Faraday's laws of electrolysis

Michael Faraday, by Thomas Phillips c1841-1842

Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by Michael Faraday in 1834.

Statements of the laws

Several versions of the laws can be found in textbooks and the scientific literature. The most-common statements resemble the following:

• Faraday's 1^st Law of Electrolysis - The mass of a substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity transferred at that electrode. Quantity of electricity refers to the quantity of electrical charge, typically measured in coulomb.

• Faraday's 2^nd Law of Electrolysis - For a given quantity of electricity (electric charge), the mass of an elemental material altered at an electrode is directly proportional to the element's equivalent weight. The equivalent weight of a substance is its molar mass divided by an integer that depends on the reaction undergone by the material.

Mathematical form

Faraday's laws can be summarized by

$m\ =\ \left({Q \over F}\right)\left({M \over z}\right)$

where:

• m is the mass of the substance liberated at an electrode in grams
• Q is the total electric charge passed through the substance
• F = 96,485 C mol⁻¹ is the Faraday constant
• M is the molar mass of the substance
• z is the valency number of ions of the substance (electrons transferred per ion).

Note that M / z is the same as the equivalent weight of the substance altered.

For Faraday's first law, M, F, and z are constants, so that the larger the value of Q the larger m will be.

For Faraday's second law, Q, F, and z are constants, so that the larger the value of M / z (equivalent weight) the larger m will be.

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

$m\ =\ \left({It \over F}\right)\left({M \over z}\right)$

and then to

$n\ =\ \left({It \over F}\right)\left({1 \over z}\right)$

where:

• n is the amount of substance ("number of moles") liberated: n = m / M
• t is the total time the constant current was applied.

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

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

Here t is the total electrolysis time. Please note that tau is used as the current I is a function of tau.

Further reading

• Serway, Moses, and Moyer, Modern Physics, third edition (2005).

See also

• Electrolysis
• Michael Faraday
• Faraday constant
• Faraday's law of induction