View source for Faraday's laws of electrolysis

{{Short description|Physical laws of electrochemistry}}
[[Image:M Faraday Th Phillips oil 1842.jpg|thumb|upright|right|[[Michael Faraday]]]]

'''Faraday's laws of electrolysis''' are quantitative relationships based on the [[electrochemistry|electrochemical]] research published by [[Michael Faraday]] in 1833.<ref>{{cite journal | first = Michael | last = Faraday | author-link = Michael Faraday | year = 1834 | title = on Electrical Decomposition | url = http://www.chemteam.info/Chem-History/Faraday-electrochem.html | journal = Philosophical Transactions of the Royal Society | doi = 10.1098/rstl.1834.0008 | volume=124 | pages=77–122| s2cid = 116224057 | url-access = subscription }}</ref><ref>{{cite journal | author = Ehl, Rosemary Gene |author2=Ihde, Aaron | title = Faraday's Electrochemical Laws and the Determination of Equivalent Weights | journal = Journal of Chemical Education | year = 1954 | volume = 31 | issue = May | pages = 226&ndash;232 | doi = 10.1021/ed031p226 | bibcode=1954JChEd..31..226E}}</ref><ref name=":0" />

== First law ==

'''Michael Faraday''' reported that the mass ({{mvar|m}}) of a substance deposited or liberated at an electrode is directly proportional to the charge ({{mvar|Q}}, for which the [[International System of Units|SI]] unit is the [[ampere]]-[[second]] or [[Coulomb (unit)|coulomb]]).<ref name=":0">{{cite web|title=Faraday's laws of electrolysis {{!}} chemistry | url=https://www.britannica.com/science/Faradays-laws-of-electrolysis | access-date=2020-09-01 | website=Encyclopedia Britannica |language=en}}</ref>
<math display="block">m  \propto Q \quad \implies \quad \frac{m}{Q} = Z</math>

Here, the constant of proportionality, {{mvar|Z}}, is called the [[Electrochemical equivalent|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]] ({{mvar|E}}).<ref name=":0" />  This turns out to be the molar mass ({{mvar|M}}) divided by the valence ({{mvar|v}})
: <math>\begin{align} 
& 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{align}</math>

== Derivation ==

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

Thus, the mass {{mvar|m}} discharged is
<math display="block">
m = \frac{x M}{v N_{\rm A}} = \frac{Q M}{e N_{\rm A} v} = \frac{Q M}{vF}</math>
where 
* {{math|''N''{{sub|A}}}} is the [[Avogadro constant]];
* {{math|1=''Q'' = ''xe''}} is the total charge, equal to the number of electrons ({{mvar|x}}) times the [[elementary charge]] {{mvar|e}};
* {{math|''F''}} is the [[Faraday constant]].

== Mathematical form ==

Faraday's laws can be summarized by
: <math>Z = \frac{m}{Q}  = \frac{1}{F}\left(\frac{M}{v}\right) = \frac{E}{F}</math>
where {{mvar|M}} is the [[molar mass]] of the substance (usually given in SI units of grams per mole) and {{mvar|v}} is the [[Valence (chemistry)|valency]] of the [[ion]]s .

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

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

In the simple case of constant-[[electric current|current]] electrolysis, {{math|1=''Q'' = ''It''}}, leading to
: <math>m  =\frac{ItM}{Fv}</math>
and then to
: <math>n  =\frac{It}{Fv}</math>
where:
* {{mvar|n}} is the [[amount of substance]] ("number of moles") liberated: <math>n  = \tfrac m M</math>
* {{mvar|t}} is the total time the constant current was applied.

For the case of an alloy whose constituents have different valencies, we have
<math display="block">m = \frac{It}{F \times \sum_{i} \frac{w_i v_i}{M_i}}</math>
where {{mvar|w<sub>i</sub>}} represents the [[mass fraction (chemistry)|mass fraction]] of the {{mvar|i}}th element.

In the more complicated case of a variable electric current, the total charge {{mvar|Q}} is the electric current {{math|''I''(''&tau;'')}} integrated over time {{mvar|&tau;}}:
: <math> Q = \int_0^t I(\tau) \, d\tau </math>

Here {{mvar|t}} is the ''total'' electrolysis time.<ref>For a similar treatment, see {{cite journal | author = Strong, F. C. | title = Faraday's Laws in One Equation | journal = Journal of Chemical Education | year = 1961 | volume = 38 | issue = 2| pages = 98 | doi = 10.1021/ed038p98 |bibcode = 1961JChEd..38...98S }}</ref>

== Applications ==
* [[Electroplating]] – a process where a thin layer of metal is deposited onto the surface of an object using an [[electric current]]
* [[Electrochemical cell]]s – generates [[electrical energy]] from [[chemical reaction]]s
* [[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
* [[Anodizing|Anodization]] – a process that converts the surface of a metal into a durable corrosion-resistant [[oxide]] layer
* [[Conductive polymer]]s – [[organic polymer]]s that conduct electricity 
* [[Electrolysis of water|Water electrolysis]] – a process that uses an electric current to split water molecules into [[hydrogen]] and [[oxygen]] gases
* [[Electrolytic capacitor]]s – 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 ==
{{reflist}}

== Further reading ==
* Serway, Moses, and Moyer, ''Modern Physics'', third edition (2005), principles of physics.
* [https://pineresearch.com/shop/kb/applications/laboratory-exercises/exploring-inexpensive-electrodes/ Experiment with Faraday's laws] {{Webarchive|url=https://web.archive.org/web/20210204135917/https://pineresearch.com/shop/kb/applications/laboratory-exercises/exploring-inexpensive-electrodes/ |date=2021-02-04 }}

{{Electrolysis}}
{{Michael Faraday}}

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[[Category:Electrochemistry]]
[[Category:Electrolysis]]
[[Category:Electrochemical equations]]
[[Category:Scientific laws]]
[[Category:Michael Faraday]]