Theory of the Mutual Influence of Elements in Film Stripping Polarography: A Parametric Approach
Abstract Generated abstract
This paper develops a parametric theory for the mutual influence of elements in film stripping polarography with accumulation on solid electrodes. The authors incorporate effects at the preconcentration and anodic oxidation stages by combining parameters for depletion, active electrode surface, and metal activity in binary deposits, using thermodynamic expressions for substitutional solid solutions and alloys. Derived equations describe anodic peak currents for electronegative metals in two binary alloy cases, and computer calculations show that peak currents may increase or decrease depending on interaction parameters, concentration ratios, and other model variables. The results indicate possible gains in sensitivity but also nonlinear calibration behavior and increased determination error under uncontrolled co-deposition, with qualitative confirmation reported for Cd-Au, Cu-Au, Ag-Au, and Ni-Cr systems on graphite electrodes.
Full Text
nitrogen electrons with the \(\pi\)-electrons of the nucleus; as a result of such an electronic displacement (of the \(E_g\) type), the nitrogen atom does not fully have its unshared electrons available for proton binding.
Experimental Part
The determination of the \(pK_B\) of 9-alkyl-3-(1-aminoalkyl)carbazoles was carried out in a mixture of 80% water and 20% ethanol, by the pH of half-neutralized \(1 \cdot 10^{-2}\) molar solutions of the amines. Titration was performed at a temperature of \((25 \pm 1)^\circ\mathrm{C}\) with a \(0.1\,N\) solution of hydrochloric acid.
The pH was measured with a universal [[unclear: pH]] meter of type OP-204 with a glass electrode of type OP 700-[[unclear]] and a calomel reference electrode of type OP 801. The correctness of the pH-meter readings and the linearity of its scale were checked using 3 buffer solutions in accordance with the instrument passport.
For each of the amines, the mean pH value was taken from 3–4 determinations. The deviation of the results of individual measurements did not exceed \(\pm 0.03\) pH units. For diethylamine, the pK value is 3.38; according to the data of [3], pK is 3.077.
Literature
- E. E. Sirotkina, V. P. Lopatinskii, L. F. Kovaleva, O. T. Yakushina. Izv. TPI, vol. 250 (in press).
- A. Albert, E. Serjeant. Ionization Constants of Acids and Bases. Moscow–Leningrad, “Khimiya,” 1964.
- K. D. Nenitescu. Organic Chemistry, vol. I. Moscow, Izdatinlit, 1963.
THEORY OF THE MUTUAL INFLUENCE OF ELEMENTS IN THE METHOD OF FILM STRIPPING POLAROGRAPHY WITH ACCUMULATION. A PARAMETRIC APPROACH
A. A. Kashin, T. F. Ryashentseva, A. G. Stromberg
In a number of works on film stripping polarography with accumulation (FSP), the mutual influence of two metals on a solid electrode has been experimentally found [1–3]. A quantitative interpretation of the effect of mutual influence of elements on a solid electrode has not yet been ...
is absent.
We propose a parametric theory of the film stripping polarography method (FSP), taking into account the effect of the mutual influence of elements at all stages of the process (the preconcentration stage, the stage of anodic oxidation, and peak recording1). At the preconcentration stage, as follows from the theory of joint electrodeposition of metals, the mutual influence of elements, in the general case, consists in changes in the kinetic parameters of the reduction process. In addition, the deposition of the second component changes the nature of the active electrode surface, the microrelief of the surface, and may affect the hydrodynamic conditions of delivery of the substance to the electrode. Changes are also possible in the distribution of current density over microinhomogeneities of the surface during electrolysis. The presence of the second component may influence processes of surface migration, nucleation, and crystallization. In the formation of dispersed deposits, “islands,” statistically distributed over the electrode surface, at the stage of coalescence of the “islands” and the subsequent growth of thin and then thick films, a change in the electrical resistance of the system is possible.2 At the stage of anodic oxidation, the presence of the second component in the system determines the activity of the first in the deposit and the kinetic characteristics of the process of its anodic oxidation. It is not yet possible to carry out a quantitative allowance for all the factors listed. Therefore, in the present work we shall confine ourselves to considering the influence on the anodic current of only some of the most important factors.
