Part C · How stuff changes

13 · Redox: passing electrons

Rust, fire, batteries and breathing are all the same kind of reaction: electrons moving from one substance to another. Chapter 12 was about passing protons around. This one is about passing electrons, and it gives you a unit you already know, the volt.

Losing and gaining

When a substance loses electrons it's oxidised; when it gains them it's reduced. The two always happen together, because the electrons have to go somewhere, hence redox (reduction + oxidation). The old student mnemonic is OIL RIG: Oxidation Is Loss, Reduction Is Gain.

Zn + Cu²⁺ → Zn²⁺ + Cu

Drop a zinc strip into blue copper sulfate solution and it grows a coat of copper while the blue fades. Each zinc atom hands two electrons to a copper ion. Zinc is oxidised (it loses electrons), and copper is reduced (it gains them).

Chemists track this with oxidation states: imaginary charges you get by pretending every bond is fully ionic and giving the shared electrons to the more electronegative atom. They're bookkeeping, not measured charges. But the books always balance, and they tell you who lost electrons and who gained them.

Common trap

"Oxidation means adding oxygen." That's where the name comes from, because oxygen is the classic electron-taker. But sodium burning in chlorine (chapter 5's salt) is just as much an oxidation, with no oxygen anywhere. What matters is electrons, not which atom takes them.

Electrons roll downhill

Which way do electrons go? Toward whoever holds them more tightly, which is chapter 5's electronegativity again. Metals on the left of the periodic table hold their outer electrons loosely; oxygen and the halogens hold them hard. Chemists rank every "couple" (an oxidised form plus its reduced form, like Zn²⁺/Zn) on one scale, the standard electrode potential E°, in volts.

Here they are as an energy ladder for electrons. Higher up means the electrons are less tightly held. Pick any two couples: electrons fall from the higher one to the lower one.

Zinc in zinc ions, copper in copper ions, joined by a wire. Which way do the electrons go, and what voltage do you get?

Zinc → copper, 1.10 V. Zinc's electrons sit higher (E° = −0.76 V) than copper's (+0.34 V), so they fall from zinc to copper ions. The size of the drop is the difference, 0.34 − (−0.76) = 1.10 V. That's the Daniell cell from 1836, one of the first practical batteries.

Standard electrode potentials at 25 °C, drawn as the energy of an electron in each couple (more negative E° = higher electron energy). Click or tap two couples. The upper one gives up electrons (oxidised); the lower one takes them (reduced).

The volt is a wonderfully direct unit here. A potential difference of 1 V means each electron falling through it releases 1 eV. Per mole of electrons that's 96.5 kJ, a quantity called the Faraday constant F. So a voltage is just a free-energy change counted per electron:

ΔG = −n F E

Here n is the number of electrons transferred. The Daniell cell moves 2 electrons per zinc atom across 1.10 V: ΔG = −2 × 96.5 × 1.10 ≈ −212 kJ/mol. By chapter 11's rule (5.7 kJ/mol per factor of 10), that's an equilibrium constant around 10³⁷. The reaction goes to completion as far as any measurement could tell.

A battery is a reaction kept apart

If zinc and copper ions touch directly, the electrons jump straight across and all you get is a little heat. Separate them into two beakers and the only way for electrons to get from zinc to copper is through a wire you control. That's a battery: a reaction that wants to happen, made to send its electrons the long way round, through your phone. A salt bridge (or a porous separator) lets ions drift between the two sides to keep each beaker electrically neutral.

A Daniell cell. Left: a zinc electrode in zinc sulfate. Right: a copper electrode in copper sulfate, whose blue colour fades as Cu²⁺ is used up. Dots on the wire are electrons. Bottom: the voltage as the battery runs down, computed from the Nernst equation, with the current slowing as copper ions run short. Time is greatly sped up.

The voltage here follows the ideal Nernst equation only. Real batteries also lose voltage to internal resistance and to the extra push needed to make electrode reactions go at a useful speed (overpotential), which is why a real battery's voltage sags under load.

