How batteries work Chapter 1 Galvanic cells

Chapter 1

The galvanic cell: half-reactions, open-circuit voltage and two modes of conduction

Why does the lamp light when the switch closes, and not while it is open?

Where we are. Chapter 0 gave you the volt (a joule per coulomb), the field (the push per unit charge), the conductor at rest (one potential throughout) and the two kinds of carrier: electrons in metals, ions in liquids. Now two different metals go into a liquid, and a potential difference appears between them.

Figure 1.1 A zinc electrode in zinc sulfate and a copper electrode in copper sulfate, separated by a porous wall, joined outside by a wire with a switch, a lamp and a voltmeter reading 1.10 volts. Closing the switch makes zinc atoms leave as ions, electrons run through the wire to the copper where copper ions plate out, and sulfate drift toward the zinc. A strip below shows the potential jumping at each electrode and flat through the liquid.
zinccoppercopper sulfate solutionporous wallcation (Zn2+, Cu2+)sulfateelectronpotentialfield
The Daniell cell, the textbook battery. Two metals, two salt solutions, a porous wall, and one wire. Try this: close the switch and watch the first zinc atom leave; then open it and notice that the voltmeter still reads 1.10 V.
SourceSchematic after Winter and Brodd 2004, Figure 1. Open-circuit voltage 1.10 V computed from the standard potentials in Bard, Faulkner and White 2022, Table C.1 (Cu2+/Cu +0.340 V, Zn2+/Zn −0.7626 V vs NHE). Potential strip after their Figure 1.1.2 (open circuit) and Figure 1.5.2 (current flowing); the split between the two interfacial jumps is not measurable and is drawn schematically (their section 2.2.3). Ion drift shows direction only; the drop under load is illustrative.

Close the switch. Zinc atoms at the left electrode give up two electrons each and dissolve into the liquid as Zn2+ ions; at the right electrode Cu2+ ions take two electrons each and settle as copper metal.1,2 Each of those is a half-reaction, and neither can happen alone: each must be coupled, through a cell, to a second half-reaction running the other way.2

The electrons cannot cross the liquid, so they take the wire, from the more negative electrode to the more positive, and the lamp lights on the way.2 Inside the cell the current is carried by ions: cations drift toward the copper and sulfate toward the zinc, so no charge piles up anywhere.1,2

Open the switch and everything stops, but nothing is lost. The voltage you measure with nothing else connected is the open-circuit voltage,1 and a high-impedance voltmeter can read it without drawing any appreciable current.2 For this pair of metals it is 1.10 V: the difference between the standard potentials of the two half-reactions, +0.340 V for copper and −0.763 V for zinc.2

Where a potential sits inside the cell is the strip under the figure: it jumps at each metal|liquid boundary, in a zone so narrow that a very strong field exists there, and stays flat through the liquid; the voltmeter reads the sum of the jumps along the path from one electrode to the other.2

Chapter 3 shows how each jump is built: the chemistry moves a minute charge across the boundary, and the field of that separated charge is what the strip shows.

That is the whole trick, in Goodenough and Park’s words: the electrolyte “conducts the ionic component of the chemical reaction between the anode and the cathode, but it forces the electronic component to traverse an external circuit where it does work”.3

Worked example. Where does 1.10 V come from, and what does it buy? E = E°(Cu2+/Cu) − E°(Zn2+/Zn) = 0.340 V − (−0.763 V) = 1.10 V energy per electron round the circuit = 1.10 eV; two electrons per zinc atom per mole of zinc: 2 × 96 485 C × 1.10 V = 213 kJ Chapter 3 shows that this 213 kJ is the free energy of the reaction Zn + Cu2+ → Zn2+ + Cu, and chapter 4 turns the “per mole” into “per gram”.

A battery is a chemical reaction that is only allowed to happen through a wire.

