ON ESTIMATING THE ELECTROLYSIS CONSTANT DURING STIRRING OF A SOLUTION WITH GASEOUS NITROGEN AND A MAGNETIC STIRRER

A. A. Kaplin, V. M. Pichugina

(Presented by the scientific-methodological seminar of the KhTF)

In the polarographic method of analysis, in order to increase the intensity of delivery of a substance to the electrode, various methods of stirring the solution are used: the use of stirrers of various designs, bubbling gas through the solution being analyzed, rotation of the electrode or electrolyzer, vibration of the electrode, circulation of the solution in the narrow gap between the electrode and the vessel walls, etc. The method of anodic stripping analysis so far uses practically the first two methods: magnetic stirrers (less often propeller stirrers), gas bubbling (usually gaseous nitrogen), or joint stirring by gas and stirrer. The intensity of stirring of the solution has been estimated by the achieved sensitivity of the determination (the height of the anodic peak), which is a consequence of an increase in the degree of concentration of the metal in the electrode during accumulation in the stirred solution. However, as follows from the theory of the influence of various factors on the height of the anodic peak [1], the latter depends on a number of factors:

\[ I_a = h \cdot i_* = 3K_2 C_1^0 \cdot V \frac{1}{r} \left(1 - e^{\frac{K_1}{zF} S \frac{\tau}{V}}\right), \tag{1} \]

where \(h\) is the height of the anodic peak, mm; \(i_*\) is the sensitivity of the polarograph, a/mm; \(K_2\) is the anodic-current constant, \(a \cdot cm/g\text{-}atom\); \(C_1^0\) is the concentration of atoms in the solution, \(g\text{-}ion/cm^3\); \(V\) is the volume of the solution, \(cm^3\); \(r\) is the radius of the electrode, cm; \(S\) is the surface area of the electrode, \(cm^2\); \(K_1\) is the electrolysis constant, which is the coefficient of proportionality in the expression for the electrolysis current:

\[ i_{\mathrm{e}} = K_1 S C_1^0 . \tag{2} \]

In [2] it was proposed to estimate the intensity of delivery of a substance to the electrode by the value of the electrolysis constant \(K_1\). We have carried out an experimental estimate of the value of the constant \(K_1\) during stirring of various volumes of the working solution with gaseous nitrogen, with a magnetic stirrer, and with joint stirring of the solution by both methods; the conditions for achieving

maximum value of \(K_1\). The latter was calculated from the expression\(^1\):

\[ K_1=-\frac{q}{\tau S C_1^0}=\frac{A i_* \vartheta}{\tau S C_1^0}, \tag{3} \]

where \(q\) is the area under the anodic peak, coulombs, and \(A\) is the area under the anodic peak, \(\text{cm}^2\); \(i_*\) is the sensitivity of the polarograph, \(\text{A}/\text{cm}\); \(\vartheta\) is the time for 1 cm of the scale to pass through the recording device of the polarograph, \(\text{s}/\text{cm}\) [5]. The value \(A\) is determined by weighing the area of the paper under the anodic peak and a standard area of the same paper. In recording the anodic peak, the technique used was to stop the potential at a point somewhat more positive than the anodic-peak potential until the metal had completely left the drop. Measurements were carried out with bismuth (+3) at a concentration of \(10^{-6}\ \text{g}/\text{ml}\) \((5\cdot 10^{-9}\ \text{g-ion}/\text{cm}^3)\), prepared in \(0.25\,N\) HCl. An electrolyzer with insert cups was used in the work; the electrode was a hanging mercury drop with surface \(S=1.3\cdot 10^{-2}\ \text{cm}^2\). Other experimental conditions were: \(\tau_{\text{el}}=5\ \text{min}\), \(i_*=8\cdot 10^{-7}\ \text{A}/\text{cm}\); \(\vartheta=8.7\ \text{s}/\text{cm}\) (first speed of polarograph 7-77-4B). The constancy of the concentration of the initial bismuth solution in different series of experiments was monitored by the value of the constant \(K_1\) without stirring \((300\ \text{A}\cdot\text{cm}/\text{g-ion})\).

I. Stirring with gaseous nitrogen. The flow rate of nitrogen \((\text{l}/\text{min})\), passed through the solution being stirred (the diameter of the outlet opening of the tube was 1.5 mm), was determined by means of a gas meter of the GSB-400 type included in the gas-supply system.

