# Faraday Constant: Experimental Aspects, Example, Uses

The Faraday constant is a quantitative unit of electricity that corresponds to the gain or loss of one mole of electrons by an electrode; and therefore, at the step of 6.022 · 10 23 electrons.

This constant is also represented by the letter F, called a Faraday. One F equals 96,485 coulomb / mole. From lightning in stormy skies you get an idea of ​​the amount of electricity an F. represents.

The coulomb (c) is defined as the amount of charge that passes through a given point on a conductor, when 1 ampere of electrical current flows for one second. Also, one ampere of current is equal to one coulomb per second (C / s).

When there is a flow of 6.022 · 10 23 electrons (Avogadro’s number), the amount of electrical charge to which it corresponds can be calculated. How?

Knowing the charge of an individual electron (1,602 · 10 -19 coulomb) and multiplying it by NA, Avogadro’s number (F = Na · e ). The result is, as defined at the beginning, 96,485.3365 C / mol e , usually rounded to 96,500C / mol.

Article index

• one

Experimental aspects of the Faraday constant

• 1.1

• two

Relationship between the moles of electrons and the Faraday constant

• 3

Numerical example of electrolysis

• 4

Faraday’s Laws for Electrolysis

• 4.1

First Law

• 4.2

Second law

• 5

Use in estimating the electrochemical equilibrium potential of an ion

• 6

References

## Experimental aspects of the Faraday constant

The number of moles of electrons that are produced or consumed in an electrode can be known by determining the amount of an element that is deposited on the cathode or anode during electrolysis.

The value of the Faraday constant was obtained by weighing the amount of silver deposited in the electrolysis by a certain electric current; weighing the cathode before and after electrolysis. Also, if the atomic weight of the element is known, the number of moles of the metal deposited on the electrode can be calculated.

Since the relationship between the number of moles of a metal that is deposited on the cathode during electrolysis and the number of moles of electrons that are transferred in the process is known, a relationship can be established between the supplied electrical charge and the number of moles of electrons transferred.

The indicated relation gives a constant value (96,485). Later, this value was named, in honor of the English researcher, Faraday’s constant.

Michael Faraday, a British researcher, was born in Newington, on September 22, 1791. He died in Hampton, on August 25, 1867, at the age of 75.

He studied electromagnetism and electrochemistry. His discoveries include electromagnetic induction, diamagnetism, and electrolysis.

## Relationship between the moles of electrons and the Faraday constant

The three examples below illustrate the relationship between the moles of electrons transferred and the Faraday constant.

Na + in aqueous solution gains an electron at the cathode and 1 mole of metallic Na is deposited, consuming 1 mole of electrons corresponding to a charge of 96,500 coulomb (1 F).

Mg 2+ in aqueous solution gains two electrons at the cathode and 1 mole of metallic Mg is deposited, consuming 2 moles of electrons corresponding to a charge of 2 × 96,500 coulomb (2 F).

Al 3+ in aqueous solution gains three electrons at the cathode and 1 mole of metallic Al is deposited, consuming 3 moles of electrons corresponding to a charge of 3 × 96,500 coulomb (3 F).

## Numerical example of electrolysis

Calculate the mass of copper (Cu) that is deposited on the cathode during an electrolysis process, with a current intensity of 2.5 ampere (C / s or A) applied for 50 minutes. The current flows through a solution of copper (II). Atomic weight of Cu = 63.5 g / mol.

The equation for the reduction of copper (II) ions to metallic copper is as follows:

Cu 2+     + 2 e => Cu

63.5 g of Cu (atomic weight) are deposited on the cathode for every 2 moles of electrons that is equivalent to 2 (9.65 · 10 4 coulomb / mole). That is, 2 Faraday.

In the first part, the number of coulombs that pass through the electrolytic cell is determined. 1 ampere equals 1 coulomb / second.

C = 50 min x 60 s / min x 2.5 C / s

7.5 x 10 3 C

Then, to calculate the mass of copper deposited by an electric current that supplies 7.5 x 10 3  C, the Faraday constant is used:

g Cu = 7.5 10 3 C x 1 mol e / 9.65 10 4 C x 63.5 g Cu / 2 mol e

2.47 g Cu

## Faraday’s Laws for Electrolysis

### First Law

The mass of a substance deposited on an electrode is directly proportional to the amount of electricity transferred to the electrode. This is an accepted statement of Faraday’s first law, existing, among other statements, the following:

The amount of a substance that undergoes oxidation or reduction at each electrode is directly proportional to the amount of electricity that passes through the cell.

Faraday’s first law can be expressed mathematically as follows:

m = (Q / F) x (M / z)

m = mass of the substance deposited on the electrode (grams).

Q = electric charge that passed through the solution in coulombs.

F = Faraday constant.

M = atomic weight of the element

Z = valence number of the element.

M / z represents the equivalent weight.

### Second law

The reduced or oxidized amount of a chemical on an electrode is proportional to its equivalent weight.

Faraday’s second law can be written as follows:

m = (Q / F) x PEq

## Use in estimating the electrochemical equilibrium potential of an ion

The knowledge of the electrochemical equilibrium potential of the different ions is important in electrophysiology. It can be calculated by applying the following formula:

Vion = (RT / zF) Ln (C1 / C2)

Vion = electrochemical equilibrium potential of an ion

R = gas constant, expressed as: 8.31 J.mol -1 . K

T = temperature expressed in degrees Kelvin

Ln = natural or natural logarithm

z = valence of the ion

F = Faraday constant

C1 and C2 are the concentrations of the same ion. C1 can be, for example, the concentration of the ion outside the cell, and C2, its concentration inside the cell.

This is an example of the use of the Faraday constant and how its establishment has been of great use in many fields of research and knowledge.

## References

1. Wikipedia. (2018). Faraday constant. Recovered from: en.wikipedia.org
2. Practice Science. (March 27, 2013). Faraday’s electrolysis. Recovered from: practicaciencia.blogspot.com
3. Montoreano, R. (1995). Manual of Physiology and Biophysics. 2 gives Edition. Editorial Clemente Editores CA
4. Whitten, Davis, Peck & Stanley. (2008). Chemistry. (8th ed.). CENGAGE Learning.
5. Giunta C. (2003). Faraday electrochemistry. Recovered from: web.lemoyne.edu