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The anode is the electrode at which the net electrode chemical reaction is oxidation: the reacting chemical species loses Electrons. This definition is independent of terminal sign. See IUPAC Gold Book: anode.

During Daniell cell discharge, a zinc chemical atom becomes a ${\mathrm{Zn}}^{2+}$ cation, leaving two Electrons in the electrode; those Electrons leave through the external electrical circuit. The zinc anode is the negative terminal. In an externally driven electrolytic cell, Electrons instead leave the anode through the lead to the source's positive terminal. Conventional current in that lead points toward the anode, opposite to Electron motion. The anode can therefore be positive while still being the site of oxidation. See Daniell cell for the balanced half-reaction and electrode for the operating-mode sign conventions.

The cathode is the electrode at which the net electrode chemical reaction is reduction: the reacting chemical species gains Electrons. This definition is independent of terminal sign. During Daniell cell discharge, ${\mathrm{Cu}}^{2+}$ cations accept Electrons arriving at the copper cathode and become neutral copper. The cathode is then the positive terminal. In an externally driven electrolytic cell, the source's negative terminal supplies Electrons to the negative cathode. See Pingarrón et al., §3.4: cathode and Daniell cell.

An ion carrying electric current need not undergo reduction at the cathode. For example, in the ideal Daniell cell charge-balance picture, potassium cations arriving from a salt bridge remain dissolved while ${\mathrm{Cu}}^{2+}$ cations are consumed. Follow the half-reaction to identify the reacting species; follow electric charge conservation to account for the other moving ions.

A Daniell cell uses the zinc/${\mathrm{Zn}}^{2+}$ and ${\mathrm{Cu}}^{2+}$/copper pairs. In the separated-compartment teaching version, a zinc electrode contacts an aqueous chemical solution containing ${\mathrm{Zn}}^{2+}$, and a copper electrode contacts one containing ${\mathrm{Cu}}^{2+}$. A salt bridge supplies an ionic connection; a wire and load supply an electronic connection. During discharge,The zinc electrode loses material and copper is deposited at the cathode. Each half-reaction conserves chemical atom counts and electric charge: the first has net charge zero on each side, the second $+2e-2e=0$ on the left and zero on the right. The net reaction has $+2e$ on both sides, with no Electrons left in its chemical equation. The Zn/Cu teaching cell and these half-reactions are described in Florida State University, Redox Reactions in Voltaic Cells: Construction of a Potential Series, lab background.

Creating one mole of ${\mathrm{Zn}}^{2+}$ adds $2F$ of positive electric charge to the anode compartment's ionic inventory; consuming one mole of ${\mathrm{Cu}}^{2+}$ removes $2F$ of positive electric charge from the cathode compartment. Here $F$ is the Faraday constant. In an ideal bookkeeping example using a potassium nitrate salt bridge, two moles of nitrate anions entering the anode compartment compensate the first change, and two moles of potassium cations entering the cathode compartment compensate the second. Other ions in the cell can share the actual transport. The two compensating inventory changes do not mean that $4F$ flowed through the load: the same series electric current transports $2F$ through each cross-section of the circuit per mole of net reaction. See salt bridge.

Under standard-state conditions near $298\mathrm{K}$, tabulated reduction potentials give a cell electromotive force of approximately $1.10\mathrm{V}$. This is a reversible reference value, not a promised loaded reading; actual composition matters through thermodynamic activity. The tabulated copper and zinc values and their subtraction are given in Purdue University, Electrochemical Reactions: standard-state reduction potentials. For the net chemical equation as written, the molar Gibbs free energy change obeysThus $\mathcal{E}=1.10\mathrm{V}$ corresponds to about $-212\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ of net reaction. At fixed temperature and pressure, $-{\Delta }_{r}G$ is the maximum reversible electrical work per mole for this cell reaction. It is not automatically all the heat released by a finite-current cell. See 17.4 Potential, Free Energy, and Equilibrium (§17.4: cell potential and free energy).

The motivating observation is that a chemical reaction can produce a signed electrical reading even when its reacting materials occupy separate vessels. UC San Diego's teaching demonstration places a copper strip in $0.1\mathrm{mol}{\mathrm{L}}^{-1}$ $\mathrm{CuS}{\mathrm{O}}_4$ and a zinc strip in $0.1\mathrm{mol}{\mathrm{L}}^{-1}$ $\mathrm{ZnS}{\mathrm{O}}_4$, using two $400\mathrm{mL}$ beakers with about $300\mathrm{mL}$ of chemical solution in each. The strips connect to a voltage meter. Initially there is no ionic connection; the demonstration specifies a zero reading. A filter-paper salt bridge containing aqueous $\mathrm{N}{\mathrm{a}}_2\mathrm{S}{\mathrm{O}}_4$ then connects the chemical solutions. With the meter's positive lead on copper and negative lead on zinc, its reported readings are about $+1.1\mathrm{V}$; exchanging the leads reverses the reading. These are observations reported by the university, not data generated for this article. See UC San Diego, demonstration 9B: apparatus, bridge control and meter polarity.

