Proceedings
of the Tomsk Polytechnic Institute named after S. M. Kirov,
holder of the Order of the October Revolution and the Order of the Red Banner of Labor

Vol. 197　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1975

ANODIC AMALGAM VOLTAMMETRY

AT CONSTANT CURRENT ON A SPHERICAL

MERCURY ELECTRODE.

ON THE MINIMUM CONCENTRATION

FOR DETERMINING IMPURITIES

M. S. ZAKHAROV, V. V. PNEV

(Presented by the scientific seminar of the Department of Physical and Colloid Chemistry)

In the present work, expressions will be obtained for estimating the minimum determinable content of an impurity by the method under consideration.

The concentration of an impurity in an amalgam is characterized by the magnitude of the transition time, the expression for which on a spherical mercury electrode, for \(\vartheta^{1}\ge 0.14\), has the following form [1]:

\[ \tau=\frac{zFC^{0}_{B}r_{0}}{3i_{0}}-\frac{r_{0}^{2}}{15D_{B}}. \tag{1} \]

The capacitive current distorts chronopotentiograms and reduces the analytical capabilities of the method. Values of \(\tau\) acceptable for practical measurements [2] at given \(C^{0}_{B}\) are selected by changing the current \(i_{0}\). The greater the current at a given \(C^{0}_{B}\), the greater will be the rate of change of the potential and, consequently, the more current will go to charging the double layer. The influence of the double layer on the analytical capabilities of chronopotentiometry can be approximately estimated according to Gierst [3]. Approximately, the amount of electricity expended on the process of charging the double layer can be estimated by the formula \(Q_{c}=C_{d}\Delta\varphi\), and the amount of electricity expended on the electrochemical reaction by the formula \(Q_{\phi}=i_{0}\tau\). The error caused by the presence of capacitive current is determined from the relation

\[ \frac{Q_{c}}{Q_{\phi}}=\frac{C_{d}\Delta\varphi}{i_{0}\tau}. \tag{2} \]

Taking expression (1) into account, equation (2) can be reduced to the form

\[ \frac{Q_{c}}{Q_{\phi}}= \frac{C_{d}\Delta\varphi} {\dfrac{zFC^{0}_{B}r_{0}}{3}-\dfrac{i_{0}r_{0}^{2}}{15D_{B}}}. \tag{3} \]

For an error introduced by the capacitive current of less than one percent, from equation (3) we obtain:

\[ \frac{i_{0}r_{0}}{5FD_{B}}+\frac{300C_{d}\Delta\varphi}{r_{0}F}\le zC^{0}_{B}. \tag{4} \]

If we take \(r_{0}=4\cdot10^{-2}\ \text{cm}\); \(C_{d}=20\ \mu\text{F}\); \(\Delta\varphi=0.06\ \text{V}\) [4];

If \(D_R=2\cdot 10^{-5}\ \mathrm{cm^2/sec}\), then the following relation must hold:

\[ zC_R^0 \geq 0.0041\,i_0 + 0.93\cdot 10^{-7} \tag{5} \]

In estimating the minimum determinable concentration under the indicated conditions, \(i_0\) cannot be assigned arbitrarily, since \(\Delta\varphi_1\) depends on \(i_0\) (through \(\tau\)). From Fig. 2 of work [4] it follows that at \(\Delta\varphi_1=0.06\ \mathrm{V}\), for the irreversible process \(\vartheta'=0.50\) \(\left(\vartheta^1=\dfrac{D_R \tau}{r_0^2}\right)\). For the given \(D_R\) and \(r_0\), \(\tau=40\ \mathrm{sec}\). With this \(\tau\) and the other cited quantities, from equation (1) we obtain

\[ i_0=\frac{C_R^0}{0.0174}. \]

Substituting (6) into (5), we obtain \(C_{R,\min}^0=6\cdot 10^{-8}\ \mathrm{g\text{-}atom/ml}=6\cdot 10^{-5}\ \mathrm{g\text{-}atom/l}\). The concentration of the element in the amalgam \((C_R^0)\) is related to the concentration of ions in the solution by the relation [5]:

\[ C_R^0=\frac{\gamma C_0^0 V}{v}, \tag{6} \]

where \(\gamma\) is the coefficient of depletion of the solution during pre-electrolysis [5]; \(V\) is the volume of solution, \(\mathrm{cm^3}\); \(v\) is the volume of the mercury electrode, \(\mathrm{cm^3}\).

An expression for the minimum determinable concentration of ions in solution can be obtained by transforming equations (4) and (6):

\[ C_{0,\min}^0=\frac{v}{\gamma v}\left(\frac{i_0 r_0}{5zFD_R}+\frac{300C_d\Delta\varphi}{zFr_0}\right), \tag{7} \]

Using formula (15) of work [6], one can obtain the following expression for the minimum determinable impurity concentration in % \((a,\ \%\ \text{by weight})\) in the material being analyzed, which can be determined by the AAV method with constant current on a spherical mercury electrode with a specified error introduced by the capacitive current:

\[ a_{\min}=C_{0,\min}^0\frac{AV}{10g}; \tag{8} \]

where \(A\) is the atomic weight of the element.

Let us make a numerical estimate of \(a_{\min},\ \%\) and \(C_{0,\min}^0\) under the following experimental conditions: the error introduced by the capacitive current is equal to 1%; \(z=2\); \(g=1\); \(A=100\); \(\gamma=0.63\) [5]; \(V=1\ \mathrm{ml}\); the values \(r_0\), \(\Delta\varphi_1\), \(C_d\), \(D_R\) are given above. The calculation gives: \(C_{0,\min}^0=2.6\cdot 10^{-8}\ \mathrm{M}\); \(a_{\min}=2.6\cdot 10^{-7}\%\).

Conclusions

Expressions have been obtained for estimating the minimum determinable impurity content in an amalgam and in solution by the AAV method with constant current on a spherical mercury electrode. A numerical estimate has been made of the minimum determinable concentration of an element in the amalgam and in solution.

REFERENCES

1. M. S. Zakharov, V. V. Pnev. Electrochemistry (in press).
2. P. Delahay. New Instruments and Methods in Electrochemistry, IL, Moscow, 1957.
3. L. Gierst. Dissertation, Brussels University, 1952. Cited after P. Delahay, IL, Moscow, 1957.
4. M. S. Zakharov, V. I. Bakanov. Izv. TPI (present collection).
5. A. G. Stromberg. Izv. SO AN SSSR, No. 5, 76 (1962).
   A. G. Stromberg. Zavod. labor., 29, 387 (1963).
   A. G. Stromberg. Ibid., 31, 1175 (1965).
   Yu. A. Karbainov, A. G. Stromberg. Zh. analit. khimii, 20, 769 (1965).
   E. K. Spirin. Ibid., 20, 781 (1965).
6. A. G. Stromberg, A. A. Kaplin. Ibid., 20, 1043 (1965).