Effect of Preconcentration and Electrodissolution Conditions on the Shape of the Anodic Peak in Amalgam Accumulation Polarography
Abstract Generated abstract
This study examines how preconcentration and electrodissolution conditions affect the anodic stripping peak of lead in amalgam polarography. Using a mercury drop electrode and recording polarography, the authors measured peak height, peak area, half-peak width, and lead recovery as functions of lead concentration, electrolysis time, drop radius, potential sweep rate, and supporting electrolyte. The results show proportional increases of peak height and area with lead concentration and electrolysis time under suitable conditions, empirical dependences of peak height and width on sweep rate that vary with drop radius, and near-complete anodic recovery of lead. In alkaline media, high lead concentrations produced broadened or double peaks, attributed to formation of a sparingly soluble surface film rather than stepwise oxidation.
Full Text
E. A. ZAKHAROVA, L. N. POPOVA
EFFECT OF PRECONCENTRATION AND ELECTRODISSOLUTION CONDITIONS ON THE SHAPE OF THE ANODIC PEAK IN AMALGAM STRIPPING POLAROGRAPHY
(Presented by the scientific seminar of the Department of Physical Chemistry)
A number of works [1, 2, 3, 4, 5] have been devoted to the question of the influence of various factors on the height of the anodic peak in amalgam stripping polarography. However, the influence of various factors on the width of the anodic peak, the area under the peak, and the percentage yield of metal from the drop has scarcely been studied. The aim of the present work is to study the dependence of the shape of the anodic peak of lead (height, area, half-peak width) and the percentage yield of lead on the concentration of its ions in solution, the electrolysis time, the radius of the mercury drop, the rate of potential change, and the concentration and nature of the background electrolyte.
In this work a recording polarograph LP—55A (Czechoslovakia) was used, with a maximum absolute sensitivity of \(0.26 \cdot 10^{-8}\) A/mm/m. The electrolyzer with insert cups was similar to that described earlier [1]. The working electrode was a mercury drop obtained by electrolysis from a solution of \(\mathrm{Hg}_2(\mathrm{NO}_3)_2\) at the end of a platinum wire (\(d = 0.5—0.3\) mm) for 15—120 sec at a current of 30 mA. The size of the drop was regulated by the time of mercury deposition. The volume of the solution analyzed was 5 ml; the rates of potential change were 20, 100, 200, 400 mV/min. Intermediate rates of 75, 150, 300 mV/min were obtained by applying a voltage of 3 V to the potentiometric drum.
The measurement procedure was as follows. The height of the anodic peak was measured as the difference between the total anodic current at the peak summit and the residual current. The width of the half-peak was taken to be the width of the peak at the point corresponding to half its height, in millivolts. To calculate the percentage yield, the electrolysis current, the electrolysis constant, and the anodic current, we calculated the area under the anodic peak with stopping of the potential. The stopping procedure was as follows: upon reaching the anodic peak, the change in potential was stopped, and on the rotating photodrum the change in limiting current with time at constant potential was recorded until the current fell to the value of the residual current at the stopping point. The area under the peak with stopping was calculated by the weighing method (accuracy 3.7%). The area calculated in this way practically coincides (for high concentrations of lead ions in solution) with the quantity of electricity consumed for the reduction of the metal during electrolysis, found as the product of the electrolysis current and the electrolysis time. Table 5 gives, for comparison, the values of the electrolysis currents obtained by calculation from the area with stopping
and from the galvanometer readings for the same experiments. In the case where the concentration of ions in solution is low \((10^{-7}—10^{-8}\ M)\), the electrolysis current proves to be less than the residual current, and for calculating the amount of deposited and dissolved metal only measurements of the area under the peak with a stop were used. To determine the percentage yield of metal from the drop during anodic dissolution, the ratio of the area under the anodic peak with continuous change of potential in a specified potential interval (350 mV after the onset of metal dissolution) to the area under the peak with a stop was calculated.
