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Faraday's laws of electrolysis are quantitative relationships based on the electrochemical research published by Michael Faraday in 1833.^[1]^[2]^[3]

First law

Michael Faraday reported that the mass ( $m$ ) of a substance deposited or liberated at an electrode is directly proportional to the charge ( $Q$ , for which the SI unit is the ampere-second or coulomb).^[3] $m\propto Q\quad \implies \quad {\frac {m}{Q}}=Z$

Here, the constant of proportionality, $Z$ , 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 ( $E$ ).^[3] This turns out to be the molar mass ( $M$ ) divided by the valence ( $v$ )

{\begin{aligned}&m\propto E;\quad E={\frac {\text{molar mass}}{\text{valence}}}={\frac {M}{v}}\\&\implies m_{1}:m_{2}:m_{3}:\ldots =E_{1}:E_{2}:E_{3}:\ldots \\&\implies Z_{1}Q:Z_{2}Q:Z_{3}Q:\ldots =E_{1}:E_{2}:E_{3}:\ldots \\&\implies Z_{1}:Z_{2}:Z_{3}:\ldots =E_{1}:E_{2}:E_{3}:\ldots \end{aligned}}

Derivation

A monovalent ion requires one electron for discharge, a divalent ion requires two electrons for discharge and so on. Thus, if $x$ electrons flow, ${\tfrac {x}{v}}$ atoms are discharged.

Thus, the mass $m$ discharged is $m={\frac {xM}{vN_{\rm {A}}}}={\frac {QM}{eN_{\rm {A}}v}}={\frac {QM}{vF}}$ where

$N A$ is the Avogadro constant;
$Q = xe$ is the total charge, equal to the number of electrons ( $x$ ) times the elementary charge $e$ ;
$F$ is the Faraday constant.

Mathematical form

Faraday's laws can be summarized by

Z={\frac {m}{Q}}={\frac {1}{F}}\left({\frac {M}{v}}\right)={\frac {E}{F}}

where $M$ is the molar mass of the substance (usually given in SI units of grams per mole) and $v$ is the valency of the ions .

For Faraday's first law, $M, F, v$ are constants; thus, the larger the value of $Q$ , the larger $m$ will be.

For Faraday's second law, $Q, F, v$ are constants; thus, the larger the value of ${\tfrac {M}{v}}$ (equivalent weight), the larger $m$ will be.

In the simple case of constant-current electrolysis, $Q = It$ , leading to

m={\frac {ItM}{Fv}}

and then to

n={\frac {It}{Fv}}

where:

$n$ is the amount of substance ("number of moles") liberated: $n={\tfrac {m}{M}}$
$t$ is the total time the constant current was applied.

For the case of an alloy whose constituents have different valencies, we have $m={\frac {It}{F\times \sum _{i}{\frac {w_{i}v_{i}}{M_{i}}}}}$ where $w i$ represents the mass fraction of the $i$ th element.

In the more complicated case of a variable electric current, the total charge $Q$ is the electric current $I (τ)$ integrated over time $τ$ :

Q=\int _{0}^{t}I(\tau )\,d\tau

Here $t$ is the total electrolysis time.^[4]

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 coverts 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

References

^ Faraday, Michael (1834). "on Electrical Decomposition". Philosophical Transactions of the Royal Society. 124: 77–122. doi:10.1098/rstl.1834.0008. S2CID 116224057.
^ Ehl, Rosemary Gene; Ihde, Aaron (1954). "Faraday's Electrochemical Laws and the Determination of Equivalent Weights". Journal of Chemical Education. 31 (May): 226–232. Bibcode:1954JChEd..31..226E. doi:10.1021/ed031p226.
^ ^a ^b ^c "Faraday's laws of electrolysis | chemistry". Encyclopedia Britannica. Retrieved 2020-09-01.
^ For a similar treatment, see Strong, F. C. (1961). "Faraday's Laws in One Equation". Journal of Chemical Education. 38 (2): 98. Bibcode:1961JChEd..38...98S. doi:10.1021/ed038p98.