Frank J. Millero

A comparison of the equilibrium constants for the dissociation of carbonic acid in seawater media

The published experimental data of Hansson and of Mehrbach et al. have been critically compared after adjustment to a common pH scale based upon total hydrogen ion concentration. No significant systematic differences are found within the overall experimental error of the data. The results have been pooled to yield reliable equations that can be used to estimate pK1∗and pK2∗ for seawater media a salinities from 0 to 40 and at temperatures from 2 to 35°C.

Thermodynamics of the carbon dioxide system in the oceans

In the next ten years, a number of studies on the carbonate system are planned as part of the JGOFS/WOCE programs. The carbon dioxide system will be studied by measuring at least two of the controlling parameters; pH, total alkalinity (TA), total inorganic CO2 (TCO2), and the fugacity of CO2 (fCO2). The other parameters can be calculated using thermodynamic relations. In the present paper the thermodynamic equations necessary to characterize the CO2 system in the oceans as a function of salinity and temperature are given. This includes equations for the dissociation of carbonic acid, boric acid, phosphoric acid, silicic acid, water, hydrogen sulfide, and ammonia in seawater as a function of temperature (0 to 45°C) and salinity (0 to 45). The equations are of the form ln Ki = A + BT + C ln T, where A, B, and C are functions of salinity. Equations are also given for calculating the effect of temperature and salinity on the fugacity and pH of seawater using the carbonic acid constants of Roy et al. (1993a).

Synthesis of iron fertilization experiments: From the Iron Age in the Age of Enlightenment

Comparison of eight iron experiments shows that maximum Chl a, the maximum DIC removal, and the overall DIC/Fe efficiency all scale inversely with depth of the wind mixed layer (WML) defining the light environment. Moreover, lateral patch dilution, sea surface irradiance, temperature, and grazing play additional roles. The Southern Ocean experiments were most influenced by very deep WMLs. In contrast, light conditions were most favorable during SEEDS and SERIES as well as during IronEx-2. The two extreme experiments, EisenEx and SEEDS, can be linked via EisenEx bottle incubations with shallower simulated WML depth. Large diatoms always benefit the most from Fe addition, where a remarkably small group of thriving diatom species is dominated by universal response of Pseudo-nitzschia spp. Significant response of these moderate (10–30 μm), medium (30–60 μm), and large (>60 μm) diatoms is consistent with growth physiology determined for single species in natural seawater. The minimum level of “dissolved” Fe (filtrate < 0.2 μm) maintained during an experiment determines the dominant diatom size class. However, this is further complicated by continuous transfer of original truly dissolved reduced Fe(II) into the colloidal pool, which may constitute some 75% of the “dissolved” pool. Depth integration of carbon inventory changes partly compensates the adverse effects of a deep WML due to its greater integration depths, decreasing the differences in responses between the eight experiments. About half of depth-integrated overall primary productivity is reflected in a decrease of DIC. The overall C/Fe efficiency of DIC uptake is DIC/Fe ∼ 5600 for all eight experiments. The increase of particulate organic carbon is about a quarter of the primary production, suggesting food web losses for the other three quarters. Replenishment of DIC by air/sea exchange tends to be a minor few percent of primary CO2 fixation but will continue well after observations have stopped. Export of carbon into deeper waters is difficult to assess and is until now firmly proven and quite modest in only two experiments.

The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45°C

The pK1∗ and pK2∗ for the dissociation of carbonic acid in seawater have been determined from 0 to 45°C and S = 5 to 45. The values of pK1∗ have been determined from emf measurements for the cell: Pt](1 − X)H2 + XCO2|NaHCO3, CO2 in synthetic seawater|AgC1; Ag where X is the mole fraction of CO2 in the gas. The values of pK2∗ have been determined from emf measurements on the cell: Pt, H2(g, 1 atm)|Na2CO3, NaHCO3 in synthethic seawater|AgC1; Ag The results have been fitted to the equations: lnK∗1 = 2.83655 − 2307.1266/T − 1.5529413 lnT + (−0.20760841 − 4.0484/T)S0.5 + 0.08468345S − 0.00654208S1 InK∗2 = −9.226508 − 3351.6106/T− 0.2005743 lnT + (−0.106901773 − 23.9722/T)S0.5 + 0.1130822S − 0.00846934S1.5 where T is the temperature in K, S is the salinity, and the standard deviations of the fits are σ = 0.0048 in lnK1∗ and σ = 0.0070 in lnK2∗. Our new results are in good agreement at S = 35 (±0.002 in pK1∗and ±0.005 in pK2∗) from 0 to 45°C with the earlier results of Goyet and Poisson (1989). Since our measurements are more precise than the earlier measurements due to the use of the Pt, H2|AgCl, Ag electrode system, we feel that our equations should be used to calculate the components of the carbonate system in seawater.