Figure 1.2 A metal electrode beside a liquid electrolyte, sharing a boundary. In the metal only electrons move, through a lattice of fixed positive ion cores; in the liquid only ions move; at the boundary an ion takes an electron and becomes an atom. The same field points the same way in both, pushing electrons one way and cations the other.
electroncationanionfield
Two roads for charge, joined at the boundary. Why the electrons take the wire and the ions take the liquid. Try this: press Step and watch what happens at the boundary each time an ion arrives; nothing crosses without a reaction.
SourceAfter Bard, Faulkner and White 2022, section 1.1.1: charge is transported through an electrode by electrons and through an electrolyte by ions, and at the interface the two modes must be linked through an electrode reaction; free electrons in solution are very short-lived (their footnote 1). Field and force directions from their section 2.2.1 and 1.5.1. Schematic; particle speeds are not to scale.

Why do the electrons choose the wire? Because they have no other road. In a metal, charge is carried by electrons moving through a lattice of fixed ion cores; in an electrolyte it is carried by ions, and the “free” electrons a liquid might briefly hold are so short-lived that they contribute nothing to its conductivity.2

At the boundary between the two, charge can pass only if the two kinds of carrier are linked by an electrode reaction: electrons consumed or produced in the metal, ions produced or consumed in the liquid.2

The field does the rest. One field points from the positive side to the negative side; it pushes a positive ion along itself and an electron against itself, so the cations in the liquid and the electrons in the wire go round the circuit in opposite senses and meet again at the electrodes.2

In the wire, the potential difference that drives the electrons through the lamp is the one you met in figure 0.4; in the liquid, the potential slopes gently and drives the ions.2

Electrons travel in metals, ions travel in liquids, and only a reaction can hand charge from one to the other.

Figure 1.3 One cell, three cells in series, or three cells in parallel, with bars for voltage and capacity and a strip showing the potential rising once, three times in a row, or once with three paths side by side.
Cells and batteries. Voltage adds along a path; charge adds across paths. Try this: switch to series and count the steps on the strip; then to parallel and ask yourself which cell a given coulomb came from.
SourceDefinitions from Winter and Brodd 2004, footnote 1; series adds voltage and parallel adds current and run time from Goodenough and Park 2013. The strip applies the rule that a potential difference along a path is the integral of the field along it (Bard, Faulkner and White 2022, eq. 2.2.2), so differences add. The 1.5 V per cell is illustrative.

Strictly, one of these units is a cell, and several connected together are a battery, although the two words are used loosely.1 Connecting cells in series adds their voltages; connecting them in parallel adds their current and their run time.3 The strip says why the voltages add: a potential difference between two points is the sum of the rises and drops along any path between them,2 so three cells in a chain give three rises of V, and a coulomb that travels the whole chain picks up energy at each one.

Why the capacity does not add in series is a matter of counting coulombs. The cells in a chain carry one and the same current: the charge that leaves the first cell has nowhere to go but through the second and the third, so every coulomb drawn from the chain is a coulomb drawn from each cell. When one cell has given up its Q, they all have. In parallel the picture is reversed. All three + terminals are tied together and all three − terminals are tied together, so the ends of the battery see one potential difference, V, and no more; but the current is shared, each cell supplies a third of it, and together they can deliver three times the charge before they are empty. Series adds the rises along the path; parallel adds the paths.

A battery keeps its reacting materials inside, so it is a closed system: storage and conversion happen in the same box. A fuel cell is an open system, fed with fuel and oxidant from outside, so its energy is stored in a tank and converted in the cell. A supercapacitor stores charge in the electrical double layers at its electrode surfaces, without a chemical reaction.1

None of the three turns heat into work, so none is bound by the Carnot limit that caps every heat engine.1 Everything on this page happens inside a single cell.

