Dissociation constants of carbonic acid in seawater as a function of salinity and temperature

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1 Marine Chemistry 100 (006) Dissociation constants of carbonic acid in seawater as a function of salinity and temperature Frank J. Millero *, Taylor B. Graham, Fen Huang, Héctor Bustos-Serrano, Denis Pierrot Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL 33149, United States Received 17 June 005; received in revised form December 005; accepted December 005 Available online 31 January 006 Abstract Potentiometric measurements of the stoichiometric constants on the seawater ph scale for the dissociation of carbonic acid in seawater (K 1 *=[H + ][HCO 3 ]/[CO ] and K *=[H + ][CO 3 ]/[HCO 3 ]) have been made as a function of salinity (1 to 50) and temperature (0 to 50 8C). The results have been fitted to the equations (T/K) pk i pk 0 i ¼ A i þ B i =T þ C i lnt: The values of pk i 0 in pure water are taken from the early work of Harned and Davis (1943) and Harned and Scholes (1941) pk 0 1 ¼ 16:34048 þ 630:813=T þ 19:5684lnT pk 0 ¼ 90:18333 þ 5143:69=T þ 14:613358lnT: The value of the adjustable parameters A i, B i and C i for pk* 1 are given by (r =54 and N =466) A 1 ¼ 13:4191S 0:5 þ 0:0331S 5:33E 05S B 1 ¼ 530:13S 0:5 6:103S C 1 ¼ :06950S 0:5 : For pk* the parameters are given by (r =1 and N =458) A ¼ 1:0894S 0:5 þ 0:148S 3:687E 04S B ¼ 77:483S 0:5 0:051S C ¼ 3:3336S 0:5 : * Corresponding author. address: fmillero@rsmas.miami.edu (F.J. Millero) /$ - see front matter D 006 Elsevier B.V. All rights reserved. doi: /j.marchem

2 F.J. Millero et al. / Marine Chemistry 100 (006) The values of pk 1 * determined in this study are in good agreement with the seawater (SW) measurements of Mehrbach et al. (1973) and Mojica-Prieto and Millero (00) from S =15to45and0to408C. The values of pk 1 * near S =35 are also in reasonable agreement with the measurements in artificial seawater (ASW) of Goyet and Poisson (1989) and Roy et al. (1993) from 0to358C. The values of pk * in real seawater, however, do not agree with the measurement made in artificial seawater at temperatures above 5 8C. Calculations of pk 1 * near 5 8C using an ionic interaction model (Millero and Roy, 1997) suggest that the pk * results in SW are more reliable than in ASW. The equations from this study should be valid from S =0 to 50 and t =0 to 50 8C for most estuarine and marine waters (check values at S =35 and t =5 8C are pk 1 *= and pk *=8.9636). D 006 Elsevier B.V. All rights reserved. Keywords: Seawater; Carbonic acid; Dissociation constants; pk 1 ;pk ; Titration; Modeling 1. Introduction To examine the thermodynamics of the carbonic acid system in seawater from measurements of ph, total alkalinity (TA), total carbon dioxide (TCO ) and the partial pressure of carbon dioxide ( pco ) one needs reliable constants for the dissociation of carbonic acid. CO þ H O X H þ þ HCO 3 HCO 3 ð1þ X Hþ þ CO 3 : ðþ The stoichiometric constants are given by K 1 * ¼ ½H þ Š HCO 3 K * ¼ ½H þ = ½ CO Š ð3þ Š CO 3 = HCO 3 : ð4þ The concentrations (mol kg SW 1 ) are the total stoichiometric values, [H + ]=[H + ] F +[HSO 4 ]+[HF] (where the subscript F is used to designate the free proton concentration). Theoretically the measured stoichiometric constants (K 1 * and K *) for carbonic acid in seawater are related to the thermodynamic constants (K i 0 ) by K 1 * ¼ K 0 1 a H Oc CO =c H c HCO3 K * ¼ K 0 c HCO 3 =c H c CO3 ð5þ ð6þ where a i is the activity and c i is the activity coefficient of species i. A number of workers have made measurements of the stoichiometric constants for the dissociation of carbonic acid in real seawater (SW) (Mehrbach et al., 1973; Mojica-Prieto and Millero, 00) and artificial seawater (ASW) (Hansson, 1973; Goyet and Poisson, 1989; Roy et al., 1993). A summary of these studies is given in Table 1 along with the standard errors of the individual measurements being fit to the same equation (Eqs. (11) (14)). All of the individual studies have similar standard deviations, r =4 to 7 for pk 1 * and r = to 0 for pk *. The measurements by Mehrbach et al. (1973) and Mojica-Prieto and Millero (00) were made on real seawater (SW) while the measurements made by Hansson (1973), Goyet and Poisson (1989) and Roy et al. (1993) were made on artificial seawater Table 1 A summary of the measurement made on the dissociation constants of carbonic acid in real (SW) and artificial (ASW) seawater by various workers Reference Media Salinity range Temperature range (8C) r(pk 1 *) a r(pk *) a Hansson ASW (6) 0 (6) Mehrbach et al. SW (30) 0 (33) Goyet and Poisson ASW (84) 0 (90) Roy et al. ASW (80) (80) Mojica-Prieto and Millero SW (80) 8 (80) This study SW (466) 1 (458) a The values in parentheses are the number of measurements made and the standard errors are based upon fitting the measurements to the same functional form (Eqs. (11) (14)).

