From the equilibrum constants with pka1= 6.37, pka2= 10.32 at 25⁰C for pH from 0 to 14

CO₂(g) CO₂(aq)

CO₂(aq) + H₂O H⁺+ HCO₃ ^-

HCO₃^- H⁺ + CO₃^2-

[CO₂aq] = [H⁺]²/ [H⁺]² + k_a1[H⁺] + k_a1k_a2

HCO₃ - ₌ ka₁[H⁺]/ [H⁺]² + k_a1[H⁺] + k_a1k_a2

CO₃^{2- =} k_a1k_a2/[H⁺]² + k_a1[H⁺] + k_a1k_a2