The notation adopted is as follows: \(\tau\)—electrolysis time; \(l_a\)—depth of the anodic peak; \(q\)—area under the peak; \(\delta\)—width of the half-peak; \(b\)—dimensionless parameter in the equation for the dependence of the depth of the anodic peak on various factors [4]; \(I_{\mathrm{e}}\)—electrolysis current; \(K_{\mathrm{e}}=I_{\mathrm{e}}/SC_1\)—electrolysis-current constant; \(S\)—surface of the mercury drop; \(C_1\)—concentration of ions in solution; \(K_a=zFtl_a/3q\)—anodic-current constant; \(r\)—drop radius; \(v\)—volume of solution; \(W\)—rate of change of potential.
The dependence of the shape of the anodic peak of lead on the concentration of its ions in solution is presented in Fig. 1 and in Tables 1 and 2. With increasing concentration
Table 1
Dependence of the width of the anodic half-peak and of the completeness of yield on the concentration of lead in 0.1 N KOH solution
| 1 | 1 | 1 | 2 | 2 | 2 | 3 | 3 | 3 |
|---|---|---|---|---|---|---|---|---|
| \(C,\ M\) | \(\delta,\ \mathrm{mV}\) | % yield | \(C,\ M\) | \(\delta,\ \mathrm{mV}\) | % yield | \(C,\ M\) | \(\delta,\ \mathrm{mV}\) | % yield |
| \(3\cdot10^{-7}\) | 96 | 90 | \(4.2\cdot10^{-6}\) | 113 | 95.5 | \(3\cdot10^{-5}\) | 130 | 92 |
| \(6\cdot10^{-7}\) | 109 | 96.4 | \(5.0\cdot10^{-6}\) | 104 | 96.5 | \(6\cdot10^{-5}\) | 157 | 94 |
| \(9\cdot10^{-7}\) | 107 | 98 | \(6.0\cdot10^{-6}\) | 104 | 92 | \(1.5\cdot10^{-4}\) | 223 | 97 |
| \(3\cdot10^{-6}\) | 108 | 93 | \(1.2\cdot10^{-5}\) | 118 | 97.6 |
Table 2
Dependence of the amount of metal deposited during electrolysis on the concentration of lead ions in 1 N KOH solution. Experimental conditions:
\(v=3\ \mathrm{ml},\ \tau_{\mathrm{el}}=5\ \mathrm{min},\ r=0.024\ \mathrm{cm}\)
| \(C\cdot10^{7}\ M\) | \(q\cdot10^{8}\ \mathrm{coul.}\) | \(q/C\) |
|---|---|---|
| 2.5 | 85 | 3.40 |
| 5.0 | 178 | 3.55 |
| 7.5 | 270 | 3.60 |
| 32.5 | 1058 | 3.25 |
| 207.5 | 7350 | 3.52 |
of \(\mathrm{Pb}^{2+}\) \((2.5\cdot10^{-7}—2.0\cdot10^{-5}\ M)\), the area under the peak with a stop increases in direct proportion (Table 2), while the width of the half-peak remains practically unchanged (Table 1, columns 1, 2). However, with a further increase in the concentration of \(\mathrm{Pb}^{2+}\), the width of the half-peak increases (Table 1, column 3), the shape of the peak is disturbed, and double and even triple peaks appear (Fig. 4). The lower the concentration of alkali,
the double lead peaks appear earlier (Fig. 1). Thus, in a 0.01 N KOH solution, double peaks appear at a concentration of $\mathrm{Pb}^{2+} = 6 \cdot 10^{-5}\ M$, whereas in 1 N KOH, under the same conditions, even at a concentration of $4 \cdot 10^{-4}\ M$ a single peak is obtained. Working with a background of 0.1 N $\mathrm{KNO}_3$, acidified to pH = 5, we observed neither broadening of the anodic peaks
Fig. 1. Dependence of the depth of the anodic peak on the concentration of lead in solutions: 1—1 N KOH, 2—0.1 N KOH, 3—0.01 N KOH. Experimental conditions: $\varphi_{\mathrm{el}} = -1.2\ \mathrm{V}$, $\tau = 10\ \mathrm{min}$, $r = 0.04\ \mathrm{cm}$, $v = 5\ \mathrm{ml}$. The arrow indicates the appearance of double peaks.
