= Electrolysis
{wiki}
<Electrolysis> uses an external source of electrical <work> to drive <redox> <chemical reactions> at the <electrodes> of an <electrolytic cell>. Its characteristic application is forcing a <chemical reaction> in a direction that is nonspontaneous under the specified conditions: a discharging <galvanic cell> supplies electrical <work>, whereas <electrolysis> consumes electrical <work>. This makes <electrolysis> useful for producing otherwise difficult-to-obtain <chemical substances>, charging a rechargeable <battery>, and depositing a metal coating on a conducting object.<Chemistry 2e by Paul Flowers and others/17.7 Electrolysis>[§17.7]{ref}
Always identify the <anode> by <oxidation> and the <cathode> by <reduction>. In ordinary driven two-terminal operation, the source withdraws <Electrons> from the positive <anode> and delivers <Electrons> to the negative <cathode>. In a discharging <galvanic cell>, the <anode> is negative and the <cathode> positive. Thus terminal signs change with operating mode, while the reaction definitions remain valid. Through the <electrolyte>, <ions> transport <electric charge>; they need not all be consumed at an <electrode>. The <electrolyte> and <electrolytic cell> articles explain this transport and its <conventional current> direction.
For a net <chemical equation> transferring $z$ <Electrons> per reaction event, the molar reaction <Gibbs free energy> obeys
$$
\Delta_rG=-zF E_{\mathrm{chem}},
$$
where $F$ is the <Faraday constant> and $E_{\mathrm{chem}}$ is the reversible cell <electromotive force> for the reaction in the written direction. A nonspontaneous direction has $\Delta_rG>0$ and $E_{\mathrm{chem}}<0$ at fixed <temperature> and <pressure>. The ideal opposing voltage magnitude is $\Delta_rG/(zF)$; sustaining a finite <electric current> generally needs additional drive because of <electrical resistance> and finite <electrode> <reaction rates>. This thermodynamic voltage concerns the actual composition, rather than necessarily standard conditions.<Chemistry 2e by Paul Flowers and others/17.4 Potential, Free Energy, and Equilibrium>[§17.4]{ref} Not every use of <electrolysis> increases bulk chemical <Gibbs free energy>: transferring <copper> between equivalent surfaces can have zero bulk $\Delta_rG$ while the source still supplies dissipated electrical <work>. See the existing <electrolytic cell> example.
A particularly revealing experiment measures <copper> transfer instead of merely looking for a coating. Two separated <copper> <electrodes> stand in aqueous $\mathrm{CuSO_4}$ <electrolyte> in a vessel, with insulated leads to a regulated direct-current power supply, a series ammeter and a switch. A balance reads each <electrode>'s <mass> before and after a timed run. The Institute of Physics describes copper cells with ammeters, adjustable current and removable <cathodes>; its comparison uses three similar cells at $1\,\mathrm A$ for ten minutes, $0.5\,\mathrm A$ for ten minutes, and $0.5\,\mathrm A$ for twenty minutes. The specified observation to test is that deposited <copper> <mass> is proportional to <electric current> times <time>. These are documented experimental settings, not measurements generated here.<Electrolysis of copper sulfate solution by Institute of Physics>{ref}
The ideal <half-reactions> are
$$
\begin{aligned}
\text{anode, oxidation:}\quad&\mathrm{Cu}(s)\longrightarrow\mathrm{Cu}^{2+}(aq)+2e^-,\\
\text{cathode, reduction:}\quad&\mathrm{Cu}^{2+}(aq)+2e^-\longrightarrow\mathrm{Cu}(s).