The controls answer different questions. Exchanging only the meter leads checks the sign convention; it does not reverse the chemical reaction or swap the anode and cathode. Interrupting only the salt bridge tests the need for an ionic return path. Its absence prevents sustained cell electric current, but a very high-input-resistance meter may still show a transient or unstable reading while interfaces store electric charge. The zero reading specified for the university's apparatus is therefore not a universal theorem for every meter. Reconnecting the same salt bridge distinguishes a reversible interruption from a disconnected wire or exhausted chemical solution. This interpretation follows from electric charge conservation in a model allowing interfacial electric charge storage; see IUPAC Gold Book: integral capacitance of an electrode for the capacitance associated with electrode charge.

To distinguish terminal electric potential difference from delivered power, compare the nearly open-circuit reading with readings across a known resistor load. In the nearly open-circuit condition, a meter with input electrical resistance much larger than the cell's effective internal electrical resistance draws little electric current. With a load, measure its terminal electric potential difference $V$ and infer $I=V/R$ using Ohm's law; track the readings over time and repeat the nearly open-circuit reading afterwards. Keep the temperature, chemical solution compositions, immersed electrode areas, bridge geometry and electrical contacts comparable. This is a model-based extension of the documented demonstration, not a claim that UC San Diego published a load sweep. A finite-current drop can reflect ionic electrical resistance, changes of interfacial reaction rates, or depletion near an electrode; a single voltage reading cannot identify which dominates. The interfacial and composition contributions are distinguished in IUPAC Gold Book: overpotential and ^[ref].

For a deliberately simplified calculation, model the cell by a constant electromotive force $\mathcal{E}$ in series with a constant internal electrical resistance $r$, and a passive load $R>0$. Take $I$ positive from the cathode through the load to the anode. ThenThe nearly open-circuit limit $R\to \infty$ gives $V\to \mathcal{E}$ but $I\to 0$ and $P_{\mathrm{load}}\to 0$. A straight $V$-versus-$I$ line is a prediction of constant $r$, not a general law for electrochemistry. See Ling, Sanny and Moebs, University Physics II, §10.1: internal resistance, terminal voltage and load.

For the chosen values, $I=5.50\mathrm{mA}$ and $V=0.550\mathrm{V}$. Holding these toy parameters fixed for $600\mathrm{s}$ gives transported electric charge $Q=It=3.30\mathrm{C}$ and an extent of reaction $\xi =Q/(2F)\simeq 17.1\mu \mathrm{mol}$, assuming all the electric current serves the two specified half-reactions. The same $\xi$ counts zinc consumed and copper deposited, rather than equal masses. The energy budget isThe load's electrical work also becomes Joule heating when the load is a resistor. Here $\mathcal{E}Q$ accounts for the reaction's available reversible electrical work; a full cell thermal budget would also require its thermodynamic entropy contribution. Real measurements need uncertainty estimates, a specified meter input electrical resistance and calibration, and allowance for changing composition and unwanted chemical reactions. The toy value $r=100\Omega$ is not a measured property of the university's cell.

A disulfide bond is the single covalent bond between the two adjacent sulfur chemical atoms in a disulfide, conventionally written $\mathrm{R}-\mathrm{S}-\mathrm{S}-{\mathrm{R}}^{\prime }$. Here $R$ and $R^{\prime }$ stand for the attached organic groups; they may belong to the same molecule or to initially separate molecules. A disulfide bond is a chemical bridge, rather than a hydrogen bond or a mere contact between nearby groups. Two thiols, $\mathrm{R}-\mathrm{SH}$ and ${\mathrm{R}}^{\prime }-\mathrm{SH}$, can supply its two sulfur endpoints. ^[ref]

The stoichiometry of forming a disulfide bond is especially revealing. Written as an oxidation half-reaction, it isThe reverse reduction half-reaction consumes two Electrons and two hydrogen ions to restore two thiols. Both sides contain two sulfur chemical atoms; the two hydrogen chemical atoms have moved into the two hydrogen ions, and the net electric charge remains zero because $+2-2=0$. Thus one disulfide bond corresponds to two thiol groups and two transferred Electrons. These half-reactions describe redox bookkeeping, not a complete standalone chemical reaction: an accompanying reactant must accept or supply the Electrons, and pH affects the actual protonation of the groups. Mercaptoethanol can promote reduction through exchange of disulfide bonds, but adequate excess and appropriate conditions are needed; adding it does not by itself prove complete reduction. ^[ref]

