Faraday's Laws of Electrolysis - Mathematical Form

Mathematical Form

Faraday's laws can be summarized by

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, leading to

and then to

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() integrated over time :

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