Article
The values of pK1 + pK2 for the dissociation of carbonic acid in seawater

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Abstract

The values of pK1 + pK2 for the dissociation of carbonic acid have been determined in seawater as a function of temperature (0 to 45°C) and salinity (5 to 42). They were determined by the addition of NaHCO3 to seawater stripped of CO2 until the pH0 = 1/2(pK1 + pK2) was constant. The pH0 was measured using potentiometric and spectrophotometric techniques. The values of pH0 determined by the two methods are in good agreement (± 0.002). Our values of 1/2(pK1 + pK2) are in good agreement (0.005) with the results of Mehrbach et al. (1973) and the combined data have been fitted to the equation1/2(pK1+pK2)=−247.8958+6.564628 S-3.322×10−4 S2+12074.50/T+37.764148 ln T+(290.721 S+0.12980 S2)/T−0.983517 S ln Twith a σ = 0.0052. Both studies indicate that the measurements of pK2 in artificial seawater are lower than the values in real seawater. Values of the pK1 in seawater were also determined from potentiometric titrations of seawater at a few temperatures (15 to 45°C). The results are in better agreement (0.01) with the results of Mehrbach et al. between 20 to 30°C than other workers. Our results and those of Mehrbach et al. have been combined to yield (σ = 0.0056)pK1=−43.6977−0.0129037 S+1.364×10−4 S2+2885.378/T+7.045159 ln Tand (σ = 0.010)pK2=−452.0940+13.142162 S-8.101×10−4 S2+21263.61/T+68.483143 ln T+(581.4428 S+0.259601 S2)/T−1.967035 S ln TThese studies indicate that the values of K1 (SW) > K1 (ASW) by ∼0.01 and K2 (SW) < K2 (ASW) by ∼0.04 near 25°C. 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 CO32−. Further studies are needed to elucidate these interactions.

Introduction

The carbonate system in natural waters can be studied by measurements of pH, the total alkalinity (TA), the total carbonate (TCO2) and the fugacity of CO2 (fCO2). Only two of these four parameters need to be measured to characterize the CO2 system in solution providing that data are available for all the other acid/base species. These calculation require reliable dissociation constants for carbonic acidCO2+H2OH++HCO2 K1 HCO3H++CO32− K2 The dissociation constants are defined byK1=[H+][HCO3]/[CO2] K2=[H+][CO32−]/[HCO3] where [i] are the total concentrations in mol (kg sol)−1. It should be pointed out that all the constants discussed in this paper are on the seawater pH scale (pHSWS), where [H+]SWS ≈ [H+]F + [HSO4] + [HF] (where the subscript F is used to denote the free proton concentration, Dickson, 1984).

Four groups have recently made measurements of pK1 and pK2: Hansson 1973, Mehrbach et al 1973, Goyet and Poisson 1989 and Roy et al. (1993). The measurements of Mehrbach et al. (1973) were made in real seawater (SW) while the other studies were made in artificial seawater (ASW). The standard errors of the fits of the measured values of pK1 and pK2 to functions of temperature and salinity by the authors are within 0.007 and 0.011 respectively (Table 1). Comparisons of the values of pK1 and pK2 at different temperatures are shown in Figure 1. The values of pK1 are generally within 2σ = 0.014, but the values of pK2 show differences much larger than 2σ = 0.022, where the standard errors are based on the fits of the authors (Table 1). Near 25°C the measurements of pK1 in SW are 0.01 lower than the measurements in ASW; while, the measurements of pK2 in SW are 0.04 higher than the measurements in ASW.