The chemistry of the hydrogen sulfide and iron sulfide systems in natural waters

Abstract Reduced sulfur compounds are ubiquitous components of anaerobic sediments and euxinic marine environments. They are primarily produced through a complex net of both chemically and biologically mediated reactions. This results in a wide variety of dissolved and solid inorganic and organic products. Much of the recent research effort in this area has focused on biogeochemical interactions and modelling sediment diagenesis. Several excellent reviews are available on these specific topics. However, relatively little attention has been paid to more basic inorganic chemistry of this system; the topic of this review.

The oxidation kinetics of Fe(II) in seawater

Abstract The oxidation of Fe(II) has been studied as a function of pH (5 to 9), temperature (5 to 45°C), and salinity (0 to 35). The pseudo-first-order rate constant, k1, −d[Fe(II)] dt = k 1 [Fe(II)] in water and seawater was found to be a second degree function of pH over the pH range of 7.5 to 8.5 at 5°C and 6.0 to 8.0 at 25°C. The overall rate constant (k) −d[Fe(II)] dt = k[Fe(II)][O 2 ][OH − ] 2 was determined from 5 to 45°C and S = 0 to 35. The results have been fit to an equation of the form (T = 273.15 + t°C) log k = log k 0 − 3.29I 1 2 + 1.52I where logk0 = 21.56–1545/T with a standard error = 0.09. The energy of activation for the overall rate constant in water and seawater was 29 ± 2 kJmol−1. The values of the rate constant for pure water (k0) are in good agreement with literature data. The half times for seawater from some previous studies at a pH = 8.0 were slower than our results for Gulf Stream waters. Measurements on Biscayne Bay waters also yield slower half times apparently due to the presence of organic ligands that can complex Fe(II).

International one-atmosphere equation of state of seawater

The density measurements by Millero, Gonzalez and Ward (1976, Journal of Marine Research,34, 61–93) and Poisson, Brunet and Brun-Cottan (1980, Deep-Sea Research, 27, 1013–1028), from 0 to 40°C and 0.5 to 43 salinity, have been used to determine a new 1-atm equation of state for seawater. The equation is of the form (t°C; S; ϱ kg m−3) ρ=ρ0+AS+BS32+CS , where A=8.24493×10−1−4.0899×10−3t+7.6438×10−5t2−8.2467×10−7t3+5.3875×10−9t4 B=−5.72466×10−3+1.0227×10−4t−1.6546×10−6t2 C=4.8314×10−4 and ϱ0 is the density of water (Bigg, 1967, British Journal of Applied Physics, 8, 521–537). ρ0=999.842594+6.793952×10−2t−9.095290×−3t2+1.001685×10−4t3−1.120083×10−6t4+6.536336×10−9t5 . The standard error of the equation is 3.6 × 10−3 kg m−3. This equation will become the new 1-atm equation of state of seawater that has been suggested for use by the UNESCO (United Nations Educational, Scientific and Cultural Organization) joint panel on oceanographic tables and standards.