3 8 F.J. Millero et al. / Marine Chemistry 100 (006) (ASW). The values of pk 1 * determined by Mehrbach et al. (1973), Hansson (1973), Goyet and Poisson (1989) and Mojica-Prieto and Millero (00) were determined from potentiometric titrations. The values of pk * determined by Hansson (1973) and Goyet and Poisson (1989) were also determined by potentiometric methods. Roy et al. (1993) determined pk 1 * using the hydrogen electrode method. The pk * measurements by Mehrbach et al. (1973) and Mojica-Prieto and Millero (00) determined pk 1 *+pk * on seawater that had been stripped of CO with HCl. The values of ph =0.5 (pk 1 *+pk *) of these solutions were determined after the addition of HCO 3. If the ph is determined using a spectroscopic method (Clayton and Byrne, 1993), then one should be able to determine the pk * to F5 which is better than the precision from most of the titration studies. Comparisons of the measurements made in ASW and SW by various workers for S =35 seawater as a function of temperature are shown in Fig. 1. These comparisons are made relative to the measurements of Mehrbach et al. (1973) as reformulated by Dickson and Millero (1987). This was done since laboratory (Lee et al., 1996, 1997, 000; Lueker et al., 000; Mojica- Prieto and Millero, 00) and field (Wanninkhof et al., 1999; Millero et al., 00) studies on SW indicate Δ pk 1 Δ pk Hansson Goyet & Poisson -0.0 Roy et al. Mojica & Millero Temperature ( C) Fig. 1. A comparison of the values of pk 1 *and pk * from 0 to 40 8C and S =35 determined by various workers with the results of Mehrbach et al. (1973) as refit by Dickson and Millero (1987). that these constants are more reliable than those made in ASW. The pk 1 * measurements in SW by Mehrbach et al. (1973) and in ASW by Goyet and Poisson (1989) and Roy et al. (1993) are in reasonable agreement (within r =4). The pk 1 * results of Hansson (1973) from 5 to 5 8C in ASW are slightly higher than the measurements of Goyet and Poisson (1989) and Roy et al. (1993). The pk * results in SW do not agree with the results in ASW above 5 8C (see Fig. 1). These results suggest that the values of pk * in SW and ASW are different. As discussed above internal consistency studies with field and laboratory measurements of seawater have shown that the pk * measurements of Mehrbach et al. (1973) in SW are more reliable than the measurements made in ASW. The pk * SW measurements of Mojica-Prieto and Millero (00) are in good agreement with the results of Mehrbach et al. (1973).. Modeling the carbonate system in natural waters The differences in the values of pk* i near 5 8C going from ASW to SW can be attributed to changes in the activity of the H O and CO or the activity coefficients of HCO 3 and CO 3. For example, the increase in K 1 * and decrease in K * near 5 8C can be attributed to a decrease in c HCO3 and an increase in c CO3 when going from ASW to SW. If these effects are due to the boric acid in real seawater (Mojica-Prieto and Millero, 00), they can be attributed to interactions of HCO 3 with B(OH) 3 or B(OH) 4 and interactions of CO 3 with B(OH) 3 or B(OH) 4. It is also possible that the differences in the pk * in SW and ASW are related to an organic acid that is in all seawater (Millero et al., 00). Further measurements are needed to determine the cause of these differences. The measured stoichiometric constants (K 1 * and K *) for carbonic acid in seawater are related to the thermodynamic constants by Eqs. (5) and (6). The activity coefficients of H +, HCO 3, CO 3 and activities of CO and H O can be determined from ionic interaction models (Pitzer, 1991). Millero and Roy (1997) have developed a carbonate model valid from 0 to 50 8C and I =0 to 6 m. The model considers the ionic interactions in solutions of the major components of seawater and other natural waters (H Na K Mg Ca Sr F Cl Br OH HCO 3 B(OH) 4 HSO 4 SO 4 CO 3 CO HF B(OH) 3 H O). The model has been used to predict the activity coefficients of major and minor components of ions required to determine the dissociation constants of all the acids needed to examine the carbonate system in natural waters (H CO 3, B(OH) 3,

