Lessons · Electrochemistry

Electrons for hire: the zinc–copper (Daniell) cell

Electron ledger + oxidation numbers machine-checkedE° data-sourced (openstax-chemistry-2e)2 modeling assumptions (disclosed)

Dip a strip of zinc into a zinc-sulfate solution and a strip of copper into a copper-sulfate solution, then connect the two metals with a wire and bridge the beakers with a salt bridge. A current flows — the cell does electrical work — and the reason is redox: one metal gives up electrons and the other takes them. This is the species ledger again, but now the quantity that moves is electrons. Which way do they go? Track the oxidation numbers: zinc goes from 0 in the metal to +2 in solution (it is oxidized — it loses electrons, at the anode), while copper(II) goes from +2 to 0 (it is reduced — it gains electrons, at the cathode). The two standard reduction potentials decide the direction and the voltage, and the free energy follows from $\Delta G^\circ = -nFE^\circ$ .

\mathrm{Zn} + \mathrm{Cu}^{2+} \rightarrow \mathrm{Zn}^{2+} + \mathrm{Cu}

2 e⁻ transferredzinc is oxidized · copper is reduced

Oxidation numbersTrack the numbers — they must sum to each species' charge, and the ones that change reveal the electron transfer.

\mathrm{Zn}

Zn 0

\mathrm{Cu}^{2+}

Cu +2

\mathrm{Zn}^{2+}

Zn +2

\mathrm{Cu}

Cu 0

Zn rises 0 → +2 (loses electrons — oxidized), while Cu falls +2 → 0 (gains electrons — reduced). That change is the electron transfer, made countable.

Anode — oxidation

\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2\,\mathrm{e^-}

zinc(II)/zincE° = -0.7618 V

Cathode — reduction

\mathrm{Cu}^{2+} + 2\,\mathrm{e^-} \rightarrow \mathrm{Cu}

copper(II)/copperE° = 0.337 V

The electron ledgerElectrons lost at the anode = electrons gained at the cathode — the ledger closes.

1×(2 e⁻) lost = 1×(2 e⁻) gained = 2 e⁻ transferred

\mathrm{Zn}(s)\;\vert\;\mathrm{Zn}^{2+}(aq)\;\Vert\;\mathrm{Cu}^{2+}(aq)\;\vert\;\mathrm{Cu}(s)

cell notation — anode | anode ion ‖ cathode ion | cathode

cell potential E°cell1.099 V= E°(cathode) − E°(anode)

free energy ΔG° = −nFE°-212 kJ/moln = 2, F = 96485 C/mol

spontaneous?Yes ✓E°cell > 0 ⇔ ΔG° < 0

Free energy per chargeThe cell potential is free energy per unit charge: multiply the 1.099 V by the charge moved,n·F = 2 × 96485 C, and you get the work the reaction can do —ΔG° = −nFE° = -212 kJ/mol. Because E°cell is positive, ΔG° is negative: the reaction runs on its own, and the electrons flow from the Zn anode through the wire to the Cu cathode.

VerificationProven at build time — not asserted.

✓ Every species' oxidation numbers sum to its charge [oxidation states]
✓ Each half-reaction conserves atoms and charge (electrons included) [half-reactions balanced]
✓ 2 e⁻ lost at the anode = 2 e⁻ gained at the cathode [electrons cancel]
✓ E°cell = E°(cathode) − E°(anode) = 1.099 V > 0 [cell potential]
✓ ΔG° = −nFE° = -212 kJ/mol — re-derived independently [ΔG = −nFE]

✗ Common misconception: “A cell reaction and its reverse are just two ways of writing the same thing, so the cell could run either direction — maybe the copper dissolves and the zinc plates out.”

The direction is not a matter of how you write it — the standard reduction potentials decide.copper(II)/copper sits at 0.337 V, above zinc(II)/zinc at -0.7618 V, so the Cu²⁺ is reduced and theZn electrode dissolves — never the reverse. The machine confirms it: E°cell = 1.099 V is positive, so ΔG° = -212 kJ/mol is negative and this is the spontaneous direction. Running it backwards would require supplying 1.099 V (an electrolytic cell).

Modeling assumptions — author-asserted, disclosed not discharged

model Standard conditions: every dissolved species is at 1 M (unit activity), any gas at 1 bar, and the temperature is 25 °C. The tabulated $E^\circ$ values — and so $E^\circ_\text{cell}$ and $\Delta G^\circ$ — hold only there; away from standard conditions the Nernst equation corrects the voltage.
rule The standard reduction potentials are measured against the standard hydrogen electrode (defined as exactly 0 V) — a sourced convention. Only differences $E^\circ_\text{cathode} - E^\circ_\text{anode}$ are physically meaningful (the zero point is arbitrary).

Concepts in this lesson

Linked into the Chemical Atlas where an entry exists; the rest fill in as the Atlas grows.