To account for the change in the activity of the metal in the presence of a second component in the deposit, we used the basic propositions of the thermodynamics of molecular solutions /4/ and alloys /5/. When the activity of the macrophase of the pure metal is chosen as the standard state, the expression for the activity of the metal in a bimetallic system (a substitutional solid solution) in the first approximation has the form:
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The stage of preliminary holding before recording the anodic peaks requires the system to pass into an equilibrium state and may be considerably longer than in the ASP method.
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Accounting for the influence of the electrical resistance of such systems in the ASP and FSP methods is an independent problem.
\[ a_1 = m_1 N_1 \cdot \exp B_0 N_2^n \tag{1a} \]
\[ a_2 = m_2 N_2 \cdot \exp \left[-\frac{B_0 n N_2^{n-1}}{n-1} + B_0 N_2^n \right] \tag{1b} \]
and in the second, more rigorous, approximation:
\[ a_1 = m_1 N_1 \exp \left[ B_0 N_2^n - B_1 N_2^{n+1} \right] \tag{2a} \]
\[ a_2 = m_2 N_2 \cdot \exp \left[-\frac{B_0 n}{n-1} N_2^{n-1} +\left(B_0 + B_1\frac{n+1}{n}\right)N_2^n -B_1 N_2^{n+1}\right], \tag{2b} \]
where \(N_i=\dfrac{m_i}{m_1+m_2}\); \(m_i\) is the amount of the \(i\)-th metal (g-atom/cm\(^3\)); index (1) refers to the element predominant in the mixture; index (2) to the dissolved substance; \(n\) is a quantity characterizing the type of interaction; \(B_0\) and \(B_1\) are the energy parameters of the compound formed:
\[ B = Z\left(\varepsilon_{1-2} - \frac{\varepsilon_{1-2}+\varepsilon_{2-2}}{2}\right)\frac{1}{RT} \tag{3} \]
\(Z\) is the coordination number; \(\varepsilon_{i-j}\) is the interatomic bond energy.
It is proposed to take into account the mutual influence of elements at the concentration stage within the framework of the parametric theory of ASV /6/ through the value of the degree of depletion—the parameter \(\gamma\). In the general case, by analogy with the parametric theory of ASV:
\[ I_e = K_e S_e C_i \tag{4} \quad ; \quad I_a = K_a S_a a_i \tag{5} \]
\[ \gamma = 1-e^{-B}, \qquad B=\frac{K_e}{zF}\,\tau\,\frac{S_e}{V} \tag{6} \]
Anodic dissolution of a metal microdeposit from a solid indifferent electrode may be considered in comparison with oxidation of the metal from a mercury film of thickness equal to the statistical average height of all microdeposits. In a mercury film electrode, mercury is an indifferent solvent with respect to the metal. In the model under consideration it is assumed that the metal reduced on the solid electrode is distributed, as it were, in a “quasi-mercury” film of constant volume \(V\). The quantities \(K_e\) and \(K_a\) will include the fraction of the active surface, that is:
\[ K'_e=K_e\cdot \theta_e;\qquad K'_a=\frac{K_a}{V}\cdot \theta_a, \tag{7} \]
where \(\theta_e=\dfrac{S_e}{S_0}\) and \(\theta_a=\dfrac{S_a}{S_0}\) are the fractions of the active surface in the anodic and cathodic processes; \(S_0\) is the geometrical surface area of the electrode. In the course of concentration and anodic dissolution, the quantities \(\theta_e\) and \(\theta_a\) change in a complex manner. The experimentally determined \(K_e\) and \(K_a\) are averaged quantities at each of the stages.