In a protein disulfide bond, the endpoints are normally the amino acid side chains of two cysteine amino acid residues. An intrachain protein disulfide bond closes an intramolecular bridge within one polypeptide chain; an interchain protein disulfide bond connects different polypeptide chains, and can arise by intermolecular crosslinking of initially separate molecules. Forming or reducing these bridges changes covalent bond connectivity and can change protein structure, while preserving the order of amino acid residues and the peptide bonds in the protein backbone. A complete chemical account of protein primary structure includes crosslinks as well as sequence, so preservation of sequence does not imply preservation of every covalent bond. Mature insulin has two interchain protein disulfide bonds and one intrachain protein disulfide bond. ^[ref]

A bridge is useful because it constrains which parts of a polypeptide chain can move apart without breaking a covalent bond. Its placement therefore matters as well as its presence. The ribonuclease A refolding experiment provides the existing experimental example: breaking and reforming four protein disulfide bonds can accompany loss and recovery of function. Counting four bridges alone cannot tell whether their endpoints have the native pairing. This is an attractive connection between simple chemical counting and the richer problem of protein folding.

How can an experiment reveal an initially hidden disulfide bond? Ellman's reagent, also called DTNB, measures free thiols by producing a yellow absorbing species. Its reactive disulfide bond undergoes exchange with the conjugate base $\mathrm{R}-{\mathrm{S}}^{-}$ of a thiol, producing a mixed disulfide attached to $R$ and one released 2-nitro-5-thiobenzoate species, abbreviated TNB. At the assay pH, the strongly colored form is the dianion $\mathrm{TN}{\mathrm{B}}^{2-}$: one negative charge is on sulfur and the other is on the carboxylic acid-derived $\mathrm{CO}{\mathrm{O}}^{-}$ group. With excess DTNB and complete reaction, one released TNB reports one reacted thiol. George L. Ellman's 1959 paper introduced the tissue assay; it was subsequently reexamined quantitatively. ^{[ref] [ref]}

The modern apparatus can be simple: tubes, pipettes, a buffer solution, cysteine standards, DTNB, and an instrument that measures absorbance through a cuvette at wavelength $412\mathrm{nm}$. The Pierce protocol uses $50\mu \mathrm{L}$ of a $4\mathrm{mg}\mathrm{m}{\mathrm{L}}^{-1}$ DTNB stock, $2.50\mathrm{mL}$ of buffer solution, and $250\mu \mathrm{L}$ of sample. Its buffer solution is $0.1\mathrm{mol}{\mathrm{L}}^{-1}$ sodium phosphate at pH 8.0 with a metal-binding additive. After 15 minutes at room temperature, measure absorbance against a buffer solution plus DTNB blank; run known cysteine concentrations in parallel. The observable is increased yellow color and increased blank-corrected absorbance as more accessible thiols react, rather than direct imaging of disulfide bonds. These are published protocol conditions, not measurements performed for this article. ^[ref]

For a before/after test, split a purified protein sample into matched aliquots. Measure accessible free thiols in one aliquot; subject the other to complete reduction of its disulfide bonds, remove the reducing reagent, then measure the resulting thiols with fresh DTNB. Process the unreduced aliquot through a matching cleanup. Normalize to recovered protein and known dilution, since cleanup can change both. To estimate all reducible protein disulfide bonds, expose buried groups using matching protein denaturation conditions in both aliquots and calibrate in that same chemical solution; a native-accessibility measurement answers a different question. A larger corrected reading after reduction supports conversion of previously unreactive groups into detectable thiols. Attribution to disulfide bonds requires excluding other reducible sulfur modifications. This is a proposed comparison based on the detection principles, not a reconstruction of Ellman's original tissue measurements. ^[ref]

Under the Beer-Lambert law, the blank-corrected absorbance is $A=\epsilon lc$, where $l$ is the cuvette path length, $c$ is the released TNB concentration, and $\epsilon$ is its molar absorption coefficient. Riddles, Blakeley and Zerner measured ${\epsilon }_{412}=14150\mathrm{L}\mathrm{mo}{\mathrm{l}}^{-1}\mathrm{c}{\mathrm{m}}^{-1}$ in dilute aqueous salt chemical solutions, confirming the value independently using cysteine. It must not be applied indiscriminately to other solvents or protein denaturation mixtures. ^[ref] For aliquots compared on the same final volume and protein concentration basis, the ideal estimate isThe factor of two follows from the reduction stoichiometry; ${\bar{n}}_{\mathrm{S}-\mathrm{S}}$ is the number of disulfide bonds per protein molecule, or an average for a mixed population. If the aliquots have different dilutions or recoveries, convert each reading to a common sample basis before subtracting.

