By John Brennan, updated Aug 30, 2022
In a chemical system, equilibrium is reached when the forward and reverse reactions proceed at equal rates. The position of this equilibrium is governed by thermodynamics—specifically, the energy released and the entropy change during the process. At a given temperature and pressure, the ratio of reactants to products is fixed by the equilibrium constant. When the partial pressure of CO₂ is known, the equilibrium constant can be used to calculate the concentration of bicarbonate, HCO₃⁻, in solution.
All of these reactions are reversible. The equilibrium constants for each step allow us to determine the relative concentrations of CO₂, H₂CO₃, HCO₃⁻, and CO₃²⁻ at equilibrium.
Assuming room temperature (≈25 °C) and standard atmospheric pressure, we typically consider carbonate (CO₃²⁻) to be present only in trace amounts when the solution pH is ≤9. Under these conditions, dissolved CO₂, carbonic acid (H₂CO₃), and bicarbonate (HCO₃⁻) dominate. In highly alkaline media (pH >9), the balance shifts toward bicarbonate and carbonate, with carbonic acid becoming negligible.
Using Henry’s Law, the concentration of dissolved CO₂ is given by:
CO₂(aq) = (2.3 × 10⁻² mol L⁻¹ atm⁻¹) × P_CO₂
where P_CO₂ is the partial pressure of CO₂ in atmospheres.
Carbonic acid forms from dissolved CO₂ according to the equilibrium constant of the first reaction. An empirical relationship is:
H₂CO₃ = (1.7 × 10⁻³ mol L⁻¹ mol⁻¹ L) × [CO₂(aq)]
Because H₂CO₃ is a weak acid, its dissociation into H⁺ and HCO₃⁻ can be approximated using the acid dissociation constant (K_a ≈ 4.3 × 10⁻⁷). Rearranging the expression for K_a gives:
4.3 × 10⁻⁷ = [H⁺]² / [H₂CO₃]
Assuming electroneutrality, [H⁺] ≈ [HCO₃⁻] at this pH range. Solving for [HCO₃⁻] yields the desired bicarbonate concentration:
[HCO₃⁻] = √(4.3 × 10⁻⁷ × [H₂CO₃])
At equilibrium, the system balances the forward and reverse reactions, linking CO₂ partial pressure, dissolved CO₂, carbonic acid, and bicarbonate. By applying Henry’s Law and the acid dissociation constant, you can calculate the bicarbonate concentration in a solution.
