EFFECT OF LIGAND CONCENTRATION ON ANODIC AND CATHODIC PEAKS AT A STATIONARY MERCURY ELECTRODE UNDER A LINEARLY VARYING POTENTIAL

1. System Zn(Hg), Zn(2+), NH₃

A. G. STROMBERG, L. N. POPOVA

The study of the effect of ligand concentration on irreversible electrode processes makes it possible to establish the composition of complexes that take direct part in the electrode process. In doing so, the methods used have included alternating current [1—3], polarographic methods at an amalgam [3—14] and mercury [15—17] dropping electrode, and galvanostatic and potentiometric methods [18—19].

It is of interest to determine the possibility of applying, for these purposes, the ordinary technique used in the method of amalgam polarography with accumulation [20—21], since in this case the amalgam is obtained directly in the experiment itself and there is no need for special preparation of the amalgam.

In view of the fact that for a mercury film electrode there is [22] an approximate equation giving explicitly—in a form convenient for experimental verification—the dependence of the peak potential on the current and other factors, we chose this electrode. We are not aware of theoretical or experimental studies establishing the dependence of the potential of the anodic and cathodic peak at a stationary mercury electrode on ligand concentration.

The aim of the work is to carry out a comparative study of the effect of ammonia concentration on irreversible anodic and cathodic peaks at a mercury film electrode under a slow linear change of potential (0.1—1.0 volt/min) and on anodic and cathodic waves at a dropping mercury (or amalgam) electrode in the system Zn(Hg), Zn(2+), NH₃, and also to determine the possibility of establishing the composition of the complexes directly participating in the electrode process from the dependence of the anodic and cathodic peak potential at a mercury film electrode on ligand concentration.

Polarograms were recorded with a registering polarograph with an OH-101 recorder (Hungary). The electrode used was a mercury film electrode [23, 24], consisting of a silver wire (7 mm long and 1 mm in diameter), sealed into glass and coated electrolytically with a thin layer of mercury (more precisely, silver amalgam) about 5 microns thick. The electrode surface was 0.22 cm²; volume, \(1.06 \cdot 10^{-4}\) cm³; the concentration of zinc in the amalgam after preliminary electrolysis for 3 min at a potential of 1.5 volts was \(2.8 \cdot 10^{-3}\) g-at/l. The concentration of zinc in the amalgam

was determined from the area under the anodic peak by weighing the paper cut from the polarogram. The design of the dropping amalgam electrode used was the same as that described earlier [6]. In this case the amalgam dripping from the capillary was continuously prepared in an intermediate reservoir above the capillary by electrolysis. Capillary characteristics: drop time \(\tau = 0.8\) sec; mercury outflow rate \(m = 10.25\ \mathrm{mg/sec}\); \(m^{2/3}\tau^{1/6} = 4.545\ \mathrm{mg}^{2/3}\sec^{-1/2}\). The zinc concentration in the amalgam was \(2 \cdot 10^{-4}\) g-atom/l. The composition of the aqueous solution for obtaining cathodic waves and peaks was: \(2 \cdot 10^{-4}\) g-ion/l Zn (2+) \(+\ x\) mol/l NH\(_3\) \(+\ x\) mol/l NH\(_4\)Cl \(+\ (3 - x)\) mol/l NaCl. Thus, all experiments were carried out at constant ionic strength. To obtain anodic peaks, the concentration of zinc ions in the solution was \(2 \cdot 10^{-5}\) g-ion/l. The concentration \(x\) of ammonia and NH\(_4\)Cl was varied in the range from \(10^{-3}\) to 2.5 mol/l. To remove oxygen from the solution, nitrogen purified of oxygen was used. In order that ammonia should not volatilize from the solution, the nitrogen was first passed through a series of wash bottles containing ammonia solution, the concentration of which was selected so that the ammonia concentration in the electrolyzer did not change during the experiment. The ammonia concentration in the electrolyzer was checked before and after the experiment by titration. The technique for obtaining anodic and cathodic polarograms on the dropping mercury electrode [25] and the mercury film electrode [21] did not differ from the generally accepted one. The rate of change of potential, as a rule, was 0.33 V/min, except in experiments in which the dependence of the peak potential on the rate of change of potential was studied. All potential values in the text and in the figures are given in volts relative to the saturated calomel electrode (vs. SCE).

