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# Potentiometry: Fundamentals, Equations, Electrodes

To carry out this analysis, at least two electrodes are essential: one for reference and another for indicator or work. Likewise, there must be a high impedance voltmeter, with which the voltages are measured without allowing an appreciable flow of electrons between both electrodes and the solutions that surround them.

Above we have a general representation of the assembly for a potentiometric analysis. In the compartment where the indicator electrode is inserted is the species whose concentration we want to determine; while in the reference electrode we have another solution, in which we do know the concentrations of its components.

Fundamentals

The voltage that is determined in the potentiometric analysis is that of the cell, E cell , which is the difference between the voltages originated by the two electrodes, the indicator and the reference. The electrodes are sensitive to the activities of the molecules or ions that surround them, being able to accept electrons from them, or on the contrary, give them to them.

The two compartments are connected, so electrons flow from the electrode where reduction occurs (cathode), towards the electrode where oxidation takes place (anode).

However, this transfer of electrons (or current) is almost nil, since otherwise the redox reactions would evolve to completely modify the concentrations and identities of the species involved.

Instead, the voltmeter barely allows the electrons to pass through, so that there is a stable voltage reading, and the cell can reach thermodynamic equilibrium.

It is therefore said that potentiometry is a non-destructive technique, because few ions or molecules are transformed in the measurement process, which is also reversible.

### Cell potential

The cell potential is related to the activities or concentrations of the species of interest through the Nernst equation:

Where Eº is the potential of the same cell under standard conditions, F the Faraday constant, n the number of electrons transferred, R the gas constant, and Keq the equilibrium constant of the global reaction. Calculations are performed by clearing Keq from the E cell reading , and calculating the desired concentration from its equilibrium expression.

However, the concentrations should be calculated by an easier route. By convention, the cell potential is also given by the following equation:

cell = E network – E ox

Where E red is the potential for the reduction half cell, where the indicator electrode is located; while E ox is the potential for the oxidation half cell, where we have the reference electrode. Thus, the equation can be rewritten as:

cell = E indicator – E reference + E j

Being E j equal to the potential originated by the junctions of the salt bridge. In practice, E j cannot be determined, but rather ensure that its value is as minimal as possible by using very dilute solutions, or by ensuring that the compositions in both compartments are similar.

### Analyte potential

From the previous equation we can calculate E indicator , which is the potential that really interests us. With that value, we apply the Nernst equation again:

indicator = Eº – (RT / nF) ln (Red / Ox)

Red is the reduced form of the analyte or species of interest, and Ox is its oxidized form. Assuming that the analyte is the Zn 2+ cations on a metallic zinc electrode, we would have:

indicator = Eº Zn2 + / Zn – (RT / nF) ln (1 / a Zn 2+ )

Where a Zn 2+ is the activity of the Zn 2+ cation , which by experimental settings is quite close to its concentration, [Zn 2+ ]. From this equation the concentration of Zn 2+ is cleared , which, as can be seen, directly affects the value of E indicator .

The reduced form of zinc, Zn, has an activity equal to 1. Therefore, the general equation for oxidized cations of a metal that acts as an electrode will be equal to:

indicator = Eº Mn + / M – (RT / nF) ln (1 / a M + n )

But this only applies in the case of electrodes of the first kind.

## Electrodes

The electrodes, in addition to the voltmeter, are the most important elements of any potentiometric analysis. Some of them will be mentioned below.

### First species

Electrodes of the first kind are metals that oxidize to form cations, driving electrons to the voltmeter. Some of these are as follows: Ag, Zn, Cu, Hg, Sn, Tl, Cd, and Bi.

Not all metals serve as first-class electrodes, as they must not present crystalline irregularities or surfaces covered by layers of oxide that cause unstable voltages.

### Second species

Electrodes of the second kind, on the other hand, are also metallic, but also contain a salt on their surface, the solubility of which depends on the redox reactions that take place. For example, the Ag-AgCl and Hg-Hg 2 Cl 2 (calomel) electrodes are electrodes of the second kind.

### Ion selective

Ion selective electrodes, also known as membrane electrodes, are those that are sensitive to a specific ion or molecule, which is strained through a membrane designed only to pass it and not the other species in solution.

The preferred example of this type of electrode is the glass one, built to determine the concentration of H 3 O + or H + ions , and thus serve as a pechimeter.

## Applications of potentiometry

### Enviromental chemistry

Potentiometry has been used in environmental chemistry in the determination of CN  , F  and NO  ions , as well as ammonia in water currents.

### Clinical Chemistry

Selective electrodes are very useful when the matrix in the middle of the measurements is complex. Therefore, other ions and molecules will interfere with the readings.

This characteristic is especially beneficial in potentiometric determinations carried out within the same cells, where microelectrodes are injected to determine the concentrations of K + , Na + , Cl  , Ca 2+ or H + .

### Potentiometric titrations

Suppose that in the medium where we have the indicator electrode, a titrant is added that reacts with the analyte and, therefore, modifies its concentration. Changes will then occur in the E cell , corresponding in the same way to the change in pH in an acid-base titration.

Thus, plotting E cell vs. V titrant , we will be able to determine the inflection or equivalence point, and with this we will know the concentration of the analyte.

Potentiometric titrations are widely used in analytical chemistry and physicochemical laboratories. Some of the analytes that can be determined with this technique are the following: Fe 2+ , HCO  , Ca 2+ , Mg 2+ , Cu 2+ , ascorbic acid, halides, among others.

All the qualifications, to a certain extent, can be followed via potentiometric instead of resorting to the indicators and their end points.