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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.

Electrochemistry studies how chemical reactions, transport, and chemical equilibrium couple to electric charge and electric potential. In a cell, electrons travel through the external circuit, while mobile ions carry electric current through the electrolyte. At the electrodes, redox reactions connect these two forms of electric charge transport. This connection makes it possible both to obtain electrical work from a chemical reaction and to use electrical work to drive a chemical reaction.

An anode is an electrode where oxidation occurs; a cathode is an electrode where reduction occurs. These definitions refer to the chemical reactions, rather than universal positive or negative terminal signs. In a galvanic cell delivering electrical work, the anode is negative and the cathode positive. In an electrolytic cell driven by an external source, the anode is positive and the cathode negative. See Pingarrón et al., Terminology of electrochemical methods of analysis (IUPAC Recommendations 2019), §§3.1 and 3.4 and Flowers et al., Chemistry 2e, §17.2: galvanic cells.

For a worked example, consider an electrolytic cell containing molten sodium chloride, with the anode connected to the positive terminal and the cathode to the negative terminal of an external source. At the cathode, sodium cations gain electrons; at the anode, chlorine anions lose electrons:The first line has net electric charge zero on each side; the second has $-2e$ on each side. Adding the lines cancels the transferred electrons and preserves both chemical atom counts and net electric charge. The sodium product is neutral, and the chlorine product is a diatomic molecule. These equations specify molten sodium chloride; aqueous chemical solutions introduce competing water reactions. See 17.7 Electrolysis (§17.7: electrolysis of molten sodium chloride).

Electrochemistry underlies battery charging and the manufacture of chemicals by electrolysis. Its particularly useful idea is that an electron inventory in a balanced chemical equation also accounts for transported electric charge. Transport alone is a different question from an electrode chemical reaction: an ion may carry electric current through the electrolyte without itself being consumed at an electrode.

Historically, Michael Faraday introduced the terms electrode, electrolyte, anion, cation, and ion in the terminology section of his 1834 paper, Experimental Researches in Electricity, Seventh Series by Michael Faraday (§§662–667). His §667 explicitly treats the direction assigned to electric current as a convention. His ion language predates the modern electron and atomic nucleus picture used in the charge-counting example above.

For an electrolyte near chemical equilibrium, a Poisson-Boltzmann equation can approximate the distribution of ions in an electric potential. Such an equilibrium model does not by itself describe a cell carrying sustained electric current.

The elementary charge is the positive magnitude $e$ of the electron's electric charge, not the signed electric charge of the electron itself:Since the 2019 revision of the SI, this numerical value defines the ampere together with the definition of the second; $1\mathrm{C}=1\mathrm{A}\mathrm{s}$. Thus today's numerical exactness is a choice of units, whereas measured electric charges still have experimental uncertainty. An oil drop experiment can test charge quantization and the apparatus calibration; it does not supply a new uncertain defining value of $e$ in today's SI. ^[ref].

For ordinary isolated chemical atoms, ions and charged objects whose net electric charge is counted through protons and electrons, charge quantization gives $Q=ne$ with signed integer $n$. A neutral chemical atom that loses two electrons becomes an ion of electric charge $+2e$. A toy object with $10^9$ excess electrons has $Q=-0.1602176634\mathrm{nC}$. Conversely, the scale $1\mathrm{nC}/e\simeq 6.24\times 10^9$ explains why laboratory electric charge often looks continuous: billions of microscopic increments fit into a small macroscopic amount. Averaged charge density is a continuum description, not a claim that each particle has an arbitrarily divisible electric charge.

The ordinary-matter qualifier matters. In the Standard Model, quarks have electric charges $+2e/3$ or $-e/3$, and antiquarks have the opposite signs. Confinement means these are constituents of hadrons, not isolated fractionally charged particles collected by an oil drop experiment. The usual valence quark sums give $2(2e/3)-e/3=e$ for a proton and $2e/3-2(e/3)=0$ for a neutron. Thus elementary charge should not be defined as the smallest nonzero electric charge of every constituent in particle theory. ^[ref].

The beautiful experimental idea behind the oil drop experiment is to determine a microscopic electric charge by watching a visible carrier move. In his 1913 paper, Millikan timed the descent and electrically driven ascent of individual oil drops, repeatedly changing a drop's electric charge through capture of air ions. His apparatus used parallel plates separated by $16\mathrm{mm}$, a roughly $5300\mathrm{V}$ source, and an optical scale to measure travel distances. He reported multiple relationships among a given drop's inferred electric charges. He also found that uncorrected Stokes's law gave a size-dependent inferred elementary unit, and introduced a pressure-dependent slip correction. These were measured relationships with calibration and model uncertainties, not exact readings of today's defined $e$. ^[ref].

A modern instructional implementation sprays low-volatility oil of known density through a plate aperture, illuminates the drops, and follows one through a calibrated optical scale. Measure the plate spacing $d$, electric potential difference $V$, air temperature and pressure. Time a fixed distance $L$ with the electric field off to get a terminal falling speed $v_f=L/t_f$. Then choose the field polarity to drive the same drop upward and measure $v_r=L/t_r$. Repeat timings at a fixed electric charge, and compare before and after an ion-capture event. The same drop is especially useful because its radius and mass need not be inferred anew for each charge state. ^[ref].

