Coulometry

The coulometry is a method of electrochemistry .

Coulometry is a method to determine the quantitative amount of substance of an oxidizable or reducible compound. It was developed by the Hungarians László Szebellédy and Zoltán Somogyi in 1938. It was not until 1950 that the method was used more widely. Coulometry is based on the measurement of the electrical charge or amount of electricity that is converted at a working electrode . Coulometry is very similar to electrogravimetry , but the oxidized or reduced substances are not necessarily deposited on the electrode, but can also remain in solution. The complete implementation can be indicated via an indirect indicator (e.g. manganation) or is adhered to or monitored by a precise potential control or measurement. According to Faraday's law , the electrical charge is proportional to the amount of substance converted. If the electrochemical conversion of the substance to be determined (the analyte) is complete and there are no electrochemical side reactions, the amount of analyte is calculated using the Faraday constant . Since an electrochemical reaction must also take place at the counter electrode in order to close the circuit, it must be ensured that the reaction products cannot get into the area of ​​the working electrode. This can be done through a diaphragm or by means of a chemical bond (e.g. halogen with a silver counter electrode as a sparingly soluble silver halide). The coulometry finds z. B. Application when determining the water content according to Karl Fischer in the trace range or when quantifying the adsorbable organically bound halogens (AOX) in water samples.

Potentiostatic coulometry

In the potentiostatic variant of coulometry, the electrode potential is kept constant with the aid of a potentiostat . This potential control is very advantageous in order to rule out side reactions. The disadvantage is that the current strength drops sharply because of the steadily falling analyte concentration. This can make the experiment take a long time. The end of the reaction is assumed when the current drop has reached 99.9 percent. The amount of electricity sought is then calculated using the integral of the current over time. With a very small electrode surface, large concentrations and large volumes, the analysis can take days. For this reason, coulometry is a trace analysis method.

${\displaystyle Q=\int _{0}^{t}I\,\mathrm {d} t,}$

This evaluation is usually carried out by an integrating analog circuit ( integrator circuit ) or a computer program.

The calculation of the deposited or converted mass results from the following relationships:

Faraday's law : ${\displaystyle Q=n\cdot z\cdot F}$

Amount of substance : ${\displaystyle n={\frac {m}{M}}}$

Inserted and resolved for the mass m :

${\displaystyle m={\frac {M\cdot Q}{z\cdot F}}}$

Here, M the molar mass in g / mol, Q the experimentally determined charge in Coulomb , z the charge number which in reduction or oxidation of the change of the oxidation number corresponds and F the Faraday constant in C / mol.

Examples

Reduction of metal ions to metals on mercury or platinum electrodes :

${\displaystyle {\ce {Ni^2+ + 2 e^- -> Ni}}}$

Change in the oxidation level (valence level) on platinum electrodes:

${\displaystyle {\ce {Eu^2+ -> Eu^3+ + e^-}}}$

Oxidative deposition of halides on silver electrodes:

${\displaystyle {\ce {2 Br^- -> Br2 + 2 e^-}}}$

Galvanostatic Coulometry

In the galvanostatic variant of coulometry is electrolysis - current using a galvanostat kept constant. In the simplest case, this consists of a battery , a resistor of several kiloohms and a potentiometer connected in series with the electrochemical cell. The kilo-ohm resistor limits the electrical current, as it has by far the highest resistance value in the circuit. The simple device technology and the quick implementation are advantageous. The disadvantage is that the electrode potential changes during the reaction and therefore secondary reactions must be ruled out by other measures (e.g. cleaning steps during sample preparation ). The end of the reaction must be indicated by an indication method (for example by measuring the pH value ). This method can therefore also be viewed as a “titration with electrons”.

Since the current strength is kept constant, the following relationship applies to the converted charge:

${\displaystyle Q=I\cdot t}$

Indication methods

The methods below can be used for endpoint indexing. It should be noted that the quality of the method often depends on the amount of analyte and on the background matrix, e.g. B. pH buffer etc.

pH indication: The pH indication is best at pH = 7; the further you go to pH = 0 or pH = 14, the worse the indication becomes. If the analyte concentration is very low, the change in pH value is not large enough to detect a change in pH value, since water also has buffer properties.

Conductometric indication: In reactions that do not take place between pH = 6 and pH = 8, the conductivity of the protons or the hydroxide ions is too high. In addition, electrolyte salt is always added in excess to prevent migration of the analyte in the electrical field. Therefore the conductivity of the solution is generally high. At low analyte concentrations, the conductivity is not significantly changed. Thus, an indication is difficult or impossible as long as the analyte concentration is low.

