Physical Chemistry

Academician A. N. FRUMKIN, O. A. PETRII, and N. V. NIKOLAEVA-FEDOROVICH

CURRENT–TIME CURVES DURING THE REDUCTION OF ANIONS AT A DROPPING ELECTRODE

Determination of the dependence of the current \(I\) to a growing drop on the time \(t\) is a convenient method for studying the influence of adsorption on the kinetics of electrode processes. Up to the present, \(I\)—\(t\) curves have been studied for reduction processes whose rate decreases upon adsorption of neutral organic substances and organic cations \((^{1-3})^*\). It is known, however, that the rate of some reactions increases sharply upon adsorption of cations. Thus, tetrabutylammonium (TBA), tetraamylammonium (TAA), tetrahexylammonium (THA), and \(La^{3+}\) cations increase the rate of reduction of the anions \(S_2O_8^{2-}\) and \(Fe(CN)_6^{3-}\) \((^{5,6})\). These cations are effective at such low concentrations \(C\) that their amount on the surface of the growing drop is determined by diffusion \((^8)\). At the same time, the rate of reduction of anions on a surface completely covered with organic cations in a number of cases remains so high that the process is limited by diffusion of the reducible particles to the electrode surface.

We studied \(I\)—\(t\) curves for the reduction of the anions \(S_2O_8^{2-}\) and \(Fe(CN)_6^{3-}\) at a dropping mercury electrode in the presence of TBA, TAA, THA, and \(La^{3+}\) cations, and for the reduction of the anion \(PtCl_4^{2-}\) in the presence of the TAA cation. Measurements of the \(I\)—\(t\) curves were carried out with a TsLA oscillographic polarograph, model 01 \((^9)\). The values of the potentials \(\varphi\) are given in volts relative to the normal calomel electrode.

In a solution of \(10^{-3} N\ K_2S_2O_8 + 5 \cdot 10^{-3} N\ Na_2SO_4\), at \(\varphi = -0.55\), at which the limiting diffusion current \(I_d\) is observed on the \(I\)—\(\varphi\) curve, the current is proportional to \(t^{1/6}\). In the presence of various concentrations of \([(C_4H_9)_4N]J\), the \(I\)—\(t\) curve at this potential does not change. At the potential of the minimum of the \(I\)—\(\varphi\) curve, \(\varphi = -1.1\), the current is proportional to \(t^{2/3}\), i.e., it has a purely kinetic character (Fig. 1, 1). The \(I\)—\(t\) curves measured at \(\varphi = -1.1\) in the presence of various concentrations of TBA are presented in Fig. 1. It is evident from this figure that the initial portions of the \(I\)—\(t\) curves in the presence of TBA practically coincide with the curve obtained without addition of TBA. Subsequently, a sharp increase in current is observed with a comparatively small increase in time. The current reaches values exceeding the value of the limiting diffusion current and, after passing through a maximum, begins to fall, approaching \(I_d\). Similar \(I\)—\(t\) curves are also observed during the reduction of \(S_2O_8^{2-}\) in the presence of TAA, THA, and \(La^{3+}\). Figure 2a presents an \(I\)—\(t\) curve measured in a solution of \(10^{-3} N\ K_2S_2O_8 + 5 \cdot 10^{-3} N\ Na_2SO_4 + 5 \cdot 10^{-5} N\ [(C_6H_{13})_4N]Br\) at \(\varphi = -1.1\), and

* Volkova \((^4)\) obtained \(I,t\)-curves in a case where acceleration of reduction by the adsorbing substance occurs. However, the acceleration effect of the reactions studied by her is comparatively weak.

Fig. 2. Oscillograms of \(I\)—\(t\) curves

in Fig. 2б, curve 1 is an \(I—t\) curve in a solution of \(10^{-3} N\ K_2S_2O_8 + 2 \cdot 10^{-3} N\ Na_2SO_4 + 5 \cdot 10^{-5} N\ La_2(SO_4)_3\) at \(\varphi = -1.45\ \mathrm{V}\)*.

