Accounting for the Interaction of Components of Complex Systems in Anodic Current Equations
Abstract Generated abstract
This paper addresses how mutual influence among jointly deposited elements affects anodic current equations in accumulation polarographic methods for multicomponent systems. Building on a semiempirical treatment of the effect at the accumulation stage, it introduces the relative degree of depletion as a distribution coefficient and combines it with a statistical thermodynamic activity approach for ternary and more complex systems. In the regular solution approximation, the authors derive expressions linking anodic current to electrode-surface molar fractions and pair interaction parameters, and note that these parameters may be obtained experimentally or by computer comparison of measured curves with mathematical process models.
Full Text
- L. G. Baletskaya, Some Physicochemical Questions of the APN Method and Its Application in the Control of Phosphor Production. Dissertation, Tomsk, 1967.
ON ACCOUNTING IN ANODE-CURRENT EQUATIONS FOR THE INTERACTION OF COMPONENTS OF COMPLEX SYSTEMS
A. A. Kaplin, V. A. Kolpakov.
The possibility of the simultaneous determination of several elements is one of the principal advantages of the APN and PPN methods. However, the joint deposition of two or more elements on a mercury or solid electrode can lead to the appearance of an effect of mutual influence (EMI), a particular case of which is interaction in the system “determined element–electrode material.” The presence of EMI changes, in the general case, the analytical characteristics of the useful signal. In works 1, 2 we developed a semiempirical theory of EMI in the APN and PPN method. As a quantitative measure of EMI at the accumulation stage, caused by facilitation or hindrance of the discharge of one element in the presence of another, by a change in the nature of the substrate and in the magnitude of the active surface, by the mutual influence of elements on the stage of nucleation, growth of nuclei, etc., the value of the degree of depletion of the solution, \(\delta\), was adopted. In addition to this, it is expedient to introduce the relative degree of depletion, or the relative distribution coefficient,
\[ \theta=\frac{\delta_2}{\delta_1}, \]
which characterizes the changed ratio of the amount \((m_i)\) or concentration \((C_{э,i})\) of elements on the surface or in the bulk of the electrode in comparison with the solution:
\[ \theta=\frac{\rho_{э,m}}{\rho_{p}}=\frac{\rho_{э,p}}{\rho_{p}}, \quad \rho_{э,m}=\frac{m_2}{m_1},\quad \rho_{э,p}=\frac{C_{a,2}}{C_{a,1}},\quad \rho_p=\frac{C_{p,2}}{C_{p,1}}. \tag{1} \]
In the presence of EMI, the value \(\theta \ne 1\). In the general case, \(\theta\) depends on the concentration of the element in solution. To account for EMI at the stage of anodic oxidation for binary systems, it was proposed [1, 2] to use the activity method. More complicated is the derivation of an anode-current equation for the components of ternary and more complex systems. Apparently, in these variants it is also expedient to use the statistical-thermodynamic method. In the general case,
\[ I=K_a S a_i(I). \]
The activity of an element on the surface or in the bulk of the electrode is
\[ a_i=\exp\left[\frac{1}{kT}\frac{\partial \ln F}{\partial N_i}\right], \]
where \(F\) is the free energy of mixing of the system. When the free energy is represented as a sum of products by concentration, containing unknown parameters, one can obtain relations for \(a_i\) [3, 4]. Thus, for a ternary system (regular-solution approximation),
\[ a_1=N_1\exp\left\{\left[B_{12}N_2^2+B_{13}N_3^2+ (B_{12}+B_{13}-B_{23})N_2N_3\right]\right\}, \]
\[ a_2=N_2\exp\left\{\left[B_{12}N_1^2+B_{23}N_3^2+ (B_{12}+B_{23}-B_{13})N_1N_3\right]\right\}, \tag{2} \]
\[ a_3=N_3\exp\left\{\left[B_{13}N_1^2+B_{23}N_2^2+ (B_{13}+B_{23}-B_{12})N_1N_2\right]\right\}. \]
The combination of equations (1–2) makes it possible to describe the anode current as a function of the molar fractions of the elements on the electrode and of the interaction parameters \(B_{ij}\) in boundary systems. An analogous thermodynamic approach is applicable for deriving equations describing the electrochemical dissolution of oxides, including nonstoichiometric ones. The parameters \(B_{ij}\) are determined experimentally; a possible method for determining them is also the comparison, with the aid of a computer, of experimental curves or individual peaks with a mathematical model of the process implemented on a computer [5].
Literature
- A. A. Kashlin. In the collection “Advances in Polarography with Accumulation.” Publishing House of TPU, Tomsk, 1973, pp. 133–136.
- A. A. Kashlin, T. F. Ryashentseva, ibid., pp. 137–139.
- A. I. Men, Yu. P. Vorob’ev, G. I. Chufarov. Physicochemical Properties of Nonstoichiometric Oxides, Moscow, Khimiya, 1973.
- G. I. Chufarov et al. In the collection Physical Chemistry of Oxide Systems, Nauka Publishing House, 1971, pp. 95–106.
- A. A. Kashlin et al. In the collection “Advances in Polarography with Accumulation,” TPU Publishing House, Tomsk, 1973, pp. 65–66.
STUDIES IN THE CHEMISTRY OF CARBAZOLE DERIVATIVES. USE OF ACID IONIZATION OF 3-NITROCARBAZOLE FOR ITS QUANTITATIVE DETERMINATION.
V. P. Lopatinskii, I. P. Zherebtsov, S. P. Yudina, L. P. Belyanina
Ionization of 3-nitrocarbazole according to the acid type proceeds in sufficiently basic media with formation of an anion whose light-absorption maximum is located rather far from the absorption maximum of the neutral molecule and lies in the visible region of the spectrum /1/. On the other hand, 9-alkyl derivatives of 3-nitrocarbazole have insignificant absorption in the region of the anion, which makes it possible to use a photometric method for determining 3-nitrocarbazole in its mixture with 9-substituted derivatives.
Experimental part.
3-Nitrocarbazole was obtained according to /2/, m.p. 216°. 3-Nitro-9-ethylcarbazole was obtained according to /3/, m.p. 130°. 3-Nitro-9-(2-oxy)-ethylcarbazole was obtained according to /4/, m.p. 183–184°. 3-Nitro-9-(2-oxy)propylcarbazole was obtained by the interaction of 3-nitrocarbazole and propylene oxide in acetone in the presence of caustic potash by analogy with /4/, m.p. 144.5°. For photometric measurements, solutions were used—