Polyprotic Acids

Why polyprotic acids matter

• Phosphoric acid is the workhorse buffer of biochemistry. The H₂PO₄⁻/HPO₄²⁻ pair has pKa 7.20 — within 0.2 units of physiological pH 7.4 — so phosphate buffers maintain capacity exactly where enzymes operate. Cells use this on purpose: cytoplasmic phosphate at ~1 mM is the primary intracellular buffer alongside proteins.
• Carbonate buffers planetary pH. The HCO₃⁻/CO₂ couple at pKa 6.35 plus the lung's ability to expel CO₂ creates an open buffer that defends blood pH 7.40 ± 0.04. The same chemistry sets ocean pH at 8.1; rising atmospheric CO₂ has dropped surface pH by ~0.1 units since 1850, a 30% increase in H⁺.
• Sulfuric acid drives industry exactly because of its dual nature. The first dissociation is effectively complete in water (pKa ≈ −3); the second, at pKa 1.99, is moderately strong. The 6 log gap means concentrated H₂SO₄ can act as both a strong acid donor and a weaker proton donor in the same reaction — central to alkylation, nitration, and the contact process producing 250 million tonnes globally per year.
• Citric acid covers pH 3–7 with a single buffer. Three pKa values 3.13, 4.76, 6.40 spaced barely 1.5 units apart give continuous buffer capacity across four pH units. McIlvaine's citrate-phosphate buffer, formulated 1921, spans pH 2.2 to 8.0 by varying the ratio — still standard in food and biology.
• EDTA is a tetraprotic chelator. Four carboxyl pKa values 2.0, 2.7, 6.16, 10.26 plus two amines mean the fully deprotonated form, Y⁴⁻, dominates only above pH 10. Calcium and magnesium analytical titrations buffer to pH 10 with ammonia for this reason; transition metals work at lower pH because their formation constants are large enough.
• Speciation diagrams are predictive. Plot α_i(pH) for each species and you instantly see which form dominates at any pH. At pH 7.4 phosphate is ~60% HPO₄²⁻ and ~40% H₂PO₄⁻; at pH 8.1 (ocean) inorganic carbon is ~90% HCO₃⁻, ~9% CO₃²⁻, ~1% CO_2(aq).
• Titration curves have multiple equivalence points. A diprotic acid titrated with NaOH shows two inflections; a triprotic acid shows three (though the third is often weak when pKa₃ exceeds ~12 because water leveling washes it out). The mid-buffer points sit at pH = pKa_i by Henderson-Hasselbalch.

Common misconceptions

• Treating successive ionizations as independent. They are not. The acid forms exist in linked equilibria, so [H₃PO₄] and [PO₄³⁻] are coupled through pH. You cannot use Ka₁ alone to predict pH unless Ka₂/Ka₁ < 10⁻³, which holds for many but not all systems.
• Assuming H₂SO₄ is fully diprotic strong. Only the first proton ionizes completely. Concentrated sulfuric acid contains substantial HSO₄⁻, which is why dilute and concentrated H₂SO₄ behave as different reagents — concentrated is a strong dehydrator and weaker acid, dilute is a strong diprotic donor.
• Calling H₂CO₃ the dominant form in carbonated water. Less than 1% of dissolved CO₂ is actually H₂CO₃; the rest sits as CO_2(aq). The reported pKa₁ = 6.35 is the apparent constant treating CO_2(aq) + H₂CO₃ as the acid; the true H₂CO₃ pKa is closer to 3.5.
• Counting protons by formula alone. Acetic acid CH₃COOH has four hydrogens but only one is acidic. The C–H bonds are not ionizable in water (pKa > 40). Always identify which proton sits on a heteroatom adjacent to a stabilizing group.
• Writing pKa₃ for H₂SO₄. There isn't one — once SO₄²⁻ forms, the remaining hydrogens are on water, not the acid. Sulfate is a terminal conjugate base in aqueous chemistry.
• Confusing buffer capacity with buffer range. A polyprotic acid is buffered near each pKa; capacity drops to near zero between pKa values that are far apart (e.g., phosphate has weak buffering at pH 4 because the nearest pKa is 2.15 or 7.20, both more than 2 units away).