\end{aligned}
$$
Each deposited <copper> <chemical atom> requires two <Electrons>, so $z=2$. The <anode> loses <copper> and the <cathode> gains it; ideally their <mass> changes have equal magnitudes, and the bulk <copper> <cation> inventory stays constant. Local <concentrations> near the <electrodes> can nevertheless differ. The sulfate <anions> participate in ionic transport without appearing in these net <half-reactions>; electronic <electric current> in the wires becomes ionic <electric current> in the <electrolyte> through the two interfaces.<Elektrolyse, Bestimmung von e by Karlsruhe Institute of Technology, Faculty of Physics teaching laboratory>{ref}
\Image[/electrolysis-copper-process.png]
{title=Driven <copper> transfer: <oxidation> at the positive <anode> and <reduction> at the negative <cathode>}
{description=Original model schematic, not a measured trajectory map. The source withdraws <Electrons> on the left and supplies them on the right; bulk ionic <conventional current> closes the circuit. Before/after dry <electrode> <masses> and the integrated <electric current> provide independent readouts. The two <half-reactions> count the same transferred <electric charge>, so their charges must not be added together.}
Clean, rinse, dry and identify the <electrodes> before their initial weighing. After interrupting the <electric current>, rinse away adhering <electrolyte>, dry again and weigh without rubbing off the deposit. KIT's university practical explicitly calls for distilled-water rinsing, careful drying and weighing both <electrodes>; it warns that loose <copper> grains can be lost during handling.<Elektrolyse, Bestimmung von e by Karlsruhe Institute of Technology, Faculty of Physics teaching laboratory>{ref} Useful additional controls are repeated drying and weighing until the reading stabilizes, and a matched unpowered immersion followed by the same rinse/dry cycle. These controls test retained liquid, residual dissolved salts, handling loss and chemical changes unrelated to passed <electric charge>; they are proposed checks, not additional observations reported by KIT. Keep immersed <electrode> area, spacing, <electrolyte> composition and <temperature> comparable across runs, and keep the <electrodes> from touching.
Record the <electric current> as a function of <time>, together with the exact switch-on and switch-off times. Taking $I(t)\geq0$ in the chosen deposition direction, the transported <electric charge> is
$$
Q=\int_{t_0}^{t_1}I(t)\,dt.
$$
For constant <electric current>, $Q=I(t_1-t_0)$; with sampled readings, use <numerical integration> rather than assuming that one ammeter reading remained constant. The two equal-charge Institute of Physics settings each give $600\,\mathrm C$, while its shorter $0.5\,\mathrm A$ setting gives $300\,\mathrm C$. With $M_{\mathrm{Cu}}=63.546\,\mathrm{g\,mol^{-1}}$, the <mass> per <amount of substance> tabulated by KIT, and $F\approx96485.33212\,\mathrm{C\,mol^{-1}}$, ideal <Faraday's laws of electrolysis> predict
$$
m_{\mathrm{Cu}}=\frac{M_{\mathrm{Cu}}Q}{2F}
\approx\begin{cases}
0.09879\,\mathrm g,&Q=300\,\mathrm C,\\
0.19758\,\mathrm g,&Q=600\,\mathrm C.
\end{cases}
$$
These are calculated predictions for complete conversion of the measured <electric charge> into retained <copper>, not experimental results. For a stable process, doubling the <electric charge> doubles the deposited <mass>; equal <electric charge> gives equal deposited <mass> even when the <electric current> and duration differ.
\Image[/electrolysis-charge-mass.png]
{title=<Faraday's laws of electrolysis> connect transported <electric charge> to deposited <copper> <mass>}
{description=Original calculated model, with no experimental points. Left: assumed constant-current histories with equal areas $Q=600\,\mathrm C$. Right: ideal <copper> <mass> versus <electric charge> and a stipulated 80 percent current-efficiency comparison. The dashed line assumes that 20 percent of the <electric charge> drives other same-direction <electrode> reactions and that all deposited <copper> remains attached.}
The balance reading is a test of the whole model. Competing <reduction> of <water> or other <chemical species> can divert <electric current> from <copper> deposition; transient <electrode> <capacitance> can also consume part of a short pulse without producing <copper>. A fragile deposit can detach even when its formation used the expected <electric charge>. Conversely, retained <electrolyte> or salts can increase an apparent <mass> gain. Comparing <anode> loss with <cathode> gain helps detect such problems but does not identify every cause. A slope below $M_{\mathrm{Cu}}/(2F)$ alone cannot distinguish competing <chemical reactions> from lost deposit. Current efficiency measures the fraction of transported <electric charge> assigned to a specified <electrode> reaction, rather than the fraction of electrical <energy> stored chemically.<IUPAC Compendium of Chemical Terminology, fifth edition (Gold Book) by International Union of Pure and Applied Chemistry/current efficiency>{ref}
The beautiful connection is that an electrical measurement counts chemical events: integrating <electric current> and reading a balance provide two ways of following the same <Electron> <stoichiometry>. This makes <electrolysis> useful for controlling coating quantity and for testing a charge-to-<amount of substance> relation. It does not determine coating uniformity, adhesion or the required voltage, which depend on transport and <electrode> <chemical kinetics> as well.
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