an increase in heat transfer in the stabilized section by 12%, and in hydraulic resistance by 9%, was obtained.

When the number of corona electrodes of constant length in the stabilized section was increased from one to three, the heat-transfer coefficient increased from 18% for one electrode to 58% for three electrodes; the hydraulic resistances increased correspondingly from 10% to 40%.

With an increase in the length of the electrodes, the intensifying effect of the electric field on heat transfer and on hydraulic resistance also increases.

The experimental results show that an increase in the corona surface promotes a greater intensification of heat transfer.

The intensifying action of the electric field is observed within a certain voltage interval. The lower limit of the voltage applied to the electrodes is characterized by the onset of corona formation. The upper limit is the transition of the corona discharge to breakdown, at which point the voltage drops.

Taking into account the small consumption of electrical energy supplied to the electrodes, the indicated method of intensifying heat transfer may be applied in certain characteristic processes.

STUDY OF THE MECHANISM AND KINETICS OF ARSENIC DISCHARGE–IONIZATION PROCESSES ON SOLID ELECTRODES

N. A. Veits, A. A. Kaplin, A. G. Stromberg

The aim of the work was to determine the kinetic parameters of the discharge \((\alpha, K_{S2})\) and ionization \((\beta, K_{S1})\) processes of arsenic in a hydrochloric-acid medium on solid electrodes, to determine the composition of the complexes predominating in solution and directly discharged at the electrode. For the calculation, relations were used that follow from the equations for the potentials of the cathodic /1/ and anodic /2/ peaks in a complex-forming medium.

Graphite, platinum, and gold electrodes were used as indicator electrodes. The reference electrode was a saturated calomel electrode.

The transfer coefficients of the arsenic discharge process \((\alpha)\) were determined from the dependence of the potentials of the cathodic peaks \((\varphi_{p,k})\) on

the rate of change of the potential \((W)\) and from the difference of the potentials of the cathodic peaks and half-peaks \((\psi_{n,k/2})\) /1, 3/:

\[ \alpha=\frac{2.3RT}{nF}\cdot\frac{\partial \lg W}{\partial \psi_{n,a}}, \qquad \alpha=\frac{0.048}{n(\psi_{n,k/2}-\psi_{n,k})} \]

The transfer coefficients of the ionization process \((\beta)\) of arsenic were determined from the dependence of the potentials of the anodic peaks \((\psi_{n,a})\) on the rate of change of the potential and from the difference in potentials of the inflection points of the anodic polarization curve \((\Delta \psi_{\mathrm{inf}}=\psi_2-\psi_1)\) /2, 4/:

\[ \beta=\frac{2.3RT}{nF}\cdot\frac{\partial \lg W}{\partial \psi_{n,a}}, \qquad \beta=\frac{4.87RT}{nF\,\Delta \psi_{\mathrm{inf}}}. \]

The values of the coefficients \(\alpha\) and \(\beta\), determined by different methods, agree satisfactorily. It is shown that the kinetic parameters of electro-dissolution of arsenic depend on the electrode material and on the nature of the elements codeposited with arsenic (Table 1).

Table 1

Using the criteria proposed by Bragina /4/, it was shown that the process of electrooxidation of arsenic is irreversible.

The number of electrons participating in the arsenic ionization process was determined by the “standard area” method /5/ in the variant proposed in /6/. Bi and Cu were used by us as the “standard” elements. From comparison of the areas under the anodic peaks of As, Bi, and Cu on a gold electrode, the value of \(n\) for the oxidation process of As was calculated to be equal to three.

In order to determine the composition of the complexes predominating in hydrochloric-acid solution and directly participating in the electrode processes, the dependences of the equilibrium potential \((\psi_p)\), the potentials of the anodic \((\psi_{n,a})\) and cathodic \((\psi_{n,k})\)

peaks on the logarithm of the concentration of hydrogen and chlorine ions. The effect of solution pH was studied in the range \( \mathrm{pH} = 7 \div (-0.9) \) on gold and platinum electrodes at an arsenic-ion concentration of \(1 \cdot 10^{-3}\) g-ion/l. To maintain a constant ionic strength \(J = 4\), the experiments were carried out in a solution of \(x\) M HCl \(+\) \((4-x)\) M RbCl. Potentiometric measurements were performed with a high-resistance pH meter in a sealed cell under argon, in view of the experimentally established fact that arsenic is oxidized under equilibrium conditions and passes into solution from the electrode surface.

The presence on the plot of the dependence \(\varphi_p\)-pH of several sections with different tangents of the angle of inclination indicates that the composition of the arsenic complexes changes within the pH range studied.

The effect of chlorine ions was studied at \(\mathrm{pH} = 5;\ 2;\ -0.6\). Constant ionic strength (respectively \(10^{-5}\), \(10^{-2}\), and 4) was maintained with \(\mathrm{HClO_4}\).

On the basis of an analysis of the experimental dependences, the reaction orders of reduction \((q_2)\) and ionization \((q_I)\) of arsenic with respect to hydrogen and chloride ions, and the number of ligands \((p)\) entering into the composition of the complex predominating in solution, were determined:

\[ q_1=\frac{\beta nF}{2.3RT}\left(-\frac{\partial \varphi_{n,a}}{\partial \lg C_n}\right) \]

\[ -(p-q_2)=\left(\frac{\partial \varphi_{n,k}}{\partial \lg C_l}\right)\frac{\alpha nF}{2.3RT}, \qquad -p=\left(\frac{\partial \varphi_p}{\partial \lg C_l}\right)\frac{nF}{2.3RT} \]

The results are presented in Table 2.

