DETERMINATION OF THE COMPOSITION OF COMPLEXES DIRECTLY INVOLVED IN THE ELECTRODE PROCESS BY THE METHOD OF AMALGAM POLAROGRAPHY WITH ACCUMULATION (APA).

2. HYDROXIDE COMPLEXES OF ZINC

L. N. POPOVA, A. G. STROMBERG

Continuing the work on studying the possibility of applying the APA method to determine the composition of complexes participating in the electrode process [1], the hydroxide complexes of zinc were studied on a stationary mercury film electrode and on dropping mercury and amalgam electrodes.

As was shown earlier [1] using zinc ammine complexes as an example, the composition of the complexes participating in the electrode reaction can be determined by the method of amalgam polarography with accumulation from the dependence of the potentials of the anodic and cathodic peaks on the ligand concentration, using the following relations:

\[ \gamma_a=\frac{\partial \varphi_{\mathrm{pa}}}{\partial \lg C_{\mathrm{lig}}} =-\frac{b}{z\beta}q_2, \tag{1} \]

\[ \gamma_k=\frac{\partial \varphi_{\mathrm{pk}}}{\partial \lg C_{\mathrm{lig}}} =-\frac{b}{z\alpha}(p-q_1), \tag{2} \]

where

\[ b=\frac{2.3RT}{F}=0.059 \quad (\text{for }25^\circ\mathrm{C}); \]

\(\varphi_{\mathrm{pa}}, \varphi_{\mathrm{pk}}\) are the peak potentials of the anodic and cathodic waves, respectively; \(\beta, \alpha\) are the transfer coefficients of the anodic and cathodic processes; \(q_1, q_2\) are, respectively, the compositions of the discharged and ionized complexes; \(p\) is the composition of the complex predominating in solution; \(z\) is the number of electrons participating in the electrode reaction; \(C_{\mathrm{lig}}\) is the ligand concentration. The transfer coefficients \(\alpha\) and \(\beta\) are determined from the dependence of the peak potentials on the rate of change of potential \(W\) and on the film thickness \(d\) [2]:

\[ \frac{\partial \varphi_{\mathrm{pa}}}{\partial \lg W}=\frac{b}{\beta z}, \]

\[ \frac{\partial \varphi_{\mathrm{pa}}}{\partial \lg d}=\frac{b}{\beta z}, \tag{3} \]

\[ \frac{\partial \varphi_{\mathrm{pk}}}{\partial \lg W}=-\frac{b}{2\alpha z}. \]

For determining \(\alpha\) and \(\beta\), the following relations were also used [3, 4]:

\[ \varphi_{\mathrm{pk}}-\varphi_{\mathrm{pk}/2}=\frac{0.048}{\alpha z}, \tag{4} \]

\[ I_{\mathrm{pa}}=0.37\left(\frac{zF}{RT}\right)\beta WQ, \tag{5} \]

where \(Q\) is the area under the anodic peak, in coulombs.

As shown in [5], the composition of the metal complexes being discharged and formed during ionization can be determined from a polarographic study of the dependence of the anodic and cathodic half-wave potentials of an irreversible anodic–cathodic wave at an amalgam dropping electrode on the ligand concentration. This dependence is expressed by relations analogous to relations (1) and (2). The transfer coefficients \(\alpha\) and \(\beta\) are determined from the slope of the wave in semilogarithmic coordinates.

The polarograms were recorded using an OH-101 recording polarograph (Hungary). The mercury film electrode consisted of a silver wire 1 mm in diameter and 5 mm long, sealed into glass and coated electrolytically with a thin layer of mercury about 5 microns thick. A saturated calomel electrode with a surface area of 2 cm\(^2\) was used as the reference electrode. The resistance of the cell was 500 ohms; the maximum value of the current passing through the cell was \(5\cdot10^{-6}\) A, so that the voltage drop in the cell could be neglected.

Fig. 1. Dependence of the potentials of cathodic peaks and cathodic half-waves on the concentration of hydroxyl ions (curve 1; the peak potentials and half-wave potentials coincide), the potentials of cathodic half-peaks (curve 2, \(\varphi_{\mathrm{pk}}-\varphi_{\mathrm{pk},2}=-0.06\) V), the potentials of anodic peaks (curve 3), and anodic half-waves (curve 4) in a 3 M \((\mathrm{NaCl}+\mathrm{KOH})\) solution. Zinc concentration in solution: curves 1 and 2: \(C_{\mathrm{Zn}^{+2}}=3\cdot10^{-5}\) mol/L for cathodic waves; \(C_{\mathrm{Zn}^{+2}}=1\cdot10^{-4}\) mol/L for cathodic peaks; curve 3: \(C_{\mathrm{Zn}}=3\cdot10^{-5}\) mol/L. The zinc concentration in the amalgam is \(2\cdot10^{-4}\) g-atom/L (curve 4).

The construction of the dropping amalgam electrode used was the same as described earlier [6]. In this case, rubber and polyethylene joints in the apparatus were reduced to a minimum so as not to contaminate the mercury with organic surface-active sub-

substances. The amalgam dripping from the capillary was continuously prepared in an intermediate reservoir above the capillary by an electrolytic route. The concentration of zinc in the amalgam was \(2 \cdot 10^{-4}\) g-atom/l.