4 F.J. Millero et al. / Marine Chemistry 100 (006) Table The composition of artificial seawater used by various authors Hansson Roy et al. Goyet and Poisson Seawater a NaCl Na SO KCl CaCl MgCl NaF KBr SrCl Na CO 3 1 NaHCO 3 05 B(OH) 3 04 a In mol (kg soln) 1, Millero (1996). H O, HF, HSO 4,H 3 PO 4,H S, NH 4 + ). The predicted dissociation constants for a number of acids in seawater have been shown to be in good agreement with experimental measurements (Millero and Roy, 1997). The model can be used to examine the effects of composition on the carbonate constants in seawater and to compare the measurements made by various studies. The compositions of artificial seawater used in the various studies are given in Table. A calculation of the values of pk 1 * using the compositions shown in Table indicate that the differences in pk 1 * and pk * are all within F which is well within the experimental error of the measurements (see Table 1). Changes in the values of SO 4 and F show the largest effects on the values of pk i * (an increase of 001 in F increases the pk s by 5 and an increase of 01 in SO 4 increases the pk s by 5). These effects cannot account for the increase in pk 1 * and decrease in pk * when going from SW to ASW near 5 8C. A comparison of the model calculations of pk 1 * and pk * at S =35 and from 0 to 45 8C with the fitted measurements of Mehrbach et al. (1973), Goyet and Poisson (1989), Roy et al. (1993) and Mojica-Prieto and Millero (00) are shown in Fig.. The model calculations of pk 1 * are in reasonable agreement with all of the measurements from 10 to 45 8C. The model calculations of pk * are in agreement with the measurements in seawater by Mehrbach et al. (1973) and Mojica-Prieto and Millero (00). Large offsets occur in the values of pk * made in ASW by Goyet and Poisson (1989), and Roy et al. (1993). The model Carbonic Acid Δ pk 1 (Meas - Calc) Δ pk (Meas - Calc) Model Comparisons Mehrbach et al. Goyet & Poisson Roy et al. Mojica and Millero pk 1 pk Model Mehrbach et al Model Mehrbach et l Temperature ( C) S 0.5 Fig.. A comparison of the values of pk 1 * from 0 to 40 8C and S =35 determined by various workers with the model results of Millero and Roy (1997). Fig. 3. A comparison of the values of pk 1 * at 5 8C asa function of the square root of salinity (S =0 to 45) of Mehrbach et al. (1973) with the model results from Millero and Roy (1997).