The present analytical precision of the measurement in the carbon dioxide system parameters (Millero et al., 2001) is ±0.001 in pH, ±4 μmol kg−1 in TA, ±2 μmol kg−1 in TCO2 and ±3 μatm in fCO2. To calculate the unknown parameters with the same precision as the measurements, reliable constants are needed Millero 1995, Lee et al 1996. This is demonstrated in Table 2 where the effect of errors of 0.01 in pK1 and 0.04 in pK2 are examined. With an input of pH and TA or TCO2, one can determine the fCO2 and TCO2 or TA with values of pK1 or pK2. Since the uncertainties in pK1 are much less than the uncertainties in pK2, more reliable calculations of fCO2 and TCO2 or TA can be made using pK1. An input of pH and TA or TCO2 can lead to errors in the calculated values of fCO2 of 10 μatm due to errors in pK2. Calculations of the CO2 parameters using an input of TA and TCO2, fCO2 and TCO2 or fCO2 and TA require reliable values of pK2 − pK1 (Lee et al., 2000). Errors in pK2 − pK1 are largely due to errors in pK2 and give uncertainties similar to those shown for pK2 in Table 2. For example, an error of 0.04 in pK2 − pK1 with an input of TA and TCO2 can lead to errors in the calculated values of fCO2 of 26 μatm.

A number of internal consistency tests using measurements made in the laboratory Lee et al 1996, Lueker et al 2000 and at sea Wanninkhof et al 1999, Lee et al 2000, Millero et al 2002 indicate that the values of pK2 − pK1 of Mehrbach et al. (1973) are more reliable than the results of others Hansson 1973, Goyet and Poisson 1989, Roy et al 1993. The differences in the values of pK2 − pK1 of the studies in artificial seawater (ASW) with those determined in real seawater (SW) by Mehrbach et al. (1973) are around 0.04 (see Fig. 2) from 10 to 40°C. Since the values of pK1 determined by all of the studies agree within 0.01 (see Fig. 1), the differences in pK2 − pK1 are largely due to uncertainties in pK2 (see Fig. 1).

These comparisons point out the need to have reliable dissociation constants for carbonic acid. This paper describes some new measurements of the pK1 + pK2 and pK1 in real and artificial seawater. These results extend the earlier measurements of Mehrbach et al. (1973) using improved methods and examine the effect of borate on the carbonate system. By combining our results with those of Mehrbach et al. (1973), we provide equations that we feel are appropriate for calculations of the carbonate system in the oceans. Our preliminary work indicates that borate-carbonate interactions may cause the differences in the pK1 and pK2 between real and artificial seawater.

Section snippets

Experimental methods

The values of pK1 + K2 were determined in natural and artificial seawater using the methods of Mehrbach et al. (1973). The seawater is stripped of CO2 after the addition of acid (HCl). The pH was then adjusted with 0.1 N NaOH within ± 0.05 pH of the equilibrium value (pH = 1/2(pK1 + pK2). Solid NaHCO3 was then added to the solution until a constant pH was reached. Unlike the study of Mehrbach et al. (1973), the electrode was calibrated in the sample by titrating it with HCl before the

Material and methods

The seawater used in this study was Gulf Stream seawater collected off the coast of Miami. The seawater was filtered through a 0.45 μm Millipore filter before its use. The salinities of the two batches of seawater (S = 36.2 and S = 35.9) were determined with a Guildline salinometer on the Practical Salinity Scale. The salinometer was calibrated with standard seawater of known conductivity.

The artificial seawater was prepared as described by Millero (1996) according to the specifications of

Determination of pK1 + pK2 in seawater

The pH0 was determined using potentiometric and spectrophotometric techniques in seawater as a function of salinity and temperature. The potentiometric and spectroscopic values of pH0 are given in Table 4, Table 5. The values of pH0 as a function of temperature and salinity were found to be a second-degree function of temperature and salinity (Mojica Prieto, 2001). The resulting equations derived from experimental values of pH0(emf) and pH0(spec) are given bypH0(emf)=279.8873+7.707839 S

Discussion

The results from this study clearly demonstrate that the measured values of pK1 and 1/2(pK1 + pK2) by Mehrbach et al. (1973) are reliable for seawater. This is in agreement with field Wanninkhof et al 1999, Lee et al 2000, Millero et al 2002 and laboratory Lee et al 1996, Lueker et al 2000 measurements of the components of the CO2 system in seawater. More importantly these results indicate that the measurements of Hansson 1973, Goyet and Poisson 1989 and Roy et al. (1993) are reliable for

Acknowledgements

The authors wish to acknowledge the support of the Oceanographic section of the National Science Foundation and the National Oceanic and Atmospheric Association.

Associate editor: D. J. Burdige

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