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# Coulombimetry: fundamentals, types, applications

As its name suggests, the electrical charge Q, in units of coulomb, C, is measured and correlated with the concentration of the oxidized or reduced analyte at the peripheries of the electrodes. Therefore, the oxidation states of the analyte change, occurring in the process a transfer and absorption of electrons that allows the stoichiometric calculation of the desired concentration.

In coulometry, a battery or potentiostat is used to control the current or potential applied to the cells. These cells, unlike potentiometric ones, consist of a system of three electrodes, and are also equipped with a voltmeter and an ammeter.

Coulometry has the advantage of being able to perform titrations without the need to prepare or standardize standards. It also enables the quantification of very small and limited amounts of analyte, such as metal cations, inorganic compounds , and organic compounds . For example, there is a coulometer designed exclusively to measure dissolved CO 2 in samples from the ocean.

## Theoretical foundations of coulombimetry

Coulometry is based on Faraday’s law, which establishes a relationship between the electrical charge of an electrochemical cell and the amount of analyte that is being oxidized or reduced. Knowing this charge Q, as well as the charge of an electron (1.6 · 10 -19 C), we can calculate the number of electrons involved in a reaction,  e- :

e- = Q / e

On the other hand, it is known that one mole of electrons (6.02 · 10 23 ) carries an electric charge equal to 96485 C, a figure known as Faraday’s constant:

F = eN A

= 96485.3365 C / mol

Being convenient to express the number of electrons as a function of moles. Thanks to this, it is possible to resort to the stoichiometric coefficients of an electrochemical reaction, be it oxidation or reduction, taking into account how many moles of electrons the species gain or lose.

### Basic calculations

For example, consider the following chemical equation:

Ox + 2e  → Red

Measuring Q when all the Ox species has been reduced to Red, we can calculate the moles of Ox using conversion factors:

That is, since we know the electric charge for one mole of electrons, we will have how many electrons correspond to the charge xQ. But in turn, every 2 moles of those electrons are used to oxidize 1 mole of Ox.

This reasoning originates a direct formula, although it is not recommended to memorize it, but to be able to deduce it as was done above:

n = Q / (F ñ e- )

Where ñ e- is the number of moles of electrons in the chemical equation.

As long as Q can be calculated, regardless of the type of coulometry, the moles of the analyte Ox or Red can be determined; as long as the current efficiency is 100%. The latter means that all the charge Q must be the product of only one transformation, without other species being reduced or oxidized.

## Experimental foundations of coulombimetry

### Cells

Above is a diagram for a cell with three electrodes, which is commonly used in coulometric analysis. The redox reaction takes place between the working (1) and auxiliary (2) electrodes. Between them two are connected the battery, to apply the potentials to the cell, and the ammeter (A), to measure the electric currents.

However, a reference electrode (3) is needed to be able to monitor the potential of the working electrode, and thus know the variation of the potential for the auxiliary electrode. In this way, it is possible to determine the potential of the whole cell, E cell , necessary to estimate the end of the redox reactions in one of the types of coulombimetry.

Note that almost no current flows between the working electrode and the reference electrode due to the high impedance voltmeter (V), thanks to which we have a reading of the potential for the working electrode. Between these two electrodes we have a system similar to that of a potentiometric analysis: it is static and not dynamic.

### Potentials

Coulometry is, so to speak, an electrolysis performed for analytical and quantitative purposes. Therefore, we speak of applying external potentials, supplied by a battery, to carry out non-spontaneous electrochemical reactions; that is, those that have negative potentials.

Consider for example the following reactions accompanied by their respective potential standards:

Cu 2+ + 2e  ⇌ Cu (s) Eº red = +0.337 V

2 O ⇌ 1 / 2O 2 (g) + 2H + + 2e       Eº red = +1.230 V

Being the equation of the global reaction equal to:

Cu 2+ + H 2 O ⇌ Cu (s) + 1 / 2O 2 (g) + 2H +      Eº red = -0.893 V

The battery must apply a potential of 0.893 V for the electrodeposition of copper and the formation of hydrogen ions to be possible. This potential is the E cell . However, in practice, a potential greater than that calculated must be applied, since there are potentials that oppose the evolution of the reaction:

cell = E cathode – E anode – OP – IR – CP

Where,

OP: overpotential (kinetic barrier)

IR: ohmic potential (intrinsic to cells)

CP: polarization of concentrations (product of Cu 2+ decreases )

## Types of coulombimetry

There are essentially three types of coulombimetry: amperostatic, potentiostatic, and electrogravimetric.

### Ampostatic or galvanostatic

In this type of coulometry, the current flowing through the cell is kept constant through the use of an amperostat. Therefore, having the current i thanks to the ammeter reading, and also knowing the time t once the electrolysis is finished, we can calculate the charge Q associated with the transformation of the analyte:

Q = it

One consequence of keeping the current constant is that the potentials of the electrodes change, either positively or negatively. This abrupt variation is indicative that the analyte has fully reacted, which is when electrolysis is stopped and t is measured . This is the basis for coulometric titrations.

If the potential continues to be lowered or raised, other undesirable electroactive species will end up reacting. That is why the potentials associated with the transformations of interest must be fully known.

### Potentiostatic

One way to prevent other species from being oxidized or reduced is by controlling the potential of the cell for the duration of the electrolysis. This is where potentiostatic coulometry comes in, as it uses a potentiostat to set a certain potential for the cell. Unlike amperostatic coulometry, it is now the current that changes as time passes.

Due to this technical setup, we cannot calculate Q directly with the values ​​of i and t ; the current decreases with time. This is so because as the analyte reacts, fewer and fewer molecules or atoms will donate or accept electrons. Therefore, Q is equal to an integral of the area under the curve of the graph i vs t .

### Electrogravimetric

Electrogravimetric coulometry, known simply as electrogravimetry, is an electrolysis in which it is not necessary to measure charges or electric currents. Instead, the masses of the electrodes are measured before and after electrolysis.

This technique is only applied when the species that are reduced are metallic cations that are electrodeposited on the electrodes, making them heavier.

## Applications

### Potentiostatic

Potentiostatic analyzes make it possible to selectively reduce or oxidize one species at a time in the middle of a mixture. For example, they are used to determine the concentration of the following inorganic ions in trace amounts, or in complex matrices:

-Cu 2+

-As 3+

-Cd 2+

-Co 2+

-Fe 2+ and Fe 3+

-Pb 2+

-X (F  , Cl  , Br  and I  )

-Ni 2+

-Pu 3+

-Ag +

-Sn 2+

-Zn 2+

-U 6+

Also, these analyzes can be used to determine the composition of an alloy. Once the alloy is dissolved in acid, cell potentials are applied in a stepped and controlled manner, thus determining the reduced amount for each metal cation that integrates it.

### Coulometric titrations

In coulometric titrations, mediating agents are used that ensure that they neutralize or fully react with the remaining analyte. The purpose of this is to avoid that the variations of the potential, at a constant current, derive in collateral reactions. Thus, it is possible to titrate, for example, ascorbic acid using iodine as a mediator.

Some metal cations, such as Ag + , Ce 3+ , Fe 3+ , Mn 2+ , Ti 3+ , Cr 2+ , can also be determined by these titrations.

On the other hand, acid-base reactions can be followed using this technique, since the large potentials cause the water to ionize in H 3 O + or OH  , which act as titrating agents that are generated in situ; that is, they will neutralize the acids or bases present.

The CO 2 of the ocean, the precipitation reactions, and the formation of complexes with EDTA, are also possible to analyze by applying coulometric titrations, where redox indicators are added to highlight the end point of the electrolysis.

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