5 84 F.J. Millero et al. / Marine Chemistry 100 (006) appears to be in error below 10 8C probably due to the scarcity of measurements of pk 1 * in NaCl solutions at low temperatures. In summary, the model supports the measurements in real seawater by Mehrbach et al. (1973) and Mojica-Prieto and Millero (00). The measurements made by Mehrbach et al. (1973) and Mojica-Prieto and Millero (00) on SW were not made in dilute solutions so they may not give reliable constants for estuarine waters. This is shown in Fig. 3 by comparing the measurements of pk 1 * of Mehrbach et al. (1973) with the model at 5 8C. In this paper, we present measurements of real seawater over a wide temperature (1 to 50 8C) and salinity (1 to 50) range. The seawater results of this study have been fitted to equations that are valid for all marine waters over a wide range of salinity and temperature. 3. Methods The measurements were made on Gulf Stream seawater that was diluted or evaporated from a salinity near 36. The seawater was filtered through a 0.45 Am filter and stored at room temperature in 50 L P.P. Nalgene Bottles before use. The low salinity samples were made by diluting SW with pure Milli-Q water (18 mv) and the high salinity samples were obtained by slowly evaporating the SW. All the salinities below 4 were directly determined on a Guildline 8410 PortaSal Salinometer. The samples at higher salinities were determined from density measurements on a DMA 60 Mettler/Paar Density Meter. The salinities were determined from the density measurements using the 1 atm equation of state of Millero and Poisson (1981). For samples of salinity less than 8, sodium carbonate ( m) was added to aid in the determination of pk *. Since the ph of seawater (~8) is not high enough to determine an accurate value of pk *, small amounts of sodium hydroxide were added to increase the ph to ~9 10. These small additions of NaOH did not significantly change the salinity of the samples. The addition of NaOH was not necessary in dilute solutions when sodium carbonate was added. All the samples were equilibrated to the desired temperature in a Neslab RTE-1 constant temperature water bath to F0.05 8C before addition to the titration vessel. Flowing water at the desired temperature was circulated through the titration cell and around the piston delivering the HCl during an experiment. The temperatures in the constant temperature bath and in the cell were Table 3 The effects of TA (Amol kg 1 ) and TCO (Amol kg 1 ) levels and ph on the determination of the pk* 1 and pk* at various temperatures (A) Effect of fixing or floating TA and TCO on the calculated pk* 1 and pk* Fixed values of TA and TCO Floating values of TA and TCO Temperature (8C) Salinity TA TCO pk* 1 pk* DpK* 1 DpK* DTA DTCO Floating values of TA and TCO (B) Effect of initial ph on the values of pk* 1 and pk* Temperature Salinity Without NaOH With NaOH Without With pk* 1 pk* pk* 1 pk* DpK* a 1 DpK* a DpK* a 1 DpK* a b a Certified reference material. b From Mehrbach data.

6 F.J. Millero et al. / Marine Chemistry 100 (006) Table 4 Measured values of pk* 1 and pk* for carbonic acid in seawater as a function of salinity and temperature a (continued on next page)

7 86 F.J. Millero et al. / Marine Chemistry 100 (006) a a (continued on next page)

8 F.J. Millero et al. / Marine Chemistry 100 (006) a (continued on next page)

9 88 F.J. Millero et al. / Marine Chemistry 100 (006) a a (continued on next page)