Measurements of \(I—t\) curves in a \(10^{-3} N\ K_3Fe(CN)_6\) solution show that at \(\varphi = -0.5\) the current is proportional to \(t^{1/6}\), while at the potentials of the minimum of the \(I—\varphi\) curve a kinetic current flows, proportional to \(t^{2/3}\). On the basis of \(I—t\) curves measured in this solution at different \(\varphi\) and corrected for charging current, the dependence of the instantaneous current \(I_{\mathrm{inst}}\) on \(\varphi\) was constructed for \(t = 3.3\) sec. The \(I—\varphi\) curve thus obtained has a flat minimum. Thus, direct measurements confirm the conclusion regarding the shape of the reduction curve of the \(\mathrm{Fe(CN)_6^{3-}}\) anion made in [10]. In the presence of TBA, TAA, and TTA cations, at the potentials of the minimum of the \(I—\varphi\) curve the same dependence of current on time is observed as in the reduction of \(\mathrm{S_2O_8^{2-}}\). Figure 2в gives an \(I—t\) curve measured in a solution of \(10^{-3} N\ K_3Fe(CN)_6 + 5 \cdot 10^{-5} N\ [(C_4H_9)_4N]J\) at \(\varphi = -1.4\). The influence of \(\mathrm{La^{3+}}\) cations on the dependence \(I—t\) in the reduction of the \(\mathrm{Fe(CN)_6^{3-}}\) anion is analogous to the influence of organic cations and \(\mathrm{La^{3+}}\) on the reduction of \(\mathrm{S_2O_8^{2-}}\) (Fig. 3).

Fig. 1. \(I—t\) curves for the reduction of \(\mathrm{S_2O_8^{2-}}\) in a solution of \(10^{-3} N\ K_2S_2O_8 + 5 \cdot 10^{-3} N\ Na_2SO_4\) at \(\varphi = -1.1\) in the presence of \([(C_4H_9N)_4]J\) in concentrations: 1—0; 2—\(2 \cdot 10^{-5} N\); 3—\(3 \cdot 10^{-5} N\); 4—\(5 \cdot 10^{-5} N\); 5—\(10^{-4} N\); 6—\(10^{-3} N\).

A complete quantitative theory of \(I—t\) curves for the dropping electrode has not yet been created. The case of an electroreduction process whose rate depends linearly on the degree of surface coverage by a substance that may either retard or accelerate the reaction has been considered [2]. In explaining the shape of the \(I—t\) curves observed when electroreduction reactions of cations are inhibited, in [3] it was concluded that, in addition to surface coverage, it is also necessary to take into account the influence of the change in the \(\psi_1\)-potential, which, according to the Frumkin and Florianovich equation [7], leads to an exponential dependence of \(I\) on the adsorbed amount. In this case, however, only retardation of the process was considered, and a quantitative theory was given only for the initial portion of the \(I—t\) curve.

Fig. 3. \(I—t\) curves for the reduction of \(\mathrm{Fe(CN)_6^{3-}}\) in a \(10^{-3} N\ K_3Fe(CN)_6\) solution at \(\varphi = -1.6\) in the presence of \(\mathrm{La_2(SO_4)_3}\) in concentrations: 1—0; 2—\(10^{-5} N\); 3—\(2 \cdot 10^{-5} N\); 4—\(3 \cdot 10^{-5} N\); 5—\(5 \cdot 10^{-5} N\); 6—\(10^{-3} N\).

The qualitatively observed dependence of the current during the reduction of anions, in particular the appearance of maxima of \(I_{\mathrm{inst}}\) exceeding the ordinary limiting diffusion current according to Ilkovič, can be explained as follows. In the absence of a catalyst (organic cations or \(\mathrm{La^{3+}}\)), the reduction of \(\mathrm{S_2O_8^{2-}}\) and \(\mathrm{Fe(CN)_6^{3-}}\) proceeds very slowly, so that the concentration of anions in the near-electrode layer during the initial period of drop growth remains practically constant and equal to the concentration of these particles in the bulk of the solution. Therefore, by the time when an amount of catalyst sufficient to accelerate the reaction has accumulated on the electrode surface,

* The decrease in current observed in the very initial period of drop growth on many oscillograms of Fig. 2 depends on the nonfaradaic (capacitive) current, proportional to \(t^{-1/3}\) and tending to zero as \(t\) increases. Corrections for the capacitive current were introduced into the \(I—t\) curves of Figs. 1 and 3.

the number of cations, the concentration of anions near the electrode still remains high. This leads to the appearance of reduction currents exceeding the values of \(I_d\). Subsequently, however, the substance near the electrode is consumed, the current falls, and, when the concentration of anions at the surface falls to zero, it approaches the value \(I_d\). Apparently, an appreciable excess of \(I_{\mathrm{inst}}\) over \(I_d\) can be observed only under the condition of an exponential dependence of the rate of anion reduction on the degree of filling of the electrode with cations.

