The Galvanic Cell

Touching, Only Heat

Put a piece of zinc in blue copper sulfate solution and it is soon coated with red-brown copper while the blue slowly fades. The watch glass at the front left holds such a piece of zinc.

The reaction is Zn + Cu²⁺ → Zn²⁺ + Cu: each zinc atom gives up two electrons and becomes a zinc ion; a copper ion takes them and becomes copper. The electrons pass straight across where the two meet, and all the energy comes out as heat, about 219 kJ per mole (computed here from heats of formation).

To turn that energy into electricity, the electrons have to be sent the long way round.

Zn + Cu²⁺ → Zn²⁺ + Cu · about 219 kJ/mol of heat (computed)

Two Halves and a Wire

The two beakers on the bench split the reaction in two: on the left a zinc strip stands in zinc sulfate solution, on the right a copper strip in copper sulfate. The two metals are wired to a voltmeter.

The zinc and the copper ions no longer meet. The electrons the zinc gives up can only travel along the wire to the copper side, where the copper ions take them. A current flows in the wire, and the needle swings to about 1.1 V.

A device that makes electricity from a spontaneous chemical reaction is a galvanic, or voltaic, cell. The electrons and ions drawn here are a sketch, not to scale.

Left: Zn → Zn²⁺ + 2e⁻ · right: Cu²⁺ + 2e⁻ → Cu · electrons only in the wire

The Zinc Side Is Negative

Each zinc atom leaves two electrons in the metal and goes into the solution as a zinc ion: Zn → Zn²⁺ + 2e⁻. Losing electrons is oxidation, and the electrode where it happens is the anode.

The electrons left behind charge the zinc negatively, so in a galvanic cell the anode is the negative terminal. In an electrolytic cell it is the other way round: the anode is wired to the supply’s positive terminal.

The zinc under the solution slowly thins. Each ampere-hour of charge dissolves about 1.22 g of zinc (computed here with Faraday’s law).

Zn → Zn²⁺ + 2e⁻ · oxidation · anode = negative · about 1.22 g of zinc per Ah (computed)

The Copper Side Is Positive

The electrons the wire brings reach the copper’s surface and pass to the copper ions in the solution, which become copper atoms and plate onto the strip: Cu²⁺ + 2e⁻ → Cu. Gaining electrons is reduction; this electrode is the cathode, the cell’s positive terminal.

What plates out is a pink coat of pure copper, like the part of the strip under the solution here. Each ampere-hour plates about 1.19 g of copper (computed).

As the copper ions are used up, the blue slowly fades.

Cu²⁺ + 2e⁻ → Cu · reduction · cathode = positive · about 1.19 g of copper per Ah (computed)

Where 1.10 Volts Comes From

A metal in a solution of its ions is a half-cell. The potential of one half-cell can’t be measured, only the difference between two; so each is measured against the standard hydrogen electrode, set at zero, at 25 °C with its ions at 1 mol/L. That is its standard electrode potential: +0.34 V for copper, −0.76 V for zinc.

The cell’s voltage is the positive side minus the negative: 0.34 − (−0.76) = 1.10 V. The further apart the two, the higher the voltage.

As energy, a volt is a joule for each coulomb of charge. A mole of reaction can do at most about 213 kJ of electrical work, ΔG = −nFE (computed). A cell stores not electricity but chemicals that have yet to react: the zinc and the copper ions.

E°(Cu²⁺/Cu) = +0.34 V · E°(Zn²⁺/Zn) = −0.76 V · 1.10 V apart · at most about 213 kJ/mol (computed)

Ions Cross the Bridge, Not Electrons

Between the beakers stands an upside-down glass U-tube filled with agar gel made up with potassium chloride, its ends plugged with cotton. This is the salt bridge.

The left beaker keeps gaining zinc ions and the right keeps losing copper ions. Negative ions from the bridge flow into the zinc side and positive ions into the copper side, keeping both solutions neutral, so the current can keep flowing.

Electrons never cross the solutions or the bridge; in a solution or a bridge, ions carry the charge. The bridge’s salt takes no part in either reaction; it only carries charge.

Cl⁻ towards the zinc · K⁺ towards the copper · in solution and the bridge, only ions move

Lift the Bridge, the Needle Falls

Lift the salt bridge out and the circuit is broken: the current stops, the needle drops to zero, and so does the reaction.

With no ions to carry the charge across, the left beaker would charge up positive with its extra zinc ions and the right one negative, and that charge soon pushes the electrons back. Treating a beaker of solution as a ball 5 cm in radius, it takes only about 20 million zinc atoms reacting to make enough charge to cancel 1.1 V: about 2 femtograms of zinc, two thousand-million-millionths of a gram.

Put the bridge back and the needle returns to about 1.1 V.

No bridge: it stops after about 20 million zinc atoms (estimate) · the needle falls to zero

Other Pairs, Other Voltages

Any two metals make a cell, and its voltage can be read off the table of standard electrode potentials: the further apart the two, the higher the voltage, and the metal with the lower potential is the negative terminal.