Watch the voltage while it runs. It stays nearly flat for most of the run, because it depends on the ratio of zinc ions to copper ions only logarithmically:

E = E° − (RT/nF) ln Q (59 mV per factor of 10 in Q, per electron, at 25 °C)

That's the Nernst equation, and it's chapter 11 again: ΔG = ΔG° + RT ln Q, divided by −nF. A ten-fold change in the ion ratio moves a two-electron cell by only 30 mV, so the voltage only starts to sag once the copper ions are mostly gone. In practice the battery is "flat" well before that: when the copper ions run low they can't reach the electrode fast enough, and the current dies away. Strictly, E reaches zero only at equilibrium, when Q = K, and for this cell that means essentially every copper ion has been used.

Common trap

"A battery stores electricity" or "a battery runs out of electrons". A battery stores chemicals that want to react. Every electron that leaves the zinc end comes back in at the copper end; the battery's electron count never changes. What runs out is the free-energy difference: the zinc and copper ions that hadn't yet reacted.

Rust, fire and breathing

Rust is iron giving electrons to oxygen. It needs water, because the water carries ions between the spots where iron dissolves and the spots where oxygen is reduced: every rusting nail is a tiny short-circuited battery. Salt water conducts better, so it rusts faster, which is why cars rust in countries that salt their roads. Galvanised steel is coated with zinc, which sits higher on the ladder than iron: the zinc gives up its electrons first and protects the iron, even where the coating is scratched.

Burning is fast redox with oxygen, the bottom rung of most everyday ladders. Breathing is the same reaction run slowly and carefully. Your cells strip electrons from food and pass them down a chain of proteins in the mitochondria, from a carrier called NADH (about −0.32 V) to oxygen (about +0.82 V, at pH 7). That's a drop of roughly 1.1 V, spent in small steps, each pumping protons across a membrane. The proton gradient (chapter 12's protons, now as an energy store) then drives the machine that makes ATP. You run on a battery of about a volt.

Physics bridge

The electrode potential is the electron's electrochemical potential, measured in volts: the chemist's version of the Fermi level. Electrons flow from high to low Fermi level until the two sides line up, just as in a p–n junction or two metals in contact. The electrode-potential table is a table of Fermi levels for different chemical couples, all measured against a reference (the hydrogen electrode, set to 0 V by convention).

There's a neat parallel with chapter 12. pH sets the price of protons and pK_a says where each acid switches over (5.7 kJ/mol per decade). The electrode potential sets the price of electrons and E° says where each couple switches over (59 mV per decade per electron, which is the same 5.7 kJ/mol divided by F). Both are Boltzmann factors on a log scale.

Standard potentials assume 1 mol/L of everything at 25 °C, and many depend strongly on pH (oxygen's potential falls by 59 mV per pH unit). Real electrodes add kinetic barriers (overpotentials), the electrode version of chapter 10's activation energy. Lithium's potential is the most negative in the table, which is why lithium batteries are high-voltage. Their chemistry (lithium ions sliding into graphite layers) is more involved than the simple metal/ion couples here.

Tell it to a 6-year-old

Look: Three jars and three plain steel nails (not shiny galvanised ones). One jar stays empty and dry, one gets tap water, one gets salty water.
Wonder: "Which nail will go rusty first? Will the dry one rust at all?"
Try: Put a nail in each jar and look every day for a week. Draw what you see.
True sentence: "Iron slowly joins with oxygen from the air, with the water's help, and makes new stuff: rust. Salty water makes it happen faster. The dry nail hardly changes, because it needs water too."

Underneath, electrons move from the iron to oxygen, and the salt helps by carrying charge through the water: each rust spot is a tiny battery. Galvanised nails won't rust, because their zinc gives up electrons first. For a quicker demo, push a galvanised (zinc) nail and a copper coin into a lemon and read about 0.9 V on a cheap multimeter. That's not enough for most LEDs unless you chain two or three lemons. (In a lemon, the electrons are taken by the acid's protons at the copper, not by copper ions.)

Play more

Keeler & Wothers, Why Chemical Reactions Happen, the chapter on redox and electrochemistry.
Nick Lane, The Vital Question. Why life runs on proton gradients and a one-volt battery.
For both: Theodore Gray, Reactions, the photos of metals displacing each other from solution.