In the course of our investigations of the adsorption of ions to the air-water interface, we previously reported the surprising result that doubly charged carbonate anions exhibit a stronger surface affinity than singly charged bicarbonate anions. In contrast to monovalent, weakly hydrated anions, which generally show enhanced concentrations in the interfacial region, multivalent (and strongly hydrated) anions are expected to show a much weaker surface propensity. In the present work, we use resonantly enhanced deep-UV second-harmonic generation spectroscopy to measure the Gibbs free energy of adsorption of both carbonate (CO32-) and bicarbonate (HCO3-) anions to the air-water interface. Contrasting the predictions of classical electrostatic theory and in support of our previous findings from X-ray photoelectron spectroscopy, we find that carbonate anions do indeed exhibit much stronger surface affinity than do the bicarbonate anions. Extensive computer simulations reveal that strong ion pairing of CO32- with the Na+ countercation in the interfacial region results in the formation of near-neutral agglomerate clusters, consistent with a theory of interfacial ion adsorption based on hydration free energy and capillary waves. Simulated X-ray photoelectron spectra predict a 1 eV shift in the carbonate spectra compared to that of bicarbonate, further confirming our experiments. These findings not only advance our fundamental understanding of ion adsorption chemistry but also impact important practical processes such as ocean acidification, sea-spray aerosol chemistry, and mammalian respiration physiology.