Against copper, iron gives about 0.79 V, nickel 0.60 V and lead 0.47 V; zinc against silver gives about 1.56 V. These are computed for standard conditions; change the concentrations and the voltage changes.

The lithium-ion cell in a phone works on the same principle: lithium ions move back and forth between the electrodes, and the electrons go round the outer circuit. One cell gives about 3.7 V.

Standard conditions, computed: Zn–Cu 1.10 V · Fe–Cu 0.79 V · Ni–Cu 0.60 V · Zn–Ag 1.56 V

1836, a Steady Current

In 1800 Volta stacked pairs of copper (better, silver) and zinc discs with card soaked in brine between them, and made the first battery. But such cells soon weakened: hydrogen bubbling out on the copper clung to its surface and held the reaction back.

In 1836 John Frederic Daniell, professor of chemistry at King’s College London, described his constant battery in a letter to Faraday: a copper cylinder holding a tube of membrane made from an ox’s gullet, with a rod of amalgamated zinc in dilute sulfuric acid inside it and saturated copper sulfate outside. A pink coat of pure copper came out on the copper instead of hydrogen, and the current stayed perfectly steady for six hours together.

Daniell cells later powered the Atlantic telegraph cables of 1858 and 1866. By the Nernst equation, when nine-tenths of the copper ions are used the voltage has dropped by only about 0.04 V (computed here).

1800: Volta’s pile · 1836: Daniell’s cell, steady for six hours · nine-tenths of the copper ions used: only about 0.04 V lower (computed)

Rusting Is a Cell Too

Iron rusting in damp air is a galvanic cell formed at the iron’s surface: at one spot the iron gives up electrons, Fe → Fe²⁺ + 2e⁻; they travel through the iron to another spot and pass to oxygen dissolved in the water, O₂ + 2H₂O + 4e⁻ → 4OH⁻. The iron is its own wire.

Rust is hydrated iron(III) oxide; it flakes off and does not protect the iron beneath. On galvanised steel the zinc oxidises more readily than the iron, so even where it is scratched the zinc corrodes first and shields the steel.

By one estimate, extrapolated from older national studies, corrosion costs the world about $2.5 trillion a year, about 3.4 % of global GDP in 2013.

Fe → Fe²⁺ + 2e⁻ · O₂ + 2H₂O + 4e⁻ → 4OH⁻ · about 0.85 V (computed)

A Pouch of Shorted Cells

A disposable hand warmer holds iron powder, water, activated carbon, an absorbent resin, vermiculite and salt, most of it iron by weight: one safety data sheet gives 50⁠–⁠60 % iron powder and 30⁠–⁠40 % water. The one at the front right has had an end cut off and some of its dark grey mix poured out; the golden-brown flakes are vermiculite.

Its heat comes from iron rusting. Rusting is itself a galvanic cell, and here the place that gives up electrons and the place that takes them lie side by side with no wire between: the electrons go straight from the iron to the oxygen, and all the energy comes out as heat. A pouch of shorted cells.

Salt and water make the iron rust faster; according to the makers’ association, the activated carbon holds oxygen from the air next to the iron powder, and the vermiculite holds the water so the powder doesn’t clog.

Iron powder 50⁠–⁠60 % · water 30⁠–⁠40 % · activated carbon 5⁠–⁠10 % · vermiculite 5⁠–⁠10 % · salt 1⁠–⁠5 % · resin 1⁠–⁠5 % (one safety data sheet)

The Heat Comes from Iron

In the end the iron becomes hydrated iron oxides and hydroxides: rust. By heats of formation each gram of iron gives out about 7 kJ (between 7.1 and 7.5 kJ, depending on the product).

Each gram of iron takes about 0.43 g of oxygen, about 1.6 L of air (at 25 °C, computed). The warmer is sold in an airtight outer bag; only when that is torn open and air gets in through the small holes in the inner bag does it start to warm.

One common adhesive warmer is labelled 63 °C at most, 53 °C on average, for 14 hours: values measured in a 20 °C room on a warm-water plate standing in for the body, not on a person. At 44 °C for 3⁠–⁠4 hours, or 50 °C for 2⁠–⁠3 minutes, skin can suffer a low-temperature burn, so a warmer is never stuck straight on the skin.

About 7 kJ per gram of iron (computed) · about 1.6 L of air per gram (computed) · label: 63 °C at most, 53 °C on average, 14 hours

The Bench, Taken Apart

The voltmeter, the salt bridge, the zinc and copper strips with their clips, the two solutions, the hand warmer and the watch glass move apart; the leads follow the parts they join.

The part under the pointer lifts out alone and is named; left alone, the parts lift out in turn.

Voltmeter · salt bridge · zinc strip · copper strip · zinc sulfate · copper sulfate · hand warmer · watch glass