Lead-Acid Battery: The Double Sulfate That Starts Your Car

Both Plates End Up as the Same White Powder

A charged cell holds two different plates in one bath of ~37% sulfuric acid: a negative of grey sponge lead, metallic Pb with enormous internal surface area, and a positive of chocolate-brown lead dioxide, PbO₂. Discharge oxidises one and reduces the other, and the acid is a reactant at both:

• Negative plate (oxidation): Pb + SO₄²⁻ → PbSO₄ + 2e⁻ (E° = −0.359 V, quoted as the reduction)
• Positive plate (reduction): PbO₂ + SO₄²⁻ + 4H⁺ + 2e⁻ → PbSO₄ + 2H₂O (E° = +1.691 V)
• Overall: Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O

Both potentials are tabulated against free SO₄²⁻, so the half-equations beside them must be written that way. Real battery acid is not that solution — at ~5 M the sulfate is nearly all bisulfate, so the species-correct negative is Pb + HSO₄⁻ → PbSO₄ + H⁺ + 2e⁻. That is a change of standard state, not of chemistry: it moves each E° by (RT/2F) ln K_a2 ≈ 59 mV in opposite directions and restates the same cell as 1.93 V. Neither standard state is a battery; what a battery reads comes from activity.

The startling part is the product column. Lead metal and lead dioxide start four units of oxidation state apart, Pb(0) and Pb(IV), and both converge on Pb(II) as the same compound: white, insulating lead(II) sulfate. This is Gladstone and Tribe's 1882 "double sulfate" theory — the reaction that names the battery.

It also makes the cell self-limiting. PbSO₄ is a wide-gap insulator, resistivity around 10⁸ Ω·cm, so every gram deposited is a gram of dead area: discharge stops not when the lead runs out but when sulfate chokes the pores, starving the interior of electrons and fresh acid. At high current the plate skins over first, which is why only about half the active mass is ever reached.

Where 2.05 Volts Comes From, and Why Water Does Not Win

Subtract the half-cell potentials and the cell falls out: +1.691 V − (−0.359 V) = 2.05 V, the highest open-circuit voltage any commercial aqueous rechargeable cell sustains — and thermodynamically it should not exist. Water is stable over only a 1.23 V window, so the PbO₂ plate sits far above the oxygen line and the Pb plate far below the hydrogen line; both are, strictly, capable of electrolysing their own solvent. It survives on kinetics alone: lead has one of the highest hydrogen overpotentials of any metal, of order 0.5 V, and PbO₂ is nearly as reluctant to evolve oxygen — two kinetic walls that reduce a doomed system to one self-discharging a few percent a month.

Voltage tracks the acid, because the acid is a reagent. The Nernst expression for the overall reaction, with n = 2, gives E = E° + (3RT/F) ln a_± − (RT/F) ln a_w, where a_± is the mean ionic activity of H₂SO₄. That coefficient, 3RT/F = 0.077 V per e-fold or about 0.178 V per decade, is steep because three ions appear per formula unit: a full discharge cuts the mean activity roughly sevenfold, worth 0.077 × ln 7 ≈ 0.15 V, and the water term supplies about 0.03 V more, since diluting the acid frees water from its hydration shells and pushes a_w back towards 1. Empirically the sum obeys a rule any mechanic knows — open-circuit volts per cell ≈ specific gravity + 0.84 — so 1.28 gives 2.12 V per cell, or 12.7 V at the terminals, and 1.10 gives about 1.94 V. Charging runs it backwards: 14.4 V (2.40 V/cell) drives the sulfate off, deliberately a hair past the ~2.39 V/cell gassing threshold, so the tail of every charge also splits water — which is why standby strings, which must not gas, float lower at 13.5–13.8 V with a −3 mV/°C-per-cell correction.

The Hydrometer as a Fuel Gauge: A Worked Discharge

Faraday's law makes the acid a coulomb counter. Each mole of electrons consumes one mole of H₂SO₄ — 98 g of H₂SO₄ per 96,485 C — and makes 18 g of water, so the electrolyte is drained and diluted at once. Take a 12 V, 60 Ah battery with roughly 0.6 L of electrolyte per cell. At 1.28 g/cm³ that is 768 g of solution, and 1.28 acid is ~37.4 wt%, so each cell starts with 287 g of H₂SO₄ in 481 g of water. Now draw 55 Ah:

• 55 Ah × 3600 = 198,000 C, and 198,000 / 96,485 = 2.05 mol of electrons per cell.
• 2.05 mol × 98.08 g/mol = 201 g of H₂SO₄ consumed — 1.2 kg across all six cells.
• The same reaction returns 201 × (18/98.08) = 37 g of water.
• Left behind: 86 g of acid in 604 g of solution = 14.2 wt%, which is 1.10 g/cm³.