Here is the leading continuum model, retaining buoyancy. Assume a drop shaped as a sphere of radius $a$, oil and air densities ${\rho }_o$ and ${\rho }_a$, air dynamic viscosity $\eta$, and gravitational acceleration $g$. Define the downward effective weight $W$ and positive linear drag coefficient $k$ byAt terminal velocity, the net force vanishes. Falling with no electric field, the upward drag force balances weight minus buoyancy. Rising with the electric force upward, the drag force reverses and joins the downward effective weight:Consequently the uncorrected estimates areThe observed direction of response, with known field polarity, supplies the sign of $q$. A suspended drop gives the alternative balance $|q|E=W$, but it still requires a determination of $W$: balancing a drop alone does not determine its electric charge.

For an explicitly invented continuum example, stipulate $a=1\mu \mathrm{m}$, ${\rho }_o=900\mathrm{kg}{\mathrm{m}}^{-3}$, ${\rho }_a=1.2\mathrm{kg}{\mathrm{m}}^{-3}$, $\eta =1.8\times 10^{-5}\mathrm{Pa}\mathrm{s}$, $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$, $q=-5e$ and a downward $E=10^5\mathrm{V}{\mathrm{m}}^{-1}$. The balances predict $W\simeq 3.69\times 10^{-14}\mathrm{N}$, $v_f\simeq 0.109\mathrm{mm}{\mathrm{s}}^{-1}$ and $v_r\simeq 0.127\mathrm{mm}{\mathrm{s}}^{-1}$. Substituting those speeds recovers $|q|=5e$ within rounding. This checks the algebra; it is not a precision prediction for real micrometre drops, which need a slip correction.

The inference has two distinct parts. Compare inferred electric charges or charge changes with a common unit, seeking $q_i\simeq n_{i}e$ within uncertainty, rather than demanding exact ratios of rounded measurements. Then establish the absolute scale through electric field, density, dynamic viscosity and distance/time calibration. If the observed steps are all even multiples, their common spacing alone cannot exclude an unobserved smaller unit. Air motion, evaporation and mistimed crossings can alter inferred electric charge without an ion-capture event. Small Reynolds number supports Stokes's law, but does not by itself justify its no-slip continuum coefficient: a significant ratio of air mean free path to drop radius requires a slip correction. Millikan's comparison of different drop sizes and pressures addressed that systematic limitation; the modern PASCO manual also includes the correction. Agreement supports charge quantization for the observed carriers within experimental resolution, rather than proving a universal statement about every possible particle.

Multiplying $e$ by the Avogadro constant gives the Faraday constant, $F=N_{A}e$, the electric charge per mole of singly charged carriers. This connects counting individual electric charges with bulk electrochemistry. ^[ref].

An ion is a chemical atom or a group of chemical atoms with a nonzero net electric charge. A positive ion is a cation; a negative ion is an anion. The whole entity carries the electric charge: a hydronium ion is a group of four chemical atoms with net charge $+e$. This definition agrees with ^[ref].

For an ordinary ion containing only atomic nuclei and electrons, let $N_p$ count all its protons and $N_e$ all its electrons. Each proton contributes the elementary charge $+e$, each electron contributes $-e$, and neutrons contribute zero. ThereforeThe signed integer $z$ is the net electric charge number. Removing an electron increases $z$ by one; adding an electron decreases $z$ by one. Changing the electron count leaves the atomic number, and therefore the identity of the chemical element, unchanged.

For example, a neutral sodium chemical atom has $11$ protons and $11$ electrons. Its cation ${\mathrm{Na}}^{+}$ still has $11$ protons, but only $10$ electrons, so $q=(11-10)e=+e$. A neutral chlorine chemical atom has $17$ protons and $17$ electrons; its anion ${\mathrm{Cl}}^{-}$ has $17$ protons and $18$ electrons, so $q=(17-18)e=-e$. These are particle inventories, not pictures of atomic orbitals. See 2.6 Ionic and Molecular Compounds (§2.6: ions and ionic compounds).

One sodium chloride formula unit accounts for one ${\mathrm{Na}}^{+}$ cation and one ${\mathrm{Cl}}^{-}$ anion, whose net electric charges sum to zero. Ordinary solid sodium chloride is an extended arrangement of ions, rather than discrete $\mathrm{NaCl}$ molecules. This is a useful distinction: a neutral material can contain charged constituents, and its chemical formula tells us their ratio without claiming that each pair is a separate molecule.

Ion bookkeeping connects chemistry to electric current: moving ions can transport electric charge, while stationary ions cannot supply a transport current density. In electrochemistry, both signs of ions can contribute to the same conventional current. An ion opposing a fixed electric charge is called a counterion.

Her institutional profile identifies her as a chemist whose research areas include electrochemistry and theoretical chemistry.

An oxidation increases an oxidation state, recording loss from the formal electron assignment. For $\mathrm{Zn}\to {\mathrm{Zn}}^{2+}+2e^{-}$, the increase is $0\to +2$. Oxidation need not involve oxygen.^[ref]

In the electrochemistry examples here, oxidation is loss of electrons by a chemical species; it occurs at the anode. That electrode definition holds in both a galvanic cell and an electrolytic cell; it does not fix terminal polarity. The oxidized chemical species serves as the reducing agent in the coupled redox.

A reduction decreases an oxidation state, recording gain in the formal electron assignment. For ${\mathrm{Cu}}^{2+}+2e^{-}\to \mathrm{Cu}$, the decrease is $+2\to 0$. The reduced chemical species serves as the oxidizing agent in the coupled redox.^[ref]

In the electrochemistry examples here, reduction is gain of electrons by a chemical species; it occurs at the cathode. That electrode definition holds in both a galvanic cell and an electrolytic cell; it does not fix terminal polarity.

A solid electrolyte carries electric current through mobile ions while remaining a solid. The distinction between ionic and electronic electrical conductivity matters: different charge carriers serve different roles in electrochemistry.