Dissociation constants for carbonic acid determined from field measurements

Abstract

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 (TCO 2) and the fugacity of carbon dioxide ( fCO 2). In this paper, we have examined the field measurements of pH, fCO 2, TCO 2 and TA on surface and deep waters from the Atlantic, Indian, Southern and Pacific oceans to determine the p K 1, p K 2 and p K 2−p K 1. These calculations are possible due to the high precision and accuracy of the field measurements. The values of p K 2 and p K 2−p K 1 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 p K 1 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 p K 1+p K 2 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 p K 2−p K 1 (0.05 at 20°C) in real and artificial seawater determined by different investigators are mainly due to differences in p K 2. These differences may be related to the interactions of boric acid with the carbonate ion. The values of p K 2−p K 1 determined from the laboratory measurements of Lee et al. and Lueker et al. at low fCO 2 agree with the field-derived data to ±0.016 from 5°C to 25°C. The values of p K 2−p K 1 decrease as the fCO 2 or TCO 2 increases. This effect is largely related to changes in the p K 2 as a function of fCO 2 or TCO 2. The values of fCO 2 calculated from an input of TA and TCO 2, which require reliable values of p K 2−p K 1, also vary with fCO 2. The field data at 20°C has been used to determine the effect of changes of TCO 2 on p K 2 giving an empirical relationship: pK 2 TCO 2 = pK 2−1.6×10 −4( TCO 2−2050) which is valid at TCO 2>2050 μmol kg −1. This assumes that the other dissociation constants such as K B for boric acid are not affected by changes in TCO 2. 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 fCO 2 on the level of fCO 2 or TCO 2 in ocean waters ( σ=29.7 μatm in fCO 2). An input of pH and TCO 2 yields values of fCO 2 and TA that are in good agreement with the measured values (±22.3 μatm in fCO 2 and ±4.3 μmol kg −1 in TA). The cause of the decrease in p K 2 at high fCO 2 is presently unknown. The observed inconsistencies between the measured and computed fCO 2 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.