Faraday's law 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 ($m$) of elements deposited at an electrode is directly proportional to the charge ($Q$; SI units are ampere seconds or coulombs).

$\begin m &\propto Q \\ \implies \frac &= Z \end$

Here, the constant of proportionality, $Z$, 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.

Second law

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 is directly proportional to their chemical equivalent/equivalent weight ($E$). This turns out to be the molar mass ($M$) divided by the valence ($v$)

:$m \propto E$
:$E = \frac$
:$\implies m_1 : m_2 : m_3 : ... = E_1 : E_2 : E_3 :...$
:$\implies Z_1 Q : Z_2 Q : Z_3 Q : ... = E_1 : E_2 : E_3 : ...$ (From 1st Law)
:$\implies Z_1 : Z_2 : Z_3 : ... = E_1 : E_2 : E_3 : ...$

Derivation

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

So the mass discharged
$\begin m & = \frac \\ & = \frac \\ & = \frac \end$
where $N_$ is the Avogadro constant, ''Q'' = ''xe'', and $F$ is the Faraday constant.

Mathematical form

Faraday's laws can be summarized by

:$Z = \frac = \frac\left(\frac\right) = \frac$

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, $M$, $F$, and $v$ are constants, so that the larger the value of $Q$ the larger $m$ will be.

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

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

:$m =\frac$

and then to

:$n =\frac$

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

$m = \frac$

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''(''$\tau$'') integrated over time $\tau$:

:$Q = \int_0^t I(\tau) \, d\tau$

Here ''t'' is the ''total'' electrolysis time.For a similar treatment, see

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

{{DEFAULTSORT:Faraday'S lawS Of electrolySiS

Electrochemistry
Electrolysis
Electrochemical equations
Scientific laws