of $\mathrm{Pb}^{2+}$, nor the appearance of double peaks. The literature contains examples of a similar distortion of the anodic peak shape for $\mathrm{Pb}^{2+}$ in alkali solutions [6, 7]; however, no substantiated explanation of this phenomenon has been given. We assumed that the cause of the appearance of double $\mathrm{Pb}^{2+}$ peaks in KOH solutions may be the formation of an insoluble film of lead hydroxide. This is confirmed by the observed dependence of the appearance of double peaks on the KOH concentration (Fig. 1) and by the non-diffusion character of the descending branch of the first peak after the potential sweep is stopped (Fig. 4, curve 2). In addition, we obtained a comparatively large cathodic peak immediately after stopping the potential at the first peak and visually observed a film on the mercury surface at a high concentration of lead in the solution. The assumption of stepwise oxidation of lead from the amalgam ($0 \to 1$ and $1 \to 2$, corresponding to the first and second peaks) was not confirmed, since coulometric measurements showed that all the lead is oxidized to the divalent state. The areas, in coulombs, under the first and second peaks with stopping (Fig. 4, curves 2, 3) coincided with one another and were equal to the amount of electricity consumed in the reduction $\mathrm{Pb}^{2+} \to \mathrm{Pb}^{0}$ during electrolysis.
It is known that the height of the anodic peak depends on the rate of potential change during the anodic dissolution of a metal from an amalgam, and most authors consider that, for a stationary drop, the height of the anodic current depends on $W^n$, where $n = 1/2$, similarly to cathodic peaks. We have shown experimentally, however, that in the investigated range of radii $I_a = kW^n$, where the exponent $n$ is a function of the radius of the mercury drop (Fig. 2). This dependence is in agreement with theoretical
considerations and experimental data for a film electrode, showing that as the radius of the mercury drop decreases the exponent \(n\) tends to unity, and as the radius increases—to 0.5 [8].
As the rate of change of potential increases, the width of the anodic half-wave increases (Fig. 3). This dependence can be expressed by the empirical formula: \(\delta = KW^m\), where the exponent \(m\) is a function of the drop radius. When the radius changes from 0.03 to 0.06 cm, the exponent \(m\) changes from 0.2 to 0.3. The larger the radius of the drop, the greater—at the same rate of change of potential—the half-wave width and, consequently, the lower the resolving power.*
Fig. 2. Dependence of the height of the anodic peak on the rate of change of potential for different radii of the mercury drop. The numerical values of the radii (cm) and the slopes of the straight lines are, respectively: 1—0.0028 and \(0.83 \pm 0.02\); 2—0.035 and \(0.73 \pm 0.02\); 3—0.054 and \(0.67 \pm 0.02\). Experimental conditions: background \(1\,N\) KOH, \(C_{\mathrm{Pb}^{2+}} = 7.9 \cdot 10^{-6}\,M\); \(\tau = 3\) min, \(v = 5\) ml.
The influence of the electrode radius on the shape of the anodic peak of \(\mathrm{Pb}^{2+}\) is shown in Table 4. The peak height and the area under the peak increase, respectively, in proportion to the radius and to the square of the radius, while the half-wave width increases only slightly. Theoretical considerations, however, show that for small drops the ratio of the surface of the drop to its volume increases—
Fig. 3. Dependence of the width of the anodic half-wave on the rate of change of potential for different radii of the mercury drop. The values of the radii (cm) and the slopes of the straight lines are, respectively: 1—0.028 and 0.20; 2—0.054 and 0.27. Experimental conditions: background \(1\,N\) KOH, \(C_{\mathrm{Pb}^{2+}} = 7.9 \cdot 10^{-6}\,M\); \(\tau = 3\) min; \(v = 5\) ml.