As a hypothetical calculation, choose $c_{\mathrm{protein}}=10\mu \mathrm{mol}{\mathrm{L}}^{-1}$ in each final cuvette, two free thiols and two disulfide bonds per protein molecule, and $l=1\mathrm{cm}$. Before reduction, $c_{\mathrm{SH}}=20\mu \mathrm{mol}{\mathrm{L}}^{-1}$ gives $A=0.283$; complete reduction adds four thiols per protein molecule, so $c_{\mathrm{SH}}=60\mu \mathrm{mol}{\mathrm{L}}^{-1}$ gives $A=0.849$. The difference $0.566$ gives $c_{\mathrm{S}-\mathrm{S}}=20\mu \mathrm{mol}{\mathrm{L}}^{-1}$ and ${\bar{n}}_{\mathrm{S}-\mathrm{S}}=2$. The published tube volumes imply a dilution factor $2.80/0.250=11.2$; reversing that dilution multiplies both thiol and protein concentrations by 11.2 and leaves the bridge count per protein molecule unchanged.

Controls determine whether that arithmetic has chemical meaning. Use fresh cysteine standards and a processed blank without protein to detect color generated by residual reducing reagent. Even a reducing reagent containing no thiols can interfere: Han and Han showed that tris(2-carboxyethyl)phosphine, abbreviated TCEP, reduces DTNB to two TNB equivalents per TCEP. ^[ref] In the hypothetical model, $5\mu \mathrm{mol}{\mathrm{L}}^{-1}$ residual TCEP in only the reduced cuvette would add $A=0.1415$ and falsely add $0.5$ bridge per protein molecule. A stable endpoint and agreement after a further reduction treatment help check completion. A sample without DTNB checks its own color; cloudy samples can also attenuate light without producing TNB. Match pH, temperature, accessibility and calibration chemical solution, and minimize delay that permits reoxidation. If two already-free but buried thiols become accessible only in the reduced aliquot, they mimic one new disulfide bond per protein molecule. Finally, bulk absorbance supplies a count under these assumptions: it does not locate the cysteine endpoints, distinguish intrachain from interchain bridges, or establish the native pairing of a protein disulfide bond.

An electrode is an electronic electrical conductor in contact with an electrolyte. In a cell carrying sustained redox electric current, chemical reactions at this interface exchange Electrons with chemical species. An electrode can participate in the chemical reaction, as the dissolving zinc anode of a Daniell cell does, or provide a conducting surface without appearing in the net chemical equation. This distinction is illustrated by active and inert electrodes in Flowers, Theopold, Langley and Robinson, Chemistry 2e, §17.2.

The interface connects two kinds of electric charge transport: Electrons in the external electrical circuit and ions in the electrolyte. The same Electron does not travel through the wire, swim through the salt bridge, and complete a circuit! The half-reactions account for how electronic and ionic transport meet. This is the useful idea behind both obtaining electrical work in a galvanic cell and supplying electrical work in an electrolytic cell.

Name an electrode from its net chemical reaction: oxidation means anode, and reduction means cathode. State the operating mode before assigning terminal signs. For a galvanic cell supplying a passive load, the anode is negative and the cathode positive; for an ordinary two-terminal electrolytic cell driven by a source, the anode is positive and the cathode negative. Here positive means higher terminal electric potential than the other electrode, not a claim that the bulk material has a large positive net electric charge. See Pingarrón et al., Terminology of electrochemical methods of analysis (IUPAC Recommendations 2019), §§3.1 and 3.4.

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.^[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 obeyswhere $F$ 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 ${\Delta }_{r}G>0$ and $E_{\mathrm{chem}}<0$ at fixed temperature and pressure. The ideal opposing voltage magnitude is ${\Delta }_{r}G/(zF)$; 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.^[ref] Not every use of electrolysis increases bulk chemical Gibbs free energy: transferring copper between equivalent surfaces can have zero bulk ${\Delta }_{r}G$ 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 $\mathrm{CuS}{\mathrm{O}}_4$ 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.^[ref]

The ideal half-reactions areEach 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.^[ref]

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.^[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 $I(t)\ge 0$ in the chosen deposition direction, the transported electric charge isFor 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 $M_{\mathrm{Cu}}=63.546\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$, the mass per amount of substance tabulated by KIT, and $F\approx 96485.33212\mathrm{C}\mathrm{mo}{\mathrm{l}}^{-1}$, ideal Faraday's laws of electrolysis predictThese 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.