Table 2

The studies carried out make it possible to propose the following mechanism for the discharge and ionization processes of arsenic in hydrochloric acid.

In the region \( \mathrm{pH}=3 \div 0 \):

equilibrium in solution:

\[ H_3AsO_3 \rightleftarrows As(OH)_2^{+} + OH^{-}; \]

discharge process:

\[ As(OH)_2^{+} + 3\bar e \longrightarrow As^{\circ} + 2OH^{-}; \]

ionization process:

\[ As^{\circ} + OH^{-} \longrightarrow As(OH)^{2+} + 3\bar e \]

After certain transformations,

\[ 2As^{\circ} + 2OH^{-} = 2As(OH)^{2+} + 6\bar e \]

\[ 2As^{\circ} + 2OH^{-} + H_2O = 2As(OH)^{2+} + H_2O + 6\bar e \]

\[ 2As^{\circ} + 2OH^{-} + H_2O = As_2O_3 + 4H^{+} + 6\bar e \]

we obtain the equation

\[ 2As^{\circ} + 3H_2O = As_2O_3 + 6H^{+} + 6\bar e, \]

for which [7] gives the value of the standard potential

\[ \varphi^{\circ} = +0.234\ \mathrm{V}\ (\mathrm{N.H.E.}) \]

and

\[ \varphi_p = \varphi^{\circ} - \beta\,\mathrm{pH}. \]

Experimentally we obtained an analogous dependence of \(\varphi_p\) on the pH of the solution:

\[ \frac{\partial \varphi_p}{\partial \mathrm{pH}} = -0.05,\qquad \varphi^{\circ}_{\mathrm{exper.}} = +0.309\ \mathrm{V}\ (\text{recalculated to N.H.E.}). \]

It may be assumed that the equilibrium \(As/As_2O_3\) is established. This is confirmed by the fact that \(\varphi_p\) is practically independent of the concentration of arsenic ions in the solution in this pH region.

For the region \( \mathrm{pH}=0 \div -0.9 \), the following mechanism is proposed:

equilibrium in solution:

\[ AsCl_3 \rightleftarrows As^{3+} + 3Cl^{-}; \]

discharge process:

\[ As(OH)_2^{+} + 3\bar e \longrightarrow As^{\circ} + 2OH^{-}; \]

ionization process:

\[ As^{3+} + 3\bar e \longrightarrow As^{\circ}. \]

With regard to the mechanism of the discharge and ionization processes of arsenic in the region \( \mathrm{pH}=7 \div 3 \), it is difficult to draw an unambiguous conclusion. The experimental data indicate the independence of the equilibrium potential and of the potentials of the cathodic and anodic peaks both from the concentration of \(H^{+}\) ions and from the concentration of \(Cl^{-}\) ions. It is quite possible that a completely different equilibrium exists in this region, since \(\varphi_p\), \(\varphi_{\mathrm{pa}}\), and \(\varphi_{\mathrm{pc}}\) change discontinuously upon transition from this pH region to the region \( \mathrm{pH}=3 \div 0 \).

On the basis of the data obtained, the values of the rate constants of arsenic discharge \((K_{S2})\) and ionization \((K_{S1})\) at \(\mathrm{pH}=2\) on a gold electrode were estimated.

\[ \lg K_{S2}=1.14+\frac{1}{2}\lg(D\alpha nW)+(p-q_2)\lg C_{\Omega} +\frac{\alpha nF}{2.3RT}\left(\psi_{n,k}-\varphi^{\circ}\right); \]

\[ \lg K_{s1}=\lg \frac{\beta W}{S a_{\infty}\gamma R T} -\frac{\beta nF}{2.3RT}\left(\varphi_{n,a}-\varphi^{0}\right) -q_{1}\lg C_{n}; \]

\[ K_{s2}=1\cdot 10^{-10}\ \text{cm/sec};\qquad K_{s1}=7\cdot 10^{-8}\ \text{cm/sec}. \]

The calculated values of the constants indicate the irreversibility of the arsenic discharge–ionization processes under the conditions studied.

Literature

1. A. G. Stromberg, L. N. Popova. Elektrokhimiya, 4, 39, 1968.
2. N. A. Kolpakova. Dissertation, TPI, Tomsk, 1968.
3. H. Matsuda, Y. Ayabe, Z. Elektrochem., 63, 1164, 1959.
4. X. Z. Brainina. Inversion Voltammetry of Solid Phases, Moscow, “Khimiya,” 1972.
5. E. A. Zakharova. Izv. TPI, 128, 53, 1964.
6. E. K. Spirin. Dissertation, TPI, Tomsk, 1965.
7. Pourbaix M., Atlas d’équilibres électrochimiques, Paris, 1963.

SMOOTHING OF EXPERIMENTAL RESULTS ON THE BASIS OF THE USE OF A NONPARAMETRIC APPROACH

A. I. Ruban

In problems involving the study of chemical-technological objects, an integral part is the smoothing of experimental results, i.e., the construction of regression dependences between variables. For these purposes the method of least squares (MLS) is usually used. However, it has a number of substantial limitations that narrow the range of its application.

In the present work a general approach to smoothing experimental results is proposed. It is more universal than MLS and leads to comparatively simple computational algorithms.

I. Problem Statement

Let us assume that there is a system of random variables \(Y, X_1,\ldots,X_k\), related to one another by an unknown static dependence. On the basis of experimental data it is necessary

\[ \begin{gathered} y_1,\ x_{11},\ldots,\ x_{1k},\\ y_2,\ x_{21},\ldots,\ x_{2k},\\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\\ y_n,\ x_{n1},\ldots,\ x_{nk}, \end{gathered} \tag{I.1} \]