How Acidic Is Carbonic Acid?

Carbonic, lactic, and pyruvic acids have been generated in aqueous solution by the transient protonation of their corresponding conjugate bases by a tailor-made photoacid, the 6-hydroxy-1-sulfonate pyrene sodium salt molecule. A particular goal is to establish the pK_a of carbonic acid H₂CO₃. The on-contact proton transfer (PT) reaction rate from the optically excited photoacid to the carboxylic bases was derived, with unprecedented precision, from time-correlated single-photon-counting measurements of the fluorescence lifetime of the photoacid in the presence of the proton acceptors. The time-dependent diffusion-assisted PT rate was analyzed using the Szabo-Collins-Kimball equation with a radiation boundary condition. The on-contact PT rates were found to follow the acidity order of the carboxylic acids: the stronger was the acid, the slower was the PT reaction to its conjugate base. The pK_a of carbonic acid was found to be 3.49 ± 0.05 using both the Marcus and Kiefer-Hynes free energy correlations. This establishes H₂CO₃ as being 0.37 pK_a units stronger and about 1 pK_a unit weaker, respectively, than the physiologically important lactic and pyruvic acids. The considerable acid strength of intact carbonic acid indicates that it is an important protonation agent under physiological conditions.