Fig. 1. Effect of ammonia concentration on the potentials of anodic (curve 3) and cathodic (curve 1) peaks on a mercury film electrode and on anodic (curve 4) and cathodic (curve 2) polarograms on a dropping zinc amalgam (\(2 \cdot 10^{-4}\) g-atom Zn) electrode in a solution of zinc ions. Experimental conditions are indicated in the text.

The results of the experiments are presented in Figs. 1–4. It is seen from Fig. 1 that the character of the dependence on ammonia concentration for the potentials of cathodic peaks on the film electrode and for the cathodic half-wave potentials is approximately the same (see curves 2 and 1 in Fig. 1); both curves are approximately parallel and almost coincide at high ammonia concentrations. However, as the ammonia concentration in the solution increases, the potential of the anodic peak on the film electrode changes much more strongly toward negative potentials than the anodic half-wave potential on the dropping amalgam. It is interesting to note that, as is seen from Fig. 1, the cathodic half-wave potential is located somewhat before the cathodic peak on the kinetic (ascending) branch of the peak, whereas the anodic half-wave potential is situated considerably more positive (by 0.1–0.2 V) than the anodic peak potential and, thus, all the metal has time to leave the amalgam film before the limiting current is reached. As far as we know, this feature of anodic peaks on a film electrode has not yet been noted in the literature. In the region of accessible ...

At sufficiently high ammonia concentrations (from 0.03 M to 2.5 M NH\(_3\)), the dependence \(\varphi_{\mathrm{p}}, \lg C_{\mathrm{NH}_3}\) is approximately linear both for peaks and for waves (Fig. 1); moreover, the transfer coefficients \(\alpha\) and \(\beta\) (determined from the slope coefficient of the waves), the anodic-current constant \(K'_2\), and the half-width \(\delta\) (Figs. 2, 3) remain approximately constant.

The anodic-current constant \(K'_2\) on a film electrode is a constant quantity independent of the thickness of the mercury film of the electrode:

\[ K'_2=\frac{K_2}{d}, \tag{1} \]

where \(K_2\) is the constant coefficient in the equation

\[ I_2=K_2 S c_2, \tag{2} \]

\(I_2\) is the height of the anodic tooth, A; \(S\) is the surface area of the electrode, cm\(^2\); \(c_2\) is the concentration of the metal in the amalgam, mol/cm\(^3\).

At lower values of the ammonia concentration (from 0.03 M to 0.001 M), the character of the dependence of all these quantities on the ammonia concentration changes substantially (Figs. 1, 2, 3). We believe that this can be explained by a change in the mechanism of discharge and ionization of the electrode process for zinc at low ammonia concentrations.

Fig. 2. Dependence on ammonia concentration of the anodic-current constant \(K'_2\) (curve 1) and of the half-width \(\delta\) (curve 2). The experimental conditions are indicated in the text.

Fig. 3. Dependence on ammonia concentration of the transfer coefficients of the anodic and cathodic (\(\alpha,\beta\)) processes, calculated from the slope coefficient of the anodic and cathodic waves at a dropping amalgam electrode. The experimental conditions are indicated in the text.

From the slopes of straight lines 2 and 4 in Fig. 1 at high ammonia concentrations, in accordance with the calculation method presented in papers [7—14], we find from experiments with an amalgam dropping electrode the composition of the discharging zinc complexes, Zn(NH\(_3\))\(_2^{2+}\) (\(q_1=2\)), and the composition of the complexes formed directly in the stage of ionization of zinc atoms from the amalgam, Zn(NH\(_3\))\(^{2+}\) (\(q_2=0.65\)), in accordance with our previous calculations.

