National Oceanic and
Atmospheric Administration
United States Department of Commerce


FY 2003

Dissociation constants for carbonic acid determined from field measurements

Millero, F.J., D. Pierrot, K. Lee, R. Wanninkhof, R.A. Feely, C.L. Sabine, R.M. Key, and T. Takahashi

Deep-Sea Res. Pt. I, 49(10), 1705–1723, doi: 10.1016/S0967-0637(02)00093-6 (2002)

A number of workers have recently shown that the thermodynamic constants for the dissociation of carbonic acid in seawater of Mehrbach et al. are more reliable than measurements made on artificial seawater. These studies have largely been confined to looking at the internal consistency of measurements of total alkalinity (TA), total inorganic carbon dioxide (TCO2) and the fugacity of carbon dioxide (fCO2). In this paper, we have examined the field measurements of pH, fCO2, TCO2 and TA on surface and deep waters from the Atlantic, Indian, Southern and Pacific oceans to determine the pK1, pK2 and pK2 – pK1. These calculations are possible due to the high precision and accuracy of the field measurements. The values of pK2 and pK2 – pK1 over a wide range of temperatures (-1.6–38°C) are in good agreement (within ±0.005) with the results of Mehrbach et al. The measured values of pK1 at 4°C and 20°C are in reasonable agreement (within ±0.01) with all the constants determined in laboratory studies. These results indicate, as suggested by internal consistency tests, that the directly measured values of pK1 + pK2 of Mehrbach et al. on real seawater are more reliable than the values determined for artificial seawater. It also indicates that the large differences of pK2 – pK1 (0.05 at 20°C) in real and artificial seawater determined by different investigators are mainly due to differences in pK2. These differences may be related to the interactions of boric acid with the carbonate ion.

The values of pK2 – pK1 determined from the laboratory measurements of Lee et al. and Lueker et al. at low fCO2 agree with the field-derived data to ±0.016 from 5°C to 25°C. The values of pK2 – pK1 decrease as the fCO2 or TCO2 increases. This effect is largely related to changes in the pK2 as a function of fCO2 or TCO2. The values of fCO2 calculated from an input of TA and TCO2, which require reliable values of pK2 – pK1, also vary with fCO2. The field data at 20°C has been used to determine the effect of changes of TCO2 on pK2 giving an empirical relationship:

pK2TCO2 = pK2 – 1.6 × 10–4 (TCO2 – 2050)

which is valid at TCO2 > 2050 µmol kg–1. This assumes that the other dissociation constants such as KB for boric acid are not affected by changes in TCO2. The slope is in reasonable agreement with the laboratory studies of Lee et al. and Lueker et al. (–1.2 × 10–4 to –1.9 ×10–4). This equation eliminates the dependence of the calculated fCO2 on the level of fCO2 or TCO2 in ocean waters (σ = 29.7 µatm in fCO2). An input of pH and TCO2 yields values of fCO2 and TA that are in good agreement with the measured values (±22.3 µatm in fCO2 and ±4.3 µmol kg–1 in TA). The cause of the decrease in pK2 at high fCO2 is presently unknown. The observed inconsistencies between the measured and computed fCO2 values may be accounted for by adding the effect of organic acid (~8 µmol kg–1) to the interpretation of the TA. Further studies are needed to elucidate the chemical reactions responsible for this effect.

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