Sodium chloride was used as the indifferent electrolyte, and potassium hydroxide hydrate as the ligand; the concentration of the latter was varied from 0.1 to 3.0 M. At the same time, the sum of the concentrations \(\mathrm{NaCl}+\mathrm{KOH}\) in all experiments was the same and equal to 3 M. Thus, the investigations were carried out at the same ionic strength, equal to three. The rate of change of potential was, as a rule, \(5.5 \cdot 10^{-3}\) V/sec, except in experiments in which the dependence of the peak potential on the rate of change of potential was studied.

Figure 1 shows the dependence of the potentials of the anodic and cathodic peaks and half-waves of zinc on the hydroxide concentration. The linear character of this dependence indicates that, in the given range of changes in the concentration of hydroxide ions, one zinc complex each participates in the cathodic and anodic processes. From the tangents of the angles of inclination of the straight lines, the compositions of these complexes were determined. In this case the coefficients \(\alpha\) and \(\beta\) at the stationary electrode were determined by several methods (Figs. 1, 2, Table 1) (see equations 3, 4, 5).

Fig. 2. Effect of the rate of change of potential on the potential of the cathodic (curve 1) and anodic (curve 2) peak at a mercury film electrode in a solution of \(0.5\) M KOH \(+\) \(2.5\) M NaCl. \(C_{\mathrm{Zn}}^{+2}=1 \cdot 10^{-4}\) mol/l (curve 1); \(C_{\mathrm{Zn}}^{+2}=3 \cdot 10^{-5}\) mol/l (curve 2); \(\alpha=0.42\), \(\beta=0.26\) (3)

Fig. 3. Dependence of the anodic peak potential on the thickness of the mercury film of the electrode in a solution of \(0.5\) M KOH \(+\) \(2.5\) M NaCl. Zinc concentration in solution \(3 \cdot 10^{-5}\) mol/l; \(\beta=0.29\) (3)

According to literature data [7, 8], in alkaline solutions of zinc the complex of composition \(\mathrm{Zn(OH)}_{4}^{2-}\) predominates.

The results of the investigation for determining the composition of the complexes participating in the electrode process at dropping and stationary mercury film electrodes are presented in Table 2. The data given in the table are averages of two or three series of measurements.

As is seen from this table, investigations at dropping and stationary electrodes give identical results for the values of \(\alpha\) and \(\beta\) and for the compositions of the complexes discharged and formed upon ionization. In accordance with previously published data of one of us, obtained at a dropping—

Table 1

Values of the coefficients \(\alpha\) and \(\beta\) at different concentrations of hydroxide ions

…amalgam electrode [5, 6], the mechanisms of the cathodic and anodic processes are different. This is indicated by the deviation from unity of the sum of the transfer coefficients \((\alpha+\beta \simeq 0.7)\) and by the different composition of the complexes directly participating in the cathodic and anodic processes. According to

Table 2

the data obtained, the electrode processes in this system proceed according to the following equations:

cathodic process:

\[ [\mathrm{Zn}(\mathrm{OH})_4]^{2-} \rightleftarrows \mathrm{Zn}(\mathrm{OH})_2 + 2\mathrm{OH}^{-}, \]

\[ \mathrm{ZnOH}_2 - 2e + \mathrm{Hg} \rightleftarrows \mathrm{Zn}(\mathrm{Hg}) + 2\mathrm{OH}^{-}; \]

anodic process:

\[ \mathrm{Zn}(\mathrm{Hg}) - 2e + \mathrm{OH}^{-} \rightleftarrows [\mathrm{ZnOH}]^{+} + \mathrm{Hg}, \]

\[ [\mathrm{ZnOH}]^{+} + 3\mathrm{OH}^{-} \rightleftarrows [\mathrm{Zn}(\mathrm{OH})_4]^{2-}. \]

Thus, in solution the complex \([\mathrm{Zn}(\mathrm{OH})_4]^{2-}\) predominates, but the complexes \([\mathrm{Zn}(\mathrm{OH})_2]\) and \([\mathrm{ZnOH}]^{+}\) participate in the electrode process.

Conclusions

1. A comparative study has been carried out of the influence of hydroxyl ions on the potentials of anodic and cathodic peaks at a stationary mercury film electrode and on the half-wave potentials at dropping mercury and amalgam electrodes.

2. The compositions of the complexes directly participating in the electrode process and the transfer coefficients \(\alpha\) and \(\beta\) have been determined. It is shown that identical results are obtained on both types of electrodes (dropping and film), also agreeing with the polarographic data of previous studies.

3. Thus, the method of amalgam polarography with accumulation at a mercury film electrode can be used to determine the composition of complexes undergoing discharge and formed during ionization. The advantage of this method in comparison with classical polarography is a considerably simpler experimental procedure.

LITERATURE

1. A. G. Stromberg, L. N. Popova. Izvestiya TPI (in press).
2. V. A. Igolinsky, A. G. Stromberg. Izv. TPI (in press).
3. H. Matsuda, Y. Ajabe. Z. Electrochem., 59, 6, 1955.
4. V. E. Gorodovykh. Electrochemistry (in press).
5. A. G. Stromberg. Zh. fiz. khimii, 38, 2999, 1964.
6. A. G. Stromberg. Proceedings of the 4th Conference on Electrochemistry, Publishing House of the Academy of Sciences of the USSR, 1959, p. 213.
7. H. Gerischer. Z. phys. Chem., 202, 301, 1953.
8. H. Matsuda, Y. Ajabe. Z. Elektrochem., 63, 1164, 1959.