It was of interest to test the applicability of the Itoginskii equation [22] for completely irreversible anodic teeth on an amalgam film electrode at a low rate of potential variation, derived under the assumption that throughout the entire process of electro-dissolution of the metal from the amalgam the distribution of the metal in the mercury remains uniform. In this case, for the formation of a complex during dissolution of the metal from the amalgam, we obtain the equation:

\[ \varphi_{\mathrm{pa}}=\varphi^\circ-\frac{b}{z\beta}\left(\lg K'_s-\lg dW\beta z+q_2\lg c_3+1.6\right), \tag{3} \]

where $\varphi_{\mathrm{na}}$ is the potential of the anodic peak, V; $\varphi^\circ$ is the formal electrode potential; $W$ is the rate of change of the potential, V/sec; $\beta$ is the transfer coefficient in the anodic process; $z$ is the number of electrons participating in the electrode process; $q_2$ is the composition of the complex formed upon ionization of the amalgam; $K_s$ is the standard rate constant of the discharge–ionization process of the complex of composition $q_2$, cm/sec; $c_3$ is the ligand concentration, mole/liter. It follows from equation (3) that the composition of the complexes $q_2$ can be determined from the slope $(\gamma'_{\mathrm{na}})$ of the straight line in the coordinates $\varphi_{\mathrm{na}}, \lg c_3$:

Fig. 4. Effect of the rate of change of potential on the anodic peak potential at a mercury film electrode against the background of 0.2 M NH$_4$OH + 0.2 M NH$_4$Cl + 2.8 M NaCl.

\[ q_2=\gamma'_{\mathrm{na}}\frac{\beta}{b}. \tag{4} \]

The theoretical dependence of the anodic peak potential on the rate of change of potential in a plot with coordinates $\varphi_{\mathrm{na}}, \lg W$, in accordance with equation (3), should be represented by a straight line with slope $b/\beta$. Hence $\beta$ can be determined (Fig. 4).

From the theory of irreversible polarographic waves [14, 27] it follows that the composition of the complexes formed upon ionization of the amalgam $(q_2)$ is related to the slope of the straight line in the coordinates $\varphi_{1/2}, \lg c_{\mathrm{NH}_3}$ by the relation:

\[ \gamma'_{1/2\,\mathrm{a}}=q_2\frac{b}{\beta}. \tag{5} \]

For the composition $q_1$ of the discharging complexes we had [14, 27]:

\[ \gamma'_{1/2\,\mathrm{k}}=(p-q_1)\frac{b}{\alpha}. \tag{6} \]

($p$ is the composition of the complexes predominating in solution.) Taking into account the approximate parallelism of the straight lines in the coordinates $\varphi_{\mathrm{pk}}, \lg c_{\mathrm{NH}_3}$ and $\varphi_{1/2\,\mathrm{k}}, \lg c_{\mathrm{NH}_3}$ (Fig. 1), it is evident that from the slope $\gamma_{\mathrm{pk}}$ in the coordinates $\varphi_{\mathrm{pk}}, \lg c_{\mathrm{NH}_3}$ one can determine the composition $q_1$ of the discharging complexes. The values of the transfer coefficient $\alpha$ can be determined from the relation [28]:

\[ \alpha=\frac{0.048}{(\varphi_{\mathrm{pk}/2}-\varphi_{\mathrm{pk}})z} \tag{7} \]

Table 1

As can be seen from Table 1, the results of calculations by the formulas given above, from experimental data obtained with a mercury film electrode, give essentially the same results as experiments with amalgam and mercury dropping electrodes. The difference in the values of \(q_2\) is apparently explained by the fact that the mechanism of anodic dissolution of the metal from the amalgam on a stationary electrode differs from the mechanism of the anodic process on a dropping amalgam electrode, since in the case of the film electrode we have not pure mercury but a silver amalgam. The course of the anodic process is probably also influenced by the slow adsorption of ammonia during the preliminary electrolysis.

Conclusions

1. A comparative study was carried out of the dependence on ammonia concentration (in the concentration range from 0.001 to 2.5 \(M\) \(NH_3\)) of the potentials of anodic and cathodic peaks at a mercury film electrode and of the anodic and cathodic half-wave potentials at a dropping amalgam electrode in a solution of zinc ions.

2. It has been shown that a mercury film electrode can be used to determine the composition of the complexes participating in the electrode process.

3. It has been established that at low ammonia concentrations a number of features are observed for peaks and waves which, apparently, should be explained by a change in the mechanism of the electrode process.

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