On the Deviation of the Potential at a Metal-Oxide Electrode

N. V. Podbornov, V. N. Titov

(Presented by the scientific seminar of the Faculty of Physics and Engineering)

Metal-oxide electrodes have a number of advantages over glass electrodes. They are simpler in design. Sensors based on them have a low electrical resistance. They can be used in measuring the pH of fluoride media, where the use of glass electrodes is in principle excluded.

The occurrence of a potential at a metal-oxide electrode and its dependence on the active concentration of hydrogen ions can be explained by taking into account the existence on the electrode surface of a sparingly soluble metal hydroxide; the reaction of interaction of the metal with hydroxyl ions can be expressed by the following equation:

\[ Me + n\,\mathrm{OH}^{-} \rightleftarrows Me(\mathrm{OH})_{n} + n\bar e . \tag{1} \]

The magnitude of the resulting potential is expressed as follows:

\[ E = E^{0} - \frac{2.3RT}{n \cdot F}\lg a_{\mathrm{OH}^{-}}^{n}\cdot \frac{a_{Me}}{a_{Me(\mathrm{OH})_{n}}}. \tag{2} \]

Since the activity of the metal ions and the activity of the metal hydroxide, owing to the low solubility, are constant quantities, equation (2) takes the form

\[ E = E^{\prime} - \frac{2.3RT}{F}\lg a_{\mathrm{OH}^{-}} \tag{3} \]

or, taking into account that \(a_{\mathrm{OH}^{-}} = \dfrac{K_{w}}{a_{\mathrm{H}^{+}}}\),

\[ E = E^{\prime\prime} + \frac{2.3RT}{F}\lg a_{\mathrm{H}^{+}}. \tag{4} \]

It follows from the above that the form of equation (4) does not depend on the valence of the hydroxide formed by the metal. If the process described by equation (4) alone determined the magnitude of the potential, then the factor \(\dfrac{\Delta E}{\Delta \mathrm{pH}}\) would have to be, at \(25^\circ\mathrm{C}\), 59 mV per 1 pH unit.

In reality, however, the ratio \(\dfrac{\Delta E}{\Delta \mathrm{pH}}\) differs from the theoretically calculated value and is, for the most part, smaller than it.

The cause of these deviations has not been finally explained.

When a metal-oxide electrode is immersed in a solution, its surface becomes covered with a layer of hydroxide, which has a different structure for different electrodes. Thus, for a tungsten electrode the structure of this hydroxide is loose and soot-like, whereas for an antimony electrode it is denser. Such a more or less developed hydroxide surface possesses a large surface energy and, consequently, a high adsorption capacity. Since reaction (1) proceeds primarily in the surface layer, the activity of the \(\mathrm{OH}^{-}\) ions in which, owing to adsorption forces, is not equal to the activity of these ions in solution, it is not the activity of hydroxyl ions in solution that should be substituted into expression (3), but the activity of hydroxyl ions in the near-electrode adsorption layer. This idea was expressed by K. Schwabe [1]. He attempted to relate the active concentrations of hydroxyl ions in the near-electrode layer and in solution by the Bedeker–Freundlich equation and, for the bismuth electrode, proposed the dependence

\[ a_{\mathrm{OH}^{-}}=\kappa a_{\mathrm{OH}^{-}}^{0.88}. \]

The equation is empirical, and the physical meaning of the coefficients remains unclear.

Adsorption, in principle, always occurs in those cases where two phases are in contact, at least one of which consists of readily mobile particles. Depending on the type of interaction between the phases, chemical and physical adsorption are distinguished. From the standpoint of the effect on a metal-oxide electrode, only physical adsorption is of interest. Since, for the establishment of a reversible potential, the possibility of easy desorption is just as important as the occurrence of adsorption itself, in the case of chemical adsorption desorption is always hindered. Since the process proceeds rapidly and reversibly, not only chemisorption is excluded, but under certain conditions so is physical adsorption, if it does not satisfy this requirement; i.e., equations suitable for describing physical adsorption in the region of capillary condensation are unsuitable.