Fig. 4. \(I\)—\(t\) curves for the reduction of \(\mathrm{PtCl}_4^{2-}\) in a solution of \(10^{-3}\,N\,\mathrm{K}_2\mathrm{PtCl}_4 + 4\cdot10^{-3}\,N\,\mathrm{Na}_2\mathrm{SO}_4\) at \(\varphi=-0.87\) in the presence of \([(\mathrm{C}_5\mathrm{H}_{11})_4\mathrm{N}]\mathrm{Br}\) in concentrations:
1 — 0; 2 — \(2\cdot10^{-5}\,N\); 3 — \(3\cdot10^{-5}\,N\); 4 — \(4\cdot10^{-5}\,N\) (oscillogram in Fig. 2g); 5 — \(5\cdot10^{-5}\,N\); 6 — \(10^{-4}\,N\); 7 — dependence of \(I_d\) on \(t\) in the reduction of \(\mathrm{PtCl}_4^{2-}\); 8 — \(I\)—\(t\) curve in a solution of \(10^{-3}\,N\,\mathrm{K}_2\mathrm{S}_2\mathrm{O}_8 + 5\cdot10^{-3}\,N\,\mathrm{Na}_2\mathrm{SO}_4 + 3\cdot10^{-5}\,N\,[(\mathrm{C}_5\mathrm{H}_{11})_4\mathrm{N}]\mathrm{Br}\) at \(\varphi=-1.1\).

In work (7) it was found that the effect of \(\mathrm{La}^{3+}\) cations on the reduction of \(\mathrm{S}_2\mathrm{O}_8^{2-}\) and \(\mathrm{Fe}(\mathrm{CN})_6^{3-}\) decreases, and at sufficiently low values of the \(\mathrm{La}^{3+}\) concentration, for example \(1.2\cdot10^{-5}\,N\), disappears completely at strongly negative \(\varphi\). It was suggested that the cause of this is a decrease in the drop time of the mercury electrode, as a result of which \(\mathrm{La}^{3+}\) does not have time to become adsorbed. From the \(I\)—\(t\) curves measured in the reduction of \(\mathrm{S}_2\mathrm{O}_8^{2-}\) and \(\mathrm{Fe}(\mathrm{CN})_6^{3-}\) in the presence of \(\mathrm{La}^{3+}\) at different values of \(\varphi\), we constructed the dependence \(I_{\mathrm{inst}}-\varphi\) at constant \(t\). It turned out that \(\mathrm{La}^{3+}\) cations at \(C=1.2\cdot10^{-5}\,N\) accelerate the reduction of anions both at less negative and at more negative \(\varphi\), but the effectiveness of their action in the former case is higher. This phenomenon is apparently due to the fact that, under the indicated measurement conditions, the concentration of \(\mathrm{La}^{3+}\) at the electrode surface is the same at different \(\varphi\), and the effectiveness of their action should be higher at weak surface charges, when the concentration of \(\mathrm{K}^+\) in the double layer is lower.

It was established earlier from measurements of \(I\)—\(\varphi\) curves (5) that TAA in small concentrations accelerates the reduction of \(\mathrm{PtCl}_4^{2-}\) at potentials of the descending branch of the polarographic curve, whereas at higher concentrations it inhibits this process. The results of measurements of \(I\)—\(t\) curves in the reduction of \(\mathrm{PtCl}_4^{2-}\) in the presence of TAA are presented in Fig. 4. At low TAA concentrations an acceleration of the reduction of \(\mathrm{PtCl}_4^{2-}\) is observed at the surface, and the initial portions of the \(I\)—\(t\) curves obtained in this case resemble the initial portions of the \(I\)—\(t\) curves described above. However, when a sufficiently large amount of TAA accumulates at the electrode surface, the reduction process of \(\mathrm{PtCl}_4^{2-}\) slows down. Comparison of curves 3 and 8 in Fig. 4 shows that TAA accelerates the reduction of \(\mathrm{PtCl}_4^{2-}\) considerably more weakly than the reduction of \(\mathrm{S}_2\mathrm{O}_8^{2-}\). The reasons for this were analyzed in (5). To explain the data obtained in the present work, it is apparently insufficient to use only the previously developed ideas on the influence of organic cations on the reduction of anions (5); it is probably also necessary to take into account the blocking of the surface by adsorbed cations, which leads to inhibition of the reaction. When the acceleration of the process by cations is expressed relatively weakly, inhibition of the reaction occurs at high degrees of filling.

