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Faraday’s constant , represented by the symbol F , is one of the fundamental constants in physics and chemistry and represents the absolute value or magnitude of the electric charge of one mole of electrons . The constant is named after the physicist and chemist Michael Faraday, who carried out important studies on electromagnetism and electrochemistry, especially on the electrolysis process. It is a constant that is frequently used in physical and chemical calculations involving large numbers of charge carriers, such as ions or electrons.
Faraday’s constant equation
Because it represents the value of the charge on one mole of electrons, Faraday’s constant can be expressed in terms of the charge on each electron and the number of electrons in one mole of electrons. The charge of each electron is nothing more than the elementary charge, e , one of the most important universal constants in physics. On the other hand, the number of electrons present in a mole of electrons is given by Avogadro’s number, N A , so Faraday’s constant can be expressed as:
Value of Faraday’s constant
Like any constant that is not dimensionless, the value of Faraday’s constant depends on the units in which it is expressed. The value of this constant currently accepted by the United States National Institute of Standards and Technology (NIST) in the international system of units (SI) is:
However, it is common to use this constant in other units to avoid the need for conversions during calculations:
| F = | 96 485.33212 Asmol -1 |
| F = | 26.80148114 Ahmol -1 |
| F = | 96 485.33212 JV -1 .mol -1 |
| F = | 96.48533212 kJ.V -1 .mol -1 |
| F = | 96 485.33212 JV -1 .gram-equivalent -1 |
| F = | 96.48533212 kJ.V -1 . gram-equivalent -1 |
| F = | 23 060.54783 cal.V -1 .mol -1 |
| F = | 23.06054783 kcal.V -1 .mol -1 |
| F = | 23 060.54783 cal.V -1 .gram-equivalent -1 |
| F = | 23.06054783 kcal.V -1 . gram-equivalent -1 |
Uses of Faraday’s Constant
in electrolysis
The first use that was given to Faraday’s constant is in the field of electrolysis. In it, Faraday’s constant allows determining the amount of electrical charge that needs to be transferred to produce a given mass of a substance by electrolysis, or the mass or number of moles of substance produced, given the amount of electricity passed through the cell. This is done through the following relationship:
Where I represents the current intensity in amperes (A), t is the running time in seconds (s), n e is the number of moles of electrons transferred and F is Faraday’s constant. The number of moles of electrons can be determined by stoichiometry or simply by means of the mass of the metal divided by its equivalent weight:
This equation or the previous one can be solved to find the desired variable.
Nernts equation
Another case in which Faraday’s constant is used is in electrochemistry, specifically in the use of the Nernst equation. This equation makes it possible to calculate the reduction potential of an electrode that is found in non-standard conditions (concentrations other than 1M and/or gas pressures other than 1 atm.).
This equation is:
where Q is the reaction quotient, E0 is the standard reaction potential, n is the number of electrons transferred in the reaction, T is the absolute temperature, R is the ideal gas constant, and F is Faraday’s constant.
The reaction quotient for a reaction of type aA + bB → cC + dD, is given by the quotient of the product of the concentrations of the products raised to their stoichiometric coefficients and the product of the concentrations of the reactants raised to theirs:
Calculation of the equilibrium potential of an ion in the cell membrane
The Nernst equation can also be used to determine the potential of concentration cells, which contain the same solutes, but at different concentrations. A particular application of this use is in calculating the equilibrium potential of an ion that is found at different concentrations on both sides of the cell membrane.
In this case, the standard reaction potential is zero (since no chemical reaction occurs) so the equilibrium potential is given by:
where z represents the electrical charge of the ion (with all its sign), and C inside and C outside are the concentrations of the ion inside and outside the cell, all other factors being the same as before.
Gibbs free energy calculation
Finally, another application of Faraday’s constant is in the calculation of the Gibbs free energy variation of an oxidation-reduction reaction that occurs in an electrochemical cell. This relationship is given by:
Where E cell is the potential of the electrochemical cell, n the number of exchanged electrons and F is Faraday’s constant.
It is worth mentioning that these are just a few examples of the use of Faraday’s constant in chemistry. There are other equations in which this constant comes to light.
Note on faraday and farad
In carrying out calculations in electrochemistry and other areas, Faraday’s constant, F, appears frequently, as we have just seen. But there is also a unit of charge called a faraday (with a small f). Care must be taken not to confuse faraday with Faraday’s constant as they are not the same.
The faraday is a dimensionless unit of electrical charge that is equal to the charge released by one gram-equivalent of substance involved in an electrochemical reaction.
Michale Faraday also carried out studies on electromagnetism, including studies on capacitance. In honor of the prominent English scientist, the fundamental unit of electrical capacitance was called the farad and has nothing to do with faraday or Faraday’s constant.
References
NIST, Fundamental Physical Constants
Bolívar, G. (2019, July 31). Faraday’s Constant: Experimental Aspects, Example, Uses . lifer. https://www.lifeder.com/faraday-constant/
Chang, R. (2008). Physical Chemistry for the Chemical and Biological Sciences (3rd ed.). MCGRAW HILL EDUCATION.
Chang, R., & Goldsby, K. (2013). Chemistry (11th ed.). McGraw-Hill Interamericana de España SL
González, M. (2010, November 16). Faraday’s constant . The Chemistry Guide. https://quimica.laguia2000.com/conceptos-basicos/constante-de-faraday
Chemistry.ES. (n.d.). Faraday’s constant . https://www.quimica.es/enciclopedia/Constante_de_Faraday.html