In parametric form, accounting for the mutual influence of elements in the quantitative estimation of the anodic current of one of the alloy components is simplified when a carbon paste electrode is used, if the electroactive substance is a powder of a previously thermally prepared alloy. The absence of an electroconcentration stage makes it possible to exclude the mutual influence of elements during their simultaneous electroreduction on the electrode and to simplify the relations for the anodic current with allowance for the parameter \(\gamma\). In relations (5), the anodic current will be proportional to the activity of the metal (g-atom \(\cdot\ \text{cm}^{-3}\)) in the volume of the paste. During anodic oxidation of a metal from an alloy, the activity of the metal can be represented by equations (1,2). Thus, the parametric theory of the anodic peak of a metal during its oxidation from an alloy for a paste electrode is a special case of that considered above for a solid electrode.
In the present work we shall consider the analysis of the parametric equations of the anodic peak of an electronegative metal during its anodic dissolution from a binary alloy in the more general case, namely for a solid electrode in the presence of an electrochemical concentration stage.
Let us consider two variants.
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The electronegative metal is the solvent with respect to the electropositive one.
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The binary alloy is formed on the basis of the electropositive metal.
Using relations (1,4–6), for \(\theta \le 0.05\) the equations of the anodic peak take the following form:
variant I
\[ I_{a_1}=K'_{a_1}\cdot \frac{K'_e}{z_1F}\cdot S_0^2\tau C_1\cdot \frac{\rho_1\rho_2}{1+\rho_1\rho_2}\cdot \exp\left[B_0\left(\frac{1}{1+\rho_1\rho_2}\right)^n\right], \tag{8a} \]
variant 2
\[ I_{a_2}=K_{a_2}\cdot \frac{K_{e_2}}{Z_2F}\cdot S_0^2 \tau C_2 \frac{1}{1+\rho_1\rho_2} \exp\left[-\frac{B_0 n}{n-1}\left(\frac{1}{1+\rho_1\rho_2}\right)^{n-1} +B_0\left(\frac{1}{1+\rho_1\rho_2}\right)^n\right]. \tag{8b} \]
Similarly, taking into account relations (2, 4–6), for the second approximation:
variant 1
\[ I_{a_1}=K'_{a_1}\cdot \frac{K'_{e_1}}{Z_1F}\cdot S_0^2 \tau C_1\cdot \frac{\rho_1\rho_2}{1+\rho_1\rho_2} \exp\left[ B_0\left(\frac{1}{\rho_1\rho_2+1}\right)^n - B_1\left(\frac{1}{1+\rho_1\rho_2}\right)^{n+1} \right], \tag{9a} \]
variant 2
\[ \begin{aligned} I_{a_2}={}&K'_{a_2}\cdot \frac{K'_{e_2}}{Z_2F}\cdot S_0^2 \tau C_2\cdot \frac{1}{1+\rho_1\rho_2}\cdot \exp\Bigg[ -\frac{B_0 n}{n-1}\left(\frac{1}{1+\rho_1\rho_2}\right)^{n-1} \\ &+\left(B_0+B_1\frac{n+1}{n}\right)\left(\frac{1}{1+\rho_1\rho_2}\right)^n - B_1\left(\frac{1}{1+\rho_1\rho_2}\right)^{n+1} \Bigg], \end{aligned} \tag{9b} \]
where
\[ \rho_1=\frac{C_1}{C_2}; \qquad \rho_2=\frac{K'_{e_1}}{K'_{e_2}}\frac{Z_2}{Z_1}. \]
Using equations (8) and (9), the peak-current values were calculated on an M-220 computer for different values of \(\rho_1\), \(\rho_2\), \(B_0\), and \(n\), under the assumption that \(K_e\) and \(K_a\) do not depend on \(\rho_1\). Some results of the calculations are given in Tables 1 and 2.