10 F.J. Millero et al. / Marine Chemistry 100 (006) a a: The missing values of pk * are not given since they are unreliable due to the precipitation of MgOH at high ph. measured with a Guildline 9540 Digital Resistance Thermometer calibrated by the company. The temperature inside the cell was measured before and after each titration. The values agreed to F0.1 8C which is equivalent to an error of F09 in pk 1 * and F16 in pk *. The recorded temperature of a run is the mean of the initial and final values. The titration system (Millero et al., 1993) consists of a closed water jacketed plexiglass cell with a ROSS 8101 glass ph electrode and an Orion 90-0 double junction Ag/AgCl reference electrode. Some measurements were made using an Orion ROSS Reference Half-Cell electrode. The titrant is delivered with a Metrohm 665 Dosimat titrator and the emf is measured with an Orion 70A ph meter. The system is controlled by a personal computer (Millero et al., 1993) using a National Instrument s Labwindows/CVI environment. The titration is made by adding ~0.5 M HCl (in 0.45 M NaCl) to seawater past the carbonic acid end point. A typical titration records the emf after the readings become stable (0.05 mv) and adds enough acid to change the voltage to a pre-assigned increment (9 mv). This provides more data points in the range of a rapid increase in the emf near the endpoints. The values of pk 1 * [mol (kg soln) 1 ] were determined using a non-linear curve-fitting procedure developed by Johansson and Wedborg (198) and Dickson (1981). This procedure was modified to a more buser-friendlyq Excel version by Dr. Pierrot. The program determines the E*,pK 1 *,pk *, TA and TCO of the sample from the full titration (N50 pts). The electrodes are calibrated over the entire range of the titration with the computer code giving a value of E* that is constant at a given temperature and salinity. The dissociation or association constants needed in the computer code were taken from the literature (B(OH) 3 from Dickson, 1990a; HF from Dickson and Riley, HSO 4 from Dickson, 1990b, H O from Millero, 1995). The dissociation constants are on the seawater ph scale (Dickson, 1984) ½H þ Š SWS ¼½H þ Šþ½HSO 4 Šþ½HFŠ ð7þ where the brackets represent concentrations in mol (kg soln) 1 (Millero, 1995). The total seawater scale is given by ½H þ Š T ¼½H þ Šþ½HSO 4 Š: ð8þ The two ph scales are related by (Dickson, 1984) ph SWS ¼ ph T þ log 1 þ b HSO4 ½SO 4 Š T log 1 þ b HSO4 ½SO 4 Š T þ b HF ½FŠ T ð9þ where the subscript T represents the total concentration and the bs are the association constants for the formation of HSO 4 (Dickson, 1990b) and HF (Dickson and Riley, 1979) at the ionic strength and temperature of the solution. The calculations were carried out in a manner similar to the methods described by Goyet and Poisson (1989). As pointed out by these authors, care is needed in fitting titration data with many variables. To test the reliability of the computer code a number of titrations as a function of temperature were made on certified reference material provided by Dickson (004) with known values of TA and TCO. The derived values of pk 1 * on these samples are given in Table 3. The values of pk 1 * determined with and without the known values of TA and TCO (floating) gave similar results that were in good agreement with the values of Mehrbach et al. (1973). The floating values of TA and TCO are also in good agreement with the certified values. In a second series of studies, we examined the values of pk * obtained with and without the addition of NaOH. These results indicate that to obtain reliable values of pk * that agreed with the results of Mehrbach et al. (1973) or Mojica-Prieto and Millero (00), one needs to increase the ph and the concentration of the CO 3 ion. In a few of the titrations at high salinity the precipitation of Mg(OH) appeared to occur yielding unreliable values of pk *. This was apparently due to the loss of the MgCO 3 complex. Since the interactions of Mg + with HCO 3 are small, it did not cause any significant errors in the determination of pk 1 * (Millero and Roy, 1997). 4. Results and calculations The titrations were made on seawater samples as a functionoftemperature(1to50)andsalinity(1to50).

11 90 F.J. Millero et al. / Marine Chemistry 100 (006) pk 1 pk Model 10 o C 0 o C 30 o C 40 o C 50 o C Fig. 4. The measured values of pk 1 * from 10 to 50 8C as a function of the square root of ionic strength (I). The smooth curves are the values calculated from the model of Millero and Roy (1997). The measured values of pk 1 * determined from the titrations are given in Table 4. These results are the individual titrations that were used in the fitting of the equations. The values of pk 1 * as a function of I 0.5 from 10 to 50 8C are compared to the model calculations (Millero and Roy, 1997) in Fig. 4. The measurements are in good agreement with the model over this temperature range and approach the pure water values in dilute solution. As stated earlier this is not the case at temperatures below 10 8C at high ionic strengths (see Fig. ). I 0.5 Δ pk 1 Δ pk σ = Salinity σ = Temperature ( C) +σ To examine internally the consistency of the measurements made at each temperature the results were first fitted to equations of the form pk i * pk 0 i ¼ AS 0:5 þ BS þ CS ð10þ pk i * pk 0 i ¼ AI 0:5 þ BI þ CI ð11þ where the ionic strength I =19.9S /( S), and the values in pure pk i 0 are determined from Harned -σ +σ Fig. 5. The differences between the measured and fitted values of pk 1 * as a function of salinity and temperature. -σ Table 5 Coefficients for the fits of the values of pk* 1 and pk* in seawater as a function of temperature, salinity and ionic strength Salinity Ionic strength pk* 1 coeff. pk* coeff. pk* 1 coeff. pk* coeff. S 0.5 a I S a I S a 5.33E I S 0.5 /T a I 0.5 /T S/T a I/T S 0.5 lnt a I 0.5 lnt Std. error Number

