Carbonate System Equilibria

Introduction

The carbonate system is more than a textbook diprotic acid. Dissolved CO₂ can exchange with a gas phase, a small portion hydrates to carbonic acid, and proton-transfer equilibria connect that pool to bicarbonate and carbonate. The dominant dissolved form depends on pH, while total dissolved inorganic carbon can change if CO₂ enters or leaves. This coupling matters in water chemistry, mineral dissolution and biological buffering.

Core explanation

Write the sequence CO₂(g) ⇌ CO₂(aq), CO₂(aq) + H₂O ⇌ H₂CO₃, H₂CO₃ ⇌ H⁺ + HCO₃⁻, and HCO₃⁻ ⇌ H⁺ + CO₃²⁻. Many teaching treatments combine dissolved CO₂ and the small true H₂CO₃ population as an effective acid form, often written CO₂ or H₂CO₃ . When using a tabulated first dissociation constant, check whether it belongs to true H₂CO₃ or this combined pool; mixing definitions makes calculated species ratios wrong.

For a closed aqueous system with fixed total dissolved inorganic carbon CT, a useful balance is CT = [CO₂ ] + [HCO₃⁻] + [CO₃²⁻]. At lower pH the proton-rich CO₂ side is favoured. At intermediate pH bicarbonate often dominates. At sufficiently high pH carbonate gains importance. These are qualitative regions; exact boundary pH values depend on the chosen equilibrium constants, temperature and ionic strength.

The second dissociation ratio is [CO₃²⁻]/[HCO₃⁻] ≈ Ka2/[H⁺] in a dilute concentration model. Thus increasing pH by one unit increases the carbonate-to-bicarbonate ratio tenfold if Ka2 remains fixed. Likewise, the first effective ratio links bicarbonate to CO₂ . These ratio equations are powerful because they show direction without requiring a complete nonlinear solution when pH is known.

An open system behaves differently from a sealed one. If CO₂ escapes from a carbonated liquid, the dissolved CO₂ concentration falls and related equilibria adjust. If atmospheric CO₂ enters an alkaline solution, it can be consumed into bicarbonate or carbonate, changing the solution's total carbon and acid-base balance. A mass balance based on a fixed CT is invalid if a substantial amount of carbon enters or leaves during the process.

Carbonate also participates in solubility equilibria. For CaCO₃(s) ⇌ Ca²⁺ + CO₃²⁻, Ksp involves free calcium and carbonate. Adding acid consumes CO₃²⁻ by protonating it to bicarbonate and ultimately CO₂ , lowering the ion product and often promoting calcium carbonate dissolution. This is a coupled-equilibrium effect; one must not evaluate Ksp using total inorganic carbon as though all of it were free CO₃²⁻.

Charge balance adds another check. In a simple sodium carbonate solution, positive charge from Na⁺ and H⁺ must equal negative contributions from OH⁻, HCO₃⁻ and twice CO₃²⁻, along with any other ions present. Carbonate species have different charges, so treating all dissolved carbon as one monovalent species violates electroneutrality.

OpenStax discusses the carbonate, carbon dioxide and calcium carbonate coupling at https://openstax.org/books/chemistry-2e/pages/15-3-coupled-equilibria. Use that qualitative framework while keeping clear whether the model is open or closed to CO₂.

Step-by-step reasoning

1. Decide whether CO₂ gas exchange is allowed. 2. Choose a consistent CO₂ /H₂CO₃ equilibrium-constant convention. 3. Write the carbon mass balance if total dissolved carbon is fixed. 4. Use pH and Ka ratios to identify likely dominant forms. 5. Include free CO₃²⁻, not total carbon, in any carbonate Ksp expression.

Visual explanation

Draw a vertical pH axis beside CO₂ ⇌ HCO₃⁻ ⇌ CO₃²⁻. Put lower pH near CO₂ , higher pH near CO₃²⁻, and a gas-exchange arrow into the CO₂ box.

Real-world analogy

Three linked reservoirs exchange water through gates, while the first reservoir also has a pipe to the outside. pH adjusts the internal gates; the gas pipe means the total amount inside may change.

Real-world example

Acidic water can dissolve calcium carbonate because protonation lowers free carbonate ion. The equilibrium then allows more solid CaCO₃ to dissolve while calcium and inorganic carbon remain accounted for.

Why?

Why can a carbonate mineral dissolve more readily when acid is added? Acid converts some free CO₃²⁻ into HCO₃⁻ or CO₂ , reducing the precipitation ion product and allowing more solid to dissolve toward equilibrium.

Common misconception

“All dissolved inorganic carbon is carbonate ion.” At many ordinary pH values bicarbonate or CO₂ is more abundant; Ksp calculations require the free CO₃²⁻ concentration.

Worked example

Suppose the second dissociation pKa2 is 10.3 and pH is 9.3 in a dilute model. Then [CO₃²⁻]/[HCO₃⁻] = 10^(pH−pKa2) = 0.10. Bicarbonate is ten times as abundant as carbonate for this two-species comparison. If pH rises to 10.3, the ratio becomes 1. The result does not yet tell the absolute concentrations without CT and the CO₂ contribution.

Quick check

1. Which concentration belongs in Ksp for CaCO₃: total inorganic carbon or free CO₃²⁻? Answer: Free CO₃²⁻ concentration or activity; total carbon includes CO₂ and HCO₃⁻ that do not enter this Ksp expression directly.

Exam focus

State open versus closed CO₂ conditions and use a consistent first-acid-constant convention. Keep the carbon mass balance and charge balance separate.

Advanced insight

The equilibrium-constant definition for CO₂ differs from that for true H₂CO₃ because most molecular dissolved CO₂ is not hydrated carbonic acid. A numerical calculation must use constants and species definitions from the same convention.

Summary

Carbonate speciation links dissolved CO₂, bicarbonate and carbonate through gas transfer and two acid-base stages. pH controls relative forms, while gas exchange can change total dissolved carbon. Carbonate mineral equilibria depend on free CO₃²⁻, not the whole carbon pool.

Practice questions

1. What is the carbon mass balance for a closed three-form model? Answer: CT = [CO₂ ] + [HCO₃⁻] + [CO₃²⁻]. 2. Which carbonate-family ion has charge −2? Answer: CO₃²⁻. 3. What happens to [CO₃²⁻]/[HCO₃⁻] as pH rises by one unit at fixed Ka2? Answer: It rises tenfold under the dilute ratio approximation. 4. Why can an open beaker violate a fixed-CT calculation? Answer: CO₂ can enter or leave, changing the total dissolved inorganic carbon.