Figure 1.4 A table of eighteen energy-storage systems against five criteria for a battery: a closed system, faradaic redox reactions, oxidation and reduction at separate electrodes, ions through an electrolyte while electrons go round an outside circuit, and electrical energy delivered. Each mark says whether a system meets, partly meets or does not meet a criterion; the last column gives the verdict: battery, hybrid or not a battery.
meets the criterionpartlydoes not
Is it a battery? Five tests applied to eighteen systems. Try this: tap Fuel cell and then Redox flow. Both keep their reactants in tanks; why does only one pass?
SourceThe IUPAC and IEC definitions, the five operational criteria, the marks and the verdicts are those of Villevieille, Novák and Girault 2026, Tables 1 and 2, including the partial mark for graphite; the notes in the readout follow their text.

What makes a battery a battery?

We have used the word battery freely. It now covers systems that store energy in very different ways, and a 2026 Comment by Villevieille, Novák and Girault asks which of them deserve it.4 Let us start with the official words. IUPAC gives no formal definition of a battery: it defines an electrochemical cell as a system of at least two electron conductors, the electrodes, in contact with ionic conductors, the electrolytes, and mentions batteries only as examples of such cells. The International Electrotechnical Commission defines a battery as one or more electrochemical cells fitted with the devices needed for use, such as a case, terminals, marking and protective devices.4

Those definitions say how a battery is built, not how it works. The Comment adds five operational criteria, all of which must hold. C1: the system is closed, so the electroactive species stay inside it. C2: energy is stored and released through reversible oxidation and reduction, that is, through faradaic reactions; the current they carry is what IUPAC calls a faradaic current, the current that results from the electrooxidation or electroreduction of an electroactive substance. C3: oxidation and reduction happen at distinct electrodes, separated by an ion-conducting medium. C4: ions migrate through the electrolyte while electrons flow through an external circuit. C5: stored chemical energy is delivered as electrical energy through that circuit.4 On discharge, oxidation takes place at the negative electrode and reduction at the positive one; on charge, the other way round.4

Applied to real systems, the criteria sort them cleanly. Redox-flow cells pass even though their two liquids sit in tanks outside the cell, because the reactants stay inside the system; the liquids are called the negolyte and the posolyte, not anolyte and catholyte, because anode and cathode swap between charge and discharge. Fuel cells do not pass: fuel and oxidant are fed from outside, so the system is open. Metal-air cells, whose positive electrode takes its oxygen from the air, are hybrids. Capacitors and supercapacitors store charge without faradaic reactions and are not batteries; a pseudocapacitor, which stores charge through fast faradaic reactions confined to surfaces while behaving like a capacitor, meets two of the tests only in part and is not a battery either.4

The same test settles the stranger uses of the word. The “thermal battery” of the handbooks is a battery: a primary cell whose salt electrolyte is solid at room temperature and is melted with pyrotechnic material to start it. A store of heat sold as a “thermal battery” is not, because it makes no electricity without a turbine and generator; nor are nuclear, quantum and mechanical “batteries” such as a flywheel, which deliver electricity without electrochemistry. A “structural battery”, which carries mechanical loads as well as storing energy, passes all five tests.4

A provocation about graphite. The table marks lithium-ion cells with a graphite negative electrode as only partly meeting C2. Citing a recent analysis, the Comment argues that no redox reaction tied to energy storage takes place in graphite, which works instead as a lithium-ion volumic capacitor; it still classes these cells as batteries.4 This is one group’s proposal, not settled usage, and in this course we keep the usual picture of lithium inserted into graphite (chapter 7).

Figure 1.5 A timeline of eight milestones from Volta’s pile of about 1800 to the Nobel Prize of 2019. Choosing a milestone draws that cell with its electrodes and electrolyte in their real colours and gives its electrodes, its electrolyte and, where the source gives it, its cell reaction.
From Volta’s pile to the lithium-ion cell. Try this: compare Daniell’s cell with figure 1.1, then find the first cell that could be recharged.
SourceDates, electrodes, electrolytes and cell reactions after Arote 2022, section 1.2.3 and section 1.4; the 1886 dry cell after Faruque et al. 2026, Table 1. The drawings show the materials in their real colours and are not to scale.