12 F.J. Millero et al. / Marine Chemistry 100 (006) Δ pk σ = Salinity +σ -σ Similar equations as a function of ionic strength can be formulated by replacing S with I. The coefficients used were arrived at by using an F- test and are shown in Table 5 along with the standard errors of the fits (r =54 for pk 1 * and r =1 for pk *). The differences between the measured and calculated values of pk 1 * are shown in Figs. 5 and 6). Most of the deviations for pk 1 * are within r ( and 0.0, respectively). 5. Discussion Δ pk and Bonner (1945), Harned and Davis (1943), and Harned and Scholes (1941) as refit by Millero (1979) pk ¼ 16:34048 þ 630:813=T þ 19:5684lnT ð1þ pk 0 ¼ 90:18333 þ 5143:69=T þ 14:613358lnT ð13þ The average standard deviations for the individual temperatures varied from 9 to 78 for pk 1 * (weighted average 48, N = 466) and 49 to 30 for pk * (weighted average of 0, N =458). All of the measurements as a function of temperature and salinity have been fitted to equations of the form pk i * pk 0 i ¼ A i þ B i =T þ C i lnt ð14þ The adjustable parameters have been fitted to functions of salinity using equations A i ¼ a 0 S 0:5 þ a 1 S þ a S B i ¼ a 3 S 0:5 þ a 4 S σ = Temperature ( C) +σ Fig. 6. The differences between the measured and fitted values of pk * as a function of salinity and temperature. -σ ð15þ ð16þ Comparisons of the results of pk 1 * calculated from Eqs. (14) (17) with earlier workers shown in Figs. 7 and 8) are summarized in Table 6. Our calculated results of pk 1 * from 0 to 40 8C and S =1 to 45 are in good agreement with the measurements of Mehrbach et al. (r = F 66, N = 30) and Mojica- Prieto and Millero (r =F86, N = 59). The pk 1 * results of Roy et al. (r =F0.098, N = 56) and Goyet and Poisson (r =F0, N =93) show larger offsets. It should be pointed out that the Roy et al. results from Δ pk 1 (Meas - Calc) Δ pk 1 (Meas - Calc) Hansson Mehrbach et al. Goyet & Poisson Roy et al. Mojica & Millero Temperature ( C) Salinity C i ¼ a 5 S 0:5 þ a 6 S: ð17þ Fig. 7. A comparison of our values of pk 1 * as a function of temperature and salinity with literature values.

13 9 F.J. Millero et al. / Marine Chemistry 100 (006) Δ pk (Meas - Calc) Δ pk (Meas - Calc) Mehrbach et al. Mojica & Millero Temperature ( C) Salinity Fig. 8. A comparison of our values of pk * as a function of temperature and salinity with literature values. S =5 are not included in this comparison because they appear to be in error. The 10 8C results of Goyet and Poisson also appear to be too low compared to our work. If this data is eliminated their results are in good agreement with our results (r =F8, N =84). The pk 1 * measurements of Hansson show much larger differences than the other studies (r =F, N =70) with our work. Our new equations are in agreement with most of the earlier measurement of pk 1 * on SW and ASW within their experimental errors of the previous studies. Our calculated results for pk * are compared to the measurements of Mehrbach et al. (1973) and Mojica- Prieto and Millero (00) in Fig. 8 from S =1 to 45 and 0 to 45 8C. Our calculated results (Table 6) are in good agreement with the measurements of Mehrbach et al. (r =F3, N =33) and Mojica-Prieto and Millero (r =F4, N = 140). Comparisons with the pk * studies by other workers using ASW are not shown since there are large offsets above 10 8C (see Fig. 1). Our equations fits all of seawater experimental measurements of pk * within the experimental measurements of the earlier studies. Our equations for the dissociation constants of carbonic acid are valid over a wide range of salinity and temperature. The pk 1 * equations are in agreement with most of the earlier measurements in SW and ASW within the standard error of their measurements. The pk * equations are in agreement with earlier measurements in SW. Since the dissociation constants are frequently used to calculate the parameters (ph, TA, TCO and fco ) controlling the CO system in natural waters, it is important to examine the errors involved in these calculations using various inputs. This was done by examining the calculations of two unknown parameters with an input of ph TA, ph TCO, fco TA, fco TCO and TA TCO. The calculations were made at S =35 and t =5 8C, TA=400 Amol kg 1 and two levels of ph (8.094 and 7.576), fco (350 and 1400 Aatm) and TCO (05.3 and Amol kg 1 ). The results are tabulated in Table 7 for errors of 6 in pk 1 * and 1 in pk *. These uncertainties in the constants do not cause significant errors in the calculated values of TA and TCO. The errors due to uncertainties in pk 1 * range from 0 to 6 for ph and 4.7 to 19.5 Aatm in fco. The errors due to uncertainties in pk * range from 04 to 77 in ph and 17.9 to.7 Aatm in fco. The uncertainties in ph and fco are higher at higher levels of TCO. On can estimate the probable errors due to uncertainties in pk 1 * from the square root of the sum of the individual errors squared. It should be pointed out the errors will be larger when one accounts for the errors in the experimental parameters (F3 Amol kg 1 in TA, F Amol kg 1 in TCO, F in ph and F Aatm in fco ). It is clear from these calculations that one should make direct measurements of fco rather than calculating it from the other parameters if one requires high precision or accurate values of fco for surface waters. Table 6 Comparisons of the standard deviations of the differences between our measurements and other authors Author r(pk*) 1 No. r(pk*) No. Mehrbach et al Hansson 70 Goyet and Poisson a 84 Roy et al. 98 b 56 Mojica and Millero 86 c This study a Minus the measurements at 10 8C. b Minus the measurements at S =5. c Minus the measurements at S =5.