Photometric indication: If the initial concentration is very low, the extinction coefficient of most analytes is too low to perceive a significant change in the extinction. Due to the high concentration of conductive salt and auxiliary reagent, matrix-related disturbances can occur.

Biamperometer indication by means of an indicator electrode: A very small potential or a very small current is applied to an indicator electrode and an auxiliary reagent is added to the solution, which is converted instead of the analyte. Since a reaction at the cathode and at the anode must be allowed for the unhindered current flow and the dissolved salt is only present in one oxidation state (oxidized or reduced), only a small residual current flows. As soon as the coulometry is started, the auxiliary reagent is converted, which then converts the analyte and reacts back. The species important for the oxidation / reduction is converted again, so the current flow remains very small. After the analyte has been converted, the oxidized and the reduced form will be present in the solution as a result of the reaction. This allows the current to flow on the indicator electrode (which usually consists of two Pt pins), since the electrochemical processes can now take place on the anode and the cathode. If a defined current is applied, the potential drops; if a fixed potential is applied, the current increases after the analyte has been completely converted. Since in galvanostatic coulometry an increase in potential occurs over time, an auxiliary reagent must be used in excess anyway, which makes the increase in potential negligibly small. This auxiliary reagent can then easily be used to determine the endpoint. Fortunately, the voltage drop or the increase in current in the solution does not depend on the analyte concentration, but rather on the indicator electrode surface (keep it as small as possible) and the concentration of the auxiliary reagent.

example

There are cerium (IV) ions are determined. These ions are reduced during the determination:

${\displaystyle {\ce {Ce^4+ + e^- -> Ce^3+}}}$

The actual reduction takes place in that an auxiliary reagent (e.g. an iron (III) salt) added in excess is cathodically reduced during the electrolysis and the reduced form then supplies the electrons during the oxidation:

${\displaystyle {\ce {Fe^3+ + e^- -> Fe^2+}}}$

${\displaystyle {\ce {Fe^2+ -> Fe^3+ + e^-}}}$

As long as all cerium (IV) ions have not been reduced, the concentration of iron (III) ions remains constant and a constant current flows. The end point of the coulometric determination is reached when the current strength decreases.

Chronocoulometry

The chronocoulometry is basically a chrono amperometry , i. H. a potential jump experiment is carried out and the change in the electrolysis current is monitored with a high temporal resolution (microseconds). However, it is integrated over time in order to preserve the converted electrical charge. The aim is to determine the substances on the surface of the working electrode. These are converted in a very short time, while substances dissolved in the electrolyte first have to diffuse to the electrode surface. The electric current caused by the latter process of falls, according Cottrellgleichung with from. Therefore, a mathematical distinction can be made between the conversion of dissolved and deposited substances. ${\displaystyle {\sqrt {t}}}$

Coulometer

There are two different types of coulometers:

• Coulometers as devices with which the analytical method coulometry is carried out. For example, there are such coulometers for determining water in the trace range or for determining CO ₂ in gases.

• Coulometers that are used to determine electrical quantities in a direct current circuit, namely the total charge or a constant current strength. In the 19th century and the first half of the 20th century, these devices, invented by Michael Faraday, were widely used in science and technology. In the 19th century, coulometers were called voltameters , for details such as the explanation of the different types see there. These coulometers do not perform quantitative analysis as described in this article and are no longer part of analytical coulometry today.

literature

• Karl Abresch, Ingeborg Claassen: The coulometric analysis . Verlag Chemie, Weinheim 1961 (monographs on “Angewandte Chemie” and “Chemie-Ingenieur-Technik”; 71).
• Karl Abresch, Karl Heinz Büchel : The coulometric analysis . In: Angewandte Chemie , Vol. 74 (1962), No. 17, p. 685, ISSN  1433-7851
• Gustav Kortüm : Textbook of Electrochemistry . 5th edition Verlag Chemie, Weinheim 1972, ISBN 3-527-25393-9 (EA Weinheim 1952)
• Mathias Wünsche: Simultaneously conducted investigations into the electrochemical growth of copper films using coulometry, microgravimetry and light reflection . Dissertation, Free University of Berlin 1994.
• Georg Schwedt : Analytical chemistry . 2nd edition Wiley-VCH Verlagsgesellschaft, Weinheim 2008, pp. 175 ff., ISBN 978-3-527-31206-1