Carbon Thermodynamics

An understanding of the thermodynamic relationships in the inorganic carbon system is important in evaluating the mechanisms controlling the distribution of CO₂ in the oceans. The CO₂ system in the oceans can be characterized by measuring at least two of the experimentally determined parameters

1. pH
2. Total Alkalinity (TALK)
3. Total inorganic carbon dioxide (TCO₂)
4. Fugacity of CO2 (fCO₂),

providing that constants are available for the other acid/base species in seawater (Millero, 1995). Reliable dissociation constants of carbonic acid are needed to calculate the components of the CO₂ system from these measurements. The stoichiometric dissociation of carbonic acid in seawater are given by

K₂ = [H⁺] [CO₃^2-]/[HCO₃^-] (2)

where the brackets are used to denote the concentration in µmol/kg of seawater and the proton concentration is on the seawater scale, [H⁺]_SWS = [H⁺]_F {1 + [SO₄^2-]_T/K_HSO4 + [F^-]_T /K_HF} (K_HSO4 and K_HF are the dissociation constants for HSO₄^- and HF, respectively and the subscripts F and T represent the concentration of the free and total proton).

The stoichiometric dissociation constants pK₁ and pK₂ for carbonic acid have been determined by a number of scientists (Mehrbach et al., 1973; Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993). The measurements by Mehrbach et al. (1973) were made on real seawater; while the other studies were made in artificial seawater. The more measurements of Goyet and Poisson (1989) and Roy et al. (1993) were in reasonable agreement and thus were combined by Millero (1995). At room temperatures the values of pK₁ and pK₂ determined in real seawater are 0.01 and 0.04 respectively, higher than the measurements made in artificial seawater. The examination of the internal consistency of laboratory (Lee et al., 1996; Lueker et al., 2000) and field (Wanninkhof et al., 1999; Lee et al; 2000) measurements of fCO₂, TCO₂ and TALK have indicated that the constants of Mehrbach et al. (1973) are more reliable than those of other scientists. The calculation of fCO₂ from an input of TALK and TCO₂ and calculations of other parameters from an input of fCO₂ and TALK or TCO₂ require reliable values of pK₂ pK₁ (or K₁/K₂). Thus, the field measurements suggest that the values pK₂ - pK₁ from Mehrbach et al. (1973) are more reliable than other laboratory studies. More recently (Millero et al., 2002) the high precision CO₂ field measurements made as part of the WOCE and JGOFS programs in the Atlantic, Indian, Southern and Pacific oceans for surface waters (-1.6 to 38^oC) yield values of pK₂ and pK₂ - pK₁ in good agreement (within 0.005) with the results of Mehrbach et al. (1973). The calculated deep water measurements of pK₁ and pK₂ at 4 and 20^oC are also in agreement (within 0.01) with all the constants determined in laboratory studies. These studies confirm the earlier internal consistency tests and indicate that the measured values of pK₁ and pK₂ of Mehrbach et al. (1973) 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^oC) in real and artificial seawater determined by different investigators are mainly due to differences in pK₂. The values of pK₂ - pK₁ determined from the laboratory measurements of Lee et al. (1996) and Lueker et al. (2000) at low fCO₂ agree with the field-derived data.

The values of pK₂ - pK₁ determined in these laboratory studies and the recent field measurements decrease as the fCO₂ or TCO₂ increases. This effect is largely related to changes in the pK₂ as a function of fCO₂ or TCO₂. One can account for these effects using the empirical relationship:

pK₂^TCO2 = pK₂ - 1.6 x 10^-4 (TCO₂ - 2050)

which is valid at TCO₂ > 2050 µmol/kg. At present the cause of this effect is unknown. It may be related to interactions of CO₃^2- with B(OH)₃ or the presence of organic acids in seawater. The cause of the decrease in pK₂ at high fCO₂ is presently unknown. Further studies are needed to elucidate the chemical interactions responsible for this effect.