14 F.J. Millero et al. / Marine Chemistry 100 (006) Table 7 Uncertainties in the determination of CO parameters at S =35 and t =5 8C due to errors of 6 in pk 1 * and 1 in pk * a,b Uncertainties due to error in pk* 1 Input variables fco (Aatm) DTCO (Amol kg 1 ) TA (Amol kg 1 ) ph fco (Aatm) ph TA ph TCO fco TA fco TCO TA TCO Uncertainties due to errors in pk* Input variables fco (Aatm) DTCO (Amol kg 1 ) DTA (Amol kg 1 ) DpH DfCO (Aatm) ph TA ph TCO fco TA fco TCO TA TCO a Initial inputs of TA=400 Amol kg 1, ph=8.094 and 7.576, TCO =05.3 and Amol kg 1, respectively for fco =350 and 1400 Aatm at 5 8C. The calculations were made using pk*= and pk*= at 5 8C and S =35 from Mehrbach et al. (1973). b The total probable error (pe) can be estimated from the square root of the sum of the errors due to pk* 1 and pk* squared, pe=[(dpk*) 1 +(DpK*) ] 0.5. The equations can be used to examine the thermodynamics of the carbonate system in most estuarine and marine waters. It should be pointed out that our equations assume that seawater is diluted with pure water. This may not be the case for some estuarine systems. If the composition is known one can use Pitzer models (Millero and Roy, 1997; Millero and Pierrot, 1998) to account for the difference in the composition of estuarine waters that differ from seawater diluted with pure water. Acknowledgements This work was supported by the Oceanographic Section of National Science Foundation and the National Oceanic and Atmospheric Administration. References Clayton, T., Byrne, R.H., Spectrophotometric seawater ph measurements: total hydrogen ion concentration scale calibration of m-cresol purple and at-sea results. Deep-Sea Res. 40, Dickson, A.G., An exact definition of total alkalinity and a procedure for the estimation of alkalinity and total inorganic carbon from titration data. Deep-Sea Res. 8A, Dickson, A.G., ph scales and proton-transfer reactions in saline media such as seawater. Geochim. Cosmochim. Acta 48, Dickson, A.G., 1990a. Thermodynamics of the dissociation of boric acid in synthetic seawater from to K. Deep-Sea Res. 37, Dickson, A.G., 1990b. Standard potential of the reaction: AgCl(s)+1.H (g)=ag(s)+hcl (aq), and the standard acidity constant of the ion HSO 4 in synthetic sea water from to J. Chem. Thermodyn., Dickson, A.G., 004. Reference material batch information ( www-mpl.ucsd.edu/people/adickson/co _QC/Level1/Batches. html). Dickson, A.G., Millero, F.J., A comparison of the equilibrium constants for the dissociation of carbonic acid in seawater media. Deep-Sea Res. 34, Dickson, A.G., Riley, J.P., The estimation of acid dissociation constants in seawater from potentiometric titrations with strong base: I. The ion product of water K w. Mar. Chem. 7, Goyet, C., Poisson, A., New determination of carbonic acid dissociation constants in seawater as a function of temperature and salinity. Deep-Sea Res. 36, Hansson, I., A new set of acidity constants for carbonic acid and boric acid in seawater. Deep-Sea Res. 0,