* Subsequent investigations carried out by us showed that, over a broader range of \(W\) values, the graphs in Figs. 2 and 3 are represented by curved lines, which indicates a dependence of the exponents \(n\) and \(m\) both on the radius of the mercury drop and on the rate of change of potential (note added in proof).
is taken up and, consequently, the peaks must begin to form already because of more rapid depletion (which is also observed experimentally for the film electrode). From Table 3 it is seen that the electrolysis current is directly proportional to the surface area of the mercury drop. Therefore, under the given conditions one should strive to choose the optimum radius of the mercury drop [4].
Table 3
Dependence of the electrolysis current on the surface area of the mercury drop.
Experimental conditions: \(C_{\mathrm{Pb}^{+2}} = 5 \cdot 10^{-6}\ \mathrm{M}\), \(v = 5\ \mathrm{ml}\)
| \(S\), mm\(^2\) | 1,28 | 1,70 | 2,00 | 2,41 | 2,66 | 3,26 | 3,56 |
|---|---|---|---|---|---|---|---|
| \(I_{\mathrm{e}}\cdot 10^8\), A | 59,9 | 74 | 97,5 | 107 | — | 131 | 136,5 |
| \(I_{\mathrm{e}}/S\) | 46,4 | 43,5 | 47,6 | 44,5 | — | 41,2 | 38,4 |
Table 4
Effect of the radius of the mercury drop on the shape of the peak and on the percent yield of lead.
Experimental conditions: background—\(0.1\,N\ \mathrm{KNO_3}\); \(C = 1 \cdot 10^{-5}\ \mathrm{M}\ \mathrm{Pb}^{2+}\); \(\tau = 3\) min, \(W - 400\ \mathrm{mV/min}\)
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|
| \(r\), cm | \(I_a \cdot 10^6\), A | \(I_a/r \cdot 10^5\) | \(q \cdot 10^5\), coul | \(q/r^2 \cdot 10^2\) | \(\delta\), mV | % yield |
| 0,032 | 1,59 | 5,95 | 1,49 | 1,42 | 75 | 94,5 |
| 0,040 | 1,95 | 4,81 | 2,49 | 1,30 | 80 | 93 |
| 0,046 | 2,36 | 5,10 | 2,74 | 1,28 | 85 | 93 |
| 0,051 | 2,48 | 4,86 | 3,36 | 1,29 | 87 | 91,9 |
The effect of the electrolysis time on the shape of the anodic peak of \(\mathrm{Pb}^{2+}\) was studied on different backgrounds (Table 5). In \(0.1\,N\ \mathrm{KNO_3}\) (\(\mathrm{pH}=5\)) the peak height and the area under the peak increased proportionally with time, as also followed from the theoretical conclusions [4], when the dimensionless parameter \(b < 0.1\). The half-peak width on this background depends on time, which also follows from its independence of concentration. However, the dependence
Table 5
Dependence of the shape of the anodic peak on the electrolysis time for a \(3.8 \cdot 10^{-6}\ \mathrm{M}\) lead solution in \(0.1\,N\ \mathrm{KNO_3} + \mathrm{HNO_3}\) (\(\mathrm{pH} - 5\))
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| \(\tau\), min | \(I_a \cdot 10^8\), A | \(q \cdot 10^8\), coul | \(\dfrac{I_a \cdot 10^8}{\tau}\), A/min | \(\dfrac{q \cdot 10^8}{\tau}\), coul/min | \(\delta\), mV | \(b\) | \(I_{\mathrm{e}}\cdot 10^8\)—residual current A\(^1\) | \(I_{\mathrm{e}}\cdot 10^8\), A\(^2\) | \(K^{2}_{\text{calc.}}\), A·cm·mol\(^{-1}\) |
| 1 | 22,1 | 368 | 22,1 | 368 | 74,0 | 0,0008 | 5,2 | 6,13 | 807 |
| 2 | 41,6 | 720 | 20,8 | 360 | 74,0 | — | 5,2 | 6,0 | 790 |
| 10 | 176,8 | 3346 | 17,7 | 335 | 69,6 | — | 5,2 | 5,1 | 670 |
| 20 | 369,0 | 7240 | 18,4 | 362 | 78,3 | — | 5,2 | 5,6 | 740 |
| 40 | 738,0 | 14250 | 18,45 | 357 | 78,3 | — | 5,2 | 5,85 | 770 |
| 60 | 1170 | 22050 | 19,5 | 368 | 78,3 | 0,0476 | 5,2 | 6,13 | 807 |
\(^1\) \(I_{\mathrm{e}}\)—electrolysis current according to the galvanometer readings (amperes).
