Physical constant
Formula symbol ${\ displaystyle F \,}$
value
SI 9.648 533 212 331 001 84e4th ${\ displaystyle \ textstyle {\ frac {\ mathrm {A \, s}} {\ mathrm {mol}}}}$
Uncertainty  (rel.) (exactly)
Relation to other constants
${\ displaystyle F = N _ {\ mathrm {A}} \ e}$

The Faraday constant is the electric charge of a mole of singly charged ions. It plays an important role in Faraday's laws . ${\ displaystyle F}$

## Value and unity

It is calculated from the Avogadro constant and the elementary charge: ${\ displaystyle N _ {\ mathrm {A}}}$ ${\ displaystyle e}$

${\ displaystyle F = N _ {\ mathrm {A}} \ cdot e}$

and has the value:

${\ displaystyle F = 6 {,} 022 \, 140 \, 76 \ cdot 10 ^ {23} \ cdot 1 {,} 602 \, 176 \, 634 \ cdot 10 ^ {- 19} {\ frac {\ mathrm {C}} {\ mathrm {mol}}} = 96 \, 485 {,} 332 \, 123 \, 310 \, 0184 \, {\ frac {\ mathrm {C}} {\ mathrm {mol}}} }$.

Since the constants and are defined with exact numerical values in the SI system , the value of exactly can also be specified. ${\ displaystyle N _ {\ mathrm {A}}}$${\ displaystyle e}$${\ displaystyle F}$

## meaning

The Faraday constant is often used in calculations in physics and chemistry , especially electrochemistry . It is an unchangeable quantity, i.e. a natural constant . It is used when the turnover of substances is linked to electrical charges, for example in electrolysis , for example in electroplating , or in fuel cells and batteries . It is therefore not only important in science , but also in technology , especially in electroplating .

It is also used to calculate the change in energy that one mole of electrons absorb or release when passing through a potential difference (i.e. the molar energy difference), and is used in practice for calculating general reaction parameters such as converting electrical potentials into free energy. An energy of 1 kJ / mol corresponds to 1000 J / ( N A / mol −1 ) broken down to one particle , and expressed in electron volts (eV) with 1 eV = 1 J e / C this is 1000 eV / ( F / ( C mol −1 )) ≈ 0.01 eV.

## Historical

The Faraday constant is named after Michael Faraday , whose fundamental work made its first determination possible. It was determined for the first time in a galvanic deposition from the electrical charge of the flowing current and the deposited amount of silver. 1 mol of silver are carried about 96,500 Coulomb deposited (C).

### Simple derivation

Electrolysis (general)

Let us consider the electrolysis of silver - representative of all substances with a single positively charged ion :

${\ displaystyle \ mathrm {Ag ^ {+} + e ^ {-} \ longrightarrow Ag \ downarrow}}$

This formula naturally also applies if, instead of just one silver atom and only one electron , one mole of each of these particles is used (one mole of particle corresponds to about 6.022 · 10 23 particles):

${\ displaystyle \ mathrm {6 {,} 022 \ cdot {} 10 ^ {23} \, Ag ^ {+} + 6 {,} 022 \ cdot {} 10 ^ {23} \, e ^ {-} \ longrightarrow 6 {,} 022 \ cdot {} 10 ^ {23} \, Ag \ downarrow}}$

The amount of charge to be able to deposit one mole of silver is determined from the elementary charge of a single ion and the number of particles in a mole. The number of particles in a mole is expressed by Avogadro's constant . ${\ displaystyle Q}$ ${\ displaystyle e}$ ${\ displaystyle N _ {\ mathrm {A}}}$

The Faraday constant as the amount of charge per mole (i.e. to deposit one mole of silver, for example) results from: ${\ displaystyle F = Q / n}$${\ displaystyle Q}$

${\ displaystyle F = {\ frac {Q} {n}} = N _ {\ mathrm {A}} \ cdot e = {\ frac {6 {,} 022 \ cdot {} 10 ^ {23}} {\ mathrm {mol}}} \ cdot {} 1 {,} 602 \ cdot {} 10 ^ {- 19} \, \ mathrm {C} \ approx 96,500 \, {\ frac {\ mathrm {C}} {\, \ mathrm {mol}}}}$

In the case of substances whose chemical valency differs from the value 1, the molar charge is a corresponding multiple of the Faraday constant. ${\ displaystyle z}$

### determination

Until the revision of the International System of Units on May 20, 2019, the Faraday constant was a quantity that had to be determined experimentally. Its value was up to May 19, 2019 according to measurement accuracy

${\ displaystyle F = 96 \; 485 {,} 332 \; 89 \; (59) \; {\ frac {\ mathrm {C}} {\ mathrm {mol}}} = 96 \; 485 {,} 332 \; 89 \; (59) \; {\ frac {\ mathrm {As}} {\ mathrm {mol}}}}$,

thus with a standard uncertainty of 0.000.59  C  ·  mol −1 .

They were usually determined coulometrically by electrolysis , in which Faraday's laws could be used to calculate the mass, molar mass , charge and time (duration of the electrolysis). ${\ displaystyle F}$${\ displaystyle Q}$