The dependence of \(K_1\) on the position of the nitrogen jet relative to the mercury drop was first estimated (at constant \(V\)): the nitrogen jet at the wall of the beaker, the nitrogen jet washing the electrode, and the nitrogen jet in an intermediate position. The corresponding values of \(K_1\) were 2900, 3500, and 2500. Thus, maximum stirring is achieved when the nitrogen jet washes the electrode. In subsequent experiments this mutual arrangement of the nitrogen jet and the electrode was used.

Next, the dependence of the value of \(K_1\) was studied in working-solution volumes of 0.5, 2, and 4 ml with a varying gas flow rate: from 0.2 to 1 l/min. The upper limit of the gas flow rate was restricted by the value \(V\) at which splashing of the solution was observed. The results are given in Fig. 1 (curve 1).

II. Stirring with a magnetic stirrer. The magnetic stirrer, sealed into a glass tube 10 mm long, was set in rotation by a magnetic core mounted on the shaft of a motor with a number of revolutions regulated from a transformer (from 100 to 6000 rpm). The number of revolutions was measured with an Orion 237 1/8 stroboscope (Hungary).

The position of the electrode relative to the stirrer was preliminarily chosen such that maximum stirring was achieved. In this case the mercury drop was approximately 1 cm above the magnetic stirrer. The following was studied

\(^1\) Expression (3) can be used only in the absence of depletion of the solution,

\[ b=\frac{K_1}{zF}S\frac{\tau}{V}<0.1 \]

[1,6]. In most of our experiments, depletion of the solution was practically absent. Only in experiments with the smallest volume (0.5 ml) and with a large volume of stirring gas did the degree of depletion become noticeable \((b>0.1)\). In this case the calculation was carried out by the formula [6]:

\[ K_1=\frac{zFV}{S\tau}\cdot 2.3\cdot \lg\left(1-\frac{g}{zFCV}\right). \tag{3a} \]

The greatest degree of depletion in our experiments \((V_p=0.5\ \text{ml};\ v=0.8\ \text{l}/\text{min})\) reached about 0.2, and the numerical value according to formula (3a) exceeded by 10% the value of \(K_1\) calculated by formula (3).

dependence of the constant \(K_1\) on the number of revolutions of the magnetic stirrer (in a volume of 2 ml in the range 100–2000 rpm; the upper limit of the number of revolutions is limited by slippage of the stirrer). The results are presented in Fig. 1. The maximum value of the constant \(K_1\) was reached at \(n=1100\) rpm.

III. Simultaneous stirring by a magnetic stirrer and by bubbling gaseous nitrogen. The constant \(K_1\) was estimated in the stirred solution at the maximum number of revolutions (1100 rpm) and the limiting gas flow rate, at which no additional increase in the value of \(K_1\) is observed in each analyzed volume.

From Fig. 1 it follows that the intensity of stirring of the solution (the constant \(K_1\)) depends both on the gas flow rate and on the volume of the solution being analyzed. With an increase in the nitrogen flow rate from 0.2 to 0.8 l/min, the constant \(K_1\) increases, approaching its maximum value. In the range 0.4–0.8 l/min, for volumes of (2–4) ml, the change in \(K_1\) is insignificant; in a volume of 0.5 ml of solution, the change in \(K_1\) with increasing flow rate is more noticeable (from 1100 to 2300 A·cm/g-ion).

Fig. 1. Curve 1–3. Dependence of the electrolysis constant on the nitrogen flow rate (\(v\), l/min) in different solution volumes. Experimental conditions: 0.25 N HCl; bismuth (+3); \(C=5\cdot10^{-9}\) g-ion/cm\(^3\); \(S=1.3\cdot10^{-2}\) cm\(^2\); \(\tau=5\) min; \(i=8\cdot10^{-7}\) A/cm. Curve 1—\(V_p=0.5\) ml; curve 2—\(V_p=2\) ml; curve 3—\(V_p=4\) ml; curve 4—dependence of \(K_1\) on the number of stirrer revolutions in a solution volume of 2 ml.

With a decrease in volume from 4 ml to 0.5 ml during stirring with gaseous nitrogen, the constant \(K_1\) also increases, reaching the maximum value 2300 A·cm/g-ion at \(V=0.8\) l/min. A further increase in the nitrogen flow rate in this volume leads to splashing of the solution. When the solution (\(V=2\) ml) is stirred with a magnetic stirrer, the dependence we obtained differs somewhat from data of other authors, for example [7], who indicate a limit to the increase in peak height at \(n>600 \div 800\) rpm. As follows from the graph in the coordinates \(K_1, n\) (curve 4, Fig. 1), the value of \(K_1\) increases sharply with increasing \(n\) from 900 to 1100 rpm. In this case, rupture of the liquid occurs with the formation of very fine air bubbles (cavitation effect) and a stepwise increase in the intensity of stirring (the value of \(K_1\) increases from 1100 to 1500 A·cm/g-ion). A further increase in the number of revolutions—to 2000 rpm—does not lead to an increase in \(K_1\). Thus, from comparison of curves 2 and 4 (Fig. 1) it follows that at \(n=600 \div 800\) rpm the stirring intensity of two ml of solution by a magnetic stirrer and by gaseous nitrogen is approximately the same. At \(n=1100\) rpm, stirring by a magnetic stirrer is approximately 1.5 times more effective than by gaseous nitrogen.