From Volta’s pile to the lithium-ion cell

The cell of figure 1.1 has a long history. Around 1800 Alessandro Volta built the first real battery, a pile of zinc and silver sheets separated by cloth soaked in salt water. In 1836 John Frederic Daniell put a copper electrode in copper(II) sulfate and a zinc electrode in zinc sulfate, the two solutions separated by a porous partition: our figure 1.1, with Zn + Cu2+ → Zn2+ + Cu as its cell reaction.5

The first rechargeable battery to be produced commercially was Gaston Planté’s lead-acid cell of 1859: lead and lead dioxide in dilute sulfuric acid, PbO2 + 2H2SO4 + Pb ⇌ 2PbSO4 + 2H2O.5 It still serves in cars and uninterruptible power supplies.6 In 1866 Georges Leclanché’s zinc-carbon cell paired zinc with manganese dioxide and carbon in ammonium chloride solution; for commercial use the liquid was replaced by a paste, and the first dry cell, a variant of the Leclanché cell, followed in 1886.5,6 In 1901 Waldemar Jungner and Thomas Edison introduced nickel-cadmium and nickel-iron cells. For many years nickel-cadmium was the rechargeable cell of choice, until the toxicity of cadmium sent the search elsewhere.5

Lithium was the next step: the lightest of these metals, with a very negative electrode potential. Sony brought out the first commercial lithium-ion battery in 1991, with LiCoO2 as the positive electrode and carbon as the negative, and in 2019 John Goodenough, Stanley Whittingham and Akira Yoshino received the Nobel Prize in Chemistry for the development of lithium-ion batteries.5,6 Chapter 2 follows the insertion electrodes behind that cell from 1972 on (figure 2.7).

Figure 1.6 A family tree of batteries. Batteries divide into primary, single-use cells (zinc-carbon, alkaline, silver oxide, lithium-MnO2) and secondary, rechargeable cells (lead-acid, nickel-cadmium, nickel-metal hydride, nickel-zinc, lithium-ion), each shown with its two electrode materials in their real colours and its nominal voltage. Lithium-ion cells are sorted again by electrolyte (liquid, gel polymer, solid) and by shape (coin, cylindrical, prismatic, pouch).
primarysecondarylithium-ion
A family tree of batteries. Try this: find the two cells that pass 2 V, and say what they share.
SourceFamilies, examples, uses and the sorting of lithium-ion cells after Arote 2022, sections 1.2, 1.4 and 1.7; electrode materials and nominal voltages after Winter and Brodd 2004, Table 2, as in figure 3.1 (nickel-zinc is not in that table and is shown without a voltage). The two small bars give each cell’s negative and positive electrode materials in their real colours; cadmium is drawn with the zinc colour, NiOOH with the carbon one and the metal hydride with the steel one.

Primary and secondary

Not every battery is meant to be recharged. Batteries fall into two broad families. Primary batteries are single-use: they store and give energy but cannot be recharged, so they are discarded after use. They suit household items that need little energy, such as radios, watches, remote controls and toys.5 Secondary batteries are rechargeable: an external current reverses the reaction that makes the electricity, so they store and supply energy over many cycles. They power telephones, computers and cameras, and now hybrid electric vehicles.5

The commonest primary cells are dry cells, and a dry cell need not be dry: its electrolyte is a paste. Zinc-carbon is the most common. Alkaline cells, with potassium hydroxide as the electrolyte, store more energy and leak less; they cost more but perform better in extreme weather.5 Among secondary cells, lead-acid, with lead-alloy and lead-oxide electrodes in dilute sulfuric acid, is the most common wet cell, and nickel-metal hydride, nickel-cadmium and nickel-zinc are also in common use.5

Lithium-ion cells are themselves sorted two ways. By electrolyte there are three kinds: conventional cells with an organic liquid, polymer cells with a gel polymer electrolyte and solid cells with a solid electrolyte. By shape there are four: coin, cylindrical, prismatic and pouch.5 The voltages in the figure make a point we return to in chapter 3: the only cells above 2 V are built on lithium.1

You can now explain why a cell has a voltage even when nothing is connected, where inside the cell that voltage sits, why the electrons take the wire and the ions the liquid, and why voltages add in series.

