Faraday constant

Physical constant
Surname	Faraday 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). ${\displaystyle F}$ ${\displaystyle Q}$

Web links

• Elaboration: Determination of the Faraday constant by electrolysis

Individual evidence

1. ↑ ^{a b} CODATA Recommended Values. National Institute of Standards and Technology, accessed August 3, 2019 .  Value for the Faraday constant. The value is also exact as the product of two exact values, but in CODATA it is only given with the first ten valid digits, followed by periods. The numbers given in the info box are all valid.