\(^2\) \(I_{\mathrm{e}}\)—electrolysis current calculated from the area under the peak with stopping.
\(I_a-\tau\) in \(0.1N\) KOH deviates from linearity when \(b\) is still \(<0.1\), simultaneously with broadening of the peak (Table 6, columns 7, 8). Such a character
Table 6
Constants of the anodic current for lead.
Experimental conditions: \(r=0.40\ \mathrm{cm},\ C=5\cdot10^{-6}\ \mathrm{M},\ W=400\ \mathrm{mV/min}\)
| Background | \(\tau\), min | \(I,\cdot 10^3\), A | \(q\cdot 10^8\), C | \(I_a/q\) | \(K'_a\), A·cm/mol | \(I_a/\tau\) | \(\delta\), mV |
|---|---|---|---|---|---|---|---|
| \(0.1N\) KOH | 1 | 23.2 | 498 | 0.046 | 119 | 23.2 | 78.3 |
| \(0.1N\) KOH | 5 | 113 | 2360 | 0.048 | 123 | 22.6 | 104 |
| \(0.1N\) KOH | 10 | 201 | 4980 | 0.040 | 103 | 20.1 | 113 |
| \(0.1N\) KOH | 20 | 350 | 8680 | 0.040 | 103 | 17.5 | 136 |
| \(0.1N\) KOH | 40 | 626 | 15700 | 0.040 | 103 | 15.6 | 139 |
| \(0.1N\) KOH | 60 | 793 | 17110 | 0.046 | 119 | 13.2 | 139 |
| \(0.1N\) KNO\(_3\) (pH = 5) | 2 | 41.6 | 720 | 0.058 | 149 | ||
| \(0.1N\) KNO\(_3\) (pH = 5) | 5 | 89.2 | 1575 | 0.057 | 147 | ||
| \(0.1N\) KNO\(_3\) (pH = 5) | 10 | 176.8 | 3346 | 0.058 | 150 | ||
| \(0.1N\) KNO\(_3\) (pH = 5) | 20 | 369 | 7240 | 0.051 | 132 | ||
| \(0.1N\) KNO\(_3\) (pH = 5) | 40 | 738 | 14250 | 0.052 | 134 | ||
| \(0.1N\) KNO\(_3\) (pH = 5) | 60 | 1170 | 22050 | 0.053 | 137 |
of the dependences of the height and half-width of the peak on time against an alkali background can be explained by the formation of an insoluble film on the surface of the drop, hindering the diffusion of the metal from the amalgam.
The method of calculating the area under the peak with stopping makes it possible to calculate easily the constants of the electrolysis current and of the anodic peak, which is usually difficult to do for small concentrations of ions in solution by measuring electrolysis currents with a galvanometer. Tables 5 and 6 present the constants calculated against backgrounds of \(0.1N\) KOH and \(0.1N\) KNO\(_3\). The value of the anodic-current constant is important for the calculation method of amalgam polarography, since this constant depends only on the diffusion coefficient of the metal atoms in the amalgam, the degree of reversibility of the electrode process, and the rate of change of potential.
Fig. 4. Double peak of lead \((\mathrm{Pb}^{2+}=1\cdot10^{-4}\ \mathrm{M})\) against a background of \(0.1N\) KOH (1); 2—the same, recorded with stopping of the change in potential after obtaining the first peak (the stop is indicated by an arrow); 3—the same, recorded with stopping of the change in potential at the second peak. Experimental conditions: \(\tau=10\) min, \(r=0.04\) cm, \(v=5\) ml, galvanometer sensitivity \(1/100\).
