On the Minimum Concentration of Impurities Determined by Anodic Amalgam Polarography with a Constant Electrode Potential
Abstract Generated abstract
This paper develops theoretical estimates for the minimum impurity concentrations measurable by anodic amalgam polarography with a constant electrode potential. Using the current time relation for linear semi-infinite diffusion after charging of the electrical double layer, the authors derive expressions for the minimum detectable concentration in the amalgam, in solution, and as a weight percent impurity in a sample. Numerical calculations for a spherical mercury electrode show that, under favorable reversible oxidation conditions, very low impurity levels may be estimated, with calculated limits reaching about 3 x 10^-11 percent for a 1 g sample. The paper also notes that increasing instrumental sensitivity may not reduce detection limits proportionally, because capacitive current interference can require longer recording times and thereby reduce the faradaic current term.
Full Text
On the Minimum Concentration of Impurities Determined by the Method of Anodic Amalgam Polarography with Constant Electrode Potential
M. S. Zakharov, L. F. Trushina
(Presented by the scientific seminar of the Department of Physical and Colloid Chemistry)
In the AAP method with a constant electrode potential, the anodic current of electro-dissolution of the amalgam is better recorded not at the moment the potential is applied to the electrode, but after some time. When sufficiently concentrated electrolytes are used \((1\text{–}2M)\), the electrical double layer has time to charge within \(3\cdot 10^{-4}\) sec [1]; consequently, to determine the content of an element in the amalgam, the current must be recorded after this time. For such a short time [2], on mercury film and spherical electrodes, electro-dissolution of the amalgam will occur under conditions of linear semi-infinite diffusion. In this connection, to estimate the minimum concentrations determined by the method of anodic amalgam voltammetry with constant potential (AAP with CP), it is necessary to use the equation of the \(i\)—\(t\) curve for linear semi-infinite diffusion [3].
\[ i(t)=zFSC_R^0K_s\exp\left[\frac{\beta zF}{RT}(\varphi-\varphi^\circ)\right]\exp(Q^2t)\operatorname{erfc}(Qt^{1/2}), \tag{1} \]
where \(\varphi\) is the electrode potential at which electro-dissolution of the amalgam occurs.
\[ Q=\frac{k_f}{D_o^{1/2}}+\frac{k_b}{D_R^{1/2}}, \tag{2} \]
\(K_f\) and \(K_b\) are the rate constants of the electroreduction and electrooxidation processes at any electrode potential.
The minimum value of the anodic current \((i_m)\) for measuring it with a specified accuracy (for example, 10% relative) is related to the sensitivity of the instrument \((i_x)\) by the following relation [4]:
\[ i_m=h_m i_x, \tag{3} \]
where \(h_m\) is the magnitude of the anodic current that can be measured with the specified accuracy.
From equations (1) and (3) one can obtain an expression for estimating the minimum concentration \((C_{R,m}^0)\) of metal atoms in the amalgam by the AAP with CP method.
\[ C_{Rm}^0= \frac{i_xh_m} {zFSK_s\exp\left[\frac{\beta zF}{RT}(\varphi-\varphi^\circ)\right]\exp(Q^2t)\operatorname{erfc}(Qt^{1/2})}. \tag{4} \]
Taking into account the known relation between the concentration of metal atoms in the amalgam and the concentration of ions in the solution [4], one can obtain an equation for estimating the minimum concentration in solution, \(C^0_{0,m}\), that can be determined by the AAV–CPP method.
\[ C^0_{0,m}= \frac{w i_* h_m} {zF\gamma V S K_s \exp\left[\frac{\beta zF}{RT}(\varphi-\varphi^0)\right]\exp(Q^2t)\operatorname{erfc}(Qt^{1/2})}. \tag{5} \]
Using the known relations between the concentration of impurity ions in solution and the impurity content \((a,\ \text{wt. }\%)\) in a weighed portion \((g)\) of material [4], we obtain an expression for a theoretical estimate of the minimum impurity content \((a_m,\%)\).
\[ a_m,\%= \frac{A w i_* h_m} {10 zF\gamma S K_s \exp\left[\frac{\beta zF}{RT}(\varphi-\varphi^0)\right]\exp(Q^2t)\operatorname{erfc}(Qt^{1/2})}. \tag{6} \]
Let us estimate the minimum concentrations determinable by the AAV method with CPP on a spherical mercury electrode at various sensitivities of the recording instrument and various overvoltage values under the following conditions:
\[ r_0=4\cdot10^{-2}\text{ cm};\quad \alpha=3-0.5;\quad D_R=D_0=2\cdot10^{-5}\text{ cm}^2/\text{s}; \]
\[ z=2;\quad h_m=10\text{ mm};\quad A=100;\quad g=1\text{ g};\quad \gamma=0.63; \]
\(V=1\) ml. The results of the calculations are given in Table 1. It is evident from them that elements whose amalgams are oxidized reversibly can be deter-
Table 1
Minimum concentrations determinable by the AAV method with CPP
| \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | ||
|---|---|---|---|---|---|---|---|---|---|
| \(i_x,\ \text{A/mm}\) | \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | |
| \(k_s,\ \text{cm/s}\) | \(\Delta\varphi,\ \text{V}\) | \(1\cdot10^{-2}\) | 0.04 | \(1\cdot10^{-2}\) | 0.1 | \(1\cdot10^{-4}\) | 0.04 | \(1\cdot10^{-4}\) | 0.1 |
| \(C^0_{R,m}\) | g-atom/l | \(2.4\cdot10^{-7}\) | \(2.4\cdot10^{-8}\) | \(7\cdot10^{-8}\) | \(7\cdot10^{-9}\) | \(2.4\cdot10^{-5}\) | \(2.4\cdot10^{-6}\) | \(7\cdot10^{-6}\) | \(7\cdot10^{-7}\) |
| \(C^0_{0,m}\) | mol/l | \(1\cdot10^{-10}\) | \(1\cdot10^{-11}\) | \(3\cdot10^{-11}\) | \(3\cdot10^{-12}\) | \(1\cdot10^{-8}\) | \(3\cdot10^{-9}\) | \(3\cdot10^{-9}\) | \(3\cdot10^{-10}\) |
| \(a_m,\ \%\) | wt. | \(1\cdot10^{-9}\) | \(1\cdot10^{-10}\) | \(3\cdot10^{-10}\) | \(3\cdot10^{-11}\) | \(1\cdot10^{-7}\) | \(1\cdot10^{-8}\) | \(3\cdot10^{-8}\) | \(3\cdot10^{-9}\) |
mined at concentrations down to \(3\cdot10^{-11}\%\) when using a 1 g weighed portion of the analyzed sample.
It should not apparently be assumed that, with an increase in the sensitivity of the instrument, the minimum determinable concentration will also decrease in direct proportion. In all likelihood, as the sensitivity of the instrument is increased, at still longer times the influence of interferences due to the capacitive current will be manifested. Consequently, in order to eliminate distortion of the anodic faradaic current by the capacitive current, the former will have to be recorded at a longer time from the moment the potential is applied to the electrode. This will lead to a decrease in the denominator term
\[ \exp\left[\frac{\beta zF}{RT}(\varphi-\varphi^0)\right]\exp(Q^2t)\operatorname{erfc}(Qt^{1/2}), \]
which will cause the decrease of the minimum determinable concentration to lag behind the increase in the sensitivity of the recording instrument.
Conclusions
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Theoretical equations have been obtained for estimating the minimum determinable concentration by the method of anodic amalgam voltammetry with constant potential.
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A numerical estimate has been made of the minimum concentration determinable by this method.
References
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