Recently Mojica Prieto and Millero (2002) have determined the values of (pK₁ + pK₂) for carbonic acid in seawater as a function of temperature (0 to 45^oC) and salinity (5 to 42). Their measurements were in good agreement (0.005) with the results of Mehrbach et al. (1973). The pK₁ in seawater were also determined in this study from at a few temperatures (15 to 45^oC). The results are in better agreement (0.01) with the results of Mehrbach et al. between 20 to 30^oC than other scientists. The measurement of Mojica Prieto and Millero (2002) and Mehrbach et al. have been combined to yield s = 0.0056:

pK₁ = -43.6977 -0.0129037 S + 1.364 x 10^-4 S² + 2885.378/T + 7.045159 ln T

and s = 0.010:

pK₂ = -452.0940 + 13.142162 S - 8.101 x 10^-4 S² + 21263.61/ T + 68.483143 ln T + (-581.4428 S + 0.259601 S² ) / T -1.967035 S ln T

These studies indicate that the values of K₁ (SW) > K₁ (ASW) by ~0.01 and K₂ (SW) < K₂ (ASW) by ~0.04 near 25^oC. Measurements of pK₁ + pK₂ and pK₁ in artificial seawater with and without boric acid show the same trends, indicating that the effect is due to interactions of boric acid with HCO₃^- and CO₃^2-. Further studies are needed to elucidate these interactions.

References

• Dickson, A. G. and J. P. Riley. 1979. The estimation of acid dissociation constants in seawater from potentiometric titrations with strong base. I. The ion product of water K_w. Marine Chemistry 7:89-99.
• Goyet, C. and A. Poisson. 1989. New determination of carbonic acid dissociation constants in seawater as a function of temperature and salinity, Deep-Sea Research 36:1635-54.
• Hansson, I. 1973. A new set of acidity constants for carbonic acid and boric acid in seawater. Deep-Sea Research 20:461-78.
• Lee, K., F. J. Millero, and D. M. Campbell. 1996. The reliability of the thermodynamic constants for the dissociation of carbonic acid in seawater. Marine Chemistry 55:233-46.
• Lee, K., F. J. Millero, R. H. Byrne, R. A. Feely, and R. Wanninkhof. 2000. The recommended dissociation constants for carbonic acid in seawater. Geophysical Research Letters 27:229-32.
• Mojica P., and F.J., Millero. 2002. The values of pK₁ + pK₂ for the dissociation of carbonic acid in seawater, Geochimical et Cosmochimica Acta 66(14):2529-40.
• Lueker, T.J., A. G. Dickson, and C. D. Keeling. 2000. Ocean pCO₂ calculated from dissolved inorganic carbon, alkalinity, and equations for K₁ and K₂; validation based on laboratory measurements of CO₂ in gas and seawater at equilibrium. Marine Chemistry 70:105-19.
• Mehrbach, C., C. H. Culberson, J. E. Hawley, and R. N. Pytkowicz. 1973. Measurement of the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure. Limnology and Oceanography 18:897-907.
• Millero, F.J. 1995. The thermodynamics of the carbonic acid system in the oceans. Geochimical and Cosmochimical Acta 59:661-67.
• Millero, F.J., D. Pierrot, K. Lee, R. Wanninkhof, R. A. Feely, C. L. Sabine, and R. M. Key. 2002. Dissociation constants for carbonic acid determined from field measurements, Deep-Sea Research, in press.
• Prieto M., and F. J. Millero. 2002. The determination of pK₁ + pK₂ in seawater as a function of temperature and salinity. Geochim. Cosmochim. Acta, 66:2529-40.
• Roy, R.N., K. M. Vogel, C. P. Moore, T. Pearson, L. N. Roy, D. A. Johnson, F. J. Millero, and D. M. Campbell. 1993. The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45^oC. Marine Chemistry 44:249-267.
• Wanninkhof, R., E. Lewis, R. A. Feely, and F. J. Millero. 1999. The optimal carbonate dissociation constants for determining surface water pCO₂ from alkalinity and total inorganic carbon. Marine Chemistry 65:291-301.