Carbonate system pH correction: CO₂ dosing, alkalinity and calcium carbonate saturation

Carbon dioxide is a weak, self-buffering acid. Its use for pH correction of alkaline water and effluent is governed by three coupled sets of physics: the carbonate equilibria, the slow hydration of dissolved CO₂, and gas–liquid mass transfer. This note sets out each, with a worked dose calculation checked by a second route.

Technical note, RB Solutions Ltd, 22 October 2026

Species of the aqueous carbonate system

Dissolved inorganic carbon (DIC, symbol C_T) exists as three species: dissolved carbon dioxide together with the small fraction hydrated to carbonic acid, written jointly as H₂CO₃*; the bicarbonate ion HCO₃⁻; and the carbonate ion CO₃²⁻. True H₂CO₃ is a minor component of H₂CO₃*, and the composite convention is the one adopted in standard texts [1]. The total is a conserved quantity under acid or base addition, while it changes when CO₂ is added, stripped or precipitated as carbonate solids.

Dissociation constants and ionisation fractions

The two acid dissociation equilibria are characterised by the constants K₁ and K₂:

At 25 °C, pK₁ = 6.35 and pK₂ = 10.33 [1][2]. Dividing each species by C_T gives the ionisation fractions α₀, α₁ and α₂, functions of pH alone at fixed temperature and ionic strength:

Temperature dependence

The constants shift appreciably over the range of UK water temperatures. Plummer and Busenberg fitted the equilibrium data for the CO₂–H₂O–CaCO₃ system from 0 °C to 90 °C as empirical functions of absolute temperature [2]; for K₁:

Table 1 lists values evaluated from those expressions. Each 25 °C entry reproduces the tabulated reference value [1], which serves as a check that the coefficients have been transcribed correctly.

Two consequences follow. Cold water holds markedly more CO₂ at a given partial pressure, and the higher pK₂ at low temperature moves the bicarbonate–carbonate boundary upwards by roughly 0.2 pH units between 25 °C and 5 °C. Calcite also becomes slightly more soluble as temperature falls, which is the reason scaling is concentrated on heated surfaces.

Henry's law and the gas–liquid equilibrium

The equilibrium between gaseous and dissolved CO₂ follows Henry's law:

At 25 °C, log₁₀ K_H = −1.47 [1][2], so K_H = 0.034 mol L⁻¹ atm⁻¹. Under pure CO₂ at 1 atm the saturation concentration is therefore about 34 mmol L⁻¹, or 1.5 g L⁻¹ using a molar mass of 44.01 g mol⁻¹ [5]. That saturation value is the driving-force ceiling for any CO₂ dissolution system. Elevated pressure in an injection line raises it proportionally.

Alkalinity, DIC and the effect of CO₂ addition

Total alkalinity is the acid-neutralising capacity relative to the CO₂ equivalence point. For a system in which carbonate species, hydroxide and protons dominate the proton balance, it is [1][3]:

The central property for pH correction is that adding CO₂ increases C_T but leaves alkalinity unchanged, since CO₂ is the reference species of the proton condition [1]. A strong mineral acid does the reverse: it consumes alkalinity at constant C_T. Because Alk is conserved under CO₂ dosing, the DIC required to reach a target pH follows directly:

This self-limiting behaviour is the main process advantage of CO₂. Once the bicarbonate region is reached, further CO₂ moves pH only slowly, because the H₂CO₃*/HCO₃⁻ pair buffers around pK₁. Even at saturation under 1 atm of CO₂, a water with a few mmol L⁻¹ of alkalinity cannot be driven much below pH 5 to 6. Sulfuric or hydrochloric acid has no such floor, and an overdose can take the stream to pH 2 to 3.

Worked example: CO₂ dose for an alkaline effluent

Inputs. An effluent at 25 °C has pH 11.0 and C_T = 2.0 mmol L⁻¹, with a flow of 50 m³ h⁻¹. The target is pH 8.0. Activity coefficients are taken as unity (dilute solution), and constants are those of Table 1 at 25 °C.

Route 1, alkalinity conservation. At pH 11.0, α₁ = 0.1758 and α₂ = 0.8242, so Alk = 2.0 × (0.1758 + 2 × 0.8242) + 1.0 − 0.00 = 4.648 meq L⁻¹, of which 1.0 meq L⁻¹ is hydroxide. At pH 8.0, α₁ = 0.9735 and α₂ = 0.0046. The required C_T is (4.648 − 0.001) / (0.9735 + 0.0091) = 4.729 mmol L⁻¹. The dose is therefore ΔC_T = 2.729 mmol L⁻¹, or 120 mg L⁻¹ CO₂. At 50 m³ h⁻¹ this is 6.0 kg h⁻¹ of CO₂ dissolved, before any transfer inefficiency.

Route 2, reaction stoichiometry. Hydroxide reacts as OH⁻ + CO₂ → HCO₃⁻, consuming 1.000 mmol L⁻¹. Carbonate reacts as CO₃²⁻ + CO₂ + H₂O → 2HCO₃⁻, consuming 2.0 × 0.8242 = 1.648 mmol L⁻¹. The final solution at pH 8.0 retains free H₂CO₃* of 4.729 × 0.0219 = 0.104 mmol L⁻¹, which adds to the demand. A residual carbonate of 0.022 mmol L⁻¹ remains unconverted, which reduces it. The sum is 1.000 + 1.648 + 0.104 − 0.022 = 2.730 mmol L⁻¹, agreeing with Route 1 to within rounding. A forward check, solving the charge balance for pH at Alk = 4.648 meq L⁻¹ and C_T = 4.729 mmol L⁻¹, returns pH 8.00.