Under certain conditions the \(I\)—\(t\) curves measured in dilute solutions at potentials of the descending characteristic of the \(I\)—\(\varphi\) curve are distor-

are accompanied by current oscillations. For the first time, self-oscillations during the reduction of \(S_2O_8^{2-}\) on mercury were discovered in \((^{11})\). In Fig. 2e an \(I-t\) curve is presented, obtained by us in a solution of \(10^{-3}\,N\,K_2S_2O_8+3\cdot10^{-5}\,N\,[(C_4H_9)_4N]J\) at a cell voltage \(U=-1.29\) V (anode—Hg in the same solution). Self-oscillations are also observed in \(10^{-3}\,N\,K_3Fe(CN)_6\) when a resistance \(R=47\) kΩ is connected to the cell (Fig. 2e, \(U=-0.8\) V). Self-oscillations in a solution of \(10^{-3}\,N\,K_2PtCl_4+3\cdot10^{-5}\,N\,[(C_4H_9)_4N]J\) are shown for \(U=-1.09\) V in Fig. 2z and for \(U=-1.10\) V in Fig. 2k. In a solution of \(10^{-3}\,N\,K_2PtCl_4+5\cdot10^{-5}\,N[(C_4H_9)_4N]J+10^{-1}\,N\,Na_2SO_4\) at \(U=-1.2\) V it is possible to observe current oscillations for different moments in the life of the drop (Fig. 2i, \(R=30\) kΩ). The observation of oscillations in this case is also of interest because, on the \(I-\varphi\) curve in the solution studied, there is a descending characteristic but no polarographic maximum of the first kind. Oscillations are observed during the reduction of the anion \(CrO_4^{2-}\), for which the \(I-\varphi\) curve has a descending characteristic \((^{12})\), in a solution of \(10^{-3}N\,K_2CrO_4+3\cdot10^{-5}\,N\,(C_4H_9)_4NJ\) at \(U=-0.97\) V (Fig. 2zh). The dependence of the frequency and amplitude of the self-oscillations on the voltage in the cases studied is in agreement with the results of \((^{11})\) and, apparently, is connected with the different state of the near-electrode layer at the initial moment of the oscillations. The form of the oscillations coincides with that described in \((^{11})\), although in some cases more complex oscillations were observed (in Fig. 2l, some of the oscillations of Fig. 2z are shown on a scale enlarged 16 times in \(t\)). In \(10^{-3}\,N\,K_2S_2O_8\), \(10^{-3}\,N\,K_2PtCl_4\), and \(10^{-3}\,N\,HgCl_2\) without additives, oscillations are not observed under the conditions in which these studies were carried out; instead, current jumps occur up to the values of \(I\) at the polarographic maximum. However, in the first two cases, on passing to the maximum, characteristic zigzag delays, described in \((^{11})\), are observed (shown by arrows in Fig. 2m, \(10^{-3}\,N\,K_2S_2O_8,\ U=-1.1\) V)*. From the experiments carried out it follows that the oscillations disappear when the resistance in the circuit is decreased; therefore, in the main part of the work the measurements were made with solutions containing \(Na_2SO_4\) in small concentrations.

Department of Electrochemistry
Moscow State University
named after M. V. Lomonosov

Received
22 XI 1960

CITED LITERATURE

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* The fact that the oscillations are better observed in the presence of small additions of TBA is probably connected with the influence of the cations on the \(I-\varphi\) curve, in particular with the appearance on it of a small segment of limiting current separating the polarographic maximum of the first kind and the descending branch of the \(I-\varphi\) curve. At the same time, the oscillations that are observed in the presence of \(La^{3+}\) or small (of the order of \(10^{-4}N\)) additions of \(Na_2SO_4\) nevertheless differ in frequency and amplitude from the oscillations obtained with additions of TBA.