Electrolysis with Inert Electrodes
Electrolysis uses a direct current to drive a non-spontaneous redox process in an electrolytic cell. With inert electrodes (platinum or graphite), the electrodes provide a surface for electron transfer and are not consumed, so products are determined by which dissolved species are most easily reduced or oxidized. The main quantity computed is the charge passed (and resulting moles of electrons) to predict product amounts.
Core definitions and essential formulas
\[
Q = I \cdot t
\]
\[
n_{e^-} = \frac{Q}{F}
\]
\[
n_{\text{product}} = \frac{Q}{zF}
\]
\(Q\) is charge (C), \(I\) is current (A), and \(t\) is time (s). \(F \approx 96485~\mathrm{C\,mol^{-1}}\) is the Faraday constant. \(z\) is the number of electrons required per mole of product in the relevant half-reaction. In an electrolytic cell the cathode is negative and hosts reduction, while the anode is positive and hosts oxidation.
How to interpret results
Larger \(I\) or longer \(t\) increases \(Q\), which increases \(n_{e^-}\) and therefore increases the moles (and mass) of products formed. Cathode products depend on whether metal ions can be reduced or whether water is reduced to hydrogen and hydroxide in aqueous solution; very reactive metal cations tend to remain in solution while \(\mathrm{H_2}\) forms. Anode products depend on whether anions are oxidized (such as halides to \(\mathrm{X_2}\)) or whether water is oxidized to \(\mathrm{O_2}\) when anions like \(\mathrm{SO_4^{2-}}\) or \(\mathrm{NO_3^-}\) are present. Typical outputs include identified anode/cathode products and calculated moles based on \(z\) for each half-reaction.
- Wrong time units: convert minutes or hours to seconds before using \(Q=I\cdot t\).
- Incorrect \(z\): \(z\) must come from the balanced electrode half-reaction for the reported product.
- Electrode sign mix-up: cathode is negative (reduction), anode is positive (oxidation) in electrolysis.
- Ignoring water competition: in aqueous solutions, water can discharge instead of certain ions.
Micro example: If \(I=1.50~\mathrm{A}\) for \(t=20.0~\mathrm{min}=1200~\mathrm{s}\), then
\(Q=1800~\mathrm{C}\) and \(n_{e^-}=\dfrac{1800}{96485}=0.0187~\mathrm{mol}\).
For \(\mathrm{2Cl^- \rightarrow Cl_2 + 2e^-}\), \(z=2\) so \(n(\mathrm{Cl_2})=\dfrac{Q}{2F}=0.00933~\mathrm{mol}\).
Use this tool to identify likely electrode products and compute amounts for aqueous electrolysis when electrodes are inert and Faraday’s law applies. Do not use it for reactive electrodes that dissolve or plate as part of the chemistry; a common next step is using electrode potentials and the Nernst equation to compare discharge preferences under nonstandard concentrations.