The arithmetic lands exactly on the hydrometer card's number, because these batteries are close to acid-limited: rated capacity is set partly by how much sulfate the bath can give up. Two riders. Density is temperature-dependent, needing about 0.0007 g/cm³ per °C (0.004 per 10 °F) of correction against the 27 °C reference. And dilute acid freezes: 1.10 g/cm³ freezes at −8 °C, against −57 °C at 1.265 g/cm³ — leave a battery flat on a January night and the ice expands ~9% and splits the case.

Dissolution and Precipitation That Stay Put

Why is this reversible at all, when the product is an insulator that forms on both plates? Because the lead never travels. PbSO₄ is sparingly soluble — K_sp ≈ 1.6 × 10⁻⁸ at 25 °C (tabulations run to ~2.5 × 10⁻⁸) — and the battery acid suppresses it further. In ~4.8 M H₂SO₄ nearly all the sulfate is bisulfate; using K_a2 ≈ 10⁻², free SO₄²⁻ sits near 10⁻² M, so [Pb²⁺] = K_sp/[SO₄²⁻] ≈ 2 × 10⁻⁶ M, under a milligram per litre.

That trace is the whole mechanism. Lead leaves the plate as a whisper of dissolved Pb²⁺ and re-precipitates within a few µm of where it left, so reversing the current runs the same dissolution–precipitation backwards on the spot: PbSO₄ + H⁺ + 2e⁻ → Pb + HSO₄⁻ at the negative, PbSO₄ + 2H₂O → PbO₂ + HSO₄⁻ + 3H⁺ + 2e⁻ at the positive. Compare the rechargeable zinc cell, where zinc dissolves in alkali as freely soluble zincate, wanders, and returns as dendrites — which is why zinc secondaries remain hard and this one does not.

Everything else in the plate exists to keep that microstructure fine. The positive holds both α-PbO₂ (mechanically robust) and β-PbO₂ (electrochemically livelier). The negative carries expanders: barium sulfate, isostructural with PbSO₄ and so a template seeding many small crystals rather than a few big ones; lignosulfonate, which adsorbs on growing faces; and carbon black. Without them the sponge lead sinters into low-area metal within a few dozen cycles.

Cold Cranking, Milliohms and the Real Hardware

A starter battery's job is not energy, it is power, and Camille Faure's 1881 pasted plate — a cast lead grid carrying a paste of lead oxides, cured and then formed — is what makes that possible, spreading active material thin over a large area. Modern SLI batteries stack a dozen or more thin plates per cell on Pb–Ca–Sn grids, reaching an internal resistance of only ~3–5 mΩ at 25 °C.

SAE J537 turns that into a purchasable number. Cold cranking amps: hold the battery at −18 °C, pull the rated current for 30 s, and the terminals must stay at or above 7.2 V — 1.2 V per cell. Budget a 500 A rating: from a cold open-circuit near 12.6 V, the internal drop may not exceed (12.6 − 7.2)/500 ≈ 10.8 mΩ. The test is cold because even that generous allowance is only two or three times the warm resistance, and cold is unkind: acid viscosity roughly triples between 25 °C and −18 °C, sulfate diffusion into the pores slows to match, and charge-transfer kinetics fall off exponentially. Neighbouring ratings do not convert: reserve capacity is minutes at 25 A to 10.5 V, the C/20 amp-hour figure a twenty-hour trickle, and EN 50342 rates cranking on a different profile at the same −18 °C.

Capacity is itself rate-dependent, roughly as Peukert's law I^kt = constant with k ≈ 1.1–1.3 against ~1.05 for lithium, so a 60 Ah battery delivers nowhere near 60 Ah while cranking. Grid metallurgy is the other lever: antimony resists creep and suits deep cycling, but migrates to the negative and lowers the hydrogen overpotential, so the cell gasses and needs watering, while calcium–tin grids gas far less — all that "maintenance-free" means.