15 94 F.J. Millero et al. / Marine Chemistry 100 (006) Harned, H.S., Bonner, F.T., The first ionization constant of carbonic acid in aqueous solutions of sodium chloride. J. Am. Chem. Soc. 67, Harned, H.S., Davis Jr., R.D., The ionization constant of carbonic acid in water and the solubility of carbon dioxide in water and aqueous salt solutions from 0 to 50 8C. J. Am. Chem. Soc. 65, Harned, H.S., Scholes, S.R., The ionization constant of HCO 3 from 0 to 50 8C. J. Am. Chem. Soc. 63, Johansson, O., Wedborg, M., 198. On the evaluation of potentiometric titrations of seawater with hydrochloric acid. Oceanol. Acta 5, Lee, K., Millero, F.J., Campbell, D.M., The reliability of the thermodynamic constants for the dissociation of carbonic acid in seawater. Mar. Chem. 55, Lee, K., Millero, F.J., Wanninkhof, R., The carbon dioxide system in the Atlantic Ocean. J. Geophys. Res. 10, Lee, K., Millero, F.J., Byrne, R.H., Feely, R.A., Wanninkhof, R., 000. The recommended dissociation constants for carbonic acid in seawater. Geophys. Res. Lett. 7, 9 3. Lueker, T.J., Dickson, A.G., Keeling, C.D., 000. Ocean pco calculated from dissolved inorganic carbon, alkalinity and equations for K 1 and K : validation based on laboratory measurements of CO in gas and seawater at equilibrium. Mar. Chem. 70, Mehrbach, C., Culberson, C.H., Hawley, J.E., Pytkowicz, R.M., Measurement of the apparent dissociation constants of carbonic acid in seawater at atmospheric pressure. Limnol. Oceanogr. 18, Millero, F.J., The thermodynamics of the carbonate system in seawater. Geochim. Cosmochim. Acta 43, Millero, F.J., Thermodynamics of the carbon dioxide system in the oceans. Geochim. Cosmochim. Acta 59, Millero, F.J., Chemical Oceanography. CRC Press, Boca Raton, FL. Millero, F.J., Pierrot, D., A chemical equilibrium model for natural waters. Aquat. Geochem. 4, Millero, F.J., Poisson, A., International one-atmosphere equation of state of seawater. Deep-Sea Res. 8, Millero, F.J., Roy, R.N., A chemical equilibrium model for the carbonate system, in natural waters. Croat. Chem. Acta 70, Millero, F.J., Zhang, J.Z., Lee, K., Campbell, D.M., Titration alkalinity of seawater. Mar. Chem. 44, Millero, F.J., Pierrot, D., Lee, K., Wanninkhof, R., Feely, R., Sabine, C.L., Key, R.M., Takahashi, T., 00. Dissociation constants for carbonic acid determined from field measurements. Deep-Sea Res. 49, Mojica-Prieto, F.J., Millero, F.J., 00. The values of pk 1 +pk for the dissociation of carbonic acid in seawater. Geochim. Cosmochim. Acta 66, Pitzer, K.S., Theory: ion interaction approach: theory and data collection. In: Pitzer, K.S. (Ed.), Activity Coefficients in Electrolyte Solutions, vol. I, nd ed. CRC Press, Boca Raton, FL, pp Roy, R.N., Roy, L.N., Lawson, M., Vogel, K.M., Porter-Moore, C., Davis, W., Millero, F.J., Campbell, D.M., The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45 8C. Mar. Chem. 44, Wanninkhof, R., Lewis, E., Feely, R.A., Millero, F.J., The optimal carbonate dissociation constants for determining surface water pco from alkalinity and total inorganic carbon. Mar. Chem. 65,