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Dissociation Constants for Carbonic Acid Determined from Field

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Dissociation Constants for Carbonic Acid Determined from Field Deep-Sea Research I 49 (2002) 1705–1723 Dissociation constants for carbonic acid determined from field measurements Frank J. Milleroa,*, Denis Pierrota, Kitack Leea,b, Rik Wanninkhofb, Richard Feelyc, Christopher L. Sabinec, Robert M. Keyd, Taro Takahashie a Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149-1098, USA b NOAA Atlantic Oceanographic and Meteorological Laboratory, 4301 Rickenbacker Cswy, Miami, FL 33149, USA c NOAA Pacific Marine and Environmental Laboratory, 7600 San Point Way NE, Seattle, WA 98115, USA d Atmospheric and Ocean Science Program, Princeton University, Princeton, NJ 08544, USA e Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY 10964-8000, USA Received 20 April 2001; received in revised form 1 April 2002; accepted 24 June 2002 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 (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 À pK1: These calculations are possible due to the high precision and accuracy of the field measurements. The values of pK2 and pK2 À pK1 over a wide range of temperatures (À1.6–381C) are in good agreement (within 70.005) with the results of Mehrbach et al. The measured values of pK1 at 41C and 201C are in reasonable agreement (within 70.01) with all the constants determined in laboratory studies. These results indicate, as suggested by internal consistency tests, that the directly measured values of pK1þpK2 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 À pK1 (0.05 at 201C) 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 À pK1 determined from the laboratory measurements of Lee et al. and Lueker et al. at low fCO2 agree with the field-derived data to 70.016 from 51Cto251C. The values of pK2 À 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 À pK1; also vary with fCO2. The field data at 201C has been used to determine the effect of changes of TCO2 on pK2 giving an empirical relationship: TCO2 À4 pK2 ¼ pK2 À 1:6 Â 10 ðTCO2 À 2050Þ À1 which is valid at TCO2>2050 mmol kg . 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 À4 À4 Lueker et al. (À1.2 Â 10 to À1.9 Â 10 ). This equation eliminates the dependence of the calculated fCO2 on the level *Corresponding author. Tel.: +1-305-361-4706; fax: +1-305-361-4144. E-mail addresses: [email protected] (F.J. Millero). 0967-0637/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0967-0637(02)00093-6 1706 F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 of fCO2 or TCO2 in ocean waters (s ¼ 29:7 matm in fCO2). An input of pH and TCO2 yields values of fCO2 and TA that À1 are in good agreement with the measured values (722.3 matm in fCO2 and 74.3 mmol kg in TA). The cause of the decrease in pK2 at high fCO2 is presently unknown. The observed inconsistencies between the measured and computed À1 fCO2 values may be accounted for by adding the effect of organic acid (B8 mmol kg ) to the interpretation of the TA. Further studies are needed to elucidate the chemical reactions responsible for this effect. r 2002 Elsevier Science Ltd. All rights reserved. þ þ 2À À 1. Introduction ½H SWS ¼½H Ff1þ½SO4 T=KHSO4 þ½F T=KHFg (KHSO4 and KHF are the dissociation constants for À The carbon dioxide system in the oceans can be HSO4 and HF, respectively, and the subscripts F characterized using any two of the four measur- and T represent the concentration of the free and able parameters, pH, total alkalinity (TA), fuga- total proton). city of carbon dioxide (fCO2) and the total The stoichiometric dissociation constants pK1 inorganic carbon dioxide (TCO2) providing that and pK2 have been determined by a number of constants are available for the other acid/base workers (Mehrbach et al., 1973; Hansson, 1973; species in seawater. Dissociation constants of Goyet and Poisson, 