Combined stirring of the solution by gaseous nitrogen and a magnetic stirrer (at \(n=1100\) rpm, \(V=0.8\) l/min) does not lead to a substantial increase in the electrolysis constant. Thus, for a volume of 2 ml, with combined stirring, the value of \(K_1\) is 1200 A·cm/g-ion,

i.e., even somewhat less than when stirring only with a magnetic stirrer.

Let us make an approximate estimate of the maximum sensitivity of determination that can be achieved on a hanging mercury drop electrode (\(r=0.04\ \text{cm};\ S=2\cdot10^{-2}\ \text{cm}^2\)) in a volume of \(0.5\ \text{ml}\) when stirring the solution with gaseous nitrogen (\(V=0.8\ \text{l/min},\ K_1=2300\ \text{A}\cdot\text{cm}/\text{g-ion}\)), i.e., at the maximum obtained value of \(K_1\). Let us take some experimental values of the quantities necessary for the calculation [1—4]: \(\tau=30\ \text{min}=1800\ \text{s}\); half-peak width \(\delta=0.06\ \text{V}\); rate of change of potential \(w=0.2\ \text{V/min}\simeq3\cdot10^{-3}\ \text{V/s}\); \(z=3\). The value of the dimensionless parameter

\[ b=\frac{K_1}{zF}S\frac{\tau}{V}\simeq1.6. \]

Thus, under the adopted conditions of analysis, the degree of depletion of the solution is \(\gamma=1-e^{-b}=0.8\). This means that the selected conditions approach the optimum. Let us take the value of the minimum quantity determinable with a specified accuracy at a polarograph sensitivity \(i=1\cdot10^{-9}\ \text{A/mm}\), peak height \(h\) equal to \(10\ \text{mm}\). Then \(I_a=h\cdot i=1\cdot10^{-8}\ \text{A}\). At \(\delta=0.06\ \text{V}\), the effective half-peak width is

\[ \delta_{\text{eff}}=\frac{\delta}{w}=20\ \text{s}. \]

The area under the anodic peak is

\[ q=I_a\cdot\delta_{\text{eff}}\cdot\nu, \]

where \(\nu\) is a coefficient characterizing the electrode shape and, for a mercury drop electrode, is equal to 1.4 [2—3]. Then \(q=2.8\cdot10^{-7}\ \text{coulomb}\). From expression (3),

\[ C_1^0=\frac{q}{\tau S K_1}=10^{-12}\ \text{g-ion}/\text{cm}^3=1\cdot10^{-9}\ \text{g-ion}/\text{l}. \]

For a weighed portion of the material analyzed of \(1.0\ \text{g}\) (\(A=100\)), this corresponds to \(5\cdot10^{-9}\) weight percent. Thus, when stirring the solution only with gaseous nitrogen in a volume of \(0.5\ \text{ml}\), \(10^{-8}\div5\cdot10^{-9}\) weight percent of an impurity in high-purity materials can be determined. On the basis of the calculations presented, we have developed a method for determining \(10^{-8}\) Bi in indium from a \(0.2\ \text{g}\) weighed portion [3].

Conclusions

1. The dependence of the electrolysis constant on the rate of passage (volume) of gas through the electrolyte solution and on the number of revolutions of the magnetic stirrer has been studied. It is shown that, with a solution volume of \(0.5\ \text{ml}\), the electrolysis constant reaches the greatest value: \(K_1=2300\ \text{A}\cdot\text{cm}/\text{g-ion}\).

2. An approximate calculation has been made showing the possibility of achieving a sensitivity of \(10^{-8}\div5\cdot10^{-9}\%\) from a \(1\ \text{g}\) weighed portion when working with a solution volume of \(0.5\ \text{ml}\) and under the condition that the solution is stirred only by gas bubbling (nitrogen).

REFERENCES

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6. A. G. Stromberg, V. I. Kuleshov. This collection, p. 129.
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