# Faraday constant

Faraday constant | |
---|---|

Common symbols | F |

SI unit | coulomb per mole (C/mol) |

In SI base units | s⋅A⋅mol^{−1} |

Derivations from other quantities | F = eN_{A} |

Value | 9.64853321233100184×10^{4} C⋅mol^{−1} |

In physical chemistry, the **Faraday constant** (symbol *F*, sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge (*q*) by the amount (*n*) of elementary charge carriers in any given sample of matter: *F* = *q*/*n*; it is expressed in units of coulombs per mole (C/mol).
As such, it represents the "molar elementary charge",^{[1]} that is, the electric charge of one mole of elementary carriers (e.g., protons). It is named after the English scientist Michael Faraday. Since the 2019 redefinition of SI base units,^{[1]} the Faraday constant has an exactly-defined value, the product of the elementary charge (*e*, in coulombs) and the Avogadro constant (*N*_{A}, in reciprocal moles):

*F*=*e*×*N*_{A}- = 1.602176634×10
^{−19}C × 6.02214076×10^{23}mol^{−1} - = 9.64853321233100184×10
^{4}C⋅mol^{−1}. - Or
- 96500 C/mol

## Derivation

The Faraday constant can be thought of as the conversion factor between the mole (used in chemistry) and the coulomb (used in physics and in practical electrical measurements), and is therefore of particular use in electrochemistry. Because there are exactly *N*_{A} = 6.02214076×10^{23} entities per mole,^{[1]} and there are exactly 1/*e* = 10^{19}/1.602176634 elementary charges per coulomb,^{[1]} the Faraday constant is given by the quotient of these two quantities:

*F*= *N*_{A}/1/*e* = 9.64853321233100184×10^{4}C⋅mol^{−1}.

One common use of the Faraday constant is in electrolysis calculations. One can divide the amount of charge (the current integrated over time) by the Faraday constant in order to find the chemical amount of a substance (in moles) that has been electrolyzed.

The value of *F* was first determined in the 1800s by weighing the amount of silver deposited in an electrochemical reaction, in which a measured current was passed for a measured time, and using Faraday's law of electrolysis.^{[2]} Until about 1970, the most reliable value of the Faraday constant was determined by a related method of electro-dissolving silver metal in perchloric acid.^{[3]}

## Other common units

- 96.485 kJ per volt–gram-equivalent
- 23.061 kcal per volt–gram-equivalent
- 26.801 A·h/mol

## Faraday – a unit of charge

Related to the Faraday constant is the "faraday", a unit of electrical charge. Its use is much less common than of the coulomb, but is sometimes used in electrochemistry.^{[4]} One faraday of charge is the charge of one mole of elementary charges (or of negative one mole of electrons), that is,

- 1 faraday =
*F*× 1 mol = 9.64853321233100184×10^{4}C

Conversely, the Faraday constant *F* equals 1 faraday per mole.

The faraday is not to be confused with the farad, an unrelated unit of capacitance (1 farad = 1 coulomb / 1 volt).

## Popular media

*The Simpsons* episode "Dark Knight Court" has Mr. Burns asking Comic Book Guy how much he wants for his entire comic book inventory. He says "the speed of light expressed as dollars" and Mr. Burns tells Smithers to "just give him Faraday's Constant". The check is written for $96,485.34.

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