1989; Roy et al., 1993). A carbonic acid are needed to calculate the compo- summary of these results is given in Table 1. The nents of the CO2 system from these measurements. standard errors (1s) of the fits of the experimental The stoichiometric dissociation of carbonic acid in measurements to functions of temperature and seawater are given by salinity are 0.002–0.007 for pK1 and 0.006–0.013 CO þ H O3Hþ þ HCOÀ; ð1Þ for pK2. The measurements made by Mehrbach 2 2 3 et al. (1973) were made on real seawater; while the À3 þ 2À other studies were made in artificial seawater. HCO3 H þ CO3 : ð2Þ Mehrbach et al. (1973) determined pK1 from The dissociation constants K1 and K2 are defined potentiometric titrations and pK1+pK2 by addi- by tions of NaHCO3 to seawater devoid of CO2 until þ À the pH was constant (pH=[pK1+pK2]/2, when K1 ¼½H ½HCO3 =½CO2; ð3Þ TCO2=CA, the carbonate alkalinity). They calcu- þ 2À À lated pK2 by subtracting the pK1 from the K2 ¼½H ½CO3 =½HCO3 ; ð4Þ measured values of pK1+pK2. Hansson (1973) where the brackets are used to denote the determined the values of pK1 and pK2 from À1 concentration in mol kg of seawater and the potentiometric titrations of Na2CO3 in artificial À proton concentration is on the seawater scale, seawater (without F and B(OH)3). Goyet and Table 1 Summary of measurements made on the dissociation constants of carbonic acid in seawater by various workersa Author Temp. range (1C) Salinity range Std. Errorb Values at S ¼ 35 and 251C pK1 pK2 pK1 pK2 Hansson (1973) 5–30 20–40 0.007 0.009 5.850 8.942 Mehrbach et al. (1973) 2–35 26–43 0.006 0.010 5.837 8.955 Goyet and Poisson (1989) À1–40 10–50 0.007 0.011 5.848 8.919 Dickson and Millero (1987) 0–35 20–43 0.008 0.013 5.845 8.945 Roy et al. (1993) 0–45 5–45 0.002 0.006 5.847 8.916 a All the constants have been converted to the seawater scale. b The standard errors are 1s from fits of pK1 and pK2 as a function of temperature and salinity. F.J. Millero et al. / Deep-Sea Research I 49 (2002) 1705–1723 1707 Poisson (1989) determined the values of pK1 and Carbonic Acid Constants pK from potentiometric titrations of Na CO in 6.2 2 2 3 Goyet & Poisson artificial seawater (without B(OH)3). Roy et al. 6.1 Hansson (1993) determined the values of pK1 in artificial Mehrbach et al. À seawater (devoid of F and B(OH)3) measuring 6.0 Roy et al. the cell potential with a hydrogen silver–silver 1 5.9 chloride electrode system. These measurements pK S = 35 were made on solutions with various amounts of 5.8 NaHCO3 that were equilibrated with gas mixtures σ = 0.0061 of CO2 and H2. Roy et al. (1993) determined the 5.7 values of pK2 from potentiometric measurements in artificial seawater with mixtures of NaHCO 5.6 3 -10 0 10 20 30 40 50 and Na2CO3. Temperature (oC) Millero (1979) examined the pK1 and pK2 determined by Hansson (1973) and Mehrbach 5.97 et al. (1973) using thermodynamic equations that Hansson could be extrapolated to pure water. Dickson and 5.94 Mehrbach et al. Millero (1987) combined the measurements of Roy et al. 5.91 Mehrbach et al. (1973) and Hansson (1973) to 1 produce constants that were suggested for general 5.88 t = 25oC use in oceanography. The more recent measure- pK ments of Goyet and Poisson (1989) and Roy et al. 5.85 σ = 0.0065 (1993) were in reasonable agreement and were 5.82 combined by Millero (1995). More recently the examination of the internal consistency of labora- 5.79 tory (Lee et al., 1996; Lueker et al., 2000) and field 10 15 20 25 30 35 40 45 (Wanninkhof et al., 1999; Lee et al., 2000) Salinity measurements of fCO , TCO and TA have 2 2 Fig. 1. Values of pK1 of various workers for carbonic acid indicated that the constants of Mehrbach et al. (Mehrbach et al., 1973; Hansson, 1973; Goyet and Poisson, (1973) are more reliable than those of other 1989; Roy et al., 1993) as a function of temperature (S ¼ 35) and salinity (251C). Goyet and Poisson (1989) did not make any workers.
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