Mechanism of stepwise ionization

For a diprotic acid H₂A, two equilibria coexist: H₂A ⇌ HA⁻ + H⁺ with Ka₁ = [HA⁻][H⁺]/[H₂A], and HA⁻ ⇌ A²⁻ + H⁺ with Ka₂ = [A²⁻][H⁺]/[HA⁻]. The ratio Ka₁/Ka₂ = K_combined drives the linked system, but for predictive work the two are nearly always treated separately because Ka₁ typically exceeds Ka₂ by 10⁴ to 10⁶. Statistically a neutral H₂A has two protons to lose and one negative charge to attract back, while HA⁻ has one proton to lose and two negative charges (after the next deprotonation) to attract — the electrostatic asymmetry alone predicts ΔpKa ≈ 3–4 from Coulomb's law in water at room temperature; symmetry and solvation push it to the observed 4–6.

The triprotic case adds a third equilibrium HA²⁻ ⇌ A³⁻ + H⁺. For phosphoric acid the three Ka values span 10¹⁰, so at any pH the system is well-approximated by the dominant pair. The fraction α_n of each species is α_n = K₁K₂...K_n·[H⁺]³⁻ⁿ / D, where D = [H⁺]³ + K₁[H⁺]² + K₁K₂[H⁺] + K₁K₂K₃. Plotting α_n vs pH gives the speciation diagram every analytical chemistry course teaches.

Brønsted and Lowry's 1923 framework treats each step as a proton transfer to water, with the conjugate base of one step becoming the acid of the next. The leveling effect of water sets a practical floor near pKa = 0 (any acid stronger than H₃O⁺ looks equally strong in dilute aqueous solution) and a ceiling near pKa = 14 (anything weaker than water is leveled to OH⁻). Outside that window — concentrated sulfuric acid for super-acids, liquid ammonia for super-bases — the leveled protons re-emerge.

Variant comparison: common polyprotic acids

Acid	pKa1	pKa2	pKa3	pKa4	Notable use
H3PO4 (phosphoric)	2.15	7.20	12.35	—	Cell buffers, fertilizer, soft drinks
H2SO4 (sulfuric)	~−3	1.99	—	—	Lead-acid batteries, contact process
H2CO3 (carbonic)	6.35	10.33	—	—	Blood pH, ocean carbonate system
H3AsO4 (arsenic)	2.19	6.94	11.50	—	Mimics phosphate, classic toxicology
Citric acid	3.13	4.76	6.40	—	McIlvaine buffer pH 2.2–8.0, food acid
EDTA	2.00	2.70	6.16	10.26	Metal chelation titrations
Oxalic acid	1.25	4.14	—	—	Rust removal, kidney stones
H3BO3 (boric)	9.24	~12.7	~13.8	—	Eyewash, neutron capture

Applications and examples

• Phosphate buffered saline (PBS). Classic recipe: 137 mM NaCl, 2.7 mM KCl, 10 mM Na₂HPO₄, 1.8 mM KH₂PO₄ — sets pH 7.4 by sitting on the H₂PO₄⁻/HPO₄²⁻ midpoint with the right ratio from Henderson-Hasselbalch.
• Bicarbonate IV in metabolic acidosis. Clinicians infuse NaHCO₃ to raise blood pH back into the 7.35–7.45 range. The lungs then dump excess CO₂, locking the open-system advantage of the carbonate equilibrium.
• Soft drink acidity. Phosphoric acid concentration of ~0.05% gives Coca-Cola its pH around 2.5 — well below the first equivalence point, so the dominant species is the fully protonated H₃PO₄.
• EDTA titration of water hardness. Titrate Ca²⁺ + Mg²⁺ with EDTA at pH 10 (NH₃ buffer); endpoint detection with Eriochrome Black T. Standard since 1948 for measuring grains-per-gallon hardness.
• Ocean acidification monitoring. Surface ocean DIC (dissolved inorganic carbon) speciation is solved every cruise from pH, alkalinity, and pKa₁, pKa₂ of carbonic acid corrected for temperature, salinity, and pressure.