Table 1
Values of \(I_a\) (A) for different \(\rho_1\), \(B_0\), and \(n\), calculated on a computer by formula (8a).
\[ C_1=1\cdot 10^{-8}\ \text{g-ion}/\text{cm}^3;\quad \rho_2=1;\quad K_{a_1}=1\cdot 10^{-1};\quad \frac{K_{e_1}}{ZF}=5\cdot 10^{-3}. \]
| \(\rho_1\) | \(n=1.2\), \(B_0=+10\) | \(n=1.2\), \(B_0=-10\) | \(n=1.5\), \(B_0=+10\) | \(n=1.5\), \(B_0=-10\) | \(n=2\), \(B_0=+10\) | \(n=2\), \(B_0=-10\) |
|---|---|---|---|---|---|---|
| 0.01 | \(1.54\cdot 10^{-6}\) | \(1.43\cdot 10^{-6}\) | \(1.50\cdot 10^{-6}\) | \(1.47\cdot 10^{-6}\) | \(1.49\cdot 10^{-6}\) | \(1.48\cdot 10^{-6}\) |
| 0.05 | \(1.85\cdot 10^{-6}\) | \(1.10\cdot 10^{-6}\) | \(1.58\cdot 10^{-6}\) | \(1.29\cdot 10^{-6}\) | \(1.46\cdot 10^{-6}\) | \(1.40\cdot 10^{-6}\) |
| 0.1 | \(2.39\cdot 10^{-6}\) | \(7.77\cdot 10^{-7}\) | \(1.79\cdot 10^{-6}\) | \(1.04\cdot 10^{-6}\) | \(1.48\cdot 10^{-6}\) | \(1.26\cdot 10^{-6}\) |
| 0.5 | \(1.45\cdot 10^{-5}\) | \(6.89\cdot 10^{-8}\) | \(6.85\cdot 10^{-6}\) | \(1.46\cdot 10^{-6}\) | \(3.04\cdot 10^{-6}\) | \(3.29\cdot 10^{-7}\) |
| 1 | \(5.82\cdot 10^{-5}\) | \(9.65\cdot 10^{-9}\) | \(2.57\cdot 10^{-5}\) | \(2.19\cdot 10^{-8}\) | \(9.14\cdot 10^{-6}\) | \(6.16\cdot 10^{-8}\) |
Table 2
Values of \(I_a\) (a) for various \(\rho_1, B_0, n\),
calculated on a computer by formula (8d)
\[ C_2 = 1 \cdot 10^{-8}\ \text{g-ion}/\text{cm}^3;\quad \rho_2 = 1;\quad K_{a_2}=1 \cdot 10^{-1};\quad \frac{k e_2}{ZF}=5 \cdot 10^{-3}. \]
| \(\dfrac{1}{\rho_1}\) | \(n=1.2\), \(B_0=+1.0\) | \(n=1.2\), \(B_0=-1.0\) | \(n=1.5\), \(B_0=+1.0\) | \(n=1.5\), \(B_0=-1.0\) | \(n=2\), \(B_0=+1.0\) | \(n=2\), \(B_0=-1.0\) |
|---|---|---|---|---|---|---|
| 50 | \(1.01\cdot10^{-8}\) | \(2.14\cdot10^{-4}\) | \(2.03\cdot10^{-7}\) | \(1.06\cdot10^{-5}\) | \(5.41\cdot10^{-7}\) | \(3.99\cdot10^{-6}\) |
| 20 | \(1.01\cdot10^{-8}\) | \(2.01\cdot10^{-4}\) | \(2.03\cdot10^{-7}\) | \(1.01\cdot10^{-5}\) | \(5.27\cdot10^{-7}\) | \(3.87\cdot10^{-6}\) |
| 10 | \(1.01\cdot10^{-8}\) | \(1.84\cdot10^{-4}\) | \(2.02\cdot10^{-7}\) | \(9.18\cdot10^{-6}\) | \(5.06\cdot10^{-7}\) | \(3.67\cdot10^{-6}\) |
| 5 | \(1.00\cdot10^{-8}\) | \(1.55\cdot10^{-4}\) | \(2.01\cdot10^{-7}\) | \(7.76\cdot10^{-6}\) | \(4.73\cdot10^{-7}\) | \(3.30\cdot10^{-6}\) |
| 1 | \(9.65\cdot10^{-9}\) | \(5.82\cdot10^{-5}\) | \(1.82\cdot10^{-7}\) | \(3.08\cdot10^{-6}\) | \(3.54\cdot10^{-7}\) | \(1.58\cdot10^{-6}\) |
From these calculations the following main conclusions may be drawn:
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The magnitude of the anodic current, depending on the magnitude and sign of \(B_0\), on the ratio of the concentrations of the two elements in solution, and on the values of other parameters \((\rho_2; n)\), may either increase or decrease. This conclusion follows, in particular, from the results given in Tables 1 and 2. An increase in the anodic current may be used to raise the sensitivity of the determination of individual elements. A decrease in the anodic peak of the electronegative element was made the basis for the indirect determination of the more electropositive element /7/.