So what is inside the box, part by part, and what does each part do?

Go deeper: primary and secondary cells

A primary battery is assembled in the charged state and used until exhausted. A secondary, or rechargeable, battery can be restored to its charged condition by a current flowing in the opposite direction to the discharge current; since secondary batteries are usually assembled in the discharged state, they must be charged before their first use.1 To charge, a power supply is connected across the cell and its voltage is adjusted; the interfacial potential differences shift, especially at the electrode|electrolyte boundaries, and current can be driven in either direction.2 Which reactions can be run backwards, and which cannot, is a question for the modules still to come.

The mathematics of this chapter

Zn → Zn2+ + 2e−  Cu2+ + 2e− → Cuthe two half-reactions; neither can run alone

Zn + Cu2+ → Zn2+ + Cuthe cell reaction, their sum; n = 2 electrons per zinc atom

Ecell = E°(Cu2+/Cu) − E°(Zn2+/Zn) = 0.340 − (−0.763) = 1.103 Vopen-circuit voltage at unit activities, from the standard potentials against the hydrogen electrode (figure 1.1)

E = φCu′ − φCu = Σ Δφinterfacesthe voltage between two like leads is the sum of the potential steps met along the path through the cell: the two metal|liquid jumps plus the metal|metal contact potentials; only the sum is measurable (the strip under figure 1.1)

ΔG = −nFE = −2 × 96 485 × 1.103 = −213 kJ/molthe electrical work a mole of the reaction can do (chapter 3 derives it)

Vseries = Σ Vi, Qseries = Qcells in a chain: potential differences along a path add; the same current threads every cell, so each coulomb passes all of them (figure 1.3)

Vparallel = V, I = Σ Ii, Qparallel = Σ Qicells side by side: one potential difference between the joined ends; the current, and therefore the charge, is shared

References for this chapter

Numbers in the text refer to this list. All references of the course, with the chapters that use each one.

  1. 1 M. Winter, R. J. Brodd, "What Are Batteries, Fuel Cells, and Supercapacitors?", Chemical Reviews 104, 2004, 4245-4269. doi:10.1021/cr020730k
  2. 2 A. J. Bard, L. R. Faulkner, H. S. White, "Electrochemical Methods: Fundamentals and Applications", Wiley, 3rd edition, 2022.
  3. 3 J. B. Goodenough, K.-S. Park, "The Li-Ion Rechargeable Battery: A Perspective", Journal of the American Chemical Society 135, 2013, 1167-1176. doi:10.1021/ja3091438
  4. 4 C. Villevieille, P. Novák, H. H. Girault, "Your battery may not be a battery", Nature Nanotechnology, 2026, Comment, published online 15 October 2026. doi:10.1038/s41565-026-02296-w
  5. 5 S. A. Arote, "Fundamentals and perspectives of lithium-ion batteries", chapter 1 of Lithium-ion and Lithium–Sulfur Batteries: Fundamentals to Performance, IOP Publishing, 2022, pp. 1-1 to 1-26. doi:10.1088/978-0-7503-4881-2ch1
  6. 6 O. Faruque, M. J. Isalm, O. Faruq, M. M. Alam, "A comprehensive review of past and present developments of Li-ion batteries", Discover Sustainability 7, 2026, 881. doi:10.1007/s43621-026-02920-8

Cite this page

Using this page in teaching, a thesis or an article? Cite it as follows; the date is the last update of the course.

Shyma Sajeevan, A. (2026). The galvanic cell: half-reactions, open-circuit voltage and two modes of conduction. How batteries work. https://asajeevan.github.io/batteries/galvanic-cells/

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