The solubility of iron in seawater

The solubilities of iron(III) hydroxides in seawater were determined in Gulf Stream seawater as a function of pH (2 to 9), temperature (5 to 50 °C) and salinity (0 to 36). Our results at S=36 and 25 °C near a pH of 8 are in agreement with the measurements of Byrne and Kester [Mar. Chem. 4 (1976a) 255] and Kuma et al. [Limnol. Oceanogr. 41 (1996) 396] (0.2 to 0.3 nM). The solubilities at 5 °C are considerably higher than at 25 °C and decrease with a decrease in salinity. Near a pH of 8, the solubilities as a function of temperature (T/K) and ionic strength [I=19.922S/(1000−1.005S)] can be estimated from The results at low pH (2 to 5) and S=36 have been used to determine the limiting solubilities of Fe(OH)3(s) which have been fitted to the equation (σ=0.08) The values of KFe(OH)3* are in good agreement with those determined in 0.7 m NaCl. The solubilities as a function of pH, temperature and salinity have been used to determine the stability constants for the formation of Fe(OH)2+, Fe(OH)2+ and Fe(OH)3. The hydrolysis constants at I=0.74 (S=36) have been fitted to the equations The results for log β1* and log β2* at 25 °C are in reasonable agreement with the values in 0.7 m NaCl. The value of log β3* in seawater is larger than the value in 0.7 m NaCl due to the formation of Fe(III) complexes with organic matter. The higher solubilities in seawater (0.3–0.5 nM) compared to the values in 0.7 m NaCl (0.011 nM) are due to the formation of Fe3+ complexes (FeL) with natural organic ligands (L). By diluting seawater (S=36) with 0.7 m NaCl, we have been able to show that the solubilities approach the values in NaCl at the same ionic strength and temperature. The differences in the solubility of Fe in seawater and 0.7 m NaCl near a pH have been used to calculate ligand concentrations [L′]=0.1–0.2 nM (not complexed with iron) using a literature value of the stability constant (K′FeL=1011.5). The results at different temperatures have been used to determine a value of ΔH=7±5 kcal mol−1 for the formation of FeL.

Consistent fractionation of 13C in nature and in the laboratory: Growth‐rate effects in some haptophyte algae

The carbon isotopic fractionation accompanying formation of biomass by alkenone-producing algae in natural marine environments varies systematically with the concentration of dissolved phosphate. Specifically, if the fractionation is expressed by epsilon p approximately delta e - delta p, where delta e and delta p are the delta 13C values for dissolved CO2 and for algal biomass (determined by isotopic analysis of C37 alkadienones), respectively, and if Ce is the concentration of dissolved CO2, micromole kg-1, then b = 38 + 160*[PO4], where [PO4] is the concentration of dissolved phosphate, microM, and b = (25 - epsilon p)Ce. The correlation found between b and [PO4] is due to effects linking nutrient levels to growth rates and cellular carbon budgets for alkenone-containing algae, most likely by trace-metal limitations on algal growth. The relationship reported here is characteristic of 39 samples (r2 = 0.95) from the Santa Monica Basin (six different times during the annual cycle), the equatorial Pacific (boreal spring and fall cruises as well as during an iron-enrichment experiment), and the Peru upwelling zone. Points representative of samples from the Sargasso Sea ([PO4] < or = 0.1 microM) fall above the b = f[PO4] line. Analysis of correlations expected between mu (growth rate), epsilon p, and Ce shows that, for our entire data set, most variations in epsilon p result from variations in mu rather than Ce. Accordingly, before concentrations of dissolved CO2 can be estimated from isotopic fractionations, some means of accounting for variations in growth rate must be found, perhaps by drawing on relationships between [PO4] and Cd/Ca ratios in shells of planktonic foraminifera.

Stability constants for the formation of rare earth-inorganic complexes as a function of ionic strength

Abstract Recent studies have been made on the distribution of the rare earths (La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) in natural waters relative to their concentration in shales. These metals have also been used as models for the behavior of the trivalent actinides. The speciation of the rare earths in natural waters is modelled by using ionic interaction models which require reliable stability constants. In this paper the stability constants for the formation of lanthanide complexes ( k mx ∗ ) with Cl−, NO3−, SO42−, OH−, HCO3−, H2PO4−, HPO42−, and CO32− determined in NaClO44 at various ionic strengths have been extrapolated to infinite dilution using the Pitzer interaction model. The activity coefficients for free ions (γM,γx) needed for this extrapolation have been estimated from the Pitzer equations. The thermodynamic stability constants (KMX) and activity coefficients of the various ion pairs (γMX) were determined from In ( solK MX ∗ γ M γ x ) = In K mx + In (γ MX ). The activity coefficients of the ion pairs have been used to determine Pitzer parameters (BMX) for the rare earth complexes. The values of BMX were found to be the same for complexes of the same charge. These results make it possible to estimate the stability constants for the formation of rare earth complexes over a wide range of ionic strengths. The stability constants have been used to determine the speciation of the lanthanides in seawater and in brines. The carbonate complexes dominate for all natural waters where the carbonate alkalinity is greater than 0.001 eq/L at a pH near 8.