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 () of elements deposited at an electrode is directly proportional to the charge (; SI units are ampere seconds or coulombs). Here, the constant of proportionality, , is called the electro-chemical equivalent (ECE) of the substance. Thus, the ECE 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 (). This turns out to be the molar mass () divided by the valence () Derivation A monovalent ion requires 1 electron for discharge, a divalent ion requires 2 electrons for discharge and so on. Thus, if electrons flow, atoms are discharged. So the mass discharged is where is the Avogadro constant; is the total charge, equal to the number of electrons () times the elementary charge ; is the Faraday constant. Mathematical form Faraday's laws can be summarized by where is the molar mass of the substance (usually given in SI units of grams per mole) and is the valency of the ions . For Faraday's first law, are constants; thus, the larger the value of , the larger will be. For Faraday's second law, are constants; thus, the larger the value of (equivalent weight), the larger will be. In the simple case of constant-current electrolysis, , leading to and then to where: is the amount of substance ("number of moles") liberated: is the total time the constant current was applied. For the case of an alloy whose constituents have different valencies, we have where represents the mass fraction of the -th element. In the more complicated case of a variable electric current, the total charge is the electric current integrated over time : Here is the total electrolysis time. 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 Electrochemistry Electrolysis Electrochemical equations Scientific laws