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A deviation from linearity is observed in the dependence of the anodic-peak magnitude of the electronegative element on its concentration in solution at a constant concentration of the electropositive element. The degree of deviation depends on the values of \(n\), \(B_0\), and the concentration of the second metal. This may make it difficult to determine impurities by the calibration-curve method or by the method of additions of a standard solution.
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The relative error in determining the electronegative element increases as \(\rho_1\) and \(n\) decrease and as \(B_0\) increases. This worsens the analytical capabilities of the stripping-polarography method in the presence of an uncontrolled content of an electropositive element in solution.
The character of the calculated dependences of the magnitude of the anodic peak of the electronegative element on the concentration of the electropositive metal in solution, and of the deviation from the calibration curve, has been confirmed for the systems $Cd-Au$; $Cu-Au$; $Ag-Au$; $Ni-Cr$ for commensurate amounts of the components of the electrolytic alloy on a graphite electrode.
In the systems $Cu-Au$; $Ag-Au$; $Ni-Cr$, in the dependence of the current of the electronegative element on the concentration of the electropositive one, at a constant concentration of the former in solution, an increase in the peak of the electronegative element is observed in the region of small concentrations of the electropositive element, much smaller than that of the electronegative one. With a further increase in the concentration of the electropositive element, i.e., with commensurate amounts of the components in solution, an exponential decrease occurs in the anodic peak of the more electronegative metal, coinciding in character with the calculated data. The character of the deviation of the calibration curve of the electronegative element at a constant concentration of the electropositive element in all the indicated systems coincides with the theoretical one.
Literature
- E. M. Roizenblat, Kh. Z. Brainina, Elektrokhimiya, 5, 396, 1969.
- Kh. Z. Brainina. “Inversion Voltammetry of Solid Phases,” Moscow, 1972.
- L. F. Trushina, A. A. Kashin. ZhAKh, 25, 1616, 1970.
- I. Prigogine, R. Defay. “Chemical Thermodynamics,” Novosibirsk, Nauka Publishers, 1966.
- K. Wagner. “Thermodynamics of Alloys,” GONTI, Moscow, 1957.
- A. G. Stromberg. Izvestiya SO AN SSSR, 5, 76, 1962.
- T. F. Ryashentseva, A. A. Kashin. Izv. TPI, present volume, p. 13.
INDIRECT DETERMINATION OF CHROMIUM (III) BY THE METHOD OF POLAROGRAPHY WITH ACCUMULATION ON A GRAPHITE ELECTRODE
T. F. Ryashentseva, A. A. Kashin
The possibility of determining chromium by polarography with accumulation after concentrating it on the electrode in the form of a metal has thus far not been experimentally confirmed. Apparently, this is connected with the low solubility of chromium in mercury, as well as with the rapid passivation of metallic chromium in aqueous solutions, which complicates the process of its anodic oxidation.
Several methods are known for the indirect determination of chromium using polarography with accumulation /1–3/. The basis ...