Comparison with sulfuric acid. Holding C_T at 2.0 mmol L⁻¹, alkalinity at pH 8.0 is 2.0 × (0.9735 + 0.0091) + 0.001 = 1.966 meq L⁻¹. The acid must therefore remove 4.648 − 1.966 = 2.682 meq L⁻¹, equal to 1.341 mmol L⁻¹ H₂SO₄ or 132 mg L⁻¹ (molar mass 98.08 g mol⁻¹ [5]). The result is summarised in Table 2.

The mass doses are similar, yet the residual chemistry differs. CO₂ adds no anion, leaves a well-buffered effluent and cannot overshoot into the acid range. Mineral acid adds sulfate or chloride, which matters where a discharge consent under section 118 of the Water Industry Act 1991 [6] or an environmental permit limits those ions or limits corrosivity to concrete.

CO₂ hydration kinetics

Only the hydrated species shift pH. Dissolved CO₂ reacts by two parallel paths, direct hydration and reaction with hydroxide [1][7]:

At 25 °C, k_CO2 is approximately 3 × 10⁻² s⁻¹ and k_OH− approximately 8.5 × 10³ L mol⁻¹ s⁻¹ [1]. The resulting half-lives are given in Table 3.

The table explains a common commissioning observation. Above about pH 10 the hydroxide path is fast and the reaction keeps pace with dissolution. As the stream approaches pH 8, conversion slows to tens of seconds, and a pH probe placed a few seconds downstream of the injection point reads high. The controller then over-doses CO₂, which drifts the pH low further downstream. A pipe reactor or tank sized for several hydration half-lives at the target pH, about 78 s for 95 % conversion at pH 8 and 25 °C (t₉₅ = ln 20 / k_obs), is therefore required before the measuring point. The temperature dependence of both constants lengthens these times in cold water.

Gas–liquid mass transfer and the kLa

The rate at which gaseous CO₂ enters solution is described by the two-film model [3][8]:

The enhancement factor exceeds unity when the hydroxide reaction is fast compared with diffusion through the film. In strongly alkaline liquor, CO₂ is consumed within the film and absorption is rapid. Near neutrality E approaches 1 and transfer is purely physical [8]. The design consequences are as follows:

• Fine-bubble diffusers in open tanks lose undissolved CO₂ to atmosphere in proportion to (1 − transfer efficiency). Efficiency rises with depth, because both residence time and partial pressure increase with hydrostatic head.
• In-line injection into a pressurised pipe raises C* in proportion to absolute pressure and achieves near-complete dissolution when the pipe length after injection exceeds the bubble dissolution length. This should be verified by calculation for each line velocity.
• Because alkalinity is conserved and the final pH depends only on C_T, any CO₂ stripped later, for example at a free-falling weir or in an aerated tank, raises pH again. This needs particular attention after aeration downstream of pH correction.

Langelier saturation index and calcium carbonate precipitation potential

The Langelier saturation index (LSI) compares measured pH with the pH at which the water would be in equilibrium with calcite at its actual calcium and bicarbonate content [4]:

A positive LSI indicates supersaturation and a tendency to deposit CaCO₃. A negative LSI indicates undersaturation and a tendency to dissolve carbonate, which leaves cementitious linings and protective scales unprotected. For example, a water at 25 °C with 2.5 mmol L⁻¹ calcium (100 mg L⁻¹ Ca), 2.0 mmol L⁻¹ bicarbonate and pH 8.0 gives pH_s = (10.33 − 8.48) + 2.60 + 2.70 = 7.15 and LSI = +0.85. Including activity coefficients would raise pH_s and reduce the index, so the simplified figure is conservative with respect to scaling.

CO₂ dosing is the standard means of bringing a lime-softened or hydroxide-precipitated water back towards LSI ≈ 0. It converts carbonate to bicarbonate at constant alkalinity and lowers pH towards pH_s, without adding a foreign anion. Where an alkaline effluent contains calcium, the dose calculation and the LSI calculation must be performed together. Overshooting the LSI downwards dissolves scale that may protect existing pipework, while undershooting allows calcite to form on probes, diffusers and the pipe reactor itself. The precipitation potential, in mg L⁻¹ CaCO₃, is obtained by solving the same equilibria for the quantity of CaCO₃ removed to reach saturation [3]. It is the more useful design figure where solids handling has to be sized.

Design checklist for CO₂ pH correction

References

1. Stumm, W. and Morgan, J.J. (1996) Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters, 3rd ed. New York: Wiley.
2. Plummer, L.N. and Busenberg, E. (1982) The solubilities of calcite, aragonite and vaterite in CO₂–H₂O solutions between 0 and 90 °C. Geochimica et Cosmochimica Acta, 46(6), 1011–1040. doi:10.1016/0016-7037(82)90056-4
3. Crittenden, J.C., Trussell, R.R., Hand, D.W., Howe, K.J. and Tchobanoglous, G. (2012) MWH's Water Treatment: Principles and Design, 3rd ed. Hoboken: Wiley.
4. Langelier, W.F. (1936) The analytical control of anti-corrosion water treatment. Journal of the American Water Works Association, 28(10), 1500–1521.
5. Green, D.W. and Southard, M.Z. (eds) (2019) Perry's Chemical Engineers' Handbook, 9th ed. New York: McGraw-Hill.
6. Water Industry Act 1991, section 118. legislation.gov.uk/ukpga/1991/56/section/118
7. Johnson, K.S. (1982) Carbon dioxide hydration and dehydration kinetics in seawater. Limnology and Oceanography, 27(5), 849–855.
8. Danckwerts, P.V. (1970) Gas–Liquid Reactions. New York: McGraw-Hill.

Related technical notes

• Hydroxide precipitation of metals
• Mass and energy balance methodology
• UK drinking water regulations