Reversible equilibria have a statistical-dynamic nature and must be described by the corresponding equations. Such an equation for the case of adsorption is the Langmuir equation. According to its formulation [2], one may write

\[ a_{\mathrm{OH}^{-}}^{\prime}=a_{\infty}\frac{a_{\mathrm{OH}^{-}}}{\dfrac{1}{b}+a_{\mathrm{OH}^{-}}}, \tag{5} \]

where \(a_{\mathrm{OH}^{-}}^{\prime}\) is the activity of hydroxyl ions in the adsorption layer of the metal hydroxide;

\(a_{\mathrm{OH}^{-}}\) is the activity of these ions in the electrolyte solution;

\(a_{\infty}\) is a coefficient characterizing the limiting concentration of hydroxyl ions in the adsorbed layer; it determines the number of adsorption centers per unit surface of the electrode.

\(b\) is the Langmuir adsorption constant.

Replacing \(a_{\mathrm{OH}^{-}}\) in equation (3) by \(a_{\mathrm{OH}^{-}}^{\prime}\) and substituting its value, after a series of transformations one can obtain the expression

\[ E=E^{0\prime\prime}+\frac{2.3RT}{F}\lg a_{\mathrm{K}^{+}}-f_{\mathrm{ads}}, \tag{6} \]

where

\[ f_{agc}=\frac{2.3RT}{F}\lg\frac{a_{\infty}}{\frac{1}{b}+a_{\mathrm{OH}^{-}}}. \tag{7} \]

The Langmuir adsorption constant, or adsorption-equilibrium constant, which depends on the heat of adsorption [3],

\[ b=g\exp\left(\frac{\bar Q}{RT}\right), \tag{8} \]

where \(g\) is the entropy factor.

The heat of adsorption is not constant over the entire surface. Usually adsorption proceeds first of all at those places where the attraction is greatest and where the heat of adsorption has the greatest value; these surface areas may be called the most active. For them the heat of adsorption is largest, and, consequently, the Langmuir constant has maximum values. When the active areas are occupied, with an increase in the concentration of hydroxyl ions, adsorption proceeds on less active areas with a lower heat of adsorption; consequently, the values of the Langmuir constant gradually decrease with increasing concentration of hydroxyl ions. If it is assumed that the heat of adsorption decreases according to a logarithmic law with increasing activity of hydroxyl ions, i.e.,

\[ a_{\mathrm{OH}^{-}}=\exp\left(-\frac{N\bar Q}{RT}\right), \tag{9} \]

where \(N\) is an experimental coefficient depending on the state of the surface, then, taking into account that \(\frac{1}{b}\gg a_{\mathrm{OH}^{-}}\), one can obtain the equation

\[ E=E_{1}+\frac{2.3RT}{F}\left(1-\frac{1}{N}\right)\lg a_{\mathrm{H}^{+}}. \tag{10} \]

Denoting

\[ \frac{2.3RT}{F}\left(1-\frac{1}{N}\right)=K, \]

we have the usual equation by which experimental data are customarily described.

By determining experimentally the coefficient “\(K\)” for different electrodes, it can be shown that the smallest values are characteristic of tungsten electrodes; next come bismuth and antimony electrodes. Thus, among these three electrodes the antimony electrode has the smallest adsorption capacity, and the tungsten electrode the greatest. An analogous conclusion can be reached by studying the structure of the oxide. In the antimony electrode it is denser, whereas in the tungsten electrode it is looser—soot-like.

Taking into account the large role played in the potential of the metal-oxide electrode by the hydroxide layer, its structure should, as far as possible, be kept constant, i.e., one should avoid using metal-oxide electrodes (this applies especially to tungsten ones) for measuring the pH of media that can disrupt the structure of this layer, for example, media possessing abrasive properties.

REFERENCES

1. K. Schwabe. Fundamentals of pH Measurement Technique, translated from German, Foreign Literature Publishing House, Moscow, 1962.

2. J. de Boer. The Dynamic Character of Adsorption, translated from English, Foreign Literature Publishing House, Moscow, 1962.

3. Ya. I. Gerasimov et al. Course of Physical Chemistry, Goskhimizdat, Moscow, 1963.