The calculations we carried out of the percentage yield of metal from the mercury drop during the anodic cycle showed that in all the cases studied \((W=20\text{--}400\ \mathrm{mV/min};\ r=0.028\text{--}0.054\ \mathrm{cm};\ \tau=1\text{--}60\ \mathrm{min},\ C=6\cdot10^{-8}\text{--}6\cdot10^{-4}\ \mathrm{M})\), the yield of lead proved to be practically equal-
…equal to 100% (see Tables 1 and 4). The data obtained in [9] on a 50% or lower yield of the metal under approximately the same conditions are themselves called into question by the authors, since the amount of metal liberated during electrolysis was calculated from the electrolysis current, which includes uncontrolled currents due to the reduction of oxygen and hydrogen ions, always present in the solution. We eliminated the influence of these uncontrolled factors by calculating the amount of metal liberated by electrolysis from the area under the anodic peak with a stop.
Conclusions
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The influence on the depth and shape of the anodic peak of lead of various factors has been studied: the concentration of lead ions in the solution, the electrolysis time, the radius of the mercury drop, the rate of change of potential, and the nature and concentration of the background.
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It has been shown that the depth of the anodic peak and the area under the peak (the amount of anodically dissolved metal) vary in proportion to the electrolysis time and the concentration of lead ions, while the half-peak width does not change.
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It has been shown that the dependence of the depth of the anodic peak on the rate of change of potential is given by the empirical expression $I = K W^n$, where $0.5 < n < 1$. The exponent $n$ depends on the radius of the mercury drop; with increasing radius, the exponent $n$ decreases from 0.83 to 0.67 over the studied interval of mercury-drop radii (from 0.028 to 0.051 cm), in accordance with the requirements of theory.
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It has been shown that, with an increase in the rate of change of potential from 20 to 400 mV/min, the half-peak width increases, and this dependence can be expressed by the empirical equation: $\delta = K W^m$, where the exponent $m$, with increasing radius of the mercury drop, increases from 0.20 to 0.27 over the studied interval of radii.
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It has been established that the percentage yield of lead during anodic dissolution is close to 100% in all cases studied.
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It has been shown that, with increasing lead concentration on a KOH background, double peaks appear on the polarogram. A series of experimental data has been obtained which confirms the hypothesis that the formation of a sparingly soluble film is the cause of the appearance of double peaks.
References
-
A. G. Stromberg, M. S. Zakharov. On increasing the sensitivity of the method of amalgam polarography with preconcentration. Methods of Analysis of Chemical Reagents and Preparations, issue 5–6, IREA, Moscow, 1963, p. 16.
-
G. Nickelly, W. Cooke. Polarography with anodic dissolution. Anal. Chem., 29, 933, 1957.
-
S. I. Sinyakova, Shen Yu-chi. Influence of various factors on the height of anodic peaks. Dokl. Akad. Nauk SSSR, 31, 101, 1960.
-
A. G. Stromberg. On the question of the influence of electrolysis time, solution volume, and mercury-drop radius on the depth of the anodic peak in amalgam polarography. Izv. SO AN SSSR, No. 5, 76, 1962.
-
L. N. Vasil’eva, E. I. Vinogradova. Dependence of the concentration of metal in a mercury drop on the preconcentration time, taking into account depletion of the solution. Zavod. laborator., 28, 1427, 1962.
-
A. G. Stromberg, V. E. Gorodovykh. Polarographic determination of $10^{-7}$ M lead. Zavod. laborator., 26, 46, 1960.
-
S. I. Sinyakova, N. V. Markova. Determination of impurities of zinc, lead, and copper in acids and alkalis. Zavod. laborator., 27, 521, 1961.
-
V. A. Igolinskii. Study of the influence of the rate of change of potential on the depth of the anodic peak in the method of amalgam polarography on a film electrode. Izv. TPI (in press).
-
K. W. Gardiner, L. B. Rogers. Coulometric determination of microquantities of cadmium and zinc. Anal. Chem., 25, 1393, 1953.