Planté, Faure and the Double-Sulfate War

Gaston Planté built the first rechargeable cell in 1859, presenting it to the French Academy of Sciences the following year: two lead sheets separated by rubber strips, rolled into a spiral and immersed in sulfuric acid. Its capacity came from repeated charge–discharge "formation" cycles that slowly roughened one sheet into PbO₂, which could take months. Faure's 1881 pasted plate collapsed that into a manufacturing step, and within a decade European central stations were buffering their generators with lead accumulators.

The chemistry stayed contested far longer than the engineering. John Gladstone and Alfred Tribe published the double sulfate theory in 1882, arguing that both plates convert to PbSO₄; rival schemes had the negative forming an oxide, or invoked lead hydride, and the dispute ran for decades partly because dissecting a working plate destroys the evidence. The decisive argument was thermodynamic: precise electromotive-force measurements across acid concentration and temperature — notably Harned and Hamer's 1935 work on the Pb | PbSO₄ | H₂SO₄ | PbO₂ cell — reproduce the Nernst behaviour the double-sulfate stoichiometry demands, and no other.

Commercial destiny was fixed in 1912, when Charles Kettering's electric self-starter appeared on the Cadillac Model 30. Sealed formats followed — gel cells from Sonnenschein in 1957, absorbent glass mat in the 1970s–80s — both valve-regulated (VRLA): the electrolyte is immobilised and the headspace starved of liquid, so oxygen made at the positive diffuses to the negative and is consumed as 2Pb + O₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O instead of venting. Lead-acid batteries are recycled at roughly 99% in the United States, the highest rate of any consumer product.

How It Dies, and What It Is Not

Sulfation is the signature death. Fresh discharge product is fine, high-surface-area PbSO₄ that redissolves readily, because small crystals are more soluble than large — Gibbs–Thomson, ln(S_r/S_∞) = 2γV_m/rRT. With PbSO₄'s molar volume of 48 cm³/mol and an interfacial energy of order 0.1 J/m², 2γV_m/RT is only a few nanometres: 10 nm crystallites are tens of percent more soluble than bulk, µm crystals within a fraction of a percent of it. Leave a battery discharged for weeks and Ostwald ripening does exactly that, until the coarse sulfate will not redissolve at any voltage a charger can safely apply. Pulse "desulfator" gadgets are sold against this; no convincing evidence says they work.

The slower killer in float service is positive grid corrosion: the lead grid carrying the PbO₂ is itself oxidised, growing and embrittling until a conductor severs. Being Arrhenius, service life roughly halves per 10 °C — a VRLA string rated ten years at 25 °C is a five-year string in a 35 °C room. The hazards are chemical too: overcharge splits water into a 2:1 mix of H₂ and O₂, flammable from 4% to 75% in air, and a spark from a clamp sprays 37% sulfuric acid. The USS Cochino was lost off Norway in August 1949 to a battery explosion and hydrogen fire; the Exide secondary-lead smelter in Vernon, California closed in 2015, leaving lead and arsenic across thousands of nearby homes.

Finally, the misconceptions. Top up with distilled water, never acid — water is what electrolysis removed, while the sulfate sits on the plates and returns on charge, so added acid leaves the cell over-concentrated and accelerates grid corrosion. Lead-acid has no "memory effect" (that is nickel-cadmium); its aversion to deep discharge is sulfation. And a lithium "drop-in" is not interchangeable: LiFePO₄ rests near 3.3 V across most of its range, so it has no gauge of its own and needs a management system to do what sulfuric acid does for free.

Lead-acid and the cells it gets confused with

Cell	Nominal volts per cell	Delivered specific energy	What the electrolyte does
Flooded lead-acid (SLI starter)	2.05 V standard, 2.12 V rested	30–40 Wh/kg	Reagent: 98 g H₂SO₄ per 96,485 C; density falls 1.28 → 1.10 g/cm³
VRLA — AGM or gel	2.05 V standard, 2.12 V rested	30–40 Wh/kg	Same reagent, immobilised in glass mat or silica gel; evolved O₂ recombines internally
Lithium iron phosphate (LiFePO₄)	3.2 V	90–160 Wh/kg	Spectator: Li⁺ shuttles between hosts, concentration barely moves, no hydrometer possible
Lithium-ion NMC	3.6–3.7 V	150–250 Wh/kg	Spectator: carbonate solvent plus LiPF₆ conducts only
Nickel-cadmium (pocket plate)	1.2 V	20–35 Wh/kg	KOH conducts; water is consumed but concentration hardly changes