First Law

Faraday's first law of electrolysis states that the mass (m) of a substance liberated or deposited at an electrode during electrolysis is directly proportional to the total quantity of electric charge (Q) passed through the cell:

Since charge relates to current by $I = Q/t$, so that $Q = It$, this proportionality becomes

where Z is called the electrochemical equivalent of the substance being produced at that electrode. Setting I = 1 A and t = 1 s (so Q = 1 C exactly) reduces the equation to simply $m = Z$ — which is exactly how the electrochemical equivalent is defined: the mass of substance deposited or liberated at an electrode by exactly one coulomb of charge.

Relating Z to molar mass. For a general reduction $M^{n+}\text{(aq)} + ne^{-} \rightarrow M\text{(s)}$, precipitating one mole of $M^{n+}$ as metal M requires n moles of electrons, i.e. a charge of $nF$. So the mass deposited by one coulomb of charge — the electrochemical equivalent — works out to

$Z = \dfrac{\text{Molar mass of } M}{n \times 96500} \qquad \text{or equivalently} \qquad Z = \dfrac{\text{Equivalent mass}}{96500}$ …