Faraday's laws of electrolysis. Faraday's laws of electrolysis are quantitative relationships based on the electrochemical research published by Michael Faraday in 1833.

First law 

Michael Faraday reported that the mass () of a substance deposited or liberated at an electrode is directly proportional to the charge (, for which the SI unit is the ampere-second or coulomb).

Here, the constant of proportionality, , is called the electro-chemical equivalent (ECE) of the substance. Thus, the ECE can be defined as the mass of the substance deposited or liberated per unit charge.

Second law 

Faraday discovered that when the same amount of electric current is passed through different electrolytes connected in series, the masses of the substances deposited or liberated at the electrodes are directly proportional to their respective chemical equivalent/equivalent weight ().  This turns out to be the molar mass () divided by the valence ()

Derivation 

A monovalent ion requires one electron for discharge, a divalent ion requires two electrons for discharge and so on. Thus, if  electrons flow,  atoms are discharged.

Thus, the mass  discharged is

where 
  is the Avogadro constant;
  is the total charge, equal to the number of electrons () times the elementary charge ;
  is the Faraday constant.

Mathematical form 

Faraday's laws can be summarized by
 
where  is the molar mass of the substance (usually given in SI units of grams per mole) and  is the valency of the ions .

For Faraday's first law,  are constants; thus, the larger the value of , the larger  will be.

For Faraday's second law,  are constants; thus, the larger the value of  (equivalent weight), the larger  will be.

In the simple case of constant-current electrolysis, , leading to
 
and then to
 
where:
  is the amount of substance ("number of moles") liberated: 
  is the total time the constant current was applied.

For the case of an alloy whose constituents have different valencies, we have

where  represents the mass fraction of the th element.

In the more complicated case of a variable electric current, the total charge  is the electric current  integrated over time :
 

Here  is the total electrolysis time.

Applications 
 Electroplating – a process where a thin layer of metal is deposited onto the surface of an object using an electric current
 Electrochemical cells – generates electrical energy from chemical reactions
 Electrotyping – a process used to create metal copies of designs by depositing metal onto a mold using electroplating
 Electrowinning – a process that extract metals from their solutions using an electric current
 Electroforming – a process that deposits metal onto a mold or substrate to create metal parts
 Anodization – a process that converts the surface of a metal into a durable corrosion-resistant oxide layer
 Conductive polymers – organic polymers that conduct electricity 
 Water electrolysis – a process that uses an electric current to split water molecules into hydrogen and oxygen gases
 Electrolytic capacitors – a type of capacitor that uses an electrolytic solution as one of its plates

See also 
 Electrolysis
 Faraday's law of induction
 Tafel equation

References

Further reading 
 Serway, Moses, and Moyer, Modern Physics, third edition (2005), principles of physics.
 Experiment with Faraday's laws

Electrochemistry
Electrolysis
Electrochemical equations
Scientific laws
Michael Faraday