreversible are the oxidation–reduction processes of the given element. Thus, for example, for zinc, among the divalent elements studied, the electrode process is the most irreversible and the value of \(\gamma_{\mathrm{e}}^{\ne}\) is the smallest. For lead and cadmium, whose electrode processes are more reversible than that of zinc, larger values of \(\gamma_{\mathrm{e}}^{\ne}\) are also observed. From Table 1 it is evident that \(\gamma_{0}^{\ne}\) for all elements in the media studied is less than unity. Consequently, the constants of the anodic current for the cases studied are smaller than the constants of the electrolysis current (5). The values of \(\gamma_{0}^{\ne}\), even for a single element in different electrolytes, are different. According to (5), under the selected standard conditions \(\gamma_{0}^{\ne}=f(K_{2}^{\ne})\) (28). For one and the same element \(K_{2}=f(\delta)\) (29). Taking (26) and (29) into account, one may conclude that the magnitude \(\gamma_{0}^{\ne}\) can characterize the reversibility of the anodic process; moreover, the more irreversible the process, the smaller the value of \(\gamma_{0}^{\ne}\). Thus, for example, for zinc, whose electrode process is more irreversible than that of cadmium and lead, the value of \(\gamma_{0}^{\ne}\) is also smaller than for the latter two elements. From expressions (1) and (12) it is evident that, under the selected standard conditions \((K_{1}^{\ne}=500 z)\):

\[ \gamma_{\mathrm{p}}^{\ne}=f(K_{3}^{\ne}). \tag{30} \]

In work [7], at a high rate of change of the potential (oscillographic polarography), taking into account linear semi-infinite diffusion, the expression is given

\[ K_{3}^{\mathrm{irrevers.}}=3.01 \cdot 10^{5} z^{3/2}(\omega D_{1})^{1/2}\alpha^{1/2}, \tag{31} \]

where \(\alpha\) is the transfer coefficient;
\(D_{1}\) is the diffusion coefficient of the ions in solution.

For our case, where spherical diffusion and a slow change of potential are observed, \(K_{3}^{\mathrm{irrevers.}}\) will likewise depend on \(D\), \(z\), and \(\alpha\) (at constant \(\omega\)). Consequently, the magnitude \(\gamma_{\mathrm{p}}^{\ne}\) will depend on the degree of reversibility of the electrode process and on the nature of the ion.

Thus, the experimental data obtained show that, in accordance with the theoretical considerations, the polarographic coefficients presented above can serve as characteristics of the sensitivity and reversibility of electrode processes.

References

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