Faraday's laws of electrolysis

Michael Faraday reported that the mass(${\displaystyle m}$) of elements deposited at an electrode in g is directly proportional to the charge (${\displaystyle Q}$) in coulombs.[3]

${\displaystyle m\propto Q}$

${\displaystyle Q=Amperes*seconds}$

${\displaystyle \implies {\frac {m}{Q}}=Z}$

Here, the constant of proportionality ${\displaystyle Z}$ is called the Electro-Chemical Equivalent (e.c.e) of the substance. Thus, the e.c.e. can be defined as the mass of the substance deposited/liberated per unit charge.

Faraday discovered that when the same amount of electric current is passed through different electrolytes/elements connected in series, the mass of the substance liberated/deposited at the electrodes in g is directly proportional to their chemical equivalent/equivalent weight (${\displaystyle E}$).[3] This turns out to be the molar mass (${\displaystyle M}$) divided by the valence (${\displaystyle v}$)

${\displaystyle m\propto E}$

${\displaystyle E={\frac {Molar\ mass}{Valence}}}$

${\displaystyle \implies m_{1}:m_{2}:m_{3}:...=E_{1}:E_{2}:E_{3}:...}$

${\displaystyle \implies Z_{1}Q:Z_{2}Q:Z_{3}Q:...=E_{1}:E_{2}:E_{3}:...}$ (From 1st Law)

${\displaystyle \implies Z_{1}:Z_{2}:Z_{3}:...=E_{1}:E_{2}:E_{3}:...}$

A monovalent ion requires 1 electron for discharge, a divalent ion requires 2 electrons for discharge and so on. Thus, if ${\displaystyle x}$ electrons flow, ${\displaystyle {\frac {x}{v}}}$ atoms are discharged.

So the mass discharged ${\displaystyle m}$

${\displaystyle ={\frac {xM}{vN_{A}}}}$ (where ${\displaystyle N_{A}}$ is Avogadros number)

${\displaystyle ={\frac {QM}{eN_{A}v}}}$ (From Q = xe)

${\displaystyle ={\frac {QM}{Fv}}}$

Where (${\displaystyle F}$) is the Faraday constant.

Faraday's laws can be summarized by

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

where ${\displaystyle M}$ is the molar mass of the substance (in grams per mol) and ${\displaystyle v}$ is the valency of the ions .

For Faraday's first law, ${\displaystyle M}$, ${\displaystyle F}$, and ${\displaystyle v}$ are constants, so that the larger the value of ${\displaystyle Q}$ the larger m will be.

For Faraday's second law, ${\displaystyle Q}$, ${\displaystyle F}$, and ${\displaystyle v}$ are constants, so that the larger the value of ${\displaystyle {\frac {M}{v}}}$ (equivalent weight) the larger m will be.

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

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

and then to

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

where:

• n is the amount of substance ("number of moles") liberated: n = 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

${\displaystyle m={\frac {It}{F\times \sum _{i}{\frac {w_{i}\times v_{i}}{M_{i}}}}}}$

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(${\displaystyle \tau }$) integrated over time ${\displaystyle \tau }$:

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

Here t is the total electrolysis time.[4]

• Electrolysis
• Faraday's law of induction
• Tafel equation

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