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.^[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.

An electrolytic cell uses an external source of electrical work to drive electrode chemical reactions. In the ordinary two-terminal driven mode, its positive anode supports oxidation and its negative cathode supports reduction. The source removes Electrons from the anode and supplies Electrons to the cathode; through the electrolyte, net conventional current goes from anode toward cathode. Terminal signs refer to the driven cell's terminals relative to each other. The source supplies electrical power to the cell. See 17.7 Electrolysis (§17.7: electrolysis and electroplating).

For example, transferring copper from a soluble copper anode onto a conducting object at the cathode has the ideal half-reactionsTheir sum transfers copper between surfaces. For identical bulk states, this transfer need not have a positive bulk Gibbs free energy change; finite electric current still needs applied drive to overcome losses. Thus "consumes electrical work" does not mean every electrolytic cell stores all that work as chemical Gibbs free energy. Electrolysis can instead redistribute material. The charge-to-amount relation remains $\xi =Q/(2F)$ when only these half-reactions carry the electric current; competing water reactions would change the deposited amount. The electroplating principle and charge accounting are described in 17.7 Electrolysis (§17.7: electroplating and quantitative aspects).

The University of Washington's teaching demonstration makes this material transfer visible with a copper electrode and a stainless-steel electrode in a glass cell containing $0.5\mathrm{mol}{\mathrm{L}}^{-1}$ $\mathrm{CuS}{\mathrm{O}}_4$. The external source connects its positive lead to copper and negative lead to steel; the reported observation is a copper coating on the steel. Reversing the source polarity removes the deposited copper again: the coated surface now supports oxidation and acts as the anode. This polarity reversal changes the drive, unlike swapping the measurement leads in the Daniell cell voltage and load experiment. Coating appearance alone does not measure charge efficiency or exclude competing chemical reactions. See University of Washington, Electroplating Copper on Stainless Steel: apparatus and reversible coating demonstration.

The copper cathode in this driven example is negative, while the copper cathode of a discharging Daniell cell is positive: both support exactly the same reduction half-reaction. Likewise, an anode need not lose material if its conducting surface is absent from its net half-reaction. Neither terminal sign nor a universal mass-change rule defines an anode or cathode.

Faraday's laws of electrolysis state that the mass of material formed or consumed by a specified electrode reaction is proportional to the transported electric charge, and that equal electric charge produces masses proportional to $M/z$ for different reactions. Here $M$ is the product's mass per mole, and $z$ is the positive number of Electrons transferred per product entity. For complete use of the electric charge in that reaction,The first relation uses the Faraday constant; the second uses half-reaction stoichiometry; the third converts amount of substance to mass. For equal transported electric charge in two ideal cells,The number $z$ belongs to the balanced half-reaction, rather than to the metal's name alone: copper deposited from ${\mathrm{Cu}}^{2+}$ needs $z=2$. These modern forms of both laws are given in KIT's practical.^[ref]

If other same-direction electrode reactions share the measured electric current, define an integrated current efficiency $\eta =Q_{\mathrm{product}}/Q$. Provided the product is neither subsequently consumed nor lost, the retained mass isHere $0\le \eta \le 1$ follows from the specified same-direction partition of electric current. It is not a universal bound on every signed partial-current convention: IUPAC notes that simultaneous oxidation and reduction at one electrode can produce a current-efficiency ratio above one.^[ref] When efficiency varies during a run, use the charge-weighted ratio above, rather than an unweighted average over time. If deposition removes material from a multicomponent chemical solution, specify which chemical species is being counted and balance its half-reaction before choosing $z$.

Michael Faraday's accessible 1834 paper, Experimental Researches in Electricity, Seventh Series, §783 states proportionality between chemical action and the quantity of electricity passed. In §§789–791 he describes connecting a molten tin-chloride cell in series with a water-decomposition charge indicator, weighing the receiving electrode before and after, and comparing the deposited metal with the indicator's gas readout. The common series electric current makes these two readouts comparable. This was a quantitative test of chemical equivalents, rather than merely an observation that a deposit appeared. It is historical evidence, not a suggested classroom procedure; the modern Electron-counting derivation above uses concepts unavailable to Faraday.^[ref]